Artist'

CHARACTERIZATION OF POLYETHYLENES: FROM THERMAL FRACTIONATION TECHNIQUES TO SPECTROMETRY 4

Keywords: Polymerization process Slurry, gas phase, solution phase Slurry, gas phase, solution phase Supercritical ethylene Pressure (Mpa)

REMERCIEMENTS

À la suite d'une expérience en analyse dans le domaine de l'environnement dans le groupe CARSO, j'ai intégré le CNRS en 2001. Mes activités ont débuté au sein du Service Central d'Analyse. Riche de ces diverses expériences, j'ai choisi en 2006 de me rapprocher du monde de la recherche et d'intégrer le laboratoire C2P2 alors dirigé par Roger Spitz. Cette thèse est donc une suite logique de mon immersion dans la recherche. Dans un premier temps, je souhaite remercier l'ensemble des membres du jury. J'ai beaucoup d'admiration pour vos carrières et vos travaux et je suis très fier que vous ayez accepté d'évaluer mes travaux de thèse. Je ne pensais pas la tâche si compliquée pour exprimer avec justesse l'ampleur de mes remerciements. J'ai naturellement une pensée de remerciement pour les anciens directeurs de l'unité, Roger Spitz et Bernadette Charleux qui m'ont fait confiance et m'ont soutenu dans mes envies de développement analytique. Un grand merci à mes encadrants, Tim McKenna et Christophe Boisson, qui m'ont guidé dans le monde exigeant et rigoureux de la recherche. C'est un honneur d'être sur la liste des docteurs que vous avez initiés. Merci Tim pour m'avoir « bousculé » tout le long cette thèse et d'avoir su me transmettre régulièrement le message : « il est plus que temps d'achever cette thèse ». Cela a porté ces fruits. Merci Christophe pour les débats scientifiques tellement riches, tes corrections toujours pertinentes et les discussions personnelles si amicales. Merci pour ton immense bienveillance, c'est sans nul doute la combinaison de tes qualités scientifiques et de ton altruisme qui ont rendu cette expérience aussi passionnante.

« Les personnes silencieuses ont les esprits les plus bruyants. » Stephen Hawking

Plus particulièrement, je souhaite exprimer toute mon affection à mes amies du laboratoire. Manel, tu as été le catalyseur pour démarrer cette thèse, mon bras droit qui m'a permis de dégager du temps pour m'investir dans ce

Je veux tout spécialement remercier mon copain de bureau, Franck, tes conseils en général et en particulier pour la rédaction m'ont été précieux. Sébastien et Franck(s) le running avec vous et nos confabulations pendant ces sorties sont toujours agréables. Damien, Fabrice, merci pour vos idées précieuses qui ont enrichi ce manuscrit et alimenté mes réflexions. Elodie, Pierre-Yves, Vincent, Jean je suis très fier de vous avoir comme collègue. Merci très particulier à Mathieu et à Edgar pour votre disponibilité et vos inestimables contributions.

Je tiens à témoigner toute ma reconnaissance aux personnes extérieures au laboratoire qui m'ont aidé, discrètement, et sont au fil du temps devenu des amis : Fernande Da Cruz-Boisson pour le support en RMN, Stéphane Lebras pour le support en infrarouge, Ronan Cozic pour l'aide en spectrométrie de masse, Laurent Constant pour ton efficacité à réparer la chromatographie. I would also like to express my friendship and gratitude to Benjamin Monrabal and Alberto Ortin from PolymerChar, Joao Soares from University of Alberta and Tibor Macko from Fraunhofer institute for many friendly and valuable discussions about thermal fractionation techniques.

Nombreux sont ceux que je veux, aussi, remercier pour leur implication dans ce travail lors de stages de Master (Alissa, Anne, Arnaud, Bérangère, Claire Marie, Emilie, Gisèle, Islem, Laetitia, Sofia), de projets CPE (Nicolas, Constance, Florence, Rémi, Thibault, Alexane, François) et de stages d'IUT (Guillaume, Nicolas, Pierre). Ce travail a abouti grâce à votre investissement toujours passionné et vos idées continuellement passionnantes.

Merci aux étudiants et doctorants du laboratoire c'est un bonheur et une grande richesse de vous côtoyer.

Et surtout, merci à ma famille, trouver les mots justes est compliqué. Ma femme tout d'abord, merci pour ton soutien, ta patience et pour m'avoir épousé pendant cette thèse. Merci à ma belle-famille qui m'a appris les plaisirs de se dépasser pour atteindre des sommets. Merci à ma belle-famille avec qui j'aime partager, dans la fumée d'un « Romeo y Julieta », des mystères de la science. Merci à mes enfants pour vos illustrations, je vous chéris. Merci à mes parents pour vos encouragements. Vous m'avez donné tellement d'armes pour réaliser ce type de défis. Cette thèse est probablement pour vous, avant tout. Je sais la fierté que vous éprouvez et je n'ai pas toujours les mots pour vous exprimer la mienne.

"Ce qui compte ne peut pas toujours être compté, et ce qui peut être compté ne compte pas forcément."

Albert Einstein

ABSTRACT

Eighty-eight copolymers of ethylene with α-olefins (propene, hexene, octene, octadecene and norbornene) have been prepared using the Et(Ind)2ZrCl2 and (nBuCp)2ZrCl2 complexes activated with methylaluminoxane. These complexes led to a large range of high-density polyethylene (HDPE) linear lowdensity polyethylene (LLDPE) with various chemical compositions. They were referred as PE models. Their average comonomer contents were determined by 1 H-and 13 C-NMR.

The PE models (HDPE and LLDPE) were characterized by high temperature size exclusion chromatography (HT-SEC) and showed a narrow molar mass distribution as expected for polymers obtained with single site catalysts. A method was developed to access to the degree of long chain branching (LCB) in polyethylene (PE). The viscometer detector of the SEC was used to determine the LCB by measuring the ratio of the intrinsic viscosity of a PE sample and a standard linear polyethylene. An original approach has been proposed to investigate the effect on the intrinsic viscosity of short chain branching (SCB) in LLDPE and correct this effect for the LCB measurement. The results agreed well with that of NMR studies.

The LLDPE models which are homogeneous in chemical composition, were used as standards to calibrate thermal fractionation techniques: TREF, CRYSTAF, CEF, TGIC and SGIC. The main purpose of this work was to provide calibration curves for all existing thermal fractionation techniques, for various types of comonomers and for a wide range of α-olefin contents. The obtained calibration curves have been gathered for the first time in a unique work. They have been used and will be used to access the chemical composition distribution (CCD) of polyethylenes with heterogeneous chemical compositions.

The well-defined and well-characterized LLDPE models were exploited for the development of rapid methods to determine the comonomer content for polyethylene samples. Chemometric methods, applied to mid and near IR spectra, were constructed and provided accurate results. Consecutive to this work a similar approach was established to quantify the chemical composition of ethylene-butadiene copolymers that exhibit more complex structures. Finally, a method using thermogravimetric analysis (TGA) coupled to mass spectrometry (MS) revealed a new way to access the type of comonomer used in the synthesis of LLDPE.

In summary, this thesis work shows on the one hand the interest of separative techniques to access to CCD and on the other hand the power of spectrometry to rapidly obtain the average chemical composition of unknown polyolefin samples. Les PE modèles, bien définis et bien caractérisés, ont ensuite pu être utilisés pour le développement d'autres méthodes plus rapides de mesure de composition chimique. Ils ont servi à construire des méthodes chimiométriques, appliquées aux spectres moyen et proche IR, pour la prédiction de la teneur en comonomère dans des échantillons inconnus.

Suite à ces travaux, une approche similaire a été mise en place afin de quantifier la composition chimique de copolymères éthylène-butadiène qui présentent des structures plus complexes. Comme elles sont rapides, simples et sans préparation d'échantillons, ces méthodes chimiométriques ont montré leur potentiel pour caractériser les polymères.

Enfin, une méthode utilisant l'analyse thermogravimétrique (ATG) couplée à la spectrométrie de masse a montré une nouvelle façon d'accéder au type de comonomère utilisé lors de la synthèse du LLDPE.

Ce travail de thèse a montré d'une part l'apport unique des techniques de séparation pour accéder à la CCD et d'autre part la puissance de la spectrométrie pour obtenir rapidement la composition chimique moyenne d'un copolymère.

MOTS-CLES

Polyéthylène -LLDPE -caractérisation des polymères -chromatographie d'exclusion stériquefractionnement thermique -TREF -CRYSTAF -CEF -TGIC -SGIC

RESUME SUBSTANTIEL

Il y a un siècle, en 1920, Staudinger a démontré l'existence de « longues molécules » qu'il décrivait comme de longues chaînes constituées d'unités moléculaires répétitives liées par des liaisons covalentes. [1] Ses travaux pionniers, récompensés par le prix Nobel de chimie en 1954, [2] ont conduit à de nombreuses avancées.

Aujourd'hui, les polymères forment l'un des groupes de matériaux les plus attractifs grâce à leurs propriétés polyvalentes et uniques qui les rendent omniprésents dans notre vie quotidienne. Ils ont des atouts indéniables qui permettent à la société de répondre à de multiples défis. Par exemple, les plastiques d'emballage réduisent le gaspillage alimentaire ; les matériaux isolants synthétiques utilisés dans les bâtiments nous aident à réduire notre consommation d'énergie ; les matériaux légers dans les transports permettent d'économiser l'énergie et réduisent les émissions de CO2 ; les polymères biocompatibles sont impliqués dans des avancées médicales et sauvent des vies. En répondant aux exigences de plus en plus strictes de nombreuses applications, ils sont encore au coeur de nombreuses innovations dans les domaines de l'emballage, du transport, du BTP, de la médecine et même de l'écologie.

En particulier, l'industrie des polyoléfines a évolué de façon spectaculaire. Aujourd'hui, avec une production annuelle d'environ 170 millions de tonnes, elle représente à elle seule plus de 60% de la production de plastique et progresse encore tous les ans d'environ 4%. [3] Les polyoléfines sont constituées simplement d'atomes de carbone et d'hydrogène qui selon leurs organisations aboutissent à divers matériaux aux propriétés spécifiques. Plusieurs centaines de grades de polyoléfines, qui possèdent autant de propriétés variées, sont actuellement commercialisés.

Avec le polypropylène (PP), le polyéthylène (PE) est une classe majeure de polyoléfines. II existe principalement trois types de polyéthylènes regroupés selon leur densité (Table 1) : (1) Le polyéthylène haute densité (HDPE) présente une structure assez linéaire, (2) le polyéthylène basse densité (LDPE) présente une structure très ramifiée comprenant des ramifications longues et courtes (LCB et SCB) (3) et le polyéthylène basse densité linéaire (LLDPE) est caractérisé par des ramifications courtes (SCB). Les LLDPE industriels sont issus de la copolymérisation d'éthylène avec une -oléfine par catalyse Ziegler-Natta. La longueur des ramifications dépend directement du comonomère utilisé lors de la synthèse.

Table 1 : Classification des polyéthylènes selon leurs structures.

Type de PE HDPE LLDPE LDPE

Structure

Bien que le LDPE soit produit par procédés radicalaires, la majorité des polyoléfines sont synthétisées par catalyse de coordination. Ils sont mis en oeuvre dans des unités de production en continu utilisant des procédés en phase gazeuse et en suspension.

Les récents développements en chimie de polymérisation utilisant des catalyseurs mono-sites ont donné naissance à des systèmes catalytiques toujours plus performants. Ils permettent de contrôler finement la structure des chaînes de polymères. Associés aux avancées en procédés de polymérisation avec l'utilisation de réacteurs multiples en cascade, ils ont conduit à la production directe de polyoléfines de performances.

Tous ces progrès ont permis, entre autres, d'orienter la composition chimique (organisation des carbones et hydrogènes) des matériaux pour atteindre des propriétés spécifiques. Ces remarquables avancées représentent de grands défis pour la caractérisation de ces matériaux. Il est donc essentiel de développer des outils analytiques nouveaux pour explorer et comprendre ces structures de plus en plus complexes.

La mesure de la composition chimique moyenne, obtenue habituellement par densité ou « melt flow index » en milieu industriel ou par RMN en laboratoire de recherche, ne suffit plus. Il faut accéder à la distribution de composition chimique seulement accessible par des techniques de fractionnement thermique. Ces techniques dédiées à la caractérisation des polyoléfines sont assimilées à des méthodes séparatives de chromatographie liquide.

Ce travail de thèse est focalisé sur l'implantation et le développement de méthodes basées sur ces techniques séparatives.

Pour mettre en place ces nouvelles méthodes, il a été nécessaire, dans un premier temps, de préparer nos propres étalons. Ainsi, 88 copolymères d'éthylène avec des -oléfines (propène, hexène, octène, octadécène et norbornène) ont été synthétisés en utilisant les complexes Et(Ind)2ZrCl2 (Figure 1) et (nBuCp)2ZrCl2 activés par le méthylaluminoxane. Les LLDPE modèles, bien définis et bien caractérisés, ont ainsi pu être utilisés pour le développement de méthodes alternatives de mesure de la composition chimique. Ce sont les techniques de spectrométrie, largement utilisés par les laboratoires de recherche, qui ont été envisagées comme outils alternatifs. Dans ce 4 ème chapitre nous nous sommes intéressés en particulier à la spectroscopie infrarouge à transformée de Fourier (FTIR) et au couplage de l'analyse thermique et de la spectrométrie de masse.

La spectroscopie infrarouge est utilisée depuis de nombreuses années pour la caractérisation des polyoléfines. Le développement de la chimiométrie, outils mathématiques et statistiques pour obtenir des informations à partir d'un grand nombre de données, permet une nouvelle approche dans l'exploitation des spectres obtenus. La chimiométrie permet d'atteindre des informations sur les polymères en observant l'ensemble des longueurs d'ondes significatives des informations recherchées. Nous avons montré qu'elle peut s'appliquer efficacement à la fois au moyen infrarouge et au proche infrarouge sur les LLDPE (première partie du chapitre) mais aussi sur d'autres types de copolymère comme des copolymères éthylène-butadiène qui présentent des structures complexes (seconde partie du chapitre). Nos polymères modèles ont ainsi servi à construire des méthodes chimiométriques, appliquées aux spectres IR, pour la prédiction de la teneur en comonomère dans des échantillons inconnus. Comme elles sont rapides, simples et sans préparation d'échantillons, ces méthodes chimiométriques ont montré leur potentiel pour caractériser les polyéthylènes (Figure 4).

La dernière partie du chapitre concerne la spectrométrie de masse particulièrement difficile à employer pour l'analyse des polymères. Le couplage de l'analyse thermo gravimétrique (ATG) avec la spectromètrie de masse a révélé tout son potentiel pour comprendre la structure de LLDPE inconnus. Le couplage a permis, par dégradation thermique, d'obtenir des fragments significatifs des LLDPE analysés qui ont été ensuite identifiés par la spectrométrie de masse. Cette méthode permet d'identifier le type d'α-oléfines utilisé lors de la synthèse.

Figure 4 : Analyse en composantes principales (PCA, principal component analysis) pour un intervalle de confiance de 95% moyen infrarouge (a) et en proche infrarouge (b) pour des copolymères éthylènehexène. Les échantillons ont été séparés de manière distincte en quatre groupes (bleu, rouge, vert et marron) en fonction de leur teneur en 1-hexène (en mol%).

Ce travail de thèse a montré d'une part l'apport unique des techniques séparatives de fractionnement thermique pour accéder à la CCD et d'autre part la puissance de la spectrométrie pour obtenir rapidement la composition chimique moyenne de copolymères. Polymers form one of the most attractive groups of materials thanks to their versatile and unique properties which make them ubiquitous in our daily lives. They have assets that allow society to respond to multiple challenges. For example, packaging plastics reduce food waste; high performance synthetic insulation materials help us to reduce our energy consumption; lightweight materials in transport save fuel and reduce CO2 emissions; biocompatible polymers enable medical advances that save human lives.

NOMENCLATURE Acronyms

And they still have great potential for development.

Thanks to the progress made in synthesis, polymers remain at the heart of many innovations in medicine, electronics, transport, ecology, and construction. Indeed, the development of polymerization techniques makes it possible to envisage the preparation of a large variety of macromolecules with well-defined structures and compositions. Thus, recent polymerization tools have made it possible to modulate the composition of macromolecule chains and therefore their properties to better meet the increasingly strict requirements of numerous applications. In particular, the development of catalyst systems has greatly contributed to facilitating the production of polyolefins with new properties which constitute a fascinating range of materials.

With an annual production of around 170 million tons per year and an annual increase of around 4%, polyolefins alone represent more than 60% of plastic production. [1] Depending on the arrangement of the carbon and hydrogen atoms, various polyolefin materials with different properties can be obtained. This combination of carbon atom and hydrogen leads to the composition of several hundred grades of polyolefins.

Polypropylene (PP) is an important class of polyolefins. Atactic polypropylene (aPP), in which methyl groups are randomly distributed along the chain, is also manufactured, and exhibits characteristics similar to waxes. Syndiotactic polypropylene (sPP) results in a regular alternation in the orientation of these methyl groups. Isotactic polypropylene (iPP) includes all the methyl groups placed on the same side of the polymer backbone, leading to the formation of a helix. The stack of these helices forms polypropylene crystals which give the polymer high flexural rigidity, which is the basis of most of its properties. iPP is by far the most commonly produced polypropylene.

With polypropylene, polyethylene (PE) is a major class of polyolefins. Basically, there are three classes of polyethylene. High-density polyethylene (HDPE) displays a fairly linear structure, low-density polyethylene (LDPE) features highly branched structures comprising long and short branching (LCB and SCB), and linear low-density polyethylene (LLDPE) is characterized by short chain branches (SCB). LLDPE are produced with Ziegler-Natta catalysts by copolymerization of ethylene with an -olefin, the branch length depends directly on the comonomer used during the synthesis.

Although LDPE is produced by a radical process, the vast majority of polyolefins are synthesized by coordination catalysis. Catalysts have undergone many developments which have given rise to ever more efficient catalytic systems. They are generally obtained in continuous production units using gas phase and slurry processes. Advances in catalyst systems and in polymerization processes make it possible to manipulate polymer chain structures and combine polymers in the form of blends. The modification of polymerization conditions in a single reactor and the use of cascade reactors have led to the direct production of blends constituting high performance materials.

All this progress has made it conceivable to orient the distribution of molar mass and the distribution of chemical composition during polymerization to achieve specific properties. It is therefore essential to develop analytical tools to explore and understand these increasingly complex structures.

This thesis work is centered on the characterization of polyolefins and in particular semi-crystalline polyethylene (HDPE et LLDPE), a topic which presents particular constraints and challenges. Indeed, the steric exclusion mode, which is governed by only the loss of entropy. The macromolecule enters the pores of the stationary phase without interaction with it. The higher the molar mass of the macromolecules, the faster they will be excluded from the pores. When this elution mechanism is used, the analytical method is called size exclusion chromatography (SEC).

polymer
the interactive mode, which is governed by the variation of the enthalpy energy generated during interactions between the polymer and the stationary phase. This technique is then called interactive chromatography (IC). Liquid chromatography under critical conditions (LCCC) allows the elution of polymers regardless of their molar mass. This method is widely used to separate amphiphilic block copolymers. In this work two methods based on this mode and functioning for LLDPE were developed: solvent gradient interactive chromatography (SGIC) and thermal gradient interactive chromatography (TGIC).

the crystallization mode, which is governed by the capacity of a polymer to crystallize, as in crystallization analysis fractionation (CRYSTAF), or be re-eluted after a crystallization step as in temperature rising elution fractionation (TREF) and crystallization elution fractionation (CEF). These methods can be applied only for semi-crystalline polymers and are actually used only to separate polyolefins.

In this work, these different existing separation modes were used, developed, and installed in our laboratory to achieve fine characterizations of the complex structures of LLDPE samples. To fully exploit these recent techniques, our strategy was based on successive stages: the synthesis of well-defined LLDPE models, the complete characterization of these LLDPE by conventional techniques (NMR, SEC, DSC), and the calibration of thermal fractionation methods. Finally, taking advantage of the synthesis of LLDPE models that are well controlled regarding composition and well characterized, new analytical tools based on spectroscopy have been developed. This second line of research focused on the development of original tools with coupling methods (TGA and mass spectrometry) and the exploitation of complex spectroscopic data by chemometric tools.

This manuscript is divided into four chapters that describe these different steps:

Chapter 1 reviews the main industrialized polyolefin materials. In the second part, the various methods used for ethylene polymerization and copolymerization with -olefins are described. Particular attention is paid to the coordination polymerization carried out with Phillips, Ziegler-Natta and metallocene catalysts. Finally, the different analytical tools used to understand the structure (molar mass, long chain branching, regioregularity) and the composition (chemical composition with short chain branching) of polyolefins are presented and described in-depth. Both well-known techniques such as size exclusion chromatography, spectroscopy (NMR, infrared) and thermal analysis (differential scanning calorimetry), and original fractionation techniques are presented (CRYSTAF, TREF, CEF, TGIC).

We synthetized LLDPE models before calibrating our original fractionation techniques which are described beforehand. In Chapter 2, the copolymerization conditions of ethylene with various types of α-olefins (propylene, hexene, octene, octadecene, and norbornene) are described. The complex rac-ethylene bis(indenyl)zirconium (IV) dichloride (rac-Et(Ind)2ZrCl2) was used due to its efficient incorporation of comonomers and its ability to produce homogeneous LLDPE samples with respect to their molar masses and their composition. Afterwards, the chemical composition of all the samples was measured precisely with 1 H and 13 C NMR. In parallel, high temperature size exclusion chromatography was used to measure the molar masses of the samples and also to study the ability of the viscometer to measure their long and short chain branching in PE.

Chapter 3 is the heart of this thesis work. Prepared LLDPE models were used to calibrate the various thermal fractionation techniques recently installed in our unit. The advantages and specificities of each technique are discussed and illustrated. Finally, a complete calibration panel is provided for all these techniques and applicable for most industrial LLDPE samples. Some examples of applications are given to illustrate their uses. Three published articles based on these works are presented at the end of the chapter.

Finally, Chapter 4 is dedicated to the development of the spectroscopic method. The NMR and fractionation techniques described previously are time consuming and sometimes a faster analysis is preferred. The spectroscopic method coupled with chemometric tools and thermal analysis coupled with mass spectrometry provided a rapid and precise solution to measure the chemical composition of polyolefins. This chapter consists of three publications published in peer-reviewed journal.

The main objective of all these developments is to support researches in the field of polyolefin synthesis and polymerization processes.

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Polyolefins are made from simple and commonly accessible monomers which only contain carbon and hydrogen. Despite their simplicity, they are used in a wide range of applications: packaging, car bumpers, construction, agriculture, toys, gas pipelines, etc. Since many years, they have been the largest class of synthetic polymers. The success of polyolefins is mainly due to their low production cost, large-volume production processes, reduced environmental impact, and adjustable mechanical properties.

For all these reasons, the polymerization of olefins into polymers with various microstructures continues to be widely studied by industrial and academic laboratories. The PCM (polymérisation, catalyse, matériaux) team in the CP2M (catalyse, polymérisation, proceeds et matériaux) laboratory focuses its research activity on polymer synthesis and polymerization processes. It is of great importance for researchers to understand the chemistry that is involved during the different steps of polymer synthesis. This PhD project is mainly focused on the integration in the laboratory of new characterization techniques and original analytical methods to improve understanding of the impact of polymerization chemistry and processes on polymer properties.

This bibliographic study is organized on the basis of polymer properties. First, an overview of ethylene polymerization is provided with the presentation of the different industrial processes used to produce polyolefins. The second section focuses on advanced analytical techniques for the characterization of polyolefins.

INTRODUCTION TO POLYMERS

Since they were developed in the 1950s, polymers have achieved spectacular success because of their indisputable qualities: ease of manufacturing, low cost, mechanical strength, transparency, lightness, etc.

For instance, polymers contribute to reduce transport emissions with lighter materials. They have been revealed as ideal materials for many applications like packaging, building construction, automobiles, agriculture (Figure 1-1a), and are gradually taking the place of other materials, such as metals and glass.

Today, between 100 and 140 kg of polymers per year and per citizen are consumed in Europe and the United States. This consumption will be further accelerated (Figure 1-1b), so it seems essential to maintain research and development efforts in this field. Thermoset polymers contain chains that cross-link together during the synthesis process to form an irreversible chemical bond. They are ideal for high temperature applications and cost-effective, but they cannot be remolded, reformed, or recycled.

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Thermoplastic resins feature a broad range of performances. They generally offer high impact resistance, remolding capacity and mostly high recyclability. Among the thermoplastics, polymers may exist in amorphous and crystalline form. In the amorphous state, macromolecules become entangled in complex ways. In the crystalline state the macromolecular chains are organized and must therefore have a very regular structure. However, polymers are never totally crystalline and are considered as a mixture of amorphous and crystalline phases.

Polyolefins belong to the thermoplastic family. They are produced from a simple family of monomers, the -olefins, with the general formula CnH2n. They can be divided into polyethylene (PE), isotactic polypropylene (iPP) and olefin-based elastomers such as ethylene-propylene-diene monomer rubber (EPDM), polyisobutylene (PIB), and ethylene propylene rubber (EPR). PE, the polyolefin used most, will be an important subject of this work.

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POLYETHYLENES

Polyethylene, a basic repetition of -CH2-groups, is produced by polymerizing the ethylene molecule. With an annual global production of approximately 100 million tons, polyethylenes (PEs) are the main commercial polymeric material [1,2] and the most widely used polymers in the world (Figure 1-2). Their use has grown rapidly because they are composed of simple monomers (they contain only carbon and hydrogen) and they offer a very varied range of products whose mechanical, rheological, and optical properties provide many applications. low-density polyethylene (LDPE); 0.910 to 0.940 g cm -3 linear low-density polyethylene (LLDPE); 0.916 to 0.940 g cm -3 Additionally, ASTM D1248 further defines two additional density classes at either density extreme: very low-density polyethylene; ≤0.910 g cm -3 very high-density polyethylene; >0.960 g cm -3 Some examples of PE applications according to their density are shown in Figure 1-3.

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Figure 1-3: Polyethylene uses and applications according to their density.

CLASSIFICATION BASED ON BRANCHING STRUCTURE

PEs can be classified according to their branching structure (Table 1-1). The mechanism of polymerization controls the organization of the monomers linked in the polymer chain and the branching structure. HDPE has no or only a small amount of branching and is a very crystalline polymer (around 70% of crystallinity).

They are manufactured with Ziegler-Natta or Phillips catalysts. LDPE contains a combination of long and short chain branching from 20 to 30 CH3 groups per 1000 carbons. They are produced via radical polymerization and have typical properties: flexibility, processability, transparency.

The branching in LLDPE is predominantly short chain branching. This class of PE is synthetized by copolymerization of ethylene with an α-olefin which allows the insertion of a short-chain branching into the main chain and thus impacts the crystallinity of the material. [3] The α-olefins frequently used are 1butene, 1-hexene and 1-octene. [1,4] The crystallinity and then the physical properties of LLDPE can be adjusted by varying the comonomer content. [3,5] Consequently, it is highly relevant to quantify the amount of comonomer units incorporated into LLDPE during the polymerization process.

POLYPROPYLENES

Polypropylenes belong to the polyolefin family and has applications both as a plastic and a fiber. It is distributed in 3 families according to its geometry: isotactic (iPP), syndiotactic (sPP) and atactic (aPP)

(Figure 1234). The properties of iPP are similar to that of polyethylene but it is slightly harder and more heat and chemical resistant. [1] Figure 1 described the first efficient polymerization system for sPP synthesis based on ansa-fluorenylcyclopentadienyl catalysts. [6] iPP production is based on heterogenous Ziegler-Natta catalysts [7] and supported metallocene catalysts. [8] Compared to sPP, it offers an attractive properties/cost ratio and leads the market. In polypropylene block copolymers, the amount of ethylene is higher, up to 15%. It has comonomer units arranged in blocks. [9,10] The regular arrangement makes polymer more rigid and less brittle than the random copolymer. [11] These materials are appropriate for applications demanding high impact strength. [12] 1.3.1.3 High impact polypropylene iPP is very fragile at low temperatures due to its elevated glass transition temperature (around 20°C) [13] .

Its application in cold environments is therefore not possible. The incorporation of an ethylene-propylene elastomer (EPR) in this material improves its toughness and its impact resistance in subzero temperatures. [14,15] The addition of a certain amount of EPR into an iPP semi-crystalline matrix serves to adapt the final properties of the resulting material called high impact polypropylene (hiPP). The inclusions of the amorphous EPR phase prevents the propagation of cracks in the crystal matrix and absorbs the energy of impacts, while the iPP provides rigidity to the material. This balance between toughness and stiffness will depend on the final percentage of rubber in the material. [16][17][18] hiPP is useful in applications which require impact resistance. hiPPs are mainly used in packaging, houseware, film, pipe applications, automotive bumpers and electrical segments. [15,16] The development of these essential polymers largely used in everyday life, requires the control and understanding of chemistry and reaction engineering via the development of advanced and specific characterization techniques. This thesis work resides fully in this framework. It aims to develop novel analytical methods to better understand the structure of polymers and thus better interpret the chemical processes involved during the polymerization steps.

To effectively achieve this objective, it is first necessary to understand the chemistry and processes of olefin polymerization.

CHARACTERIZATION OF POLYETHYLENES: FROM THERMAL FRACTIONATION TECHNIQUES TO SPECTROMETRY 1-37

POLYMERIZATION OF OLEFINS

Depending on the polymerization process, several grades of polyethylene can be produced. They are obtained by chain reactions via various synthesis methods:

Free-radical polymerization under high pressures (120-300 MPa) and high temperatures (140-325°C) produces LDPE containing long and short chain branching. The process was developed in 1933.

Chromium catalysis or Phillips process, the first catalytic polymerization of ethylene by the Phillips

Petroleum Company (CrO3-silica catalyst, Figure 12345). The process was developed in the 1950s. Originally, Ziegler and co-workers at the Max Planck Institute in Germany proved the ability of the Al-C bond of trialkylaluminium to insert ethylene via the "Aufbau" reaction. [19] Afterwards, a major breakthrough was achieved when they polymerized ethylene with the TiCl4/AlEt3 system under mild conditions. [20] Subsequently, Natta and co-workers at Milan Polytechnic were the first to produce iPP with a TiCl3/AlEt2Cl combination. [21,22] For these major discoveries Karl Ziegler and Giulio Natta were awarded the Nobel Prize for chemistry in 1963.

Several generations of Ziegler-Natta catalyst have been successively developed to improve activities and stereoregularity in the case of propylene polymerization. [23] In particular, the evolution towards the supported catalyst TiCl4 on MgCl2 developed by Mitsui Chemical Inc. improves not only the activity but also the control of the polymer structure and particle morphology. The use of the heterogeneous system (with a support in contrast with a homogeneous or soluble system) has enabled the production of new grades of polymers such as HDPEs and LLDPEs. Despite developments, Ziegler-Natta catalysts are multisite.

• Metallocene complexes used for single site catalysis have led to new evolutions in polymer structure.

The metallocene complexes consist of two aromatic groups such as cyclopentadienyl ligands (Cp) linked to the metal center. The first titanocene dichloride (Cp2TiCl2), activated by aluminium alkyls AlEt2Cl and AlEt3, was reported by Breslow, Newburg and Natta. [24][25][26] Although the cocatalysts proved ineffective for the activation of complexes and led to poor activity, these catalysts contributed to understand the mechanism of polymerization. Later, Ewen and Kaminsky discovered the highly active Cp2ZrCl2/MAO. [27][28][29] Methylaluminoxane (MAO, Figure 123456789) was revealed to be a major activator for group 4 metallocene complexes (Figure 123456).

Figure 1-6: Example of metallocene complexes with sandwich structure: ferrocene [30] which is not active for olefin polymerization and zirconocene.

• The development of post-metallocene catalysts has given rise to intense interest in understanding ligand/metal effects on the catalyst behavior. [31] For instance, Brookhart and co-workers have reported catalysts with a late transition metal (nickel(II) and palladium(II)) combined with a bulky diimine ligand, which produce high molar mass polyolefins and a well-controlled microstructure (Figure 1234567).

Figure 1-7: Brookhart α-diimido metal catalysts.

1-39

This catalyst system offers a complete range of materials from highly branched polyolefins, without the need for an α-olefin, to linear ones. [32] Post-metallocene catalysts that have received commercial attention were initially developed by DOW and Exxon with the constrained geometry catalysts (CGC). [33] The CGCs feature more accessible active site than metallocene catalysts (Figure 12345678). Thus, the open nature of the active site allows the efficient copolymerization of ethylene with α-olefins such as hexene and octene [34,35] . Stevens et al. also have reported that high molar mass polymers could be produced. [36] Figure 1-8: General structure of constrained geometry complexes (CGC).

A wide range of molecular catalysts have been developed, expanding the tool box for making polyolefin materials with improved performances. [37] However, investigating the development of olefin polymerization catalysts falls outside the scope of this chapter. CCD. Note that the association of molecular catalysts (metallocene and post-metallocene) has led to advanced multi-site catalysts providing high performance resins via the control of short branching in low and high molar masses fractions. [38] Some of the analytical methods developed in this work have required the use of ethylene copolymers with narrow MWD and CCD. Metallocene catalysts were therefore logically used to produce well-defined polymers that were used as standards.

PHILLIPS CATALYSTS

Phillips catalysts were the first catalysts to be industrialized, in the 1950s, to produce HDPE. At present, Phillips Petroleum utilizes a highly active catalyst, chromium oxide on a high-surface area silica, to produce high-density polyethylene. It gives a highly linear and very crystalline polymer, but the presence of LCB characterizes this class of HDPE. [39] Phillips catalysts lie on a hexavalent chromium supported on a silica surface. To make the catalysts, the silica gel carrier is impregnated with a chromic (III) acetate compound followed by calcination to "activate" the catalyst. During this activation, chromium (III) oxidizes to Cr(VI) on the silica surface. Chromate species including monochromate, dichromate and polychromate are formed. Only a fraction of about 1 wt% chromium is catalytically active. [4,40] The chromate species of the Phillips catalysts in contact with the ethylene monomer may be reduced to lower valence states of Cr (II), leading to elevated ethylene polymerization activity without using any co-catalysts. [40] Although Phillips catalysts are used to produce some 40-50% of the world's HDPE, the polymerization mechanism is still under investigation, the main question being the structure of the active species.

Various initiation mechanisms have been proposed in the literature including the Cossee mechanism, [41][42][43] the metallacycle mechanism, [44][45][46] the carbene mechanism [46][47][48] and the proton transfer mechanism. [42] Scheme 1-1: Overview of Cossee (a) metallacycle (b) carbene (c) and proton transfer (d) mechanism for Phillips catalysts.

ZIEGLER-NATTA CATALYSTS

Heterogeneous Ziegler-Natta catalysis is based on a transition metal salt as precursor, such as TiCl4 or VCl4, supported on silica or magnesium chloride and associated with a co-catalyst. Among the common trialkylaluminums (AlR3) used as co-catalysts, AlMe3 (TMA), AlEt3 (TEA), Al(i-Bu)3 (TIBA) are the most popular. The activation process with AlR3 features several steps including chlorine abstractions, metal alkylation and reduction to Ti (III).

The variation of the atomic arrangements around the titanium impacts the properties of the catalyst and consequently its activity and its selectivity. First generation Ziegler-Natta catalysts for propylene polymerization consist of particulate titanium trichloride crystals. The main advances of this system are the use of a support (MgCl2) and internal donors which improve the activity, the control of molar mass distribution and the particle morphology. [20,26,49,50] Internal donors help to control catalyst selectivity by blocking certain sites. Ziegler-Natta catalytic polymerization follows a coordination-insertion mechanism.

1-42

The full polymerization mechanism, which comprises several steps with initiation, propagation and chain termination, was described by Cossee and Arlman. [43,[51][52][53] 1.

METALLOCENE CATALYSTS

The structure of metallocene catalysts adopts a sandwich-type form, where the transition metal is located between two cyclopentadienyl (Cp) rings (Figure 123456). A well-studied example of a metallocene catalyst is based on Cp2ZrCl2. Since metallocene catalysts are soluble, they can be used as homogeneous and heterogeneous catalysts, where they are carried on inert supports such as silica, alumina and magnesium dichloride.

Commonly used to activate the Ziegler-Natta catalysts, trimethylaluminum was logically first chosen as an activator for metallocene catalysts but led to low activity. Kaminsky and Sinn discovered that methylaluminoxane (MAO) efficiently activated metallocene pre-catalysts. [27,54] The complex structure of MAO is produced by the hydrolysis of trimethyl-aluminum. [55][56][57] Many structural models have been proposed (Figure 123456789). Many factors can be changed to adapt the catalytic behavior of metallocene catalysts such as the nature of transition metal, the co-catalyst/catalyst ratio, the substituent on the cyclopentadienyl rings and the polymerization conditions. These factors regulate the catalyst's activity, the comonomer response, the regioselectivity and the stereospecificity of olefin insertion. [58] The symmetry forced by the ligands around the active site determines the coordination and insertion of the monomers and, consequently, the orientation of the growing polymer chain.

The polymerization mechanism with metallocene catalysts is similar to the Ziegler-Natta mechanism. [59,60] The first step of the polymerization mechanism is the formation of an active site. It is created by the reaction of a pre-catalyst and the co-catalyst. The co-catalyst alkylates the pre-catalysts and extracts one ligand (halogen or methyl) to form a cationic active site and a non-coordinating anion. As a Lewis acid, the cocatalyst also serves to protect active species by trapping impurities (water traces, oxygen, CO2, mercaptans, etc.) which poison the reaction.

Polymerization occurs via a coordination-insertion mechanism. The active species has both a metal-carbon bond and a coordination site for the monomer in cis position. Polymerization takes place in two steps. The first corresponds to the coordination of the olefin, and the second step consists of the insertion of the olefin into the metal-carbon bond, releasing a coordination site capable of accepting a new olefin. Transfer reactions are key elements of the catalytic mechanism because they make it possible to form a large number of chains per metal center. Among these transfer reactions, the -H elimination reaction is the main transfer reaction, leading to vinyl terminated polymer chains. o Rheology. 1 The branching is classified as LCB when the length of the branches is longer than a few hundred carbon atoms, corresponding to 2 or 3 times the entanglement molar mass. [61][62][63][64] CHARACTERIZATION OF POLYETHYLENES: FROM THERMAL FRACTIONATION TECHNIQUES TO SPECTROMETRY 1-46 In this work, all these techniques (except AF4) were employed and contributed to the development of new characterization methods. They were established in our laboratory to be used as routine techniques and to help research subjects in chemistry and processes of polymerization.

STRUCTURE OF POLYETHYLENE

The structure of polyethylene can be described on different levels, starting from the macromolecule chain to the macroscopic material. Five levels can be observed:

(I) the macromolecular structure resulting directly from the polymer synthesis reactions, (II) the conformational structure, i.e. the spatial arrangement of the macromolecular chain,

(III) the level of the amorphous and crystalline phases, (IV) the organization between them in the form of spherulites constitutes the microscopic level, (V) and finally, the last level represents the macroscopic material.

Macromolecular structure (level I)

The macromolecular structure is defined by the polymerization method (single site catalysts, multi-site catalysts, radical polymerization) and can be characterized by different analytical techniques (NMR, HT-SEC, TREF, CRYSTAF, CEF). The random coil arrangement of the macromolecular chain concerns the amorphous phase of the polymer.

The tangled structure of polyethylene plays an important role in the mechanical behavior of the polymer by giving it viscoelastic properties. The linear organization of chains is related to the crystalline phase of the polyethylene. The most stable configuration is the orthorhombic phase whose parameters, determined by Bunn [65] , are: a = 0.740 nm, b = 0.493 nm, c = 0.253 nm, c axis corresponds to the orientation of the macromolecular chains. Later, the crystalline structures were also determined by X-ray scattering [66,67] and neutron scattering for deuterated PE. [68,69] The stability of the PE is ensured by the inter-macromolecular Van der Waals force between the chains, which is weaker in energy than the intra-molecular covalent bonds between the atoms constituting the chain (Table 1-3). In the molten state the polyethylene chains are randomly aligned and entangled. If they are cooled quickly, the chains remain frozen and the resulting polymer structure is disordered. Nevertheless, if the crystallization is slow enough, the polymer chains tend to take an orderly configuration in crystalline lamella. The growth of the polyethylene crystal occurs radially in all directions, resulting in a spherical arrangement called spherulites (Figure 1-13). They are organized in a succession of structured crystalline lamellae interrupted by amorphous regions. These semi-crystalline arrangements have sizes that vary from a few micrometers to several millimeters [70][71][72] depending on the number of nucleation sites. Larger spherulites are obtained in the case of a few nucleation sites.

CRYSTALLINITY

Depending on their entanglement, the polyolefin chains exist in two states: amorphous or semi-crystalline.

If they are not organized, the polymer is amorphous. To be organized and form crystals, the chains should have a regular structure which allows their stacking, as shown in Figure 1-14.

Figure 1-14: The semi-crystalline microstructure of PE containing crystalline and amorphous regions. Inside the crystalline lamellae, the polymer chains are parallel to each other and perpendicular to the amorphous regions. Amorphous and crystalline regions are intimately linked. is the lamella thickness (5-10 nm); LP is the long period of the crystalline structure.

The crystalline phase is characterized by the melting temperature (Tm), the crystallization temperature (Tc) and the enthalpies associated with these phenomena. These parameters, linked to the ability of the polymer to crystallize, are usually determined by the following techniques:

Differential scanning calorimetry (DSC) Differential scanning calorimetry (DSC) is a thermal analysis technique that measures the differences in heat exchange between an analyzed sample and a reference. It is used to determine phase transitions:

the glass transition temperature (Tg) of amorphous phases, the melting and crystallization temperatures and, the enthalpies of reaction, melting and crystallization.

Heat exchanges between the polymer and the equipment can be endothermic or exothermic depending on the transition event. Thus, for example, a melting absorbs heat in order to be able to increase its 1-50 temperature at the same rate as the reference. The melting is, therefore, an endothermic phase transition because it absorbs heat. Conversely, the sample can undergo exothermic events, such as crystallization, when it releases heat to the system.

The heat energy required during the melting of a semi-crystalline PE is the melting enthalpy. It can be quantified (Figure 1-15) and compared to that required by 100% crystalline PE with a known melting enthalpy value. An enthalpy of 293 J g -1 for a 100% crystalline material is commonly used. [START_REF] Wunderlich | Thermal Analysis[END_REF][START_REF] Schick | [END_REF] This analytical technique was widely used in this work. The dependence of the melting temperature on crystallite thickness ( ) can be expressed by the Gibbs-Thomson equation:

(1-1)
where Tm is the melting temperature, Tm 0 is the equilibrium melting temperature of the infinitely thick crystal, σe is the interfacial free energy, Hu is the melting enthalpy per repeating unit, and is the crystallite thickness (Figure 1 -14).

This relation can be applied directly to DSC measurement to calculate the lamellae thickness. However, this value can be also obtained by direct experimental measurement.

X-ray scattering

Small angle X-ray scattering (SAXS) revealed the stacking of crystallites. This regular arrangement of chains produces narrow diffraction peaks while the amorphous regions produce broad halos. The lamellae thickness and the degree of crystallinity can be measured by integrating the relative intensities of the peaks and halos. [75][76][77][78][79] Infrared (IR) and Raman spectroscopy

The infrared absorption spectra of crystalline polymers exhibit characteristic peaks which are missing in amorphous polymers. The degree of crystallinity can be estimated from the analysis of these bands. [80] As an alternative, Raman spectroscopy using vibrational bands in the wavenumber region 900-1500 cm -1 can provide a reliable calculation of crystallinity. [81,82] Nuclear magnetic resonance (NMR)

The mobility of protons differs in the crystalline and amorphous regions of polyethylene. Solid state 1 H NMR spectroscopy is affected by the different mobilities of atoms. The spectrum of a semi crystalline PE shows the overlap of a narrow peak and a broad peak. The mobile protons of the amorphous phase contribute to the narrow peaks, whereas the protons blocked in the crystalline phase contribute to the broadening of the peaks. The degree of crystallinity, related to the number of protons in each region, is obtained by the deconvolution of the spectrum. [83,84] Solid-state 13 C NMR signals can also be studied to estimate the degree of crystallinity. The nuclei of the same atoms in the amorphous and crystalline parts do not encounter exactly the same magnetic field, resulting in different signals in the 13 C NMR spectrum. The degree of crystallinity of PP samples, estimated by the deconvolution of CH3 signals, has been reported in previous works. [85][86][87][88] The degree of crystallinity depends slightly on the molar mass (mostly for low molar masses) and especially on the chemical composition of the polymer. These are, therefore, two essential parameters for the characterization of materials which are determined respectively by size exclusion chromatography and thermal fractionation techniques. These techniques will be described in the next sections.

MOLAR MASSES

Chain length is expressed in terms of molar masses, corresponding to the molar mass of the monomers and the number of monomer units inside the chain. The molar masses of polymers dictate numerous properties such as thermal behavior, chemical resistance, viscosity, tensile strength, toughness, impact resistance, etc. Higher molar masses are associated with higher physical properties, while lower molar masses are associated with lower properties. [89] Excessively low molar masses are not appropiate for industrial applications that require that products preserve their shape.

A polymer is a statistical set of macromolecular chains of different lengths and therefore of different molar masses. We often need to describe the shape of a distribution using only a few numbers. For this reason, polymer molar masses are described as averages calculated from the molar masses of all the chains.

The commonly used average molar masses, [START_REF] Pasch | HPLC of polymers[END_REF] classically determined by size exclusion chromatography, are described below.

Number average molar mass:

The number average molar mass is the statistical molar mass average of all the polymer chains in the sample. It is based on the number of polymer chains in a sample. This is the first moment of the distribution and is defined by:

(1-2)
where Mi is the molar mass of a chain (g mol -1 ), Ni is the number of chains having a molar mass of Mi, and xi is the mole fraction of chains having a molar mass of Mi.

M n can be measured by methods that determine the number of molecules in a sample of a given weight;

for example, colligative methods such as the end-group assay.

Weight average molar mass:

The weight average molar mass is calculated from the weight fraction distribution of different sized molecules (Equation 1-3). This is the second moment of the distribution.

1-53 (1-3) where Mi is the molar mass of a chain (g mol -1 ), Ni is the number of chains having a molar mass of Mi and wi is the weight fraction of chains having a molar mass of Mi.

M w considers the molar mass of a chain in determining contributions to the molar mass average. The larger the chain, the more the chain contributes to M w. M w is changed to higher values and is always greater than M n. M w can be determined by techniques that are sensitive to the molar size, such as light scattering techniques. There is an equivalent weight proportion of macromolecules on each side of M w in the molar mass distribution. As a general formula, different average molar masses can be calculated using the n th moment of the distribution defined as follows.

(1-4)

where: n = 1 gives M w n = 2 gives M z n = 3 gives M z+1

The higher averages are increasingly sensitive to high molar masses and therefore are more difficult to measure with precision. They are associated with methods that measure the motion of polymer chains, such as diffusion.

As shown in Figure 1-16, for all polymers, the average molar mass always ranks in the following order: M n < M w < M z < M z+1.

Viscosity average molar mass

Molar mass can also be calculated from the viscosity of a polymer in a solution. Viscosity is the measure of resistance to flow. Long polymer chains have difficulty in flowing due to friction and entanglement between the chains presenting higher viscosity. In the viscosity average molar mass measurement method, the flow of the polymer solution through a capillary is measured. This method is also known as intrinsic viscosity analyzer (IVA).

First, Staudinger and then Flory assumed the [η] to be proportional to the polymer molar mass. [START_REF] Tanford | Physical chemistry of macromolecules[END_REF][START_REF] Flory | Principles of polymer chemistry[END_REF] Later, Mark, [START_REF] Mark | [END_REF] Houwink [START_REF] Houwink | [END_REF] and Sakurada [START_REF] Sakurada | Nihon Kagakusenikenkyusho Koensyo[END_REF] correlated the intrinsic viscosity with molar mass using the Mark-Houwink-Sakurada Equation 1-5:

[η] = K.M α (1-5)
where K and α (0.5 -1) are constants varying with the polymer, solvent, and temperature.

The value of α gives information about the conformation of the polymer in the solvent. It is equal to 0 for spherical conformation, 0.5 for statistical coil conformation, 0.8 for chains in good solvent and up to 1 for rigid rod conformation. These constants must be determined experimentally by plotting the logarithm of the intrinsic viscosity as a function of the logarithmic molar mass (Figure 1-17) and fitting the best straight line to the following Equation 1-6:

log η = log K + α.log M (1-6)
The intersection with the y-axis of a linear fit of data gives the constant log K, the slope of the curve gives the constant α. These parameters, relating viscosity to molar mass, can be found in the literature for polyethylene in commonly used solvents. [START_REF] Wagner | [END_REF]97] For PE in 1,2,4 TCB at 135°C, the value of α is around 0.7. The viscosity average molar mass M v, which is not measured by SEC but by a viscometer analyzer (IVA) is calculated as:

(

Where Mi is the molar mass of a chain, Ni is the number of chains having a molar mass of Mi, α is the Mark Houwink value.

Dispersity

The dispersity is a representation of the broadness of a molar mass distribution of a polymer and is defined by Equation 1-8:

Ð = M w / M n (1-8)
The larger the dispersity, the broader the molar mass distribution. A narrow polymer where all the chain lengths are equal (such as a protein) has a Ð = 1. The best controlled synthetic polymers have a Ð of 1.02 to 1.10. Ziegler-Natta and Phillips catalysts typically yield polymer with a high Ð, whereas metallocene catalysts yield Ð values of 2.0, in theory (Table 1-4).

High temperature size exclusion chromatography (HT-SEC) is used to measure the average molar masses of polyolefins requiring high analysis temperatures. It is because of their high crystallinity that polyolefins 1-56 display limited solubility at room temperature and must therefore be dissolved at high temperature in particular solvents, such as toluene, xylene, ortho-dichlorobenzene and 1,2,4-trichlorobenzene. [98] Table 1-4: Dispersity obtained with different polymerization reactions.

Polymerization Dispersity

Anionic polymerization 1.02 -1.5

Cationic polymerization Broad

Chain polymerization 1.5 -3.0

Step polymerization 2.0 -4.0 Average molar masses and molar mass distribution are, therefore, relevant parameters to be measured to characterize polymers. The most widely recognized technique to determine the MWD of polyolefins is high temperature size exclusion chromatography (HT-SEC). [START_REF] Striegel | Modern size-exclusion liquid chromatography: practice of gel permeation and gel filtration chromatography[END_REF][START_REF] Scholte | [END_REF] However, many LLDPEs are produced with the incorporation of comonomers to extend and tune PE performances. Therefore, it is also necessary to measure the so-called chemical composition, which depends on comonomers content, to characterize these materials.

CHEMICAL COMPOSITION

For LLDPE, the average chemical composition and its distribution (CCD) [START_REF]Polyolefin Characterization: Recent Advances in Separation Techniques[END_REF] are important parameters because they strongly impact the properties of LLDPE. The chemical composition corresponds to the comonomer or to the short chain branching (SCB) content in LLDPE chains. The increase in comonomer content will therefore decrease the crystallinity by breaking the regularity of the chains.

The heterogeneity of this distribution is due to the behavior of the multi-site catalysts, where each site gives a chain with different microstructures, and possibly to variations in the monomer concentration and the temperature during polymerization. To completely define the structure of a copolymer, it is therefore necessary to have access to the distribution in chemical composition in addition to the average.

Various techniques, which will be discussed in the following part, are available for measuring the CCD of polyolefins. These are separative techniques that allow, in the same way as SEC, to determine a distribution.

Crystallization based techniques

Most polyolefins are semi-crystalline, and their melting temperatures can reach up to 165 °C for iPP. The crystallization temperature mainly depends on the structure of the polymer with the comonomer content, and the degree of branching for PE (chemical composition) and tacticity for the PP. The polymer chains, with low crystallinities will crystallize out of the solution at a temperature lower than those with a higher crystallinity. Flory developed the crystallization theory of polymers [START_REF] Flory | [END_REF] that was used to propose the principles of polymer fractionation in solution. Monrabal [START_REF]Temperature Rising Elution Fractionation and Crystallization Analysis Fractionation[END_REF] summarized it in Equation 1-9.

(1-9)

where Tm 0 is the melting temperature of the pure polymer, Tm is the melting temperature of the copolymer in the solvent, R is the gas constant (8.314 J mol -1 K -1 ), Hu is the melting heat per polymer repeating unit, and N2 is the amount of comonomer incorporated.

This equation, which assumes that ΔHu is constant over the whole range of crystallization temperatures, links the chemical composition of a polymer to its elution temperature. It can be applied for ethylene copolymers. This equation has been the basis for developing thermal fractionation techniques such as temperature rising elution fractionation (TREF), crystallization analysis fractionation (CRYSTAF) and the more recent crystallization elution fractionation (CEF) techniques.

CHARACTERIZATION OF POLYETHYLENES: FROM THERMAL FRACTIONATION TECHNIQUES TO SPECTROMETRY

1-58

The working principles and advantages of each approach will be discussed in the next sections.

Temperature rising elution fractionation TREF

The experimental TREF technique was the first well-established method to fractionate chains according to their crystallizability. The method was initially described by Desreux and Spiegels in 1950 [START_REF] Desreux | [END_REF] and has been applied since the 1990s by Wild [START_REF] Wild | Temperature rising elution fractionation[END_REF][START_REF] Wild | New Adv. Polyolefins[END_REF] for polyolefins. The fractionation by TREF involves three main steps (Figure 1-18). reported that the crystallization step has a strong influence on the separation, and that the decrease in the cooling rate results in better resolution. [START_REF] Soares | [END_REF] Elution is monitored by an infrared detector which generates the distribution curve of the chemical compositions. This detector has little dependence on temperature fluctuations and good sensitivity to the C-H bonds widely present in polyolefins. Absorbance is measured at 3.5 μm which correspond to the symmetrical elongation frequency of the C-H bonds. An additional viscometer detector which is molar mass sensitive can be added in the system.

TREF was used to analyze the composition of various polyolefins such as copolymers of ethylene [108,109] and propylene, [110][111][112] polyolefin blends [113,114] and separate isotactic polypropylenes according to their tacticity. [111,115] More details on the analytical conditions are described in the various reviews published on TREF by Wild, [116] Fonseca, Harrison, Soares and Hamielec [START_REF] Fonseca | Modern techniques for Polymer Characterisation[END_REF] and Monrabal. [START_REF]Temperature Rising Elution Fractionation and Crystallization Analysis Fractionation[END_REF] 1.

Crystallization analysis fractionation (CRYSTAF)

As TREF is time-consuming, a more recent technical approach was developed by Monrabal in 1991. [119,120] Crystallization analysis fractionation (CRYSTAF) analyzes the distribution of short chain branching only during the crystallization step, which is performed in a similar way to TREF.

The CRYSTAF analysis is based on the continuous crystallization of polymer chains in dilute solution. When the temperature decreases, the chains progressively crystallize. First, the most crystalline chains precipitate at high temperatures and are followed by the chains of lower crystallinity. At a given temperature interval, an aliquot of the polymer solution is collected and filtered, and its concentration is determined by an IR detector. In CRYSTAF, the analysis is carried out in stirred crystallization vessels without support. When the temperature decreases, the most crystalline fractions (linear chains) precipitate first, resulting in a decrease in the concentration of the polymer solution. This step is followed by the precipitation of increasingly branching fractions (or less crystalline chains) as the temperature decreases (Figure 12345678910111213141516171819). At the lowest temperature, there remains in solution the amorphous fraction corresponding to highly branched chains that have not crystallized.

The IR detector measures the concentration of the solution at each step of sampling. A curve (orange curve in Characterizations of ethylene [121][122][123] and propylene [124,125] copolymers were described by various teams.

Furthermore, Sarzotti et al reported the molar mass effect on CRYSTAF separation above 10,000 g mol - 1

. [126] CRYSTAF is an indisputably fast technique for separating samples, however it presents a poor resolution compared to TREF.

Crystallization elution fractionation (CEF)

In 2007, Monrabal et al developed a new experimental technique based on a similar separation principle and offering considerable time savings: crystallization elution fractionation (CEF). [127,[START_REF]Crystallization based separations for semicrystalline polymers[END_REF] CEF (Figure 1-20) was developed by combining the separation power obtained in the crystallization cycle (equivalent to CRYSTAF), with that obtained in the elution melting cycle (equivalent to TREF). The dynamic mode used during the crystallization stage requires a longer column than TREF but allows rapid separation and better resolution than TREF and CRYSTAF. Despite this improvement, various problems are still present:

Co-crystallization has further complexified the separation of various families with poor precision and accuracy.

CHARACTERIZATION OF POLYETHYLENES: FROM THERMAL FRACTIONATION TECHNIQUES TO SPECTROMETRY

1-61

Polyolefins with a comonomer content greater than about 8 mol % are unable to crystallize. This limit can be increased using cryogenic options, but the high freezing temperature of the solvent is a constraint.

Figure 1-20: Schematic representation of a CEF experiment; the device is similar to that of TREF.

Two new techniques, well described by Monrabal, [START_REF] Monrabal | [END_REF] have been developed to improve chemical composition measurement: Solvent Gradient Interaction Chromatography and Thermal Gradient Interaction Chromatography (SGIC and TGIC). With these techniques, the negative effect of cocrystallization is reduced, and amorphous polymers can finally be analyzed. These techniques combine both separation by crystallization as in previously described techniques and separation by adsorption on the stationary phase of the column.

Solvent gradient interactive chromatography, SGIC

High performance liquid chromatography is a well-known technique used to separate polymer chains according to their composition. For a long time it was limited to ambient temperature with liquid adsorption chromatography (LAC). The interaction mechanisms involved in LAC have been widely studied.

[ 130, 131] In 2003, Macko et al reported for the first time the use of high temperature HPLC to separate polyolefins with a silica-based column. [132][133][134][135] Later, Macko and Pasch showed that polyolefins can be adsorbed and separated in a Hypercarb porous graphitic carbon column using a solvent gradient from decanol to TCB. [136][137][138][139][140] The use of the Hypercarb column was a major discovery in polyolefin characterization. Following this, a large variety of ethylene-α-olefin copolymers were separated using this approach known as solvent gradient interaction chromatography (SGIC). [141][142][143][144][145][146] SGIC (Figure 1-21) can be used to separate for the first-time amorphous polyolefins with high α-olefin content. Due to the variation of the solvent composition during analysis, most common detectors cannot be employed. Classically, the evaporative light scattering detector (ELSD) , insensitive to the solvent gradient, is used even if the detector's output is nonlinear with concentration. A technical approach using a temperature gradient instead of a solvent gradient has recently enabled the use of conventional detectors for polyolefin characterization.

Temperature gradient interaction chromatography (TGIC)

A temperature gradient interaction chromatography (TGIC) instrument, based on an adsorptiondesorption mechanism under a temperature gradient, has recently been developed by Cong et al. [START_REF] Cong | High temperature liquid chromatography of Polyolefin[END_REF] The TGIC instrument (Figure 1 However, TGIC chromatography has lower peak resolution than crystallization-based techniques. This is reflected in calibration curves (elution temperature versus comonomer content) with lower slopes for TGIC. Enhancing its resolution is an active topic of research [START_REF] Inwong | [END_REF][149][150][151] that could further increase the number of its applications. A few publications have discussed the separation mechanism and the effect of analysis conditions. Monrabal et al. proposed that it is the ethylene segments in ethylene-α-olefin copolymers which adsorb strongly on the support, and that the tertiary branched carbons weaken this interaction.

Therefore, copolymers with a low α-olefin content have longer ethylene sequences and desorb from the surface at higher temperatures than copolymers with higher α-olefin contents. [152,153] Graphitic carbon is the most common support for polyolefin separation. Nevertheless, Monrabal et al.

proposed that all supports having atomically flat surfaces can be useful for TGIC fractionation, strengthening the case that copolymers interact with the column via flat ethylene sequences. [152,153] They showed that adsorption is based on a weak interaction of van der Waals forces between the polyolefin chains and the flat surface. The increase in α-olefin content inhibits this interaction, thus lowering the desorption temperature.

Soares et al. studied the effect of the solvent, the characteristics of the column (particles size, column length) and various analytical conditions on the TGIC chromatograms of individual samples and their blends. [START_REF] Inwong | [END_REF][149][150] Neither average particle size (3 and 5 μm) nor column length (10 and 25 cm) played a major role in the fractionation. They showed that o-dichlorobenzene increased elution temperatures and had slightly better resolution than 1,2,4-TCB. Furthermore, they found that smaller injection volumes reduced column loading effects and minimized the co-adsorption/co-desorption effects. Finally, they demonstrated that the heating rate and the elution flow rate strongly impacted separation, while the cooling rate had no significant effect on the TGIC profiles.

Inwong et al. developed a mathematical model for TGIC fractionation based on population balances,

assuming a non-equilibrium, multi-stage adsorption-desorption mechanism. Their model fitted the experimental results of individual ethylene-octene samples and their binary blends were measured under several operating conditions adequately. [START_REF] Inwong | [END_REF] All these fractionation techniques are limited by the molar masses of the polymers that can be studied.

Indeed, several researchers have agreed that molar mass has no impact on separation if it is high enough (> 25,000 g mol -1 ). [149,154] 1-65

The next chapters focus first on LLDPE synthesis to provide a complete set of various comonomer contents and types. The aim of the following part is to demonstrate and propose new tools and methods with various items of equipment to characterize polyolefins structures.

The distributions of molar masses and chemical compositions are a direct consequence of the polymerization conditions: catalyst type, process, and so forth. Therefore, the accurate characterization of molar mass and structure, including short and long chain branching, is of great importance when establishing final composition-property relationships and conducting research on polymerization.

EXPERIMENTAL PART

« La connaissance s'acquiert par l'expérience, tout le reste n'est que de l'information » Albert Einstein

2-74

There are no commercial LLDPE with known and certified chemical compositions. A specific know-how is available in our laboratory for the controlled synthesis of well-defined polymers. I decided to take advantage of the CP2M researchers' skills, and in particular those of Christophe Boisson, in metallocene catalysis to conceive polymers that will serve as standards for the development of new analytical methods.

With the support of Christophe Boisson, I supervised three internship students who produced a wide range of well-defined copolymers. We have tested and chosen catalyst systems already known and studied by our laboratory in previous works.

The objective of the following part was to synthetize LLDPE models with various types and amount of comonomer as illustrated in the figure below.

LLDPE models

2.1 REACTION MEDIUM

PRE-CATALYSTS

In order to obtain model polymers with homogeneous chains both in molar mass and in chemical composition, metallocene-type catalysts were used. The choice of catalysts was guided by previous work carried out in the laboratory [1] where homogeneous LLDPEs with low dispersity were obtained.

The complex used first, rac-ethylene bis(indenyl)zirconium (IV) dichloride (rac-Et(Ind)2ZrCl2), allows efficient incorporation of comonomers, and it is known in particular for its use in the synthesis of isotactic polypropylene, because of the C2-symmetry of the complex and the presence of two homotopic sites for active cationic species (Figure 2-1). The second complex used, Bis (n-butylcyclopentadienyl) zirconium dichloride ((nBuCp)2ZrCl2), leads to less efficient copolymerization (Figure 2-2). A lower response to the comonomer is obtained due to the steric hindrance of its ligands. However, polymers with narrow molar mass distribution were prepared.

CO-CATALYST

Methylaluminoxane (MAO) is the co-catalyst of choice for metallocene complexes. For the experiments, a commercial solution of MAO at 10% by mass in toluene was purchased from Aldrich. It was stored under inert atmosphere at -20°C.

SOLVENT

The toluene used as solvent was purchased from Biosolve and dried in a Mbraun solvent purification system equipped with activated alumina and copper catalyst columns.

MONOMER

Ethylene (99.95%) was purchased from Air Liquid and purified by passing it through 3 different columns in order to remove the impurities (H2O, O2, CO2 and H2):

• a copper oxide support CuO (from BASF) for the elimination of O2 and CO,

• an activated molecular sieve which eliminates water,

• an alumina column which eliminates the sulfur compounds.

COMONOMERS

The tested comonomers are the α-olefins most often used industrially for the synthesis of polyolefins.

• Propylene, a gaseous compound, was used directly without purification.

• 97% commercial hexene is placed on CaH2 overnight and then distilled by cryo-distillation for purification.

• 98% commercial octene is bubbled through a molecular sieve and used without further purification.

• Octadecene (90%) is purified by simple degassing under vacuum.

• Norbornene is in solid form at room temperature (melting temperature = 42 °C). Norbornene in a melting state is placed on sodium for one day and then distilled for purification. A solution of norbornene in toluene is then prepared in order to simplify the sampling.

The various comonomers used in this work and the corresponding copolymers that were obtained are summarized in Figure 23.

COPOLYMERIZATION

A general procedure of the copolymerization is described below:

The complex was weighed in a glove box, and 25 mL of toluene was added. The solutions were stirred until dissolved. 300 mL of toluene, 0.3 mL of MAO, and between 0 and 20 mL of the comonomer were introduced into a 500 mL reactor. 100 μL of the pre-catalyst solution (1.5 mM), prepared previously, was either introduced in the reactor before ethylene pressurization. Polymerization was performed at 80°C under a constant pressure of 4 bar. The reaction exotherm was controlled to keep the reaction conditions as stable as possible. At the end of the reactions, the ethylene feed was stopped, and 5 ml of methanol was introduced in the reactor. The polymer was cleaned with acidified methanol and dried under vacuum at 90°C for 3 hours.

For the series with propylene as comonomer, gas mixtures with different ethylene-propylene ratios were prepared. They were introduced at 3 bar into the reactor that already contained toluene, MAO and the pre-catalyst.

COPOLYMERIZATION CONDITIONS

To obtain a homogeneous polymer with the most stable polymerization conditions, an injection chamber was implemented to inject the catalyst under ethylene pressure. Firstly, the comonomer, the solvent and the MAO were added in the reactor. In the next step, the reactor was fed with 3.8 bar of ethylene pressure and heated to 80 °C. Once the temperature was stable, 100 μL of the pre-catalyst solution, previously diluted in 10 ml of toluene and introduced into the injection chamber, was pushed inside the reactor using an ethylene pressure of 4 bar (Figure 234). This protocol allows the rapid injection of the pre-catalyst solution in stable conditions.

The distribution of the chemical composition of the LLDPE obtained when injecting the catalyst under ethylene pressure was compared to a sample synthetized without the injection chamber. In these conditions the pre-catalyst was introduced directly in the reactor at ambient temperature. Indeed, the catalysts and the α-olefin capable of polymerizing were present inside the reactor. In addition, when they were introduced into the reactor fed with ethylene, they did not immediately attain the polymerization temperature (80 °C). A temperature drift occurred with the risk of forming different microstructures of chains at the beginning of the reaction, affecting the homogeneity of the material. Chains with a high comonomer content have shorter ethylene sequences that are more difficult to crystallize. These chains form thinner lamellae and consequently melt at lower temperatures. On the contrary, chains with fewer comonomer and longer ethylene sequences melt at higher temperatures.

Thus, the different peaks obtained after the SIST treatments reveal the different crystals due directly to the comonomer distribution. The DSC curve from LLDPE synthetized with the injection chamber (blue curve in Figure 2-5 (b)), clearly shows a narrower distribution compared to the LLDPE obtained with the classical protocol (red curve in Figure 2-5 (b). Indeed, the population of strong crystallinity (peak of higher temperature) is greatly reduced, leading to a narrower distribution. This population appeared at the beginning of polymerization when the thermal conditions were not yet stable. The injection chamber protocol appeared to be effective in achieving better homogeneity for our sample and was used systematically thereafter.

BEHAVIOR OF METALLOCENE COMPLEXES

Six series of copolymer models were prepared with these synthesis conditions. For each series, various comonomer contents were added in the reactor in order to obtain different comonomer contents inserted in the chain. The synthesis conditions are reported in Table 2-1. Volume of toluene = 330 mL, a % of comonomer in the reactor, b [Al]MAO = 2.4-3.0 mM. For each reaction the activity changed according to the following values:

(1) variation in activity from 3.9 x 10 6 up to 1.5 x 10 8 g mol -1 h -1

(2) variation in activity from 1.8 x 10 7 up to 7.6 x 10 8 g mol -1 h -1

(3) variation in activity from 3.4 x 10 7 up to 1.5 x 10 8 g mol -1 h -1

(4) variation in activity from 9.4 x 10 6 up to 1.4 x 10 8 g mol -1 h -1

(5) variation in activity from 3.8 x 10 6 up to 2.6 x 10 8 g mol -1 h -1 (6) variation in activity from 2.5 x 10 5 up to 2.7 x 10 7 g mol -1 h -1

The evolution of comonomer in the polymer versus comonomer in the feed is plotted in Figure 23456. The ability of both catalyst systems to incorporate comonomer was evaluated according to the content of comonomer available in the reaction medium. As reported by Lehmus and co-workers, we observed that the content of incorporated comonomer is proportional to the α-olefin in the reaction medium. [2] A linear 2-82 response of insertion was observed for low comonomer content. When the comonomer content in the reactor was greater than 50 mol%, the insertion was no longer linear but was greatly increased. A major difference in the incorporation of 1-hexene was observed between both catalysts. The comonomer was incorporated more easily when using the Et(Ind)2ZrCl2. This behavior depending on the steric hindrance provided by the ligand, in Et(Ind)2ZrCl2 complex, was reported previously. [3,4] The authors also calculated the reactivity ratio for ethylene by 13 C NMR for both complexes. They were evaluated at 51 and 160 for Et(Ind)2ZrCl2 and (n-BuCp)2ZrCl2 complexes, respectively. These values confirm the better comonomer insertion that we observed for the Et(Ind)2ZrCl2 complexes.

Following the synthesis of our model samples, the next step was the characterization by NMR to measure the average comonomer content, and by high temperature size exclusion chromatography (HT-SEC) to measure the average molar masses and the molar mass distribution. The SEC's viscometric detector was also used to measure the long chain branching and to propose a method for measuring the short chain branching.

DETERMINATION OF COMONOMER CONTENT BY NMR

NMR uses an external magnetic field which interacts with the magnetic properties of nuclei to obtain information about the molecular structure of a sample. Different nuclei can be chosen for NMR experiments depending on the need: 1 H, 13 C, 15 N, 19 F, 31 P… 1 H and 13 C are generally applied for polyolefin NMR spectroscopy. The structural information was obtained thanks to the chemical shift (ppm) in the spectrum which represents the E (Equation 2-1) relative to the reference proton. Tetramethylsilane (TMS), whose chemical shift is assigned at 0 ppm, is generally chosen as the reference.

(2-1)

Where h is Planck's constant, the gyromagnetic ratio and B the external magnetic field.

For the LLDPE samples, NMR spectroscopy requires a high temperature and specific solvents which do not evaporate at high temperature. To perform a quantitative analysis, certain universal spectrometer parameters should be selected, as described by Malz and coworkers. [5] In particular, probe tuning and the relaxation delay should be specifically adjusted for LLDPE.

For 1 H NMR, the area of each signal is directly proportional to the number of protons associated with the signal. 1 H NMR is widely used to determine composition of polyolefins such as end-groups, [6] unsaturation, [7,8] functional groups [9] and alkyl branches. Since the signal area can be quantitative, NMR has the great advantage of giving a direct value of the comonomer content in our copolymers without calibration.

13

C NMR is widely applied to explore the microstructure of polyolefins. It has been successfully applied to assess tacticity [10][11][12] and comonomer sequences. [13][14][15][16] Because, in our case, the copolymers have a homogenous composition, the average value obtained by NMR is a fair representation of the structure of our samples. This part describes the instrumentation, parameter setting, and methods used to quantify the comonomer units inserted in the copolymer chains Methyl chain-ends were neglected in the calculations because the molar masses of the copolymers are high (> 20 kg mol -1 ). Nevertheless, at low comonomer content, lower than 2 mol%, the sensitivity of 1 HNMR was not sufficient. In this case 13 C NMR was used as an alternative for the determination of the α-olefin content.

Ethylene-norbornene copolymer:

For ethylene-norbornene, the NMR spectra shown in Figure 2-8 are quite different. The peaks were assigned according to Bergström's publication. [17] I2 is the integral of bridgehead hydrogen signals from norbornene, and I1 is the integral of the remaining hydrogen signals (from norbornene and ethylene).

I1 = 4E + 9H I2 = 3H %= H E+H = 4×I 2 3×I 1 -5×I 2 Octene I1 = 4E + 13O I2 = 3O = O E+O = 4×I 2 3×I 1 -9×I 2 Octadecene I1 = 4E + 33OD I2 = 3OD %= OD E+OD = 4×I 2 3×I 1 -29×I 2 Norbornene I1 = 4E + 8N I2 = 2N %= N E+N = 2×I 2 I 1 -2×I 2
with I1 being the signal intensity of the CH2 and CH protons of the polyethylene chain at 1.3 ppm, I2 is the signal intensity of the methyl at 0.9 ppm and CH at 2.15 ppm for norbornene. E, P, H, O, OD and N are the relative intensities of ethylene, propylene, hexene, octene, octadecene and norbornene units, respectively.

QUANTIFICATION BY 13 C NMR

For low amounts of α-olefin comonomers the triplet intensity at 0.9 ppm was low, the signal to noise ratio was not acceptable to ensure reliable results. 13 C NMR (Figure 23456789) was then carried out under the following conditions:

• Analysis temperature = 100 °C,

• 3: 1 volume mixture of 1,2,4-trichlorobenzene and toluene-d8,

• Concentration: 100 mg ml -1 ,

• 10 mm PA-SEX (Selective X) probe,

• Calibration: chemical shifts of PE at 30.06 ppm. EHH.

The 13 C NMR spectra is somewhat more complex; the peaks were assigned according to the publications by Randall [13] and Galland [18] . After integrating the spectral regions, the mole fractions of the comonomer were calculated by applying the following equations in Table 2-3. After measuring the comonomer content, we determined their average molar mass and their molar mass distribution by HT-SEC. To obtain a complete view of the microstructure of our model copolymers, we furthermore studied the presence of long chain branching (LCB).

2-90

DETERMINATION OF MOLAR MASS AND BRANCHING BY HT-SEC

I am in charge of the high temperature size exclusion chromatography (HT-SEC) in our laboratory. After setting up the instrument, I developed the sample preparation and analysis and performance evaluation protocols for the highly specific measurement of polyolefins. [19] The beginning of this section outlines the results of these evaluations in order to fully understand the accuracy of the measurements obtained on our LLDPE models.

First, the SEC has been used for the measurement of the molar masses according to several implanted methods which are described below. Afterwards, it has also applied to better understand the structure of our polymers through the advanced exploitation of light scattering and viscosimetric detectors.

The HT-SEC analyses were performed using a Viscotek system (Malvern Panalytical, Worcestershire, UK) equipped with three columns (PLgel Olexis 300 mm x 7 mm I.D. from Agilent Technologies). 200 L of sample solution with a concentration of 5 mg mL -1 was eluted in 1,2,4-trichlorobenzene at a flow rate of 1 mL min -1 at 150°C. The mobile phase was stabilized with 2,6-di(tert-butyl)-4-methylphenol (200 mg L -1 ).

Online detection was performed with a differential refractive index detector, a dual light scattering detector (LALS and RALS) and a viscometer for absolute molar mass measurement. OmniSEC 5.12 software from Malvern Panalytical (Worcestershire, UK) was used for the calculations.

CALIBRATION METHODS

Three main methods using different types of detector were established to measure the molar mass of the sample.

Conventional Calibration

Conventional calibration needs only a single concentration detector, a refractive index (RI), to obtain the relative molar masses. They are determined from the elution volume measured by means of a calibration CHARACTERIZATION OF POLYETHYLENES: FROM THERMAL FRACTIONATION TECHNIQUES TO SPECTROMETRY 2-91 curve, set up with the standards of known molar masses. The PS and PE standards were used to construct the calibration curves for our HT-SEC.

Universal Calibration

To improve conventional calibration, we use an additional detector, the four capillary differential viscometer detector. The viscometer coupled with the refractive index detector makes it possible to construct the universal calibration introduced by Benoit and co-workers in 1967. [20] The universal calibration method has proved to be very convenient. The column is calibrated with a series of certified narrow standards, PS in our case. Using this calibration, absolute molar masses can be assessed for polymers whose chemical composition or structure differs from those of the calibration standards.

Nevertheless, a universal calibration curve is available only for a set of columns in a particular solvent and at a particular temperature. The universal calibration with the viscometer allows the measurement of absolute molar masses as well as other parameters related to the structure of polymers such as intrinsic viscosity ([η]), hydrodynamic radius (Rh), Mark Houwink parameters (α and K), branching number (Bw), and frequency (λ).

Light scattering

With the introduction of online light scattering detection, which also provides the absolute molar mass of a sample, the use of universal calibration has begun to decline. The light scattering method does not depend on column calibration to correlate sample retention volume to molar mass. Light scattering measures the overall intensity of the light scattered from a molecule which is directly proportional to its molar mass using the Rayleigh equation [21] and Debye theory [22,23] . The treatment method of Zimm [24][25][26] allowed condensing the results of the light scattering theory in a straightforward equation: [27] (2-2)

with Rθ being the excess Raylelgh ratio of the scattered light (intensity of the scattered light by the sample in excess of the light scattered by the pure solvent), c is the mass concentration, M w is the weight average molar mass, A2 is the second virial coefficient. P(θ), the angular dependence of the scattered light is defined by:

(2-3)

with Rg being the root mean square radius or radius of gyration and q is the form factor calculated by:

(2-4)

where n0 is the index of refraction of the solvent, λ is the vacuum wavelength of the laser.

Finally, K is a constant calculated by:

(2-5)

Where NA is Avogadro's number and dn/dc is the refractive index increment of the polymer solution.

CHARACTERIZATION OF POLYETHYLENES: FROM THERMAL FRACTIONATION TECHNIQUES TO SPECTROMETRY

2-93

To obtain the value of molar mass M w we must calculate the virtual intensity of light scattered at θ=0°. In this case, according to Equations (2-3) and (2-4) sin θ and, therefore, q are both equal to zero, which implies that P(θ) is equivalent to 1. To obtain the intensity of light scattered at θ=0°, two methods can be used. The first method uses an extrapolation of the light scattered at different angles to get that at zero degrees (multi-angle light scattering, MALS). The second solution is the direct measurement of the scattered light close to θ=0° and assume that the difference is negligible. The measurement at θ=0° is practically impossible because the non-scattered laser light overloads the photodiode detector. Therefore, the determination of molar mass is performed with a single angle at θ=7° (low angle light scattering, LALS).

The LALS instrument, with a complementary measurement angle at 90°, is proposed by Malvern Panalytical. Alternatively, MALS instruments are commercially available with two angles (Agilent Technologies), 3 angles, 18 angles (Wyatt Technology), 7 angles (Brookhaven Instruments) and 20 angles (Malvern Panalytical).

According to Equations (2-1) and (2-4) we also need to measure the polymer concentration (c) or to know the value of the refractive index increment (dn/dc).

Light scattering calibration requires no outside standards for column calibration as the sample is measured directly. Nevertheless, it remains necessary to calibrate the system with a standard sample to obtain the detector responses reported in RI is the viscometer, RALS and LALS are the right-angle light scattering detector and the low angle light scattering detector, respectively, IV the viscometer detector. The offset is the volume of tubing between the detectors, and the calibration factor is the instrumental constant of each detectors.

Reproducibility of molar mass average

The reproducibility of the measurements by HT-SEC was evaluated. A same sample was analyzed under the same conditions over a period of several weeks (Figure 2-10). For each measurement, it was dissolved in TCB at a concentration of 5 mg mL -1 and lightly stirred for one hour at 150 °C before injection. The data in Table 2-5 show that the determination of M n has more error than the other values. This is mainly due to the difficulty of integrating the distribution in a repeatable way in the low molar mass side of the distribution due to the noise and this impacts the value of M n more than that of M w. Concerning the measures of intrinsic viscosity ([η]), they show good reproducibility, demonstrating that the viscometer can be used efficiently for the branching calculation in the following part.

Using these experiments, we subsequently consider that the average molar mass will be given with an accuracy of 10% (Table 2345). This value is higher for HT-SEC compared to ambient temperature SEC because of the noisier detector signal whose noise increases with temperature.

Degradation during sample preparation

The analysis conditions, 150 °C in the TCB, are aggressive. Polymers may be degraded during the Therefore, in order to avoid any degradation during preparation, it was necessary to reduce the dissolution time to a maximum of 10 hours. Nitrogen can also be added in the vials during dissolution to remove oxygen and avoid the degradation of the polymer chains.

Determination of the molar mass of our LLDPE samples

Various parameters must be known to calibrate the system and analyze the unknown samples. The factor of concentration variation must be explained since it is specific to HT-SEC and has an impact on the accuracy of the molar mass measurement. The samples are prepared at ambient temperature and analyzed at 150°C; because of the volume expansion due to the temperature, the concentration of the sample decreases. To obtain the volume variation factor, we need to measure the density of TCB at 150°C according to Equation 2-6.

(2-6)

Where DT (g ml -1 ) is the effective density of the solvent at temperature T, DTo (g ml -1 ) is the density of the solvent at a reference temperature, at 25°C it is equal to 1.4547 g ml -1 , k is the temperature coefficient (0.0012), T is the experimental temperature and To is the reference temperature (°C).

At 150°C, the calculated value for DT is 1.252 g ml -1 . The volume variation factor is therefore 1.4745/1.252 = 1.1619. Therefore, the factor used to correct the concentration is 1/1.1619 = 0.86. The concentration of the samples prepared at ambient temperature and analyzed at 150°C should be multiplied by this factor.

Our model samples were analyzed by the different calibration methods, but the results showed similar values. Therefore, only the molar masses obtained by light scattering were reported in the characterization results which are summarized in Appendix 1. We observed that the molar masses of the copolymers prepared with Et(Ind)2ZrCl2 and (n-BuCp)2ZrCl2 were dependent on the comonomer content. They decreased slightly as the comonomer content increased. This behavior was observed and reported previously. [28] 2.4.

Calculation method

Depending on the polymerization method, PEs have different amounts of long chain branching (LCB).

HDPEs obtained with Ziegler-Natta catalysts have a linear structure and contain only a few SCBs and no LCBs. For LDPE, obtained by free-radical polymerization at high temperatures and pressures, LCB is due to intermolecular chain transfer instead of short chain branching, resulting from intramolecular chain transfer. [29] Chromium catalysts produce polyethylene with small amounts of LCB. LCB has been the topic of intense investigation in the case of polymers obtained with metallocene catalysis. CGC catalyst was the first single site system reported to produce LCB. [30] The Cp2ZrCl2 and Et(Ind)2ZrCl2 catalysts with MAO have been reported to also produce few LCBs in polyethylene. [31] This part of the work consists in investigating LCB content and frequency using size exclusion chromatography. Both the molar mass and the intrinsic viscosity of each fraction of the eluted polymer can be determined with light scattering detector (LALS and RALS) and viscometer detector. The LCB frequency can be obtained from either the viscometer detector or the light scattering detector, as explained in the following part.

2-98

The product of the intrinsic viscosity [ ] and molar mass is proportional to the size of the molecule (hydrodynamic volume ), which is the basis of the separation performed in the chromatograph column

(Equation 2-7). = . [ ] (2-7)
The intrinsic viscosity of a dilute polymer is described by the empirical Mark-Houwink-Sakurada (MHS)

Equation 2-8.

[ ]= .

(2-8)

where and are the MHS constants.

Parameter depends on the temperature and solvent and according to Flory [32] it varies from 0.5 for theta conditions to 0.8 in a good solvent.

For a given molar mass, branched polymer chains have a smaller hydrodynamic volume than linear ones. [33- 35] The intrinsic viscosity ratio between a branched polymer and a linear one with the same molar mass leads to the viscosity branching factor, ʹ (Equation 2-9). Its value is comprised between 0 and 1.

(2-9)

where [ ] is the intrinsic viscosity for the branched (b) and linear polymer (l) considered at the same molar mass fraction.

The branching factor (Equation 2-10), obtained by the ratio of the radius of gyration of the branched polymer to the radius of gyration of a linear one, is calculated by light scattering detection.

(2-10)

where 2 is the mean-square radius of gyration for the branched (b) and linear polymer (l) considered at the same molar mass fraction. is used for measuring the number of LCBs, according to equation 2-10, when the measurement is performed with a light scattering detector. To reach this value, the gyration radius (Rg) of the macromolecule should be accessed, and for this purpose the molar masses must be sufficiently high. This is not the case for our samples. As described below, conditions of angular dependence are necessary to be able to measure Rg.

Angular dependence: At high molar mass (Rg > 15 nm), the intensity of scattered light varies with the measurement angle (anisotropic scatterers), but for low molar mass (Rg < 15 nm) there is no angular dependence on the intensity of the scattered light (isotropic scatterers). Rg (Equation 2-2) is calculated by measuring the slope of the angular dependence curve with the intensity of the scattered light. In isotropic condition, the slope of the curve is zero and does not allow the measurement of Rg. The data cannot be used to calculate Rg. We commonly estimate that Rg has a value of 15 nm for a PE around 100 Kg mol -1 , meaning that for our polymers with lower molar mass, light scattering cannot be used to measure Rg and therefore the number of LCBs. In this case, the viscometer data should be used.

Assuming Flory-Fox [32] the relationship between the viscosity branching factor ( ʹ) and the branching factor ( quation 2-11.

( -11) where is the drainage factor.

It depends on the measurement conditions (solvent, temperature) and also on the type of branching. [36] The reported values of are in the range of 0.5-1.5. [34,37,38] It is 0.5 for a star branched polymer and 1.5 for a comb branched polymer. For LLDPE under identical experimental conditions, a value of 0.75 for was determined previously. [39,40] We have used this value for our calculations.

Zimm and Stockmayer proposed different formulae corresponding to each type of branching. They demonstrated that for randomly branched polymers whose branches are tri-functional and randomly distributed in length, the branching factor (g) [34] and the branching frequency (λ) can be deduced from Equation 2-12 and 2-13, respectively.

(2-12

)
where ̅ is the weight-average number of branch points per molecule (branching number).

(2-13

)
where 0 is the molar mass of the repetitive unit (CH2: 14 g mol -1 ) and the molar mass for the elution fraction .

Long chain branching content in LDPE and HDPE

Multidetector HT-SEC allows the simultaneous and independent calculation of intrinsic viscosity and molar mass for each elution fraction.

The intrinsic viscosity versus molar mass, also called the Mark-Houwink-Sakurada plot (MHS) [41] , can be plotted on the entire molar mass distribution. In this work we have used the MHS plot to quantify the LCB in our LLDPE, as described by various researchers. [42][43][44][45] Before analyzing our LLDPE samples, we studied 3 commercial LDPE samples containing SCB and LCB. In contrast, a certified polyethylene sample (BRPE0) was used as non-branched sample. Unfortunately, its range of molar masses is rather low and was not appropriate for comparison with the other samples.

Hence, it seemed interesting to add an HDPE sample synthetized with a Ziegler-Natta catalyst known to have no branching (dark blue curve in Figure 23456789101112). In addition, a certified branched LDPE (BRPE14) was also analyzed (green curve in Figure 2 The MHSs plotted of the LDPE samples were constructed and compared to the linear certified reference and HDPE. The MHS plot of the HDPE fits well with the linear reference and shows that the sample has no branch. It was used, as a linear reference in addition to the certified polyethylene, to increase the molar mass range that can be studied.

Concerning LDPE, the MHS plot shows that, at a given molar mass, the intrinsic viscosity is lower than that of the linear structure due to the smaller hydrodynamic size of the branched molecules. The amplified deviation of the LDPE viscosity from the linear reference with an increase in molar masses is characteristic of a randomly branched polymer.

It can be seen that the intrinsic viscosity curves of HDPE and LDPE do not intersect at low molar mass.

Wood-Adams [41] reported that this behavior is correlated to the presence of SCB in the LDPE. proposed by Flory and Fox: [32] (2-14)

with NA being the Avogadro's constant, and [η] the intrinsic viscosity.

The slope and intercept of the MHS curve provide the α and K Mark-Houwink parameters, respectively, according to Equation 2-15.

log [η]=log K+ α log M (2-15)
The calculation of the MHS parameters clearly shows that the slope, affected by the branching, is lower for LDPE (α = 0.5) than for HDPE (α = 0.7). LDPE1 with the lower α value is the most branched polymer.

These values are in accordance with values reported in previous work on polyethylene in TCB. [46][47][48] The Zimm-Stockmayer equations can be used to quantify the branching content, step by step, following the procedure below. The value λ represents the LCB frequency for 1,000 carbon atoms. To obtain this value, initially, the intrinsic viscosity of the sample was divided by the intrinsic viscosity of the linear reference (HDPE) for each slice of the molar mass distribution. The ratio g' was calculated using Equation We observe that the number of branches (Bw, red curve) is not constant in the molar mass distribution; it increases with the molar mass of the chains. When the chains are longer, they are more branched even if branch frequency decreases (λ, green curve).

The λ value obtained for the certified branched polymer (1.6 branches for 1,000 C) is quite similar to the certified value (1.4 branches for 1,000 C) which validates the method. The branch frequency is calculated close to zero for the HDPE sample, as expected. Conversely, LDPE1, with a branch frequency of 5.5

branches for 1,000 C, is the most branched sample.

The LCB frequency was calculated by comparing the viscosity of a branched polymer with that of a linear one using the Zimm-Stockmayer methodology. The HT-SEC with the viscometer detector is a powerful technique capable of obtaining the molar masses distribution and structural information at the same time.

The method was applied for our LLDPE samples to determine their LCB content. Previously, the LCB amount was calculated by 13 C NMR to compare the results obtained by HT-SEC and validate the method.

Long chain branching calculation by 13 C NMR

The 13 C NMR spectroscopy provides another experimental technique for measuring LCB. [14] Unlike the SEC, it gives directly LCB content without using references. Three representative LLDPE models with various comonomer contents were selected to study their LCB by 13 C NMR (Figure 2-15).

Conventionally, the signal at about 14 ppm linked to CH3 is used. However, this method has a limitation.

When the α-olefin comonomer has more than six carbon atoms, the chemical shift detected for LCB is the same as that detected for the inserted comonomer. Recent studies have reported that it is possible to differentiate branches longer than six carbon atoms, but this requires high-resolution experiments. [49] A second and more critical restriction is that this approach cannot separate the CH3 of branches from the CH3 of chain ends, which cannot be negligible in the case of low levels of LCB.

Given these considerations we decided to use a CH signal at 38 ppm. The CH from the butyl branch is clearly visible at 38.0 ppm for the EC12 sample. At low comonomer content (IB10), we can observe close to this signal at 38.1 ppm another signal which we have assigned to the CH of the LCB. This signal is easy to integrate when the content of the comonomer remains low (IB10 and EC01). As the comonomer content increases, the signal from the LCB overlaps the butyl branch signal and cannot be used to calculate the LCB content. The LCB frequency was determined for three LLDPE samples with no or low comonomer content.

The values, calculated with the signal at 38.0 ppm, are reported in

Branching in our LLDPE samples

Initially, we measured the impact of LCB on the MHS plot using HDPE and LDPE. Concerning our LLDPE models containing mainly SCB, we can expect a mixed behavior in the MHS plot. According to Soares and Hamielec, few LCBs are also present in LLDPE obtained by metallocene catalysts. [31,50] Six ethylene-hexene copolymers with various hexene contents from zero to 20.7 mol% were analyzed. Their MHS curves were plotted in Figure 2-15 and compared to the linear reference (BRPE0, black curve). The plot of the homopolyethylene sample EC01 (pink curve, Figure 2345678910111213141516) attests the presence of few LCBs because the intrinsic viscosity of the sample is slightly lower than that of the linear reference, in high molar mass portion. The curves follow a straight line that can be described by the MHS coefficients (α and K).

Nevertheless, unlike LCB, SCB did not affect the slope of the curve but the K parameters. The samples were analyzed consecutively in the same sequence, and the data were processed with the same calibration. a Intrinsic viscosity value. The average number of branch points per 1,000 carbon atoms (branching frequency) determined by b HT-SEC using Zimm-Stockmayer equations and c NMR (BBO probe of 10 mm in TCB/toluen-d8 3/1 at 100°C) using the signal at 38 ppm (method described in the previous part). *calculated value of LCB using a SCB correction as described below.

For samples EC01 and IB10, Table 2-8 shows that the values obtained with the HT-SEC measurements agree well with the values of the 13 C NMR. These results demonstrated the high sensitivity of this method to very low levels of LCB. Since the viscometer detector is very sensitive to high molar masses, we obtained high-quality data from this part of the distribution and thus high sensitivity.

However, for the other samples with higher comonomer contents, the Zimm-Stockmayer equations could not be used to calculate the LCB due to the presence of a non-negligible amount of SCB. Indeed, the presence of SCB in the copolymers affected the viscosity of the sample. Their LCB contents could not be measured before the SCB effect was corrected. Since the low molar mass part of the distribution was not affected by LCB but only by SCB, we use this part to determine the α and k values impacted only by SCB.

These values were used as a virtual linear reference to calculate the LCB content for the whole distribution by applying the Zimm-Stockmayer equations. For each sample, a linear curve depicting a virtual reference without LCB, was constructed using the low molar mass portion (M < Log 4.8). These linear curves were used to determine the intrinsic viscosity over The linear curves of the virtual references are all parallel to that of the linear control (BRPE0). The slopes of these curves were found to be similar and equal to 0.71±0.01. These curves and the calculated values (with an asterisk in Table 2-8) show that the LCB content is low and decreases when the comonomer content increases in LLDPE samples. No curvature on the high molar mass portion of the MHS plots was observed for the samples with high comonomer content, which confirmed the absence or low level of LCB.

Deslauriers and co-workers have described an alternative LCB determination method by multiangle light scattering. [51] They have also established a similar method to correct SCB effects using infrared and NMR results. Yau and co-workers have also proposed a new approach to correct the SCB in the measurement of LCB for LDPE samples. [52] We clearly observed, from the results in Table 2-8, the decrease in the Log K value with increasing comonomer level in the copolymer. The variation of Log K with the comonomer content was plotted in In conclusion, the Mark-Houwink-Sakurada plot gives clear insights about the branching of PE. We can measure the impact of LCBs, in high molar mass portion of the distribution, with the local slope of the curves which is related to the α value of Mark-Houwink-Sakurada. In an original approach, we proved that the influence of short chain branching (comonomer content) is transcribed on the K value of Mark-Houwink-Sakurada. Using the plot in Figure 2 Lastly, the viscometer detector and the Zimm-Stockmayer equations were also involved to measure the LCB in our copolymer. The results were compared with NMR measurements. Since elution in fractionation techniques can be influenced by LCB, it is necessary to measure their content in our models beforehand.

This study demonstrated the low content of LCB. Based on these results, we assumed that LCB would have a negligible effect to the elution of samples when analyzed by fractionation techniques.

3-114

Before using our LLDPE as standards for calibrating fractionation techniques, we studied them by differential scanning calorimetry (DSC). Like certain thermal fractionation techniques, the principle of DSC is also based on the crystallization capacity of polymers, but in the solid state for DSC. For the fractionation techniques, the separation occurs in a solvent that allows the behavior of each chain to be separated individually.

Thus, DSC characterization is the first approach used to understand the thermal behavior of our copolymer samples. These samples also provide the opportunity to calibrate a simple technique that is well-known and commonly used in research laboratories. The effect of α-olefin incorporation on polymers properties can be assessed by measuring crystallinity, melting temperature and crystallization temperature.

After the DSC approach, we used our copolymer models to calibrate the thermal fractionation techniques Differential scanning calorimetry (DSC) is frequently employed to characterize the physical properties of polymers via the measurement of their thermal properties. [1][2][3] The instrument measures the heat flow that occurs in a sample when it is heated or cooled. The physical transitions frequently determined for polymers are:

Melting temperature and enthalpy of melting, Crystallization temperature and enthalpy of crystallization, Glass transition temperature for the amorphous fraction of a polymer.

The instrument consists of two heat flow sensors, one is used for the unknown sample and the second is used as a reference, which is an empty crucible. The instrument measures the difference of the heat flow between both sensors as a function of temperature during a temperature program. DSC is applied to detect and measure any change in heat capacity caused by glass transition and any change in enthalpy caused by melting and crystallization. DSC is used to obtain information on chemical composition; various advanced methods can be used such as stepwise isothermal segregation (SIST), [4] successive selfnucleation annealing (SSA) [5] and step crystallization. [6] The advantage of DSC is easy sample preparation which does not need dissolution in solvent at high temperature. However, DSC suffers not only from low resolution but also from co-crystallization effects related to the low mobility of the chain in the molten state.

EQUIPMENT AND ANALYTICAL CONDITIONS

Thermal characterization was performed with a Mettler Toledo DSC3 apparatus (FRS5 DSC sensor).

Samples were weighed (around 10 mg) and sealed in 40 μL aluminum pans. Aluminum is largely inert. The pans were pierced with a fine needle by the sample changer directly before measurement. They were heated with an empty aluminum pan as reference from -20 °C to 180 °C at 10°C min -1 . This value is important to mention because the heating and cooling rates have an impact on the crystallization and melting of PE, as reported by Schick. [7] Two successive heating and cooling stages were performed and only the second run was considered. Dry nitrogen with a flow rate set at 50 mL min -1 was used as the purge gas. The melting temperature was obtained from the top of the peak values. The crystallinity of samples was calculated in the second heating step using the expression: [1] X = ∆Hf / ∆Hfo x 100 (3-1) where Hf (J g -1 ) is the melting heat of the sample and Hf0 (= 293 J g -1 ) the melting heat of a 100% crystalline polyethylene.

TEMPERATURE AND HEAT FLOW CALIBRATION

Calibration for the temperature scale and the heat flow were performed using metallic standards, In and Zn, and water. It was carried out following the instrument supplier's instructions and ASTM E967-18, suggesting the calibration of the temperature and enthalpy with the values reported in Table 3-1. Sample preparation: indium and zinc pellet, pressed flat, pre-melted.

The DSC curves (Figure 3-1) show the melting of water, indium and zinc, which are compared to the defined temperature. The melting points were taken at the onset of the melting process which is defined as the temperature given by the intercept of the extrapolated slope of the melting curve and the base line. Melting temperatures and melting enthalpies were calculated for all the samples. As shown in Figure 3-2, the melting temperature of the samples clearly increases with their molar mass whereas the melting enthalpy (reported as crystallinity) is less impacted in this range of mass. The measured crystallinity varies from 80% to 90% which corresponds to enthalpies of 234 to 264 J g -1 . These values show that the PEs with low molar masses have a particularly high crystallinity. Indeed, for our copolymer model, with higher molar masses, enthalpies were measured around 190 J g -1 for the highest (crystallinity of 65%). Small chains can easily organize into a crystalline lamella (Figure 1-14) without folding up on themselves and without disrupting the lamellar growth. Therefore, the amorphous part is reduced, and the crystallinity is increased.

Some peaks show shoulders or even a second melting peak indicating that the samples are crystallized in various kinds of lamella. This behavior was also observed for our copolymer samples.

When the molar mass increases beyond 5,000 g mol -1 the value of the melting temperature is less impacted and reaches 133 °C for a mass of 7 300 g mol -1 . For our homo PE samples with a mass around 20,000 g mol, we obtained a plateau around 137 °C (±1 °C) which seems to be the maximum value of the melting temperature of PE. This behavior was interpreted by assuming that chains with shorter lengths crystallize as extended chains. [8][9][10][11] The chains of greater lengths crystallize in the form of folded chains, increasing the melting temperature. We will see in a further part that this temperature can be sharply increased in the case of PEs with very high molar masses (UHMWPE) and greatly exceed 140 °C. For the following work we will estimate that the molar masses higher than 10,000 g mol -1 (this is the case for our copolymers) will not impact the melting temperatures.

The relation between the melting temperature and the chain length in polyethylene has been investigated by various researchers. In particular, we considered two equations which link the melting temperature to the length of the chain. Garner and coworkers proposed the following equation: [12] (3-2)

with Tm as the melting temperature and n the number of carbons in the polymer chain.

However the best-known relationship can be reported in the following form: [8] (3-3) with T0, a and b are constant Broadhurst and co-workers obtained their best fit with experimental values using T0 = 414.3 °K, a=-1.5 and b=5.0.

This equation was formulated and determined with samples of paraffins with a carbon number varying from 44 to 100. The extrapolation of the equation for PE samples, with molar masses higher than paraffins, should be used with caution. Nevertheless, the authors reported that the crystal mesh of paraffins is also orthorhombic, like those observed for PE samples. The crystallization of short chains like the paraffins shown here does not occur in folded form. This is the complete olefin chain which is organized with other chains that form the crystal mesh. The organization is quite different for PE samples, for which each chain is organized in folded form. However, we compare in Table 3-2 the value measured for our sample and that obtained by Equations 3-2 and 3-3 from Garner and Broadhurst and their co-workers. The values are quite similar. However, we can note some explanations for the variations. The value of the melting temperature is affected by the heating rate. To avoid this effect, it would be interesting to create new equations based on the onset of melting temperature which is not impacted by the heating rate.

Apart from the measurement errors, the dispersity of the polymer is not considered in the equation but doubtless also affects the shape of the peak and then the temperature at the top of the melting peak.

CHARACTERIZATION OF POLYETHYLENES: FROM THERMAL FRACTIONATION TECHNIQUES TO SPECTROMETRY 3-120

EFFECT OF COMONOMER CONTENT ON DSC PROFILES

All the copolymer models were analyzed by DSC using the analytical conditions detailed in 3-1-1. Because the molar masses of our copolymer models were higher than 10,000 g mol -1 , the measured melting We observed an almost linear response for all types of copolymers. Although ethylene-hexene and ethylene-octene copolymers have a similar calibration curve (when expressed in mole percentage, Figure 3-5a), for the others, the slope of the curve is different. The melting temperatures are affected not only by the number of branches but also by the length and type of branches (or comonomer). For this reason, we have also chosen to plot the graphs as a function of mass percentage instead of mole percentage.

For ethylene-propylene and ethylene-octadecene copolymers which represent the two extremes in terms of branching length the slopes are surprisingly similar in the graph expressed in mole percent. When we convert to mass percentage, they become radically different.

Conversely, for the ethylene-norbornene copolymers, the slope is the lowest in both plots. The greater steric hindrance of the norbornene molecule explains the lower melting temperature for the same comonomer content than for an ethylene-hexene copolymer. In the following part, to better understand their thermal behavior, crystallization and enthalpy exchanges will also be studied for these ethylenenorbornene copolymers.

The very short branches due to propylene have little effect on the crystallized capacity of the copolymer and therefore have less impact on the melting temperatures than branches due to hexene or octene comonomer.

CHARACTERIZATION OF POLYETHYLENES: FROM THERMAL FRACTIONATION TECHNIQUES TO SPECTROMETRY

3-122

Regarding octadecene, it is quite surprising that the melting is so little impacted with respect to other αolefins. Perhaps the octadecene branches, longer than those of the other comonomers, have the ability to crystallize with their neighbors and the ethylene backbone and thus less decreased the melting temperature. Investigations by X-ray scattering techniques could bring some clarification. The mass representation for this copolymer seems particularly suitable as the value of R 2 increases. The sample that contains 20 mol% of hexene has a low crystallinity and displays a broad peak in the DSC thermogram. The peak temperature (Figure 3-5a) is above the linear fit curve, 21°C instead of 18°C, which means that the crystallinity is higher than expected. When using a mass representation (Figure 3-5b) it appears that this point is better included into the linear fit.

The DSC technique, which is available in many research and control laboratories, provides an easy and rapid way to determine the comonomer content in LLDPE. In order to use it to determine the molar percentage of comonomer in LLDPE from the melting temperature we inverted the previous curves and obtained the following plots (Figure 3456). The relationships between thermal parameters and comonomer content were calculated and are reported in Table 3-3. These equations are only suitable for LLDPEs obtained with metallocene catalysts. For polyethylenes produced with Ziegler-Natta multisite catalysts, the chains are heterogeneous in composition, so there are comonomer-rich fractions that are not or poorly represented by the melting peak. For these copolymers obtained with ZN catalysts, there are also equations proposed by Hosoda. [15]

MELTING AND CRYSTALLIZATION ENTHALPY

A thorough thermal analysis was performed for ethylene-norbornene (Figure 34567) and ethylene-hexene (Figure 3-8) copolymers. The other thermal parameters were also investigated: crystallization temperature, melting and crystallization enthalpy, and the melting temperature onset peak.

ETHYLENE-NORBORNENE COPOLYMERS

The insertion of norbornene into the PE backbone reduces crystallinity and melting temperature, and the crystallization temperature decreases as the insertion of the comonomer increases. As seen in Figure 34567, the insertion of norbornene decreases the melting and crystallization enthalpies. The "inverted" melting and crystallization equations resulting from the calibration curves, which correlate comonomer content with temperatures and enthalpies, are given in Table 3-3. Using these calibrations, we can evaluate the norbornene content in unknown ethylene-norbornene copolymers by various ways, up to 6 mol% and for molar masses above 10,000 g mol -1 .

ETHYLENE-HEXENE COPOLYMERS -EFFECT OF LOW COMONOMER CONTENT

Various works report a linear evolution of the melting temperature with the comonomer content, as noted previously. Nevertheless, we observed that for low comonomer contents the variation of melting temperature with the comonomer content was not linear. We decided to investigate behavior for low The resulting "inverted" equations from the calibration curves, which correlate the comonomer content with temperature and enthalpies, are given in Table 3-3. Using these calibrations, we can evaluate the hexene content in unknown ethylene-hexene copolymers by various ways, up to 21 mol% and for molar masses above 10,000 g mol -1 .

ETHYLENE-HEXENE COPOLYMERS -ONSET MELTING TEMPERATURE

The onset of melting temperature (Tm onset) is another representation of the melting temperature (Figure 3456789). It was also used to study the melting temperature and hexene content relationship. The onset melting temperature corresponds to the value given by the intersection between the baseline and the tangent at the inflection point. The value of the onset peak is known to be independent of the heating rate [16] and probably provides greater robustness to the measurement. In any case, it is an additional measure that can be added to the others. The onset of melting temperature was calculated for various ethylene-hexene copolymers and an additional equation was established and is reported in Table 3-3. The method using the onset of melting temperature is not better than the others since the value of R-squared is a little lower than that of the other equations. However, it is interesting to use it as an additional assessment of hexene content, as this method does not require another measurement and can be carried out at the same time as that of the temperature of the melting peak. The choice of the temperature onset is however more problematic in the case of copolymers that present several populations of chemical composition. The value will be representative of a single family but not of the whole polymer.

The equations that correlate the melting and crystallization peak temperatures (Tm, Tc) and the melting and crystallization enthalpies ( Hc, Hm) to the comonomer content for various copolymers are all summarized in Table 3-3. These equations can be easily used to determine the comonomer content for an unknown LLDPE with a classical DSC analysis. These equations were replicated many times during this doctoral work and have always been constant, proving the robustness of the method. They depend only on the heating rate which must be set at 10°C min -1 . For good accuracy, the quantity of the sample weighed must be around 10 mg, and an aluminum pan of 40 μl must be used. The most important parameter to be observed is the use of two heating steps and the calculation of the melting temperature must be carried out during the second step. The profile obtained during the first step of DSC depends on the storage conditions of the sample and on its thermal history and should not be used for the calculation. The first step of the DSC experiment permits melting and crystallizing the sample under controlled conditions. The result will thus reflect the real chemical composition of the polymer. where Tm is the melting temperature at the top of the peak, Tm onset is the melting temperature at the onset of the peak, Tc the crystallization temperature, Hm and Hc the enthalpy of melting and crystallization, and R-Square in brackets. ). The eluent dissolved fractions of increasing crystallinity.

The polymer solution concentration was monitored with an infrared detector measuring total CH absorption in the 2700-3000 cm -1 range.

CEF analytical conditions

The samples at a concentration of 2 mg mL -1 were dissolved in 10 mL vials in 1,2,4-TCB at 160°C for 1 hour.

At the end of the dissolution period, the samples were transferred to the injection loop (200 μL) and injected into the CEF column using an isocratic pump. The samples were fractionated according to their crystallization ability using two temperature cycles (Figure 3 -11). During the crystallization step, the column temperature was decreased to 35°C, at a rate of 2°C min -1 , under continuous 1,2,4-TCB flow (0.05 mL min -1 ). During the elution step, the fractions deposited were gradually dissolved as the temperature increased to 130 °C at 4°C min -1 using a continuous 1,2,4-TCB flow (1 mL min -1 ).

The infrared detector measured the concentration of the eluted fractions to obtain the CEF profile.

TGIC analytical conditions

The instrument was equipped with a Hypercarb column from Thermo Scientific containing particles of graphitic carbon (average particle size 5 μm, pore size of 250 Å). The dimensions of the column were 100×4.6 mm 2 (LxID). The samples at a concentration of 1 mg mL -1 were dissolved in 10 mL vials for 1 h at 150 °C with 1,2,4-TCB containing 300 ppm of BHT and purged with nitrogen to protect the polymer against oxidative degradation. 200 μL of the sample solution was injected into the column at 160 °C. This technique requires a cooling (adsorption) and a heating (desorption) step (Figure 3 -12). A cooling ramp of 20 °C min -1

to 40 °C was applied to promote polymer adsorption. Elution began isothermally at 40 °C for 5 min at a flow rate of 0.5 mL min -1 , followed by a heating ramp at 2 °C min -1 to desorb the polymer. An infrared detector was used to monitor the components' concentrations and compositions when the chains were eluted from the column. The main operating conditions are reported in Table 3-4.

SGIC analytical conditions

The device consisted of a combination of an Agilent high temperature chromatography system (PL XT-220), a high pressure binary gradient pump and an evaporative light scattering detector (PL-ELS 1000) from Polymer Laboratories.

The system was equipped with a Hypercarb column from Thermo Scientific containing particles of porous graphitic carbon (average particle size 5 μm, surface area of 120 m 2 g -1 , pore size of 250 Å). The dimensions of the column were 100×4.6 mm 2 (LxID). The samples were dissolved for 2h to 5h in 2-ethyl-1-hexanol at 160 °C. 50 μL of the sample solution at a concentration of 1-2 mg mL -1 was injected into the column at 160 °C. This technique first requires an adsorption step. The polymer was absorbed onto the column due to the effect of the solvent which caused the polymer to stay on the column. The sample adsorbed was then progressively desorbed by a linear gradient, starting with alcohol and ending by o-DCB. 2-ethyl-1-hexanol is an adsorption promoting solvent, and o-DCB is a desorption promoting solvent.

An evaporative light scattering detector was used to monitor the components' concentrations when the chains were eluted from the column according to their compositions.

Calibration

The incorporation of comonomers into the polymer chains induces a decrease in the crystallinity of the

This part will focus on the methods developed and implemented in our laboratory using these various and original thermal fractionation instruments. Our copolymer models obtained with metallocene catalysts and characterized by HT-SEC, DSC and NMR can be used to establish robust calibration equations. They indicate the elution temperatures, the crystallization temperatures, and the elution volumes as a function of the comonomer content. A review of these equations is given at the end of this part as a tool to characterize

future synthesized polymers in the laboratory.

FRACTIONATION TECHNIQUES BASED ON CRYSTALLIZATION.

TREF, CRYSTAF and CEF are separative analytical techniques allowing the fractionation of semi-crystalline

polymers according to the differences in crystallizability of the polymer chains. As expected, as the comonomer content increases in the sample, the elution temperature decreases. The broadness of the peak is related to the chemical composition homogeneity of the sample. Most of them were unimodal, which means that the polymerization was carried out under homogeneous conditions.

TREF

The peak shape for samples with high comonomer contents shows that polymerization in these conditions was more difficult to control. As reported by Soares and coworkers [17] we observed the broadening of the peaks as the comonomer content increased.

The peak that elutes around 30°C is due to the soluble chains that cannot crystallize in these conditions, and its area is directly proportional to the amount of amorphous chains. This peak area rises dramatically when the comonomer content increases.

For each series, a linear regression was performed and correlation coefficients higher than 0.99 were obtained. The equations are reported in Table 3-9. The ethylene-propylene copolymers behave very differently from the other copolymers because the effective volume occupied by the methyl groups is much lower. This behavior was also observed for DSC. The samples remain more crystalline due to the short methyl branches.

For ethylene-norbornene and ethylene-octadecene copolymers the hindrance of the branching was more marked compared to octene or hexene branches and had more impact on elution time.

Consequently, these classes of copolymer required their own calibration curve. The behavior of ethylene-octadecene copolymers changes more considerably in solution (for TREF) than in the molten state (for DSC). The long branches of octadecene decrease the crystallinity and increase the solubility of the polymer when it is in solution.

The ethylene-hexene and ethylene-octene copolymers led to very similar calibration lines. A common calibration for both these comonomers was therefore possible.

The ethylene-hexene copolymers showed the same characteristics on the TREF profile whatever the catalysts used for their preparation. It was therefore possible to use the same curve for various metallocene catalysts in the range of zero to eight mol% of comonomer. This study should also be continued with other metallocene catalysts in order to generalize these conclusions. If the catalyst or the polymerization conditions favor the creation of ethylene or comonomer sequences, crystallization could be affected, making the calibration inappropriate.

Variation in analytical conditions

In the literature we found various analytical conditions. An exploration of different analytical parameters was carried out on our device by various Master students, whom I supervised. Here, we will discuss only a part of this work.

During the crystallization step, the polymer fractions with chains of different compositions are separated. This is the most important step in the TREF experiment. We therefore had to optimize this step. The analysis with two crystallization rates and with cryo-accessories were compared. Cryo-TREF analysis was performed by Alberto Ortin from the PolymerChar company using our copolymer models. In this condition, sub-ambient analyses (-20°C) were performed using liquid nitrogen to decrease the temperature limit of The related equations for each experiment, reported in Table 3-5, are similar; a crystallization rate of 0.5 and 0.2 will give comparable results. However, at 0.2 °C min, the slope of the curve decreases slightly, showing a slightly better resolution but significantly increasing the analysis time. The cryo accessory shows that is able to analyze a wider range of branched copolymers up to 9 mol% for hexene.

Table 3-5: Calibration equation for ethylene-hexene copolymers for the various analytical conditions.

Analytical conditions Equation

Cr 0.5 (°C min) Hexene (mol%) = -0.153xTe+15.55

Cr 0.2 (°C min) Hexene (mol%) = -0.151xTe+15.47

Cryo TREF a -Cr 0.2 (°C min) Hexene (mol%) = -0.151xTe+15.26

a sub-ambient analyses (-20°C) using liquid nitrogen and o-DCB (melting point -17.00 °C) as solvent, Cr cooling rate during the crystallization step (°C min), Te elution temperature (°C). Experimental conditions: heating rate = 1°C min -1 .

CRYSTAF

As described previously, TREF has been widely used to measure the chemical composition distribution of Like TREF, CRYSTAF separation reveals a linear relationship between the crystallization temperature and the comonomer content (Figure 3 -18). A lower resolution and a lower analytical range were observed for CRYSTAF than for TREF. For instance, the sample with 6.3 mol% of hexene is not well resolved and a large part of the sample appeared in the amorphous fraction. This sample was better resolved with TREF.

CRYSTAF is, therefore, a rapid analysis technique which allows the simultaneous measurement of several samples for a fairly short time, but it does not reach the resolution and the range of the TREF.

CEF

The effects of co-crystallization, widely studied by Soares and co-workers, [18,19] weakens the resolution of TREF and CRYSTAF. This effect occurs when polymer chains of distinct compositions tend to crystallize simultaneously and result in a broadening of peaks. This effect can be minimized by the operating conditions. A slow cooling rate is necessary to minimize the co-crystallization but increases the analysis time. The CEF method enables faster analysis, compared to TREF and CRYSTAF, by applying dynamic crystallization during the first step (Table 3456). The approach minimizes co-crystallization effects by segregating crystallites inside the column. Therefore, the analysis offers a high resolution in a shorter time.

In this part our LLDPE models were used to construct calibration curves for our CEF, recently installed in our laboratory.

Setting of instrument parameters

Before starting the analysis, some instrumental constants have to be determined. The CEF and TGIC analysis were done with the same device, so the calibration process was similar. Several instrumental parameters must be adjusted:

The solvent signal to be subtracted from the signal of the sample,

The constants of the infrared detector and the viscometer: KIR and KIV

The volume between the column and the detector: Kcol-det

The volume between the detectors: Kdet-det

The composition (CH3/1000C) measured with the IR detector.

To calibrate the above parameters, several experiments are necessary:

First, the analysis of 1,2,4-TCB stabilized with 2,6-di(ter-butyl)-4-methylphenol (200 mg L -1 ) was performed with the same method used to analyze the sample. It will be subtracted from the signal of the succeeding samples.

Next, a standard sample, whose intrinsic viscosity was known, was prepared carefully to know the concentration injected. The NBS1475 served as a reference material for this calibration step. It is a high-density polyethylene having a molar mass: M w = 52 kg mol -1 and M n = 18 kg mol -1 and an intrinsic viscosity of 1.01 dl g -1 in 1,2,4-TCB. This experiment allowed the calibration of the following parameters: KIR, KIV, Kdet-det, Kcol-det. The values obtained for each coefficient are reported in Table 34567.

KIR is the response factor for the IR and allowed measuring the concentration of the sample according to the Beer-Lambert law:

A = ε l C = KIR C (3-4)
Where A is the infrared absorbance, ε is the molar attenuation coefficient, ℓ is the optical path length of the cell, c is the concentration of the sample.

Calibration of methyl/methylene ratio for IR detector

The infrared detector (IR5) is equipped with two cells. One sensor is sensitive to the stretching vibrations in the C-H bonds of methyl groups (CH3 at 2960 cm -1 ) and the second sensor is sensitive to the C-H bonds in the methylene groups (CH2 at 2920 cm -1 ). Since methyl groups indicate branches, it is possible to determine their number by using the IR detector directly. To quantify the methyl content in unknown samples for the calculation of the comonomer content, it is necessary to calibrate the IR detector with standards of known methyl content.

We used ethylene-butene copolymers provided by the PolymerChar company and some of our ethylenehexene copolymers as standards to calibrate the IR detector. For this calibration, the mol% of the comonomer was translated into a methyl number for 1000C (CH3/1000C) according to Equation 3-5. In these conditions the methyl chain ends were neglected.

(3-5)

With CH3/1000C is the methyl number for 1000C, mol% is the comonomer content, Cn is the number of carbons in the α-olefin comonomer. The measurement of methyl groups frequency (CH3/1000C) by IR has the advantage of being universal and can be used for various ethylene/α olefin copolymers. For unknown samples measured in this way, we can reverse the calculation of the corresponding mol% value depending on the comonomer type with Equation 3-5.

Use of viscometer

The CEF and TGIC system is equipped with a viscometer detector. It is useful to determine the molar masses of the copolymer analyzed. The Mark-Houwink-Sakurada relationship [20,21] links the intrinsic viscosity, measured by the device, to the molar masses of the polymers thanks to the K and α coefficients.

(3-7)

with [η] being the intrinsic viscosity of the compound (mL mol-1), M is the molar mass of the compound (g mol-1), K (mL g-1) and α are the characteristic coefficients of the polymer/solvent couple at a given temperature (for PE in 1,2,4-TCB at 150 °C, K = 73.6 x10-6 L g-1 and α = 0.67).

For each fraction separated by chemical composition, the viscometer can access the intrinsic viscosity making it possible to link the molar masses to a fraction of comonomer content.

Calibration of CEF with copolymer models

After adjusting the instrumental constants, our copolymer samples were analyzed by CEF (Figure 3-20).

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Similar behaviors and profiles from TREF were observed. As expected, the analysis time was significantly reduced by a factor of 3 for the same resolution. The ethylene-propylene sample with 2.3 mol% of propylene shows a clear shoulder in its CEF profile. For this sample, the polymerization conditions probably drifted during the synthesis, resulting in a second population of chemical compositions. CEF can thus, be a powerful and precise tool for controlling synthesis conditions.

We plotted the elution peak temperature obtained by CEF as a function of the comonomer content. The calibration curves for the five series of copolymers are traced and overlayed in Figure 3-21:

The ethylene-propylene copolymers have a specific behavior compared to the other copolymers because of the capacity of incorporation of the methyl groups in the crystallites. This behavior was also observed for TREF and DSC.

For ethylene-norbornene and ethylene-octadecene copolymers, the steric hindrance of the branches affects the elution time. Therefore, these copolymers require their own calibration curve as observed for TREF.

A common calibration for ethylene-hexene and ethylene-octene copolymers can be used since the calibration lines are comparable.

FRACTIONATION TECHNIQUES BASED ON INTERACTION

Fractionation techniques based on crystallization have several limitations when characterizing ethylene copolymers. Two innovative techniques have been developed to improve the measurement of comonomer contents: solvent gradient interaction chromatography and thermal gradient interaction chromatography (SGIC and TGIC). With these methods, co-crystallization is reduced, and amorphous polymers can finally be analyzed. These techniques combine separation by crystallization and by adsorption on the surface of the column stationary phase.

TGIC

A new and original technique developed by Cong and commercialized by PolymerChar was installed in our laboratory. The TGIC separation is based on the interaction of the sample with the column and therefore can also be applied for non-crystalline polymers. We used this instrument to investigate its capacity to separate highly branched copolymers and other kinds of ethylene copolymers such as ethylene-butadiene and ethylene/vinyl acetate copolymers. Although they were analyzed by TGIC, the results will not be discussed here. This part is focused to the analyses by TGIC of our copolymer models: profiles of ethylenehexene copolymers in Figure 3-22 and profiles of ethylene-norbornene copolymers in Figure 3-23. For TGIC, the behaviors of ethylene-propylene copolymers and ethylene-norbornene copolymers are similar to those observed for other crystallization-based techniques (TREF, CRYSTAF, CEF). However, the calibration curve for ethylene-propylene copolymers is very different from the other curves. It reveals that the CH3 groups are less disruptive to the interactions between the backbone and the column than the other bulkier groups.

For octadecene, the behavior is quite different from that observed with crystallization-based techniques. It is also slightly different from the other copolymers; the slope of the curve is significantly higher than that of ethylene-hexene copolymers. This means that the branches are long enough to interact by themselves with the hypercarbon column, which leads to an increase in the elution temperature.

As expected, the working range of ethylene-hexene copolymers is broader than for all other fractionation techniques. Indeed, we efficiently separated ethylene-hexene copolymers up to 21 mol% of hexene. With CEF and the other techniques the limit was around 7 mol% of hexene.

CHARACTERIZATION OF POLYETHYLENES: FROM THERMAL FRACTIONATION TECHNIQUES TO SPECTROMETRY

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An order of one or even an order of three can be used for a better fit of data points at high comonomer contents. In this case (> 20mol%) the polymer is mainly amorphous and the crystallization mechanism is not involved. The significance of the elution temperature is then very different, as it combines both polymer/column interaction and dissolution. This could also explain why the elution temperature does not follow a simple linear rule and a deviation is observed for high comonomer content.

Figure 3-24: TGIC calibration curves for the different series of copolymers. Experimental conditions for TGIC: cooling rate = 20°C min -1 , cooling flow = 0 mL min -1 , heating rate = 2°C min -1 , heating flow = 0.5 mL min -1 , solvent = 1,2,4-TCB.

Variation in analytical conditions

Many variations of TGIC parameters were tested by Soares and co-workers. [22,23] Our optimal analytical conditions were selected using their conclusions. However, inspired by the CEF method, we decided to test the impact of adding a flow of the solvent during the cooling step (cooling flow) in the method. For CEF, this adjustment allowed increasing the resolution.

The comparison was therefore carried out between the classical analytical method named "TGIC-a" and the proposed method with a cooling flow named "TGIC-b". The analytical conditions for these two methods are detailed and compared in Table 3-8.

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The efficiency and resolution of both methods were compared. We observed a shift of 1 °C in the elution temperature, without a change in the shape of the peaks. Regarding the result we cannot consider an increase in resolution between the peaks. It can be concluded that there was no significant variation regardless of the used method. It is therefore advisable to use the classical method without a cooling flow.

TGIC's broad range of separation, reaches 50 mol% of octene. 5 This range is better than other techniques based on crystallization, but it is still narrower than that of SGIC, which covers the full range of comonomer incorporation. The latter technique was also applied to our copolymer models in the next section. The analysis of our copolymer samples was used to construct calibration curves to correlate the comonomer content versus the elution volume at the top of the peak (Figure 3-27). The elution volume is directly proportional to the comonomer content as with all the other fractionation techniques and it is also affected by the length of the branches.

The calibration curves showed good linearity, proving the considerable interest of this technique. The analytical range is wide, ethylene-hexene copolymers up to 20 mol% were efficiently separated by the method.

Various analytical conditions were assessed: type of mobile phase, temperature, solvent, etc. This work, focusing on the variation of analytical conditions for improving the separation of our copolymers, was published in Macromolecular Chemistry and Physics. This publication is a subsequent part of this chapter.

COMPARISON OF TECHNIQUES (CEF AND TGIC)

It is agreed that CEF can effectively replace thermal fractionation techniques based on crystallization (TREF and CRYSTAF), the following part will be devoted to the comparison of this technique with the TGIC technique. In particular, their separation efficiency, their working range and the impact of molar masses on the separation of these two techniques were confronted. Elution volume, Ve (mL)

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The comparison of TGIC and TREF for a series of ethylene-octene copolymers has been reported 17 , demonstrating that resolution with TREF is slightly better than with TGIC for medium density resins. TREF and other crystallization techniques are also more appropriate for industrial LLDPE materials with low comonomer content. However, since the separation mechanism is not based on polymer crystallization, TGIC covers a wider compositional range down to the amorphous region, which crystallization techniques cannot reach. In addition, TGIC requires shorter analysis times because adsorption/desorption mechanism is faster than crystallization.

ULTRA-HIGH MOLECULAR WEIGHT POLYETHYLENE (UHMWPE)

Impact of molar mass on elution temperature

Molar mass is a parameter that influences the elution temperature of the copolymer. Indeed, Soares and coworkers [23] determined that the molar mass of the polymers studied had no impact on separation if M n is higher than 25 kg mol -1 . In order to determine our own detection limit and the linear range of our For both techniques, a minimum molar mass of 720 g mol -1 is necessary in order to observe a peak outside the soluble fraction. A plateau is reached at 110 °C for CEF and at 138 °C for TGIC for samples having molar masses greater than 17 Kg mol -1 . The limit announced by previous works is therefore slightly higher than that obtained in our conditions.

Nevertheless, the last polymer in Figure 3-29 has a very high molar mass (M n = 1 200 Kg mol -1 and Ð = 1.8)

and shows an unusual behavior both in CEF and in TGIC. The polymer elutes at higher temperatures than usual (115 °C against 110 °C for CEF and 139 °C instead of 138 °C for TGIC). Polymers of high molar mass seem to crystallize in a different way for CEF and thus are eluted at high temperature. The elution temperatures obtained for high molar mass PE are significantly higher than that obtained for our synthetized homo-PE. This behavior has not yet been discussed in the literature, and it seems important to study it more precisely. This is the subject of the following part.

UHMWPE melting process (DSC)

Ultra-high molecular weight PE (UHMWPE) is a class of high-performance polymers with unique properties such as Dyneema® fiber of DSM. They paved the way for new applications to obtain materials that are both ultra-strong and ultra-light. This type of PE is more and more studied in our laboratory and therefore we were also interested in its behavior when analyzed by thermal fractionation techniques. Further For UHMWPE we observed an elevated melting temperature measured by DSC, up to 144°C, during the first heating step. However, a lower melting temperature and crystallinity were observed for the second heating step after a 5-minutes isotherm at 180°C followed by a cooling at a rate of 10°C min -1 .

Similar results were reported by Rastogi and co-workers who investigated the melt behavior of UHMWPE by DSC. [26][27][28][29] They proposed that the higher temperature peak (144°C) obtained in the first step could be attributed to the polymer chains which are disentangled and producing exceptionally large crystalline lamellae than those usually observed. The use of homogeneous single-site catalyst makes possible to obtain a disentangled UHMWPE. Indeed, in this system, the active sites are dispersed and distant from each other. During the propagation reaction, the chains being far apart, they are unlikely to get entangled (Figure 3-31 a).

In the DSC experiment, upon crystallization from the melt state, most of the entanglements are trapped in the solid leading to a lower melting temperature (136 ° C) in the second melting step. Concerning the CEF experiments of our UHMWPEs (Figure 3-32), we observed a peak at 110°C as expected for homo-PE and as the molar mass of the samples increased, a shoulder at high elution temperature was clearly visible in the profile. The intensity of the shoulder increased with the molar mass; it even became the major peak of the sample with the highest molar mass (black profile in Figure 3-32). The CEF profile suggests the presence of two types of crystallites as observed in DSC annealing experiments.

As Rastogi et al showed by DSC, UHMWPEs have the ability to crystallize at high temperature forming large lamellae when conditions allow. These chains are eluted at higher temperature. The peak at 115°C corresponds to these disentangled chains. Perhaps the conditions are not totally favorable to disentanglement and we observe a second peak at lower temperature due to entangled chains.

CHARACTERIZATION OF POLYETHYLENES: FROM THERMAL FRACTIONATION TECHNIQUES TO SPECTROMETRY

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These entangled chains can appear for two reasons:

1-depending on their distance from the stationary phase of the column, which acts as a nucleating agent and favors the creation of small lamellae (110°C). If the distance between the chain and the surface of the column increases, it has less effect on the chains. They crystallize into lamellae of larger thicknesses that melt at higher temperatures (115°C). A test, described in the following section, was performed in DSC to measure the crystallization, and melting temperature in solvent condition but without a support (column).

2-depending on the local concentration of the polymer chains. If the concentration is below the critical concentration, the chains do not interact with each other and do not entangle; if the concentration is higher, the chains can interact and entangle. Both conditions can be observed in the CEF. Large lamellae can be created when the chains in solution are far apart. They can crystallize slowly in the same way as disentangled chains produced with a homogeneous single-site catalyst. A small-angle X-ray scattering (SAXS) study will be conducted to follow the crystal lattice of these high molar mass PE as a function of temperature under solvent conditions (1,2,4-TCB). This study will probably clarify the understanding of the second peak formation.

This high-molar mass effect is less observed in TGIC analysis. It can be justified by the different separation in TGIC since it is not only based on crystallization.

The lower limit given by Soares and co-workers is therefore not the only one to be considered for the samples. We can conclude that samples between 17 Kg mol -1 and 1 million Kg mol -1 can be compared with each other. The only effect of separation is the length and content of branching. Below or beyond this limit, the molar mass of the polymer will impact its elution.

CEF is also a means of identifying the presence of very high-molar mass chains in a sample when an elution peak appears around 115°C.

UHMWPE melting and dissolution process (DSC)

To better understand the behavior of UHMWPE in CEF further investigations were carried out. DSC experiments were conducted under solvent condition on a medium molar mass HDPE (30 kg mol -1 ) as a reference and a UHMWPE (6,000 Kg mol -1 ). To be as close as possible to the concentration required in CEF a quantity of 0.1 mg of sample was added in 100 μl of 1,2,4-TCB in a 120 μl medium pressure crucible. A 3-155 temperature program identical to that of CEF was used: dissolution at 150°C, cooling to 25°C at a rate of 2°C min -1 and heating at 4°C min -1 to 130°C.

Figure 3-33: DSC curves acquired on an UHMWPE (6,000 kg mol -1 ) and an HDPE (30 kg mol -1 ) with a first heating rate at 10°C min -1 to 130°C, a cooling rate at 2°C min -1 and a second heating rate at 4°C min -1 under nitrogen atmosphere. Similar DSC curves were observed for different UHMWPE.

For UHMWPE, during the first heating, a melting peak at high temperature (117°C) appears. This peak increases with the molar mass of the UHMWPE sample. For a UHMWPE of 2,000 Kg mol -1 it was observed a little below at 115°C. The thickness of the lamellae seems to be linked to molar mass.

During low-rate cooling (-2°C min-1), two peaks appear for UHMWPE. The one at low temperature (86°C) is similar to that observed for a conventional HDPE of medium molar mass. This value is similar to that obtained by CRYSTAF for HDPE samples (Figure 3 -17). The presence of a second peak is not usually observed in DSC under bulk (solvent-free) conditions. Under solvent and low-velocity cooling conditions, UHMWPE can crystallize as a long lamella in the disentangled mode. A second fraction, which probably corresponds to entangled chains, crystallizes at lower temperatures.

During the second heating, corresponding to the elution in the CEF experiment, two peaks were observed.

The temperature of the lower peak, at 97°C, is similar to that of HDPE. The second peak is 6°C higher in temperature. This behavior is similar to that observed previously in the CEF experiments. We can assume that the higher peak is related to disentangled chains and the lower one to entangled chains. The conditions of low polymer concentration in solution promote the emergence of the peak at high temperature.

CONCLUSION

Over the past 10 years, driven by the development of increasingly controlled synthesis methods and of polymers with increasingly better-defined structures, many developments have been achieved regarding the characterization of polyolefins. Several novel and original fractionation techniques were invented and developed, and we had the opportunity of installing some of them in our laboratory to improve the analytical capability of our team.

The proficiency, in our laboratory, of controlled synthesis methods via the use of metallocene catalysts for the polymerization of olefins allowed us to conceive copolymer models and to calibrate all the fractionation techniques used to characterize the main industrial ethylene-α-olefin copolymers. The calibration equations that can now be used in industrial and academic laboratories, and in control and research services, are summarized in Table 3-9.

Table 3- Te: elution temperature, Tc: crystallization temperature, Ve: elution volume, R 2 : R-squared, the square of the sample correlation coefficient ranges from zero to one.

To illustrate the use of these equations, two industrial samples were characterized by CEF (Figure3-33). As shown the CEF analysis (like TREF, CRYSTAF, TGIC or SGIC) enabled the measurement of:

the distribution of the different families (% by mass of soluble fraction, weakly and highly crystalline fraction), the composition in terms of branching of each fraction (CH3/1000C and the mol% of hexene content) with the use of the calibration curve constructed previously, the viscosimetric average molar masses on each fraction when a viscometer is used.

However, a difficulty persists if we do not know the comonomer inserted in an unknown LLDPE, i.e. we cannot choose a suitable calibration method and must restrict ourselves to measuring the number of CH3/1000C. It was therefore important to extend this thesis work to develop methods for identifying the comonomer inserted in the LLDPE or, in other words, measuring the length of the branching.

The following part attempts to tackle this subject by proposing two different and innovative strategies.

The first method used the ability of FTIR to provide a broad range of information about the structure of LLDPE through all the wavelengths absorbed in medium IR and near IR. The finesse of this information can only be fully exploited using chemometric tools. FTIR coupled with chemometrics was then developed to rapidly obtain access to chemical composition.

The second strategy employs mass spectrometry, widely used in analytical laboratories but difficult to apply to polymers. In order to make it usable for understanding the structure of our copolymers, we coupled it to thermogravimetric analysis (TGA). This coupling made it possible to split the copolymers into very specific fragments which could be identified and quantified by mass spectrometry. The method has been shown to be effective in identifying the type of comonomer used during the synthesis of a LLDPE sample.

All of this work is described in three publications that constitute the whole of Chapter 4 of this thesis.

The catalytic synthesis of ethylene copolymers has made it possible to synthesize LLDPE models with narrow distributions in chemical composition and molar mass. These polymer models have enabled us to

successfully calibrate the different thermal fractionation techniques from TREF to SGIC.

We have shown that fractionation techniques are unique tools for accessing to chemical composition distribution. These separation techniques can be compared to liquid chromatography. Like the latter, they require dissolution of the samples, which for polyolefins is tricky and implies aggressive solvents and elevated temperatures. In this context of sample preparation, it is necessary to be aware both on the proper dissolution of the polymer and to avoid its degradation. Consequently, preparation and analysis times are time consuming and delicate. It is advantageous to develop also quicker techniques to reach the chemical composition.

Spectroscopy techniques are widely used by research laboratories, they can be powerful tools for measuring chemical composition. In this chapter we are interested in two techniques of spectroscopy the infrared spectroscopy (FTIR) and mass spectrometry.

FTIR has been widely used for many years for the characterization of polyolefins. The development of chemometric techniques now allows a new approach in the exploitation of the spectra obtained.

Chemometrics make it possible to obtain information on polymers by observing several wavelengths connect to the information requested. We have shown that it can be applied effectively both to medium infrared and near infrared on LLDPE (first part of the chapter) but also on other types of copolymer such as ethylene-butadiene which has complex structures (second part of the chapter).

Regarding mass spectrometry, which are difficult to use in the context of polymers, we have explored the interest of a coupling with thermogravimetric instrument. This led to obtain significant fragments of the degraded copolymers that were identified by mass spectrometry.

Each of the three sections of this chapter has been published in the journal Macromolecular Chemistry and

Physics. Each section has its own references. Reproduction of publications has been requested from the editor and accepted to be included in the thesis.

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CHEMICAL COMPOSITION OF HEXENE BASED LLDPE BY IR SPECTROSCOPY AND CHEMOMETRICS

This article describes a rapid investigation method, based on a combination of mid and near infrared spectroscopy and chemometrics tools, for measuring the amount of hexene in LLDPE. We have used our well-defined copolymers to calibrate the PLS model. The processing and the assessment of the obtained regression models are discussed and show that the methods are efficient, accurate and fast.

Mid and near infrared (MIR and NIR) spectroscopy associated with the partial least squares (PLS) method makes it possible to rapidly characterize the composition of linear low-density polyethylene (LLDPE) in a

large range of 1-hexene content from 0 to 21 mol%. LLDPEs are produced using zirconocene catalysts activated with methylaluminoxane. PLS regression methods for MIR and NIR are constructed from this series of LLDPEs to quantify the 1-hexene content in unknown copolymers. In this case, the PLS regression method aims to correlate the 1-hexene content in the copolymers with their IR spectra. Multivariate calibration models are constructed by the PLS algorithm on pretreated data of MIR and NIR analyses. They are tested and validated by comparing results obtained by NMR and the PLS analyses for four unknown ethylene-1-hexene copolymers.

INTRODUCTION

With an annual global production of approximately 100 million tons, polyethylenes (PEs) are the main commercial polymeric materials. [1,2] They are typically classified into three main families such as high-density polyethylene (HDPE; 0.940 to 0.970 g/cm3), low-density polyethylene (LDPE; 0.910 to 0.940 g/cm 3 ) and linear low-density polyethylene (LLDPE; 0.916 to 0.940 g/cm 3 ). HDPE has no or only a small amount of branching (SCB), LDPE contains a combination of long (>C6) and short chain branching, while the branching in LLDPE is predominantly from short chain branching. This last one is synthetized by copolymerization of ethylene and an α-olefin which allows the insertion of a short-chain branching into the main chain and thus impacts the crystallinity of the material. [3] The frequently used α-olefins are 1-butene, 1-hexene and 1-octene. [1,4] The crystallinity and then the physical properties of LLDPE can be adjusted using different content of comonomer. [5,6] Consequently, it is highly relevant to quantify the amount of comonomer units incorporated into LLDPE during the polymerization process.

Various analytical techniques have been developed to quantify the short chain branching content. It has been widely investigated using spectroscopy like Fourier transform infrared (FTIR) [7][8][9][10] , proton and carbon nuclear magnetic resonance (H-NMR and 13 C-NMR) [11][12][13][14] . Liquid chromatography based on crystallibility of polyolefins has been established by Wild, Monrabal, Soares and Pasch through temperature rising elution fractionation (TREF) [15][16][17][18][19] and crystallization analysis fractionation (CRYSTAF) [20,21] . However, these techniques cannot be used for the separation of amorphous fractions of the polymers. The combination of high temperature liquid chromatography with a Hypercarb column operating with a temperature gradient [22][23][24][25][26][27] was introduced by Cong and Macko and allow the analysis of amorphous polymers. These high temperature fractionation techniques were able to determine the chemical composition distribution (CCD) of LLDPE. In addition, thermal analysis coupled with mass spectrometry [28][29][30][31] has been employed to measure the branching type and the content of α-olefins in LLDPE.

However, these approaches are time consuming due to the sample preparation (dissolution at high temperature with toxic solvent) for most techniques and the time required to record and process the data.

In many instances, for example in the case of high throughput experiments or during recycling process, it is desirable to determine the polymer composition in a shorter time.

Infrared spectroscopy is a consistent and an essential analytical method for exploring polymer composition. [32,33] More specifically, Fourier transform infrared spectroscopy in attenuated total reflection mode (ATR-FTIR) [34][35][36] and near infrared (NIR) [37][38][39] equipped with an integrating sphere might be advantageous for measuring the chemical composition of LLDPE as inexpensive sample preparation is sufficient for theses technique. While many previous studies [9,40,41] are based on absorbance attributable to branch type there are few publications on quantitative studies. [7,42,43] In work of Blitz and McFaddin, [7] FTIR calibration for different branch type (methyl, ethyl, butyl, hexyl) in LLDPE based on absorption of only one wavelength was reported. Sano et al and Shimoyama et al described methods to predict density in LLDPE by applying chemometrics tools to Raman spectra [42] and near IR spectra [43] . In this present study we propose to calibrate IR analysis of LLDPE with a large and complete set of polymers up to 21 mol% of 1-hexene and with multiple absorption bands in order to increase the robustness and precision of the method.

Because structural changes in ethylene-1-hexene copolymers cause low modifications in MIR and NIR spectra, the use of chemometrics techniques are required to highlight differences in polymer spectra.

Partial least-squares (PLS) regression is commonly used to improve the resolution in analytical signals that can be overlaid for intricate materials. [44][45][46][47][48] In particular, we demonstrated, in a previous work, that PLS regression can be efficiently used for quantitative determination of composition of ethylene-butadiene copolymers. [49] This work proposes an original method based on infrared spectroscopy and chemometrics. Firstly, copolymers containing various proportions of 1-hexene were synthetized using the zirconocene catalyst. [50][51][52] Secondly, the average composition of the copolymers was measured using 1 H and 13 C-NMR spectroscopy. The homogeneity in molar mass and chemical composition was also controlled by high temperature size exclusion chromatography (HT-SEC) and thermal gradient interaction chromatography (TGIC). Subsequently, the copolymers were used to construct the PLS model with NIR and MIR data.

EXPERIMENTAL SECTION

Polymerization method

All manipulations were performed under dry argon, using standard Schlenk techniques and glovebox. 1hexene was dried over CaH2 prior to use. Toluene and heptane were dried on 3 Å molecular sieves. Methylaluminoxane (MAO) 10% wt. in toluene was purchased from Aldrich and triethylaluminium (AlEt3) was purchased from Albemarle and used as heptane solution (1 M). Ethylene (99.5%) from Air Liquide was purified by passing on three successive columns containing respectively molecular sieves, alumina and a copper catalyst. The metallocene complexes rac-Et(Ind)2ZrCl2 and (nBuCp)2ZrCl2 were purchased from Sigma-Aldrich. The activating support was prepared as described in previous work. [53] Ethylene polymerizations were performed in a 500 ml glass reactor equipped with a stainless-steel blade stirrer and an external water jacket to control the temperature. MAO and the required amounts of 1-

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hexene were introduced in a flask containing 300 mL of heptane. The mixture was transferred in the reactor under a stream of argon. The argon was then pumped out before introducing the ethylene or a mixture of ethylene-propylene. Temperature and pressure were then progressively increased up to 80 °C and 3.8 x 10 5 Pa. 100 μL of a solution (1.5 mM in toluene) of rac-Et(Ind)2ZrCl2 and (nBuCp)2ZrCl2 were then introduced in the reactor under 4 x 10 5 Pa of ethylene to start the polymerization. The pressure was kept constant at 4 x 10 5 Pa during the polymerization. After 30 minutes of reaction, the polymerization was stopped by releasing the pressure and cooling down the reactor to the room temperature. The resulting mixture was poured in 400 mL of methanol. The polymer was collected by filtration, washed with methanol and dried under vacuum.

In the case of slurry polymerization using the supported rac-Et(Ind)2ZrCl2 catalyst, a similar procedure was used. However the Al(i-Bu)3 (1 M solution in heptane), the activating support, the metallocene precatalyst (1 mM solution in toluene), and 1-hexene were introduced successively in the flask containing 300 mL of heptane. The mixture was transferred in the reactor and the polymerization started by pressurization of the reactor to 4 x 10 5 Pa.

Characterization

High temperature size exclusion chromatography

High temperature size exclusion chromatography (HT-SEC) analyses were performed using a Viscotek system, from Malvern Instruments, equipped with a combination of three columns (PLgel Olexis from Agilent Technologies, 300 mm × 7.5 mm, 13μm). Samples were dissolved in 1,2,4-trichlorobenzene (TCB) with a concentration of 5 mg mL -1 by heating the mixture for 1 h at 150°C. 200 μL of sample solutions were injected and eluted with 1,2,4-TCB using a flow rate of 1 mL min -1 at 150 °C. 2,6-di-tert-butyl-4methylphenol (BHT) was added to the eluent (200 mg L -1 ) in order to stabilize the polymer against oxidative degradation. Online detection was performed with a differential refractive-index detector and a dual lightscattering detector (LALS and RALS) for absolute molar mass determination. OmniSEC software version 5.2 was used for data acquisition and calculation.

Thermal Gradient Interaction Chromatography

TGIC experiments were performed using an instrument from PolymerChar (Valencia, Spain) to characterize the composition distribution in samples. The instrument was equipped with a Hypercarb column from Thermo Scientific. The samples were dissolved in 10 mL vials for 1 h at 150 °C with 1,2,4-trichlorobenzene A vast set of ethylene-1-hexene copolymers (Table 4-1) was obtained by changing comonomer content during synthesis. The catalyst used in this work led to polymers with the controlled molecular structure in molar mass and in comonomer composition. They were analysed by HT-SEC, TGIC and NMR before using them to construct the PLS models.

a catalytic systems based on the complexes [1] rac-Et(Ind)2ZrCl2 and [2] (nBuCp)2ZrCl2 [3] supported rac-Et(Ind)2ZrCl2 used for the preparation of ethylene-1-hexene samples. b Number average molar mass and dispersity obtained with HT-SEC, c 1-hexene content determined with 1 H NMR and 13 C NMR, d elution peak temperature, 1-hexene content and dispersity of chemical composition obtained by TGIC, nd not determined 4.1.3.1 Interpretation of NMR spectra 13 C NMR spectra was used to determine and quantify the chemical composition of homopolymers and copolymers with a 1-hexene content below 4% (Figure 4-1). The 13 C NMR spectra of highly branched linear low-density polyethylene is tricky and requires a detail analysis of monomer sequences. [54] In that case 1 H-NMR was used to provide reliable 1-hexene content since the signal of methyl chain end can be neglected.

Calculation of 1-hexene content has been reported in a previous work. [18]

Chemical composition distribution

The molar masses and the dispersity of samples are reported in Table 4-1. The SEC profiles, in Figure 4-2a, show a unimodal molar masses distribution. The TGIC peak of the samples elutes in decreasing order of comonomer content, as observed in previous works. [24,27,[55][56][57][58] The elution temperature of 11 samples, issued from homogeneous catalyst [1, 2] and supported catalyst [3], were plotted (Figure 4-2b). The peaks are rather narrow and have a similar distribution to a Gaussian which confirms that all polymers were quite homogeneous in composition.

Quantifications of the 1-hexene content by TGIC were very similar to the values obtained by NMR. As NMR is a more conventional method, it has been chosen as the main reference method for developed models.

Interpretation of MIR spectra

The copolymer samples were analysed by MIR spectroscopy using ATR accesory. Figure 4-3 shows the comparison of FTIR spectra of a homopolyethylene and four ethylene-1-hexene copolymers. LLDPE showed a relatively simple infrared spectrum (Figure 4-3), the major absorption bands observed have been reported previously. [47,59,60] The IR spectra of LLDPE, containing different amounts of hexene, were found to have significant differences in four different regions. Four ratios of very close bands were studied. When the comonomer content increases in the copolymer we observed that the ratio of the peak intensity 2914 cm -1 /2847 cm -1 , 1472 cm -1 /1462 cm -1 and 1378 cm -1 /1369 cm -1 increased while the ratio of the peak intensity 730 cm -1 /718 cm -1 decreased significantly.

In Figure 4-3b, the ratio of absorption at 1378 cm -1 (due to methyl groups C H deformation) versus absorption at 1369 cm -1 (due to methylene group C H deformation) clearly shows a trend with the variation of 1-hexene amount in the copolymer. For the homo-polyethylene, no absorption was observed at 1378 cm -1 whereas as the comonomer content increased in the copolymer, the intensity of this peak increased. The splitting of absorption bands is due to semi-crystalline properties of LLDPE as described in previous work [61] . Comonomer content has a slight impact on different parts of the IR spectrum. In order to consider all these modifications on the spectrum, the chemometric analysis was applied in this study.

Interpretation of NIR spectra

The absorption spectrum of a representative sample is shown in Figure 4-4. In agreement with previous work, [62][63][64] the assignments of the eight main absorption bands are reported in NIR spectra are composed of overlapping overtones and combinations of bands originating from the MIR.

They contain a wealth of information on the chemical and physical properties of the copolymers. Since it 4-212 was a considerable effort to deduce some characteristic of LLDPE microstructure from the spectra, the data were exploited using chemometric tools.

The spectrum of dissolved polymer (Figure 4

Chemometric study

The goal of this work was to obtain a robust method to determine the 1-hexene content of an unknown copolymer with MIR and NIR spectroscopy. A partial least squares regression (PLS) model [44,45,65] was used.

Calibration set

In order to determine composition of an unknown ethylene-1-hexene copolymer, calibration methods for MIR and for NIR were created with a set of 41 samples described above. The wide range of composition of ethylene-1-hexene copolymers, from 0% to 20.7 mol%, was particularly interesting for this purpose. The performance index plot was used to measure the divergence between the model and actual data. It allows the determination of the PLS factor number (Table 4-4) to be used to properly describe the variables. As the number of PLS factors increased, the performance index plot increased. When the curve reaches its maximum, this value corresponds to the optimum number of PLS factors. Including more PLS factors, the model will fit the calibration set better but can lead to an 'over-fitting' of the model and to a poorer prediction for unknown sample. The choice of four factor number in the calibration model was a balance between optimizing the explain variance and limiting the model complexity.

Preprocessing method

Several data pre-processing methods were applied. The first derivate of the NIR and MIR signals was chosen in order to reduce the baseline offset and the instrumental drift. In the derivation process, noise can increase which requires a smoothing. The Savitzky-Golay algorithm [66][67][68] was used for smoothing the signal and to reduce the impacts of varying baseline, variable path lengths, and high stray lights due to scatter effects. A polynomial order of 2 and a segment length of 7 points were applied. The pre-processing method was applied both to the whole spectrum and to the spectral region selection. A principal component analysis (PCA) scores for factor 1 and factor 2, in Figure 4-5, summarized more variation in the data than any other pair of components. The closer the samples were in the score plot, the more similar they were. The plot for MIR (Figure 4-5a) and for NIR (Figure 4-5b) shows that when 1hexene content increase, from blue to brown, the sample was clearly shifted to the right. This means that the amount of comonomer had a real impact on the spectra and that it could be measured using PLS regression. The scores plot shows that the separation of the four regions of different hexene levels was better for the MIR model than for the NIR model. The both score plot show that the sample 41 was considered as outlier. This sample was different from the others, not because of an analytical error, but because of the high amount of hexene. It was considered a false outlier and was not removed to preserve the large range of analyses. Sample 41 was analyzed and used twice in the model to give more weight to this sample which is located alone at the end of the calibration. In addition, the sigmoid-shaped curvature of the score plots indicates that there were interactions between the predictors. Adding more factor to the model would improve it.

Scores

Spectral region selection

One approach was based on spectral region selection in which the wavelengths with low correlation were eliminated. In the contribution plot for MIR (Figure 4-6a), three spectral regions contribute significantly to the discrimination. In order to improve the model and eliminate the wavenumbers likely generating noise, we decided to select only the interesting spectral region: the bands from 3000 to 2750 cm -1 , from 1500 to 1300 cm -1 and from 800 to 630 cm -1 . This corresponds well to the main absorption wavenumbers of polyethylene (2914 cm -1 , 2847 cm -1 , 1472 cm -1 , 1462 cm -1 , 730 cm -1 and 718 cm -1 ) indicated in previous work. [49] For NIR, the contribution plot (Figure 4-6b) made it possible to select the bands from 9000 to 7800 cm -1 , from 6400 to 5400 cm -1 and from 4800 to 4000 cm -1 . Although we observed an absorption between 7500 to 6900 cm -1 , this range was not selected in the model. The NIR model has been improved without the use of this range mainly impacted by the solvent.

Calibration and validation

Using the samples different models were created, six of them are reported in 4-3 (blue data for calibration and red data for validation). The axes units are expressed in mol% (1-hexene content).

The assessments of the six PLS models are summarized in Table 4-4. analysed by MIR and NIR. The IR spectra obtained were exploited using chemometric tools and correlate with NMR results. The PLS method was revealed to be rapid, highly efficient and low-cost for determining the composition of copolymers even if characteristic vibrations of 1-hexene are indistinguishable in the spectrum. The proposed methodology provides also the great advantage of non-destructive measurement. The method is highly satisfactory based on its good repeatability and accurate results. This study shows that chemometric analysis of MIR and NIR spectrum is an easy and a valuable tool to understand the chemical composition of copolymers. The developed models can be applied for routine analysis of unknown samples with satisfactory results.

RAPID DETERMINATION OF THE CHEMICAL COMPOSITION OF ETHYLENE-BUTADIENE COPOLYMERS USING FTIR SPECTROSCOPY AND CHEMOMETRICS

FTIR method coupled with chemometrics elaborated with our LLDPE models has shown that it was particularly fast and efficient to determine the chemical composition of unknown samples. We have taken advantage of the method developed for LLDPEs with simple structures to transfer it to ethylene-butadiene copolymers which present particularly complex microstructures.

Infrared spectroscopy by attenuated total reflection (ATR-FTIR), combined with partial least square (PLS) method provides a fast characterization of ethylene-butadiene copolymers intricate composition. The PLS regression method is constructed to quantify ethylene, 1,2-butadiene (vinyl), trans-1,4-butadiene and 1,2cyclohexane units in the copolymer. These rings are formed by intramolecular cyclisation during polymerization. The performance of PLS models is evaluated by comparing the result obtained by 13 C NMR and the model for three unknown samples. It is shown that the proposed method allows to accurately estimate the chemical composition of ethylene-butadiene copolymers in a much shorter time than NMR.

INTRODUCTION

Neodymium metallocenes are unique catalysts for the copolymerization of ethylene with butadiene. A new class of elastomers was obtained using metallocene complexes of supported ansa-bis(fluorenyl) neodymium complexes in combination with MgR2. [1,2] These elastomers, obtained with readily available monomers (ethylene and butadiene) display an intricate and original microstructure. The butadiene insertion leads to unsaturated moieties consisting of unsaturated groups: internal trans double bonds and vinyl branches. In addition, this insertion leads to the formation of 1,2-cyclohexane rings. These rings are formed by a mechanism of intramolecular cyclisation involving vinyl units. [1,2] Properties of the ethylenebutadiene copolymers are directly linked to their composition and consequently it is highly relevant to fully characterize their chemical composition. The characterization of these polymers was performed by 1 H and 13 C NMR analyses. [3,4] NMR investigations permitted an accurate determination of the chemical composition of these copolymers. However, these analyses are reliable and accurate but are time consuming due to the sample preparation, the time required to record the spectrum and process the data.

In many instances, for example in the case of high throughput experiments, it is desirable to determine the polymer composition in a shorter time.

Infrared spectroscopy is a consistent and an essential analytical method for exploring polymer composition. [5][6][7][8][9] More specifically, Fourier transform infrared spectroscopy in attenuated total reflection mode (ATR-FTIR) [10][11][12] might be advantageous for measuring the chemical composition of ethylenebutadiene copolymers as this technique requests straightforward sample preparation. Because structural changes in aliphatic ethylene-butadiene copolymers, cause low modifications in FTIR spectra, the use of chemometrics techniques are required to highlight differences in the polymer spectra. Partial leastsquares (PLS) regression is a popular algorithm and generally used to improve the resolution of signals that can be superimposed in complex materials. [13][14][15][16][17] In particular, MIR spectroscopy combined with PLS methods is used to develop quantitative determination of copolymer composition. [18,19] A combination of ATR-FTIR spectroscopy and chemometric tools was developed in the present article to quantify the chemical composition of ethylene-butadiene copolymers. The FTIR was calibrated by using NMR as a direct technique for measuring copolymer composition.

EXPERIMENTAL SECTION

Materials

Three neodymium metallocene complexes were selected: [Me2(C13H8)2Nd(BH4)2Li(THF)]2 (1), 2) and [Me2Si(C5Me4)(C13H8)Nd(BH4)] (3). The preparation of complexes 1 and 2 was reported previously. [1,2,20,21] Complex 3 was obtained as a green powder by reaction of Me2Si(C13H8)(C5Me4)Li2Et2O [22] with Nd(BH4)3(THF)3 in tetrahydrofuran (THF).

[Me2Si(C5H4)(C13H8)Nd(BH4)2][Li(THF)] (

Polymerization procedure

Polymerizations were performed in toluene using precatalysts 1, 2 and 3 in association with n-butyl-noctyl-magnesium (BOMAG). In a typical procedure, a catalyst solution was prepared by successive addition of n-butyl-n-octyl-magnesium and of one precatalyst in toluene. The catalyst solution was stirred during 10 minutes and then introduced in a reactor. The polymerization was started by addition of the mixture of monomers at the desired temperature. At the end of polymerization, the reaction was quenched with methanol. The reaction medium was then poured in a solution of methanol containing 2,2ʹ- Methylenebis(6-tert-butyl-4-methylphenol) (0.5 wt%). The polymer was filtered off, washed with methanol and dried under vacuum

Analytical techniques

Depending on the solubility of polymers, molar masses were measured with ambient size exclusion chromatography (SEC) in tetrahydrofuran (THF) or with high temperature size exclusion chromatography (HT-SEC) in 1,2,4-trichlorobenzene (TCB).

Size exclusion chromatography in THF

SEC measurements were performed with a Viscotek TDAmax system from Malvern Instruments that consists of a sample delivery module (GPCmax) and a tetra detector array, including light scattering, a fourcapillary differential viscometer, a differential refractive index detector (RI), and a diode array UV detector.

THF was used as the mobile phase at a flow rate of 1 mL min -1 . All polymers were injected at a concentration of 3 mg mL -1 after filtration through a 0.45 μm pore-size membrane. The separation was carried out on a guard column and three columns (SDVB, 5 μm, 300 × 7.5 mm I.D.) from Polymer Standard Service. Columns and detectors were maintained at 40 °C. The OmniSEC 5.02 software was used for data acquisition and data processing. A conventional calibration constructed with narrow polystyrene (Polymer Standards Service, Mainz, Germany) was used to calculate average molar masses.

High temperature size exclusion chromatography

HT-SEC analyses were performed using a Viscotek system, from Malvern Instruments, equipped with a combination of three columns (Polefin 300 mm x 8 mm I.D. porosity of 1 000 Å, 100 000 Å and 1 000 000 Å) from Polymer Standards Service. Samples were dissolved in 1,2,4-TCB with a concentration of 5 mg mL - using a flow rate of 1 mL min -1 at 150 °C. 2,6-di-tert-butyl-4-methylphenol (BHT) was added to the eluent (200 mg L -1 ) in order to stabilize the polymer against oxidative degradation. Online detection was performed with a differential refractive index detector. A conventional calibration curve, obtained with polystyrene standards (Polymer Standards Service, Mainz, Germany) in the range of 500 to 4.2x10 6 g mol -

1

, was used to calculate the molar mass distribution of the samples. Data were acquired and processed with the OmniSEC 5.02 software.

Nuclear magnetic resonance spectroscopy

The chemical composition of ethylene-butadiene copolymers was determined by NMR using a Bruker 400

Avance III spectrometer operating at 400 MHz for 1 H and 100.6 MHz for 13 C. 1 H spectra were obtained with a 5 mm BBFO+ probe at 363 K and the 13 C spectra were obtained with a 10 mm PA-SEX probe at 363 K. A 3:1 volume mixture of tetrachloroethylene and benzene-d6 was used as solvent. Chemical shifts were measured in ppm using benzene (at 7.15 ppm) as reference for 1 H NMR and polyethylene chains (30.00 ppm) for 13 C NMR the resonance.

Fourier transform infrared spectroscopy

Infrared spectra were recorded using a Nicolet iS50 FTIR spectrometer from Thermo Fisher Scientific. The spectrometer is equipped with a diamond crystal ATR accessory and a deuterated triglycine sulfate (DTGS)

detector and KBr optics. Before each measurement, the diamond crystal was carefully cleaned with ethanol and dry in ambient air. A small amount of sample in powder state was pressed directly on the diamond crystal with a constant pressure of 27 kg. Background and sample were acquired using 32 scans at a spectral resolution of 4 cm -1 from 4 000 to 400 cm -1 . At least every 60 minutes a new background spectrum was acquired. Spectral data were obtained with OMNIC Software from Thermo Fisher Scientific.

Chemometric analysis of the copolymer spectra was achieved using a partial least squares (PLS) method with TQ Analyst software from Thermo Fisher Scientific.

RESULTS AND DISCUSSION

Chemical composition of ethylene-butadiene copolymers

The present work was developed to determine the chemical composition of intricate ethylene-butadiene copolymers in a straightforward way. The copolymerization of ethylene with butadiene using neodymium Insertion of ethylene in the central carbon corresponds to a 2,1-butadiene insertion providing a vinyl unit and possibly the formation of a cyclohexane moiety via a subsequent intramolecular cyclisation involving two ethylene units. [1, 2, 23, 24] Insertion of ethylene on the terminal carbon corresponds to a 4,1butadiene insertion providing exclusively trans-1,4-butadiene units. The regioselectivity of butadiene insertion (2,1 vs 4,1) is obtained considering the ratio between vinyl and cyclohexane units versus trans-1,4 units. This ratio follows the order of complex 1 > 2 > 3. Since there is competition between chain growth and cyclisation after the formation of a vinyl branch, the ratio between cyclohexane and vinyl units can be changed varying the monomer concentration. The lower the monomer concentration, the higher the number of cyclohexane units.

Taking advantage of the impact of the catalyst structure and of the polymerization conditions on the chemical structure of ethylene-butadiene copolymers a vast range of copolymers was prepared by changing these reaction parameters. Results reported in Table 4-7 show the impact of the catalyst properties and polymerization conditions on the chemical composition of copolymers.

Interpretation of NMR spectra

The precise determination and quantification of the chemical composition of ethylene-butadiene copolymers by 1 H NMR and 13 C NMR analyses have been reported. [4] For NMR analyses, samples must be dissolved in aggressive solvent and more than 4 hours of acquisition are necessary in order to obtain good resolution. Figure 4-10 shows the high field resonance region of 13 C NMR spectra for three polymers synthetized with metallocene catalysts 1-3. Although well documented, [4,25,26] the assignment of the chemical shifts and the determination of the chemical composition are tedious. This figure highlights the complex chemical structure of ethylene-butadiene copolymers. Molar masses of samples were determined by SEC (Table 4567).

Interpretation of IR spectra

Copolymer samples were analysed with ATR-FTIR spectroscopy. Polyethylene shows a relatively simple infrared spectrum (Figure 4-11a). The splitting of bands (717-731 cm -1 and 1462-1472 cm -1 ) is due to interactions between chains in the crystalline phase. [27,28] The absorption bands corresponding to vinyl units and trans-1,4-butadiene units are well known in the literature. [29][30][31][32][33][34] They were assigned to the corresponding vibrational mode of each type of monomer unit in the ethylene-butadiene copolymers (Table 4-8). To determine the quantity of vinyl units and trans-1,4butadiene units in polybutadiene, an infrared band specific to each unit has been identified by Morero et al [35] . Those specific bands are known as 908 cm -1 for vinyl units and 964 cm -1 for trans-1,4-butadiene units.

trans-1,4-butadiene units which possesses a zero dipole moment do not show stretching of the double bond at 1640 cm -1 . This band is only assigned to vinyl units.

The IR spectra of cyclohexane include a strong band at 2914 cm -1 of stretching absorption and a band at 1472 cm -1 of bending and scissoring absorption. These bands, corresponding to the cyclohexane unit absorption, are difficult to identify because they overlap to that of other units present in the polymer backbone.

Due to the complexity of assigning a peak to cyclohexane units, chemometric analysis was developed and validated in this study.

Calibration set

In order to determine composition of an unknown ethylene-butadiene copolymer, a calibration was created with our fully characterized samples described above. The wide range of composition of available ethylene-butadiene copolymers is particularly interesting for this purpose (Table 456789). The idea is to determine with an ATR-FTIR analysis the composition of an unknown copolymer: ethylene content and the percentage of trans-1,4-butadiene units, vinyl units and cyclohexane units respectively. A partial least squares regression (PLS) model [36][37][38][39] was used with the four components and their relative compositions. The PLS calibration model was developed and popularized in analytical science by Wold in the 1960's [40][41][42] and was extensively used in chemistry by Martens, [37] Naes, [37,43,44] and Höskuldsson. [45] Many ways for optimizing the calibration curve of the chemometric method were considered (Table 4-10).

Performance index

The effect of the choice of spectral range, the format of the data or the smoothing method (Norris or Savitzky-Golay smoothing [46][47][48] ) were studied. This smoothing is frequently used as a pre-treatment that can eliminate noises such as baseline-drift. The performance index (PI) was chosen to measure the accuracy of the method. This number indicates the adequacy between the calculated polymer compositions and NMR measurements for the four units. The higher the performance index (range 0-100), the better the agreement between calculated values and NMR data. This allowed us to determine whether the changes made to optimize the method improved its performance. The following procedure was chosen. Only the spectral ranges containing structural information were selected and the part contributing to the noise was removed. In this study the spectral ranges from 600 to 1800 cm -1 and from 2600 to 3200 cm -1 were both selected. The first derivate of the IR signal was chosen in order to reduce the baseline offset and the instrumental drift. In the derivation process, noise can increase which requires a smoothing. Norris derivative filter were used for smoothing the signal and to reduce the impacts of varying baseline, variable path lengths, and high stray lights due to scatter effects. In the Norris smoothing, the segment length and the gap between segments were both set at 5.

Prediction performance

Two parameters [49] were used as indicators of the validity of the proposed model:

-RMSEC: root mean square error of calibration -the value corresponds to the error calculated using the calibration standards. RMSEC is expressed in mol% (Equation 4-3).

(4-3)

-RMSEP: root mean square error of prediction -Some of our samples are used as internal standards for validation of the method (Table 4567). This value is a measure of the average uncertainty that can be expected when predicting new samples. RMSEP is expressed in mol% (Equation 4-4).

(4-4) N = number of samples; Np = number of samples in prediction set; = model predicted value for sample i; A = number of PLS factors in model; r²: the correlation coefficient provides the same information for these methods as it does for simple Beer's law.

In order to validate the model, RMSEC and RMSEP values have to be low and similar and r² close to one. Root mean squared error of cross-validation (RMSEC) were plotted as a function of the number of PLS factor used in the calibration models. As the number of PLS factors is increased, the prediction error reduces. When the curve reaches its minimum, this value corresponds to the optimum number of PLS factors. Including more PLS factors, the model will fit the calibration set better but can lead to an 'overfitting' [50] of the model and to a poorer prediction for unknown sample.

Number of factors in PLS regression

From Figure 4-12, it is possible to determine that 3 parameters could be suitable for the quantification of ethylene, trans-1,4-butadiene and vinyl units and 6 factors are adequate for cyclohexane units.

Calibration and validation

With all those optimised parameters the model was created using 20 calibration samples and 10 validation samples (Table 4567). Figure 4-13 shows the calibration curve for the quantification of each units in the copolymers. For each parameter, a high value was obtained for the correlation coefficient; except for 1,2-cyclohexane, RMSEP/RMSEC ratio is close to 1. For 1,2-cyclohexane units number of factor is higher than that obtained for other units. Finally, it appears that the method is reliable for the determination of the content of ethylene in copolymers and for the measure of trans-1,4 and vinyl units. The prediction of 1,2-cyclohexane units seems to be the weakness of this method but considering the accuracy of all other parameters we can also evaluate efficiently cyclohexane units by difference.

Repeatability of the model

To verify repeatability of the method, an unknown ethylene-butadiene copolymer was measured 10 times with the same operator. Afterwards the PLS model was applied on all FTIR spectra to quantify each unit. 5.5 6.8 6.2 6.0 6.0 5.7 6.8 5.9 6.9 6.1 6.2 0.5

A good repeatability for all parameters was observed based on the data reported in Table 4-12. Since low sigma values were calculated, we can conclude that the proposed model is precise.

Validation of the model

With all those observations it seems that the method for the quantification of an unknown copolymer is feasible. In order to validate the model in real conditions, three new ethylene-butadiene copolymers were synthesized and analysed with both NMR and the proposed FTIR models. The results are given in Table 4-13. The predicted values obtained by FTIR are quite close to NMR results, which shows that the PLS model can be applied as a routine analysis. Considering this result, we can also conclude that the proposed model is precise and also accurate.

CONCLUSION

In this study an ATR-FTIR method combined with PLS modeling was developed for the simultaneous determination of 4 units in ethylene-butadiene copolymers. A series of 30 original copolymers with a wide variety of chemical composition was synthetized, characterized by NMR and then analysed by ATR-FTIR.

The obtained infrared spectra were exploited using chemometric tools. A PLS model was then performed using the correlation between the chemical structure of ethylene-butadiene copolymers determined by NMR and FTIR spectra. The PLS method was revealed to be rapid, highly efficient and low-cost for determining the composition of ethylene-butadiene copolymers even if characteristic vibrations of the 1,2-cyclohexane groups were indistinguishable in FTIR spectrum. The proposed methodology provides also the great advantage of non-destructive measurement. The method is highly satisfactory based on its good repeatability and precise results. This study shows that chemometric analysis of ATR-FTIR spectrum is an easy and a valuable tool to understand the chemical composition of copolymers and can be extended to other kind of intricate polymers. The developed models can now be use for routine analysis of unknown samples with satisfactory results.

AN ADVANCED TECHNIQUE FOR LINEAR LOW-DENSITY POLYETHYLENE COMPOSITION DETERMINATION: TGA-IST16-GC-MS COUPLING

An innovative technique TGA-IST16-GC-MS, thermogravimetric analysis combined with gas chromatography and mass spectrometry, was used to characterize LLDPE. We have used our well-defined copolymer models to validate this original method. The IST16 interface collects the gases produced during the degradation of the copolymer before GC-MS analysis. A specific signature of the comonomer present in LLDPE is identified and can be used for quantitative analysis of comonomer content.

An innovative method based on thermogravimetric analysis combined with gas chromatography and mass spectrometry, TGA-IST16-GC-MS, was developed for measuring the comonomer type and the comonomer content in a series of linear low-density polyethylene (LLDPE). LLDPE such as copolymers of ethylene and octene or ethylene and hexene were synthetized using the Et(Ind)2ZrCl2 / MAO zirconium-metallocene catalyst. Their characterization with TGA-IST16-GC-MS system were compared to the one of polyethylene prepared under similar conditions and used as reference. TGA-IST16-GC-MS allowed discriminating the comonomer type (hexene or octene) and content.

Combining the versatility of thermal analysis and the accuracy and sensitivity of mass spectrometry, this original method proved to be very useful for routine characterization of LLDPE. It has the advantage of being quicker and more easily performed that traditional means of obtaining copolymer compositions such as nuclear magnetic resonance (NMR), or through separation techniques such as TREF.

INTRODUCTION

Polyethylenes (PEs), which include low-density polyethylene (LDPE), linear low-density polyethylene (LLDPE) and high-density polyethylene (HDPE), constitute the most common industrial class of synthetic polymers with an annual global production of approximately 100 million tons [1,2] . LLDPE is produced by copolymerization of ethylene with an α-olefin which introduces short-chain branching (SCB) and thereby decreases the crystallinity of final polymer [3] . The most commonly used α-olefins for this purpose are 1butene, 1-hexene and 1-octene [4,5] which allow fine tuning of the crystallinity and thereby the properties of resulting polyolefin. The suitability for different applications can be achieved just by variation of the comonomer content. Therefore, it is of high interest to measure the amount of comonomer units (or SCB) incorporated into the PE chains.

Various analytical methods have been employed to determine the nature and degree of SCB.

Spectroscopic methods like carbon-13 nuclear magnetic resonance 13 C-NMR [6][7][8] and infrared (IR) [9][10][11][12] have been widely developed to measure SCB. More recently liquid chromatography based on crystallisation and thermal fractionation has been developed by Wild, Monrabal, Soares, Cong and Macko through temperature rising elution fractionation (TREF) [13][14][15] , crystallization analysis fractionation (CRYSTAF) [13, 15- 18] and interactive liquid chromatography [19][20][21][22][23] . Thermal analysis with pyrolysis-GC [24][25][26] has been also employed to measure branching in PE.

This work proposes a new method based on thermogravimetric analysis (TGA). TGA is generally associated to mass spectrometry (MS) [27] and IR spectroscopy [28,29] in order to identify the gaseous compounds emitted during thermal decomposition. However, for polymer with complex microstructures like LLDPE, IR and direct MS cannot unambiguously determine the nature of most components of gas mixtures. In these cases, coupling TGA with GC-MS offers promising advantages. The emitted compounds are first separated by GC, then identified and quantified by MS.

In this paper, an innovative coupling technic is introduced, which significantly increases the number of data points collected. It combines TGA, GC-MS and an innovative gas-storage interface (IST16) with a 16loop fractions collector inserted between the TGA and the GC [30] . The analytical tool is called hereafter TGA-IST16-GC-MS and provides an efficient way to take advantage of the MS technique.

Copolymers containing various proportions of 1-hexene and 1-octene were prepared using the zirconium catalyst rac-Et(Ind)2ZrCl2 activated with methylaluminoxane (MAO) [31][32][33] . The average composition of the copolymers obtained was then elucidated using TREF, 1 H and 13 C-NMR spectroscopy. Subsequently, the copolymers were further investigated by TGA-IST16-GC-MS.

EXPERIMENTAL PART

Method of polymerization

Experiments were performed in a dry-argon atmosphere, using Schlenk techniques. Metallocene complex rac-Et(Ind)2ZrCl2 and methylaluminoxane (MAO, 10 wt% in toluene) were purchased directly from Sigma-Aldrich. The comonomer, 1-hexene and 1-octene, were distilled over CaH2. Toluene and n-heptane were dried over 3 Å molecular sieves. Polymerizations were performed in a 500 mL glass reactor equipped with a blade stirrer and an external water jacket for temperature control as described in a previously article [34] .

Polymerization was stopped by adding methanol and the mixture obtained was poured into methanol. The precipitated polymer was collected by filtration, washed with methanol, and dried under vacuum.

Characterization

High temperature size exclusion chromatography (HT-SEC)

HT-SEC analyses were performed using a Viscotek system, from Malvern Instruments SA, equipped with three columns (PLgel Olexis from Agilent Technologies, 300 mm × 7.5 mm, 13μm). 200 L of a sample solution with a concentration of 5 mg mL -1 were injected and eluted in 1,2,4-trichlorobenzene at a flow rate of 1 mL min -1 at 150 °C. The mobile phase was stabilized with 2,6-di(tert-butyl)-4-methylphenol (200 mg L -1 ) to avoid polymer degradation. Online detection was performed with a differential refractiveindex detector and a dual light-scattering detector (LALS and RALS) for absolute molar mass determination.

OmniSEC software version 5.2 was used for data acquisition and calculation.

NMR spectroscopy

The comonomer contents were determined by NMR spectroscopy using a Bruker Avance III 400 spectrometer operating at 400 MHz for 1 H-NMR and at 100.6 MHz for 13 C-NMR spectroscopy. 1 H-NMR and 13 C-NMR spectra were obtained at 90 °C with a 5 mm QNP probe and a 10 mm PA-SEX probe respectively.

A 3:1 mixture of 1,2,4-trichlorobenzene and toluene-d8 was used as the solvent. Chemical shifts were measured in ppm using the toluene signal (CHD2 at 2.185 ppm) for 1 H-NMR spectroscopy and the polyethylene backbone signal (at 30.06 ppm) for 13 C-NMR spectroscopy.

1 H-NMR analyses were preferentially used to determine the -olefin content in copolymers. The spectrum is composed of two main peaks: the signals of the CH2 and CH protons of the polyethylene chain at 1.3 ppm and the signal of the methyl side groups at 0.9 ppm. Since high molar mass copolymers were synthetized, the methyl chain ends were neglected.

However, at low comonomer contents (< 1 mol%, samples 2 and 5), the resolution obtained in the 1 H-NMR spectra was too low and the methyl chain could not be neglected. In these cases, the 13 C-NMR spectra were used for the determination of the -olefin content as described in a previous article. [34] Temperature rising elution fractionation (TREF)

TREF measurements were performed to measure the chemical composition distribution (CCD) of sample. Eluted fractions corresponding to increasing crystallinity and decreasing comonomer content were thus obtained. The concentration of the polymer solution was monitored with an IR detector measuring the total CH absorption in the range from 2700 to 3000 cm -1 .

TGA-IST16-GC-MS experiments

The on-line combination of GC-MS with TGA was applied to characterize gases released during the thermal degradation of the LLDPE samples.

Thermogravimetric analysis (TGA)

TGA was performed with a Mettler Toledo TGA/DSC 1, equipped with a DSC heat flow element for simultaneous detection of enthalpy variations. The temperature sensor of the equipment was calibrated using indium and zinc standards. All samples were accurately weighed (20 mg) into 150 μL aluminum oxide 4-247 crucibles. The samples were heated from 40 °C to 600 °C at 10 °C min -1 in dry nitrogen atmosphere at a flow rate of 30 mL min -1 .

Storage interface (IST16)

The composition of the gas mixture emitted during TGA experiment varies too quickly for a direct analysis by GC-MS instrument. These gases released during thermal decomposition were first collected in the IST16 device. A preheated transfer line between the TGA and IST16 storage device allowed the gases to enter one of the sixteen storage loops. These gases were stored until completion of the TGA run (Figure 4-14a). Afterwards, facilitated by the second transfer line connecting the IST16 with the GC, each fraction collected were injected into the chromatographic column for separation (Figure 4-14b). Sixteen detailed gas chromatograms were acquired, and emitted compounds can be identified. All loops, valves and inert flow paths were installed in an isothermal oven and maintained at 250 °C. The temperature of both transfer lines was set at 250 °C. For all samples, the decomposition events took place between 400 °C and 540 °C. The storage temperatures were therefore chosen accordingly, as listed in Table 4-14. The listed temperatures are the upper limits of the ranges.

Gas chromatography-mass spectrometry (GC-MS)

A 7890B GC instrument, equipped with a capillary column and a 5977C mass selective detector from Agilent Technologies were used.

Helium was selected as the GC carrier gas. The flow rate through the chromatographic column was set at 1 mL min -1 with a split ratio of 4:1. The column temperature was held initially at 40 °C for 10 minutes, increased up to 300 °C at 10 °C min -1 and held at 300 °C for 24 minutes. The injector temperature was set to 280 °C.

The mass spectrometer was operated in the conventional electron ionization mode at an electron multiplier voltage gain of 1 V/V, with a mass scan range from 5 to 500 amu at a scan rate of 5.6 sec -1 . The National Institute of Standards and Technology spectra library was used to identify the compounds.

RESULTS AND DISCUSSION

Copolymers of ethylene with 1-hexene or 1-octene (Table 4-15) were prepared using the zirconiummetallocene catalyst Et(Ind)2ZrCl2 / MAO. A homopolymer (HDPE -sample 1) was also synthesized and used as a reference. The comonomer distribution of the synthesized samples was measured by TREF and the comonomer content was determined by NMR spectroscopy. All samples were subsequently investigated by TGA-IST16-GC-MS coupling.

Polymer characterization

The molar masses and the dispersity of polymers were determined by HT-SEC (Table 4-15). The copolymers exhibited a unimodal molar mass distribution. The TREF peak temperature of the samples gradually decreases as the comonomer content decreases, as observed in the previous works. [34, 35] Due to the high comonomer content in samples 7 and 8, the resulting copolymers are soluble at ambient temperature, and no peak was observed in TREF experiments.

TREF profiles in Figure 4-15 show that the signals collected are rather narrow and confirm that all copolymers are homogeneous in composition as expected with a metallocene catalyst. Because of their uniform comonomer distribution the copolymers are further employed below as models for TGA-IST16-GC-MS measurements. The mass spectrum of Figure 4-16 shows that HDPE typically cleaved in a specific manner and its thermal decomposition produced three types of aliphatic hydrocarbons: α, ω-diene, α-alkene, and n-alkane.

Alkanes and alkenes were the main emitted products. The major compounds observed during the degradation contained 9 and 10 carbons.

The mechanism of thermal decomposition has been postulated in previous studies. [36][37][38][39] according to the authors, the thermal decomposition of PE is a radical chain reaction. It can be separated into 3 steps, comparable to the polymerization of vinyl compounds, with an initiation step, a depropagation step and a termination step. Minor amounts of cyclic compounds were also detected; in decreasing order, we found cyclopropane, cyclopentene, toluene, benzene, cyclohexene, cyclohexane and cyclopentane.

For this work, we will focus on the major alkane and alkene degradation products from C4 to C11. Table 4-16 shows the retention time of the mean peaks observed in the mass spectrum and the name of the corresponding fragments. The polymer chain breaks preferentially at the branches. This outcome relies on the branched structure of copolymers [40][41][42] . Ethylene-octene copolymers display hexyl branches (C6). As a result of the scission of these branches, the C6 fragments increased significantly in the mass spectra. According to the mechanism proposed in Scheme 4-5, these fragments result from the α scissions on a tertiary carbon atom.

Figure 4-19 clearly showed that C6 compound (hexane and 1-hexene cumulated amounts), compared to other fragments, increase significantly as the octene content increases in the copolymer. We therefore considered that the C6 compounds are the main signature of ethylene-octene copolymers. Indeed, the thermal decomposition of ethylene-hexene copolymers leads to more butane and 1-butene signals in the corresponding spectra and C4 content increases significantly as the hexene content increases in the copolymer. This C4 fragments were the result of -scissions on the butyl branch and were obtained in a similar way as C6 fragments previously proposed for ethylene-octene copolymers.

The scission mechanism proposed by Haney [36] supports the results observed with a main formation of C4 compounds for ethylene-hexene copolymers and C6 compounds for ethylene-octene copolymers.

Based on the strong correlation between the degradation products measured by TGA-IST16-GC-MS and the type of comonomer inserted into LLDPE, this method can provide very valuable information on the nature of branching. The sensitivity of this method is obviously high as low amount of comonomer, down to 0.5 mol% could be detected. Based on these results, our TGA-IST16-GC-MS system was calibrated and use in the following to efficiently quantify the amount of comonomer for unknown samples.

Figure 4-21: Emission profiles from the TGA analysis of ethylene-hexene copolymers (sample 5-8). The ordinate axis corresponds to the peak's intensities in the gas chromatograms for each component.

Quantitative calibration

Since 1-hexene and hexane could be separated in the mass spectrum of ethylene-octene copolymer, two separate calibrations were performed, one from the hexane fragments and the other from 1-hexene fragments.

Many parameters can affect the polymer degradation including the mass of samples, the contamination and the cleanliness of the system particularly of the transfer line. Thus, in order to normalize the peak intensities of hexane and 1-hexene, we used the peak of decane and 1-decene as internal standards, respectively. This assumes that decane and 1-decene were produced by the polymer backbone degradation independently of the comonomer content. Then, the area ratios obtained were plotted as a For ethylene-octene copolymers (samples 2-4), two curves were created. In Figure 4-22a, the curve based on alkane detection displays and the curve based on alkene detection displays versus the mole fraction of octene inserted in the copolymer and measured by NMR. Sample 1 was used as a reference and provided the background signal value of hexane and 1-hexene fragments for an unbranched polymer.

For ethylene-hexene copolymers (samples 5-8), only one curve was created because the butane and the 1-butene fragments were not resolved by GC-MS. The curve in Figure 4-22b shows versus the mole fraction of hexene inserted in the copolymer and measured by NMR. Sample 1, which had no branching, was again used as a reference. The calibration curves show, that for low amounts of octene or hexene comonomers, the method is very sensitive because the slope of the curve is very high. This slope decreases and apparently ends up reaching a plateau beyond 20 mol% of hexene.

CONCLUSIONS

The present paper describes a novel approach based on thermal degradation for the assessment of nature and degree of SCB in LLDPE samples. This method was applied for two classes of prepared homemade LLDPE. Ethylene-hexene and ethylene-octene copolymers were synthesized with a metallocene complex catalyst and characterized by HT-SEC and TREF to assess their homogeneity. SCB or comonomer content were measured by NMR. The TGA-IST16-GC-MS coupling system, working on an inert atmosphere, was used to provide further details on LLDPE composition. Its main advantage is that various LLDPE decomposition products can be identified and quantified despite the very complex decomposition mechanism. As previously described, alkane, alkene and diene fragments were observed from LLDPE degradation. In addition, we also observed aromatic compounds like benzene, toluene and cyclopentene.

This novel approach allows determining the nature and total content of SCB in copolymers. We demonstrated that during the degradation of LLDPE, a major detection of C4 fragments or C6 fragments was respectively signature of ethylene-hexene or ethylene-octene copolymers. With the help of a calibration created during this work, comonomer content could be determined. This method appears as a good substitute to NMR analysis that requires toxic solvent and long dissolution times.

The recycling process of plastic waste is of increasing economic and ecological importance. It is an objective that the recycling industry is trying to achieve. In order to identify different LLDPE to be recycled, the proposed approach can be effectively applied in a recycling process after specific separation step (flotation, magnetic, eddy currents…). LLDPE prepared by metallocene catalysis are of course simple samples with low chemical composition distribution and low molar mass dispersity. They have served as effective models for developing and validating the method. The study could be now generalized to more complex polyolefin like LLDPE resulting from heterogeneous catalysis or mixtures of different type of LLDPE as we can find during recycling process.

Thanks to the development in polymerization chemistry based on the design of single-site catalysts, and advances in polymer engineering with the use of cascade reactor systems, the properties and performances of polyolefins can be tuned and optimized for specific applications. The chains structures of tailor-made polyolefin have become even more complex. These remarkable advances present great challenges for characterization. Indeed, the measurement of average chemical content by NMR and density by melt flow index is not enough to predict the polymer properties. We should access to complete molar mass distribution (MWD) and chemical composition distribution (CCD) of polyolefins.

To achieve these objectives, original tools, invented by talented researchers such as Monrabal, Soares, All these fractionation techniques are based on the separation of polymer chains by crystallization or by interaction on a column. These techniques are relative techniques, which must be calibrated by correlating the crystallization or elution temperature with the comonomer content in order to obtain quantitative information.

To achieve these objectives, several sets of ethylene/α-olefin copolymers synthesized with metallocene catalysts under controlled conditions were prepared and used as standard. Eighty-eight LLDPE samples 1-The effect of molar mass on separation was studied. As reported by several researchers, a low molar mass has an impact on the elution time, but we also observed that a very high molar mass (higher than 10 6 g mol -1 ) also has an impact on the elution time. The specific organization of crystallites in the case of high molar masses shifts the elution temperatures upwards, especially for CEF.

-

The TGIC profiles of the LLDPE models have been compared to that of CEF profiles. The TGIC chromatograms were broader than the CEF profiles, indicating a poorer resolution mainly for low comonomer contents. Conversely, TGICs offer a wider analytical range.

3-The CCD analysis range derived from SGIC was broader than those obtained with CRYSTAF. The physical principles underlying the two methods are different: CRYSTAF is based on crystallization and SGIC on polymer adsorption-desorption. Consequently, SGIC is applicable to the whole composition range of LLDPE (from 0 to 100% of comonomer), whereas crystallization-based techniques are limited to semi-crystalline components.

4-A new thermodynamic framework to understand the fractionation mechanism in TGIC was proposed.

Using simulation methods, we have discussed the enthalpic and entropic interactions between LLDPE chains and the graphene column. The adsorption energy of various samples of LLDPE on graphene at different temperatures was calculated, showing that the steric hindrance of the comonomer (or SCB) reduces the number of contacts between the polymer chain and graphene and thus the enthalpy of adsorption. When the density of the comonomer is low, the measured adsorption energy remains negative (favorable for adsorption) above the elution temperature of the polymer. However, for this polymer, an increase in persistence length is observed during adsorption. The increase in persistence length would decrease the conformational entropy of the polymer and thus counteract the favorable adsorption energy.

This entropic contribution could explain the narrowing of the peak observed experimentally for a low density of comonomers, at a high elution temperature. This model accurately reproduced the elution temperatures measured experimentally by the TGIC.

We have shown that fractionation techniques are unique ways to access distribution in chemical composition. However, these separation techniques are considered as a demanding task due to the requirement of toxic solvents and high temperature for sample dissolution. In this context, care must be taken to ensure that the polymer is properly dissolved and to avoid any degradation. This delicate preparation requires long analysis times. It was of real interest for research and analysis laboratories to develop in parallel faster and simpler techniques to access the chemical composition.

The LLDPE models, which are well defined and well characterized, have thus been used for the development of alternative methods for measuring chemical composition. Spectrometry techniques, widely used by research laboratories, have been considered as alternative tools. We are particularly interested in FTIR and in the coupling of thermal analysis to mass spectrometry.

FTIR has been used for many years for polyolefin characterization. The development of chemometrics (mathematical and statistical tools to obtain information from a large amount of data) allows a new approach in the exploitation of the obtained spectra. Chemometrics makes it possible to obtain information on polymers by observing all the significant wavelengths of the information sought. We have shown that it can be efficiently applied both in the mid-infrared and near-infrared on LLDPE but also on other types of copolymers such as ethylene/butadiene which have complex microstructures. Our model polymers have been used to build chemometric methods, applied to IR spectra, for the prediction of comonomer content in unknown samples. As they are fast, simple and without sample preparation, these chemometric methods have shown their great potential to characterize polymers.

Lastly, the coupling of thermo-gravimetric analysis (TGA) with mass spectrometry has revealed its full potential for understanding the structure of LLDPE. The coupling allowed, by thermal degradation, to obtain significant fragments of the analyzed LLDPE which are then identified by mass spectrometry. This method allows the identification of the type of α-olefins used during the synthesis.

This thesis work shows on the one hand the unique contribution of thermal fractionation techniques to access the CCD and on the other hand the power of spectrometry to quickly obtain the average chemical composition of olefin copolymers.

All these methods developed allow us to better identify the structure of the polyolefins synthesized in our laboratory, to better understand the chemical mechanisms that take place during the different stages of polymerization, and to efficiently enhance the polymerization processes. These tools will benefit the current and future research topics of the laboratory, the research work of my fellow researchers and my industrial partners who wish to better understand the materials they have produced and used.

Beyond the synthesis of our LLDPE models, the main contributions of this thesis in the field of polyolefin characterization are summarized below and in Figure C2: A complete table of calibration curve for all fractionation techniques and for a wide range of LLDPE (propylene, hexene, octene, octadecene, norbonene) is now available.

Finally, our well-defined LLDPE models were also used to develop original spectrometric methods.

The combination of FTIR and chemometrics has proven to be a rapid method for measuring the comonomer content in polyolefins.

The coupling of TGA and mass spectrometry has proven to be a valuable tool to access the type of comonomer.

Figure C2: Overview of the thesis work carried out from the synthesis of different types of ethylene/αolefin copolymers with a metallocene catalyst to the calibration of thermal fractionation techniques.

This work has opened up new routes for analysis of polyolefins.

Other copolymers are currently being studied by thermal fractionation techniques:

Ethylene/vinyl acetate copolymers Ethylene/vinyl acetate (EVA) copolymers are important commercial polymer materials. Their properties can be adjusted according to the vinyl acetate content, so it is necessary to precisely quantify the comonomer content. Different methods can be used to analyze the average chemical composition of EVAs such as NMR, TGA and FTIR. In future work, a new method will be developed to measure by thermal fractionation the chemical composition and especially its distribution. TGIC appears to be appropriate for separating EVA copolymers according to their composition.

Ethylene/butadiene copolymers Ethylene/butadiene copolymers are elastomers obtained from simple monomers but have a complex and original structure. Indeed, the insertion of butadiene leads to unsaturated fragments (internal trans double bonds and vinyl branches) as well as 1,2-cyclohexyl rings. The properties of these elastomers are directly related to their composition and it is therefore important to fully characterize their chemical composition.

The ability of these fragments to interact with the TGIC column has not yet been demonstrated.

The ability to use other analytical techniques to measure the comonomer content in LLDPE is being explored using our LLDPE models:

Rheology

Rheology is generally used to obtain information about LCB on polyolefins but few publications describe the effect of SCB on rheological behavior. Our LLDPE models will be measured by rheology to assess the impact of short chain branching. This work will provide calibration curves for rheology and show that it is possible to predict the co-monomer content in LLDPE using rheological measurements. The first measurements of the branch contents predicted from the zero shear viscosity analysis of the samples are in good agreement with those evaluated by NMR.

Raman spectroscopy

Raman spectroscopy is a powerful technique for qualitative and quantitative analysis, it is non-destructive and can be integrated into industrial applications. It offers several advantages over other conventional spectroscopic techniques, for instance Raman spectra have intense and well resolved spectral peaks.

These peaks often correspond to fundamental transitions and thus provide direct and easy-to-interpret chemical information. Our LLDPE models will be analyzed by Raman spectroscopy in order to construct a new PLS model for the prediction of comonomer content in unknown samples. The use of statistics and chemometrics is also essential to the success of this project.

Applications

Industrial applications

The methods developed in this work have been used regularly for industrial partners to better understand the materials they use or synthesize. The comonomer content for LLDPE as well as the PE or PP content in the case of a mixture are recurrently measured by thermal fractionation techniques and through the calibrations set up. For example, the methods have been applied as part of analytical services for various industrial companies to characterize polyolefin cosmetic bottles, electrical cable jacketing, and food and medical packaging.

Plastic in ocean

Working in the polymer field is very fascinating and I really believe in the benefits of plastics for our future society. I also believe that we have not been able to manage our waste, especially plastics, and that it is now high time to change our behavior. Therefore, it is quite natural that I am also involved in the issue of plastics pollution in the oceans.

The characterization of plastic marine debris is necessary to better understand their fate in the environment and their interaction with organisms. These marine debris are mainly composed of polyolefins. In this field, I am working on the characterization of plastic debris collected in the subtropical gyre of the north Atlantic during the "Expedition 7th Continent" maritime campaign. [1][2][3] These thesis works will most likely find new and concrete applications to face these societal challenges.

  KEYWORDSPolyethylene -LLDPE -SEC -TREF -CRYSTAF -CEF -TGIC -SGIC -thermal fractionation techniques -DSC -polyolefins characterization -FTIR spectroscopy -chemometrics TITRE Caractérisation des polyéthylènes : des techniques de fractionnement thermique à la spectrométrie. RESUME Quatre-vingt-huit copolymères d'éthylène avec des -oléfines (propène, hexène, octène, octadécène et norbornène) ont été synthétisés en utilisant les complexes Et(Ind)2ZrCl2 et (nBuCp)2ZrCl2 activés par le méthylaluminoxane. Ces complexes ont permis d'obtenir une large gamme de polyéthylène haute densité (PEHD) et de polyéthylène basse densité linéaire (PEBDL) de compositions chimiques variées. Leurs teneurs moyennes en comonomères ont été déterminées par la RMN 1 H et du 13 C. Les PE modèles (HDPE et LLDPE) ont été analysés par chromatographie d'exclusion stérique haute température et ont montré une distribution de masse molaire étroite comme prévu avec des catalyseurs mono-site. Ces polymères modèles ont été utilisés pour créer une méthode de mesure du degré de ramification à longue chaîne (LCB) dans le PE. Le détecteur de viscosimétrie de la SEC a été utilisé pour déterminer le LCB en mesurant le rapport de la viscosité intrinsèque du polymère ramifié et d'un polymère linéaire. Une approche originale a été proposée pour étudier la ramification à chaîne courte (SCB) dans le LLDPE et corriger leurs effets dans la mesure du LCB. Les mesures concordaient bien avec les études RMN. Comme ces copolymères ont une composition chimique homogène, ils ont été utilisés comme étalons pour calibrer les techniques de fractionnement thermique : TREF, CRYSTAF, CEF, TGIC et SGIC. Ces travaux ont fourni des courbes d'étalonnage pour toutes les techniques de fractionnement existantes, pour différents types de comonomères et pour une large gamme de teneurs en α-oléfines. Ces courbes d'étalonnage sont rassemblées pour la première fois dans un travail unique. Elles ont été utilisées et seront utilisées pour accéder à la distribution de composition chimique (CCD) de copolymères hétérogènes.

Figure 1 :

 1 Figure 1 : Complexe Et(Ind)2ZrCl2 utilisé pour la synthèse des copolymères

Figure 2 :

 2 Figure 2 : Familles de copolymères synthétisés dans cette étude

Figure 3 :

 3 Figure 3 : Chromatogramme CEF pour un échantillon de composition chimique hétérogène (a) et distribution de composition chimique obtenue grâce aux étalonnages mis en place (b). Suite à la présentation de cette première étape d'étalonnage des différentes techniques de fractionnement, trois publications soumises et acceptées dans des journaux à comités de lecture illustrent la fin du chapitre. Elles (1) décrivent l'étalonnage de la TREF et son application à l'analyse de copolymères hétérogènes en composition chimique obtenus par catalyse Ziegler-Natta, (2) comparent les techniques CRYSTAF et SGIC et (3) discutent des interactions enthalpiques et entropiques qui entrent en jeu entre les chaines de LLDPE et la colonne en graphène utilisée en TGIC. Je suis auteur principal de la première publication et co-auteur des deux suivantes.

  molecular weight polyethylene LLDPE models This term will be frequently used throughout the document and includes all ethylene-αolefin copolymers synthesized to calibrate analytical techniques Symbols Weight-average number of branch per molecule : FROM THERMAL FRACTIONATION TECHNIQUES TO SPECTROMETRY

  materials are mixtures of various chains called distributions. There can be several types of distributions in the same material: chain length distributions or molar mass distributions, chemical composition distribution and structure distribution. Furthermore, as semi-crystalline polymers, polyolefins are insoluble in any solvent at room temperature which makes their analysis trickier than for most other polymers. The analysis of such complex entities cannot be limited to the use of a single characterization technique but must involve an array of several techniques. The C2P2 laboratory has gradually acquired and expanded its analytical capacity with coherent and complementary techniques which are summarized in the Figure below. The main objective of this thesis work was to extend the analytical capabilities of the laboratory with modern tools and new characterization methods. Part of this work lies on the implementation of original fractionation techniques for polyolefin characterization, to develop state of the art methods and to use these techniques to their maximum capacities. These techniques, based on the ability to separate polymer chains in solution according to their composition, belong to a specific part of the liquid chromatography family. Liquid chromatography is a technique widely used for the characterization of polymers. Indeed, the modularity of this analytical technique regarding polymer elution possibilities allows obtaining a great deal of information such as the distribution of molar masses and of the chemical composition of polymer chains. Several liquid chromatography techniques were used in this work for the characterization of LLDPE by various separation modes.

Figure 1 - 1 :

 11 Figure 1-1: Distribution of demand for plastics in Europe in 2018 (a) and prediction of the evolution of polymer production in giga ton per year.(b) Source: PlasticsEurope Market Research Group (PEMRG) A polymer is a set of macromolecules formed by the covalent linking of a large number of repeating units called monomers. There are different families of synthetic polymers that can be characterized by their properties. These properties are defined by both the monomer chemistry and the molecular organization in the polymer chain. First, polymers can be classified into two vast families distinguished by their heat behavior: thermosets and thermoplastics.

Figure 1 - 2 :

 12 Figure 1-2: Distribution of European plastics demand by type in 2017. Source: PlasticsEurope Market Research Group (PEMRG)

- 4 :

 4 Figure 1-4: Polypropylene tacticity -Isotactic (iPP), methyl groups (CH3) arranged on one side of the carbon chain -syndiotactic (sPP), alternating methyl group (CH3) arrangement -atactic (aPP), irregular methyl group (CH3) arrangement aPP is amorphous and has almost no commercial value. Both iPP and sPP exhibit high melting temperatures due to the organization of their chains. They are both semi-crystalline. sPP can only be produced with specialized metallocene catalysts, resulting in expensive production. In 1988, Ewen et al.

Figure 1 - 5 :

 15 Figure 1-5: Chromium catalyst • The Ziegler-Natta catalysis process was developed by Karl Ziegler and Giulio Natta in the 1950s.

Figure 1 - 9 :

 19 Figure 1-9: Schematic structures of methyaluminoxane

Figure 1 - 10 :

 110 Figure 1-10: Generalized structure of a metallocene catalyst with M = Ti IV , Zr IV , Hf IV and X = MAO-Me or B(C6F5)4.

1. 5 . 1 . 2

 512 Conformational structure (level II) The macromolecular chain is characterized by a local conformation which corresponds to the relative orientation of the lateral groups of the chains. The local conformation depends on the local covalent structure and the interactions between atoms. It results from the possibilities of rotation around the covalent bonds as a function of the steric hindrance of the various groups attached to the chain. A second characteristic of macromolecular chains is the overall chain conformation. PE macromolecular chains can adopt two global conformations: linear or random coil (Figure 1-11).

Figure 1 - 11 :

 111 Figure 1-11: Global chain conformation of polyethylene; linear conformation (a), random coil conformation (b)

1. 5 . 1 . 3

 513 Crystalline structure (level III) The crystalline structure of polyethylene is formed by the periodic assembly of chains having a regular conformation, linked together by Van Der Walls bonds (Figure 1-12).

Figure 1 - 12 :

 112 Figure 1-12: Schematic representation of the crystal structure of polyethylene.

Figure 1 - 13 :

 113 Figure 1-13: Spherulite structure showing the molecular level of the chain arrangements and the alignment of polymer chains.

Figure 1 -

 1 Figure 1-15: DSC thermogram of an HDPE with the second heating cycle (red) and the cooling cycle (blue).

Figure 1 - 16 :

 116 Figure 1-16: Molar mass distribution and position of the average molar masses. 1.5.3.3 Higher average molar masses: ,

Figure 1 - 17 :

 117 Figure 1-17: Molar mass distribution (red) and Mark Houwink plot (blue) of a broad polyethylene sample. The slope of the linear fitting of the Mark Houwink curve gives α (0.669) and the intercept gives log K (-3.362).

Figure 1 - 18 :

 118 Figure 1-18: Schematic representation of a TREF experiment with two separation cycles. The column connected to a pump and to the IR detector is filled with an inert support like glass beads or stainless-steel shot.First, the sample is dissolved in a suitable solvent (generally TCB or DCB) at high temperature and then introduced into a column. A slow decrease in temperature causes the polymer to crystallize. During this step, the polymer is deposited in a less and less crystalline layer on a solid support constituting the stationary phase of the column. Although the polymer is separated into layers of different crystalline structures at the end of this step, TREF requires a second temperature cycle. During this step, the polymer fractions with different crystallizabilities are dissolved by increasing the temperature. As the temperature increases, the solvent elutes the different fractions in increasing order of crystallinity.Soares and Hamielec

Figure 1 -

 1 19a) is obtained, representing the concentration of the polymer remaining in solution as a function of the temperature. The first derivative (blue curve in Figure 1-19a) of this curve represents the variation of the polymer concentration in the solution as a function of the temperature.

Figure 1 - 19 :

 119 Figure 1-19: Schematic representation of a CRYSTAF experiment. The device is similar to that of TREF without the need for a column. Cumulative curve (orange) and CCD curve (blue) (a).

Figure 1 - 21 :

 121 Figure 1-21: Schematic representation of an SGIC experiment.

  -22) consists of an isocratic pump, an autosampler, an adjustable temperature oven and detectors(IR and viscometer). The experiments are similar to those of CEF, with two analytical cycles. Initially, the polymer solution is injected into the top of the graphite carbon column at high temperature. Then, separation can start with the cooling cycle in which the polymer chains with low α-olefin content are adsorbed first at the higher temperatures. As the column temperature decreases, the chains with higher amounts of α-olefin are adsorbed. Conversely, when the temperature increases, during the second cycle, the chains can be desorbed and eluted from the column according to their chemical composition. An on-line IR detector measures the concentration of polymer eluted from the column. Finally, since the fractionation mechanism is not based on polymer crystallization, three main advantages can be highlighted compared to crystallization techniques: (1) the copolymers are separated over a wider range of composition, (2) the analysis time is reduced by adsorption and desorption processes which are quicker than crystallization, (3) there are no co-crystallization effects.

Figure 1 - 22 :

 122 Figure 1-22: Schematic representation of a TGIC experiment. The device is similar to that of CEF with a graphite carbon column instead of an inert support column.

Figure 2 - 1 :

 21 Figure 2-1: Complex Et(Ind)2ZrCl2.Figure 2-2: Complex (nBuCp)2ZrCl2.

Figure 2 - 3 :

 23 Figure 2-3: Copolymers synthesized by coordination polymerization.

Figure 2 - 4 :

 24 Figure 2-4: Reactor and synthesis conditions used to obtain our copolymer models.

Figure 2 - 5 :

 25 Figure 2-5: Temperature program used for the DSC SIST (a) and DSC thermogram during heating after SIST treatment for the sample obtained with the standard protocol (red curve) and the sample obtained using the injection chamber (blue curve) (b).

Figure 2 - 6 :

 26 Figure 2-6: Influence of comonomer concentration in the reactor on their incorporation in ethylenepropyle, ethylene-hexene, ethylene-octene and ethylene-octadecene copolymers.

  : FROM THERMAL FRACTIONATION TECHNIQUES TO SPECTROMETRY 2-84

by 1 H

 1 NMR and13 C NMR spectroscopy.NMR experiments were performed in the NMR Polymer Service of the Institut de Chimie de Lyon (FR5223)with the friendly and expert support of Fernande Da Cruz-Boisson.

  CHARACTERIZATION OF POLYETHYLENES: FROM THERMAL FRACTIONATION TECHNIQUES TO SPECTROMETRY 2-852.3.1 QUANTIFICATION BY 1 H NMRThe mole fraction of the comonomer in the copolymers was measured by proton NMR on a Bruker Avance III 400 spectrometer operating at 400MHz.Analytical conditions:• Analysis temperature = 100 ° C,• 3: 1 volume mixture of 1,2,4-trichlorobenzene and toluene-d8,• Concentration: 10 mg ml -1 ,• 5 mm QNP (Quadrupole Nuclear Probe) probe,• Calibration: chemical shifts of CHD2 at 2.185 ppm.The samples were dissolved in the NMR tube by heating the tube in a heating block at 150°C for 2 hours.

Figure 2 -

 2 Figure 2-7: 1 H NMR spectrum of an ethylene-hexene copolymer in TCB/toluene-d8 at 373 K.

The 1 H

 1 NMR spectrum is composed of only two main signals. The methyl branches at 0.9 ppm can be easily distinguished from the proton signals of the ethylene backbone at 1.3 ppm (Figure 2-7). Regarding propylene, octene and octadecene comonomers the signal assignments are similar. CHARACTERIZATION OF POLYETHYLENES: FROM THERMAL FRACTIONATION TECHNIQUES TO SPECTROMETRY 2-86

Figure 2 -

 2 Figure 2-8: 1 H NMR spectrum of an ethylene-norbornene copolymer in TCB/toluene-d8 at 373 K. After integrating the spectral regions with Topspin software (Bruker), the mole fractions of the comonomer were calculated by applying the following equations inTable 2-2.

Figure 2 -

 2 Figure 2-9: 13 C NMR spectrum of an ethylene-hexene copolymer (9 mol% of hexene) and peak assignments in TCB/toluene-d8 at 373 K (b). 1: 1B4; 2: 2B4; 3: HEH; 4: EEHH; 5: EEHE; 6: 3B4 EHH; 7: 3B4 EHE; 8: EEE; 9: EEEH; 10: HEEH; 11: 4B4; 12: EEHE; 13: 4B4 EHH + EEHH + HEH; 14: CH EHH; 15: CH EHE; 16:EHH.

Figure 2 - 10 :

 210 Figure 2-10: Calibration curves for HT-SEC with a curve fit of order 3. Conventional calibration with PS standards (CC PS, red curve), conventionnal calibration with PE standards (CC PE, red curve) and universal calibration with PS standards (UC, blue curve). PLgel Olexis columns (inner diameter: 7.5 mm, length: 300mm, particle size: 13μm) from Agilent were used. The various calibration curves used in this work are plotted in Figure 2-10. A curve fit order of three was used to correlate the molar mass of standards and the elution time. We observed that the calibrations with PS and PE standards are distinct, showing that the steric hindrances of PS and PE, in 1,2,4-TCB are different.

Figure 2 - 11 :

 211 Figure 2-11: Repeatability of average molar masses and dispersity obtained by light scattering (square) and conventional calibration (circle) for a sample of LLDPE. The data were acquired and processed by light scattering to obtain the absolute molar mass as well as by conventional calibration (created with narrow and certified polyethylene standards) where only the signal from the refractometer was used.

  dissolution step. To limit degradation, an antioxidant (BHT, Butylhydroxytoluene or 2,6-Di-tert-butyl-4methylphenol) was added in the solvent. This degradation affects the values of the molar masses. Thus, to optimize the dissolution time of the samples, an LLDPE was subjected to high temperature (150 °C) for several hours. This sample was injected regularly, and we monitored the evolution of the molar masses as a function of the time spent at 150 °C (Figure2-12).

Figure 2 - 12 :

 212 Figure 2-12: Effects of dissolution time at 150°C on the molar masses and dispersity for an LLDPE sample. The molar masses are stable (inside the measurement error) for up to ten hours at 150 °C, afterwards the values measured decrease significantly. The M w values are more impacted, meaning that the long chains are degraded first and become more breakable.

D

  CHARACTERIZATION OF POLYETHYLENES: FROM THERMAL FRACTIONATION TECHNIQUES TO SPECTROMETRY2-96

  -12).

Figure 2 -

 2 Figure 2-13: Mark-Houwink-Sakurada plot for 5 PE samples and a linear reference polymer (black line). The dark blue curve is an HDPE from the Ziegler-Natta catalyst, LDPE1 is LPDE 165 from Exxon Mobil, LDPE2 and LDPE3 are LDPE3020 and LDPE Lupolen 3020, respectively, from LyondellBasell. BRPE0 and BRPE14, linear and branched, respectively, are reference materials.

2- 9 .

 9 It is plotted for each slice of the distribution with the blue curve in Figure 2-14. The next step was the calculation of the branching factor (g) obtained with Equation 2-11 and 0.75 as the value for . Afterwards, Equation 2-12 allowed the calculation of the number of branches (Bw), plotted by the red curve in Figure 2-14. Last but not least, the branch frequency (λ) was calculated with Equation 2-13 and plotted for each slice of the distribution (green curve).

Figure 2 - 14 :

 214 Figure 2-14: Molar mass distribution (grey dash) and viscometer parameters calculated with MHS equations for sample LDPE2.

Figure 2 -

 2 Figure 2-15: 13C NMR spectrum of an HDPE EC01 (0 mol%) and ethylene-hexene copolymer IB10 (0.1 mol% of hexene) and EC12 (2.5 mol% of hexene) in TCB/toluene-d8 at 373 K and assignments of short chain branching (SCB) and long chain branching (LCB).

Figure 2 -

 2 15 shows that the MHS plot for various LLDPE shifts downwards as the comonomer content increases. All curves are linear in the low molar mass portion of the distribution and tend to curve slightly for samples EC01 and CHARACTERIZATION OF POLYETHYLENES: FROM THERMAL FRACTIONATION TECHNIQUES TO SPECTROMETRY 2-105 EC12 in the high molar mass portion, highlighting that LCBs are prevalent in high molar mass chains for these samples.

Figure 2 - 16 :

 216 Figure 2-16: Mark-Houwink-Sakurada plot for six LLDPE samples with a linear PE reference (black line). [η] is the intrinsic viscosity in dL g -1 , and M is the molar mass of the polymer. K and α values were calculated and are reported inTable 2-8.

Figure 2 - 17 :

 217 Figure 2-17: Correction of SCB impact on viscosity. The curve simulates a linear reference without LCB, fitted with the value of viscosity in the low molar masses part of the distribution and extrapolated for high molar masses. For the sake of clarity, all the samples are not plotted in the figure.

Figure 2 - 108 Figure 2 - 18 :

 2108218 Figure 2-18 and a calibration curve using a first order polynomial that fits the experimental data was drawn.

  that are installed in our laboratory. Prior to this work, these techniques were used only as comparison techniques with which samples profiles were qualitatively compared with each other. This work will allow quantitative measurements of the comonomer content through the establishment of calibrations. OF COMONOMERS IN THERMAL BEHAVIOR OF LLDPE BY DSCVarious properties of polymers can be quantitatively determined using thermoanalytical techniques.

Figure 3 - 1 :

 31 Figure 3-1: Typical water, indium and zinc DSC thermograms used for the heat flow and temperature calibrations.

3. 1 . 3

 13 EFFECT OF MOLAR MASS ON DSC PROFILES DSC was used to measure the effect of comonomer content on LLDPE thermal behavior. Firstly, this part investigates the influence of the molar mass of the copolymers on the melting temperature and enthalpy, expressed in term of crystallinity according to Equation 3-1, measured by DSC. It aims at correlating the thermal behavior of copolymers with their variation of molar mass. Commercial samples of HDPE from Polymer Standard Service (PSS, Germany), certified for molar mass with a narrow dispersity (around 1.1) usually used to calibrate our HT-SEC instrument, were analyzed. They ranged from 750 to 7300 g mol -1 .

Figure 3 - 2 :

 32 Figure 3-2: Effect of molar mass on the melting temperature of HDPE with various molar masses from 750 g mol -1 to 7 300 g mol -1 . DSC thermogram during the second heating with a rate of 10°C min -1 under nitrogen atmosphere.

  temperatures were only affected by the comonomer content. Their thermal parameters (temperature and enthalpy of melting, temperature and enthalpy of crystallization, percent crystallinity) are reported in Appendix 1. Several thermograms of the various types of copolymers are plotted in Figure 3-3.

Figure 3 - 3 :

 33 Figure 3-3: DSC thermograms of the second heating with a rate of 10°C min -1 under nitrogen atmosphere for LLDPE with various comonomer contents. The obtained melting peaks are unimodal and quite narrow, showing that the copolymers are homogeneous in chemical composition. For all types of copolymers the melting temperature decreases as the comonomer content increases in the backbone.

Figure 3 - 4 :

 34 Figure 3-4: LLDPE with three different comonomer contents (the branches are represented as incurved vertical lines) resulting in three lamellar thicknesses l1, l2, and l3. High comonomer content (a), medium comonomer content (b) and low comonomer content (c). The evolution of the melting peak (top of the peak) was plotted, in Figure 3-5, as a function of the comonomer content expressed in mole percentage (a) and mass percentage (b) for the different types of copolymers.

Figure 3 - 5 :

 35 Figure 3-5: Temperature of the melting peak obtained by DSC during the second heating for different comonomer contents expressed in mole percent (a) and mass percent (b) for different types of comonomers. Heating rate of 10°C min -1 under nitrogen atmosphere.

Figure 3 - 6 :

 36 Figure 3-6: Calibration curves based on temperature of the melting peak obtained by DSC during the second heating for different comonomer contents expressed in mole percent for different types of comonomers. Heating rate of 10°C min -1 under nitrogen atmosphere.

Figure 3 - 7 :

 37 Figure 3-7: Temperature and enthalpies of melting and crystallization of ethylene-norbornene copolymers with various norbornene content (mol%). Second run, heating rate of 10°C min -1 under nitrogen atmosphere.

  CHARACTERIZATION OF POLYETHYLENES: FROM THERMAL FRACTIONATION TECHNIQUES TO SPECTROMETRY3-125 comonomer content and produced additional ethylene-hexene copolymers with very low comonomer contents (< 1 mol%) to complete the initial linear calibration curve. The plots reported in Figure3-8show that an empiric calibration using a third order polynomial fils well the experimental data. It is even more necessary to have a good fit for low comonomer content portion and for the calibrations of melting and crystallization enthalpy.

Figure 3 - 8 :

 38 Figure 3-8: Temperature and enthalpies of melting and crystallization of ethylene-hexene copolymers with various hexene content (mol%). Second run, heating rate of 10°C min -1 under nitrogen atmosphere.

Figure 3 - 9 :

 39 Figure 3-9: Illustration of the temperature at the top of the peak (Tm ), the onset and the endset temperature during a heating step.

3. 3

 3 CALIBRATION OF THERMAL FRACTIONATION TECHNIQUES 3.3.1 ANALYTICAL CONDITIONS Firstly, the temperature rising elution fractionation (TREF) and the crystallization temperature analysis fractionation (CRYSTAF) techniques were carried out to characterize our LLDPE samples in terms of chemical composition distribution (CCD). A CRYSTAF-TREF 300 model manufactured by Polymer Char S.A.(Valencia, Spain) was used. Secondly, crystallization elution fractionation (CEF) and thermal gradient interaction chromatography (TGIC) experiments were performed using a CEF/TGIC instrument from PolymerChar (Valencia, Spain). Afterwards, our copolymer models were employed to calibrate an innovative solvent gradient interaction chromatography (SGIC) method in the framework of a collaboration with the Fraunhofer Institute for Structural Durability and System Reliability, Plastics Division, Department of Materials Analytics, Darmstadt, Germany. The analytical conditions are described in the following parts.3.3.1.1 TREF analytical conditionsExperimentally, about 80 mg of the sample was dissolved at high temperature (150 °C) in 20 mL of 1,2,4trichlorobenzene (1,2,4-TCB) stabilized with 2,6-di(tertbutyl)-4-methylphenol. 0.5 ml of the sample solution was loaded into the TREF column of 9 mm i.d. and 15 cm length at 120 °C. The temperature was slowly decreased to 35 °C at a rate of 0.5 °C min -1 to allow the polymer to crystallize. A second cycle was used to quantify those fractions by pumping solvent while the temperature was being increased (1 °C min - 1

3. 3 . 1 . 2

 312 CRYSTAF analytical conditions 20 mg of the sample was dissolved at 150 °C in 30 mL of 1,2,4-TCB stabilized with 2,6-di(tertbutyl)-4methylphenol. After the dissolution of the sample, the temperature of the solution was stabilized at 110 °C and then decreased at a rate of 0.1 °C min -1 to 25 °C. At regular intervals, a part of the solution is sent to the IR detector thermostatically controlled at 150°C to follow the concentration of the soluble part. CRYSTAF technique has been patented by The Dow Chemical Company and manufactured and marketed by PolymerChar. The different parts of the instrument, which can also be used in TREF mode, are shown in Figure 3-10.

Figure 3 -

 3 Figure 3-10: CRYSTAF-TREF instrument overview. CRYSTAF and TREF methods can be performed in the same instrument. CRYSTAF analyzes the sample during the crystallization step and TREF during the dissolution step.

Figure 3 - 11 :

 311 Figure 3-11: Temperature program applied to the CEF method.

Figure 3 - 12 :

 312 Figure 3-12: Temperature program applied to the TGIC method.

  sample. Polymer crystallizing at a lower temperature will also elute at a lower temperature for thermal fractionation techniques based on crystallization (TREF and CEF). Separation by TGIC and SGIC also leads to a similar behavior, the more branched chains are eluted first followed by less and less branched ones which increasingly interact with the Hypercarb column. An overall representation of the separation for all the techniques is shown schematically inFigure 3-13.

Figure 3 - 13 :

 313 Figure 3-13: Principle of polymer chain fractionation according to their comonomer content for TREF, CRYSTAF, CEF, TGIC and SGIC. These techniques aim to measure the CCD in polyolefins.

Figure 3 -

 3 Figure 3-14 shows various measurement profiles obtained by TREF which illustrate the evolution of the elution temperature of copolymers as a function of comonomer content.

Figure 3 - 14 :

 314 Figure 3-14: TREF profiles of individual copolymer models with various comonomer contents. Experimental conditions: cooling rate = 0.5°C min -1 , heating rate = 1°C min -1 , solvent = 1,2,4-TCB.

Figure 3 - 15 :

 315 Figure 3-15: TREF calibration curves for the different series of copolymers. Experimental conditions: cooling rate = 0.5°C min -1 , heating rate = 1°C min -1 , solvent = 1,2,4-TCB. The superposition of the curves of the four series of copolymers presented in Figure 3-15 allows making the following observations:

  the instrument. Ortho-dichlorobenzene (o-DCB) was used as solvent because of its lower melting temperature (-17°C) than that of 1,2,4-TCB. The calibration curves for each condition are plotted and overlayed in Figure 3-16.

Figure 3 - 16 :

 316 Figure 3-16: Comparison of cooling rate effect during crystallization step. Experimental conditions: cooling rate = 0.5°C min -1 and 0.2°C min -1 , heating rate = 1°C min -1 , Cryo TREF = sub-ambient analyses (-20°C) using liquid nitrogen and o-DCB.

  LLDPE samples. It requires two temperature cycles. The fractionation in CRYSTAF needs only one temperature cycle. During the decrease in temperature, the concentration of the polymer in solution (the soluble part) is monitored by the IR detector, and a cumulative curve is obtained. The first derivative of the data provides the CRYSTAF distribution as a function of crystallization temperature. The first derivative is plotted for various LLDPE copolymers in Figure3-17. The sample profiles obtained were very similar to the TREF profiles. The square at 30°C represents the soluble part of the sample. This part is bigger when the comonomer content increases as observed in TREF. The crystallization temperature is expected to be lower than the melting temperature as observed in DSC and this is even more true in solution. It would be even more interesting here to further decrease the temperature (as in the cryo-TREF experiments).

Figure 3 - 17 :

 317 Figure 3-17: CRYSTAF profiles of individual copolymer models with various comonomer contents. Experimental conditions: cooling rate = 0.1°C min -1 , solvent = 1,2,4-TCB.

Figure 3 - 18 :

 318 Figure 3-18: CRYSTAF calibration curves for the different series of copolymers. Experimental conditions: cooling rate = 0.1°C min -1 , solvent = 1,2,4-TCB.

Figure 3 - 19 :

 319 Figure 3-19: Results of the detection of the content of methylene (CH2) as well as methyl (CH3) in an ethylene-hexene sample (a). Calibration of the IR detector with ethylene-butene (black points) and ethylene-hexene copolymers (green points) (b).The IR band ratio (methyl over methylene absorbance, I1960/I1920) was calibrated to methyl groups frequency (CH3/1000C) using LLDPE standards. During this thesis work the equation was calculated several times and the error estimated (in brackets) could be evaluated. The equation(3-6) obtained is given below:

Figure 3 - 20 :

 320 Figure 3-20: CEF profiles of individual copolymer models with various comonomer contents. Experimental conditions: cooling rate = 2°C min -1 , cooling flow = 0.05 mL mn -1 , heating rate = 4°C min -1 , heating flow = 1 mL min -1 , solvent = 1,2,4-TCB.

Figure 3 - 21 :

 321 Figure 3-21: CEF calibration curves for the different series of copolymers. Experimental conditions: cooling rate = 2°C min -1 , cooling flow = 0.05 mL mn -1 , heating rate = 4°C min -1 , heating flow = 1 mL min -1 , solvent = 1,2,4-TCB

Figure 3 - 22 :

 322 Figure 3-22: TGIC profile of individual ethylene-hexene copolymer models with various comonomer contents. Experimental conditions: cooling rate = 20°C min -1 , cooling flow = 0 mL min -1 , heating rate = 2°C min -1 , heating flow = 0.5 mL min -1 , solvent = 1,2,4-TCB.

Figure 3 -

 3 Figure 3-23: TGIC profile of individual ethylene-norbornene copolymer models with various comonomer contents. Experimental conditions: cooling rate = 20°C min -1 , cooling flow = 0 mL min -1 , heating rate = 2°C min -1 , heating flow = 0.5 mL min -1 , solvent = 1,2,4-TCB.The other families of copolymers (ethylene-propylene, ethylene-octene, and ethylene-octadecene) were also analyzed. We plotted the temperature of the elution peak obtained by TGIC as a function of the comonomer content. The set of calibration curves obtained are compared in Figure3-24.

Table 3 - 8 :

 38 Detailed parameters for methods TGIC-a and TGIC-b. 2,4-TCB. For this comparison, six ethylene-hexene samples with various hexene contents were analyzed by the two methods and the profiles obtained are plotted in Figure 3-25.

Figure 3 - 25 :

 325 Figure 3-25: Profiles of ethylene-hexene copolymers with various contents of hexene (in mol%) measured by the classic method (TGIC-a) shown by the solid line and by the method with the cooling flow (TGIC-b) by the dashed line. Solvent: 1,2,4-TCB.

3. 3 . 3 . 2 SGIC

 332 Tibor Macko and co-workers have recently developed an innovative SGIC. To complete the calibration of all the fractionation techniques available, we proposed our copolymer samples to Tibor Mack to perform an original calibration dedicated to SGIC. Ethylene-propylene, ethylene-hexene, ethylene-octene and ethylene-octadecene copolymers were injected into the SGIC instrument after optimizing the analytical conditions. The elution profiles obtained are plotted in Figure3-26.

Figure 3 - 26 :

 326 Figure 3-26: SGIC profiles of individual copolymer models with various comonomer content. Experimental conditions: temperature = 160°C, flow rate = 1 ml min -1 , mobile phase = 2-ethyl-1-hexanol to 1,2,4-TCB, Hypercarb column from Thermo Scientific (average particle size 5 μm).

Figure 3 - 27 :

 327 Figure 3-27: SGIC calibration curves for the different series of copolymers. Experimental conditions: temperature = 160°C, flow rate = 1 ml min -1 , mobile phase = 2-ethyl-1-hexanol to 1,2,4-TCB, Hypercarb column from Thermo Scientific (average particle size 5 μm).

  apparatus, various homo-PE samples of known and certified molar masses were injected. The elution temperature peaks as a function of the molar mass are plotted in Figure 3-29.

Figure 3 - 29 :

 329 Figure 3-29: Impact of molar mass on the elution temperature of homo-PE for CEF and TGIC. Experimental conditions for CEF: cooling rate = 2°C min -1 , cooling flow = 0.05 mL mn -1 , heating rate = 4°C min -1 , heating flow = 1 mL min -1 , solvent = 1,2,4-TCB. Experimental conditions for TGIC: cooling rate = 20°C min -1 , cooling flow = 0 mL min -1 , heating rate = 2°C min -1 , heating flow = 0.5 min -1 , solvent = 1,2,4-TCB.

  investigations were performed with polymers synthesized by Astrid Cordier during her thesis work in our laboratory. Several UHMWPE samples obtained with a single phenoxy-imine-methoxy (SFI) catalyst were analyzed by DSC (Figure 3-30) and also characterized by CEF and TGIC (Figure 3-32).

Figure 3 - 30 :

 330 Figure 3-30: DSC curve acquired on the first and second heating runs on two disentangled UHMWPE (>1,200 kg mol -1 ). Heating rate of 10°C min -1 under nitrogen atmosphere. Similar DSC curves were observed for different molar masses.

Figure 3 - 31 :

 331 Figure 3-31: Schematic model of the folded crystal structure of (a) a nascent disentangled sample and (b) a nascent entangled sample. The entanglements are circled in red.

Figure 3 - 32 :

 332 Figure 3-32: Comparison of TGIC and CEF profiles for UHMWPE synthetized with a phenoxy-imine (SFI) catalyst. Experimental conditions for CEF: solubilization temperature = 160°C for 2h, cooling rate = 2°C min -1 , cooling flow = 0.05 mL mn -1 , heating rate = 4°C min -1 , heating flow = 1 mL min -1 , solvent = 1,2,4-TCB, concentration = 2 mg ml -1 . Experimental conditions for TGIC: solubilization temperature = 160°C for 2h, cooling rate = 20°C min -1 , cooling flow = 0 mL min -1 , heating rate = 2°C min -1 , heating flow = 0.5 mL min -1 , solvent = 1,2,4-TCB, concentration = 1 mg ml -1 .

9 :

 9 Calibration equation for various thermal fractionation techniques.

Figure 3 - 34 :

 334 Figure 3-34: CEF profiles for two industrial samples. Experimental conditions: cooling rate = 2°C min -1 , cooling flow = 0.05 mL mn -1 , heating rate = 4°C min -1 , heating flow = 1 mL min -1 , solvent = 1,2,4-TCB.The analysis shows the presence of three families of polyethylene chains: a soluble fraction (25°C) with high comonomer content, the semi-crystalline fraction (60 to 90°C) with medium comonomer content and the highly crystalline fraction (100 to 115°C) with low comonomer content. The CEF measurement allowed us to measure the molar comonomer content of each of these families and their weight proportion. The ratio of each family has a strong impact on the mechanical properties of the final material.

Figure 3 -

 3 33, b weight fraction of each family, c the intrinsic viscosity which can give the molar mass information via the Mark-Houwink-Sakurada parameters, d number of CH3 groups per 1000 carbons.

Figure 4 - 1 :

 41 Figure 4-1: 13C NMR spectra (TCB/toluene-d8, 363 K) of sample 23 with 2,2 mol% of 1-hexene, a), resonance region of 1H NMR spectra (TCB/toluene-d8, 363 K) of sample 40 with 13,6 mol% of 1-hexene b).

Figure 4 - 2 :

 42 Figure 4-2: SEC a) and TGIC b) profiles of a set of ethylene-1-hexene copolymers ranging from 0 to 20.7 mol% of 1-hexene.

Figure 4 - 3 :

 43 Figure 4-3: MIR spectra overlay of a polyethylene and four copolymers with various comonomer contents.

  -4b) were more noisy but more robust and repetitive compare to spectrum obtained with solid sample (Figure4-4a). A PLS model was constructed with both kinds of preparation. The NIR spectrum of the solvent, used for the sample dissolution, was acquired separately (Figure4-4c).

Figure 4 - 4 :

 44 Figure 4-4: NIR spectra of a copolymer (sample 12) a) in solid state b) dissolved in 1,2,4-trichlorobenzene and c) solvent alone.

Figure 4 - 5 :

 45 Figure 4-5: A principal component analysis (PCA) scores for factor 1 and factor 2 with confidence intervals of 95% of a) MIR and b) NIR for ethylene-1-hexene copolymers sample. Samples were disctinctly separated into four groups (blue, red, green and brown) depending of 1-hexene content (in mol%).

Figure 4 - 6 :

 46 Figure 4-6: The contribution plot describes how individual variables contribute to the model, 3 spectral regions were clearly highlighted a) in MIR and b) in NIR. Variables represents the wavenumber in cm -1 . The brackets indicate the wavenumber ranges selected to be included in the models.

  dissolved sample in 1,2,4 TCB, b whole spectrum or spectral region selection (3000-750, 1500-1300 and 630-800 cm -1 for MIR ; 9000-7800, 6400-5400 and 4800-4000 cm -1 for NIR), c first derivative and Savitzky-Golay smoothing, d range of the 1-hexene content in samples used for calibration.With four factors and a spectral region selection, the performance index plot reached a maximum of 97.7% for MIR (method [b] in Figure4-7) and a maximum of 97.2% for NIR (method [e] in Figure4-7). It was, once again, improved for methods with a reduced 1-hexene content range (method [c] and [f]).

Figure 4 - 7 :

 47 Figure 4-7: Evolution of performance index (in %) in function of the number of PLS factors for the six models reported in Table 4-3. The numerical values of the performance index for the different tests are compared in Table 4-4. We observed that spectral region selection, with superior interpretability, significantly improved performance of the model and produced the lowest prediction error. Figure 4-8 shows the calibration curve for the quantification of 1-hexene content using different parameters detailed in Table 4-3 to construct the regression.

Figure 4 - 8 :

 48 Figure 4-8: Correlation diagrams between predicted and reference values of the dataset for the six models reported in Table4-3 (blue data for calibration and red data for validation). The axes units are expressed in mol% (1-hexene content).

Figure 4 - 10 :

 410 Figure 4-10: High field resonance region of 13C NMR spectra (TCE/C6D6, 363 K) of copolymers synthetized using the 3 different complexes selected for this study (V = vinyl unit; Cy = 1,2-cyclohexane unit; T = trans-1,4 unit). Sample 3 complex 1 a), sample 26 complex 3 b), sample 25 complex 2 c). NMR analyses are reliable since the molar masses (Mn) of all polymers are high enough to neglect any inaccuracy due to the signals of chain-ends.

Figure 4 -

 4 11 shows the comparison of FTIR spectra of a homopolyethylene and three copolymers synthesized using catalysts based on complexes 1-3.

Figure 4 - 11 :

 411 Figure 4-11: MIR spectra of a polyethylene a) and of copolymers synthetized using the 3 different complexes. Sample 3 complex 1 b), sample 26 complex 3 c), sample 25 complex 2 d).

Figure 4 -

 4 Figure 4-12 illustrates the change in autopredictive error for different numbers of PLS factors.

Figure 4 - 12 :

 412 Figure 4-12: Evolution of RMSEC in function of the number of PLS factor used for ethylene (a), trans-1,4butadiene (b), vinyl (c) and cyclohexane (d) units.

Figure 4 - 13 :

 413 Figure 4-13: Correlation diagrams between the IR predicted values and the reference values for ethylene (a), trans-1,4 (b), vinyl (c) and 1,2-cyclohexane (d) units obtained by NMR. o stands for calibration points, + stands for validation points. The axes units are expressed in mol%.

  They were carried out using a CRYSTAF-TREF 300 model manufactured by Polymer Char S.A. The fractionation in TREF is based on the progressive deposition of polymer with decreasing crystallinity on an inert glass beads support inside the column (from Polymer Char S.A. 150 mm × 9 mm). The polymer is thus segregated in layers with different chemical structures. Experimentally, 80 mg of sample were dissolved in 20 mL of 1,2,4-trichlorobenzene stabilized with 2,6-di(tert-butyl)-4-methylphenol at 150 °C. 0.5 mL of the sample solution was loaded into the column. The temperature was slowly decreased to 35 °C at a rate of 0.5 °C min -1 to allow the polymer to crystallize. A reverse cycle was performed to quantify these fractions by rinsing solvent through the column while gradually increasing the temperature at 1 °C min -1 .

a) Loops 1 Figure 4 - 14 :

 1414 Figure 4-14: IST16 in storage mode a) and in injection mode b).

Figure 4 - 15 : 1 4. 3 . 3 . 2

 4151332 Figure 4-15: TREF profile of poly(ethylene-co-octene) (samples 2-4) and poly(ethylene-co-hexene) (samples 5-8) copolymer with a crystallization rate of 0.5 °C min -1 4.3.3.2 Thermal decomposition of the HDPE

Figure 4 - 16 :

 416 Figure 4-16: Mass spectrum (Total Ion Current) resulting from the thermal degradation of a HDPE polymer (sample 1). Each triplet consists of α, ω-diene, α-alkene and n-alkane at each carbon number. a) total spectrum b) zoom on C10.

Figure 4 -

 4 Figure 4-17 shows the amount of different main alkenes and alkanes observed corresponding to different temperatures during TGA experiment. Each substance was identified by MS and its amount was calculated from the peak intensity in the gas chromatogram (Figure 4-16).

Figure 4 - 17 :

 417 Figure 4-17: Emission profiles of a) alkenes and b) alkanes compounds from TGA analysis of sample 1 (HDPE). The left ordinate axis corresponds to the peak intensities in the gas chromatograms for each alkane and alkene component. The right ordinate axis refers to the TGA curve.

4. 3 . 3 . 3

 333 Thermal decomposition of ethylene-octene copolymerDegradation profiles were obtained for the ethylene-octene copolymers (samples 2, 3 and 4) under conditions similar to those used for the reference sample.

Figure 4 -Scheme 4 - 5 :

 445 Figure 4-18: GC/MS result (extracted ion m/z = 41) for ethylene-octene copolymer, sample 3.

Figure 4 - 19 :

 419 Figure 4-19: Emission profiles from the TGA analysis of ethylene-octene copolymers (sample 2, 3 and 4). The ordinate axis corresponds to the peak's intensities in the gas chromatograms for each component, alkane and alkene fragments were cumulated (C6 = hexane and hexene fragments cumulated).4.3.3.4 Thermal decomposition of ethylene-hexene copolymers

Figure 4 -

 4 Figure 4-20: GC-MS result (extracted ion m/z = 41 or total ion current) for an ethylene-hexene copolymers, sample 8.

  : FROM THERMAL FRACTIONATION TECHNIQUES TO SPECTROMETRY 4-257 function of the comonomer content previously determined by NMR (Table 4-15) to construct the calibration curves.

Figure 4 - 22 :

 422 Figure 4-22: Calibration curve for a) ethylene-octene copolymers obtained with samples 2 to 4 b) ethylenehexene copolymers obtained with samples 5 to 8. Hexene and hexane fragments measured during the degradation of ethylene-octene copolymers between 420°C and 540°C. C4 fragments measured during degradation of ethylene-hexene copolymer between 420°C and 540°C.

Cong, Pasch ,

 Pasch Brull and Macko, have been commercialized. This PhD work focuses on the implementation and development of methods based on thermal fractionation techniques that allow access to CCD in LLDPE.

  were synthesized and characterized by NMR to measure the levels of inserted comonomer. As the type of comonomer has an impact on separation, several samples with different types of comonomers (propene, hexene, octene, norbornene, octadecene) and different levels of comonomers (up to 20%) were used to calibrate the fractionation technique, each leading to an equation appropriate for the different types of LLDPE. These calibration curves are brought together for the first time in a single work. They have been and will be used to access the chemical composition distribution (CCD) of polyethylenes (HDPE and LLDPE) with heterogeneous composition as shown in Figure1.

Figure C1 :

 C1 Figure C1: Chromatogram acquired by TGIC for a heterogeneous sample (a) and chemical composition distribution curve obtained from the calibration (b). Calibration for ethylene/hexene copolymers. Parallel to this calibration work, investigations have shown certain characteristics specific to each technique.

1 H

 1 NMR and13 C NMR methods were described to measure the comonomer content. High temperature was implemented: o for the molar masses' determination o for long chain branching measurement o for short chain branching measurement Method to measure comonomer content by DSC through melting and crystallization temperature and melting and crystallization enthalpy were constructed. We have calibrated different thermal fractionation techniques. o based on crystallization (CRYSTAF, TREF, CEF) o based on interactions (TGIC, SGIC)

Table 1 -

 1

	Catalyst	Transition metal	Process	Characteristics
	Phillips	Cr	Heterogeneous a	No cocatalyst / Broad molar mass
				distribution
	Ziegler-Natta Ti	Heterogeneous and	Alkyl aluminum cocatalysts / Broad
			Homogeneous b	molar mass distribution
	Metallocene Zr, Ti, Hf	Heterogeneous and	Methylaluminum or borate cocatalyst
			Homogeneous	/ narrow molar mass and chemical
				distribution

2: Commercial catalysts and their characteristics.

Table 1 -

 1 2 summarizes the main types of industrial catalyst used to produce HDPE and LLDPE. Ziegler-Natta and Phillips catalysts are considered as multiple-site catalysts leading to heterogeneous polymers with broad molar mass distribution (MWD) and broad chemical composition distribution (CCD). Conversely, metallocene catalysts, as single site catalysts, produce homogenous polyolefins with narrow MWD and

Table 1 -

 1 3: Energy and distance of covalent bonds and Van der Waals interactions in PE.

		Covalent bonds		Van der Walls interactions
		C-C	C-H	C…C	C…H	H…H
	Energy (KJ mol -1 )	19.8	23.7	0.1-0.5	0.7-1.2	0.1-0.5
	Distance (nm)	0.154	0.109	0.34-0.85	0.29-0.70	0.23-0.60
	1.5.1.4 Spherulite (level IV)

Table 2 -

 2 1: Polymerization conditions of the six series of LLDPE models

	Série	1	2	3	4	5	6
	Comonomer	Propylene	1-Hexene	1-Hexene	1-Octene	Octadecene	Norbornene
	Feed a	2-39 mol%	1-88 mol%	11-64 mol%	9-59 mol%	21-69 mol%	5-68 mol%
	Catalysts	Et(Ind)2ZrCl2	Et(Ind)2ZrCl2	(nBuCp)2ZrCl2 Et(Ind)2ZrCl2	Et(Ind)2ZrCl2	Et(Ind)2ZrCl2
	Catalyst	1.5x10 -7 mol	1.5x10 -7 mol	1.6x10 -7 mol	1.5x10 -7 mol	1.8x10 -6 mol	1.5x10 -6 mol
	Co-catalysts b MAO	MAO	MAO	MAO	MAO	MAO
	Ratio Al/Zr	3000	3000	3000	3000	3000	3000
	Temperature 80°C	80°C	80°C	80°C	80°C	80°C
	Reaction time 15 min	30 min	30 min	30 min	30 min	30 min

Table 2 -

 2 2: Comonomer content calculation by proton NMR.

	Comonomer	Intensity	Mol fraction
	Propene	I1 = 4E + 3P I2 = 3P	%=	P E+P	=	4×I 2 3×I 1 +I 2
	Hexene

Table 2 -

 2

	3: Comonomer content calculation by 13C NMR
	Comonomer	m = (Iα+Iβ)/2		I (CH2)		Mol fraction
		δ (ppm)	Expres	δ (ppm)	Expression
	Propene
		Iα: 37.5 Iβ: 27.4	m = 2xP	29 -31	I(CH2)=2xE-3P	%=	m I CH 2 +	m

with Iα and I being the carbon atoms located in α and positions, respectively, of the branch in the backbone chain (Figure

2-9

). To improve the accuracy on the measurement, we use the average value (m) defined as m = (Iα + I )/2, I(CH2) is the integral value of the signals between 29 and 31 ppm. E, P, H, O and OD are the relative intensities of ethylene, propene, hexene, octene and octadecene units, respectively.

A large number of each type of copolymer has been synthesized and characterized by NMR. The mole fractions calculated by NMR are reported in Appendix 1. These copolymers could then be used as standards to construct calibration curves for the different fractionation techniques: TREF, CRYSTAF, CEF and TGIC. For SGIC technique, a collaboration with Tibor Macko of the Fraunhofer Institute for Structural Durability and

System Reliability, Darmstadt (LBF) has been undertaken. The copolymers were employed to correlate the elution times obtained by fractionation techniques to the amount of comonomers.

Table 2 -

 2 4.

Table 2 -

 2

		Offset (ml)	Calibration factor
	RI	0	287794
	RALS	-0.066	5.36x10 -7
	LALS	-0.066	1.36x10 -7
	IV	0.099	1.2

4: Offset (volume between detector) and calibration factors (constant for each detector) for the light scattering method.

Table 2 -

 2

		Light scattering			Conventional calibration			Viscometer
		M n	Mp	M w	Ð	M n	Mp	M w	Ð	[η] a
		kg mol -1	kg mol -1	kg mol -1		kg mol -1	kg mol -1	kg mol -1		dl g -1
	Average	13.6	27.5	39.5	2.9	12.2	26.3	38.4	3.2	1.30
	Standard deviation	1.3	1.3	2.7	0.3	0.9	1.5	2.2	0.2	0.04
	%	9.7	4.7	6.7	10.3	7.3	5.7	6.0	6.9	3.1

5: Values of repeatability measurements obtained by HT-SEC with 21 runs for molar mass average, dispersity and intrinsec viscosity (viscometer detector).

a intrinsic viscosity obtained with the viscometer detector.

Table 2 -

 2 6: Parameters for high temperature size exclusion measurement in 1,2,4 TCB at 150°C.

	dn/dcPS a

a Used to perform universal calibration with PS standards; b,c required to measure the absolute molar masses with light scattering and universal calibration for PE and PP samples; d used to measure the absolute molar masses with light scattering; e Intrinsic viscosity of PS sample with a weight average molar mass of 99 Kg mol -1 ; used to calibrate the viscometer. f Factor used to correct the sample concentration at high temperature, required to obtain the absolute molar masses with light scattering and universal calibration if the dn/dc is not known or to obtain sample recovery.

  2 LONG CHAIN BRANCHINGMolar mass and its distribution, short chain branching (SCB) and long chain branching (LCB) are the key parameters that control the properties of LLDPE. The LCB can change the melt rheological behavior and

enhance the processability of PE. During polymerization, few polymer chains are produced with unsaturated vinyl chain ends. Depending on the conditions, these macromonomers can be inserted into a growing polymer chain resulting in LCB. Although this has not been discussed extensively in the literature, we can assume that LCB may influence the elution time measured by thermal fractionation techniques. It is, therefore, of great importance to evaluate the LCB content in our samples. This part will discuss the method used to measure LCB by HT-SEC.

Table 2 -

 2 7: Zimm-Stockmayer equations applied to HDPE, LDPE and certified PE samples. hydrodynamic radius calculated with intrinsic viscosity and molar mass, b MHS parameters obtained with the slope and the intercept of the curve, c long chain branching frequency per 1000 carbon atoms, d certified PE samples purchased from American Polymer Standards, the certified values given by the producer are in brackets, the other values were acquired by HT-SEC. Some parameters can be obtained with the MHS plots to characterize the polymers, they are reported in

	Sample	M w	M n	[η]	Rh a	α b	Log K b	λ c
		Kg mol -1	Kg mol -1	dL g -1	nm			for 1000 C
	LDPE1	240.6	24.4	1.2	16.0	0.47	-2.30	5.5
	LDPE2	100.3	27.1	1.1	11.7	0.54	-2.62	2.8
	LDPE3	90.5	19.1	1.0	10.8	0.53	-2.53	2.8
	BRPE 0 d	48.5 (52.0)	17.1 (18.3) 1.0 (1.01)	8.4	0.71	-3.20	(0)
	BRPE 14 d	79.9 (88.2)	22.2 (23.0) 0.9 (0.90)	9.8	0.57	-2.67	1.6 (1.4)
	HDPE	254.8	110.7	4.6	25.8	0.69	-3.01	0.01

a

Table 2 -

 2 7. The hydrodynamic radius of the polymer is calculated according to the viscosity relation (Equation 2-14) where the volume of the macromolecule is replaced by the hydrodynamic radius, as

Table 2

 2

-8.

Table 2 -

 2 8.

Table 2 -

 2

	Sample	Comonomer	[η] a	α	Log K	λSEC b	λNMR c
		(mol%)	(dL g -1 )			(CH3/1000C) (CH3/1000C)
	BRPE0	0	1.0	0.71	-3.20
	EC01	0	1.1	0.70	-3.19	0.25	0.17
	IB10	0.1	1.1	0.71	-3.18	0.62	0.73
	EC12	2.5	1.0	0.72	-3.18	0.09*	-
	ECHS4	7.6	0.97	0.70	-3.26	0.02*
	EC22	9	0.94	0.71	-3.76	<0.02*
	ECHS6	13.6	0.99	0.72	-3.84	<0.02*
	ECHS7	20.7	0.98	0.72	-4.08	<0.02*

8: Determination of Mark-Houwink-Sakurada parameters and the branching frequency for several samples.

  CHARACTERIZATION OF POLYETHYLENES: FROM THERMAL FRACTIONATION TECHNIQUES TO SPECTROMETRY 2-107 the entire molar mass distribution that a polymer without LCB would have. We can therefore calculate g' (Equation 2-9) with the new values of [η]l and determine the LCB content with the Zimm-Stockmayer equations. With this method, the SCB content did not affect the LCB calculation. The values obtained are reported in Table 2-8.

  -18, we can generate a calibration curve that can be applied to unknown PE samples to measure the comonomer content by using Log K value obtained by HT-SEC:

	2.5 CONCLUSION
	Eighty-eight LLDPE samples were obtained through the copolymerization of ethylene with various sort of
	α-olefines using metallocene-type catalyst. The rac-Et(Ind)2ZrCl2 and (nBuCp)2ZrCl2 complexes were used
	and lead in homogeneous samples both in molar masses and in chemical composition. The resulting
	copolymers constitute a wide range of LLDPE with varying amounts of comonomers and different types of
	comonomers. They constituted our standards for the following parts. They are also representative of
	industrial LLDPEs that can be found in daily life.
	Comonomer content (mol%) = 44.22 + 38.12 Log K + 7.91 (Log K) 2	(2-16)
	The copolymer models have been characterized. First and foremost, the comonomer content was
	With R-Square = 0.987 determined by 1 H NMR and 13 C NMR. The calculation methods adapted to each comonomer have been
	described in this part.

Furthermore, the molar masses were measured by HT-SEC showing similar values between samples and, as expected, narrow distributions for all of them. The values are reported in Appendix 1.

Table 3 -

 3 1: Melting temperature and enthalpy of standards used for the calibration.

	Reference substance	Temperature (°C)	Enthalpy (J g -1 )
	Water	0 (± 0.5)	334.5 (± 16.7)
	Indium	156.6 (± 0.3)	28.5 (± 0.6)
	Zinc	419.5 (± 0.7)	107.5 (± 3.8)

Table 3 -

 3 2: Experimental melting temperature values compared to theoretical values obtained with Garner and Broadhurst equations, respectively.

	M n	N a	Tm	Tm	Tm b	Tm	Tm b
			experimental	calulated		calulated
				Garner		Broadhurst
	g mol -1		°K	°K		°K
	7300	521	405.1	403.8	-1.4	409.2	4.1
	6500	464	405.3	403.2	-2.1	408.6	3.2
	2500	178	401.1	395.5	-5.5	399.6	-1.4
	2200	157	398.8	393.8	-5.0	397.7	-1.1
	1950	139	396.3	392.0	-4.3	395.6	-0.7
	1430	102	393.0	386.3	-6.6	389.1	-3.8
	1110	79	384.5	380.3	-4.3	382.3	-2.2
	750	53	365.8	367.5	1.8	368.2	2.5

a number of carbons in the polymer chain, b deviation between the calculated value and the experimental melting temperature.

Table 3 -

 3 3: Equation to calculate the comonomer content using melting and crystallization parameters obtained by DSC.

	Comonomer	Melting and crystallization temperature	Melting and crystallization enthalpies
	propene	30.1-0.22xTm
		(0.978)
	hexene	22.6-0.17xTm
		(0.979)
		23.69 -0.12xTm-0.0016xTm 2 +8.6E-6xTm 3	23.97-0.38x Hm+0.002x Hm 2 -4.0E-6x Hm 3
		(0.989)	(0.946)
		21.37-0.19xTc-5.8E-4xTc 2 +5.8E-6xTc 3	25.02-0.35x Hc +0.0015x Hc 2 -1.6E-6x Hc 3
		(0.991)	(0.924)
		14.2-0.112xTm onset
		(0.973)
	octene	20.0-0.16xTm
		(0.972)
	octadecene	30.8-0.23xTm
		(0.980)
	norbornene	14.36-0.10xTm	8.13-0.056x Hm
		(0.985)	(0.982)
		15.04-0.13xTc	8.00-0.054x Hc
		(0.991)	(0.954)

Table 3 -

 3 4: Summary of operating conditions.

	Parameters	Symbol	Values	Unit
	Cooling rate	Cr	20	°C min -1
	Cooling cycle		150 -40	°C
	Cooling flow rate	Fc	0	ml min -1
	Heating rate	Hr	2	°C min -1
	Elution flow rate	Fe	0.5	ml min -1

Table 3 -

 3 6: Duration of an analysis by fractionation techniques for one sample.

	Technique	TREF	CRYSTAF	CEF	TGIC
	Duration (min)	260	260	80	120

Table 3 -

 3 7: CEF and TGIC calibration constants.

	Infrared	Viscometer	Column CEF	Column TGIC	Inter-detector
	KIR	KIV	Kcol-det	Kcol-det	Kdet-det
	0.436 ± 0.006	0.0886 ± 0.0008	3.315 ± 0.005	1.329 ± 0.005	0.187± 0.005

Table 3 -

 3 10: Quantitative results for Blue and Red samples obtained by CEF experiments.

	Fraction	Soluble		Weakly crystalline	Highly crystalline
		Blue a	Red a	Blue	Red	Blue	Red
	Wt Fraction b	10%	34%	15%	21%	75%	45%
	IV (dL g -1 ) c	1.0	1.1	1.5	2.4	2.0	2.9
	CH3/1000C d	50	70	21	24	1	2
	Comonomer content (mol %) >9%	>9%	4.6%	5.3%	0%	0%

a Blue and Red samples corresponding to CEF profiles in

Table 4 -

 4 1: Characterization of ethylene-1-hexene copolymers obtained with zirconocene catalyst.

	Sample Cata a	M n (Ɖ) a kg.mol -1	Hex c mol%	Tp d °C	Hex d mol%	Cw/Cn d
	1	1	60 (2.9)	0.0	132.5	0.1	2.5
	2	1	51 (3.2)	0.0	132.5	0.0	2.5
	3	1	50 (3.4)	0.0	nd	nd	nd
	4	1	44 (3.0)	0.0	nd	nd	nd
	5	1	51 (3.1)	0.0	nd	nd	nd
	6	2	49 (3)	0.2	132.0	0.3	3.0
	7	1	41 (3.8)	0.3	131.7	0.3	2.0
	8	1	21 (2.2)	0.4	130.8	0.2	1.3
	9	2	24 (3.4)	0.5	131.0	0.4	3.0
	10	3	36 (3.1)	0.7	nd	nd	nd
	11	3	48 (2.6)	0.7	130.8	0.7	1.1
	12	3	33 (4.1)	1.0	130.5	0.6	1.2
	13	1	40 (2.6)	1.1	nd	nd	nd
	14	3	29 (4.7)	1.1	nd	nd	nd
	15	3	51 (2.2)	1.2	129.4	0.9	2.0
	16	2	52 (3.1)	1.5	126.9	1.2	2.0
	17	3	56 (2.3)	1.5	nd	nd	nd
	18	1	54 (2.6)	1.6	nd	nd	nd
	19	3	25 (3.7)	1.8	129.4	0.7	1.4
	20	2	56 (3.1)	1.9	128.7	1.2	1.1
	21	1	36 (1.8)	2.0	124.3	1.8	1.6
	22	2	35 (2.3)	2.0	nd	nd	nd
	23	1	40 (1.7)	2.2	123.1	2.1	1.3
	24	1	40 (2)	2.2	nd	nd	nd
	25	1	28 (2.2)	2.2	nd	nd	nd

1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00 2.05 2.10 ppm

		37.98				33.98 34.36				30.00 30.47	29.42		27.20				23.38								14.15
															1.442								1.062
	39	38	37	36	35	34	33	32	31	30	29	28	27	26	25	24	23	22	21	20	19	18	17	16	15	ppm

Table 4 -

 4 2.

	Table 4-2: Assignments of NIR bands of ethylene-1-hexene copolymers.
	NIR	Wavenumber [cm-1]	Assignment	Comments
	LLDPE	8600 à 8000	second harmonic oscillation of CH, CH 2 ,CH 3	large, medium, gaussian look
		7300 à 6800	first harmonic oscillation of CH,	very large, medium
			CH 2 , CH 3
		7200		medium, thin
		5800 à 4800	//	elevation of the base line
		5780 5620 5600 à 5400	first harmonic oscillation of CH, CH2, CH3	very intense, thin intense, thin medium, large
		4400 à 4200	combination of CH, CH2, CH3	very intense

Table 4

 4

	-3. Since common

Table 4 -

 4 3: Processing parameters of six PLS models for MIR and NIR

	Model	IR	Sample a	Spectrum b	Pre-treatment c	Range d (mol%)
	[a]	MIR	solid	whole	derivative SG	0-21
	[b]	MIR	solid	selection	derivative SG	0-21
	[c]	MIR	solid	selection	derivative SG	0-4
	[d]	NIR	solid	whole	derivative SG	0-21
	[e]	NIR	dissolved	whole	derivative SG	0-21

Table 4 -

 4 4: Assessment of the PLS models for MIR and NIR

	Model	[a] MIR	[b] MIR	[c] MIR	[d] NIR	[e] NIR	[f] NIR
	Number of factors 4	4	4	4	4	4
	Performance index 97.4	97.7	98.5	91.8	97.2	98.2
	RMSEC	0.6	0.5	0.1	1.0	0.3	0.1
	rc²	0.98	0.99	0.99	0.96	0.99	0.98
	RMSEV	0.9	0.6	0.2	1.6	1.7	0.4
	rv²	0.97	0.98	0.97	0.86	0.85	0.84

Table 4 -

 4 7: Chemical composition of ethylene-butadiene copolymers obtained by the combination of complex 1, 2 or 3 and BOMAG.

	Complex	Sample	M n (Đ) a	Ethylene b	Trans-1,4 b	Vinyl b	1,2-cyclohexane b	Usage c
			[kg mol -1 ]	[mol%]	[mol%]	[mol%]	[mol%]
		1	21.4 (3.9)	72.7	7.6	11.4	8.3	C
		2	31.3 (2.0)	80.7	4.9	5.3	9.1	C
		3	13.6 (1.5)	79.3	4.2	8.6	7.8	V
		4	14.0 (1.4)	79.8	3.8	9.1	7.4	V
		5	24.8 (2.3)	73.0	7.3	11.3	8.3	C
		6	25.8 (2.2)	73.5	6.9	11.2	8.4	C
		7	29.2 (1.6)	72.9	7.1	11.9	8.2	C
		8	31.3 (1.6)	73.5	6.7	11.6	8.2	V
	1	9 10	32.5 (2.0) 45.7 (1.5)	80.8 80.3	4.9 4.6	5.2 6.7	9.1 8.4	V C
		11	40.3 (1.4)	80.8	4.4	6.4	8.3	C
		12	9.2 (1.9)	82.1	3.1	11.5	3.3	C
		13	-	86.0	2.5	10.0	1.5	V
		14	18.5 (1.9)	76.2	4.1	18.0	1.7	C
		15	-	91.9	1.5	6.0	0.6	C
		16	-	83.2	2.7	12.4	1.7	C
		17	-	92.9	1.3	5.0	0.8	V
		18	13.2 (1.3)	93.6	1.6	1.1	3.7	C
		19	23.3 (1.6)	94.5	1.1	1.1	3.3	C
		20	44.7 (1.9)	95.6	0.8	0.7	2.9	C
		21	16.0 (1.9)	60.5	38.2	1.1	0.2	V
		22	14.6 (1.9)	64.3	34.5	1.0	0.2	C
	2	23	9.4 (2.7)	73.2	25.9	0.7	0.2	C
		24	13.3 (2.1)	72.4	26.7	0.7	0.2	V
		25	13.2 (2.0)	71.7	27.3	0.8	0.2	C
		26	47.7 (2.0)	61.5	25.1	11.3	2.1	C
		27	53.4 (2.0)	65	22.9	9.8	2.3	V
	3	28	59.5 (1.7)	63.8	24.1	9.7	2.4	C
		29	40.5 (2.2)	68.5	20.9	8.4	2.2	V
		30	79.3 (1.9)	61.9	24.9	11.2	2.1	C
	a Number average molar mass and dispersity obtained with ambient SEC and HT-SEC, b determined with
	1H NMR and 13C NMR, c C: calibration standards used to create the model V: validation standards used to
	calculate the performance index.

Table 4 -

 4 8: Major bands in MIR spectra of polyethylene and ethylene-butadiene copolymers

	Spectrum	Wavenumber	Assignment	Comments
		[cm -1 ]
	PE	2914	C	Asymmetric and symmetric stretching of CH2
		2847	C	Intense and sharp
		1472	CH2	Bending of CH2, intense, doublet due to
		1462	CH2	crystallinity
		730	C	Rocking of CH2, medium, doublet due to
		718	C	crystallinity
	Copolymer	3073	ν=CH2	Weak, sharp (vinyl unit)
		1640	νC=C	Medium sharp (vinyl unit)
		994	ωCH	Weak (vinyl unit)
		964	ωCH	Intense (trans-1,4 double bond)
		908	ωCH2	Intense (vinyl unit)
		682	ωCH	Intense (vinyl unit)
	=stretching, = bending, =rocking, ω =wagging
	4.2.3.4 Chemometric study

Table 4 -

 4 9: Composition range of ethylene-butadiene copolymers used in the model

	Unit	Range [mol%]
	Ethylene	60.5 -95.6
	trans-1,4-butadiene	0.8 -38.2
	Vinyl	0.7 -18
	1,2-Cyclohexane	0.2 -9.1

Table 4 -

 4 10: Performance index (PI) for different tests

	Method	Spectral range [cm -1 ]	Data format	Smoothing	PI a
	1	400-4000	No derivative	No	94.0
	2	400-4000	First derivative	No	95.9
	3	600-1800 and 2600-3200	First derivative	No	96.1
	4	600-1800 and 2600-3200	First derivative	Norris	97.0

Table 4 -

 4 11: Calibration and validation parameters of PLS models for each paramters

		Ethylene	trans-1,4	Vinyl	1,2-cyclohexane
	RMSEC	0.64	1.04	0.74	0.18
	r²	0.998	0.995	0.990	0.999
	RMSEP	0.61	0.89	0.92	0.45
	r²	0.998	0.998	0.980	0.993
	Number of factors	3	3	3	6

Table 4 -

 4 12: Calibration and validation parameters of PLS models for each units.

	Test	1	2	3	4	5	6	7	8	9	10	Average
	Ethylene	75.6 78.6 78.2 77.3 77.4 76.9 77.8 74.8 78.9 76.9	77.2	1.3
	[mol%]
	Trans-1,4
		8.6 6.3 6.1 6.7 6.6 8.2 6.4 8.2 6.0 7.0	7.0	1.0
	[mol%]
	Vinyl
		10.7 9.1 9.3 9.9 9.9 10.5 8.7 10.5 9.0 10.1	9.8	0.7
	[mol%]
	Cyclohex
	[mol%]

Table 4 -

 4 13: Comparison of NMR and IR data of three unknown ethylene-butadiene copolymers for the validation of the chemometric method.

	Sample	A		B		C
		NMR	IR	NMR	IR	NMR	IR
	Ethylene [mol%]	77.9	79.3	81.9	82.2	79.0	78.1
	Trans-1,4 [mol%]	4.0	3.7	3.3	2.5	3.9	3.9
	Vinyl [mol%]	8.3	9.0	12.7	12.5	15.3	14.5
	Cyclohexane [mol%]	10.7	8.1	2.1	2.0	1.8	2.3

Table 4 -

 4 14. Corresponding storage temperatures and loop numbers.

	TGA:
		-400 420 430 440 450 460 470 480 490 500 510 520 530 540	-
	T in °C
	IST16
	loop a)	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16

Table 4 -

 4 15: Characterizations for the ethylene-α olefin copolymers.

			M n (Ð) a)	α-olefin content b)	Te c)
	Sample	α-olefin
			Kg mol -1	mol%	°C
	1	-	60.2 (2.9)	0	101.8
	2	Octene	41.0 (2.6)	0.6	96.2
	3	Octene	32.4 (1.8)	1.7	89.5
	4	Octene	32.2 (1.8)	5.6	66.4
	5	Hexene	24.4 (3.4)	0.5	97.7
	6	Hexene	29.5 (1.8)	5.1	68.1
	7	Hexene	26.4 (2.3)	13.6	*
	8	Hexene	26.4 (2.3)	20.7	*
	a) Determined by HT-SEC with light scattering detector. Ð = dispersity. b) Determined by 1 H-or 13 C-NMR
	spectroscopy. c) Elution temperature determined by TREF, * no peak observed in TREF experiment.

Table 4 -

 4 16: Alkenes and alkanes compounds and corresponding retention time.

	Compound	1-Butene / butane	1-Pentene/pentane	1-Hexene	Hexane	1-Heptene	Heptane	1-Octene	Octane	1-Nonene	Nonane	1-Decene	Decane	1-Undecene	Undecane
	RT
	(min) 4.6	5.1	5.8	5.9	8.0	8.3	12.6 12.9 16.2 16.5 18.6 18.8 20.6 20.8

by heating the mixture for 1 h at 150°C.

μL of sample solutions were injected and eluted in 1,2,4-TCB

CHARACTERIZATION OF POLYETHYLENES: FROM THERMAL FRACTIONATION TECHNIQUES TO SPECTROMETRY

CHAPTER II SYNTHESIS OF LLDPE MODELS AND THEIR CHARACTERIZATION

Three LLDPE industrial samples of unknown composition were characterized by CEF and TGIC to illustrate the information that can be obtained by these techniques. The Figure 3-28 shows a representation of comonomer content distribution obtained using the calibration equation constructed with our copolymer models. The x-axis corresponding to the elution volumes on the chromatogram is thus transformed into the amount of comonomer. This is the chemical composition distribution curve.

The analytical range (in mol% of comonomer) for TGIC is wider than that for CEF; in TGIC amorphous samples can be separated. However, with CEF a better resolution is obtained as can be seen in Figure 3-28. Indeed, the blue and orange samples showed two peaks, indicating the presence of two families with various comonomer contents in CEF and a third peak characteristic of the amorphous part. All these fractions can be easily quantified by CEF. Conversely, a broader elution peak is observed on the TGIC profiles with a drag towards the region where the second peak is expected. Obviously, CEF leads to better separation for complex samples. Comonomer distributions were obtained using the calibration curve for ethylene-hexene copolymers from Table 3-9. Experimental conditions for CEF: cooling rate = 2°C min -1 , cooling flow = 0.05 mL mn -1 , heating rate = 4°C min -1 , heating flow = 1 mL min -1 , solvent = 1,2,4-TCB. Experimental conditions for TGIC: cooling rate = 20°C min -1 , cooling flow = 0 mL min -1 , heating rate = 2°C min -1 , heating flow = 0.5 mL min -1 , solvent = 1,2,4-TCB.

3-156

A column filled with inert beads is used in CEF to promote crystallization of chains. By being able to crystallize at higher temperature than in DSC they are solubilized or eluted at higher temperature: 110 and 115°C in CEF instead of 86 and 89°C in DSC.

In order to enhance these developments and to extend the exploitation of these techniques and the understanding of their separation mechanism, three papers have been published. The first one presents and details the calibration of the TREF instrument using the LLDPE models; the second highlights the advantages and disadvantages of the SGIC techniques versus CRYSTAF; the last one is focused on the fractionation mechanisms in TGIC.

The first publication, titled "Homogeneous copolymers of ethylene with α-olefins synthesized with metallocene catalysts and their use as standards for TREF calibration", was published to describe the DSC and TREF calibration. Various co-authors were involved in this project. Emilie Cossoul was the student I supervised to produce copolymer samples and perform characterizations. Laetitia Baverel characterized the samples by HT-SEC. Elsa Martigny was the PhD student who produced the heterogeneous samples with a classical Ziegler-Natta catalyst to illustrate the method. We had valuable discussions with Tibor The third publication, titled "Molecular dynamic simulation of ethylene-hexene copolymer adsorption onto graphene: new insight into thermal gradient interaction chromatography", was published with Fabrice Brunel, a researcher in our group. This work aims at understanding the fractionation mechanism and interactions that occur in a graphene column with LLDPE chains during TGIC experiments. These adsorption mechanism of copolymers on the graphene surface of the column was studied by molecular dynamics simulation. Fabrice Brunel performed simulations and my work focused on TGIC experiments to strengthen and validate the model. (TCB) containing 300 ppm of BHT and purge with nitrogen to protect the polymer against oxidative degradation. 200 μL of sample solution at a concentration of 1 mg mL -1 were injected into the column at 150 °C. This technique requires a cooling (adsorption) and a heating (desorption) step. A cooling ramp of 20 °C min -1 down to 40 °C was applied to promote polymer adsorption. Elution begins isothermally at 40 °C during 5 min at a flow rate of 0.5 mL min -1 followed by a heating ramp at 2 °C min -1 to desorb the polymer. An infrared detector was used to monitor the components' concentration and composition when the chains were eluted from the column.

CHAPTER IV CHEMICAL COMPOSITION OF ETHYLENE COPOLYMERS USING SPECTROMETRY

CHEMICAL COMPOSITION OF ETHYLENE COPOLYMERS USING

Because TGIC separates by adsorption it has the possibility to extend the range of polymers to be analyzed towards the amorphous region which is limited by crystallization techniques (TREF, CRYSTAF). Then, LLDPE with high content of comonomer can be separated.

Nuclear magnetic resonance spectroscopy

Comonomer contents of copolymers were determined by NMR using a Bruker Avance III 400 spectrometer operating at 400 MHz for 1 H-NMR and 100.6 MHz for 13 C-NMR. 1 H-NMR spectra were obtained with a 5mm QNP probe at 373 K and the 13 C-NMR spectra were obtained with a 10 mm PA-SEX probe at 373 K. A 3:1 volume mixture of 1, 2, 4-trichlorobenzene and toluene-d8 was used as solvent. The chemical shifts were measured in ppm using for 1 H-NMR the reference of toluene (CHD2 at 2.185 ppm) and for 13 C-NMR the resonance of the major backbone methylene carbon resonance (CH2 at 30.00 ppm) as internal references.

Mid infrared spectroscopy

Mid infrared (MIR) spectra were recorded using a Nicolet iS50 Fourier transform infrared (FTIR) spectrometer from Thermo Fisher Scientific. The spectrometer was equipped with an attenuated total reflection (ATR) module (single-bounce diamond crystal) and a deuterated triglycine sulfate detector and KBr optics. Before each measurement, the diamond crystal was carefully cleaned with ethanol and dried in ambient air. A small amount of sample in powder state was pressed directly on the diamond crystal with a constant pressure of 7 x 10 7 Pa. Background and sample were acquired using 32 scans at a spectral resolution of 4 cm -1 from 4 000 to 400 cm -1 . Spectral data were obtained with OMNIC Software from Thermo Fisher Scientific. The ATR spectra were not corrected for pathlength. Three replicates for each sample were made and compared. If they were similar, only one spectrum was selected and used for the model. They were different for one sample and it was not used in this work.

Near infrared spectroscopy

CHARACTERIZATION OF POLYETHYLENES: FROM THERMAL FRACTIONATION TECHNIQUES TO SPECTROMETRY 4-206 Near infrared (NIR) spectra were collected using a Nicolet iS50 FTIR spectrometer from Thermo Fisher Scientific under nitrogen. The spectrometer was equipped with an integrating sphere (Thermo Scientific Smart NIR).

The synthetized LLDPE gives, for some of them, a heterogeneous powder agglomeration. Working on the raw samples was difficult and a second method using a solvent to dissolve samples was also performed.

To obtain a homogenous solution, 40 mg of polymer in 200 μL of 1,2,4-TCB, with BHT as stabilizer, was dissolved in a 2 ml vial. Then the vials were heated up to 150 °C for 1 hour in order to entirely dissolve the sample. Since glass does not absorb in NIR the samples were analyzed directly through the vials.

Background and samples were acquired using 32 scans at a spectral resolution of 4 cm -1 from 11 000 to 3 800 cm -1 . Spectral data were obtained with OMNIC Software from Thermo Fisher Scientific.

Chemometrics tools

Chemometric analyse of NIR and MIR spectra were achieved using a partial least squares (PLS) method with two different softwares. TQ Analyst software from Thermo Fisher Scientific and The Unscrambler X 10.5.1 software from Camo were used to analyze NIR and MIR data, construct the models and quantify the unknown samples.

RESULTS AND DISCUSSION

Chemical composition of ethylene-1-hexene copolymers

The present work was developed to determine 1-hexene content in LLDPE in a straightforward way. The copolymerization of ethylene with 1-hexene using metallocene catalysts provides polymers with various comonomer content (Scheme 1). Scheme 4-1: Chemical structure of ethylene-1-hexene copolymers

Performance index

The performance index (PI), that indicates the adequacy between the calculated polymer compositions and NMR measurements, was chosen to measure the accuracy of the method. The higher the performance index (up to 100) is, the better the agreement between calculated and NMR values are. This parameter, reported for each method in Table 4-4, allowed us to decide whether the modifications of the preprocessing data improve the accuracy of the method.

Prediction performance

The performance of the model was evaluated with the root mean square error of calibration (RMSEC), the root mean square error of validation (RMSEV) and the correlation coefficient (r). These values were reported in Table 4-4. RMSEC (mol%) corresponds to the error calculated using the standards and was calculated with Equation 4-1.

(4-1) RMSEV (mol%) was calculated with a cross validation method. The Kernel algorithm [46][47][48] was selected. It can be expected to perform well in our case with data containing many samples and few variables. A sample was removed from the calibration set and predicted with a model created with the remaining samples. The procedure was repeated by omitting each of the samples from the calibration set. RMSEV value was a measure of the average uncertainty that could be expected when predicting new samples, and was calculated with Equation 4-2:

Number of factors in PLS regression

4-219

The RMSEV values for the MIR model were slightly better than that values of NIR model. Finally, it appears that the methods [b] and [e] were reliable for the determination of the 1-hexene content in copolymers containing high comonomer content (up to 21 mol%). For lower content the methods [c] and [f] will be the most efficient and suitable. The repeatability and the validity of both methods were evaluated using new samples.

Repeatability of the model

A repeatability test for the measurement of 1-hexene content using the MIR and NIR methods ([c] and [f]) was performed. An unknown ethylene-1-hexene copolymer was measured 10 times by the same operator, in a short period of time. Afterwards, the PLS models [c] and [f] were applied to all IR spectra to quantify the 1-hexene content. A good repeatability of both methods was observed based on the data plot in Figure 456789. An average of 1.59 mol% with a standard deviation of 0.05 were obtained for MIR method [c] and an average of 1.60 mol% and standard deviation of 0.08 were obtained for NIR method [f]. Since a very similar average value for both methods and low sigma values were obtained, we concluded that the proposed models were accurate. Furthermore, the values were in good agreement with the 1.50 mol% obtained by NMR. The relative standard deviation (RSD) for each model was calculated using 10 replicates of the same sample. It is reported in The values calculated by the models all show a bias in the same direction: the predicted results are all higher than the NMR results. This indicates that there is a small source of systematic error in the case of LLDPE obtained with Ziegler Natta catalyst and analyzed by these models. However, the predicted values obtained by IR are quite close to NMR results, which shows that the PLS model can be applied as a routine analysis. Considering this result, we can also conclude that the proposed model is reliable and accurate.

CONCLUSION

In this study a MIR and NIR method combined with PLS modeling was developed for a rapid determination of 1-hexene units in LLDPE. A series of 41 copolymers with a wide variety of chemical composition was synthetized. SEC profiles and TGIC profiles showed that all polymers were quite homogeneous in molar mass and composition. They were then characterized by NMR to determine 1-hexene content, and The modification of the ligand around the metal center alters the regioselectivity of butadiene insertion.

As shown in Scheme 4-3, insertion of butadiene leads to an allyl intermediate.

Scheme 4-3: Various units obtained after butadiene insertion for ethylene-butadiene copolymers.

GENERAL CONCLUSION