Je Remercie Le Professeur

Roberto Lazzaroni

La Professeure Jannick

Ricardo Jiménez Riobóo

Thibaut Le Docteur

Alexandre De Neef

Cédric Samuel
email: cedric.samuel@imt-lille-douai.fr

Grégory Stoclet

Mohamed Rguiti

Christian Courtois

Philippe Dubois

Jérémie Soulestin

Jean-Marie Raquez

Processing of PVDF-based Electroactive/Ferroelectric Films: Importance of PMMA and Cooling Rate From the Melt State on the Crystallization of PVDF Beta-Crystals

Keywords: Ferroelectric polymers, Poly(vinylidene difluoride), Poly(methyl methacrylate), Miscible blends, Flash DSC Ferroelectric polymers, Poly(vinylidene difluoride), Poly(methyl methacrylate), Miscible, Flash DSC, Poling, Piezoelectricity

Si l'on prend la peine de se poser un instant, et regarder quelque peu en arrière, force est de constater que cette thèse n'est pas l'aboutissement de quatre, mais de six années de travail. En effet, les deux premières années (Master) ont été consacrées à la découverte des fondements de la piézoélectricité des polymères sous la direction du Professeur Philippe Dubois, chef de service du SMPC à l'époque. Par la suite, ma thèse aura été réalisée sous la codirection du Professeur Jérémie Soulestin de l'IMT Lille Douai et du Professeur Jean-Marie Raquez de l'UMONS et dorénavant chef de service du SMPC. En bref, tout un cycle hystérétique dans le milieu académique, ce qui fait donc énormément de personnes à remercier après toutes ces années enrichissantes au sein du secteur académique et plus particulièrement à l'UMONS et à l'IMT Lille Douai. C'est également grâce au financement de ces deux universités ainsi que du projet Européen « Interreg -BIOHARV » que cette thèse a pu aboutir. Tout d'abord, je ne peux que commencer par remercier le Professeur Philippe Dubois et le Professeur Jean-Marie Raquez, sans qui je n'aurais simplement pas eu la possibilité de me lancer dans cette expérience qu'est la thèse. Malgré mon parcours asymétrique, ceux-ci m'ont fait confiance et m'ont intégré au sein du SMPC afin de réaliser une thèse sur un sujet encore inexploré au sein de l'UMONS.

Ben, merci pour tout ce que tu m'as apporté, autant du point de vue scientifique (je me sens optimisé) qu'au niveau humain. Tes conseils avisés et ta bienveillance m'ont permis de me surpasser à chaque étape de ce long processus.

Je vais désormais passer la frontière afin de remercier le Professeur Jérémie Soulestin et le Docteur Cédric Samuel. Vous savez à quel point la phrase qui suit m'attriste, mais ces français-là méritent vraiment leurs deux étoiles. Cédric, un énorme merci pour ton soutien indéfectible en tant qu'encadrant principal. Il y a des personnes qui nous marquent durant un parcours académique, et tu fais définitivement partie de celles-là.

Je tiens également à remercier le service de génie électrique de l'UMONS et tout particulièrement Manu Bury qui m'a permis de me faire la main sur la polarisation haute tension et d'en acquérir les connaissances élémentaires. Le service CHIPs de Materia Nova mérite également mes remerciements.

Cette thèse ne fut pas seulement basée sur l'échange de la cotutelle. En effet, de multiples collaborations extra-universitaires ont permis à ce projet d'évoluer grandement.

Au sein de l'Université de Lille, j'ai eu l'opportunité de travailler avec le Docteur Sophie Barrau et le Docteur Grégory Stoclet, alias le magicien de la DRX. À l'Université de Maubeuge, j'ai eu le plaisir de rencontrer Mohamed Ben Achour, qui travaille de son côté sur le PLA piézoélectrique. Merci pour ces échanges enrichissants. Enfin, je tenais à remercier el Doctor Ricardo Jiménez Riobóo pour son accueil au sein

Chapter I: General introduction

During these last years, we are facing up to new smart technologies in the aim to make our daily life easier with an increased energy demand. The ultraconnectivity or global monitoring, commonly called Internet of Things (IoT) (Figure I.1), is one of the faster-growing area that urgently needs to be specifically developed without (or limited) environmental footprint while keeping possible technological breakthroughs and economic growth.

In this context, piezoelectric and ferroelectric materials are among the most emerging players in materials science, driving the development of high technologies in a large range of industrial sectors such as information and telecommunications, healthcare, automotive, aerospace, defense, microelectronics and others. These smart materials have the ability to convert mechanical energy into electrical energy and, unlike other energy sources such as non-renewable fossil energy, mechanical energies represent a renewable and green energy source. Indeed, numerous surrounding mechanical energy sources such as vibrations, shocks and drafts could be converted into exploitable or storable electricity by piezoelectric materials. Piezoelectric energy generation has the merit of being inexhaustible, environmental-friendly, very sensitive, nonharmful, less restricted by the working environment and more importantly economically advantageous.

Figure I.1: Representation of the internet of things

For many years, piezoelectric materials have already been used in many "first-generation" applications such as transducers (ultrasonic, sonar system, ballistic), actuators (vibration controllers, high-precision and small strains), sensors (tactile/haptic systems, accelerometers, pressure/stress/strain/impact gauges), acoustic devices (speakers, headphone, audio-frequency microphone) and electricity generators (high-voltage power sources). In 2019, the worldwide market of piezoelectric materials is estimated to be approximately 1 billion USD (35% for only piezoelectric actuators). For 2024, a potential growth of 6 -10% is estimated for this first-generation application. However, new smart applications are expected which suggests a much steady market growth for piezoelectrics. More recently, ferroelectric and piezoelectric materials have extended their application fields to photovoltaics (organic photovoltaics), memory applications (FeFET, FeRAM) and microelectromechanical systems (Figure I.2). However, these materials are also expected to play a key role in the field of self-powered wireless sensors (for IoT and healthcare) and energy harvesters/microgenerators devices. The global market of piezoelectric materials therefore begins to grow in the field of "energy harvesting devices". The IoT is certainly one of the most influential triggers and the advantages of piezoelectric energy harvesting devices are the possibility of battery-less, extended lifetime, reduced maintenance costs with, of course, positive sustainable development aspects. IoTs are therefore a new development target for many R&D centers, universities, recent start-ups and numerous key industry players (Samsung Electronics, General Electrics, Hewlett Packard, Xerox, Microsoft Technology, Apple, Ricoh, Fujifilm, Canon, Epson, Merck, Arkema, Honeywell, Boeing, etc.).

Although the field of IoT is booming, piezoelectric and ferroelectric polymer materials have not yet reached their full technological maturity in this field, unlike piezoelectric and ferroelectric ceramics. Indeed, these polymers provide many advantages such as flexibility, stretchability, resistance to chemical attacks and ease of implementation at the industrial scale. Major efforts are still required to overcome current technological challenges through a better understanding of these materials as well as the development of advanced techniques to obtain cost-competitive piezoelectric systems at the material/processing level.

The present PhD thesis is carried out in a context of understanding and mastering the knowledges related to the behavior of piezoelectric polymers processed by melt-state extrusion techniques, which can be applied on an industrial scale. A special emphasis was made on the design of piezoelectric materials based on poly(vinylidene fluoride) (PVDF), PVDF being the most popular piezoelectric polymer. To control the polar crystalline PVDF phase, the blending route was chosen by the addition of poly(methyl methacrylate) (PMMA) as a polymeric partner. This manuscript outline is composed of three main chapters.

The first part presents the state of the art and introduce the current research in the field. The various dielectric behaviors are first reported followed by a mapping of PVDF and its peculiar crystalline properties as well as the interest of the PVDF/PMMA blends.

The fourth chapter is devoted to optimizing the implementation/processing of the PVDF/PMMA blends in order to obtain thin films with enhanced polar beta phase content without pre-/post-treatments. Various advanced techniques have been employed to precisely study the crystallization of PVDF under high cooling rates and different amounts of PMMA. Then, the conditions for obtaining the PVDF polar phase have been gathered in a crystal phase diagram. A second part presents prospective studies carried out to characterize the ferroelectric properties of melt-processed PVDF/PMMA blends.

The fifth chapter proposes the study of the impact of functional PMMA copolymers on PVDF crystallization as well as ferroelectric and piezoelectric properties of PVDF blends. A crystalline study was carried out on melt-processed blends of PVDF and PMMA copolymers in order to observe their impacts on PVDF crystallization. Subsequently, the study of the ferroelectric properties of these blends made possible to identify the most interesting compositions. Finally, the polarization conditions and the piezoelectricity were studied in detail to open up different ways of improvements for PVDF/PMMA blends.

Finally, a general conclusion summarizes the main results obtained during this PhD thesis, as well as some research perspectives in order to improve the performance of the proposed thin non-stretched PVDF films.

Chapter II: State of art

II.1. Ferroelectric and piezoelectric polymers:

fundamentals and applications 1.1. General considerations Traditionally, dielectric materials are derived from inorganic materials such as porcelain [START_REF] Harrison | [END_REF] , mica 2 , and quartz [START_REF] Scott | [END_REF] (ceramics and crystals) but more interestingly, polymers can also be used as efficient dielectric materials. They have the advantage of being easily processed and flexible but also finely tailored for various dielectric applications 4 . The dielectric properties (dielectric constant, dielectric losses, polarizability, etc.) of any polymer depend on their chemical composition and internal structure. Most of dielectric polymers are semicrystalline polymers and such dielectric polymer materials could present piezoelectric and/or pyroelectric and/or ferroelectric properties depending on their internal crystalline structure and organization.

When a dielectric material is placed under an electric field, an internal polarization is induced inside the material. Induced polarizations includes electronic, ionic, orientational/dipolar, and interfacial polarization 5 . Each polarization is associated with a dielectric loss at a specific frequency. Dipole polarization, dipole density and occurrence of organized dipole domains are basic phenomenon linked to dielectric behaviors of polymers (Figure II.1).

Linear dielectric polymers 6,7 , more often just called dielectric polymers is a material with the capacity to be polarized under electrical field in order to store the electrical charge. The resulting polarization P or electrical displacement D is linear with the applied electric field E. This type of material is not influenced by the strength of the electrical field, i.e.  𝑟 (relative permittivity or dielectric constant) is constant 8 . This can be explained by the fact that a linear dielectric does not have any net dipole, no dipole coupling capacity and no spontaneous polarization (that quickly returns to zero with removal of electric field). Several polymers display linear dielectric behavior such as poly(ethylene) (PE), poly(ethylene terephthalate) (PET), biaxially-oriented poly(propylene) (BOPP), poly(methyl methacrylate) (PMMA), modified PMMA, poly(phenylene sulfide) (PPS), poly(carbonate) (PC) and poly(ether ether ketone) (PEEK). Thin-film capacitors represent the most common application of these linear dielectric polymers.

Dipolar glasses have similar behavior with isolated dipoles. The interactions between dipoles are weak and no coherent domains are formed. This behavior is essentially observed for ceramics, but Bonardd S. and co. demonstrated in the case of several glassy polymers 5,9 . With relatively high dielectric constants and low dissipation factors, the dipolar glassy polymers can be used for energy storage with minimal energy losses. In the case of high dipole interactions and organization into large coherent domains, a spontaneous/remanent polarization could be observed with potential ferroelectric properties. The dipoles present in these polymers can be arranged upon different dipole sizes and domain structures, as shown in Figure II.1 with charge-discharge responses of typical ferroelectric/relaxor materials. In the following points, their different properties are described.

Ferroelectric polymers

Similar to ferromagnetic materials, ferroelectric polymers [10][11][12] exhibit spontaneous polarization, i.e., an effective electric dipole moment without external electric field. This spontaneous polarization 13 can be reversibly switched by an external field without any change in the domain structure. To characterize the ferroelectric effect, the (D-E) or (P-E) hysteresis loops allow identifying the electric displacement D (or the polarization P) as a function of applied electric field. The resulting polarization D reflects the dipole orientation and the existence of a high spontaneous polarization (at zero electric field, D close to D max ) with reverse polarization (as illustrated by a hysteresis loop, Figure II.2) is generally accepted as proof of ferroelectricity. The most well-known ferroelectric polymer is the poly(vinylidene fluoride) (PVDF), but it is rarely used in its natural state. In fact, the ferroelectric crystalline structure is not generally induced during classical processing. A lot of studies have been focused on different ways to promote specifically the ferroelectric crystalline phase. The use of copolymers like PVDF-TrFE is an example and the most common ferroelectric polymer material but there are other polymers 15 as the poly(trifluoroethylene) (PTFE), cyano-(co)polymers and poly(vinyl chloride or fluoride) (PVC or PVF). One can mention out that biobased ferroelectric polymers are available on the market, odd-number nylons (PA…) 16 , poly(ureas) (PU) 17,18 and poly(lactic acid) (PLLA) 18,19 . In spite of their interest, they currently have lower ferroelectric properties than PVDF.

Most of ferroelectric polymers undergo a structural phase transition from a high-temperature no-ferroelectric (or paraelectric) phase into a low-temperature ferroelectric phase. This specific transition temperature is called Curie temperature (T C ), i.e., the temperature limit for ferroelectric applications. This paraelectric-to-ferroelectric transition usually leads to strong anomalies in the dielectric, elastic, thermal and other properties of the material 20,21 with changes in the crystal unit cell dimensions and ferroelectric domain sizes (Figure II.2).

Several other intermediate dielectric behaviors could also exist depending on the coherent ferroelectric domain size and interactions strengths. Among them, one can mention relaxor ferroelectric and antiferroelectric behaviors. The relaxor ferroelectric (RFE) behavior is a result of random defect insertions into a ferroelectric material. The normal ferroelectric polymer P(VDF-TrFE) is converted into a relaxor ferroelectric 22,23 (ex. P(VDF-TrFE-CFE)) thanks to a chemical approach or in other cases by electron beam irradiation 24 . A significantly reduced remanent polarization (at zero electric field) and dramatically improved discharged energy density are obtained. Relaxor polymers show generally strong dielectric constants, low loss dielectric and a low hysteresis, making the relaxor ferroelectric polymers good candidates for energy storage.

An antiferroelectric dielectric behavior is observed with peculiar ferroelectric domains containing two sublattices polarized spontaneously in antiparallel directions or with a ferroelectric phase that can be induced by applying a strong electric field. Experimentally, the reversal of the spontaneous polarization in ferroelectrics is observed as a single hysteresis loop (Figure II.1). The induced phase transition in antiferroelectrics is observed as a double hysteresis loop (Figure II.1), when a low-frequency AC field of a suitable strength is applied. So far, no inherent antiferroelectric crystalline phase has been identified for polymers. These behaviors are still new for semi-crystalline polymers and their fundamental mechanisms have not yet been fully understood. The antiferroelectric behavior with double hysteresis loops has been reported first for β-PVDF at temperatures below -60 °C20 and P(VDF-TrFE) with VDF content lower than 50 mol% 25,26 . The double hysteresis loop consists of a dipole depolarization step at low fields and a polarization reverse step at high fields. It only appears in the first stage a few (D-E) cycles and eventually transforms into a single hysteresis loop upon repeated cycling. Therefore, this behavior is attributed to imperfect P(VDF-TrFE) crystals cooled from the melt with the coexistence of ferroelectric and paraelectric phases 25 .

Even though antiferroelectric and relaxor ferroelectric behavior are not well-known and controlled, several applications are already expected. With these specificity, they can naturally claim the place in high energy storage capacitors as a defibrillator capacitor or a DC-link capacitor for electric vehicles . They also present electrocaloric property, which has a great potential to realize solid-state cooling devices 27 .

Piezoelectric polymers

The piezoelectric behavior of polymer is a specific coupling between dielectric and mechanical behaviors of dielectric material. The French physicists Jacques and Pierre Curie discovered the piezoelectricity in 1880. These specific materials have the property to produce electrical charges across their boundaries in response to applied mechanical stress, called the direct piezoelectric effect [START_REF] Bonardd | [END_REF] . The relationship between induced charges per unit area and the applied stress is linear and reversible (the reverse piezoelectric effect, the internal generation of a mechanical strain resulting from an applied electrical field).

The nature of the piezoelectric effect for a polymer is closely related to the occurrence of electric dipole moments. The dipole density or polarization (dimensionality [C.m/m 3 ]) may be calculated by summing up the dipole moments per volume unit of the crystallographic unit cell 29 . As every dipole is a vector, the dipole density or polarization P is a vector. Dipoles close to each other tend to be aligned in regions called Weiss domains. These domains are usually randomly oriented but can be aligned using the poling process. Not all piezoelectric materials can/need to be poled.

The quasi-majority of piezoelectric materials in practical use (with the important exception of several materials such as quartz or specific oriented polymers) are ferroelectric. In a ferroelectric material, the remanent polarization could be modified with the applied stress to give rise to piezoelectricity. Every ferroelectric material is piezoelectric but not every piezoelectric material is ferroelectric. Indeed, such effects could also appear when asymmetrical chemical structures are present in the crystalline state or even in the amorphous state 30 . The following Figure II.3 shows a non-exhaustive comparison between three main materials having a piezoelectric behavior. Each material has these advantages and drawbacks. For polymers, the value of piezoelectricity is clearly lower than ceramics, but polymers are much easier to be processed (temperature of process, thin film, microfabrication …) and have a better stretching capacity. In this respect, each material will target specific applications. In the specific case of polymers, different piezoelectric categories may be considered as illustrated and explained in details by Harrison 31 . In the case of this study, only bulk piezoelectric polymers will be considered and especially semicrystalline piezoelectric polymers. In this case, the piezoelectric effect of this category is due to the molecular structure of the polymer, its semi-crystalline structuration and its orientation. 1.4. Advanced applications of ferro/piezoelectric polymers Piezoelectric materials find every-day uses such as the ignition source for lighters, push-start propane barbecues, time/frequency reference sources in quartz watches and amplification pickups for some guitars 18,31,32 . The piezoelectric effect also represents the basic phenomena for a number of scientific microscopy techniques with atomic resolution such as scanning tunneling microscope (STM), atomic force microscope (AFM) and scanning near-field optical microscopy (SNOM).

Sensors and actuators are important applications of piezoelectric polymers. Numerous examples are found in the medical field. These materials could be used as sensors 33,34 for prosthesis, orthotics or noninvasive cardiopulmonary operations or artificial muscles, as depicted by De Rossi 35 and Sheng-Guo 34 . In the acoustic field, piezoelectric polymers are used for hydrophones 36 , shock wave sensors, surface acoustic wave sensors, as depicted by Howarth and Rittenmyer 37 .

Today, the researches about piezoelectric polymer materials are focusing on specific applications in energy harvesting. The aim is to develop energy harvesters 38 from mechanical energy (wind, motion, vibration, strain …) and convert it into electricity. Numerous potential applications are thus observed in the field of IoT for piezoelectric polymers as energy sources or sensors. Table II.1 shows a list of potential sector, applications, locations and devices using piezoelectric polymers. This table demonstrates that the potential applications for piezoelectric materials are very broad.

It could be also noticed that, in the Internet of Things (IoT) sector, ferroelectric polymers could also be used through the realization of FeRAMs 39 , ferroelectric random access memories, using the bi-polarizability as a binary language. The advantages of these non-volatile FeRAMs include fast read/write speed, minimum energy consumption, long cycle life and high flexibility of these polymers (PVDF-TrFE). Note that the robotic based on ferroelectric materials is also a growing sector for medical operations 40 and spatial exploration among others.

II. 2. PVDF: Synthesis, crystallinity, processing and properties

Generalities

Fluorinated polymers such as PVDF with high fluorine contents exhibit high thermal resistance, aging resistance and weather resistance with excellent inertness to solvents, hydrocarbons, acids, alkalines, low surface energy (oil and water repellency), low flammability, low refractive index, and low moisture absorption. Hence, these specialty polymers have found many applications 41 in building industry, petrochemical and automotive industries, aerospace and aeronautics, chemical engineering, optics and microelectronics.

PVDF is a semi crystalline polymer having the repeating unit (CH 2 -CF 2 ) (Figure II.5). The glass transition (T g ) and melting (T m ) temperatures of the amorphous and crystalline PVDF regions are in the range of -45/-30 and 155/192 °C, respectively. Physical and electrical characteristics of PVDF have been reported in various reviews [42][43][44] , and depend upon the molecular weight, molecular weight distribution, chain configuration, crystalline form, and chain defects 45 . Among these properties, PVDF is attractive for its piezoelectric (Kawai 46 Considering its excellent combination of properties and processability, the PVDF is the second fluoropolymer after PTFE (Teflon), in terms of production volume. Furthermore, its high level of intrinsic crystallinity (ca. 40-60%) results in good mechanical properties (stiffness, toughness and creep resistance). However, PVDF has also two main disadvantages: high melting point (cost of process) and poor solubility in common organic solvent 43,44 (only soluble in DMF, DMSO, DMAc and NMP).

PVDF synthesis

PVDF 43 is usually synthesized by a radically-initiated VDF polymerization in aqueous emulsion or suspension at temperature of 10-130°C under pressures ranging from 10-300 atm (or in supercritical CO 2 51 ). The reaction is heterogeneous and the process needs a fluorinated surfactant. Polymerization procedures, temperatures, pressures, recipe ingredients, monomer feeding strategy and post-polymerization processing have a great influence on product characteristics and quality, as discussed in well-documented reviews 43,52 . However, the synthesis is not safe in conventional conditions, its explosive limit is 5.8-20.3 vol % of VDF in air, for example. The piezoelectricity in such a material may be due to several effects: ➢ When the material is strained, dielectric constants of the crystalline and amorphous parts may change differently leading to an electro-strictive effect. ➢ The elastic constants of the crystalline and amorphous parts may be different leading to a piezoelectric effect. ➢ The crystalline parts have an intrinsic piezoelectricity as in quartz.

PVDF crystalline structures

Researchers have identified at least five different crystal structures for PVDF. The five crystal phases are referred differently depending on the authors, but the most common naming scheme is α, β, γ, δ and . The most frequently studied are α, β, and γ crystal phases [54][55][56] . This polymorphism is directly related to the slightly larger van der Waals radius of the fluorine atom (1.35 Å) 57 versus that of the hydrogen one (1.20 Å). The different conformations are also strongly dependent on processing and electrical, thermal or mechanical treatments that the polymer undergoes.

A. Alpha phase

The most common polymorph, α phase (form II), having a trans-gauche configuration (TGTG′) (Figure II.8) has a nonpolar conformation of the polymeric chains. Hydrogen and fluorine atoms are alternated in a regular way on both sides of the chain, giving a helical structure 58 . The helical molecular shape is much lower in energy than the planar zigzag formation (β-phase), which is most likely why the α phase is readily formed from the melt 59 . Dielectrically speaking, it has a dipole moment normal to the chain axis, the molecular chains arrange their dipoles in an antiparallel array, therefore it results a non-polar, centro-symmetric unit cell. Applications, linked to this specific phase, are essentially focused as membranes on chemical industry, construction and biotechnology.

B. Beta phase

The β crystal 60 phase (form I) of PVDF forms a planar zigzag (TT). The alltrans structure of β phase PVDF forces the fluorine atoms along the carbon backbone to come closer together and overlap their van der Waals radii (Figure II.9). The simple head to tail organization and planar zigzag structure creates a very organized crystal. This structure allows tighter packing density and reduces the intermolecular strain allowing greater chain movement. Thermodynamically, it is the most stable phase. The β form of PVDF has superior dielectric permittivity 41 thanks to the orientation perpendicular of dipoles to the polymer chain axis and are parallel to each other 61 . This form is not centrosymmetric and is thus intrinsically piezo-, pyro-, and ferroelectric. The β-phase is the one with the highest dipolar moment per unit cell (8 × 10 -30 C.m) when compared to the other phases 62 .

The amount of head-to-head or tail-to-tail monomers along the backbone determines how easily the β phase will get formed. These imperfections along the carbon chain allow more space between the fluorine atoms and make the β phase more stable. A certain percentage of these HH or TT defects during polymerization decreases the likelihood of β phase formation. Some studies have shown that both HH / TT units are distributed randomly along the polymer chain. The temperature at which PVDF is synthesized, determines the number of headto-head (HH) and tail-to-tail (TT) units that occur in polymer chains. The percentage of head to head occurring in most commercially available PVDF is approximately 5%.

C. Gamma phase

The intermediate polar conformation (TTTGTTTG′) phase γ (form III) is formed when the polymer is moderately stressed or when high-temperature annealing is applied. This phase is formed during melt crystallization at temperatures above 160 °C and reaches its highest value nearby 170 °C63 . The molecular chains are packed in parallel in the non-centrosymmetric, polar crystal (Figure II.10). This form is less known than the other forms and less employed 64 .

D. Identification of polar phases

In this regard, the β and γ phases are the most electrically active phases, their promotion within the material is an on-going pursuit due to the strong interest in application areas such as sensors, actuators, batteries, filters, chemical warfare protection, magnetoelectric, and, more recently, in the biomedical field [65][66][67] . Different strategies have been therefore developed to obtain the electroactive phases of PVDF, mainly focusing on the development of specific processing procedures and the inclusion of specific fillers.

The two phases of PVDF first discovered were the α and β-phase, which are clearly identified by FTIR and X-ray diffraction 62 . However, γ-phase has caused some confusion in its identification and has been mistakenly reported as the β-phase 68 . These mistakes have persisted for a long time and still happen nowadays due the considerable less attention directed to the properties of the γphase 69 . A careful interpretation of the results provided by the combination of FTIR, XRD and DSC are enough to identify the correct phase of PVDF 55,[70][71][72][73][74][75][76] and Table II.2). Indeed, the use of more than one technique is sometimes needed due to the superposition of the peaks of β, γ and α-phases on individual technique. [77][78][79] or applying different conditions such as mechanical stretching of the α-phase 55,[80][81][82][83] , high pressure [84][85][86] , poling under a high electrostatic field 87 , ultra-fast cooling [88][89][90] , by addition of nucleating fillers or nanoparticules [91][92][93] , hydrated ionic salt 94 , blending etc.. Currently, four main procedures commonly employed to promote the beta phase.

A. Stretching

Piezoelectric PVDF films formed in most industrial processes rely on β modification obtained by rolling or drawing of the α-PVDF at elevated temperatures. Starting from the α-phase, stretching is the most employed technique to obtain the β-phase. Conversion of α into β-phase takes place at stretching temperatures in the range of 70 -100 °C, at a stretching ratio of about 3 -5 (L final /L initial ). It is seen from the literature 81,95 that the critical temperature for obtaining α-to-β transformation is 140°C. Above this temperature, α-to-β transformation does not occur. Although the mechanical deformation itself introduces some preferred crystallite orientation, it does not affect considerably the orientation of molecular dipoles 96 . Therefore, the piezoelectricity measured directly after mechanical deformation is still low. Considerable enhancement of dipole orientation leading to high piezoelectricity is achieved by additional polarization of previously deformed material 97 . It was shown 98,99 that the piezoelectric constant of PVDF samples prepared under the same poling conditions increases with both fraction of β crystallites and degree of crystallinity (influenced by stretching ratio and temperature, Figure II.12).

Figure II.12: d 33 coefficient and β-phase content (%) for PVDF with stretching ratio of R = 5 at increasing stretching temperatures (on left) and for PVDF with increasing stretching ratios R at 80°C 100 (on right).

B. Copolymers

Copolymerization is the most common and efficient method to perform effective changes in the main properties for commercial polymers. As a result, copolymerization usually modifies the symmetry of the polymeric chain and modulates both intramolecular and intermolecular forces, so that properties such as melting point, glass transition temperature, crystallinity, stability, elasticity, permeability and chemical reactivity may be varied within wide limits Contrary to PVDF, and under specific molar ratios, it presents always the ferroelectric β crystalline phase. The addition of the third fluoride in the TrFE monomer unit generates a high electrostatic repulsion in the PVDF chain with the consequence to (Figure II.14) favor the all-trans conformation and to induce therefore the ferroelectric β-phase independently of the processing method. This situation occurs when the VDF content is between 50 and 80% 102 , corresponding also to the range of the ferroelectric behavior of the copolymer. As previously said, the PVDF-TrFE is not the only ferroelectric PVDFbased copolymer, another example is P(VDF-HFP). It consists in the incorporation of the amorphous phase of hexafluoropropylene within the PVDF homopolymer. The presence of ferroelectric properties in this copolymer is strongly dependent on the preparation method of the film (high impact of the amorphous phase from HFP). PVDF has also been modified by the introduction of chloride trifluoride ethylene (CTFE) on the polymer chain, producing the P(VDF-CTFE) copolymer. The introduction of bulky CTFE makes the structure loose, which result in an easier orientation of dipoles under external electric field. The piezoelectric constant, d 33 for this copolymer, for example, reaches the value of 140 pC/N 105 . Moreover, this type of copolymers has also shown a good compatibility with the ionic liquids (ILs). Jin Yang et al. 106,107 proposed that the nanostructuration effect is strongly dependent on the diffusion ability and the dipolar interaction strengths of ILs with P(VDF-CTFE) due to the difference in the chemical structures.

In summary, the copolymerization approach allows promoting the polar phase of PVDF, but there are several drawbacks. Indeed, the realization of a copolymer is related with a much higher production cost, together with a decreased Curie temperature transition, limiting mainly their physical applications.

C. Nanofillers

Some important advances have been obtained in order to unveil the main interactions, driving the nucleation of the electroactive phases of PVDF using specific fillers. The nucleation of the electroactive β-phase in such nanocomposites obtained by melt processing was attributed to the interaction between the negatively charged particles and the polymer CH 2 groups, having a positive charge density 108 . The electroactive β-PVDF is nucleated by the presence of BaTiO 3 ceramic fillers with a β-phase maximum of ∼80% 109 . This effect strongly dependent on the filler size and almost independent of the filler content. The nucleation of the ferroelectric phase is strongly influenced both by geometrical factors due to the nanosize of the fillers and, by interactions at the interface between the local electric field around nanoparticles and PVDF dipoles.

Recently, nanoclay and carbon nanotubes have been the main focus as means of enhancing the formation of β-phase crystals in PVDF films. For PVDFclay nanocomposite, the intensity of reflections characteristic (XRD) of the α-phase decreases with nanoclay content. The peak disappears at nanoclay content of 2-5 wt.% (Cloisite, Montmorillonite, Smectite…).

D. Blends

The ferroelectric and piezoelectric properties of PVDF, can be improved by chemical modification through copolymerization, by the addition of nanofillers to create a composite and by physical modification through stretching, with their own disadvantages. However, another technique as a good potential to improve the piezoelectric/ferroelectric properties of PVDF is solvent-or melt-blending 110- 112 .

Their properties depend to a large extent on the miscibility of the components. A miscible "mixture" is intimately mixed thanks to thermodynamic forces. The distinct interactions promoting miscibility are delivered by dipole van der Waals interactions or by hydrogen bonding. Thanks to a strong electric dipole in its monomer unit, PVDF is miscible with certain number of polymers having a strong molecular electric moment. Melt-blending is a simple and easy process very interesting from industrial point of view. Knowing the thermal stability problem of ferroelectric PVDF-TrFE, the PVDF-based blending could improve the maximum operating temperature through the enhancement of the structure stability by specific interactions with the additive. Furthermore, the approach can resolve the problem of up scaling of applications at reasonable cost. A specific point is presented below on the blends (II.3. Blends based on PVDF).

Polarization, poling and ferro/piezoelectric properties of PVDF-based polymers

A. Generalities

Each PVDF chain has a coupling of positive and negative charges referred to as a dipole. The negatively charged fluorine atoms are coupled with the positively charged hydrogen atoms. The dipoles are rigidly attached to the carbon backbone and their orientation depends on the polymer crystal structure. The β phase has a highly polar arrangement of hydrogen and fluorine atoms. The dipoles along the carbon backbone, and within the crystal, align themselves maximizing spontaneously polarization within the unit cell 113,114 .

The strong dipole formed by the all-trans conformation of the carbon backbone, and parallel arrangement of the chains in the crystalline unit cell create a net charge in β phase structure of PVDF. When β forms naturally the net charge is zero because the dipoles are arranged randomly. However, when a large electric potential is applied across the material, the dipoles align and produce a net positive charge. An example of the dipole alignment can be seen in This dipolar alignment, or poling, must be performed on any piezoelectric polymer before it can be used piezoelectrically. The mechanisms associated to poling are not very well understood. What is known is that crystals within a polymer are influenced by a sufficient electric field and create a net polarization. This net polarization aligns the individual crystals within the polymer causing them to collectively respond to changes in their surroundings and gives PVDF its strong piezoelectric characteristics.

Poling is a group of widely used techniques to reorient the polymer with the aim of increasing the net polarization 116 vector in the 3 directions (opposite to the electrical field, direction 1). Usually, poling is undertaken using an electric field applied (from DC or AC current) along the thickness axis of the piezoelectric material at elevated temperatures 32 . The two most common methods of poling are electrode and corona techniques, which are shown schematically in Figure II.17 (a and b). Electrode poling is simple, as it only requires electrodes (coated) on both sides of the film, as shown in Figure II.17 (a). The enclosure can be filled with an insulating fluid or in a heated vacuum to avoid breakdown of the polymer. Intimate contact between the polymer surfaces and the electrodes is required to achieve, in the β phase of PVDF, enhancement of dipoles polarization 32 . Poled ferroelectric materials 117 are characterized by the remanent polarization (the amount of polarization remaining after the poling field is removed, P R ) and by the coercive field (the field required to flip half of the previously induced remanent polarization so that the net remanent polarization is zero, E c ). Remanent polarizations of up to 50-75 mC/m² and coercive fields of 100 to 120 MV/m are typical of PVDF. To characterize these properties which allow to identify the importance of ferroelectricity, the Sawyer-Tower method 118,119

B. Impact of polarization conditions

The degree of polarization is correlated with applied voltage until a saturation level. The same polarization response can be achieved at any temperature, but poling time increases at lower temperatures (usually below 70°C) and can produce a non-uniform distribution within the film. The best uniformity is achieved by applying electric fields for an extended period at temperatures above 90°C. The polarized β-phase is stable and the decay of polarization is only significant at temperatures above 140°C [120][121][122][123] . However, the hysteresis loops obtained in low β-phase content material are attributed to contributions of trapped charges induced during poling 124,126 , as the α-phase material does not show conditions towards switching. The degree of crystallinity has been proposed to affect the shape of the ferroelectric loops, leading to rounded loops for polymers with low degrees of crystallinity 127,128 .

A phase transition 125 of PVDF films from α crystal phase to β crystal phase was obtained at 95°C under an electric field of 150 MV/m. The movement of hysteresis implied that the non-polar α phase transited to the polar β phase under increased poled electric fields. Structural changes caused by electric field were probably due to internal rotation of molecule chains and alignments of intrinsic dipoles in crystalline phase of PVDF polymer films. The applied electric field resulting in all-trans planar zigzag conformation was induced into the β crystals. This allowed the dipoles on the polymer chains to align from normal to the direction of the applied poled electric field.

II.3. Blends based on PVDF

PVDF-based miscible blends

Unlike other crystalline polymers, PVDF exhibits miscibility with other polymers such as poly(methyl methacrylate) (PMMA) over a wide range of blend compositions 129 , where this characteristic can be useful in the fabrication of membrane with the desired properties. Poly(vinylpyrrolidone) (PVP), poly(ethylene glycol) (PEG) and poly(methyl methacrylate) (PMMA) are the three main polymer partners for PVDF. However, PVDF/PMMA are the mostly used PVDF-based blends because PMMA provides an intense miscibility with the PVDF matrix 130,131 .

The use of PVDF-based blends as membranes [132][133][134][135][136][137] is clearly the most important application. Comparing with other materials such as poly(sulfone) (PS), poly(ether sulfone) (PES) and poly(imide) (PI), PVDF is relatively more hydrophobic (linked to its surface tension). PVDF remains the best option of membrane material because it does not dissolve in common organic solvents and, by possessing low level of extractables, PVDF can be considered as a pure polymer which makes it a suitable candidate in biomedical and bio-separation applications. A 50/50 PVDF/PMMA composition is clearly beneficial with better permeation than comparable membranes of similar mean pore sizes.

Another current trend in PVDF-based blends is their use in battery applications. For example, PVDF/PMMA blend microporous membranes were used in an electrolyte liquid to form polymer electrolytes. The use of PMMA changes the membrane morphology from cellular to network structure and causes an increase of electrolyte uptake and ionic conductivity of blend membranes. Proton exchange membrane fuel cells (PEMFC) also utilize such type of membranes. The PVDF-based blend (PVDF/PET/GR) is implemented to obtain a bipolar plate for fuel cells, holding a great promise for use as an environmentally friendly power source for future transportation technology. It can be highlighted applications as polymer electrolytes for dye-sensitized solar cells (PVDF-PMMA-EC-I 2 ).

In brief, the PVDF-based blends are used for many membrane applications, but piezoelectric properties and linked applications were rarely studied and developed. The PMMA is one of the most blended with PVDF due to the high miscibility and the good complementarity between both properties.

Case of PVDF/PMMA blends

The miscibility of PVDF/PMMA blends has been studied extensively since the 1970s. These blends have been found to be completely miscible over the entire range of compositions above the PVDF melting temperature (T m ) of 170 °C and below lower critical solution temperature (LCST) of 330 • C. According to most studies 138,139 , PVDF can crystallize in the blend if its weight fraction in percent exceeds 50 wt-% PVDF (Figure II.20). The miscibility of these two polymers has been evaluated through the transparency of the blends, the Flory-Huggins interaction parameter, the glass transition temperature and so on 140 . Some researchers confirmed that PVDF/PMMA is miscible regardless of PMMA configurations [141][142][143] (syndiotactic, atactic or isotactic PMMA configurations).

The DSC thermogram shows that the melting temperature of PVDF/PMMA blends decreases with the PMMA content in the blend. For instance, the T m of PVDF/PMMA blend is 170 ºC for 30 wt-% PMMA blends. Figure II.20 shows that the blend with 30% of PMMA exhibits two crystallizations peaks. This phenomenon is explained in the literature by the melting of two distinct populations of crystals. In fact, the β crystals melt at a higher temperature than α crystals 144,145 . The decrease of crystallinity (enthalpy) and melting point are indicative of the good affinity and miscibility between PVDF and PMMA polymers. Besides, it is well-known that the PMMA is largely amorphous and does not contribute to the heat of melting. In fact, the decrease of T m in the different blends with the addition of PMMA is explained by the thermodynamic effect, which occurs in a crystalline polymer-diluent blend, valid in the case of crystalline polymeramorphous polymer system 146 . Nishi and Wang 142 concluded that the miscibility between PVDF and PMMA is stereoselective.

From FTIR analysis, it is observed that, the elongation frequency at 1721 cm -1 of PMMA carbonyl group (C = O), is shifted to higher wavelengths (1724 cm -1 ) in the PVDF/PMMA blends. This shift is due to the specific interactions between the carbonyl group of PMMA, on the one hand, and the CH 2 group of PVDF, on the other hand. This finding is indicative of the formation of a miscible blend confirmed by the results reported by Colemann and Painter 147 for PMMA/PVDF blends. The presence of a band at 882 cm -1 in the spectrum of the melted blend indicates that trans sequences of poly(vinylidene fluoride) (PVDF) in the melt state can increase upon PMMA addition. PVDF all-trans conformation allows more efficient interactions with PMMA, which are energetically more stable than the trans-gauche (TG) conformation 148 .

In order to confirm the impact of the PMMA in the crystalline phase of PVDF, a wide-angle X-ray diffraction analysis (WAXS) has been performed on different PVDF/PMMA blends. In Figure II.21, it has been found that the peak at 46,43° (identified as α-phase) and at 20,10° (β-phase), disappears when the PMMA proportion is higher than 30 wt-%. Beyond this, they are no longer found in the spectrum and the amorphous curvature becomes more and more obvious as the proportion of PMMA increases. The progressive decrease of 20.10° peak (without disappearance) shows that the matrix always present crystals of the β phase of PVDF up to a PMMA content of 30%. This observation illustrates the high level of interactions between the two polymers. Furthermore, the decrease in the PVDF crystallization with the addition of PMMA can also be explained by the fact that the diffusion of PVDF towards the crystalline surface, would have been impeded by the interactions with PMMA 145,149-153 .

Figure II.21: WAXS patterns of PVDF/PMMA blends 146

From the morphology viewpoint, using the UV-visible absorption spectra of PMMA/PVDF blend, the shape absorption edge (around 240 to 290 nm) shows a shift in band edges toward the higher wavelengths. These shifts indicate the formation of inter/intra interactions between PMMA and PVDF. The shift in absorption edge in the films reflects the variation in the optical energy band gap, E g . The optical energy band gap decreases with increasing PMMA content. The existence and variation of optical energy gap, E g , may be explained by the occurrence of local crosslinking within the amorphous phase of PMMA and PVDF.

Crystallization of the PVDF beta phase in PVDF/PMMA blends

As explained in the previous chapter, PVDF has several types of crystalline form (α, β, γ etc.). The addition of PMMA tends to promote crystallization in βphase. This is one of the most promising polymer pairs that has been reported to be compatible over a range of compositions in the solid state.

PMMA addition is responsible for the preferential formation of the β-phase upon quenching the molten blends. The drastic reduction of the crystallization rate upon addition of PMMA is a cause, which favours the formation of the β crystalline phase, reported by Hsu and Geil 88 . Indeed, the significant decreases in the rate of crystallization of PVDF upon the addition of a compatible amorphous polymer with a high glass transition temperature can be recommended as one of the best ways to enhance the efficiency of quenching, cited from an earlier study by our group 154 and will be the first experimental part of this thesis.

The degree 155 of crystallinity was found to decrease with increasing PMMA content, which was confirmed by XRD and DTA analysis. SEM micrograph shows spherulites which increase with the addition of PMMA and it becomes sharper and contains a longitudinal shape. These results can be interpreted by considering the Hodge et al. criterion which establishes a correlation between the height of the peak and the degree of crystallinity (XRD). The modifications caused by the PMMA addition modify the kinetics of PVDF crystallization and promote the expected polar β-phase.

Thermograms of the commonly used random copolymer P(VDF-TrFE) show a ferroelectric-paraelectric transition depending on composition. The Curie temperature increases with VDF content. Extrapolation suggests that the Curie temperature of neat PVDF is about 197 °C. In the DSC measurements of the PVDF/PMMA blends, no evidence could be detected in order to ascribe the Curie temperature of PVDF, which suggests that the Curie temperature of the blends remains higher than the melting temperature.

Ferroelectric and piezoelectric properties of PVDF/PMMA blends

To obtain the electrical activity of these blends, the β-phase is not the only criterium. Indeed, several parameters seem affecting the piezoelectric effect such as crystallinity, crystals size, amorphous-crystal interphase, crystalline dipole coupling and poling conditions.

When the films based on blends are molten, ice quenched, (and subsequently annealed), PVDF crystallizes in the ferroelectric β-phase. PMMA promotes the formation of the β-phase over the α-phase for steric reasons; the dipole/dipole interactions favour the trans-trans conformation of the highly polar β-PVDF over the trans-gauche conformation of the nonpolar α-PVDF. The presence of PMMA suppresses the PVDF crystallization and, hence, the roughness of blend films notably decreases with increasing PMMA content (see

Figure II.22).

The red symbols present the degree of crystallinity as derived from the DSC first heating scan. One of insets shows the rms roughness derived from AFM measurements as a function of composition. Above 40 wt-% PMMA, the films are amorphous. The crystallization is then kinetically hampered as evidenced in the phase diagram by the crystallization temperature being close to the glass transition temperature 156 . Phase-field simulations of the crystallization of PVDF from the miscible vitreous blends show that crystal growth at high PMMA fractions is retarded thermodynamically due the formation of gradients in the amorphous polymer regions with associated free energy penalty. So, in the first stage, the PMMA brings a modification of crystallization kinetics in favour of the polar phase, but in return, the crystallinity and the size of crystals can decrease too. The decrease of crystal size 114 caused by the PMMA presence is also an other specificity which promotes the polar phase. However, both effects have a negative effect on the electroactivity of the PVDF. Dynamic mechanical 129 , calorimetric 157 , and microscopic 158 studies of crystalline PVDF/PMMA blends reveal the presence of a crystalline PVDF phase and a miscible PVDF/PMMA amorphous phase. Efforts to identify the molecular origin of the dielectric response and to associate it with a specific morphology in crystalline polymers and blends have yielded a new dimension with the introduction of interphase concept. The term interphase is generally accepted upon the fact that the morphology of crystalline polymers is consisted of a crystalline lamellar phase, an amorphous phase, and a crystal-amorphous interphase. This view of morphology sheds light on important questions regarding the nature of the molecular motions and relaxations associated with each of these morphological regions. The crystal-amorphous interphase in crystalline homopolymers and polymer blends has been claimed by several authors. The initial argument could be traced to the classic studies by Flory 159,160 , who pointed out that the boundary between the ordered crystals and the disordered liquid-like regions in crystalline polymers cannot be as sharp as in monomeric systems. Since then, a number of theoretical calculations 161 and experimental measurements 162 have been performed and quantitative descriptions of the interphase have been made. The formation of an interphase in crystalline PVDF/PMMA blends has been proposed on the basis of the theoretical considerations of chain packing at the surface of lamellar crystallites 161,163 . Dielectric data for relaxations in PVDF/PMMA blends is scarce and marred by a narrow frequency range. The experimental evidence from dielectric measurements for the presence of the interphase was claimed by Hahn, Wendorff, and Yoon 164 . Concerning more specifically the characterization of the ferroelectric efficiency, some researchers as Stingelin et al. 166 observed a complex behavior related with this interphase. A typical hysteresis loop for a thin film capacitor of a PVDF/PMMA (90:10) blend is shown in the inset of (Figure II.22).

Contrary to P(VDF-TrFE) copolymer which always displays a square loop, the blend films lead to thin hysteresis loops as recorded in any conditions (applied voltage and number of cycles). As leakage currents could be ruled out, it can be attributed this response to their nanocrystalline micro-structure. The coercive field is about 110 MV/m, comparable to that reported for PVDF 167 , and higher than that reported for the ferroelectric P(VDF-TrFE). The remanent polarization is presented as a function of PMMA content in Figure II.22. The spontaneous polarization decreases with PMMA content from 5,4 μC/cm 2 at 10 wt-% PMMA to a negligible remanent polarization at 40 wt-% PMMA. The polarization depends on the annealing temperature after, e.g., ice quenching. In the case of blend films after ice quenching annealed at a low temperature of only 120 °C, according to XRD measurements the PVDF still crystallized in the ferroelectric β-phase. However, the degree of crystallinity is low and pristine PVDF are not ferroelectric. A propeller-like thin paraelectric loop was observed. The polarization is not permanent but disappears upon cooling down to room temperature. The origin therefore is different than that as recently reported electric-field induced polarization of ultrathin films of P(VDF-TrFE) 168 . XRD measurements have demonstrated that for those films the changes are permanent and due to electric-field induced crystallization. The dependence of the remanent polarization on PMMA content in the blend films is plotted in Figure II.22 together with the degree of the crystallinity. For neat PVDF a degree of crystallinity of 45 % is calculated. The crystallinity monotonically decreases with increasing PMMA content. At 40 wt-% PMMA and above, the crystallinity is negligible. The crystallization is kinetically hampered as the crystallization temperature approaches the glass transition temperature. Comparable values for the crystallinity as a function of PMMA content have been reported previously 111,169,170 . The remanent polarization is due to a permanent induced surface charge density. Not surprisingly, therefore, Finally, regarding the piezoelectricity, PVDF/PMMA blends seems to present definitely interesting properties from a scientific viewpoint and can be fruitfully used in some applications. Nevertheless, there are few references to the piezoelectricity of these PVDF/PMMA blends, despite the interesting observed ferroelectric properties. However, the general report (Figure II.25) is an exponential decrease of the piezoelectric coefficients with the PMMA addition 54,172,173 . There are considerable dielectric losses at high frequency (represented by the area of hysteresis loop) in the case of blends with a relatively high content of PMMA as compared to PVDF (Figure II.26), thus leading to both poor piezoelectric performances (Figure II.25) and electromechanical coupling coefficients. The shift towards higher temperature (and thus towards higher frequency at room temperature) of the loss peak is not appreciable in the case of low PMMA content blends. It suggests the existence of two conjugate amorphous phases (the pure PVDF amorphous phase and the amorphous/crystalline interphase). Further investigations are needed to understand the loss mechanisms at low PMMA content PVDF-PMMA blends, the complexity and the limitation with the use of PMMA in the PVDF-based blend 172 is an evidence.

II.4. General conclusion and challenges

Although the poly(vinylidene fluoride) is the most well-known ferroelectric/piezoelectric polymer, it remains poorly investigated in the related field, in particular for the origin of its ferroelectric and piezoelectric behavior. Actually, PVDF is more employed in non-piezoelectric application such as pipes with high acid resistance and low adhesive property and separating ultrafiltration membranes. However, this electroactive polymer is beginning to take more and more a leading position in the market of the electroactive materials, because its properties are very interesting in terms of flexibility, implementation, printability and impact resistance by comparison with brittle piezoelectric ceramics.

Unfortunately, achieving electroactive PVDF is not so simple as some modifications (physical or chemical) must be applied in order to transform the non-polar α-phase into the polar -phase (followed by a complex poling step). In this respect, a lot of studies were focused on the preferential development of the β-phase using different approaches (stretching, copolymerization, adding of nanofillers and polymer blends). Currently, the copolymerization remains the most effective technique which allows to obtain the most efficient and stable piezo/ferroelectric polymer material.

The challenge of this project is to investigate a simple way of obtaining the polar phase of PVDF that can be performed at the industrial scale in order to address to the more and more demanding energy harvesting applications. The blending approaches with PMMA can bring this solution in view of large possibilities offered by the miscibility with PMMA. In this context, the processing of PVDF/PMMA blends using up scalable melt-based processes of the plastic industry need to be investigated in more details with the aim to obtain highperformance piezo/ferroelectric polymer blends.

Chapter III: Research strategies

The aim of this project is to revisit the PVDF/PMMA blend approach by focusing on the melt-processing in order to control the formation of the polar βphase, as an innovative approach regarding classical solution-based processes reported in the relevant literature. In this respect, we will focus our research strategy on (1) the investigation of the melt-processability of PVDF/PMMA blends into thin film using an extrusion-calendering process as an industriallyrelevant technique, (2) the understanding of the crystallization behavior of these blends (obtained by extrusion-calendering) with their related ferro/piezoelectric performances and finally (3) the test of new approaches to boost previous performances.

Concretely, the scientific strategy was carried out into two main steps as:

➢ The first step (Chapter IV)

IV.1. Abstract

Poly(vinylidene difluoride) (PVDF) displays attractive ferroelectric/piezoelectric properties and its polar β-crystals are specifically targeted for achieving electroactive applications. However, their direct crystallization from the melt state represents a challenging task that has never been addressed using melt-state processes. The use of poly(methyl methacrylate) (PMMA) is herein investigated to promote the PVDF polar β-phase using meltblending and extrusion-calendering technologies. The presence of the -phase is here confirmed by ATR-FTIR and WAXS experiments with blends at PMMA content as low as 5wt-%. The key role of PMMA for the -phase crystallization from the melt state was unambiguously highlighted with the help of Flash DSC experiments on non-isothermal cooling mode from the melt state. PMMA is able to efficiently shift the -to- crystal transition to lower cooling rates (> 100 -200°C/s), making the achievement of PVDF polar β-phase for these blends compatible with conventional processing tools. A crystal phase diagram is proposed for PVDF/PMMA blends to highlight dual effects of both PMMA and cooling rate on the PVDF crystallization during melt-processing. Ferroelectric properties were even observed for blends containing PMMA up to 10wt-% with the highest remanent polarization obtained at 5wt-% PMMA. After 10wt-% PMMA, a progressive transition from ferroelectric to pseudo-linear dielectric behavior is observed more likely due to the presence of PMMA in the interlamellar amorphous phase of polar PVDF spherulites as shown by SAXS experiments. In this work, we successfully demonstrated that PMMA plays a key role on the crystallization of PVDF polar crystals from the melt state, enabling a large-scale and continuous extrusion processing of PVDF-based materials with attractive dielectric properties for sensing and harvesting applications.

IV.2. Introduction

Fluoropolymers such as poly(vinylidene difluoride) (PVDF) and their related copolymers represent a unique class of polymer materials with attractive ferroelectric, piezoelectric and electroactive properties [START_REF] Harrison | [END_REF][2][START_REF] Scott | [END_REF] . These polymers can find numerous applications like sensors and transducers and even for future applications in microelectronics, robotics and energy with the development of flexible sensors, actuators, piezoelectric energy harvesters, random-access memories and self-charging batteries 2,4-6 .

The elevated electroactive properties of PVDF arise from the high dipolar moment of the vinylidene difluoride (VDF) unit, combined with some specific chain conformations in the crystalline lattice 7 . PVDF-based polymers are semicrystalline with a very high crystallinity extent up to 54% 8 , and four distinct crystalline phases of different chain conformations can be observed 2 , i.e. the phase (chain configuration 100% Trans), the α-phase (configuration TGTG'), the δ-phase (similar chain conformation to -phase) 9 and the -phase (configuration T 3 GT 3 G'). Each crystalline phase presents a specific dipole moment (generated by the difference of electronegativity between the fluorine atoms and hydrogen/carbon atoms) with variable dipolar contribution per unit cell 10 , spanning between 0 -8 x 10 -30 C.m for the α-phase and -phase, respectively. Therefore, the polar -phase of PVDF is preferred to design electroactive PVDFbased materials with the highest ferroelectric/piezoelectric properties. Spontaneous/remanent polarization in the range 6.5 -9 µC/cm 2 and d 31 /d 33 piezoelectric coefficients close to 25 -35 pC/N 2,3,11-15 can be reached with such PVDF. However, the processing of PVDF into the polar -phase is not straightforward. In order to obtain the β-phase from neat PVDF, three processing methods have been reported such as the use of high pressure crystallization (>700MPa), fast quenching from the melt state (>2000°C.s -1 ) and stretching from the rubbery state under specific conditions (close to 80°C up to a stretching ratio of 5) 2 . This popular stretching approach enable to convert the α-phase into β-phase (approx. 20% of α-phase remaining), leading to interesting piezoelectric/ferroelectric properties after an adequate high-voltage poling step [START_REF] Scott | [END_REF]11,14,15 . However, in view of industrial implementation, the direct recovery of the PVDF β-phase from the melt state still represents a challenging task and other strategies have been thereby developed.

Among them, copolymerizing VDF with trifluoroethylene comonomer (TrFE) gives access to the so-called poly(vinylidenefluoride-co-trifluoroethylene) (PVDF-TrFE) copolymers with attractive electroactive properties [START_REF] Harrison | [END_REF]2 . Such copolymerization enables to get the direct recovery into the crystalline β-phase at the expense of the α-phase, independently of the processing method 2,16 . The accepted mechanism for -phase formation in PVDF-TrFE involves the chaintorsion by the introduction of bulky additional F atoms from the TrFE unit, resulting in an energetically favored 100% trans conformation. A good ferroelectric behavior is so-observed with spontaneous/remanent polarization (P R ) and piezoelectric coefficient d 33 up to 11 µC/cm 2 and -38 pC/N, respectively 2,16,17 . Varying amount of TrFE comomoner within PVDF-TrFE enables to tune their ferroelectric and relaxor behaviors. However, melt-processing of PVDF-TrFE is relatively limited by the cost of these copolymers and solvent-processing is preferred to produce devices from these materials. The decrease of the Curie temperature (ferroelectric/paraelectric transition) after copolymerization remains the main issue, restricting their utilization to low temperatures applications (< 80°C) 2,16 . The polar β-phase of neat PVDF can be also obtained after introduction of various nanoparticles such as carbon nanotubes, palladium, ferrite, BaTiO 3 nanoparticles 18-20 . In the case of carbon nanotubes, the β-phase is even observed with only 0.01 weight-% of CNT. Unfortunately, CNT can create an electrical percolation pathway within the PVDF nanocomposite 21 , making the PVDF poling step under high electric field extremely difficult 22 .

The most interesting approach to achieve a direct recovery PVDF β-phase from the melt state appears to be via melt-blending PVDF with (partially-)miscible polymers. This route represents a promising and cost-competitive approach for producing films and fibers at industrial level. Some (partially-)miscible polymers such as poly(methacrylate) can even modify the PVDF crystallization behavior and promote the PVDF β-phase crystallization. Indeed, the miscibility between poly(methyl methacrylate) (PMMA) and PVDF with related ferroelectric/piezoelectric characterizations was intensively studied and reviewed [START_REF] Harrison | [END_REF]12,17,[23][24][25][26][27][START_REF] Bonardd | [END_REF] . The direct β-phase formation from the melt state was first demonstrated by Léonard C. and coworkers 26 . The amount and tacticity of PMMA seem to play a key role on the PVDF crystallization and the authors also postulated out that the resulting PVDF crystalline phase could be governed by the crystallization temperature as a function of the cooling rate from the melt. They have also demonstrated the occurrence of specific H-bonding interactions between -CH 2 groups of PVDF and carbonyl groups of PMMA that could increase of the amount of trans sequence of PVDF segments. Similar results were also reported by Domenici C. et al. with the incorporation of 30 wt-% of PMMA into PVDF using a solvent-based approach. However, in terms of ferroelectric/piezoelectric properties, discrepancy results have been reported so far. Most of the authors reported that the spontaneous/remanent polarization, the coercitive field and piezoelectric coefficients decrease with the amount of PMMA 12,17,[START_REF] Bonardd | [END_REF] . On the contrary, Li et al. proved out that PVDF/PMMA blends could be competitive enough with PVDF-TrFE, especially for high temperature applications with stable ferroelectric properties up to 120°C at least. In a recent investigation, the dielectric behavior of PVDF-TrFE was readily tuned up by the incorporation of miscible grafted poly(methacrylates) 29 . Ferroelectric, antiferroelectric, relaxor to linear dielectric behavior were demonstrated by playing with the miscibility extent, leading to a "nanoconfinement" of PVDF -crystals. All these previous findings proved that these miscible PVDF/PMMA blends could represent promising materials with controllable properties but the mechanism behind the direct crystallization into the polar β-phase for these PVDF/PMMA miscible blends is lacking and needs to be investigated using both adequate processing conditions and optimized PMMA content. Within this research framework, advanced calorimetry techniques represent an efficient way to perfectly highlight these important features and especially the effect of the cooling rate. Recently, the crystallization of neat PVDF was investigated at high cooling rates via Flash-DSC techniques. The authors highlight a crystal modification at high cooling rates [30][31][32][33] . The β-phase crystallization at high cooling rate is still controversial, but this important finding means that the crystallization mechanisms of PVDF into -phase could be controlled from the melt state with the cooling rate 33 . To the best of our knowledge, the PMMA effect on the crystallization of PVDF at high cooling rates is still unknown, together with the fact that the use of miscible partners such as PMMA may lead to counter-intuitive effects on crystallization, especially in the crystal nucleation phase 34 .

In an effort to produce electroactive polymer films using continuous extrusion processes, the present study will focus on the role of PMMA about the crystallization extent of polar PVDF -crystals from the melt state. Several meltbased techniques (extrusion-calendering vs. thermocompression) were compared on the crystallization ability of PVDF-based blends at various PMMA content by means of WAXS and FTIR techniques. A deep insight over the role of PMMA on the crystallization of the PVDF polar -phase was obtained through Flash DSC experiments to achieve cooling rates as high as 3000°C/s and get representative information on the crystallization of PVDF/PMMA blends during film extrusion processing. A crystal phase diagram was attempted and discussed as well as the ferroelectric performances of final PVDF/PMMA films as produced by extrusioncalendering.

IV.3. Experimental section

Materials

Poly(vinylidene difluoride), hereafter called PVDF, was kindly supplied by Arkema (grade Kynar® 720, M w = 200 000 g.mol -1 ). Poly(methyl methacrylate), hereafter called PMMA, was supplied by Evonik (grade 8N, M w = 97 000 g.mol - 1 ). Throughout this contribution, all percentages are given as weight percentage (wt-%).

Methods

A. Film extrusion-calendering

The first processing method for PVDF/PMMA miscible blends is the film extrusion-calendering as described by Leveque et al. 35 . In a first step, PVDF and PMMA formulations were melt-blended in a co-rotating twin-screw extruder (Haake Rheomex PTW 16 OS, ThermoScientific, Germany) with a screw diameter of 16 mm for a L/D ratio of 40. Extrusion temperatures were set to 210°C (except for the temperature of extrusion die set at 170°C). PVDF and PMMA pellets were dry-blended, extruded (screw speed between 150 -200 rpm, mass flow rate between 1-1.2 kg/h) and pelletized. The as-produced PVDF/PMMA pellets were reprocessed by film extrusion-calendering with a Haake single screw extruder with a L/D ratio equal to 40, a temperature profile of 170-210-210-230°C (from the hopper to the die) and a screw speed of 60 rpm. The extrusion die consists of a specific slit die for film extrusion (width 150 mm, thickness 800 µm) and the film extrudate was subsequently calendered to obtain 20-120 µm-thick films. The calendering system is equipped with a cooling system using cold water (10°C) within the compression cylinders (estimated cooling rate ±200°C/s according to expected thickness).

B. Thermocompression molding

The extrusion/thermocompression process is described by Samuel et al. 34 . PVDF and PMMA were blended in an internal mixer Brabender at 210°C and 75 rpm for 10 min. The collected melt-blends were subsequently molded into thin films using a Carver press at 210°C and 10 bars for 1 min (after melting and conditioning). Then, the samples were quenched from the melt state using a coldwater flow until reaching a temperature at 20°C (estimated cooling rate ±1°C/s).

C. Flash differential scanning calorimetry (FDSC)

FDSC experiments were carried out on a Mettler-Toledo Flash DSC 36 via a specific protocol to observe the crystallization extent at different cooling rates. The measuring cell was continuously flushed with nitrogen gas and high-purity indium was used for temperature calibration of the sensor. Sample of about 35 -100 ng was placed under a microscope on the active area of the circular 500µmdiameter sensor. The procedure used for crystallization analyses is the following: heating at 1000°C/s to 210°C, isotherm at 210°C during 10 sec, cooling at controlled cooling rates between -5°C/s and -4000°C/s to -80°C, isotherm at -80°C during 10 sec, heating at 5000°C/s to 210°C/s. This procedure was repeated at different cooling rates as shown in Figure IV.1. Crystallization temperatures (T c ) were determined at the maximum of the exothermic peak observed during the cooling scan. For sake of clarity, cooling curves were normalized by the heating rate. Note that the sample mass used for FDSC was approached by measuring crystallization/melting enthalpies at low cooling/heating rates (1°C/s) using a classical Mettler Toledo DSC1.

D. Attenuated Total Reflection -Fourier Transform InfraRed spectroscopy (ATR-FTIR)

Crystal phases of PVDF/PMMA blends were identified by Fourier Transform InfraRed spectroscopy (FTIR) using a BIO-RAD Excalibur spectrometer equipped with an ATR Harrick Split Pea™ apparatus from SAFIR Cie. Spectra were recorded using a spectral width ranging from 550 to 1400 cm -1 with 4 cm -1 resolution and an accumulation of 32 scans.

E. Wide Angle and Small Angle X-ray Scattering (WAXS & SAXS)

Wide Angle X-ray Scattering (WAXS) and Small Angle X-ray Scattering (SAXS) analyses were carried out at room temperature in transmission mode on thin PVDF/PMMA films. The analyses were performed on a Xeuss apparatus (Xenocs, France) and the CuK radiation (λ=1.54 Å) was used. The sample to detector distance was set at 10cm and 1m for WAXS and SAXS experiments respectively and calibrated thanks to a Silver Behenate sample. The WAXS and SAXS patterns were recorded on a Pilatus detector (Dectris). The intensity profiles were obtained by 360° azimuthal integration of the 2D patterns using the Foxtrot software®. It was used to determine the crystalline composition of the PVDF-based blends. The diffractogram were measured at an angle value (2θ) between 5 and 30°.

F. Polarized light optical microscopy (PLOM)

Crystalline morphologies were observed by polarized light optical microscopy using Leica DM 2500M microscope (magnification x20) at equipped with a Mettler FP82 hot-stage apparatus and Mettler FP80 microprocessor. Briefly, extruded films were melted between two glass plates at 210°C for about 10 min. Then, the samples were cooled using various procedure to observe the development of crystalline structures. Images were then treated by image analysis using ImageJ software to evaluate crystal densities from micrographs.

G. Ferroelectric analysis

P-E hysteresis loops were obtained by Radiant Precision Workstation ferroelectric testing system at room temperature equipped with a high-voltage source of 10kV. The Vision5 data management software was used to obtain the results at a frequency of 1 Hertz with the normal dipolar mode, which produced a triangular signal of high voltage and enabled to measure the subsequent polarization of PVDF/PMMA films.

IV.4. Results and discussions

The direct crystallization of PVDF/PMMA into the polar -phase was first investigated on thin films produced by solvent-free processes. Thin films of thickness lower than approx. 100µm are preferred for electroactive applications to avoid excessive electric fields during high-voltage poling 37 and two sets of experiments were performed. Films were manufactured by either a continuous extrusion-calendering process or a discontinuous thermocompression process to get a clear comparison between both processes in terms of PVDF crystallization and ferroelectric properties. PMMA weight ratio within PVDF/PMMA blends was progressively increased (PVDF/PMMA 100:00, 95:05, 90:10, 80:20 and 70:30) to observe the evolution of crystalline phases as a function of the PMMA content. The characterization of the PVDF crystalline phases for each formulation and process was systematically performed using ATR-FTIR and WAXS techniques. ATR-FTIR enables to identify the crystalline phases of PVDF with the characteristic absorption peaks for the -phase (766 and 795cm -1 ) and the phase (840cm -1 ) 38 . It could be noticed that other PVDF crystalline phases such as -phase had absorption peaks close to the -phase 2 and ATR-FTIR could not easily resolve between these two phases. PMMA also presents similar absorption peaks to those of PVDF as demonstrated by Vietmann et al. 39 . In this respect, WAXS analyses are needed to distinguish the PVDF crystalline phase between the crystalline lattices related to -phase (2 = 18.3°, 19.9° and 26.6°) and phase (2 = 20.3°) 40 . Figures IV.2 and IV.3 show ATR-FTIR and WAXS characterizations, respectively, for both extrusion-calendered (thickness ±60µm) and thermocompressed blends. For neat PVDF, both processing methods give similar ATR-FTIR and WAXS patterns. ATR-FTIR absorption peaks close to 765 and 795 cm -1 are observed (Figures IV.2a&b). WAXS diffraction peaks at 2 angles close to 18.5°, 20.0° and 26.5° are in agreement with ATR-FTIR results (Figures IV.3a&b) and confirmed the presence of the crystalline -phase in all neat PVDF films. No significative trace of -phase is detected by WAXS and ATR-FTIR techniques. These observations on PVDF films produced by either extrusion-calendering or thermocompression are in agreement with the state of the art, reporting the presence of a quasi-pure nonpolar -phase. The incorporation of PMMA clearly modifies the crystalline phase of PVDF and both processes produce different trends in terms of PVDF crystalline phases. In the case of extrusion-calendering process, the apparition of the -phase at 840 cm -1 is clearly detected using a PMMA content as low as 5 wt-%, with a simultaneous decrease of absorption peaks related to the -phase (Figure IV.2a). Between 5 and 10 wt-% PMMA, -phase and -phase of PVDF both coexist after extrusioncalendering and the -phase totally disappears at 20 wt-% PMMA. WAXS patterns for extrusion-calendered films also display a similar trend (Figure IV.3) with the apparition of a small shoulder at 20.5° at 5 wt-% PMMA. Some slight differences on ATR-FTIR results could be ascribed to the crystal size effects. The -phase is also observed for PVDF/PMMA films produced by thermocompression, but 25 -30 wt-% PMMA is required to obtain the polar phase as observed by ATR-FTIR and WAXS techniques ( ). This result obtained for the thermocompression process of PVDF/PMMA blends is consistent with the previous studies reported in litterature 23,[41][42][43] . As a first conclusion, PMMA clearly promotes the PVDF -phase for both processes, but it can be readily obtained at a very low amount of PMMA close to 5 wt-% using the extrusion-calendering process in order to produce PVDF polar crystals. It could be also noticed that the presence of the PVDF -phase is also clearly discarded in our formulations and processing conditions based on the absence of its characteristic absorption peak at 1234 cm -1 (Figure IV.4). The influence of the film thickness has a significant practical importance for further production of electroactive PVDF/PMMA films. It is worth mentioning out that lower voltages are required for the poling process in the case of ultra-thin films. In this respect, additional experiments were performed by extrusion-calendering. Film thicknesses were varied from 200µm to 20µm for neat PVDF and PVDF/PMMA 95:5 films. Interestingly, neat PVDF films with thickness lower than 60µm could present a low amount of polar -phase by extrusion-calendering as observed by ATR-FTIR with the presence of a small and broad absorption peak at 840 cm -1 (Figure IV.5a). A similar effect is also observed for the PVDF/PMMA 95:5 films (Figure IV.5b). The signal intensity at 840 cm -1 related to the -phase progressively increases with decreasing film thickness as well as signal intensities related to the -phase are simultaneously decreasing. The relative amount of -phase over -phase could be enhanced by manufacturing thin PVDF/PMMA films of thicknesses as low as 20 µm, even for neat PVDF. High -phase content could be achieved by tuning the processing conditions (PMMA content, film thickness and processing method) but quantitative information about crystallization with a special emphasis on related mechanisms are clearly compulsory for further material/process optimization. The -phase formation in a miscible PVDF/PMMA blend was previously observed using other production processes and the quenching temperature from the melt state was identified as a key parameter for -phase recovery 17,[START_REF] Bonardd | [END_REF][44][45][46] . A cooling rate effect was also mentioned by Léonard et al. to explain PVDF crystal modifications at PMMA content between 20 -30 wt-% but no experiments was actually performed to confirm the role of cooling rate 26 . Thermocompression and extrusion-calendering processes significantly differ in terms of cooling rate (1°C/s for thermocompression vs. 10 -500 °C/s for extrusion-calendering) 47 and a synergistic effect between PMMA and the cooling rate on the -phase production could be here speculated to consolidate the actual and previous results. However, the efficiency of the extrusion-calendering process to induce PVDF polar crystals at low PMMA content and low film thickness could be also interpreted in term of induced orientation by uniaxial stretching in the melt state at the die, having likely an impact on the PVDF -phase recovery. In this context, various experiments were conducted to evaluate the residual orientation of PVDF/PMMA films. The orientation of the crystalline domains was first investigated by WAXS after extrusion-calendering (Figure IV.6). A slight orientation of the -phase and -phase is detected along the stretching axis but no correlation with PMMA content is obtained. The quantitative analysis indicates a poor orientation with P 2factor comprised between 0 and 0.1. Concerning the amorphous phase, shape variations after reheating to 100°C were recorded (Table IV.1) but no shape changes were again detected up to 2 hours. In this context, it can be confidently concluded that the uniaxial stretching in the melt state by extrusion-calendering does not induce any orientation, and therefore the orientation effects on the phase production can be ruled out. Table IV.1: Shape modifications of PVDF/PMMA films processed by extrusioncalendering after reheating at 100°C for 2 hours.

In an effort to identify a combination between PMMA and the cooling rate on -phase production from an unoriented melt state, PVDF/PMMA thin films were (re)melted at 210°C followed by a quenching stage to various temperatures using liquid nitrogen (LN 2 ) (-196°C), LN 2 /methanol (-80°C), cold water (0°C) and temperate water (35°C). ATR-FTIR spectra are gathered in Figure IV.7. The PMMA content required for the -phase appearance (X PMMA--start ) and -phase extinction (X PMMA--end ) are listed in Table IV.2 for all quenching medium and techniques. High efficiencies are observed using cold water or LN 2 /methanol quenching mediums with significant amounts of polar -crystals produced in neat PVDF and total extinction of the -phase at PMMA content as low as 10wt-%. Decreasing quenching efficiencies on the order cold water > LN 2 /methanol > -0,5 -0,4 -0,3 -0,2 -0,1 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 Table IV.2: Estimated PMMA content required for the -phase appearance (X PMMA--start ) and -phase extinction (X PMMA--end ) as a function of the quenching temperature/method from the melt state. Cold water (0°C) 0 10

Quenching

Mild Water (35°C) 15 20

To demonstrate both effects of PMMA content and the applied cooling rate, and more particularly to obtain quantitative information (crystallization temperature, crystallization rate, etc...) about -phase crystallization from an unoriented molten PVDF/PMMA blend, differential scanning calorimetry (DSC) techniques are of high interest in this case. However, given the use of high cooling rates during the -phase recovery, the fast scanning DSC techniques represent the most adequate tool to study the crystallization of such fast-crystallizing polymers like PVDF under cooling conditions similar to those used during processing. Flash DSC can highlight crystallization behaviors under drastic cooling conditions up to 5000°C/s and several fundamental information about the crystallizations steps/mechanisms can be obtained [48][49][50] . In particular, several authors already investigated the crystallization behavior of PVDF by Flash DSC 32,33,51,52 . An obvious change in the crystallization behavior was observed at high cooling rates but controversial conclusions were stated out. Neat PVDF was herein subjected to Flash DSC experiments with the procedure displayed in Figure IV.1. Crystallization endotherms were recorded at various cooling rates, ranging from 80 to 3000°C/s (Figure IV.8a). For cooling rates lower than 300°C/s, a single crystallization exotherm is detected in the range 100 -80°C. Knowing that the α-phase appears spontaneously for PVDF by conventional processing conditions, we can confidently assume that the single crystallization peak at low cooling rates is ascribed to the PVDF α-phase. Higher cooling rates are marked by the apparition of a second distinct exotherm at lower crystallization temperatures and this second exotherm becomes predominant at cooling rates higher than 1000°C/s. Our results are in agreement with previous ones from the literature and correlations with our extrusion-calendering experiments obviously demonstrate the crystal transition from -phase to -phase at high cooling rates for neat PVDF, hereafter called the -to- crystal transition. A /-phase co-crystallization occurs at cooling rates between 400 and 1200°C/s for neat PVDF. It could be noticed that the high cooling rate required to develop a pure -phase for neat PVDF is difficult to achieve in any industrial process and only a partial crystallization extent seems to be more realistic like in the case of our extrusioncalendered neat PVDF thin films. The cooling rate has a major influence on the crystallization of the polar -phase for neat PVDF and it is also of high interest to determine the impact of PMMA on the -to- transition. PVDF/PMMA blends with 5, 10 and 20 wt-% of PMMA were subsequently subjected to Flash DSC experiments (Figures IV.8b&c 8b&c). In addition, PMMA induces drastic changes in terms of cooling rates required to develop the polar -phase and the related diminishing of the -phase. Concerning the PVDF/PMMA blend at 5 wt-% PMMA, the -phase crystallization starts at lower cooling rate than neat PVDF (100°C/s vs 400°C/s respectively) and the -to- transition is observed in the range 100 -800°C/s, compared to 400 -1200°C/s for neat PVDF. This range again decreases at 10 wt-% PMMA to reach approx. 50 -600°C/s. FDSC consequently highlights that (i) the cooling rate from an unoriented melt state represents a key factor to convert non-polar -crystals into polar -crystals for either neat PVDF or PVDF/PMMA blends and (ii) the addition of PMMA efficiently shifts the PVDF -to- crystal transition to lower cooling rates. Note that such cooling rates are potentially achievable with some classical extrusion tools and technologies, as discussed hereafter. In the meantime, the crystallization enthalpy related -phase starts to increase until a maximum is reached followed to its own disappearance at extreme cooling rates. Note that the optimum cooling rate for a maximal -phase crystallization rate could be evaluated to 350 -400 and 2000 s -1 for PVDF/PMMA 90:10 and neat PVDF respectively. The crystallization enthalpy is significantly lower in the case of the PVDF/PMMA 90:10 blend than that of neat PVDF with a quasiamorphization at high cooling rates. A total amorphization over the entire FDSC cooling rate range is observed for the PVDF/PMMA blend with 20 wt-% PMMA (Figure IV.9a). PMMA consequently induces a high depression of all crystallization temperatures and crystallization rates within the entire FDSC cooling rate range independently of the crystal type. These phenomenon are largely attributed to the miscibility of PVDF/PMMA with a well-known inhibition of the PVDF crystallization 23,[53][54][55] . Interestingly, the -phase crystallization clearly proceeds at low temperatures typically between 55 -25°C by using high cooling rates that inhibit the -phase crystallization. Crystallization of the -phase is also possible at very low temperatures (15°C) with reduced rates as revealed by annealing experiments of the amorphous PVDF/PMMA 80:20 at low cooling rates (Figure IV.9b). We suspected that these behaviors could be related to the crystal nucleation process, i.e. a heterogeneous nucleation promoted by impurities for the -phase 51 and a low-temperature homogeneous nucleation for the -phase. Such effects could be supported by recent FDSC studies on several semicrystalline polymers such as poly(amide) 56 , poly(propylene) 31 or poly(L-lactide acid) 30 at high cooling rates. For this purpose, microscopic observations are of great importance to evaluate the crystal/nuclei density under large undercooling 57 . In this context, PLOM experiments were performed on PVDF/PMMA 90:10 thin film (Figure IV.10). Two different thermal treatments from the melt state were applied, i.e. a cooling step at 10°C/min and a quenching step into cold water (0°C) from the melt state to induce the -phase and -phase crystallization respectively. A significant increase by approx. one decade in the crystal/nuclei density is detected by quenching into cold water (approx. 10 7 nuclei/mm 3 vs 10 6 nuclei/mm 3 ). Homogenous nucleation studies were recently performed on poly(butylene terephthalate) (PBT) using various techniques such as FDSC and atomic force microscopy with typical increase of the nuclei density by 9 decades reaching 10 15 nuclei/mm 3 for homogeneous nucleation of PBT -crystals 57 . In this respect, our results concerning the low temperature -phase crystallization of PVDF seem incompatible with a homogenous nucleation process and a heterogeneous process that involves PMMA could explain these crystal density measurements. It could be noticed here that such effects still require in-depth investigations, in particular within miscible blends where peculiar effects are observed in terms of crystallization rate [58][59][60] Theoretically, the pure -phase should be observed at high cooling rates and high PMMA contents. The crystallization of the pure -phase is obtained for PVDF/PMMA blends with PMMA content higher than 20 wt-% PMMA for extrusion-calendering or 25 wt-% by thermocompression. However, within these PMMA contents, amorphous PVDF/PMMA were obtained by Flash DSC and, in this context, correlations between Flash DSC and melt-processes for the crystallization of the pure polar -phase are less accurate. Based on the FDSC analyses of PVDF/PMMA blends with PMMA content higher than 20 wt-% (Figure IV.9), it could be concluded that the polar -phase in these PVDF/PMMA blends processed either by thermocompression or extrusion-calendering could slowly crystallize during storage at ambient temperature (hereafter called "coldcrystallization" in the crystal phase diagram). After having confirmed the apparition of the ferroelectric/piezoelectric phase in presence of PMMA by using an extrusion-calendering process with an efficient quenching, it is also of high importance to investigate the ferroelectric behavior of these as-produced PVDF/PMMA blends. For this purpose, PVDF/PMMA thin films obtained by extrusion-calendering has been characterized using a ferroelectric tester to obtain dielectric properties and potential ferroelectric properties, i.e. the so-called ferroelectric hysteresis loop (Figure IV.12a). The samples were subjected to alternative electric fields (here a triangular waveform, see experimental section) to get information about their ferroelectric performances under high poling fields as well as correlations with the PVDF crystal structure. Therefore, neat PVDF and PVDF/PMMA films with a constant thickness of 40µm were here subjected to alternative electric fields with a maximal electric poling field of 2000kV/cm (corresponding to 8000V) applied perpendicular to the film surface. Subsequent dielectric behaviors are displayed in Figure IV.12a for neat PVDF and PVDF/PMMA blends with increased PMMA weight content. Together with the shape of the hysteresis loop, two main parameters could be extracted, i.e., the remanent polarization P R (the resulting polarization after poling at high electric field) and the coercive field E c (the electric field required to remove the polarization). Evolutions of P R and E c with PMMA content are plotted in Figure IV.12b. From Figure IV.12a, neat PVDF does not display a well-defined pattern of a ferroelectric materials 10,16,[61][62][63] with a rather low P R close to 2.4µC/cm². Interestingly, by adding 5% PMMA, the dielectric response drastically changes. A clear ferroelectric behavior is obtained, as suggested by the typical squareness of the hysteresis loop and high P R /E c values with a 2-fold increase in the remanent polarization P R up to 5.2µC/cm² (poling field 2000 kV/cm) (Figure IV.12b). Compared to the so-called P(VDF-co-TrFE) (P R close to 8.4µC/cm² at poling field 4000 kV/cm, a value experimentallyverified close to 9.7µC/cm² at poling field 10000 KV/cm, see Figure IV.13) and to a stretched PVDF film (P R close to 5.5µC/cm² at poling field of 2000 kV/cm) 64 , competitive performances are concluded for our PVDF/PMMA blend with 5 wt-% PMMA. This film also displays several important advantages in terms of processing and costs (no stretching is required). In this context, the enhanced phase content arising from the addition of 5 wt-% PMMA in an extrusioncalendering process plays a major role to obtain an enhanced ferroelectric behavior without any stretching steps. However, it seems that the -phase content does not represent the only important parameter to control the ferroelectric properties of PVDF/PMMA blends. Indeed, despite high -phase content, further increases of the PMMA content do not favor ferroelectric behaviors. The PVDF/PMMA blend with 10 wt-% PMMA displays a similar dielectric behavior similar to neat PVDF (Figure IV.12a) and a pseudo-linear dielectric behavior is observed at 30 wt-% PMMA with poor P R /E c . As a conclusion, the best ferroelectric performances are obtained with the incorporation of 5 wt-% PMMA and dielectric behaviors progressively switch to pseudo-linear dielectric at higher PMMA content. The origin of the above-mentioned transition from ferroelectric (5 wt-% PMMA) to pseudo-linear dielectric behavior (30 wt-% PMMA) is of high interest for further process/material optimization. It was here largely demonstrated that a quasi-pure -phase could be obtained above 10wt-% PMMA but no ferroelectric behavior is observed for these formulations. Several phenomena could be speculated for this drastic change in dielectric behavior at high PMMA contents. In a first approach, the PVDF crystallinity (normalized to PVDF content) remains constant in all blends but the overall crystalline content naturally decreases due to the addition of the miscible amorphous PMMA phase with a potential loss of ferroelectric properties. However, the spatial distribution of the amorphous PMMA phase could also play a key role on resulting ferroelectric properties and the presence of PMMA into the amorphous regions of polar PVDF spherulites is suspected on the basis of (i) the difficulty to pole -crystals at high voltages and high PMMA contents as depicted in Figure IV.12a with a low polarization at saturation and (ii) previous research articles pointing out the importance of the dipole coupling between PVDF crystal lamellas with complex relationships between the amount of -crystals, their crystal size and their surrounding amorphous phase 10,16,[61][62][63] . Strong modifications of the dielectric behavior were previously detected for PVDF-TrFE with grafted poly(methacrylates) or poly(styrene) side chains that generate relaxor/antiferroelectric-like behavior, arising from a "nanoconfinement" effect of PVDF -crystals 29,61,65,66 . In this context, the spatial distribution of PMMA with a potential segregation into the amorphous regions of polar PVDF spherulites was investigated by SAXS, a powerful technique to probe the crystalline morphology of semi-crystalline polymers at the lamellar level 24,[67][68][69][70] . Figure IV.14a displays SAXS data for various PVDF/PMMA blends produced by extrusion-calendering and a clear peak is observed for neat PVDF and all PVDF/PMMA blends for q-values in the range 0.05 -0.08. This peak is related to the regular arrangement of PVDF crystalline lamellas with its associated interlamellar amorphous phase. The long period (L p ) could be calculated from the peak position 68 and its evolution with PMMA weight content is plotted in Figure IV.14b. Interestingly, L p remains nearly constant up to 5 wt-% PMMA followed by a marked and regular increase for PMMA content higher than 10 wt-%. This increase in L p has been previously reported for numerous amorphous/semi-crystalline miscible blends (PVDF/PMMA 24,67 , PLLA/PMMA 68 , PLLA/PVPh 69 and PEO/PMMA 70 ) and was largely attributed to a (partial) segregation of the amorphous component into the interlamellar amorphous phase with an increase in the intermellar distance. PMMA is consequently (partly)-trapped into the interlamellar amorphous phase of polar PVDF spherulites with a significant swelling effect on polar PVDF lamellas. The dielectric constant and the electric field across the interlamellar amorphous phase could be inherently reduced and the transition from ferroelectric to pseudo-linear dielectric behavior at PMMA content higher than 10 wt-% is consistent with a reduction of the dipole coupling between PVDF polar lamellas. As a consequence, the amount of -crystals does not represent the only parameter controlling the final dielectric properties in PVDF/PMMA blends and a specific attention should be payed to (partial)-segregation effects of PMMA within the interlamellar amorphous phase.

IV.5. Conclusions

In this study, we demonstrated that poly(methyl methacrylate) (PMMA) acts as a β-phase promoter for PVDF-based blends by melt-state processing technologies, i.e. extrusion-calendering and extrusion-compression. PMMA contents as low as 5 wt-% are required to promote PVDF -crystals using an extrusion-calendering technology as observed by infrared spectroscopy (FTIR) and wide-angle X-ray scattering experiments (WAXS). Flash DSC experiments definitely confirmed that the cooling rate from the melt state plays a key role with a -to- crystal transition at high cooling rates for neat PVDF. The incorporation of PMMA into PVDF clearly shifts this transition to lower cooling rates, i.e., approx. 50-100°C.s -1 for 10wt-% PMMA (against 400-800°C.s -1 for neat PVDF), compatible with standards processing tools of the plastic industry. A crystal phase diagram was proposed and discussed for PVDF/PMMA to highlight the synergistic effect of PMMA content and the cooling rate on the development of PVDF -crystals using melt-state processes. Ferroelectric properties were finally established for various PVDF/PMMA compositions and an interesting ferroelectric behavior was specifically observed for a PMMA content of 5 wt-% with the highest remanent polarization. Despite high -phase content, the dielectric properties of PVDF/PMMA thin films with PMMA contents higher than 10 wt-% progressively switched to pseudo-linear dielectric behaviors at excessive PMMA of 30 wt-%. This transition seems to arise from a strong modification of the amorphous regions of PVDF polar spherulites in the presence of PMMA, as revealed by SAXS. Hence, PVDF/PMMA thin films made by extrusioncalendering could represent a cost-competitive route to electroactive polymer materials without the need of pre/post-treatments (i.e. stretching). In a forthcoming article, piezoelectric and ferroelectric characterizations will be addressed more intensively in order to state out their performances in practical applications such as actuators/sensors for Internet of things (IoT) and/or energy harvesting applications.

V.2. Introduction

For several decades, high interests have been observed for the implementation of poly(vinylidene fluoride) (PVDF) and its copolymers in the domain of piezoelectric and ferroelectric materials [START_REF] Harrison | [END_REF][2][START_REF] Scott | [END_REF] . Currently, ferroelectric and piezoelectric properties of PVDF-based materials are of great interest for many advanced applications such as flexible active materials for sensors, transducers and actuators as well as for future prospects in flexible electronics for randomaccess memories (FeRAMs) 4,5 , energy harvesters 6 , energy µ-generators 7 , artificial muscles for robotics, and (bio)microelectronic devices 8 .

The piezoelectric and ferroelectric properties of semi-crystalline PVDF arise from specific crystalline phases depending on the conformation of the CH 2 -CF 2 linkages. Among the 3 main crystalline phases of PVDF, the most thermodynamically stable is the so-called α-phase (form II, conformation TGTG') that remains non-polar with a paraelectric dielectric behavior. Unfortunately, this non-polar phase is the most commonly produced during melt-state processing of PVDF. The other two phases are polar and of high interest for piezoelectric/ferroelectric properties, γ-phase (form III, conformation TTTGTTTG') and β-phase (form I, conformation 100 % Trans). This last conformation presents the highest dipolar moments, due to a regular arrangment of hydrogen and fluorine atoms in the opposite directions resulting in a large molecular dipolar moment oriented perpendicularly to the chain axis 9 . The parallel orientation of all the monomers in the β-phase allows to reach a large spontaneous/remanent polarization of 6.5 -9 µC/cm 2 , giving a maximum piezoelectric coefficient d 33 of approx. 35 pC/N 2,3,10-14 . The amorphous phase and crystal-amorphous interphase [15][16][17] from PVDF could play an important role in its electroactive properties in particular in charge transfert/coupling between crystalline lamellae 18 .

Unfortunately, obtaining β-phase requires specific processing of PVDF that remains very restrictive. The most common industrial process employed to reach the PVDF -phase is the uniaxial cold drawing of extruded films 19 . However, the β-phase is difficult to directly obtain after a conventionnal processing step from the melt state and the -phase only appears during crystallization/solidification under high pressure or in presence of carbon nanotubes (CNTs) as nanofillers. A poling step under very high voltage (> 500 kV/cm -1 ) is also mandatory. It can be a problem in the presence of nanoparticules [20][21][22] such as electrically conductive CNT generating conductive and non polarizable PVDF materials 23 . Currently, the solvent pathway such as spin coating is favored enabling a maximum freedom on the film/active layer deposition 24 . Another alternative lies in the use of the poly(vinylidene fluoride-co-trifluoroethylene) copolymer, i.e. P(VDF-co-TrFe). The steric hindrance induced by the TrFe comonomer generates the 100 % trans configuration of the PVDF backbone and leads to stable crystalline β-phase. However, the Curie temperature (T C ) of P(VDF-co-TrFe), that refers to the transition between the ferroelectric and paraelectric dielectric behavior, drops down to 50 -70 °C25 , being much lower than the one of PVDF (172 °C) 26 . The cost of such copolymer also restricts its use in melt-state processes. Thus, other approaches are investigated to reach high -phase amount inf PVDF.

In our previous article 27 , we developed a third approach based on meltblending of PVDF with a miscible polymer, which is another possibility to achieve a direct β-phase crystallization PVDF from the melt-state. The interactions between PVDF and a (partially-)miscible polymer can modify the PVDF crystallization and directly promote the specific polar -phase [START_REF] Bonardd | [END_REF] . This is the case of poly(methyl methacrylate) (PMMA) with the occurrence of specific Hbonding interactions between the CH 2 groups of PVDF and the carbonyl groups of PMMA. An abundant literature regarding PVDF/PMMA miscibility, the phase crystallization induced by PMMA and the presence of a ferroelectric behavior for PVDF/PMMA blends [START_REF] Harrison | [END_REF][START_REF] Bonardd | [END_REF][29][30][31][32][33][34][35] has already been reported. Briefly, Leonard et al. specifically observed that the PVDF crystallization is sensitive to the cooling rate applied from the melt state. By using a solvent-based approach, Dominici C. et al. also demonstrated that the incorporation of 30 wt-% of PMMA totally promotes the β-phase to the detriment of α-phase. According to these observations, a recent investigation was performed by our group using Flash DSC to identify the impact of the cooling rate from the melt state on the crystallization of neat PVDF and PVDF/PMMA blends 27 . These thermal analyses under fast cooling rates allowed to obtain quantitative information on the crystallization temperature of non-polar and polar phases on a large range of cooling rate (-10 to -4000 °C/s). First, a high cooling rate plays an essential role on the appearance of the PVDF β-phase and the α-to-β crystal transition. The polar β-phase starts to crystallize for cooling rates higher than 400 °C/s for neat PVDF with an exclusive/full crystallization for cooling rates after 800 °C/s. The PMMA contribution showed an important impact on the α-to-β transition with a transition shifted to lower cooling rates with the increase of PMMA content. The polar phase starts its crystallization at cooling rates higher that 50-100 °C/s with 10 wt-% PMMA. These results allowed to obtain a clear crystal phase diagram of α-to-β crystal transition (with α+β mixed crystallization regime) as a function of PMMA and cooling rate. It reveals a good compatibility with standard processing tools used in the plastic industry. In a subsequent step, the extrusion-calendering processing of PVDF/PMMA blends turned out to be an efficient way to produce thin films containing high amounts of β-crystals with only 5 wt-% of PMMA as observed by wide-angle X-ray scattering (WAXS) and infrared spectroscopy experiments (ATR-FTIR). This process coupled to the addition of PMMA consequently represents a good approach to reach electroactive properties for PVDF using a cost-competitive melt-state technique without any solvent required (no supplementary pre/post treatments).

In terms of piezoelectric/ferroelectric properties, such PVDF/PMMA blends have not been deeply investigated and the litterature shows some discrepancies within the results. Some authors reported the reduced piezoelectric/ferroelectric properties such as remanent polarization and coercitive field with the incorporation of PMMA into PVDF 11,30 . Recent results from our group also demonstrated a remanent polarization close to 2.4 µC/cm² with 10 wt-% PMMA 27 at a poling field of 2000kV/cm, much weaker than the value for stretched PVDF film (close to 5.5 µC/cm² )at the same poling field) 36 . PVDF crystal size effect 37 could explain the reduction of the electroactive properties for PVDF/PMMA blends. Other researchers' groups investigated the role of amorphous/cristalline interphase in miscble PVDF/PMMA 15 and showed a significant importance of this interphase on the dielectric behavior. Stingelin et al. 30 observed a complex ferroelectric behavior for PVDF/PMMA blends with a typical hysteresis loop related to a capacitance phenomenon in the case of PVDF/PMMA blends with 10 wt-% PMMA. The capacitance phenomenon seems to indicate charge trapping during high-voltage poling. This phenomenon could be linked to the crystal-amorphous interphase and the intercrystalline amorphous region with a swelling effect induced by PMMA on the crystalline component 38 . These investigations clearly indicate complex dielectric effects in PVDF/PMMA and a clarification is required to optimize PVDF/PMMA composition and organization for ferroelectric/piezoelectric applications.

In order to improve the inner structure of the PVDF/PMMA blends, some researchers employed blocky-like copolymers based on MMA and functional comonomers. Wang P. et al. 39 reported the use of 1-vinyl-3-ethyl imidazolium bromine ionic liquids (IL) to prepare P(MMA-IL) which is incorpored into PVDF by solution mixing. The imidazolium cation of the IL through its ion-dipolar interactions with -CF 2 groups of PVDF can promote the PVDF β-phase and improve electric charge transfert in both amorphous and interphase regions. Poly(ethylene oxide)-block-poly(methyl methacrylate) 40 (PEO-b-PMMA) or poly(methyl methacrylate-co-poly(ethylene glycol) methacrylate) 41 (PMMA-co-PEGMA) mixed with PVDF could also exhibit higher ionic conductivity at room temperature (2.8 -3 x 10 -3 S.m -1 in comparison to 0.5 x 10 -3 S.m -1 for the neat PVDF). Other blocky-like copolymers were studied to modify the electroactive PVDF properties such as zwitterionic blocks 42 or poly(2-vinyl pyridine) 43 but no piezoelectric/ferroelectric were shown. It could be noticed that peculiar relaxor/antiferroelectric-like were also depicted for PVDF-based materials blends with several copolymers (P(VDF-TrFE-CTFE)-g-PMMA, P(VDF-TrFE-CTFE)g-PBMA, P(VDF-TrFE-CTFE)-g-PS) with an interesting perspectives as energy storage/supercapacitors [44][45][46][47][48][49][50][51][52][53][54] .

Based on the recent litterature, we herein propose to investigate the effect of two PMMA-based copolymers on the PVDF -phase crystallization from the melt state by extrusion-calendering followed by comparative ferro/piezoelectric characterizations. Poly(butyl methacrylate-co-methyl methacrylate (PBMA-co-MMA, namely PBMA-MMA) was first selected for its low glass transition temperature (T g ≈ 52 °C) compared to the PMMA (T g ≈ 117 °C) to potentially modify the PVDF/PMMA chain dynamics within the amorphous phase (and in particular within the interlamellar amorphous regions of PVDF). Another PMMA-based copolymer was selected, i.e. poly(methyl methacrylate-comethacrylic acid) (PMMA-co-MAA, namely, PMMA-MAA) containing an ionizable group via the methacrylic acid moiety. This copolymer is potentially able to boost the β-phase through the formation of more hydrogen interactions 55 in comparison to the classic PMMA and thus improve the subsequent piezoelectric/ferroelectric properties of PVDF-based blends. According to previous investigations from our group 27 , the present study is first focused on the influence of as-selected PMMA copolymers on the crystallization of the polar PVDF β-phase from the melt state. The copolymers were compared with the PMMA on their β-phase crystallization ability by a Flash DSC technique. Resulting PVDF-based films processed by a melt-state extrusion-calendering process were characterized by WAXS and FTIR techniques to detect and quantify crystalline phases. A particular interest was carried on the ferroelectric/piezoelectric performances as a function of nature/content of these PMMA-based copolymers. The occurance of crystalline modifications during high voltage poling and the impact of the poling temperacture on ferroelectric performances of as-produced PVDF/PMMA blends is finally revealed.

Chapter V: enhanced beta phase crystallization in melt-processed PVDF films blended with PMMAbased copolymers and impacts on subsequent ferro/piezoelectric performances 115

V.3. Experimental section

Materials

Poly(vinylidene difluoride) was kindly supplied by Arkema, France (hereafter called PVDF, grade Kynar® 720, M w 200 000 g.mol -1 , MVR 230°C-5kg 10 cm 3 /10min). Poly(methyl methacrylate) was supplied by Evonik, Germany (hereafter called PMMA, grade 8N, M w = 97 000 g.mol -1 , MVR2 30°C-3.8kg 3 cm 3 /10min). PMMA copolymers, poly(methyl methacrylate-co-methacrylic acid) (hearafter called PMMA-MAA, M w = 34500 g.mol -1 ; MAA content 1.6 mol-%) and poly(butyl methacrylate-co-methyl methacrylate) (hereafter called PBMA-MMA, M w = 138 000 g.mol -1 ; containing 21 mol-% of MMA, obtained by DSC (Fox relation)) by Sigma-Aldrich Chemistry. Throughout this contribution, all percentages are given as weight percentage (wt-%).

Processing of PVDF/PMMA-MAA & PVDF/PBMA-

MMA blends

PVDF-based blends with selected PMMA-based addtives were meltprocessed by a film extrusion-calendering/casting process as described in a previous article from our group 27 . In a first step, PVDF and PMMA (or PMMAbased copolymers) were melt-blended in a co-rotating twin-screw extruder (Haake Rheomex PTW 16 OS, ThermoScientific, Germany) with a screw diameter of 16 mm for a L/D ratio of 40. Predetermined weight ratio of PVDF and PMMA pellets were dry-blended, extruded (screw speed between 150 -200 rpm, mass flow rate between 1-1.2 kg/h) and pelletized. Extrusion temperatures were set to 210 °C (except for the temperature of extrusion die set at 170 °C). The asproduced PVDF/PMMA-based pellets were reprocessed by film extrusioncasting/calendering with a Haake single-screw extruder with a L/D ratio equal to 16, a temperature profile of 170 -210 -210 -230 °C (from the hopper to the die) and a screw speed of 60 rpm. A specific slit die for film extrusion (width 150 mm, thickness 800 µm) was used and the film extrudate was subsequently calendered to obtain 20-40 µm thick films. The calendering system is equipped with a cooling system using cold water (10 °C) within the cylinders (estimated cooling rate ± 200 °C/s according to the litterature) 27 .

Charaterizations

A. Attenuated Total reflectance Fourier Transform InfraRed spectroscopy (ATR-FTIR)

As-produced thin films were analyzed by Attenuated Total Reflectance Fourier Transform InfraRed spectroscopy (ATR-FTIR) using a BIO-RAD Excalibur spectrometer equipped with an ATR Harrick Split Pea™ apparatus from SAFIR Cie. Spectra were recorded using a spectral width ranging from 700 to 1400 cm -1 with a resolution of 4 cm -1 and an accumulation of 64 scans.

B.

Wide-angle X-Ray Scaterring (WAXS)

As-produced thin films were analyzed by Wide Angle X-ray Scattering (WAXS) carried out at room temperature in transmission mode. The analyses were performed on a Xeuss apparatus (Xenocs, France) and the CuKα radiation (l=1.54 Å) was used. The sample to detector distance was set at 10 cm and calibrated thanks to a Silver Behenate sample. WAXS patterns were recorded using a Pilatus detector (Dectris) at an angle values (2θ) between 5 and 30°.

C. DSC and Flash DSC (FDSC)

Flash DSC (FDSC) experiments were carried out on a Mettler-Toledo Flash DSC 1 via a specific protocol to observe the crystallization behavior of asproduced PVDF/PMMA-based blends at different cooling rates. The measuring cell was continuously flushed with nitrogen gas. Sample of about 35 -100 ng was placed under a microscope on the active area of the circular 500 µm-diameter sensor. The procedure used for crystallization analyses is the following: heating at 1000 °C/s to 210 °C, isotherm at 210 °C during 10 sec, cooling at controlled cooling rates between -10 °C/s and -4000 °C/s to -80 °C, isotherm at -80 °C during 10 sec, heating at 5000 °C/s to 210 °C. This procedure was repeated at different cooling rates as shown in Figure V.1. Crystallization temperatures (T c ) were determined at the maximum of the exothermic peak observed during the cooling scan. For sake of clarity, cooling curves were normalized by the heating rate.

Thermal properties of as-produced thin films were also analyzed by classical Differential Scanning Calorimetry (DSC) using a DSC Q2000 from TA Instrument. A heat-cool-heat cycle under nitrogen flow was used with heating and cooling rates of 40 °C/min. The melting temperature (T m ) and melting enthalpy Dielectric permittivities and dielectric losses were measured with a HP4284A precision LCR Meter (Agilent, PaloAlto, CA) at nine frequencies between 100 Hz and 1 MHz. Analysis was carried out by using Z-view impedance software. Experiments were performed between 180 and 420 K with a heating rate of 1.5 °C/min. blend. The evolution of PVDF crystallization temperature as a function of the cooling rate (Figure V.3) reveals a shift to lower T c for both PVDF α-and βcrystallization in PVDF/PMMA-MAA blends compared to PVDF/PMMA. As consequence, PMMA-MAA and PMMA seem to display similar performances regarding the promotion of the PVDF -phase with a slightly higher efficiency for PMMA-MAA that could be attributed to enhanced PVDF-PMMA interactions and subsequent miscibility, in agreement with several studies found in literature. In particular, Landis et al. 55 found that PMMA-MAA copolymers can alter the PVDF crystallization and the compatibility with PVDF. Infrared spectroscopy analysis suggested enhanced intermolecular interactions between PMMA-MAA copolymers and PVDF with an enhanced resulting blend miscibility.

Concerning PVDF/PBMA-MMA blends, the β-phase crystallization starts at cooling rates higher than -300 °C/s (Figure V.2C) and the α-phase crystallization seems to disappear at very fast cooling rate of -2500 °C/s. The α-β crystal transition is clearly shifted to higher cooling rates with similar values to neat PVDF. Figure V.3 also shows that PVDF crystallization temperatures shifted to higher temperatures, reaching values similar to neat PVDF. In this context, a negative effect of the PBMA-PMMA copolymer on the PVDF -phase crystallization is observed and attributed to incompatibility/immiscibility between these two components. As a conclusion, FDSC clearly suggests a positive impact of the PMMA-MAA copolymer on the PVDF β-phase formation due to miscibility between PVDF and PMMA-MAA due to hydrogen bonding interactions. PMMA-MAA leads to results similar to PMMA in terms of -phase promotion with slightly better efficiency. In the opposite, the PBMA-MMA copolymer leads to poor miscibility with PVDF without significant modifications of the and -phase crystallization.

Crystallinity of PVDF/PMMA-based films produced by extrusion-casting

The melt-state extrusion-calendering process was used to produce thin films in a thickness range of 25 -35 µm following of previous FDSC results on the PVDF crystallization in the presence of various PMMA-based. This low thickness range coupled melt-state calendering generates high cooling rates (± 200 °C/s depending on film thickness and materials) 27 which induces PVDF polar -phase. Thin films of neat PVDF, PVDF/PMMA, PVDF/PMMA-MAA and PVDF/PBMA-MMA were produced by this technique and characterized by ATR-FTIR/WAXS to observe the evolution of the PVDF crystalline phases as a function of PMMA-based copolymer type and content (5 and 10 wt-%). ATR-FTIR is an accurate characterization technique for PVDF crystalline phases that potentially enables qualitative and quantitative measurments for the β-phase (characteristic absorption peak at 840 cm -1 ) and for the α-phase (characteristic absorption peak at 766, 795 and 855 cm -1 ) 58 . ATR-FTIR spectra are displayed in Figure V.4 with a normalization to a reference peak (872 cm -1 ) to dismiss the impact of film thickness variations on IR absorbance. To discriminate the polar phases and confirm infrared analyses, WAXS characterization was used to identify the crystalline lattices 59 related to β-and α-phase at a 2θ of 20. 8° and 18.3 -19.9 -26.6°, respectively (Figure V.5).

Figure V.4A and V.5A show ATR-FTIR and WAXS characterizations of PVDF-based blends with 5 wt-% PMMA-based additives (both figures with the neat PVDF as a reference). First, the neat PVDF displays mostly the characteristic peaks of the non-polar -phase with absoption peaks close to 765, 795 and 855 cm -1 (Figure V.4). A slight β-phase crystallization is observed (840 cm -1 ) due to high quenching/cooling rates. WAXS analysis for neat PVDF films shows the apparition of a small shoulder at 20.5°, which confirm the slight amount of βphase. For PVDF/PMMA and PVDF/PMMA-MAA blends processed into thin films, a clear modification of the PVDF crystallization is observed. ATR-FTIR allows confirming a high positive influence of PMMA-MAA on the β-phase crystallization compared to PMMA (Figure V.4A) as previously shown by FDSC experiments. Indeed, the absoption peak at 840 cm -1 clearly displays a higher intensity for PMMA-MAA than PMMA. In the opposite, PVDF α-phase absorption peaks are reduced and WAXS analysis clearly confirms the effect of PMMA-MAA on β-phase crystallization with a clear β-phase pattern (20.3°) and disappearance of α-phase diffraction peak at 2θ angle close to 26. ATR-FTIR technique was used to obtain quantitative information about the content in PVDF and -crystals in as-produced PVDF-based blends. As previously observed, a quantification by WAXS is not possible because of crystal size effects and difficulties associated to background determination and peak fittings. Infrared spectroscopy is theorically able to quantify crystalline fractions of PVDF blend according to previous studies by Gregorio et al. 2,62 . Relationships between peak intensities and crystal concentration are actually known in IR transmission mode for low film thickness (<10 µm). However, the ATR-FTIR mode is preferred for as-produced films with thickness close to 30 µm and relationships developped by Gregorio et al. 2,62 were here adapted (in particular to eliminate the film thickness dependancy using the absorbance at 870 cm -1 as internal standard/reference for PVDF -, and amorphous phases). The content in -crystals was first deduced from Relation 1 using baseline-corrected absorbances at 760 cm -1 (A 760 ) and at 870 cm -1 (A 870 ). It could be noticed that the proportionality constant K 760/840 was found close to 1.4 using a reference PVDF sample fully crystallized into the -phase (X c- 55 % determined by DSC with an infinite H of 104.5 J/g 38,63,64 , A 760 /A 870 ≈ 0.8 determined by ATR-FTIR). A similar procedure is used (Relation 2) for the content in -crystals using the baseline-corrected absorbance at 840 cm -1 (A 840 ). Since no reference PVDF sample fully crystallized into -phase is available (with unknown value for infinite H), the proportionality constant K 760/840 is evaluated by Relation 3 based on previous studies by Gregorio et al. 2,62

Figure V.6 displays the evolution of PVDF crystalline phase content as a function of PMMA content for PVDF/PMMA thin films processed by extrusioncalendring. Neat PVDF films display a total crystallinity of ± 55 % (α+β crystals) with 45 -50 % of α-crystals and 5 -10 % of β-crystals. The evolution of PVDF total crystallinity as a function of PMMA content displays a continuous decrease (Figure V.6) in agreement with the PVDF/PMMA miscibility 65,66 . The α-crystals quantity clearly and quickly drops with the amount of PMMA with a total disapperance for 20 wt-%. In agreement with the -to- PVDF crystal transition with the incorporation of PMMA, The amount of -phase reachs the entire crystallinity at this peculiar PMMA content. Similar calculations were performed for PVDF/PMMA-MAA and PVDF/PBMA-MMA blends (Table V.1). First, the immiscibility of PVDF and PBMA-MMA clearly induces very low β-phase content (3 -2 % of β-crystals, total crystallinity 50 -57 %). Concerning PVDF/PMMA-MAA blends, Table V.1 shows an interesting β-phase content of 35 % (total crystallinity 45 %, -phase fraction 78 %) for only 5 wt-% PMMA-MAA in agreement with all above results from FDSC, ATR-FTIR and WAXS on this peculiar blend (enhanced PVDF/PMMA-MAA miscibility and interactions). Reduced interactions between PVDF/PMMA-MAA at high PMMA-MAA content (10 wt-%) are here confirmed by the high reduction of the -phase content (8 % of -phase, total crystallinity 52 %) confirming PVDF/PMMA-MAA demixion at elevated MAA moieties contents.

To conclude, compared to the use of PMMA, PMMA-MAA clearly modifies PVDF crystallization from the melt state and the so-called -to- crystal transition at elevated cooling rates, in agreement with an enhanced miscibility and hydrogen bonding interactions. High PVDF -phase contents in PVDF-based films produced by a melt-state extrusion-calendering is possible using PMMA-MAA in low amounts (5 wt-%). However, at higher PMMA-MAA contents, field with P R close to 2.2 µC/cm² and E C close to 825 kV/cm (Table V.2). Such results are lower than ferroelectric properties obtained by Mackey et al. 36 on stretched PVDF poled at the same electric field (P R close to 5.5 µC/cm²). Neat PVDF also displays a ferroelectric quality factor of 0.78 (ratio P R /P max ) indicating an efficient poling 74 and confirming the ferroelectric-type behavior.

Incorporating 5 wt-% of PMMA into PVDF clearly improves ferroelectric properties (Figure V.7B and V.8B) with P R up to 4.3 µC/cm² with E C close to 790 kV/cm for electric fields of 1500kV/cm with an excellent ferroelectric quality factor of 0.88 (Table V.2). However, higher PMMA content to 10 wt-% clearly reduces ferroelectric properties (Figure V.7C and V.8C) which leads to a total transformation to a quasi-linear dielectric behavior at 20 wt-% PMMA (Figure V.7D and V.8D). An optimum amount of 5 wt-% of PMMA is consequently evidenced with significative enhancement of the ferroelectric behavior for this peculiar PMMA content. The addition of 5 wt-% of PMMA-MAA copolymer into PVDF enchanced the amount of PVDF β-phase in melt-processed films and slightly better ferroelectric properties are observed in comparison with the corresponding PVDF/PMMA blend (Figure V.7E and V.8E) with P R close to 4.9 µC/cm², E C of 740 kV/cm and excellent ferroelectric quality factor of 0.85 for electric fields for 1500 kV/cm (Table V.2). Some slight differences are observed with the corresponding PVDF/PMMA blend in terms of electric field threshold (1000 kV/cm for PVDF/PMMA vs. 1100 kV/cm for PVDF/PMMA-MAA), potentially attributed to the higher quantity of PVDF β-crystals. Coercitive fields are interestingly lower in PVDF/PMMA-MAA (with higher remanent polarization) and these effects indicate that the MAA comonomer not only modifies the dipole density but also their own switching dynamics. Then, for 10 wt-% content of PMMA-MAA, its immiscibility with PVDF clearly reduces ferroelectric performances (Figure V.7F and V.8F). Figure V.9 allows concluding on the evolution of the ferroelectric properties with the electric field and the type/amount of PMMA additives. Neat PVDF needs elevated electric fields (> 1200 kV/cm) to induce ferroelectric-type dielectric behavior with high Ec values. With the addition of 5 wt-% of PMMA or PMMA-MAA, ferroelectric-type dielectric behaviors start to appear at lower electric field with significant improvements of remanent polarizations, coercitive fields and ferroelectric quality. Efficient ferroelectric films are consequently produced by a melt-state extrusion-calendering process. Also, a slightly better behavior is observed for PVDF/PMMA-MAA blend. Such effects could be related to the improvement of the β-phase rate induced by low contents in PMMA or PMMA-MAA. However, these results also allow us noticing that the initial βphase content does not seem to govern the final ferroelectric behavior to get efficient ferroelectric properties. Actually, neat PVDF with a low -phase content displays interesting ferroelectric properties and, concerning PVDF/PMMA blends, no clear correlations are observed between the remanent polarization and the initial -phase content. Others factors/parameters need to be considered for an in-depth understanding (crystalline modifications at elevated electric fields, size of PVDF -crystal and interfacial trapped charges 27 ). However, a partial αto-β crystal phase transformation under high electric field is suspected in asproduced blends 75 and this effect will be discussed in the final part of this study. The ferroelectric properties of PVDF and its relation to the polar β-phase are known to be related with final piezoelectric properties. However, the corresponding literature indicates that ferroelectric/piezoelectric properties can be affected by the presence of PMMA. In this context, piezoelectric coefficients (d 33 ) of as-produced PVDF-based blends with PMMA and PMMA-MAA were measured at room temperature by a Berlincourt piezometer with an applied dynamic mechanical stress of 0.25 N at 100 Hz (Table V.3). For sake of comparison with ferroelectric properties, thin films were poled using an alternative electric field of 1500 kV/cm (triangular waveforms, similar frequency 0.1 Hz) at room temperature inside a dielectric fluid. The piezoelectric coefficient of neat PVDF after the poling procedure gave a value close to 7 pC/N (± 1 pC/N) decreasing to a stabilized value of 5 pC/N after a storage period of 1 week (Table V.3). Thus, as-produced neat PVDF film displays a relatively high piezoelectric value without stretching treatments. PVDF/PMMA blends with 5, 10 and 20 wt-% of PMMA or PMMA-MAA were subsequently subjected to the same poling procedure, followed by piezoelectric measurements. As a general rule for these blends, the piezoelectric coefficient decreases with storage time by approx. 1 -2 pC/N after 1 week and it stabilizes. Such effect could be linked to residual electrostatic charges or/and charge losses inside the matrices due to relaxations. However, it could be stated out that stable piezoelectric properties are obtained for as-produced and as-poled PVDF/PMMA blends. Figure V.10A displays the evolution of the piezoelectric coefficient as a function of the PMMA content. The evolution of the piezoelectric coefficient closely follows the trend observed on ferroelectric properties and previously-reported results from our group 27 . Actually, a maximal d 33 value is observed with 5 wt-% of PMMA reaching piezoelectric coefficient of approx. 11 pC/N. For higher PMMA or PMMA-MAA contents, piezoelectric properties drastically decrease and, based on Table V.2, a close correlation is suspected between piezoelectric coefficients (d 33 ) and remanent polarizations (P R ). As observed in Figure V.10B, a linear relationship between d 33 and P R is obtained with a slope of approx. 2. Such linear relationships are clearly in agreement with recent models concerning the piezoelectricity of PVDF, in particular with the electrostriction model 76 that yields a linear relationship with slope close to 2.4. It could be noticed that the line does not pass through the origin with a residual piezoelectricity of approx. 1.6 pC/N as

Discussion on crystal modifications during poling

As previously expressed, the intial -phase content in as-produced PVDF/PMMA blends does not fully fit with ferroelectric properties and subsequent piezoelectric properties. Crystal modifications during high-voltage poling are suspected with a potential α-to-β crystal transformation at elevated electric fields 75 . This important aspect could explain ferroelectric properties and ATR-FTIR experiments were conducted before and after high-voltage poling on PVDF-based blends with PMMA or PMMA-MAA processed by extrusioncalendering (Figure V.11). ATR-FTIR parameters similar to the one used in the previous investigations were used and Figure V.11A & Table V.4 clearly demonstrate that crystalline modifications occur in neat PVDF films during highvoltage poling with a high increase in polar -phase content from 21 % to 29 % (unpoled to poled neat PVDF). The α-phase content clearly decreases thus confirming a α-to-β crystal transformation during high-voltage poling for neat PVDF films. Such phenomenon is also observed for PVDF-based blends with 5 wt-% PMMA or PMMA-MAA with an increase of the β-phase peaks after poling together with a decrease of α-phase peaks. The previous trends on ferroelectric properties could be explained by the optimum β-phase content after high-voltage poling with the addition of 5 wt-% PMMA or PMMA-MAA (based on Table

) B)
V.4). However, ferroelectric properties cannot be entirely correlated to final quantity of β-phase after high-voltage poling, in particular for neat PVDF and PVDF/PMMA blends with 20 wt-% PMMA. Actually, the αto -β transformation is known to occur via an intermadiate polar -phase, called α p -phase, depending on studies leading to a global -to-α p -to-β crystal transformation 77-79 under highvoltage poling. This pathway is here difficult to detect by ATR-FTIR but (i) Table V.4 highlights apparent variations in terms of crystalline content before and after high-voltage poling and (i) the α-crystal peak located at 795 cm -1 corresponding to -CH 2 rocking vibrations 80 seems to follow a different trend from other α-crystal peaks. This absorption peak does not decrease after high-voltage poling. In this context, a crystal modification from the initial α-phase into α p -phase during highvoltage poling seems consistent with our observations. Consequently, thanks to a -to-α p -to-β crystals transformation during poling, it can be assumed that a high initial β-phase content is not fully mandatory for enhanced ferroelectric and piezoelectric performances. In this context, the non-polar -phase could contribute to ferroelectric properties of neat PVDF and PVDF-based blends with PMMA or PMMA-MAA blends by its polar intermediate α p -phase. Blends with 5 wt-% PMMA-based additives consequently display an optimum -phase content and α p -phase content with optimal ferroelectric properties. In-depth investigations are required to detect the exact role of each crystalline phase (and in fine the role of PMMA-based copolymers) on ferroelectric and piezoelectric properties of PVDF-based blends with PMMA or PMMA-MAA. The impact of the extrusion-calendering process on ferroelectric properties of PVDF-based blends with PMMA or PMMA-MAA also represents a key task to be performed. 4.6. Discusion on the impact of the high-voltage poling at elevated temperature Based on above results about (i) ferroelectric/piezoelectric properties of PVDF-based blends with PMMA and PMMA-MAA processed into films by extrusion-calendering and (ii) crystal modifications linked to the high-voltage poling process, a preliminary investigation was performed on high-voltage poling at elevated temperatures. Actually, previous ferroelectric and piezoeletric characterizations demonstrated the importance of the remanent polarization on the piezoelectric coefficient. The remanent polarization seems to be partly controlled by the final amount of β-phase 81 and  P -phase induced by high-voltage poling. In this context, to improve ferroelectric properties of PVDF-based blends with PMMA or PMMA-MAA, the impact of the high-voltage poling temperature (above 50 °C) on ferroelectric properties was evaluated by using (P-E)/(I-E) hysteresis loops.

Ferroelectric properties of neat PVDF and PVDF-based blends with PMMA and PMMA-MAA (5 wt-% PMMA-based aditives) were analyzed at room temperature, 50 °C and 75 °C (Figure V.12) and quantitative informations are reported on Table V.5. In the case of neat PVDF (Figure V.12AB), highvoltage poling at 50 and 75 °C significantly increases the remanent polarization up to 3.8 and 8.1 µC/cm² respectively. Concerning the coercitive field, the impact of the high-voltage poling temperature is unclear with a significant decrease of E c at 50 °C (E c 420 kV/cm) followed by a significant elevation for a high-voltage poling temperature of 75 °C (E c 610 kV/cm). Note that the ferroelectric quality factor also shows the same trend and remains significantly lower than the one observed at room temperature. Such effects could be attributed to (i) an enhanced -to-α p -to-β transformation at elevated poling temperatures (higher P R and erratic E c evolution) and (ii) faster diplole relaxation phenomena linked to amorphous PVDF phases that reduce dipole coupling between polar crystals (lower ferroelectric quality factor and E c ) 82,83 .

The PVDF/PMMA blend with 5 wt-% PMMA displays the same positive trend regarding the impact of the high-voltage poling temperature on P R (Figure

V.12CD).

A high remanent polarization 15.2 µC/cm² is reached for poling temperatures of 75 °C. According to the previous relationship between ferroelectric and piezoelectric properties (Figure V.10), this P R value could theoretically yield to piezoelectric coefficients higher than 30 pC/N. Concerning E c and ferroelectric quality factor, a different trend is detected for neat PVDF.

Coercitive fields decrease with the poling temperature as a classical phenomenon observed for PVDF-based materials indicating faster dipole switching 82 at elevated temperatures. However, the ferroelectric quality factor reaches 0.92 at 75 °C for the PVDF/PMMA blend indicating an absence of dipole relaxation after voltage removal. This peculiar ferroelectric behavior at elevated poling temperatures is here explained by an intense charge trapping phenomenon (due to the high increase of the electrical conductivity at elevated temperatures) favoring high-quality ferroelectric properties. The later effect is clearly consistent with the temperature dependance of the electrical conductivity in PVDF/PMMA blends with a rise from approx. 0.8 to 200.10 -15 (Ω.cm) -1 between 23 °C and 90 °C respectively 84 (5 to 700.10 -15 (Ω.cm) -1 in the case of neat PVDF).

Finally, the PVDF/PMMA-MAA blend with 5 wt-% PMMA-MAA reaches giant remanent polarization values of 26.9 µC/cm² at a high-voltage poling temperature of 75 °C (Figure V.12EF) for a theoretical piezoelectric coefficient higher than 50 pC/N, in agreement with recent studies on PVDF-TrFe materials poled in peculiar conditions 76 . The ferroelectric quality factor suprisingly reaches nearly-perfect values at 75 °C close to 0.96 for the PVDF/PMMA-MAA blend. Such surprising phenomena observed for the PVDF/PMMA-MAA blends at elevated poling temperature still remains unclear but the electrical conductivity is cleary suspected to play a major role. Such conclusions could be in accordance with the ionic nature of PMMA-MAA that could trap electric charges and ionic impurities, thus playing a similar role than polar PVDF crystals on the final ferroelectric behavior.

In conclusion, high-voltage poling at elevated temperature clearly represents an interesting approach to boost ferroelectric and piezoelectric performances of PVDF-based blends with PMMA or PMMA-MAA processed by extrusion-calendering. PMMA-MAA (and even PMMA) clearly favors giant remanent polarizations at 75 °C with a high-quality ferroelectric behavior. Phenomena underlying these results are still unclear and several hypotheses need to be tested in a near future (-to-α p -to-β transformation, conductivity enhancement with trapped charges/impurities, relaxation phenomena in the amorphous phase, etc…). An important future investigation also lies on the timetemperature stability of ferroelectric/piezoelectric behavior induced by highvoltage poling at elevated temperature.

V.5. Conclusions

A series of PVDF-based blends with three PMMA-based additives were processed into thin films by melt-state extrusion-calendering and several characterizations were conducted to identify the role of PMMA-based additives on -phase crystallization and subsequent ferro/piezoelectric properties. FDSC experiments highlight significant modifications at low cooling rate using only 5 wt-% of PMMA and PMMA-MAA. In the opposite, the PBMA-MMA copolymer does not influence the -phase crystallization due to immiscibility with PVDF. The PMMA-MAA copolymer is clearly the best β-phase promoter with a narrower -to- crystal transition (-100 to -800 °C/s for PVDF/PMMA vs. -100 to -700 °C/s for PVDF/PMMA-MAA) which demonstrates the importance of PVDF/PMMA-MAA intermolecular interaction (H-bonding). The FDSC conclusions are consistent with ATR-FTIR and WAXS analysis on meltprocessed PVDF-based blends by extrusion-calendering. The addition of 5 wt-% PMMA-MAA efficiently promotes PVDF β-phase up to 35 %. The PVDF/PMMA-MAA blend seems to be a promising ferroelectric/piezoelectric material. Ferroelectric properties were established for miscible PVDF-based blends with PMMA or PMMA-MAA. The highest remanent polarization was observed with 5 wt-% PMMA-MAA with a P R value of 4.9 µC/cm² (close to stretched PVDF). Piezoelectric properties were also improved with 5 wt-% PMMA or PMMA-MAA with a maximal value close to 11 pC/N. A clear linear relationship between P R and d 33 has been demonstrated confirming the importance of ferroelectric properties on piezoelectric properties of PVDF/PMMA blends. Finally, a complex crystal transformation occurs during high-voltage poling, in accordance with a α-to-α p -to-β transformation pathway transition. A maximal amount of β-phase close to 38 -39 % is obtained with the specific use of 5 wt-% PMMA or PMMA-MAA. The role of the α p -phase is evidenced, in particular for neat PVDF. Finally, a preliminary study on the high-voltage poling at elevated temperature displayed a clear impact of high-voltage poling temperature on ferroelectric properties of PVDF/PMMA-based blend. The remanent polarization reaches a huge value of 26.9 µC/cm² for the PVDF/PMMA-MAA with a highquality ferroelectric behavior for a high-voltage poling of 75°C. PVDF/PMMA blend also shows interesting but lower ferroelectric properties close to 15.6 µC/cm² which demonstrates the benefit of the MAA monomer. These blends could theoretically yield high piezoelectric coefficient up to 50 pC/N. However, underlying phenomena behind these extreme P R values still requested in-depth investigations in a near future, in particular on the electrical conductivity on the efficiency of high-voltage poling at elevated temperatures.

Chapter VI: General conclusion and perspectives

The main aim of the present PhD thesis was to develop a new alternative pathway for the production of thin polymer films with enhanced piezoelectric and ferroelectric properties, while optimizing their implementation using melt-state processes. For many years, piezoelectric polymers have demonstrated their performances in various energy-related areas at the forefront of technology, but also their limitations related to their complexity of shaping and production capacity at low cost.

Recent researches have been focused on polyvinylidene fluoride (PVDF), which is by far the most widely used polymer in this field due to its high ferroelectric/piezoelectric performances. Unfortunately, to reach these smart applications, PVDF requires a specific crystalline morphology into the polar βphase. This crystalline phase and morphology can be obtained thanks to various processes such as stretching and copolymerization. Nevertheless, these processes make both manufacture and cost of piezo/ferroelectric polymer matrices out of industrial expectations. The main objective of this PhD thesis was to develop and optimize a material/processing route that facilitates the beta-phase morphology of PVDF using melt-state shaping process into thin films with improved ferro/piezoelectric performances.

This research project paid attention on a polymer extrusion blending approach in the aim to modify PVDF through intermolecular interactions and thus generating its polar crystalline β-phase. In this purpose, an appropriate candidate is poly(methyl methacrylate) (PMMA) which has a favorable impact on PVDF beta phase crystallization. However, up to now, most of the studies were carried out in solvent, limiting the technological transfer to the industrial world.

The first part of this PhD thesis was therefore focused on a crystallization study of PVDF/PMMA blends obtained by various implementation and shaping techniques from the melt state (extrusion-calendering films with very fast cooling and thermocompression with cooling in various media). The extrusioncalendering, interesting processing technology for the production of thin ferro/piezoelectric films, affects the PVDF crystallization kinetics because of cooling rates above -200 °C/s for thin films with 60 μm of thickness compared to kV/cm, 0.1 Hz) at room temperature. The ferroelectric hysteresis curves of the calendered films are again optimal for 5 wt-% PMMA and PMMA-co-MAA with P R close to 5 μC/cm², high ferroelectric quality factors and reduced coercitive field (E C ) in the presence of MAA. The same phenomena are also observed for the piezoelectric properties with maximum piezoelectric coefficients (d 33 ) for 5 wt-% PMMA or PMMA-co-MAA. Promising values close to 11 pC/N can therefore be achieved for potential harvesting applications. In addition, it is demonstrated that P R maintains a linear relationship with the d 33 , demonstrating the importance of ferroelectric properties on piezoelectric properties of PVDF/PMMA-based blends.

The effect of AC poling on PVDF/PMMA crystalline nature was then studied. The FTIR analysis of blends before and after poling reveals a complex crystal transformation during high-voltage poling. A phenomenon of reorientation/restructuring occurs within the PVDF crystal, indeed a α-to-α p -to-β crystallization transition is observed. The role of α p is detected and the β-phase reaches a fraction of 38 -39 % in presence of 5 wt-% PMMA or PMMA-MAA.

Finally, surprising ferroelectric properties are obtained with an AC poling procedure at elevated temperature (50 -75 °C) with giant remanent polarization values close to 16 -27 μC/cm². These values are clearly the highest values reported for the PVDF, such levels of remanent polarization should theoretically induce huge piezoelectric coefficients for a PVDF matrix, beyond 30 -50 pC/N. Such results obtained by AC poling at high temperature require in-depth prospects for understanding and improving PVDF/PMMA blends.

Based on the results obtained in the frame of the present work, several promising perspectives can be exposed as future research axes. In Chapter 3, several working hypotheses have been proposed because there is still some grey area regarding the piezoelectric behavior of PVDF in presence of PMMA, despite the important understanding obtained thanks to this work. In order to remedy these deficiencies, a very wide range of test battery could be realized to identify the main actors of the significant increase of ferroelectric properties under high temperature.

• It is currently difficult to rule out the potential effect of the mechanical properties change (T g and molecular chain size) brought to amorphous phase of the PVDF/PMMA blend. This study could not be completed due to lack of miscibility of PVDF/PBMA-MMA blend. At the sight of temperature poling results, it could be interpreted that the increase of remanent polarization comes from the modification of the mechanical properties within the amorphous phase at high temperature. It would therefore be interesting to find elements allowing the mechanical properties of the amorphous phase to be modified, without reducing the miscibility of the PMMA or the crystallinity of the PVDF. A PMMA copolymer comprising less steric bulk than PBMA-co-MMA or plasticizers might be considered.

• The molar mass of additives was not investigated in this study. In this context, a comparative study of different PMMA with various molar mass would allow to identify the best PMMA polymer chain size to interact as strongly as possible with PVDF and its β-crystallization. • The effect of PMMA-co-MAA with the presence of pendent ionizable bonds on the PVDF crystallization into polar β-phase has been demonstrated but this was not decisive on the piezoelectric properties. An additional study with a higher quantity of MAA (without reaching the critical rate) would make it possible to definitively state out on the potential effect of improvement the charge transfer via the additional ionizable groups (H-bonding). Other ionizable groups could also be tested in order to observe their impact on PVDF-crystallization, but especially the ferroelectric and piezoelectric properties. The choice must be oriented toward an element with the ability to lead an internal conductivity during the mechanical stress and the charge release. Zwitterions are good candidates due to the fact that they have two opposite electrical charges on this chain, which could promote the charge transfer under piezoelectric effect. • Another interpretation of the efficiency of the AC poling at high temperatures on ferroelectric properties could be identified by the increase of the conductivity inside the PVDF/PMMA blend. It seems pertinent that the increasing of electrical conductivity could facilitate the dipole switching and by consequence the remanent polarization as observed. It would be interesting to try to modulate the intrinsic electrical conductivity of PVDF/PMMA blends by the contribution of nano conducting particles introduced in insufficient quantity to reach percolation threshold (desired non-conductive matrix). The use of grafted PMMA by moderate conductive particles could also be of interest to study the conductivity effect on the ferroelectric and piezoelectric properties. The challenge will be to stay polarizable at high voltage and therefore electrically insulating. Particles such as oxidized graphene could be good candidates. • At the level of the characterizations, additional studies will be needed in the aim to reduce the lack of understanding still present. The dielectric spectroscopy (measurement of permittivity in function of temperature) could allow to observe and identify the origin of ferroelectric properties fluctuation brought by the blend compositions and the poling temperature (observation of ferroelectric transition, dielectric relaxation…). In order to better evaluate the application potential of PVDF/PMMA-based blends, techniques such as the measurement of d 31 (piezoelectric coefficient perpendicular to the stress axis) and the use of an energy recovery bench would make it easier to observe the actual power potential (mW) of the blends.

To finalize this PhD thesis, it would have been interesting to develop prototypes transposable to real applications, such as piezoelectric shoe sole to evaluate the real effectiveness of the material in full daily life situation. In order to achieve this footing and depending on the progress made on the control of crystallization in the polar phase, 3D printing could be a significant option. This enables to custom piezoelectric elements to be designed, which could be very complementary with the choice of developing low-costs part. At the end, these matrices are showing to be potentially very interesting for the future development of advanced piezo/ferroelectric devices such as sensors, actuators, but also smart textiles, floor coverings, etc. and therefore with a much wider application spectrum than investigated during the thesis.

  Remerciements ...................................................................................................... Chapter I: General introduction ........................................................................... Chapter II: State of art ......................................................................................... II.1. Ferroelectric and piezoelectric polymers: fundamentals and applications .......................................................................................................................... 1.1. General considerations ........................................................................ 1.2. Ferroelectric polymers ......................................................................... 1.3. Piezoelectric polymers ......................................................................... 1.4. Advanced applications of ferro/piezoelectric polymers ...................... II. 2. PVDF: Synthesis, crystallinity, processing and properties ..................... 2.1. Generalities .......................................................................................... 2.2. PVDF synthesis ................................................................................... 2.3. PVDF crystalline structures ................................................................. 2.4. Routes to ferroelectric/piezoelectric PVDF ........................................ 2.5. Polarization, poling and ferro/piezoelectric properties of PVDF-based polymers ....................................................................................................... II.3. Blends based on PVDF ............................................................................ 3.1. PVDF-based miscible blends .............................................................. 3.2. Case of PVDF/PMMA blends ............................................................. 3.3. Crystallization of the PVDF beta phase in PVDF/PMMA blends ...... 3.4. Ferroelectric and piezoelectric properties of PVDF/PMMA blends ...

Figure I. 2 :

 2 Figure I.2: Current targeted applications, in microelectromechanical systems.

Figure II. 1 :

 1 Figure II.1: Different FE domain structures (compound by dipoles) with increasing dipole-dipole or domain-domain interactions from left to right (the top panel) and corresponding electroactive responses in D-E loops (the bottom panel).

Figure II. 2 :

 2 Figure II.2: Illustration of (A) normal ferroelectric, and (C) paraelectric behaviors of the high temperature DE phase in poly(vinylidene fluoride-cotrifluoroethylene), P(VDF-TrFE). 14

Figure II. 3 :

 3 Figure II.3: Comparison of several piezoelectric materials (polymers, ceramics and crystals.)The piezoelectric phenomenon is mathematically formulated with the following equations: 𝑫 𝒊 = 𝜺 𝒐 . 𝜺 𝒊 𝒋 𝝈 . 𝑬 𝒊 + 𝒅 𝒊 𝑱 . 𝝈 𝑱

  discovered that behavior in 1969), pyroelectric (first reported in 1971 by Bergman 47 et al. and Nakamura and Wada 48 ), and ferroelectric 49,50 behaviors.

Figure II. 5 :

 5 Figure II.5: Molecular structure of the PVDF

Figure II. 6 :

 6 Figure II.6: Free radical vinyl polymerization of the monomer vinylidene fluoride to obtain PVDF under several chain conformations in the apolar α-phase and in the polar β-and γ-phases. 53 As shown in Figure II.6, after polymerization, PVDF adopts different macromolecular conformations, forming specific crystals. As function of the localization of atoms on the carbon chain, the resulting PVDF polymer has different properties and crystallization behaviors. Amorphous phase and crystalline phase differ in their dielectric and elastic properties.

  Figure II.7 summarizes different ways of producing the various phases (4) and the transformations between them.

Figure II. 7 :

 7 Figure II.7: Transformations between the four main phases of PVDF

Figure II. 8 :

 8 Figure II.8: Crystal structure of the α-phase of PVDF is in the TGTG′ conformation

Figure II. 9 :

 9 Figure II.9: Crystal structure of the β-phase of PVDF is in the all-trans conformation

Figure II. 10 :

 10 Figure II.10: Molecular orientation in the γ-phase

  Figure II.11: Characterization by WAXS (a), FTIR (b) and DSC (c) of three PVDF crystalline phases. 62

  101 . With the aim to improve the PVDF properties and to adapt it to the increasing technological demands, different PVDF-based copolymers have been developed. Poly(vinylidene fluoride-trifluoroethylene), P(VDF-TrFE), is one of the most studied copolymer (Figure II.13).

Figure II. 13 :

 13 Figure II.13: Schematic representation of the P(VDF-TrFE) repeats units 62

Figure II. 14 :

 14 Figure II.14: Representations of physical (temporary) and chemical (permanent) pinning in laterally expanded P(VDF-TrFE) crystals 6 . l 1 and l 2 are average interchain distances in PVDF and P(VDF-TrFE) and orange-red ovals with arrows represent dipolar TrFE with larger sizes). Furthermore, this copolymer presents a Curie Temperature (T C ) significantly below the melting temperature (T m ) depending on the TrFE content (Figure II.15), contrary to the elevated Curie temperature of PVDF at 195 -197 °C103,104 .

Figure II. 15 :

 15 Figure II.15: Phase diagram for P(VDF-TrFE) copolymers of specific temperature (T m , T cryst and T C (magenta: heating; green: cooling)) 23 .

  Figure II.16. Due to this net charge the polymer responds to electrical fields.

Figure II. 16 :

 16 Figure II.16: Dipoles alignment relay process in PVDF, random dipoles in blue and oriented dipoles in red with P s as saturating polarization, when each dipole is oriented. 115

Figure II. 17 :

 17 Figure II.17: Schematic of poling systems for piezoelectric polymers, (a) electrode method and (b) corona poling method. 116

  is necessary. It gives the hysteresis loop 117 of the polarization/dipole displacement as a function of the applied field (Figure II.18) and obviously others values such as the current density.

Figure II. 18 :

 18 Figure II.18: Current/Voltage loop (left scale) and polarization/voltage hysteresis loop (right scale) for PVDF, 10s cycle time, with the poling, resistive, and capacitive terms removed. The remanent polarization is defined as the polarization at zero field (P R ) and the coercive field as the field at which the polarization is zero (E c ). 117

  The hysteresis loops of β-PVDF show increasing polarization with applied field (Figure II.18). It demonstrates increasing dipole rotation and orientation in the crystalline regions 97 . It has been pointed that the amorphous region also contributes to the electroactive behavior of the material 124 . The piezoelectric coefficient d 33 of PVDF films dependence on poled electric fields were shown in Figure II.19 and was shown clearly the typical relation between the efficient polarization (here, represented by E c ± 120 MV/m) and the related piezoelectricity.

Figure II. 19 :

 19 Figure II.19: Piezoelectric coefficient d 33 dependence on poled electric fields of PVDF film (with Boltzmann distribution function) 125

Figure II. 20 :

 20 Figure II.20: DSC thermograms of PVDF/PMMA blends (heating cycle on left and cooling cycle on the right) 146

Figure II. 22 :

 22 Figure II.22: Ferroelectric phase diagram of PVDF/PMMA. (Blend films wirebar coated from DMF, molten at 200 °C in vacuum, ice quenched and subsequently annealed for 2 h at 150 °C). 156

  The theorical concept of morphology of PVDF and PVDF/PMMA blends is shown schematically in Figure II.23. In pure PVDF (Figure II.23 (A)), the noncrystalline region comprises the liquid-like region (C) and the interphase (B). The latter is a transition region, and its relaxation characteristics cannot be distinguished dielectrically from those of the liquid-like region. In PVDF/PMMA blends (Figure II.23 (B)), PMMA is excluded from the interphase and the relaxations in the interphase (B) can now be distinguished from those in the miscible phase (C) by dielectric measurements. In sum, the addition of PMMA to PVDF leads to (1) a gradual replacement of the liquid-like interlamellar PVDF region by the miscible PVDF/ PMMA phase and (2) the formation of an interphase with relaxation characteristics that are different from those of the miscible amorphous phase 165 .

Figure II. 23 :

 23 Figure II.23: Schematic of morphology of PVDF (Left) and PVDF/PMMA blends (Right) 165

  Figure II.22 shows that the remanent polarization of the PVDF/PMMA unambiguously scales with the crystallinity. A similar relation has been reported for blend films of P(VDF-TrFE) with PMMA 171 albeit that the change in entropy was plotted rather than degree of crystallinity. The remanent polarization and coercive field are presented as a function of temperature in Figure II.24 for three PVDF/PMMA blend ratios of 90:10, 80:20, and 70:30. Interestingly, for all blends the polarization is constant up to 120 °C. As a matter of fact, it increases very slightly. The coercive field decreases with temperature. The polarization of PVDF/PMMA is much more stable than that of P(VDF-TrFE). The thermal stability is directly related to the Curie temperature. The ferroelectric to paraelectric phase transition of P(VDF-TrFE) occurs below 100 °C. Therefore, above about 80 °C PVDF/PMMA blends outperform the copolymer P(VDF-TrFE).

Figure II. 24 :

 24 Figure II.24: Temperature effect on the ferroelectric parameters. Remanent polarization, P R (a), and coercive field, E C (b). PVDF/PMMA blends (in blue), 90:10 (•), 80:20 (▲), and 70:30 (⧫) wt-% and the copolymer P(VDF-TrFE) (in red). (Films coated from DMF, melted at 200 °C in vacuum, ice quenched, and subsequently annealed for 2 h at 150 °C). 156

Figure II. 25 :

 25 Figure II.25: Behavior of piezoelectric constant d 31 and d 33 vs percent weight of PMMA in PVDF/PMMA blends. 172

Figure IV. 1 :

 1 Figure IV.1:Temperature-time profiles used to investigate the crystallization for PVDF/PMMA blends during high-speed cooling by Flash DSC. The samples were characterized at different cooling rates between -5°C/s and -3000°C/s from the melt state followed by a melting step at high heating rate.

Figure

Figure IV. 3 :

 3 Figure IV.2: ATR-FTIR analysis of neat PVDF (-♦-), PVDF/PMMA 95:5 (-▼-), PVDF/PMMA 90:10 (-▲-), PVDF/PMMA 80:20 (-•-), PVDF/PMMA 70:30 (-■-) and neat PMMA (-►-) blends obtained by extrusion-calendering (a) or by thermo-compression (b) (film thickness ca. 60µm).

Figure IV. 4 :

 4 Figure IV.4: ATR-FTIR of a PVDF/PMMA (90:10) film processed by extrusioncalendering over the entire wavenumber range.

Figure IV. 5 :

 5 Figure IV.5: FTIR analysis of neat-PVDF (a) and PVDF/PMMA 95:5 (b) at different thickness 200µm (-◄-), 120µm (-♦-), 100µm (-*-), 80µm (-▼-), 60µm (-⌂-), 40µm (-▲-), 30µm (-•-) and 20µm (-■-) obtained by extrusioncalendering.

Figure IV. 6 :

 6 Figure IV.6: WAXS analysis of neat PVDF (a), PVDF/PMMA 95:5 (b), PVDF/PMMA 90:10 (c), PVDF/PMMA 80:20 (d) and PVDF/PMMA 70:30 (e). Evolution of the orientation factor P 2 as a function of PMMA weight content (f).

5 (

 5 Figure IV.7: ATR-FTIR of PVDF/PMMA films processed by extrusioncalendering and reprocessed by thermocompression at 210°C followed by quenching in LN 2 (a), LN 2 /methanol (-80°C) (b), cold water (0°C) (c) and temperate water (35°C) (d).

  ) using similar procedures to those exposed in Figure IV.1. PVDF/PMMA blends also display similar trends to neat PVDF with the -phase crystallization at low cooling rates followed by the characteristic  co-crystallization at intermediate cooling rates (Figures IV.

Figure IV. 8 :

 8 Figure IV.8: Cooling scans by FDSC at various cooling rates for neat PVDF (a), PVDF/PMMA 95:5 (b) and PVDF/PMMA 90:10 (c), PVDF/PMMA 80:20 (d). Related crystallization temperatures (d) and crystallization enthalpies (e) for phase and -phase as a function of cooling rate. Crystallization temperatures of PVDF -crystals and -crystals with related enthalpies could be extracted off from FDSC cooling traces and their respective evolutions with the cooling rate are displayed in Figure IV.8d-e for neat PVDF and the PVDF/PMMA 90:10 blend. In a first approach, the evolution of crystallization temperatures highlights the -to- crystal transition with the phase crystallization at low cooling rates (high crystallization temperatures) and the -phase crystallization at high cooling rates (low crystallization temperatures) (Figure IV.8d). It could be observed that, at a constant cooling rate, and phase crystallization temperatures clearly shift to lower temperatures with the incorporation of 10 wt-% PMMA (Figure IV.8d). The crystallization enthalpy

  .

  Figure IV.9: Flash DSC analysis of the PVDF/PMMA 80:20 blend. Cooling curves as a function of cooling rate (a) and heating curves after various annealing treatments (b).

Figure IV. 11 :

 11 Figure IV.11: Crystal phase diagram for PVDF/PMMA blends as a function of the cooling rate and weight percentage of PMMA. Experimental results by extrusion-calendering and thermocompression with pure α-phase (in red -■-), mixed α-/β-phases (grey -▲-) and pure β-phase (green -•-). Experimental results by Flash DSC are marked by stars (-*-).

Figure IV. 12 :

 12 Figure IV.12: Dielectric behavior for neat PVDF and PVDF/PMMA blends produced by extrusion-calendering (a) with related remanent polarization/coercitive field as a function of PMMA weight content (film thickness 40µm, maximal poling voltage 8000V).

Figure IV. 13 :

 13 Figure IV.13: Dielectric behavior for a P(VDF-co-TrFE) (75% TrFE, provided by PiezoTech, France) produced by thermocompression (film thickness 60µm annealed at 140°C, maximal poling field 10000 KV/cm).

Figure

  Figure IV.14: SAXS analysis of neat PVDF and PVDF/PMMA films produced by extrusion-calendering (a) with related evolutions of the -phase content (F) and long period (L p ) with the weight content of PMMA (b) (-phase content measured by ATR-FTIR 2 ).

Figure V. 2 :

 2 Figure V.2: FDSC cooling traces at various cooling rate obtained for PVDF/PMMA (A), PVDF/PMMA-MAA (B) and PVDF/PBMA-MMA (C) (5 wt-% PMMA-based additives).

Figure V. 3 :

 3 Figure V.3: Crystallization temperatures as detected by FDSC for PVDF α-& βphase as a function of the cooling rate for PVDF/PMMA blends (-▲-), PVDF/PMMA-MAA blends (-•-) and PVDF/PBMA-MMA blends (-♦-) (5 wt-% PMMA additives).

  6°. Similar analyses were performed for PVDF-based blends with 10 wt-% PMMA-based additives (Figure V.4B and Figure V.5B) and ATR-FTIR/WAXS experiments clearly show the opposite evolution in terms of PVDF crystallization. Herein, PMMA incorporation favors β-crystallization as observed by the increase of β-peak intensity (Figure V.4B) and the typical WAXS patterns of β-phase. However, at 10 wt-% of PMMA-MAA, the β-phase crystallization got drastically Chapter V: enhanced beta phase crystallization in melt-processed PVDF films blended with PMMAbased copolymers and impacts on subsequent ferro/piezoelectric performances 123 impeded with a predominant α-phase and a very low β-phase, in accordance with WAXS analysis (Figure V.5B). Such phenomenon could be attributed to PVDF/PMMA-MAA demixion for PMMA-MAA content higher than 5 wt-%, in agreement with previous conclusions from Landis et al. demonstrating that an elevated quantity of MAA moieties could have a negative effect on the resulting compatibility. Indeed, until MAA moieties content of 5.5 mol-% into PMMA, the melting temperature of PVDF in the blend was reduced. Beyond this content, the melting temperatures were approaching those of neat PVDF that indicates demixion. Another explanation could be related to difference of molecular weight 60 between PMMA-co-MAA (37 500 mol/g) and PMMA (97 000 mol/g) leading to potential melt viscosity effects 61 or reduced interaction strengths between PVDF/PMMA-MAA or modification of the UCST/LCST behaviors. Finally, ATR-FTIR and WAXS experiments confirmed FDSC results for PVDF/PBMA-MMA. Actually, PVDF-based blends with PBMA-MMA do not show any polar -phase with a predominant α-phase at 5 and 10 wt-% PBMA-MMA.

Figure V. 4 :

 4 Figure V.4: ATR-FTIR spectra of PVDF-based blends with PMMA, PMMA-MAA and PBMA-MMA processed into films by extrusion-calendering. (A) Neat PVDF (-■-), PVDF/PMMA 95:5 (-▲-), PVDF/PMMA-MAA 95:5 (-•-) and PVDF/PBMA-MMA 95:5 (-♦-). (B) Neat PVDF (-■-), PVDF/PMMA 90:10 (-▲-), PVDF/PMMA-MAA 90:10 (-•-) and PVDF/PBMA-MMA 90:10 (-♦-).

Figure V. 5 :

 5 Figure V.5: WAXS spectra of PVDF-based blends with PMMA, PMMA-MAA and PBMA-MMA processed into films by extrusion-calendering. (A) Neat PVDF (-■-), PVDF/PMMA 95:5 (-▲-), PVDF/PMMA-MAA 95:5 (-•-) and PVDF/PBMA-MMA 95:5 (-♦-). (B) Neat PVDF (-■-), PVDF/PMMA 90:10 (-▲-), PVDF/PMMA-MAA 90:10 (-•-) and PVDF/PBMA-MMA 90:10 (-♦-).

Figure V. 7 :

 7 Figure V.7: Impact of the maximal electric field on (P-E) loops for PVDF-based blends with PMMA and PMMA-MAA processed into films by extrusioncalendering. Neat PVDF (A), PVDF/PMMA 95:5 (B), PVDF/PMMA 90:10 (C), PVDF/PMMA 80:20 (D), PVDF/PMMA-MAA 95:5 (E) and PVDF/PMMA-MAA 90:10 (F) (triangular AC electric field, frequency 0.1Hz, room temperature, film thickness 25-35 µm).

Figure V. 8 :

 8 Figure V.8: Impact of the maximal electric field on (I-E) loops for PVDF-based blends with PMMA and PMMA-MAA processed into films by extrusioncalendering. Neat PVDF (A), PVDF/PMMA 95:5 (B), PVDF/PMMA 90:10 (C), PVDF/PMMA 80:20 (D), PVDF/PMMA-MAA 95:5 (E) and PVDF/PMMA-MAA 90:10 (F) (triangular AC electric field, frequency 0.1Hz, room temperature, film thickness 30-40 µm).

Figure V. 9 :

 9 Figure V.9: Evolution of the remanent polarization (left) and coercitive electric field (right) with the maximal electric field for PVDF-based blends with PMMA and PMMA-MAA processed into films by extrusion-calendering (triangular AC electric field, frequency 0.1 Hz, room temperature, film thickness 30-40 µm).

Figure V. 10 :

 10 Figure V.10: (A) Evolution of the piezoelectric coefficient d 33 with the amount of PMMA-based additives in as-produced PVDF/PMMA films by extrusioncasting. (B) Piezoelectric coefficient d 33 as a function of the remanent polarization for PVDF-based blends with PMMA and PMMA-MAA processed into films by extrusion-calendering calendering (poling by AC electric field 0.1 Hz -1500 kV/cm, triangular electrical fields, room temperature, film thickness 30-40 µm).

A

Figure V. 11 :

 11 Figure V.11: Impact of high-voltage poling on the ATR-FTIR spectra for PVDFbased blends with PMMA and PMMA-MAA processed into films by extrusioncalendering calendering. Neat PVDF (A), PVDF/PMMA 95:05 (B), PVDF/PMMA 90:10 (C), PVDF/PMMA 80:20 (D), PVDF/PMMA-MAA 95:05 (E) and PVDF/PMMA-MAA 90:10 (F). Poled (-▲-) and no poled (-•-) (poling by AC electric field 0.1Hz -1500 kV/cm, triangular electrical fields, room temperature, film thickness 30-40 µm).

Figure V. 12 :

 12 Figure V.12: Impact of the high-voltage poling temperature on the on (P-E) and (I-E) curves for PVDF-based blends with PMMA and PMMA-MAA processed into films by extrusion-calendering calendering. Neat PVDF (A-B), PVDF/PMMA 95:5 (C-D) and PVDF/PMMA-MAA* 95:05 (E-F). High-voltage poling temperature, room temperature (black curve), 50°C (red curve) and 75 °C (green curve) (maximal triangular AC electrical field 1200 kV/cm, frequency 0.1 Hz).* A different PMMA-MMA grade (PMMA HT121) is here used for hightemperature and high-voltage poling.

Table II . 1 :

 II1 Potential IoT applications of piezo/ferroelectric polymers as sensors or energy harvesting devices

Table II .2: Specific WAXS and FTIR values from main PVDF phases WAXS analysis (XRD): Diffraction angle (2θ) FTIR analysis: Wave number (cm -1 ) α

 II

		β	γ	α	β	γ
				408		431
	17.66° 18.30° 19.90° 26.56°	20.26°	18.5° 19.2° 20.04°	523 614 766 795 855	510 840 1279	512 776 812 833 840
				976		1234
	2.4. Routes to ferroelectric/piezoelectric PVDF
	As explained above, not all crystalline structures of PVDF are polar but
	several workers have proposed different methods to enhance the formation of β-
	phase (Figure

II.7).

  Most of the proposed techniques are based on a phase transformation mechanism in homopolymers and copolymers of PVDF

  In the last stage (Chapter V), PMMA-based copolymers were used to modify interactions between PVDF and PMMA-based copolymers. The first goal was to understand the parameters which dominate the apparition of the PVDF beta phase and related piezo/ferroelectric behavior of PVDF (viscosity, dipole coupling, interactions). Two types of copolymers were investigated, i.e. poly(methyl methacrylate-co-methacrylic acid) and poly(butyl methacrylate-co-methyl methacrylate). In order to demonstrate the capacity of these news blends to promote efficiently the polar phase, ferro/piezoelectricity of these blends were studied to observe the influence of these copolymers in comparison to previous neat PMMA. The results will be valorized as a second article called "Enhanced Beta Phase Crystallization and Ferro/Piezoelectric Performances in Melt-Processed PVDF Films Blended with PMMA-based Copolymers and impacts on subsequent ferro/piezoelectric performances".

	CHAPTER IV
	PROCESSING OF PVDF-BASED
	ELECTROACTIVE/FERROELECTRIC FILMS: IMPORTANCE
	OF PMMA AND COOLING RATE FROM THE MELT STATE ON
	THE CRYSTALLIZATION OF PVDF BETA-CRYSTALS

allows us to understand and control the way of obtaining the polar phase by extrusion-calendering of these PVDF/PMMA blends as a new approach. The modification of the blend composition and the use of advanced characterization techniques enable us to get important information on the influence of PMMA on the crystallization of the PVDF polar phase. Then, a ferroelectric analysis confirmed the ferroelectric character. Those results led to a first article entitled "Processing of PVDFbased Electroactive/Ferroelectric Films: Importance of PMMA and Cooling Rate From the Melt State on the Crystallization of PVDF Beta-Crystals" and was published in Soft Matter in May 2018. ➢

  The impact of PMMA as a -phase promoter is here clearly identified in this diagram. For experimental results by melt processes such as extrusion-calendering and thermocompression, the cooling rate needs to be estimated. For thermocompression, a cooling rate close to 1°C/s is obtained (the quenching time from 200 to 20°C is estimated to 3 min). For extrusion calendering, the quenching time is more difficult to evaluate and we estimated an approx. cooling rate of 200°C/s based on previous studies 47 , even if significant variations of the cooling rate could be obtained at low film thicknesses. In this context, experimental results by melt processes are plotted with squares, triangles and circles for pure -phase, / co-crystallization and pure -phase respectively in Figure IV.11. It could be observed that the experimental crystal observations after melt processes partially fit with Flash DSC experiments. The -phase is mainly obtained by thermocompression (low cooling rates) for PMMA content lower than 20 wt-% and by extrusion-calendering for neat PVDF. The / cocrystallization is only observed for PVDF/PMMA films by extrusion-calendering at 5 and 10 wt-%PMMA in accordance with Flash DSC experiments.

  .

	𝐴 870 𝐴𝑇𝑅-𝐹𝑇𝐼𝑅 𝐴 760 𝑋 𝑐-𝛼 = 𝐾 760/870	(1)
	𝐴 870 𝐴𝑇𝑅-𝐹𝑇𝐼𝑅 𝐴 840 𝑋 𝑐-𝛽 = 𝐾 840/870	(2)
	𝐾 840/870 𝐴𝑇𝑅-𝐹𝑇𝐼𝑅 = 1.26 𝐾 760/870 𝐴𝑇𝑅-𝐹𝑇𝐼𝑅

Table V . 2 :

 V2 Remanent polarization, coercitive electric field and ferroelectric quality factor for PVDF-based blends with PMMA and PMMA-MAA processed into films by extrusion-calendering (maximal triangular AC electric field 1500 kV/cm, frequency 0.1 Hz, room temperature, film thickness 30-40 µm).

		P R (µC/cm²)	E c (kV/cm)	P R /P max
	Neat PVDF	2.2	825	0.78
	PVDF/PMMA 95:5	4.3	790	0.88
	PVDF/PMMA 90:10	3.0	770	0.79
	PVDF/PMMA 80:20	0.1	n.m	0.22
	PVDF/PMMA-MAA 95:5	4.9	740	0.85
	PVDF/PMMA-MAA 90:10	0.6	n.m	0.63

Table V . 4 :

 V4 PVDF crystalline phase contents (-crystals, -crystals and +crystals) in poled PVDF/PMMA and PVDF/PMMA-MAA films produced by extrusion-calendering (evaluation by ATR-FTIR) (variation compared to unpoled films into brackets).

		X c--crystals (%) X c--crystals (%) X c-+-crystals
				(%)
	Neat PVDF	20 (-28)	29 (+21)	49 (-7)
	PVDF/PMMA 95:5	8 (-25)	38 (+19)	45 (-7)
	PVDF/PMMA-MAA 95:5	5 (-5)	39 (+4)	44 (-1)
	PVDF/PMMA 90:10	6 (-10)	33 (+6)	40 (-3)
	PVDF/PMMA-MAA 90:10	44 (0)	10 (+1)	53 (+1)
	PVDF/PMMA 80:20	1 (0)	31 (0)	32 (0)

Table V . 5 :

 V5 Remanent polarization and coercitive electric field as a function of the high-voltage poling temperature for PVDF-based blends with PMMA and PMMA-MAA processed into films by extrusion-calendering calendering (maximal triangular AC electrical field 1200 kV/cm, frequency 0.1 Hz) (Ferroelectric quality factor P R /P max into brackets).* A different PMMA-MMA grade (PMMA HT121) is here used for high-temperature and high-voltage poling.

		25 °C	50 °C	75 °C
		P R	E c	P R	E c	P R	E c
		(µC/cm²)	(kV/cm)	(µC/cm²)	(kV/cm)	(µC/cm²)	(kV/cm)
	Neat PVDF	1.8 (0.78)	610	3.8 (0.56)	325	8.1 (0.66)	420
	PVDF/PMMA 95:5	2.6 (0.87)	720	10.2 (0.94)	570	15.2 (0.92)	495
	PVDF/PMMA-MAA* 95:5	2.3 (0.79)	670	11.8 (0.94)	730	26.9 (0.96)	700

Chapter II: State of art -Ferroelectric and piezoelectric polymers

Chapter V: enhanced beta phase crystallization in melt-processed PVDF films blended with PMMAbased copolymers and impacts on subsequent ferro/piezoelectric performances

Remerciements

Security & Public Safety

Surveillance Radar/Satellite, Environ., Military, Security, Unmanned. Alexandre De Neef [START_REF] Harrison | [END_REF]2,[START_REF] Scott | [END_REF] , Cédric Samuel 2,3* , Harvey Amorin 4 , Gregory Stoclet 5 , Ricardo Jimenez Rioboo 4 , Philippe Dubois 1 , Jérémie Soulestin 2,3 , Jean-Marie Raquez 1

CHAPTER III

V.1. Abstract

High amounts of polar -crystals can be achieved in melt-processed poly(vinylidene fluoride)/poly(methyl methacrylate) blends (PVDF/PMMA) with promising results using 5 -10 wt-% of PMMA. Herein, the use of other PMMAbased additives into PVDF was investigated, in particular poly(methyl methacrylate-co-methacrylic acid) (PMMA-co-MAA) and poly(butyl methacrylate-co-methyl methacrylate) (PBMA-co-MMA) copolymers. Crystallization from the melt state of as-produced blends was first investigated using Flash DSC. While PBMA-co-MMA copolymers have no positive effect on PVDF -phase crystallization, PMMA-co-MAA copolymers act as PVDF phase promoter with an efficiency similar to PMMA, thanks to its good miscibility with PVDF. These effects are clearly confirmed by ATR-FTIR, WAXS and DSC on melt-processed films by extrusion-casting. A high PVDF -phase fraction (> 80 %) could be achieved with only 5 wt-% of PMMA-co-MAA. Ferro/piezoelectric properties were subsequently investigated and classical ferroelectric-type (P-E) loops clearly appear at room temperature for AC electric fields higher than 900 -1200 kV/cm. Enhanced remanent polarizations are reached with 5 wt-% of PMMA additives and, despite higher -phase content, PMMA-co-MAA only induces minor modifications of the ferroelectric performances (P R close to 4.9 µC/cm² vs. 4.3 µC/cm² with 5 wt-% PMMA). Highvoltage poling using alternative electric fields at room temperature (1500 kV/cm -0.1 Hz) generates stable piezoelectric properties with an optimum content of PMMA-based additives close to 5 wt-% are also highlighted (maximal d 33 coefficients 11 pC/N). A linear relationship is detected between piezoelectric coefficients and remanent polarizations in accordance with several available models and, in this respect, the origin/optimization of the remanent polarization was subsequently investigated. High-voltage AC poling clearly induces significant crystalline modifications and, finally, outstanding ferroelectric properties are observed at elevated poling temperatures of 75 °C. Giant remanent polarizations up to 15 -25 µC/cm² are obtained with PMMA or PMMA-co-MAA that could generate theoretically piezoelectric coefficients d 33 up to 50 pC/N. The high-voltage AC poling (strength and temperature) represents a key step to induce additional crystalline modifications and giant ferro/piezoelectric properties for future advanced ferro/piezoelectric-based devices.

(ΔH m ) were evaluated from the resulting DSC thermograms the first heating scan and the glass transition temperature at the second heating scan.

Figure V.1:

Temperature-time profiles used to investigate the crystallization of PVDF/PMMA blends during high-speed cooling by FDSC. The samples were characterized at different cooling rates between -10 °C/s and -4000 °C/s from the melt state followed by a melting step at high heating rate.

D. Ferroelectric & piezoelectric properties

All electrical characterizations were carried out on metallized films with Ag electrodes deposited by vaccum sputtering (Leica metallizer). Ferroelectrictype (P-E) loops were characterized at room temperature in a electronic liquid bath (FC40, 3M TM Fluorinert TM ) by a current integration method 56,57 . Lowfrequency (0.1 Hz) and high-voltage sine waves were applied by the combination of a synthesizer/function generator (HP3325B, Hewlett Packard Inc., Palo Alto, CA) and a high-voltage amplifier (Trek Model 10/40A, Medina, NY). Surface charges were measured with a homemade charge-to-voltage converter. Ferroelectric-type (P-E) loops are presented after compensation, i.e. after subtracting linear polarization and conduction contributions from the current response, by assuming a resistance and a capacitance in parallel. For each measurement (i.e. for maximal each electric field), several consecutive highvoltage cycles (3 to 5 cycles) were performed to ensure a stable dielectric behavior. The piezoelectric coefficient d 33 was obtained with a Berlincourt piezometer (Channel Products Inc. Chesterland, OH, mechanical stress condition of 100 Hz and 0,25 N) after ferroelectric-type (P-E) characterizations at the maximal electric field of 1.5 kV/cm (hereafter called AC poling method).

V.4. Results and discussions

The PVDF crystallization into the -phase from the melt state is an essential work for the development of cost-effective ferroelectric/piezoelectric polymer materials using industrially-relevant processing tools of the plastic industry. The use of PMMA and high cooling rates during thin films processing by extrusioncalendering were previously found of high interests for this purpose. In this work, we emphasize on how the use of PMMA-MAA and PBMA-MMA copolymers could impact the PVDF/PMMA miscibility extent, the related PVDF crystallization behavior and subsequent final properties. A preliminar study was conducted by Flash DSC on selected compositions to identify the impact of these PMMA-based additives and cooling rate on the β-phase crystallization. A transposition to extrusion-calendered films was then performed before ferrolectric/piezoelectric characterizations. A second distinct exotherm at lower crystallization temperatures (60 -40 °C) appears at higher cooling rates and becomes predominant above -800 °C/s. The α-to-β crystal transition lies in the range 100 -800 °C/s for PVDFbased blends with 5 wt-% PMMA, i.e. PVDF -phase crystallization starts at 100 °C/s followed by complete disappearance of the PVDF -phase at 800 °C/s.

PVDF-based blends with PMMA-MAA and PVDF/PBMA-MMA were subsequently subjected to Flash DSC experiments (Figure V.2B & V.2C) with the same thermal analysis procedures. PVDF/PMMA-MAA blends display similar trends to PVDF/PMMA: α-phase crystallization at low cooling rates followed by the characteristic α/β co-crystallization regime at intermediate cooling rates and disappearance of the -phase at higher cooling rates (Figure V.2B). The apparition of β-phase crystallization seems to start at the same cooling rate than PVDF/PMMA (-100 °C/s) with the disappearance of the -phase around -700 °C/s (slightly lower than PVDF/PMMA). The α-to-β crystal transition consequently occurs between -100 and -700 °C/s for the PVDF/PMMA-MAA immiscibility is observed with dramatic effects on -phase crystallization. PBMA-MMA demonstrated its immiscible with PVDF and does not have any interesting effects on the -phase crystallization. X c--crystals (%) X c--crystals (%) X c-+-crystals (%) At first sight, previous crystallinity characterizations enable to select interesting additives for subsequent ferroelectric/piezoelectric studies. Actually, the PVDF/PMMA-MAA blends show an interesting β-phase content of 35 % (total crystallinity 45 %, -phase fraction 78 %) for only 5 wt-% PMMA-MAA and thus represents an interesting candidate for ferro/piezoelectric applications. PBMA-MMA copolymers were not considered in the next section due to its inability to produce PVDF -phase crystals in melt-processed blends. To analyze ferroelectric properties of PVDF/PMMA and PVDF/PMMA-MAA thin films, a ferroelectric tester using Sawyer-Tower electrical circuit 67,68 was employed. The objective is to get quantitative information about (i) their ferroelectric performances under poling at high-voltage/high electric fields (AC electric field, triangular waveform) and (ii) correlations to PVDF crystal structures. The dipolar displacement (polarization, P) and the current (I) were measured as a function of the applied electric field (E) to get the characteristic (P-E) and (I-E) loops. (P-E) loops allow the identification/quantification of the ferroelectric behavior and (I-E) loops reveal charge displacements inside the analyzed materials. P-E) loops, the remanent polarization P R (permanent dipole orientation/polarization after voltage removal) is extracted with a hysteresis/ferroelectric quality factor (i.e. ratio remanent polarization/max polarization (P R /P max ), with P max , maximum dipole orientation/polarization under voltage). For (I-E) loops, the coercitive field E C (electric field required for dipole switching) is extracted. Figure V.9 gathers the P R and E c evolution as a function of the electric field for as-produced films. With an applied electric field of 1500 kV/cm, neat PVDF displays a ferroelectric-type dielectric behavior (Figure V.7A). Discrepancies are observed with previously-reported results in the corresponding litteratures 25,27,[69][70][71][72] , partly attributed to (i) the impact of the processing method using high cooling rates on the polar -phase crystallization and (ii) the compensation procedure to eliminate parasite charges during (P-E)/(I-E) measurements. The ferroelectric-type dielectric behavior seems to appear for an electric field threshold of 1200 kV/cm (Figure V.8A) with the presence of back-switching phenomena below this electric field 73 (dipole rotation without full switch/fixation). Good ferroelectric parameters are obtained at elevated electric confirmed with PVDF/PMMA blends incorporating high PMMA contents up to 20 wt-%. These effects could be ascribed to stable trapped charges introduced during poling into as-produced PVDF/PMMA.

In conclusion, interesting piezoelectric properties are observed for PVDFbased blends with PMMA and PMMA-MAA processed into films by an extrusion-calendering technique. The impact of PMMA on the piezoelectric properties is obvious with a maximal coefficient close to 11 pC/N for an optimum content of 5 wt-%. An interesting correlation with a linear relationship is obtained between piezolectric and ferroelectric properties in PVDF/PMMA and PVDF-MAA blends that points out the main importance of ferroelectric properties for further optimization.

CHAPTER VI GENERAL CONCLUSION AND PERSPECTIVES

lower cooling rates associated to thermocompression (-1 °C/s). In addition, PMMA has been confirmed as a (partial)-miscible partner for PVDF and as a promoter of the crystalline β-phase. Analytical techniques such as FTIR and DRX allow to clearly identify PVDF crystalline phase variations according to the cooling rate and the amount of PMMA content incorporated into PVDF. Indeed, Flash DSC has clearly identified the different crystalline phases depending on the cooling rate applied during processing. By the combination of all above results, it is possible to obtain a crystal phase diagram of the two main PVDF crystalline phases (non-polar α phase and polar β phase) as a function of the amount of PMMA and the cooling rate. These results make it possible to highlight a peculiar composition with only 5 wt-% PMMA which only needs a quenching step of -100 °C/s unlike pure PVDF requires a cooling rate of -400 °C/s for generating its polar β-crystals. In addition, a preliminary study of PVDF/PMMA ferroelectric properties by hysteresis (P-E) curves reveal an interesting potential of the blend with 5 wt-% PMMA by the appearance of a remanent polarization close to 5.2 μC/cm² (field of polarization 2000 kV/cm).

However, several studies found in relevant literature have already demonstrated that the presence of PMMA within the PVDF matrix results in a significant reduction of subsequent piezoelectric properties of PVDF/PMMA blends. Few researches have been made to understand in detail the underlying phenomena. In this context, the second part of our study has been focused on PVDF-based blends with two commercially available PMMA copolymers that could modify -phase crystallization of PVDF. Poly(methyl methacrylate-comethacylic acid) (PMMA-co-MAA) was used with improved hydrogen interactions (ionizable group) and poly (butyl methacrylate-co-methyl methacrylate) (PBMA-co-MMA) was chosen for its ability to modify thermal properties and ductility of PMMA. The study of the miscibility and crystallinity of these copolymers in the presence of PVDF reveals that the PBMA-co-MMA is not miscible and does not influence the crystallization of PVDF in any way. On the other hand, the presence of methacrylic acid in PMMA additives promotes the polar β-phase of PVDF with an intensity greater than PMMA. PVDF/PMMA thin films with a high amount of β-phase are thus obtained by extrusion-calendering based on the use of PMMA-co-MAA blended with PVDF. Extensive characterization of crystalline phase quantities in PVDF/PMMA blends was also performed, confirming the superior influence in the presence of MAA on the crystallization of the β-phase. The ferroelectric properties were then evaluated under an alternative electric field (AC poling) of variable intensities (700 -1500