Résumé en français

Les ionomères sont des polymères contenant une faible teneur en ions, de 0 à quelques pourcents, qui montrent un comportement associatif des ions dans la matrice polymère à laquelle ils sont ajoutés. La création de cette phase ionique discontinue va contrôler les propriétés macroscopiques du polymère. Ces dernières années, ces matériaux sont étudiés pour leurs potentielles propriétés de mémoire de forme ou d'autoréparation. Lorsque les ions présentent un comportement dissociatif (plutôt que associatif), les polymères sont des polyélectrolytes. La teneur en ion est généralement plus élevée. Ces matériaux ont des applications notamment pour les alternatives aux batteries électrolytes. Ces technologies peuvent permettre d'améliorer les propriétés mécaniques des polymères, plus particulièrement, de contrôler le compromis entre la température de transition vitreuse, les propriétés rhéologiques et les propriétés mécaniques. De plus, les interactions ioniques peuvent potentiellement retarder l'endommagement. Le contrôle de l'évolution de l'endommagement des polymères est un point clé pour contrôler leur comportement face à la déformation. Solvay a développé ces dernières années des synthèses de groupes supramoléculaires qui peuvent être greffés en tant que groupes pendants sur du poly (méthyle méthacrylate) (PMMA). Le PMMA est un thermoplastique amorphe de température de transition vitreuse autour de 110 °C. Il est souvent utilisé pour sa grande transparence. Sa principale limitation est sa fragilité. On propose ici de modifier le PMMA soit par voie de synthèse soit par formulation afin d'améliorer ses propriétés plastiques grâce à la présence d'interactions ioniques. Les ions ont souvent pour effet d'augmenter la viscosité de la matrice polymère, un compromis entre la processabilité et les propriétés est alors nécessaire.

Dans une première partie, des fonctions ioniques de sodium styrène sulfonates et de carboxylates de métaux alcalins (lithium, sodium et potassium) sont incorporées aux chaînes PMMA à hauteur de quelques pourcents molaires. L'influence des interactions ioniques sur le PMMA est d'abord observée sur la température de transition vitreuse. Puis la signature spécifique des greffons ioniques est étudiée en rhéologie. Un allongement important du plateau caoutchoutique est observé. Le temps de vie des interactions ioniques est plus long que les temps de relaxation de la chaîne. Une méthode de détermination de l'énergie d'activation des groupements ioniques est proposée. L'influence de la structure ionique (sulfonate ou carboxylate), de la nature du cation (lithium, sodium ou potassium), de la concentration ionique (jusqu'à 10 % mol) et de la masse moléculaire du polymère est étudiée.

Dans une seconde partie, des sels ioniques de structures similaires aux fonctions étudiées (avec des sulfonates et des carboxylates) et des sels de triflate sont mélangés au PMMA. Différents cations sont considérés : lithium, sodium et potassium. La teneur en ions varie de 0 à 10 % mol. La température de transition vitreuse des PMMA ioniques augmente.

Les propriétés rhéologiques sont étudiées. Les propriétés mécaniques jusqu'à rupture de ces systèmes sont mesurées par des tests en traction à différentes températures. La transition ductile -fragile et la plasticité sont modifiées dans une certaine plage de températures et de concentration ioniques. Des interactions entre les cations et les carbonyles du PMMA sont mises en évidence par spectroscopie infrarouge. Les sels de lithium créent des interactions plus fortes avec le PMMA que les sels de sodium. Une interprétation est proposée sur les liens reliant la microstructure ionique et les propriétés macroscopiques.

Abstract in English

Ionomers are polymers containing ionic groups from zero to a few percent, which exhibit ionic associative behavior. The creation of a discontinuous ionic phase control the macroscopic properties of the polymer. Recently, these materials have been studied for their potential shape memory or self-healing properties. When the ions exhibit dissociative (rather than associative) behavior, the polymers are called polyelectrolytes. The ion content is generally higher. These materials have applications particularly for alternatives to electrolyte batteries. These technologies may improve the mechanical properties of polymers, in particular, they allow to control the compromise between the glass transition temperature, the viscoelastic properties and the mechanical properties. In addition, ionic interactions can potentially delay the apparition of damages, and controlling the evolution of damages in polymers is a key point to control their behavior upon deformation.

In the last few years, Solvay has developed syntheses of supramolecular groups that can be added as pendant groups into poly (methyl methacrylate) (PMMA). PMMA is an amorphous thermoplastic with a glass transition temperature around 110 °C. It is often used for its high transparency. Its main downside is its fragility. Based on this observation, the aim was to modify PMMA, either by synthesis or by formulation, in order to improve its plastic properties thanks to strong ionic interactions. An important point in the development of ionomers is the control of the compromise between the process and the final properties. Indeed, ionic groups introduced in polymers often increase the viscosity of the polymer matrix and change the viscoelastic behavior.

In the first part of this PhD, ionic moieties of sodium styrene sulfonates and alkali metal carboxylates (lithium, sodium and potassium) are incorporated into the PMMA chains at a few molar percent. The influence of the ionic interactions on PMMA is first observed on the glass transition temperature. Then the specific signature of the ionic moieties is studied by melt rheology. An extension of the rubbery plateau is observed. The lifetime of the ionic interactions is longer than the relaxation times of the main chain. A method for determining the activation energy of ionic groups is proposed. The influence of the ionic structure (sulfonate or carboxylate), the nature of the cation (lithium, sodium or potassium), the ionic concentration (up to 10 % mol) and the molecular weight of the polymer are studied (Mw = 35 -235 kg/mol).

In a second part of this study, ionic salts of similar structures to the studied moieties (sulfonates and carboxylates) and triflate salts are mixed with PMMA. Different cations are considered: lithium, sodium and potassium and the ion content varies from 0 to 10 % mol. First, the miscibility of the various ionic salts is investigated. A focus is then made on the miscible salts, which are especially triflate salts. The glass transition temperature of PMMA blended with triflate salts increases. Rheological properties are studied. The mechanical properties up to failure of these systems are measured by tensile tests at different temperatures. The brittle to ductile transition and the plasticity are increased in a specific temperature range. Interactions between cations and carbonyls of PMMA are revealed by infrared spectroscopy. The lithium cations create stronger interactions with PMMA than sodium cation. An interpretation is proposed to explain the relation between the ionic microstructure and the macroscopic properties. Context of the study Supramolecular materials have been the subject of intense research these last decades.

The introduction of strong interactions in polymer backbones, such as hydrogen bonds, ionic interactions or metal complexations considerably modify polymers properties. Among supramolecular systems, ionomers are polymers containing a small fraction of ionic groups (usually up to 10 %) which exhibit associative behavior. Ionic moieties create a reversible secondary network. The addition of ionic moieties in non-polar polymers of low or high glass transition temperatures has been widely studied [START_REF] Chen | Ionomer dynamics and the sticky Rouse model[END_REF]- [START_REF] Zhang | Dynamics of associative polymers[END_REF]. Ionic groups have a strong impact on the polymers melt rheology: the viscosity is often increased and processes can only be performed at higher temperatures. The addition of ionic interactions may allow the properties to be tuned and better compromise between processing and mechanical properties to be achieved.

Recently, Solvay developed supramolecular species that could be introduced on polymer backbone chains. Ionic moieties such as sodium styrene sulfonates are expected to show an associative behavior and to improve the final properties of amorphous polymers such as PS or PMMA. Recent studies regarding the deformation and damage mechanisms in amorphous polymers allowed to think that ionic groups have potential for improving the mechanical properties of polymers [START_REF] Mourglia-Seignobos | Physical Mechanisms of Fatigue in Neat Polyamide 6,6[END_REF]- [START_REF] Djukic | Study of Damage Mechanisms of Amorphous and Low Semicrystalline Polymers under Tensile Deformation by Ultrasmall-Angle X-ray Scattering[END_REF]. Under large deformation, polymers undergo damages, by shear bands or crazes. The response of polymers at large strain and more specifically the strain hardening behavior is a key feature for controlling the growth of damages and thus the ultimate properties of polymers.

In this study, the influences of ionic moieties on the PMMA properties are studied.

PMMA is an amorphous thermoplastic with a glass transition temperature close to 110 °C. Its main limitation for application is its brittleness. The aim is to study the effects of the addition of ionic groups, in particular to increase the toughness. The effect of strong intermolecular interactions in PMMA remains poorly understood. Most of studied ionomers are non-polar with a poor capacity to solvate ionic species. They have low glass transition temperature and are unentangled in order to isolate the effect of ionic salts in melt rheology [START_REF] Martins | Effect of intermolecular interactions on the viscoelastic behavior of unentangled polyamide melts[END_REF]- [START_REF] Zhang | Dynamics of associative polymers[END_REF], [START_REF] Zhang | Dynamics of associative polymers[END_REF], [START_REF] Weiss | Rheological behavior of oligomeric ionomers[END_REF]- [START_REF] Leibler | Dynamics of reversible networks[END_REF].

PMMA have an intermediate polarizability, a relatively high glass transition temperature and in this study, PMMA are entangled.

Sodium styrene sulfonates and alkali metal carboxylates of lithium, sodium and potassium are added in PMMA chains. In parallel, ionic salts are blended with PMMA. The influence of ionic interactions are observed first on the glass transition temperature. Then, the viscoelastic properties are studied. The mechanical properties are investigated at various temperature in traction or compression. The parameters of the study are the ionic salt structure, the nature of the cation, the ion content and the molecular weight. The method of introduction of ionic salts (synthesis or formulation) are compared. Ionic interactions strength are studied.

Hypothesis on the relation between the ionic microstructure and the macroscopic properties are made.

Structure of the manuscript

The first chapter of this manuscript is a bibliography report on the physic and chemistry of polymers. Especially, rheological and mechanical behaviors of amorphous and entangled polymers are described. Then, a literature review reports the influence of strong ionic interactions on polymer behaviors. In the second chapter, the materials developed in this study are detailed, with experimental methods of processing and characterizations.

In the third chapter, the properties of PMMA containing ionic moieties on the main backbone are studied. Sulfonate and carboxylate moieties are used, their effect on PMMA are compared. In the fourth chapter, the properties of PMMA containing various ionic salts blended in the matrix are described. The last chapter is about the mechanical properties of PMMA / ionic triflate salts blends. The ionic microstructure is discussed. To conclude this study, a comparison of the strength of ionic interactions in PMMA is made.

Chapter I -State of art

In this first chapter, general properties of PMMA, the polymer at the center of this study are presented. Its molecular dynamics are reminded. Important knowledge to understand the melt rheology and the mechanical properties of polymers are described. Notions focus on amorphous and entangled polymers. In the last part, ionomers are defined. A literature review is made on the main characteristic of ion-containing polymers.

I.1 Poly (methyl methacrylate)

I.1.1 Generalities

PMMA is a widely used thermoplastic. With a lower resistance than glass but an higher lightness and optical transmission (92 %), PMMA is mostly used in substitution of inorganic glasses. Indeed, more economical than polycarbonate, which is also transparent, it is preferred when applications do not require extreme strength. PMMA exhibits a glassy surface. It is resistant to UV radiation (300 nm) and corrosion. Main limitations of PMMA are its brittleness, as well as its low scratch and low temperatures resistance. PMMA presents a low chemical resistance as it is soluble in many solvents such as acetone, butanone, toluene, chloroform or tetrahydrofuran. The adjacent methyl group (Figure 1) prevents packing into crystalline structure by blocking the free rotation of the main chain, which makes PMMA an amorphous polymer [START_REF] Ali | A Review of the Properties and Applications of Poly (Methyl Methacrylate) (PMMA)[END_REF]. PMMA is relatively sensitive to moisture as its polar groups create hydrogen bonding with water. Its can uptake 0.1 % to 0.4 % of water (at equilibrium after 24 h at 50 % of relate humidity) [START_REF] Ali | A Review of the Properties and Applications of Poly (Methyl Methacrylate) (PMMA)[END_REF], [START_REF] Mark | Polymer Data Handbook[END_REF].

PMMA properties allow for many applications such as in advertising (neon signs), household appliances (shower cabins, glass roofs, flat screen televisions, lighting, aquariums, acrylic paints, adhesives and coating), medical fields (optical lenses, health care equipment, dental prosthesis, ophthalmic implants), high technology (fiber optics, security parts, electronics sector), automobiles (headlights, roofs, windows) and aircraft (windows).

I.1.2 Synthesis and tacticity

PMMA is a vinyl polymer, mainly obtained by free radical polymerization from the monomer methyl methacrylate (MMA) (Figure 1). Anionic polymerization is also possible.

Figure 1 : General scheme of the polymerisation of PMMA from MMA

The conditions of polymerization determine the final tacticity. Polymer tacticity refers to the relative stereochemistry of the pendant group. Various tacticities of PMMA are displayed in Figure 2. According to the synthesis conditions (solvent, initiator…), PMMA conformations can vary from very isotactic to a very syndiotactic. The tacticity can be easily determined by 1 H NMR [START_REF] Brar | Structural investigations of poly(methyl methacrylate) by twodimensional NMR[END_REF] [START_REF] Shen | Role of Local Polymer Conformations on the Diverging Glass Transition Temperatures and Dynamic Fragilities of Isotactic-, Syndiotactic-, and Atactic-Poly(methyl methacrylate)s[END_REF].

The glass transition temperature (Tg) of PMMA depends strongly on tacticity [START_REF] Mark | Polymer Data Handbook[END_REF], [START_REF] Shen | Role of Local Polymer Conformations on the Diverging Glass Transition Temperatures and Dynamic Fragilities of Isotactic-, Syndiotactic-, and Atactic-Poly(methyl methacrylate)s[END_REF]- [START_REF] Bywater | Effect of stereostructure on glass transition temperatures of poly(methyl methacrylate)[END_REF]. Commercial grade materials generally have less than of 10 % isotactic dyads, around 30 % of atactic dyads and 50 % to 70 % of syndiotactic dyads, which gives a typical Tg in the order of 110 °C. However, Tg can vary from around 40 °C to 140 °C, for very isotactic (99 %) to very syndiotactic (99 %) PMMA respectively (Figure 2). Tacticity influences also the solubility, crystallinity, and hydrolysis of polymers. Thermal decomposition of PMMA is well described in the literature. The polymerization method determines the degradation profile, as it is represented in Figure 4. While anionic polymerization leads to one step of degradation, radical polymerization leads to 3 to 4 steps.

Defects in the free radical recombinations lead to head-to-head structures, unsaturated chain ends and other random flaws, as shown in Figure 5 and Figure 6. Note that head-to-head or head-to-tail configurations are not part of polymer tacticity but should be taken into account when considering polymer defects. Head-to-head structures are present in small proportion in PMMA (a few percent), according to the syntheses conditions.

First Kashiwagi et al. [START_REF] Kashiwagi | Effects of weak linkages on the thermal and oxidative degradation of poly(methyl methacrylates)[END_REF] interpreted the 3 steps of degradation as follows : the first step of decomposition occurs around 165 °C and corresponds to the scission of head-to-head bonds by facile homolytic scission of the chain. Steric hindrance and inductive effect of vicinal ester groups make bond dissociation energy lower than for head-to-tail bonds. The second step is observed around 270 °C and corresponds to the β scission of vinyl-unsaturated chain ends. This step leads to depolymerization of the chain (unzipping) and to the formation of the monomer MMA. The third degradation step occurs around 360 °C and corresponds to random scission of the main chain.

More recently, Manring carried out more detailed studies of each steps involved in the decomposition of PMMA and proposed somewhat different explanations. In his view, weak head-to-head bonds promote facile homolytic scission of the chain around 270 -300 °C rather that 165 °C (Figure 7a) [START_REF] Manring | Thermal degradation of poly(methyl methacrylate). 3. Polymer with head-to-head linkages[END_REF]. Secondly, the unsaturated end groups are responsible of two stages of weight loss around 180 and 270 °C (Figure 7b) [START_REF] Manring | Thermal degradation of poly(methyl methacrylate). 2. Vinyl-terminated polymer[END_REF]. This process overlaps the process of scission of head-to-head structures. Further studies show that homolytic scission of acrylate side chain groups occurs also around 350 °C (Figure 7c), overlapping also the main chain scission process [START_REF] Manring | Thermal degradation of poly(methyl methacrylate). 4. Random side-group scission[END_REF]. Stereocomplex formation in PMMA have been comprehensively studied over the past 50 years [START_REF] Feitsma | Association of stereoregular poly(methyl methacrylates): 2. Formation of stereocomplex in bulk[END_REF]- [START_REF] Schomaker | Complexation of stereoregular poly(methyl methacrylates). 11. A mechanistic model for stereocomplexation in the bulk[END_REF]. Chains of complementary tacticity twist around each other. According to Yashima [START_REF] Kumaki | Supramolecular Helical Structure of the Stereocomplex Composed of Complementary Isotactic and Syndiotactic Poly(methyl methacrylate)s as Revealed by Atomic Force Microscopy[END_REF], [START_REF] Christofferson | Molecular mapping of poly(methyl methacrylate) super-helix stereocomplexes[END_REF], a triple-stranded helix is formed, as seen in Figure 9. The isotactic chains form a double helix surrounded by a single syndiotactic chain.

Figure 9 : Helical conformation in 1:2 mixture of isotactic (it) and syndiotactic (st) PMMA with a triple-stranded helix, from [START_REF] Fitzgerald | Synthesis, Properties, and Structure of Sulfonate Ionomers[END_REF] Stereocomplexation occurs in bulk as well as in dilute solutions, between highly isotactic and syndiotactic chains, or even in atactic PMMA. According to the conditions (concentration, temperature, molecular weight, tacticity…), very compact particles of stereocomplexes are formed with sizes comprised between 5 and 30 nm [START_REF] Schomaker | Complexation of stereoregular poly(methyl methacrylates). 11. A mechanistic model for stereocomplexation in the bulk[END_REF]. In dilute solution, three categories of solvents are distinguished: very complexing (acetone, tetrahydrofuran), weakly complexing (benzene) or non complexing (chloroform) [START_REF] Kusuyama | Structural change of st-PMMA on drawing, absorption and desorption of solvents[END_REF]. The presence of this structure has been detected by DSC, with a melting peak around 170 -180 °C [START_REF] De Boer | Association of stereoregular poly(methyl methacrylates): 3. Thermal behaviour and composition of stereocomplex[END_REF]. Boer and Challa show that the complex can be removed by applying a high temperature in DSC, with an isotherm above 200 °C for a few minutes. In the present study, drying treatments at high temperature are carried out to remove possible stereocomplexes.

I.2 Polymer dynamics

I.2.1 Solid, liquid, and viscoelastic materials

Rheology is a field of science that deals with the flow and the deformation of matter (defined by Eugene C. Bingham in 1920). It describes relations between force, deformation and time. When a small strain is applied to a material, the response is linear and directly related to the initial state of the material. At larger strain, the chain conformations are modified by the applied deformation which modifies the response itself. In the linear region, small deformation are considered in dynamics or transient regime (SAOS). In the nonlinear region, large deformation are considered in permanent or transient regime (LAOS), as schematized on Figure 10.

Figure 10 : General scheme of a strain sweep test at a fixed frequency and temperature. Two region are shown : small amplitude oscillatory shear (SAOS) and large amplitude oscillatory shear (LAOS), from [40] Small amplitude dynamic oscillatory test

The most common experimental method to measure the viscoelastic properties of a polymer material is to apply oscillations of small amplitude, according to the Equation ( 1),

where γ is the shear strain, γ0 the strain amplitude, ω the angular frequency (rad.s -1 ) and t the time (s). It results in a stress with a phase shift δ in relation to the applied deformation according to the Equation (2) (Figure 11), where σ0 is the stress amplitude.

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Materials display different behaviors: purely elastic, purely viscous or viscoelastic. For a purely elastic materials δ = 0, for a newtonian liquid δ = and for viscoelastic behavior δ is in the range of 0 to . For a perfectly elastic solid and at small strain, the stress is proportional the applied strain. It is described by the Hooke's law, described in Equation (3) (4), as long as the elastic limit is not exceeded. G is the shear modulus. The model is represented in Figure 12 by a spring without any time dependence (instantaneous response).

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Viscous behavior

Similarly, for an ideal Newtonian liquid, the stress is given by an instantaneous relation between the strain rate and the stress by the Newton's law, described in Equation (4), where η is the viscosity and is the shear rate. The model is represented in Figure 12 by a dashpot moving through a viscous Newtonian fluid. The energy is implicitly dissipated as heat in the fluid.

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Viscoelastic behavior

Most of materials exhibit simultaneously elastic and viscous behaviors. They are called viscoelastic materials. Many models have been developed to characterize the viscoelastic response of materials. The most commonly admitted is the Maxwell's model. The viscoelastic response is represented by both springs and dashpots connected in series or in parallel. They store elastic energy and dissipate another part. The complex shear modulus G * (representing the stiffness and the resistance to the deformation of the material), is thus composed of two terms, one is in phase with the deformation and one in quadrature with it. G' is the storage modulus, corresponding to the elastic part of the response, and G" is the loss modulus, corresponding to the viscous part of the response. Their expressions are given in Equations ( 5), ( 6) and ( 7).

(5) (6) [START_REF] Hussein | Method for increasing fatigue resistance of polyamides[END_REF] Figure 12 : General scheme of the Hooke model for an ideal elastic solid, Newtonian model for an ideal liquid and Maxwell model for the viscoelastic material.

The ratio of G" and G' (Equation (8)) , tan δ, is called the damping factor. It is small for an elastic solid and very large for a viscous liquid. Its increase allows to determine the transition from a solid to a liquid state.

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I.2.2 Polymer dynamics in the molten state

When a deformation is applied to a polymer melts, the macroscopic deformation is the result of all the microscopic deformations that take place in the chain conformations of the material.

Chains mobility depends on various parameters such as temperature, molecular weight, entanglements, Kuhn length of the chains. A polymer chain is frequently represented by springs and beads, undergoing Brownian motion. Models have been developed to understand the evolution of the dynamic moduli in the molten state, such as the Rouse model for unentangled polymers and the reptation model for entangled polymers [START_REF] Ferry | Viscoelastic properties of polymers, 3rd Edition[END_REF], [START_REF] Doi | The Theory of Polymer Dynamics[END_REF].

I.2.2.1 Time -temperature superposition and the WLF equation

The relaxation times depend on the ability of the material to reorganize. Relaxations in the glassy state are very slow whereas in liquids relaxations may be very fast. It is not possible experimentally to access directly to the entire spectrum of relaxations times. Inertia limits the upper frequency range above 100 Hz. On the lower frequency part, experimental tests are too long below 0.01 Hz. As a consequence, the entire relaxation spectrum of polymer is obtained by making experiments at different temperatures, typically between Tg + 5 and Tg + 100°C.

The high frequency part of the spectrum is obtained by cooling the temperature, and the low frequency part is obtained by heating the temperature. The overlap between the results obtained at close temperatures allow for obtaining the so-called time-temperature superposition (TTS)

and to determine the so-called William-Landel-Ferry law (WLF).

As a consequence, a time-temperature superposition curve is obtained by measuring the relaxation of a polymer at various temperatures and applying the WLF law, with appropriate vertical (amplitude) and horizontal (time scales) shifts. The shift in time scale is given by the horizontal shift aT (Equation [START_REF] Djukic | Study of Damage Mechanisms of Amorphous and Low Semicrystalline Polymers under Tensile Deformation by Ultrasmall-Angle X-ray Scattering[END_REF]. The vertical shift bT accounts for the variation in density with temperatures (Equation ( 10)). bT is often close to 1 for each temperature. To calculate this shift, the temperature dependence of the density with temperature must to be known ρ(T). All the viscoelastic quantities of the molten state depends on to the temperature T. The factor Tref/T is used to account for this variation. The TTS principle is illustrated on Figure 13,

where C1 and C2 are WLF constants, Tref is an arbitrary chosen reference temperature, usually taken as an intermediate temperature between the glassy state and the molten state.

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Figure 13 : Time -temperature superposition (TTS) principle, using oscillatory shear rate data of polyisobutylene sample. The plot on the left shows the experimental data acquired at different temperatures, the plot on the right shows the master curve generated thanks to the application of the horizontal shift aT, from [START_REF] Rubinstein | Polymer Physics[END_REF]

I.2.2.2 Typical master curve

Once the TTS is obtained, a master curve representative of the polymer dynamics can be built. Following the evolution of the modulus over a wide range of frequency of solicitations, different domains are observable, as seen on Figure 14. These domains are described below, from right to left.

I -Glassy state

At high frequency, the polymer is in the glassy state, with a solid like behavior and a modulus typically of a few 10 9 Pa. Elastic components prevail on the viscous one. Movements are over very short distances and are limited to the vibration or the rotation of a few monomers.

The first modulus cross over, associated with the transition from the glassy state to the transition region correspond to the Kuhn monomer relaxation time τ0.

II -Transition zone

In the transition zone, the elastic modulus decreases typically from a few 10 9 to about 10 6 Pa. The second cross modulus correspond to the Rouse relaxation time between entanglements τe.

III -Rubbery plateau

The third region is given by the rubbery plateau. Modulus are in the range of 10 6 Pa.

This clear plateau appears over a certain range of frequency and is directly related to the reptation. Me is defined as the average molecular weight between topological constraints, that are entanglements. When the molecular weight of the polymers is larger to the molecular weight between entanglements M > Me, the Reptation model describes the relaxation of polymer chains [START_REF] Rubinstein | Polymer Physics[END_REF], [START_REF] De Gennes | Reptation of a Polymer Chain in the Presence of Fixed Obstacles[END_REF]. Focusing on a given polymer chain, it is surrounded by other chains, hindered

IV -Terminal zone

At low frequency, polymer chains are flowing. The considered time scales are longer than the reptation time τrep so polymer chains can fully relax, escaping from constraints created by surrounding chains. The viscous component G" prevails over the elastic component G'. In the reptation model [START_REF] Rubinstein | Polymer Physics[END_REF], [START_REF] De Gennes | Reptation of a Polymer Chain in the Presence of Fixed Obstacles[END_REF], the melt flow is reached when G' and G'' have the slopes of 2 and 1.

It is possible to determine a characteristic relaxation time with respect to another thanks to the following relations (42, (11) where τrep is the reptation time, τe is the Rouse time between entanglements, τ0 is the monomeric time, N is the monomer number per chain, and Ne the monomer number per entanglement.

In the case where the molecular weight of the polymer is below the molecular weight between entanglements (M < Me), no plateau exists. The behavior is described by the Rouse model from the low frequency regime up to the glass transition at high frequencies.

I.2.2.3 Main rheological parameters

Viscosity

The complex viscosity η*, also called the dynamic viscosity, traduce the total resistance to flow as a function of angular frequency. It contains an elastic and a viscous part, η' and η'' respectively, which are related to the elastic and viscous modulus G' and G" (Equations [START_REF] Weiss | Block copolymer ionomers: 2. Viscoelastic and mechanical properties of sulphonated poly(styrene-ethylene/butylene-styrene)[END_REF] (13)( 14)). The zero shear viscosity η0, or Newtonian viscosity is defined as the dynamic viscosity η' when ω tend to 0 (Equation ( 15)). In general the dynamic viscosity tend to a plateau at low ω, called Newtonian plateau, related to the fact that each molecule have been able to completely relax.

Plateau modulus

The plateau modulus GN 0 can be experimentally measured in two ways, either at the minimum of tan δ, or by using the so-called Van Gurp Palmen (VGP) plot. The VGP plot displays the phase angle δ as a function of the complex modulus G * (δ = f(G*)=f( ) [START_REF] Trinkle | Van Gurp-Palmen-plot: a way to characterize polydispersity of linear polymers[END_REF]. GN 0 is taken at the minimum of the curve as it could be seen on Figure 17. , from [START_REF] Trinkle | Van Gurp-Palmen-plot: a way to characterize polydispersity of linear polymers[END_REF] Molecular weight between entanglements

From the plateau modulus value, it is possible to deduce the molecular weight between entanglements Me with the Equation ( 16).

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Apparent molecular weight

The length of the rubbery plateau is delimited by the Rouse time between entanglement τe and the reptation time τrep .This length depends on M and Me, as given by the Equation [START_REF] Brar | Structural investigations of poly(methyl methacrylate) by twodimensional NMR[END_REF] obtained using the M. Doi and S. Edwards model. The exponent can vary between 3 and 3.4 if polymers follow a strict Reptation behavior. From this equation, it is possible to get the apparent molecular weight of the polymer M.

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Polydispersity

The rheological models are applicable for monodisperse polymers, but the molecular weight distribution influence the general shape of master curves. Polymers synthesis are rarely perfectly monodisperse and generally show polydispersity of about 2. The slope of G' increase at low frequency as polydisperse polymers have a broader relaxation time distribution. As a consequence, the last cross modulus, corresponding to the reptation time is delayed to lower frequency [START_REF] Liu | Evaluation of different methods for the determination of the plateau modulus and the entanglement molecular weight[END_REF]. The rubbery plateau has the same value but often less clear, since when approaching lower frequencies, smaller chains have already relaxed [START_REF]Polymer rheology: Influence of molecular weight and polydispersity -Cross -1969[END_REF].

I.2.3 Polymer dynamics in the solid state

I.2.3.1 Mechanical properties of amorphous polymers

Amorphous polymers such as PS, PC, PVC, or PMMA present a similar behavior under strain at low deformations, while at larger deformations, their behavior differ according to their ductility. Indeed, polymers can be ductile and break after a large deformation or brittle and break at small deformation. In the glassy state, when a polymer is submitted to a mechanical stress in traction or in compression, it exhibits a typical behavior described on the stress (σ)strain (ε) curve. This curve can be divided into 4 parts, as described in Figure 18. The presence of these 4 domains is observed as long as the material is ductile. If the material is brittle, only the first domain exists. The first region is called the elastic zone. At small deformations ε, the polymer exhibits an elastic behavior where the strain is proportional to the stress σ. The slope of this curve is called the Young's modulus (E) or elastic modulus and is defined by the Hooke's law in Equation ( 18).

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In the elastic zone, the deformation is instantaneous and reversible, without any dissipation of energy. As soon as the proportionality between strain and stress is broken, the deformation become anelastic upon approaching the yield stress.

II -Plasticity

After the end of the elastic zone, the stress goes up to a maximum, called plasticity threshold (or yield point) σy. Intra and intermolecular forces are overcome and segmental motion is initiated. Local monomer reorganizations are allowed thanks to the α-relaxation which is made possible as a consequence of the applied stress [START_REF] Monnerie | Deformation, Yield and Fracture of Amorphous Polymers: Relation to theSecondary Transitions[END_REF], [START_REF] Long | Dynamics in glassy polymers: The Eyring model revisited[END_REF]. The stress may decrease after the yield point until a point noted σp. This phenomena is the strain softening.

Strain softening is not always present on glassy polymers and depends on the history and aging of the samples. Strain softening may lead to localization of deformations and to crack propagation or the appearance of shear bands. It makes the materials intrinsically more brittle [START_REF] Meijer | Mechanical performance of polymer systems: The relation between structure and properties[END_REF], [START_REF] Djukic | Damage mechanisms under tensile stress of amorphous and low semi-crystalline polymers[END_REF]. The yield stress increases with decreasing temperature or increasing strain rate [START_REF] Lauprêtre | Polymer materials : macroscopic properties and molecular interpretations[END_REF],

as illustrates in Figure 19 on PMMA.

Figure 19 : Uniaxial compression stress-strain curves of PMMA sample. Left : at several temperatures and at a strain rate of 2.10 -3 s -1 , and right : at various strain rates at 50 °C, from [START_REF] Lauprêtre | Polymer materials : macroscopic properties and molecular interpretations[END_REF] III -Plastic flow In the third zone, called the plastic flow regime, the stress remains constant (flow stress).

This regime depends on the temperature, the strain rate and the structure of the polymer [START_REF] Djukic | Damage mechanisms under tensile stress of amorphous and low semi-crystalline polymers[END_REF].

The higher the strain rate, the higher the yield stress and the flow stress [START_REF] Monnerie | Deformation, Yield and Fracture of Amorphous Polymers: Relation to theSecondary Transitions[END_REF]. For some polymers, the stress softening regime is followed by the strain hardening regime during which the stress increases upon further deformation.

IV -Strain hardening

At larger deformations, the stress increases. Strain hardening is observed in highly entangled polymers such as PC, PMMA or PVC (Me = 3490 kg/mol, 9150 kg/mol, and 5410 kg/mol respectively [START_REF] Mark | Polymer Data Handbook[END_REF]). The slope of the stress-strain curves at large deformations is called the strain hardening modulus ESH and is in the order of 10 7 -10 8 Pa well below the glass transition.

The origin of strain hardening remains under debate [START_REF] Senden | Strain hardening and anisotropy in solid polymers[END_REF]- [START_REF] Wendlandt | Non-linear, rate-dependent strain-hardening behavior of polymer glasses[END_REF]. First, Haward attributed in 1993 the strain hardening origin to the entropic elasticity of entangled or cross-linked rubbery network [START_REF] Haward | Strain hardening of thermoplastics[END_REF]. This theory was supported by many studies where strain hardening modulus increase with entanglement or cross-linking densities [START_REF] Arruda | Evolution of plastic anisotropy in amorphous polymers during finite straining[END_REF], [START_REF] Arruda | Effects of initial anisotropy on the finite strain deformation behavior of glassy polymers[END_REF], [START_REF] Wendlandt | Strain-hardening modulus of cross-linked glassy poly(methyl methacrylate)[END_REF]. But while this entropic model fit with general stress-strain curves, it's also failed for many experimental results. Meijer et al. showed in 2003 that the strain hardening modulus increases linearly with temperature and this fact goes against an entropic model [START_REF] Van Melick | On the origin of strain hardening in glassy polymers[END_REF]. Furthermore, entropic model doesn't explain the magnitude of experimentally measured ESH, which was around 100 times higher than expected by the model with highly entangled network [START_REF] Hoy | Strain Hardening in Polymer Glasses: Limitations of Network Models[END_REF].

Recent theories on the origin of strain hardening are based on the viscoelastic behavior of plastic flow [START_REF] Meijer | Mechanical performance of polymer systems: The relation between structure and properties[END_REF], [START_REF] Senden | Strain hardening and anisotropy in solid polymers[END_REF], [START_REF] Hoy | Strain hardening of polymer glasses: Effect of entanglement density, temperature, and rate[END_REF], [START_REF] Kramer | Open questions in the physics of deformation of polymer glasses[END_REF]. It is now generally accepted that during deformation, polymer chains orient themselves, resulting in an anisotropic materials with enhanced properties in the strain direction. When polymers present an initial orientation due to a prestrain or an injection process, the applied deformation lead to higher stress flow and strain hardening modulus [START_REF] Charvet | Damage Mechanisms of Plasticized Cellulose Acetate under Tensile Deformation Studied by Ultrasmall-Angle X-ray Scattering[END_REF], [START_REF] Arruda | Effects of initial anisotropy on the finite strain deformation behavior of glassy polymers[END_REF]. Recently, authors [START_REF] Conca | Mechanical properties of polymer glasses : Mechanical properties of polymer glasses[END_REF]- [66] described strain hardening as a consequence of the orientation of the monomers with a local nematic order. Local monomer orientation enhances the molecular interactions between monomers. It results an increase of the free energy barriers for α-relaxation leading to strain hardening, as the monomer orientations increase progressively. This point of view is consistent with molecular dynamics simulations by Hoy and Robbins [START_REF] Hoy | Strain hardening of polymer glasses: Entanglements, energetics, and plasticity[END_REF] who have shown that strain hardening is associated to relaxation processes analogous to that in the plastic flow regime and not to entanglements. The strain hardening mechanism is currently under intense debate.

Basic mechanical properties of classical amorphous polymers

The mechanical properties of the most common amorphous polymers are listed in the Table 1. Among them, PMMA has a high Young's Modulus and a low elongation at break [START_REF] Ali | A Review of the Properties and Applications of Poly (Methyl Methacrylate) (PMMA)[END_REF].

Mechanical

I.2.3.2 Damage mechanisms in amorphous polymers

Damage mechanisms in polymers has been the subject of many studies [START_REF] Mourglia-Seignobos | Physical Mechanisms of Fatigue in Neat Polyamide 6,6[END_REF], [START_REF] Djukic | Damage mechanisms under tensile stress of amorphous and low semi-crystalline polymers[END_REF], [START_REF] Kramer | Open questions in the physics of deformation of polymer glasses[END_REF], [START_REF] Charvet | Study of mechanical properties and damage mechanisms in plasticized cellulose acetate polymers[END_REF]- [START_REF] Kramer | Fundamental processes of craze growth and fracture[END_REF], [START_REF] Kramer | Fundamental processes of craze growth and fracture[END_REF]- [START_REF] Michler | Electron Microscopy of Polymers[END_REF]. Polymer deformations under stress give rise to the observation of two typical structures: shear bands and crazes.

Shear bands

For some polymers, when a local zone reaches a very high stress concentration, a shear band can be created. They are especially present under compression and at a low strain. Shear bands appear in the direction of 45° from the loading direction and doesn't create any void in the matrix. There are two possible morphologies of shear bands. Either they are fine and localized and lead to a slow propagation of damages. This is the case for ductile materials.

Either they are coarse and diffused and lead to a fast propagation of damages. This is the case for brittle materials. Morphologies of shear bands depend on chemical structure and conditions of tests (temperature, strain rate, aging of the sample…). In the example shown in Figure 20, PMMA displays diffused shear bands whereas PS displays fine bands.

Figure 20 : Observations of shear bands by transmission optical microscopy between crossed polarizers after plane strain compression in (a) PMMA deformed at 20°C, (b) PS deformed at 20°C

from [START_REF] Michler | Electron Microscopy of Polymers[END_REF] Crazes Crazes could appear perpendicularly to the loading direction. They are ellipsoidal damages, as shown in Figure 21, present mainly under tensile test. Crazes are created according to a mechanisms in three steps: nucleation, growth and breakdown. A craze is initiated on sample defects (impurities, micro voids, and surface scratches). Under strain, this defect leads to a local increase of stress concentration at an interface of high surface tension which may lead to cavitation. Then, cracks propagate perpendicularly to the direction of the load and widen parallel to it. The growth of crazes is the result of the displacement of the craze tips on both sides of the craze and of the widening with an increase of the fibril length. From a certain size, failures appear in the center of the craze where fibrils overcome a critical length leading to a break up. General sample failure happen when crack initiation and propagation occurs inside the craze, with successive overstressing and failure of fibrils [START_REF] Kramer | Microscopic and molecular fundamentals of crazing[END_REF], [START_REF] Kramer | Fundamental processes of craze growth and fracture[END_REF]- [START_REF] Michler | Correlation between craze formation and mechanical behaviour of amorphous polymers[END_REF].

Figure 21 : Schematic drawing of a craze, from [START_REF] Michler | Electron Microscopy of Polymers[END_REF] Recently, Charvet and Djukic [START_REF] Charvet | Damage Mechanisms of Plasticized Cellulose Acetate under Tensile Deformation Studied by Ultrasmall-Angle X-ray Scattering[END_REF], [START_REF] Djukic | Study of Damage Mechanisms of Amorphous and Low Semicrystalline Polymers under Tensile Deformation by Ultrasmall-Angle X-ray Scattering[END_REF] specified the damage mechanism by crazing.

After a craze nucleates on an impurity, tensile stress relaxes around it. The cavity grows under macroscopic stress, until the tangential stress is too high and blocks the growth. This is a strain hardening effect. Once the applied stress is sufficiently high, the craze enters in a new regime of growth with a successive homogeneous nucleation of cavities. These cavities appear ahead of the craze, in the plastic zone, where the stress is the largest. When they are sufficiently large, a coalescence mechanisms extend the main craze. Fibrils are resulting of the dewetting process.

The mechanism is summarized in Figure 22.

I.2.3.3 Relationship between mechanical properties and damage morphologies

Damage morphologies are directly in correlation with mechanical properties [START_REF] Michler | Correlation between craze formation and mechanical behaviour of amorphous polymers[END_REF]. It has been proposed that in semi -crystalline polymers, crystalline structure prevents the fast growth of damages [START_REF] Seignobos | Compréhension des mécanismes physiques de fatigue dans le polyamide vierge et renforcé de fibres de verre[END_REF]. This suggests that in amorphous polymers, crazes should grow freely and unconstrained, which is not always the case. Michler [START_REF] Michler | Correlation between craze formation and mechanical behaviour of amorphous polymers[END_REF], [START_REF] Michler | Electron Microscopy of Polymers[END_REF] proposed that the deformation mechanisms in amorphous polymers are based on toughness and entanglement density. Indeed, the slower the propagation of crazes, the tougher the polymer. He observed that an increase in toughness leads to a transition from large crazes to homogeneous deformation and shear bands (Figure 23). Later, Charvet and Djukic [START_REF] Charvet | Damage Mechanisms of Plasticized Cellulose Acetate under Tensile Deformation Studied by Ultrasmall-Angle X-ray Scattering[END_REF], [START_REF] Djukic | Study of Damage Mechanisms of Amorphous and Low Semicrystalline Polymers under Tensile Deformation by Ultrasmall-Angle X-ray Scattering[END_REF] proposed that local strain hardening slows down and stabilizes the propagation of crazes, as explained previously with Figure 22. For example, PC is a very ductile polymer which deforms partially by shear bands and breaks at large deformation (typically 100%) by propagation of crazes [START_REF] Djukic | Study of Damage Mechanisms of Amorphous and Low Semicrystalline Polymers under Tensile Deformation by Ultrasmall-Angle X-ray Scattering[END_REF]. On the contrary, PS is brittle. It breaks also by propagation of crazes [START_REF] Michler | Electron Microscopy of Polymers[END_REF]. The following Table 2 summarizes the properties of the main amorphous polymers according to their mechanisms of deformation, their mechanical properties and their density of entanglements.

Polymers

I.3 Ion-containing polymers

In this Ph.D, it is proposed to add ionic interactions to PMMA in order to improve and control its properties. The main characteristics of ionic polymers are presented in the following paragraph.

I.3.1 Generalities on associative polymers

Intermolecular interactions between chains considerably modify the polymer dynamics.

Associations can be of different energy levels: ionic coordination (25 kJ/mol to 300 kJ/mol), hydrogen bonding (2 kJ/mol to 100 kJ/mol) or π-π stacking (1 kJ/mol to 9 kJ/mol) as shown in Figure 24. Lateral groups capable of interacting between each other are called stickers.

Supramolecular polymers have been recently the subject of many studies in order to understand the mechanisms involved in the association of the stickers and their dynamics [START_REF] Zhang | Dynamics of associative polymers[END_REF], [START_REF] Capek | Dispersions of polymer ionomers: I[END_REF], [START_REF] Potaufeux | A comprehensive review of the structures and properties of ionic polymeric materials[END_REF],

[1], [START_REF] Leibler | Dynamics of reversible networks[END_REF].

I.3.2 Definitions of ionomers

An ionomer is defined as an ion-containing polymer with a small amount of ionic groups, usually up to 10 -15 % mol, along the backbone chains [START_REF] Hendy | Ionic polymers[END_REF]. Ionic polymers with higher ion content are called polyelectrolytes and those with covalent cross links are called ion exchange resin. Simple definition of ionomers is thus given from the ion content. However, Eisenberg proposed a definition based on the behavior of ionic groups rather than on the ion content. His definition is the following: an ionomer is a "polymer in which bulk properties are governed by ionic interactions in discrete region (ionic aggregation)" [START_REF] Eisenberg | Introduction to Ionomers[END_REF].

Since ionic interactions are particularly strong, they dominate the behavior of the polymer (even at low content). Due to their unique properties, the understanding of their behavior is essential for the development of applications such as shape memory polymers, selfhealing polymers or antibacterial polymers. They can be found in several other applications, such as in membranes, adhesives and packaging. They are also used for enhancing the compatibility between two polymers [START_REF] M'bareck | Poly (acrylic acid) and poly (sodium styrenesulfonate) compatibility by Fourier transform infrared and differential scanning calorimetry[END_REF], [START_REF] Venugopal | Phase behaviour of poly(ethylene oxide)/poly(methyl methacrylate) blends containing alkali metal salts[END_REF].

In the current study, we focus on random ionic copolymers. We also study polymer / ionic salts mixtures. This two types of ionic copolymers are described in the next sections.

I.3.3 Random ionic copolymers

I.3.3.1 Morphology

Random ionic copolymers are composed of a host matrix, in which ionic monomers have been introduced during the synthesis. Ionic groups are randomly placed along the polymer chain. In random ionic copolymers, ionic interactions provide a physical cross-linked network.

This secondary network is reversible, it can be disrupted by external heat or strain. Ionic groups are often introduced within a low dielectric medium which is not able to dissociate them. As a consequence, polymer chains tend to take conformations where ionic groups associate themselves.

The energy between a cation and an anion in an ionic pair is described with binding energies based on coulombic interactions described by the Equation ( 19) [START_REF] Zhang | Dynamics of associative polymers[END_REF],

where Q1 and Q2 are the electric charges of the cation and of the anion, ε and ε0 the dielectric constant of the medium and of the vacuum respectively, r is the average space between charges (essentially it corresponds to the sum of the radii of the anion and the cation). It results that the dissociation is favored when r is large.

Association of ionic groups results from the competition between thermal and electrostatic energies. Thermal energy kBT leads to the dissociation of ionic pairs whereas electrostatic energy promotes association. Thus Zhang et al. [START_REF] Zhang | Dynamics of associative polymers[END_REF] describe an ionomer regime when electrostatic energy is predominant on thermal energy. In this regime, few ion pairs are associated, as described by the Equation [START_REF] Bywater | Effect of stereostructure on glass transition temperatures of poly(methyl methacrylate)[END_REF].

(20

)
Ionic groups could be associated with two ion pairs from adjacent chains, multiplets (up to 4 to 8 ion pairs) or clusters (few multiplets) as illustrated on Figure 25 [13], [START_REF] Potaufeux | A comprehensive review of the structures and properties of ionic polymeric materials[END_REF].

Figure 25 : Morphologies of ionic aggregation in ionomers : from left to right, two ion pairs, multiplet, cluster, ionic network, from [START_REF] Potaufeux | A comprehensive review of the structures and properties of ionic polymeric materials[END_REF] Ionic associations can lead to a microphase separation with an ion rich phase and an ion poor phase (mainly made up of the polymer matrix). This has been proven by many SAXS studies. Clusters (ion rich phase) display a typical size of 2 to 4 nm [START_REF] Weiss | Viscoelastic Behavior of Very Lightly Sulfonated Polystyrene Ionomers[END_REF], [START_REF] Weiss | Rheological behavior of oligomeric ionomers[END_REF], [START_REF] Eisenberg | Introduction to Ionomers[END_REF], [START_REF] De | Effect of intermolecular interactions on the viscoelastic behavior of polyamides[END_REF]. Ionic aggregations are surrounded by a zone of restricted mobility, distinct from the bulk polymer matrix. This zone, so called the core, has a size that depends on the aggregation number of the multiplet (ion content) and the stiffness of the polymer backbone. Typically the size of the core entity is small (< 50 Å) and its effect is limited to that of a physical cross-link. The model of Eisenberg describes that cores restrict the mobility of the surrounding polymer chains as described in Figure 26, [START_REF] Eisenberg | Introduction to Ionomers[END_REF], [START_REF] De | Effect of intermolecular interactions on the viscoelastic behavior of polyamides[END_REF]- [START_REF] Lefelar | Concentration and counterion dependence of cluster formation in sulfonated polystyrene[END_REF]. It is typically observed in polystyrene containing sodium methacrylate moieties. There are many parameters that influence ionic association morphology such as the dielectric constant of the polymer chains, the nature of the ion and of the counter-ion, or the density of salts. Knowledge on the strength of ionic associations allows for a better understanding of all the properties of associating polymers.

I.3.3.2 Glass transition temperatures

The glass transition temperature Tg is very sensitive to the details of polymer chemistry (side groups, cross-links…). By creating an ionic network, and if there are enough interactions, ionic groups often lead to an increase of the Tg of the host matrix. Some examples are summarized in Table 3.

I.3.3.3 Viscoelastic properties

Ionic associations change the viscoelastic properties of the host polymer. First, if the Tg is increased, the master curve of linear viscoelastic properties is shifted to higher temperatures. The average lifetime of ionic associations, also called stickers, is denoted by τs [START_REF] Chen | Ionomer dynamics and the sticky Rouse model[END_REF], [START_REF] Weiss | Rheological behavior of oligomeric ionomers[END_REF], [START_REF] Leibler | Dynamics of reversible networks[END_REF], [START_REF] Vanhoorne | Low-Shear Melt Rheology of Partially-Neutralized Ethylene-Methacrylic Acid Ionomers[END_REF]. This is the average time which a sticker spends in its ionic association. If the sticker lifetime τs is longer than the Rouse time between entanglements τe, ionic groups lead to a longer lifetime of the rubbery plateau and the terminal relaxation is delayed. According to the molecular weight between entanglements Me, and the molecular weight between stickers Ms, a second plateau may appear, as shown in Figure 27. The sticky reptation is explained by Zhang et al. [START_REF] Zhang | Dynamics of associative polymers[END_REF] as follows:

-in the first case which is Ms > Me (blue curve), there is less than one sticker per entanglement and the lifetime of stickers τs is much longer than the Rouse time between entanglements τe. An effective sticker dissociation would allow a fraction Ms/M to relax by reptation over a distance a(Ms/Me) 1/2 , with a the tube diameter. The reptation time became τrep = τs(M 3 /(MeMs) 2 ). Here, there is more entanglements than stickers so the drop in modulus at 1/τs is insignificant.

-In the second case that is Ms < Me (red curve), there is more than one sticker per entanglement, and τs is much longer than the Rouse time between entanglement τe. The equilibration of an entanglement strand is attained by the sticky Rouse mechanism. The The melt rheology of ionomers has been extensively studied by Weiss, mainly on polystyrene containing sulfonate moieties [START_REF] Weiss | Viscoelastic Behavior of Very Lightly Sulfonated Polystyrene Ionomers[END_REF], [START_REF] Weiss | Rheological behavior of oligomeric ionomers[END_REF], [START_REF] Fitzgerald | Synthesis, Properties, and Structure of Sulfonate Ionomers[END_REF]. In his papers, even if the second plateau is not clear, he highlights the presence of clusters on the loss modulus G", as shown in Figure 28. Applying a stress or increasing the temperature lead to a decrease of the lifetime of ionic associations. This dissociation -association process corresponds to the "ion hopping process" as schematized in Figure 29. The state where the ionic pair is not residing in cluster is called "free ion pair". This process allows for the stress relaxation of the portion of chain between clusters. At long times, the clusters have time for relaxing and terminal flow occurs.

I.3.3.4 Mechanical properties

Mechanical properties of amorphous ionic random copolymers have been less studied.

Some studies observed the evolution of damages with increasing concentration of ionic groups in ionomers. Hara, Sauer et al. [START_REF] Hara | Deformation and fracture behavior of polystyrene ionomer and ionomer blends[END_REF], [START_REF] Bellinger | Tensile Fracture Properties of Sulfonated Polystyrene Ionomers. 1. Effect of Ion Content[END_REF] have studied the mechanical properties of sodium sulfonate polystyrene (PS-co-NaSPS) with tensile tests at room temperature and at 10 -3 mm/s.

They found that both tensile strength and toughness increased slightly at low ion content (below 4 % mol). Toughness (described as the area under the curve) is increased significantly at higher ion content (above 4 % mol). Then reduction in toughness was observed at higher ion content (8.8 % mol). In all cases, the PS ionomer remains brittle. They proposed that around 4 % mol happens a change in the ionic morphology, with a multiplets to clusters transition. Like in neat PS, damaging mode under tensile loading is crazing, but in presence of clusters (above 4 % mol), shear banding coexist with crazes. Thus, ionic nanodomains improve crazes stability, and clusters act as stronger crosslinks than multiplets. Hara, Sauer et al. [START_REF] Ma | Poly(methyl methacrylate) Ionomers. 2. Deformation Modes under Simple Tension[END_REF] confirmed this tendency later in PMMA ionomers. Tensile tests were performed at room temperature on random ionic copolymers of methyl methacrylate and sodium methacrylic acid (PMMA-co-PMANa) films with 6 % and 12.4 % mol of sodium salts. Neat PMMA is damaged by crazing, ionomer with 6 % of sodium is damaged by crazing and shear banding while ionomers with 12 % mol of ion is damaged by shear banding only.

I.3.3.5 Literature review of some random ionic copolymers

Some of the main properties of random ionic copolymers found in the literature are summarized in Table 3. Parameters are mentioned such as the nature of the matrix, the ion content, or the nature of the ionic species.

Ionomers often consider poorly polarizable matrix which leads to ionic phase segregation such as in polystyrene. The influence of the matrix polarisability is well illustrated in the study of Chen and Colby [START_REF] Chen | Ionomer dynamics and the sticky Rouse model[END_REF]. A matrix with a low dielectric constant favors larger clusters than a matrix with a high dielectric constant, which will solvate ion pairs. Polyethylene oxide (PEO) solvates the sodium phthalate sulfonate groups thanks to its high dielectric constant

(ε ~ 10 [4]
). On the contrary, the poly (tetramethylene oxide) (PTMO) has a smaller dielectric constant (ε = 2.5 [START_REF]Dielectric Constant[END_REF]) and a lower solvation ability than PEO. In melt rheology, there is no rubbery plateau in PEO, while ionic PTMO have the apparition of a very long plateau covering a frequency range of nearly 9 decades even if polymers are unentangled (Figure 30). They explained that ionic groups are totally dispersed and solvated in the PEO matrix and that on the contrary, they build clusters and crosslinks in PTMO delaying the terminal relaxation time. Similar observations were made in the polyamides (PA) studied by Martins et al. [START_REF] De | Effect of intermolecular interactions on the viscoelastic behavior of polyamides[END_REF] which contain lithium sulfonate moieties. No phase segregation was observed by SAXS in PA.

In the study of Eisenberg, sodium sulfonate polystyrene (PS-co-NaSPS) [START_REF] Robbins | Scaling of the strain hardening modulus of glassy polymers with the flow stress[END_REF], showed large clusters. The PS matrix has a smaller dielectric constant (2.6) than polyamides (4.0, at 50 Hz) [START_REF] Mark | Polymer Data Handbook[END_REF].

Weiss also studied the viscoelastic behavior of this kind of ionomers. In unentangled polystyrene containing 2.5 % mol and 4.8 % mol of various alkali metal salts of sulfonate moieties (1 and 2 ionic groups per chain respectively), the Tg is approximately increased by 2 °C per mol of ion. Master curves are shifted to lower frequencies and a rubbery plateau appears even if the polymer is unentangled thanks to ionic associations, as shown in Figure 31.

Upon decreasing the cation size, thereby increasing the ionic interactions with the ratio charge to radius, longer plateaus are observed. The existence of a nanophase separation is observed by SAXS, with an ion rich phase and a ion poor phase. The distance between clusters is in the order of 4 to 6 nm. Table 3 : Literature review of some random ionic copolymers with alkali metal salts.

I.3.4 Polymers / ionic salts blends

I.3.4.1 Morphology

Regarding polymers / ionic salts blends, the dispersion of salts requests a high solvation capacity of the polymer matrix. Cohesive energy of the salt should be low and/or the dielectric constant of the polymer must be high. Some very polar polymers such as PEO or PA6.6 are well known to act as solvent for ionic salts. The main application of PEO / ionic salts blends is to make solid polymer electrolytes for batteries [START_REF] Kramer | Fundamental processes of craze growth and fracture[END_REF]- [START_REF] Seignobos | Compréhension des mécanismes physiques de fatigue dans le polyamide vierge et renforcé de fibres de verre[END_REF]. Numerous studies consider PEO blended with various alkali salts [START_REF] Rhodes | Cation-anion and cation-polymer interactions in (PEO)nNaCF3SO3 (n=1-80)[END_REF], [START_REF] Stolwijk | Salt-Concentration Dependence of the Glass Transition Temperature in PEO-NaI and PEO-LiTFSI Polymer Electrolytes[END_REF], [START_REF] Klongkan | Effects of the Addition of LiCF3SO3 Salt on the Conductivity, Thermal and Mechanical Properties of PEO-LiCF3SO3 Solid Polymer Electrolyte[END_REF], [START_REF] Delgado Rosero | Thermal Properties of Composite Polymer Electrolytes Poly(Ethylene Oxide)/Sodium Trifluoroacetate/Aluminum Oxide (PEO)10CF3COONa + x wt.% Al2O3[END_REF]. More recently, lithium-ion batteries based on PMMA have been the focus of a lot of attention [START_REF] Ito | Additive Effects of Lithium Salts with Various Anionic Species in Poly (Methyl Methacrylate)[END_REF]- [START_REF] Miyagawa | Viscoelastic properties of poly(methyl methacrylate) with high glass transition temperature by lithium salt addition[END_REF]. The interest of PMMA compared to PEO is its high Tg, which allows to reach better mechanical properties than PEO and its amorphous character which is preferable for the conductivity [START_REF] Bresser | Decoupling segmental relaxation and ionic conductivity for lithium-ion polymer electrolytes[END_REF].

In many studies, the dispersion of ionic salts is possible thanks to the complexation of the cation with a dipolar moment of the polymer chain. For example, in PEO/ alkali metal salts blends, the interaction between dissociated lithium or sodium and oxygen atoms of PEO was highlighted by infrared spectroscopy [START_REF] Rhodes | Cation-anion and cation-polymer interactions in (PEO)nNaCF3SO3 (n=1-80)[END_REF], [START_REF] Bernson | Coordination and conformation in PEO, PEGM and PEG systems containing lithium or lanthanum triflate[END_REF]- [START_REF] Huang | Molecular structures and normal vibrations of trifluoromethane sulfonate (CF3SO3-) and its lithium ion pairs and aggregates[END_REF]. In PMMA / lithium salts blends, interaction between dissociated lithium and oxygen atom from the carbonyl group of PMMA was also showed with infrared spectroscopy [START_REF] Ito | Additive Effects of Lithium Salts with Various Anionic Species in Poly (Methyl Methacrylate)[END_REF]- [START_REF] Miyagawa | Viscoelastic properties of poly(methyl methacrylate) with high glass transition temperature by lithium salt addition[END_REF].

I.3.4.2 Glass transition temperatures

By creating ionic interchain associations, the Tg may be increased. Some examples of polymers / ionic salts blends with increased Tg are summarized in Table 4.

I.3.4.3 Viscoelastic properties

Rheological properties of polymers / ionic salts blends are less studied than ionic groups directly added within the polymer chains. Very recently, Ito [START_REF] Ito | Additive Effects of Lithium Salts with Various Anionic Species in Poly (Methyl Methacrylate)[END_REF] build master curves of PMMA / lithium triflate blends. It was found that the application of the TTS applies well. The general shape of the master curve is shifted to lower frequencies due to the Tg increase. No change on the terminal relaxation behavior is observed for these systems.

I.3.4.4 Mechanical properties

Mechanical properties of polymers blended with ionic salts are also little studied, probably because alkali metal salts are hygroscopic. Nevertheless, recently, Yamaguchi [START_REF] Sako | Modulus enhancement of polycarbonate by addition of lithium perchlorate[END_REF] introduced lithium perchlorate (LiClO4) into polycarbonate (PC), which is an amorphous and ductile polymer. Complexation of the lithium cation with the carbonyl group was proven by FTIR. With the addition of 6 % mol of LiClO4, the toughness increases at 23 °C as compared to the unmodified PC. The ion content close to 6 % mol corresponds to the best improvement of properties. Tensile stress -strain curves are displayed in Figure 32.

Another example is the addition of lithium triflate (LiCF3SO3) in polylactic acid (PLA), which is a semi-crystalline and brittle polymer. The presence of salts increases the brittleness at 23 °C as shown in Figure 33. It is suggested that the presence of salts prevents crystallization of PLA. Klongkan [START_REF] Klongkan | Effects of the Addition of LiCF3SO3 Salt on the Conductivity, Thermal and Mechanical Properties of PEO-LiCF3SO3 Solid Polymer Electrolyte[END_REF] made the same observation in PEO containing up to 20 % wt of LiCF3SO3. Lithium triflates hinder the crystallization and the toughness of PEO is diminished.

Mechanisms leading to an increase or a decrease of the mechanical properties thanks to the presence of ionic salts remains unknown. Huang [START_REF] Lee | Impacts of Lithium Salts on the Thermal and Mechanical Characteristics in the Lithiated PEO/LAGP Composite Electrolytes[END_REF] Table 4 : Literature review of the polymers / ionic salts blends properties

I.4 Objective of the study

The objective of this Ph.D is to identify possible ways for improving the mechanical properties of PMMA, by adding ionic interactions. Mechanical properties such as strength and toughness are key for polymer applications. Polymers can be ductile or fragile. Strain hardening has been proven to make a polymer more ductile by blocking or slowing down the growth of cavities and stabilizing the deformation. Localization of deformation usually leads to early breaking of materials [START_REF] Charvet | Damage Mechanisms of Plasticized Cellulose Acetate under Tensile Deformation Studied by Ultrasmall-Angle X-ray Scattering[END_REF], [START_REF] Djukic | Study of Damage Mechanisms of Amorphous and Low Semicrystalline Polymers under Tensile Deformation by Ultrasmall-Angle X-ray Scattering[END_REF], [START_REF] Meijer | Mechanical performance of polymer systems: The relation between structure and properties[END_REF].

PMMA tends to be fragile and its strain hardening is small. For this purpose, supramolecular PMMA were synthetized with ionic covalently attached pendant groups. These ionic moieties may enhance the PMMA properties, with in particular an increase of the glass transition temperature. Ionic groups may allow a control of damage evolution enhancing the final properties. By adding intermolecular ionic interactions between chains, the cohesive energy of PMMA may increase.

A good compromise between the solid and the molten state has to be reached.

Thermoplastic modified with ionic groups are often difficult to process due to the increased viscosity. A good understanding of association lifetimes and of ionic strength allow to control this compromise between processing and properties. Indeed, it may be possible that thermally reversible ionic crosslinks allow the material to behave like a high molecular weight polymer at low temperatures, thanks to strong intermolecular interactions, while at high temperatures, this reversible crosslinks are dissociated, allowing the material to flow.

So the aim of the current study is to compare the behavior of neat and ionic PMMA, regarding the glass transition temperature, the viscoelastic properties and the mechanical properties. Various structures of ionic groups are used to study the strength of ionic intermolecular interactions and the reversible mechanisms that control solid and molten states.

The cation (lithium, sodium and potassium) and the counterion (sulfonate, carboxylate, triflate…) are varying. Some salts are added as pendant groups by copolymerization or formulated by mixing.

In the following chapter, materials, processes and experimental methods of characterization are detailed. In the third chapter, properties of random ionic copolymers, based on sulfonate and carboxylate moieties will be presented. Then in the fourth chapter, the properties of PMMA blended with various ionic salts are studied. Finally, we focus on the influence of ionic interactions on the mechanical properties of PMMA blended with triflate salts.

Chapter II -Materials and methods

In this chapter, materials, processes, and experimental methods of characterization are described. First, the polymer systems and the ionic salts studied are introduced. Two types of ionic groups are added on the PMMA backbone. One of the ionic groups is sodium styrene sulfonate (NaSPS). The second one is alkali metal carboxylate of lithium, sodium and potassium (PMAX, X = Li, Na, K). The structures of the corresponding ionic copolymers are shown in Figure 34. Other ionic salts are blended with PMMA by solvent casting or by melt extrusion. Some of these systems have been chosen to be prepared in larger quantities. The various processes are described. In the last part, methods of structural 5. 5. Three references PMMA are obtained at Mn = 27 kg/mol, 48 kg/mol and 94 kg/mol.

Note that in the following study, we discuss using the weight-average molecular weight Mw.

II.1.1.2 Poly (methyl methacrylate-co-alkali metal methyl methacrylic acid)

Another type of random ionic copolymers based on PMMA were prepared by Solvay.

Six samples were made from commercially available poly (methyl methacrylate-co-methacrylic acid), denoted PMMA-co-PMAA. The reaction is described in Figure 38. From our six different copolymers, three of them were prepared from a low molecular weight copolymer (Mw = 34 kg/mol) containing 1.6 % mol of methacrylic acid functions bought from Sigma Aldrich (product number 376914). Three others were prepared from a high molecular weight copolymer (Mw = 235 kg/mol) containing 11.4 % mol of methacrylic acid function bought from Polysciences (product number 08207-50). For all samples, the acid functions were neutralized with lithium, sodium or potassium salts. The synthesis proceeded as follows. First, the PMMAco-PMAA was dissolved in THF/H2O 50/50 wt/wt. Then, solutions of LiOH, NaOH, or KOH were added to the solution at 0.2 eq. The solution was stirred for 1 h. The polymer was precipitated in diisopropyl ether (DIPE) and then washed and filtered. Polymers were cryoground and dried for 36 h under vacuum at 120 °C to full evaporation of moisture and residual solvents. To check the efficiency of the neutralization process, the ion content was determined by inductively coupled plasma -atomic emission spectroscopy (ICP-AES) and by potentiometric titration. Their properties are detailed in Table 6 and in Table 7. The ion content reported corresponds to the ICP-AES analysis, the potentiometric titration being in accordance with these values. A PEI thermocompressor was used for this purpose (Solvay RICL). Imprint of 100 mm x 100 mm x 1.5 mm are put between two parallel plates of 50 cm x 50 cm pre-coated with a release agent. The imprint was filled with 24 g of polymers. The thermocompressions were performed at 150 °C. The cycle was the following:

-Samples were heated from room temperature to 100 °C at 20°C/min and with 20 kN.

-Then samples were heated from 100 °C to 150 °C at 10 °C/min with 20 kN.

-Samples were maintained at 150 °C and the force was increasing by 20 kN/min up to 160 kN.

-Finally, samples were cooled down to 80 °C at 15 °C/min with 20 kN.

Note that the applied force of 160 kN represent an applied pression between 100 to 160 bars because the polymer overflows by about 2 cm around the imprint.

Tensile and compressive specimens were cut from these sheets. A Charlyrobot device was used with a 3 mm drill, at 20 500 rpm and a displacement of 4 mm/s, with a single pass over all the depth of the pieces.

II.2.2 Solvent casting

PMMA mixed with ionic salts (described above in section II.1.3) were prepared by solvent casting (at Solvay RICL). The solvent casting is a method which allows to mix and put in shape polymer formulations. A polymer is dissolved in an organic solvent. Particles or salts are added to the solution. The solution is stirred and then poured into a mold. When the solvent evaporates, the final shape and structure of the blend is obtained. By controlling the solvent evaporation rate, solvent casting may allow to keep a good salt dispersion during drying.

Acetone, anhydrous 2-butanone (MEK), ethanol absolute (EtOH), methanol (MeOH), anhydrous tetrahydrofuran (THF) and toluene were purchased from Sigma Aldrich and used without any further purification. For the solvent casting method, all salts were manipulated under a dried atmosphere to prevent moisture absorption. For this purpose, a plastic glove bag was filled with nitrogen.

The solubility of salts was investigated in various solvents to find a common solvent with PMMA. Ionic salts were found soluble only in water or alcohol [START_REF] Peiffer | Solution properties of ion-containing polymers in polar solvents[END_REF], except for triflate salts which were soluble in MEK and acetone. Because PMMA is a hydrophobic polymer, a cosolvent was required: MEK/MeOH 80/20 wt/wt.

For the solvent casting process, 3 g PMMA was dissolved in 18 g of MEK. In another flask, the appropriate amount of salts (0 -10 % mol) was dissolved in 6 g of MEK and 6 g of

II.2.3 Extrusion -injection processes

Extrusion is a thermo-mechanical process where a polymer is melted and forced through a die of appropriate cross-section. A hopper brings polymers and additives through a feed throat where the material enter in contact with corotative twin screws, specifically adapted to the formulation of polymers. They mix and forces the plastic beads forward into the heated barrel.

The processing temperature, the screw profile and the rotation speed are parameters allowing to obtain the right dispersion of additives. An extrusion device is illustrated in Figure 41.

Figure 41 : Schematic illustration of an extrusion process

Then, polymer materials can be injection molded into a specific shape. The principle of the injection principle is described in Figure 42 and is the following:

1) First, pellets are incorporated into the heated barrel.

2) Then, pellets are melted along the screw. They are transported toward the injection nozzle by the rotation of the screw and its plug displacement.

3) The molten polymers, accumulated at the end of the barrel, are pushed through the injection nozzle into the mold by a displacement of the plug. The injection head (head of the screw) is equipped with a ring preventing the back flow of the material.

A counter pressure is applied to completely fill the mold.

4) The screw moves back to refill the injection head again with molten material. During this time, the molded object is cooled down and ejected from the mold.

The time cycle is the time required to produce one molded piece.

II.2.3.1 Extrusion -injection on at the laboratory scale

In parallel of the solvent casting, PMMA/ ionic salts systems (described above in section II.1.3) were also blended by extrusion. Formulations were made by melt extrusion on an laboratory device, specific for the processing of small quantities. A micro-compounder HAAKE Minilab II Rheometer CTW5 from Thermo Scientific was used (Solvay RICL). It has a capacity of 5 g (7 cm 3 ), and is equipped with two interpenetrating co-rotating screws with an integrated batch recirculation channel. An automatic bypass valve allows for the recirculation of the materials into the capillary slit backflow channel or for the final extrusion of the materials (Figure 43). The device can be inerted with a nitrogen flow.

PMMA was first cryo-grounded with a 1 mm sieve. Then, PMMA and ionic salts have If the PMMA / ionic salts blend was miscible at the extruder output, it was injection molded into tensile specimens using a Thermo Scientific Haake Minijet Pro, as shown in Figure 44. This device is equipped with an ISO 527-5A mold (Solvay RICL). The method was the following. At the extruder exit, the molten formulation was pushed directly into a heated gun at 230 °C. The gun was then placed on top of the injection machine so that the material was pushed into the mold with a determined pressure of 800 bars in 10 s. The pressure was then maintained during 10 s. The mold was at 110 °C, allowing the molten polymer to fill the mold completely before being cooled down by the temperature difference between the polymer and the mold. Specimens were removed from the mold with the help of compressed air. Powders of polymers and salts were dry mixed in the appropriate quantities. The feeding device was put under nitrogen. The temperature was at 200 °C just below the feeding device and then remained constant at 230 °C all along the screws. The screws mixed formulations at 300 rpm.

The installation has a throughput of 1300 g/h. At the extrusion output, a compressed air cooling system freezed the polymer rod. The rod was driven by a roller to be cut into pellets of around 1 mm diameter by 1 mm length. The extrusion process was schematized before in Figure 41.

Then, pellets were injection molded to obtain tensile specimens.

II.3 Methods

II.3.1 Chemical structure characterizations

II.3.1.1 Proton nuclear magnetic resonance ( 1 H NMR)

Nuclear magnetic resonance (NMR) spectroscopy is an analytical technique used to determine the molecular structure of molecules. NMR is used in the presence of atoms that possess a nuclear spin. When the corresponding nucleus is submitted to a magnetic field, it can take two energy levels, according to the direction of the field. For NMR experiments, the sample is placed into a magnetic field and absorbs electromagnetic radiations at specific frequencies.

The observed resonance frequencies depend on the considered atoms and of their chemical bonds with other atoms. 1 H NMR measurements allow to obtain information regarding hydrogen bearing functions, the number of protons in equivalent interactions environments and the number of protons carried by neighboring carbon atoms. The device is described in Figure 45.

In our study, 1 H NMR was used to determine the tacticity of PMMA, which is important since the Tg of PMMA is strongly influenced by its tacticity (see I.1.2. for more details).

Analyses are carried out on a Bruker Ascend 400 device (Solvay RICL, Analytical Laboratory, M. Lager, Y. Moskalenko). They are performed at 400 MHz in deuterated chloroform (CDCl3)

for classic PMMA and in deuterated dimethylsulfoxide (DMSO-d6) for functionalized PMMA.

Tacticity is determined with the ratio of the peaks corresponding to the α-CH3 in isotactic (mm), atactic (mr) or syndiotactic (rr) positions, as explain in the literature [START_REF] Brar | Structural investigations of poly(methyl methacrylate) by twodimensional NMR[END_REF] and in an example in Figure 46.

Figure 45 Schematic illustration of a NMR device

Figure 46 : 1 H RMN spectrum of PMMA, with the identification of peaks to the molecular structure. The tacticity is determined from the ratio between the isotactic (mm), atactic (mr) and syndiotactic (rr) peaks of the α-CH3, from [START_REF] Hussein | Method for increasing fatigue resistance of polyamides[END_REF]. The tacticity was defined in the Chapter I.1.2.

II.3.1.2 Size exclusion chromatography (SEC)

Size exclusion chromatography (SEC) is a liquid chromatography method, which split macromolecules based on their hydrodynamic volume. SEC allows thus to measure the molecular weight of polymers. A polymer sample is dissolved in a solvent. The solution goes through a porous column. Depending on the chain size, the eluted molecules can enter into the pores of the column. Longer chains cannot enter into the pores and go faster through the column.

The concentration of polymers as function of the elution time is reported. From the elution time, the use of PMMA or PS standards of known molecular weight allows to measure the corresponding molecular weight of samples. The principle is illustrated in Figure 47.

From the molecular mass distribution detected by SEC, the number-average molecular weight Mn and the weight-average molecular weight Mw are calculated according to Equations ((21)(22) [START_REF] Doi | The Theory of Polymer Dynamics[END_REF]. The ratio between Mw and Mn is the molecular weight distribution also called the polydispersity index PD, where Ni is the number of chain molecules of weight Mi. present in the commercial copolymer was measured as well as the ionic concentration after chemical modification through the measurement of the carboxylate functions (COO -).

An acid-base titration is a quantitative analysis to determine the concentration of an acid or a base in solution. The evolution of the pH is followed during a reaction where a solution called "titrant", of known concentration, neutralizes a solution called "titrated" of unknown concentration. The electrical potential difference is measured between two electrodes: a reference electrode and a glass electrode (see Figure 48). When all the reagents have been consumed, at the equivalent point, the titrant and titrated reagents have been introduced in stoichiometric proportions. A pH jump occurs and allows to determine the equivalent volume (VE). VE is obtained by the method of the derivative on the diagram of the evolution of the pH versus the volume of titrant introduced. An illustration of the principle is shown in Figure 48.

For stoichiometric coefficients equal to 1, the concentration of the titrated species is determined according to Equation ( 24),

where Cb and Vb are the concentration and volume of the titrated solution, Ca the concentration of the titrating solution and VE the volume at equivalence. For that, 0.25 g of sample was dissolved in MeOH/THF 30/30 v/v. The total reaction below occurred.

RCOOX + HCl RCOOH + XCl

At the end of this reaction (jump in pH), all the functions were in the acid form COOH.

The complete displacement of the equilibria was made by saturation with HCl (addition of 2 mL of HCl after equivalence). Then, the total number of function present in the initial commercial copolymers COOH was determined with NaOH 0.1 mol/L by the reaction below.

RCOOH + NaOH RCOONa + H2O

The concentrations of residual COOH in our samples were calculated from the difference between the measurement of carboxylate function COO -(functions neutralized by Li, Na, K) and the total number of COOH (initial concentration of functions).

II.3.1.4 Inductively Coupled Plasma (ICP)

Atomic Emission Spectroscopy with Inductively Coupled Plasma (ICP-AES) is a method for measuring the concentration of a chemical element in a material. The sample must be put into an aerosol form. Polymers are mineralized using strong acids or microwaves. The aim of the mineralization is to break all the organic bonds. The solution is then introduced in an argon plasma, placed at high temperature. The plasma is generated by inductive coupling.

A plasma is a ionized atomic gas. Thermal excitation leads to the ionization and separation of elements. ICP-AES collects the wavelengths emitted by the different elements.

Analysis were supplied by the CREALINS laboratory (6NAPSE group, Villeurbanne, M. Staffe, F.Benoit) by using a Thermo Scientific ICP -AES iCAP Duo. Samples were mineralized in an acid medium.

II.3.1.5 Infrared spectroscopy by attenuated total reflectance (ATR)

Attenuated total reflectance (ATR) infrared spectroscopy is used for the characterization of chemical functions present in organic materials. The IR beam undergoes multiple internal reflections in a crystal of high refractive index. The sample is in contact with the crystal. A small part of the IR beam enters in the sample (with a depth dp), before being reflected. The absorption spectrum depends on the type of the bonds, the way they vibrate (rotation, stretching, elongation…), the atoms involved, and the chemical environment. The principle is illustrated in Figure 49 [START_REF] Perkinelmer | Characterization of Polymers using TGA[END_REF].

In this study, ATR was used to observe changes in the chemical environment of the PMMA functions resulting from the introduction of ionic functions. The changes in the shape of characteristic peaks of PMMA were observed (Figure 50). The IR characteristic peaks of PMMA are described in Table 9. ATR spectra were acquired using an Alpha spectrometer infrared from Bruker with an ATR platinum diamond at Solvay RICL (L. Allary). The measurements allowed to access to the equivalent frequency spectrum comprised between 400 cm -1 and 4000 cm -1 with a resolution of 4 cm -1 . X-rays scattering provides information about the crystal structure of a material. An Xrays beam hits a sample and a scattered beam is emitted with a specific angle. According to the structure and the orientation of a crystal, the angle of emission will be modified. The intensity of the scattered beam is recorded as a function of the diffraction angle. Diffraction peaks are observed in directions θ according to the Bragg's law of diffraction according to the Equation ( 25),

where n is an integer, λ the wavelength of the incident beam, d the distance between planes in the crystal structure, θ the angle between the incident and the scattered beams.

The scattered intensity is recorded as a function of the scattering angle θ or, equivalently, as a function of the scattering vector q defined by the following Equations [START_REF] Moens | Progress in Reaction Mechanisms and Reactor Technologies for Thermochemical Recycling of Poly(methyl methacrylate)[END_REF]. Elastic interactions are characterized by a zero energy transfer so that the modulus of the scattered wave vector equal to the modulus of the incident wave vector . The distance d between crystalline planes, or electronic density fluctuations, can be determined from the Equation ( 27), with the peaks of the recorded intensity of the scattering wave. A beam stop is used to stop the transmitted x-rays. SAXS experiments were performed using a sample-to-detector distance of 92 cm. WAXS experiments were performed at a sample-to-detector distance of 5 cm and the q-scale was calibrated using a highly crystalline poly(oxymethylene) sample.

Even if there is no crystallization, the diffractogram of amorphous polymers exhibits peaks, one of them corresponding to the average interchain distance between polymer chains.

In PMMA two peaks are observed at 2θ = 16.81 ° and 29.49 °. This corresponds to a distance between polymer chains of 5.27 Å and a distance between pendant groups of 3.03 Å [START_REF] Lovell | Determination of the local conformation of PMMA from wide-angle X-ray scattering[END_REF], [START_REF] Ismayil | Optical and microstructural studies on electron irradiated PMMA: A positron annihilation study[END_REF]. A sample is placed on a scale, which is placed in an oven, as shown in Figure 52.

II.3.2 Thermal characterizations

Here, TGA was used to detect and quantify the degradation of PMMA. TGA measurements were carried out on a Metter Toledo instrument XS204 at Solvay RICL. Samples were heated from 30 °C to 500 °C. Temperature increased at a rate of 10 °C/min under a N2 atmosphere with a flow rate of 20 mL/min. The onset degradation temperature Td was taken with the tangent method.

where Cp is the heat capacity of the sample at constant pressure and dH/dt is the heat flow.

Changes in heat flow provides information about the thermal properties of polymers including the glass transition temperature Tg, the melting temperature Tm and the crystallization fraction.

The principle of the DSC device is illustrated in Figure 53 [START_REF] Perkinelmer | A Beginner's Guide to Differential Scanning Calorimetry (DSC)[END_REF]. Small strain dynamic oscillatory shear measurements were performed using a TA instrument ARES -G2 (Advanced Rheometric Expansion System II) at Solvay RICL. Samples were compression molded at Tg + 50 °C for 12 h under vacuum and sealed in hermetic bags.

For the test, they were placed between two 8 mm diameter Invar parallel plates, under N2 gas.

Invar is an alloy of iron (64 %) and nickel (36 %) whose main property is to have a very low coefficient of dilatation. The temperature was controlled using a forced convection oven.

Samples were equilibrated 10 min between the two parallel plates before each experiments at the test temperature. [START_REF] Feitsma | Association of stereoregular poly(methyl methacrylates): 2. Formation of stereocomplex in bulk[END_REF] where ρref is the density at the reference temperature and ρ is the density at the considered temperature T.

II.3.4 Dynamic mechanical thermal analysis (DMTA)

Dynamic mechanical and thermal analysis (DMTA) is a method for characterizing the mechanical properties of polymers in the solid state [START_REF] Ta Instruments -Waters | Dynamic Mechanical Analysis Basic Theory & Applications Training[END_REF]. For DMTA measurements, a dynamic strain γ(t) is applied to a polymer sample. This strain is expressed by the Equation ( 38),

where γ is the time dependent strain, γ0 is the strain amplitude, ω is the angular frequency and t the time.

The resulting dynamic stress σ(t) is measured. The work applied to the sample is in part restored to the polymer. It is given by the elastic modulus E'. Another part is dissipated as heat, which is given by the loss modulus E". The strain response is therefore expressed by the Equation ( 32).

(32)

The ratio between the dissipative part E" and the elastic part E' is defined by

An example of DMTA measurements on PMMA is given in Figure 55. Upon increasing the temperature, molecular relaxations may occur and correspond to slight decrease of E' for a secondary relaxation and to a larger one for the α-relaxation. These dynamic molecular relaxations can be observed on the tan δ curve by the presence of peaks.

In this study, DMTA measurements were performed with a rheometric scientific analyzer RSA -G2 from TA Instruments at Solvay RICL. Tests were performed under N2 gas, with a 3 points bending geometry with a size of 10 mm. Bars of dimension (contrary to the polycarbonate for example [START_REF] Djukic | Damage mechanisms under tensile stress of amorphous and low semi-crystalline polymers[END_REF]).

(33) (34) [START_REF] Kusuyama | Structural change of st-PMMA on drawing, absorption and desorption of solvents[END_REF] l is the sample length, l0 the initial sample length (l0 = 30 mm), F is the applied force, S and S0

the current section and the initial section of the specimen (S0 = 10 mm 2 ).

Tensile tests were performed on a Zwick / Roell Z020 universal testing machine equipped with a 2.5 kN load cell, and a thermally controlled chamber at Solvay RICL (Figure 57).

Chapter III -Random ionic copolymers

In this third chapter, PMMA containing ionic pendant moieties are studied. In the first section, sodium styrene sulfonate moieties are added on the main backbone chain. These systems are prepared by Solvay by copolymerization at 1.5 % and 3 % mol. In the second section, carboxylate moieties with lithium, sodium and potassium cations are studied. These

III.1.2 Thermal stability

The aim here is to study the thermal stability of our polymer samples by TGA under N2.

The thermal degradation profiles of PMMA and PMMA-co-NaSPS depending on the ion content are plotted in Figure 60 and Figure 61. As samples are prepared by radical synthesis, this results in 3 steps of degradation. According to Manring [START_REF] Manring | Thermal degradation of poly(methyl methacrylate). 3. Polymer with head-to-head linkages[END_REF]- [START_REF] Manring | Thermal degradation of poly(methyl methacrylate). 4. Random side-group scission[END_REF], [START_REF] Manring | Thermal degradation of saturated poly(methyl methacrylate)[END_REF], [START_REF] Ferriol | Thermal degradation of poly(methyl methacrylate) (PMMA): modelling of DTG and TG curves[END_REF], the first step, close to 180 °C, corresponds to the scission from unsaturated end groups (10 -15 % weight loss). The second step around 270 °C, comes from the scission of head-to-head bonds (10 -15 % weight loss) (these head-to-head bonds scissions has been described in Chapter I.1.3). The last step, around 350 °C, is initiated by random scissions within the polymer chains (60 -80 % weight loss).

In the presence of NaSPS moieties, the first step of degradation, corresponding to the scission of unsaturated end groups is removed. Regardless of the molecular weight, it leads to an increase of the degradation onset temperature of 40 -45 °C with 3 % mol of NaSPS moieties. Only the first step of the degradation is influenced. The shape of the curve is similar from the second peak. This is interesting from a processing point of view. We suggest that the introduction of a second monomer (sodium 4-styrenesulfonate (Na4SS)) during the synthesis leads to the formation of less unsaturated groups. The methyl methacrylate (MMA) monomers do not show the same solubility as the sodium 4-styrenesulfonate (Na4SS). The conditions of synthesis had to be adapted in presence of ionic monomers, probably leading to a modification of the kinetics of the radical polymerization. Literature has related the synthesis parameters to the thermal degradation temperature of PMMA [START_REF] Holland | The effect of polymerisation conditions on the kinetics and mechanisms of thermal degradation of PMMA[END_REF], [START_REF] Cao | Enhancing the thermal stability of poly(methyl methacrylate) by removing the chains with weak links in a continuous polymerization[END_REF].

III.1.3 Glass transition temperatures

Prior to the glass transition temperature measurement by DSC, the drying method was adapted to remove stereocomplexes. Indeed, PMMA chains often build stereocomplexes that can be detected by DSC measurements with a melting peak. This endothem is observed in 11. All systems exhibit a Tg between 125 and 130 °C. For low molecular weight samples, the Tg increases by 5 °C with 3 % mol of salts. For the higher molecular weight samples, the Tg is constant. Slight changes in tacticity or polydispersity may also be responsible for this small difference in Tg. In conclusion, we retain that all samples have roughly the same Tg.

System

III.1.4 Molecular dynamics

The evolution of the α-and β-relaxation temperatures with ionic salts are followed by Temperature sweeps were performed at 1 Hz from -50 °C to 150 °C. Results are reported in Figure 63 and in Table 12. The PMMA-co-NaSPS 60k 3% could not be analyzed since it was not processable (this point will be discussed in the next section III.1.6). When comparing all systems, one observes that the Tα is unchanged (by analogy with DSC results, Tα varies by 5 °C). Note that the α-relaxation intensity decreases in presence of ionic moieties. The βrelaxation temperature is unchanged, as well as its intensity. One may deduce that the rotation of the pendant group is not hindered by ionic moieties. 13. The monomer relaxation time τ0 is determined with , where τe is the Rouse relaxation time between entanglements and Ne is the number of monomers between entanglements. The time τe is directly observable in Figure 64 as the high frequency modulus crossover. The temperature dependence of the monomer relaxation time τ0 is reported in Figure 66. The increase of the plateau length is characteristic of non-polar matrix with low solvation ability of ionic moieties. From the molecular weight between entanglements Me (determined in the Section III.1.5.1 for the reference PMMA), we deduce that ion contents of 1.5 % and 3 % mol correspond to more than 1 and 2 stickers per entanglement respectively. Me is compared to the molecular weight between stickers Ms in Table 14. For all our samples, there is one or more than one sticker per entanglement (Ms < Me). According to Zhang et al. [START_REF] Zhang | Dynamics of associative polymers[END_REF] (see the Chapter I.3.3.3 for more details) a double plateaus should have been observed. The length of the rubbery plateau is nevertheless explained by the long lifetime of ionic association τs.

The smooth decreasing slope of the rubbery plateau may be due to the polydispersity of our samples, which is close to 2. Laboratory synthesis of polymers are rarely perfectly monodisperse. Polydisperse polymers have intrinsically broader terminal relaxation spectra than monodisperse samples. This leads to an increase of the slope of G' in the rubbery plateau and a decreasing slope for G" [START_REF] Liu | Evaluation of different methods for the determination of the plateau modulus and the entanglement molecular weight[END_REF].

The evolution of the shift factor aT of the WLF law with temperature is plotted in Figure 73. Despite the presence of salts, a WLF behavior is observed in the temperature range studied.

Note that in the case of non-polar polymer matrices for which the ionic groups build strong aggregates which persist at large temperatures, a WLF behavior is observed at low temperatures, whereas at higher temperatures, a transition towards an Arrhenius behavior may be observed. Chen et al. [START_REF] Chen | Ionomer dynamics and the sticky Rouse model[END_REF] observe this fact in a PTMO matrix containing sodium phthalate sulfonates moieties. The Tg of the ionic PTMO is -63 °C and an Arrhenius behavior appears from 20 °C.

In conclusion, PMMA, despite its intermediate polarizability, promotes aggregation of sodium styrene sulfonate moieties as is observed usually in non-polar matrices. An extension of the rubbery plateau is observed because stickers build one or more than one association per entanglement (Ms < Me).

III.1.5.3 Stickers activation energy

From the Rouse time between entanglements τe, it is possible to calculate the monomeric relaxation time τ0 with the equation τ0 = τe/Ne 2 , where Ne is the monomer number between entanglements. As just discussed, by representing the evolution of τ0 with temperature in Figure The energy required to dissociate stickers is called the activation energy of sticker Eas. τ0 is related to the activation energy Eas by the following Arrhenius Equation (37) [START_REF] Kramers | Brownian motion in a field of force and the diffusion model of chemical reactions[END_REF], [START_REF] Schomaker | Complexation of stereoregular poly(methyl methacrylates). 11. A mechanistic model for stereocomplexation in the bulk[END_REF] where τb is the ballistic time (τb = 10 -13 s), Eas is the activation energy of stickers, R the gas constant, and T the temperature. According to Kramer [START_REF] Kramers | Brownian motion in a field of force and the diffusion model of chemical reactions[END_REF], the ballistic time τb corresponds to the average time between two consecutive shocks between neighboring monomers. Each time τb, the energy received by one monomer from its neighbors is renewed randomly, with a probability proportional to . Hence the waiting time needed to reach the energy Eas is given by Equation [START_REF] Schomaker | Complexation of stereoregular poly(methyl methacrylates). 11. A mechanistic model for stereocomplexation in the bulk[END_REF]. The evolution of Eas with temperature is given in Figure 77 and Figure 78. Since samples degrade at temperatures below those corresponding to the terminal region, the Arrhenius regime cannot be reached at high temperatures, thus it is not possible to get a good estimation of the activation energy with this method.

A more appropriate method is to calculate the sticker dissociation lifetime τs from the extension of the rubbery plateau. It is similar to the method described by Chen and Colby [START_REF] Chen | Ionomer dynamics and the sticky Rouse model[END_REF], [START_REF] Zhang | Dynamics of associative polymers[END_REF]. First, the Rouse time between entanglements τe can be expressed from the reptation time τrep as describe in the Equations ( 38) and ( 39).

(38) [START_REF] Christofferson | Molecular mapping of poly(methyl methacrylate) super-helix stereocomplexes[END_REF] From the observation of the large extension of the rubbery plateau, it is possible to consider that the relaxation time between two stickers is longer that the relaxation time of the chain between entanglements. The sticker lifetime governs the reptation. Equation ( 39) is thus modified by the replacement of τe by τs. This new Equation ( 40) is valid in the case where there is one sticker per entanglement (Ne = Ns) as shown in Figure 79.

(40

)
where τrep is the reptation time, τs is the sticker dissociation lifetime, N is the average number of monomers per chain and Ne is the monomers number between entanglement.

Figure 79 : Schematic representation of an entangled polymer chain containing one sticker per entanglement (Ms = Me). Stickers form an ionic interchain bond.

In the case where there is more than one sticker per entanglement (Ms < Me), which is the case of our samples, the reptation time is given by the Equation ( 41) [START_REF] Zhang | Dynamics of associative polymers[END_REF].

(41)

From the sticker dissociation lifetimes τs, it is possible to obtain the stickers activation energy Eas with the Arrhenius Equation (42.

(42)

The corresponding values of Eas are given in Table 15. The sticker activation energy increases with the sulfonation level. The PMMA-co-NaSPS 60k 3% sample has the higher activation energy of stickers with 125 kJ/mol. This means that ionic groups may associate easier in polymers of low molecular weight.

Systems

116* Table 15 : Activation energy of stickers in PMMA-co-NaSPS, calculated from the extension of the rubbery plateau (* estimations of the last crossover modulus, not reached due to thermal degradation of the sample)

In the literature, Weiss [START_REF] Weiss | Rheological behavior of oligomeric ionomers[END_REF] determined the activation energy of polystyrene containing sodium styrene sulfonate moieties at 2.5 % and 4.8 % mol (PS-co-NaSPS, Mw = 4 kg/mol and PD = 1). He found 142 and 150 kJ/mol respectively by applying the Arrhenius equation on the shift of η0. The activation energy increases with the sulfonation level. Chen and Colby [START_REF] Chen | Ionomer dynamics and the sticky Rouse model[END_REF] estimate the activation energy of stickers Eas with the method previously described (from the extension length of the rubbery plateau) to be Eas = ~65 kJ/mol. Chen and Colby [START_REF] Chen | Ionomer dynamics and the sticky Rouse model[END_REF] used the same method of the plateau length which they determined by dielectric spectroscopy. They found that the activation energy of sodium phthalate sulfonate stickers is 14 kJ/mol in polyethylene oxide (PEO) and 58 kJ/mol in polytetramethylene oxide (PTMO). The activation energy in PEO is smaller than in PTMO, as the higher polarisability of PEO allow an easier dissociation of stickers. Indeed, a high polarisability of the matrix reduce the energy barrier allowing ionic dissociation. The dielectric constants are 2.5 for PS, 2.5 for PTMO, ~ 10 for PEO and 3.3 for PMMA [START_REF] Zhang | Dynamics of associative polymers[END_REF] [16], [START_REF]Dielectric Constant[END_REF]. The polarisability of our polymers lay in between that of the polymers studied by Chen and Colby. We would expect therefore to find an activation energy comprised between their values. On the other hand, we find stickers activation energies in the order of 100 -120 kJ/mol. This discrepancy is attribute to the different Arrhenius law they used. The time scale in the right-hand side of Equation (42 we take is the ballistic time τb between collisions whereas they consider a longer time scale, corresponding to the monomer relaxation time τ0. We think that they obtain an underestimation of the stickers activation energies by using τ0 If we took τ0 instead of τb in Equation (42, we would find activation energies comprised between 40 kJ/mol and 56 kJ/mol, which is consistent with their results.

III.1.6 Processability

We prepared our materials to get specimens for mechanical measurements.

Unfortunately, in addition to the high viscosity, degradation often occurs before the terminal flow making the process difficult. In particular, due to its large viscosity, the sample PMMAco-NaSPS 60k 3% could not be processed with any of the methods described here. First, extrusion and injection has been tried on the laboratory device Minilab (Chapter II.2.3).

However, as just mentioned, the thermal stability is not good enough to use this method.

Thermocompression was used to obtain sheets, where tensile and compression specimens were cut (Chapter II.

III.1.7.1 Compression tests

Uniaxial compression tests were first performed at 23 °C and at 2.10 -3 s -1 . Five tests were performed for each sample. Nominal stress-strain curves are obtained as shown in Figure 82 and results are reported in Table 16. We observe that the presence of sulfonate ionic groups in our samples has no effect on the mechanical properties of PMMA at 23 °C. Note that the beginning of the curve, up to 10% of deformation, corresponds to the plate alignment and correction of porosity and sample defects. This part is large since the thickness of the sample is low (1.5 mm instead of 4 mm usually). The Young's modulus is measured after this part.

Sample

Tensile tests

Then, we performed tensile tests at 90 °C and at 1.10 -3 s -1 , that is in the ductile regime of PMMA and in a temperature range were ionic associations are still strong. We prepared five samples for each measurements, but only a smaller number could be tested due to the brittleness of the samples during preparation at room temperature. It is first observed in Figure 83 and in Table 17 that the low molecular weight samples are brittle, and the high molecular weight samples are ductile. The presence of sulfonate associations decreases the toughness of PMMA which breaks at smaller deformation. More precisely, the presence of these groups lowers the Young modulus the yield stress and the elongation at break.

III.2 Effect of the introduction of alkali metal carboxylate moieties

III.2.1 Chemical structure

Six entangled alkali metal poly (methyl methacrylate-co-methacrylic acid) (PMMA-co-PMAX, X = Li, Na, K) were prepared by Solvay. Samples were based on a PMMA backbone containing carboxylic acid functions as pendant groups (PMMA-co-PMAA). There are two ion contents (1.6 and 11.4 % mol) and two molecular weights (Mw = 34 kg/mol and 235 kg/mol).

They were chosen according to the commercial availability of the PMMA containing carboxylic acid functions. The neutralization of the acid form by alkali metal cation of lithium, sodium and potassium was made by Solvay. The chemical structure is described in Figure 84. In this study, we compare samples with carboxylic acid functions (PMMA-co-PMAA) to samples with salts (PMMA-co-PMAX, X=Li, Na, K). Note that this preparation method does not change the molecular weight.

We expected that the alkali metal cation would exactly neutralize the acid fraction and that the measured ion content would be 1.6 % mol and 11.4 % mol respectively. To check this, the ion content was measured by atomic emission spectroscopy (ICP-AES) and by potentiometric titration. Results from the two analysis methods were consistent. The ion content differs from the expected nominal value meaning that the acid functions are not totally neutralized in some samples as shown in Table 18 and Table 19. For the low molecular weight and low ion content samples (Mw = 34 kg/mol, 1.6 % mol, Table 18), the reaction is incomplete with the sodium cation (0.5 % mol instead of 1.6 % mol). Moreover, the PMMA-co-PMALi 3.3 % mol sample has an ion content higher than the theoretical concentration of initial function, probably due to the presence of residual lithium. For the high molecular weight and high ion content samples (Mw = 235 kg/mol, 11.4 % mol, Table 19), the reaction is incomplete with the potassium. For unknown reasons, the measured fraction is 10 times smaller than the nominal one (1.14 % mol instead of 11.4 % mol).

III.2.2 Thermal stability

The thermal stability of our polymer samples was studied by TGA under N2. Samples from the copolymers of low ion content and low molecular weight (1.6 % mol, Mw = 34 kg/mol, Table 18) show one step of degradation, meaning that it was made by anionic polymerization (Chapter I.1.3.). The onset thermal degradation temperature is Td = 247 °C. Samples from the second copolymers, of high ion content, and high molecular weight (11.4 % mol, Mw = 235 kg/mol, Table 19) show 3 steps of degradation, meaning that is was prepared by radical synthesis. The onset thermal degradation temperature is Td = 150 °C. In both case, the presence of ionic salts do not change Td.

III.2.3 Glass transition temperatures

The glass transition temperature Tg is measured by DSC and reported in Table 20 and Table 21. Samples are carefully prepared with cryo-grounding and drying (36 h / 120 °C / vacuum) to avoid the presence of stereocomplexes (see the section III.1.3 for more details). For the low ion content samples, the Tg increases by 6 °C with 0.5 % mol of PMANa moieties. For the high ion content samples, the Tg increases by 5 °C with 10.8 % mol of PMANa. The Tg also increases with lithium and potassium. In the case of lithium, we observe an increase of Tg by 20 °C and by 5 °C only in the case of sodium. This is consistent with results from literature at low ion content: Hara and Sauer [START_REF] Ma | Poly(methyl methacrylate) Based Ionomers. 1. Dynamic Mechanical Properties and Morphology[END_REF] found an increase of 6 °C with 0.8 % mol of PMANa moieties in PMMA but not at higher ion content where the Tg is increased by 70 °C with only 12.4 % mol. In their study, the Tg increases linearly with the ion content of sodium at a rate of 6 °C/mol. No data are found in the literature with lithium and potassium cations.

System Tg

Ion %mol °C

Reference PMMA -co -PMAA 1.6% Regarding the calorimetric measurements, we observe that the shapes of the DSC curves change with the ion content. Although, we could measure the Tg values of our lithium and sodium samples at 11.4 % mol (Table 21), they were difficult to observe because the transitions are broadened, as shown in Figure 85. This phenomenon has been observed also by Hara and Sauer [START_REF] Ma | Poly(methyl methacrylate) Based Ionomers. 1. Dynamic Mechanical Properties and Morphology[END_REF] in PMMA-co-PMANa, above 12.4 % mol of PMANa. works satisfactorily for all systems.

III.2.4.1 Influence of ionic associations in ionic PMMA

As discussed, we consider here the viscoelasticity of PMMA-co-PMAX (X = Li, Na, K) containing 1.6 % mol of carboxylate moieties. Master curves regarding the frequency dependence of G' and G" of ionic PMMA are shown in Figure 86 and in Figure 87, and the main rheological features are summarized in Table 22. In the presence of PMAX moieties, master curves are shifted to lower frequencies, proportionally to the shift of the Rouse time between entanglements τe. Similarly to the case of sulfonate systems (section 1.5.2), a key feature is that the length of the rubbery plateau is extended by around 1 decade per % mol of ionic groups (independently of the cation). The plateau exhibits a smooth decreasing slope instead of a clear plateau. The terminal region is reached since samples show an high degradation temperature (Td = 247 °C), contrary to the PMMA-co-NaSPS studied in the Section III.1.

The molecular weight between entanglements Me of the reference PMMA-co-PMAA is Me = 5 900 g/mol. We deduce that the ion contents of 1.6 % mol correspond to 1 sticker per entanglement as reported in Table 22 (Ms = Me). This is consistent with our samples, where the length of the rubbery plateau is explained by the long lifetime of ionic association τs (and τs > τe).

The smooth decreasing slope of the rubbery plateau may be due to the polydispersity of our samples, which is close to 2, as explained in the section III.1.5.2. [START_REF] Liu | Evaluation of different methods for the determination of the plateau modulus and the entanglement molecular weight[END_REF].

The evolution of the WLF coefficient aT with temperature is given in Figure 88. Despite the presence of salts, a WLF behavior is observed in the temperature range studied.

III.2.4.2 Activation energy of ionic associations

The activation energy of carboxylate ionic associations is calculated in the same way as in section III.1.5.3. From the Rouse time between entanglements τe and from the WLF law (aT(T)), it is possible to calculate the monomer relaxation time τ0 as a function of temperature (with τ0 = τe/Ne 2 ). By representing the evolution of τ0 with temperature in Figure 89, a WLF behavior (equivalent to that of Figure 88) is observed. The method of calculating the activation energy of stickers Eas is thus more appropriate from the extension of the rubbery plateau. From the sticker dissociation lifetimes τs, it is now possible to obtain the activation energy Eas with τs = τb.exp(Eas/RT). The corresponding values are given in Table 23.

Note that the reference PMMA-co-PMAA contains hydrogen bonding. However, we assume that the lifetime of hydrogen bonding is smaller than τe.

System

III.3 Discussion

Sulfonate moieties

The influence of sodium styrene sulfonates (NaSPS) on the PMMA properties was investigated, with 1.5 % and 3 % mol and Mw = 60 kg/mol and 200 kg/mol. With NaSPS moieties, the Tg of PMMA is not significantly modified, as well as the mechanical properties at 23 °C. The rubbery plateau is extended, in particular by 4 decades in the PMMA-co-NaSPS 60k 3% sample. The terminal flow is delayed to higher temperatures and the viscosity is increased, these do not improve the processability. The rheology demonstrates the presence of strong ionic associations, persisting at elevated temperatures and controlling the terminal relaxation time of the main chain (τs > τe).

Similar systems have been studied in the literature. In the paper of Chen and Colby [START_REF] Chen | Ionomer dynamics and the sticky Rouse model[END_REF], an unentangled polar matrix of poly(ethylene oxyde) (PEO) (ε ~ 10) containing sodium phthalate sulfonates had no rubbery plateau (τs < τe) and a Tg increased by 43 °C. On the other hand, in the case of an unentangled less polar matrix of poly(tetramethylene oxide) (PTMO) (ε = 2.5) containing sodium phthalate sulfonates, the rubbery plateau is extended by 9 decades, while the Tg is not increased. The interpretations are the following: PEO solvates sodium phthalate sulfonate moieties. The presence of a large number of interchain bonds lead to Tg increases. In PTMO, the sodium phthalate sulfonate moieties are not solvated and the presence of clusters is expected. These clusters may have long lifetimes, leading to an increase of the plateau length.

In Weiss' articles [START_REF] Weiss | Viscoelastic Behavior of Very Lightly Sulfonated Polystyrene Ionomers[END_REF], [START_REF] Weiss | Rheological behavior of oligomeric ionomers[END_REF], non-polar polystyrene (PS) (M = 4 000 g/mol, ε = 2.5) which contain sodium styrene sulfonate moieties at 2.5 % and 4.8 % mol are studied. The rubbery plateau is extended with increasing ion content, and the Tg is increased by 2 °C/mol. As in the PTMO of Chen and Colby, the PS do not solvate sulfonates moieties. The presence of clusters is observed by X -rays analysis.

In our PMMA-co-NaSPS, ionic aggregates are formed. PMMA has an intermediate polarizability (ε = 3.3) compared to the systems studied by Chen and Colby [START_REF] Chen | Ionomer dynamics and the sticky Rouse model[END_REF], and those studied by Weiss [START_REF] Weiss | Viscoelastic Behavior of Very Lightly Sulfonated Polystyrene Ionomers[END_REF], [START_REF] Weiss | Rheological behavior of oligomeric ionomers[END_REF]. As an extension of the rubbery plateau length is observed, PMMA act as a non-polar matrix for the NaSPS moieties. The PMMA backbone and the pendant styrene sulfonate groups do not have a good affinity. As a consequence, we expect that sulfonates associate themselves, with interactions described in Figure 90. Multiplets or clusters are created. For reminder, a multiplet is defined as the association of 4 to 8 ionic pairs, clusters are associations of a few multiplets (see Chapter I for more details).

It is interesting to compare our PMMA-co-NaSPS with the PS-co-NaSPS studied by Bellinger et al. [START_REF] Hara | Deformation and fracture behavior of polystyrene ionomer and ionomer blends[END_REF], [START_REF] Bellinger | Tensile Fracture Properties of Sulfonated Polystyrene Ionomers. 1. Effect of Ion Content[END_REF]. In their work, they studied ionic PS after tensile deformation by electron microscopy. They showed that the addition of NaSPS moieties increases slightly the mechanical properties of PS at low ion content (< 4 % mol) and significantly at high ion content (between 4 and 8 % mol). Beyond 8 % mol, a decrease of the mechanical properties is observed Note that their PS-co-NaSPS remain brittle in all circumstances, and broke at about 2% of deformation. By TEM analysis, they demonstrated that fracture occurs by crazing only at low ion content (< 4 % mol). At higher ion content (between 4 % and 8 % mol), they observed the coexistence of crazes and shear bands. It is suggested that above 4 % mol, the ionic microstructure changes from multiplets to clusters. They suggested that at high ion content, ionic clusters act as strong crosslinks, stabilizing the crazes. The microscopic origin of these behaviors remains unclear. This study demonstrates the potential of NaSPS moieties to increase the ductility of brittle amorphous polymers of high Tg (around 100 °C). It would be worthwhile to study their systems at higher temperatures where the samples are ductile.

The results obtained by Bellinger et al. [START_REF] Hara | Deformation and fracture behavior of polystyrene ionomer and ionomer blends[END_REF], [START_REF] Bellinger | Tensile Fracture Properties of Sulfonated Polystyrene Ionomers. 1. Effect of Ion Content[END_REF]suggest that we should consider our PMMA-co-NaSPS of low molecular weight (Mw = 60 kg/mol) with a higher fraction of sulfonate groups, at 5 % or up to 10 % mol. Indeed, the PMMA has a higher polarizability than PS, thus a higher ionic content is required to create clusters of equivalent size, as the polarizability reduce the activation energy of stickers. The presence of strong ionic clusters seems to improve the mechanical properties. Note that in order to be processable, it would require a PMMA synthesized by anionic polymerization which exhibits high thermal stability.

Figure 90 : Ionic interchain interactions in PMMA-co-NaSPS, between two sodium styrene sulfonate moieties

Carboxylate moieties

In the second system, with carboxylate moieties (PMAX, X = Li, Na, K), the Tg of PMMA increases. The rubbery plateau is extended by about 1 decade per % mol of ionic groups. The longer plateau demonstrates the presence of strong ionic associations persisting at elevated temperatures and controlling the terminal relaxation time of the main chain (τs > τe).

From the extension of the rubbery plateau, we conclude that multiplets or clusters are created in our systems. The interaction between two carboxylates is shown in Figure 91 with the example of sodium. The scheme would be identical with lithium and potassium cations.

The cation nature has an influence on ionic associations. In the literature, Martins et al.

[2] suggest that sodium do not interact with the dipolar groups of polyamide chains, contrary to lithium. This means that the lithium cation is more likely to create ion dipole interactions than sodium. This is explained by the charge to radius ratio which is higher for lithium than for sodium (Coulomb's law) [START_REF] Israelachvili | Intermolecular and Surface Forces[END_REF]. Weiss [START_REF] Weiss | Rheological behavior of oligomeric ionomers[END_REF] made the same observations by using various cations in styrene sulfonate PS (Li + , Na + , K + , Rb + , Cs + ). The ionization potential, or Coulomb energy of the ionic pairs increase as the radius cation decrease.

It is also interesting to compare our systems with those of Ma and Sauer [START_REF] Ma | Poly(methyl methacrylate) Ionomers. 2. Deformation Modes under Simple Tension[END_REF], [START_REF] Tsou | Blends of poly(methyl methacrylate) (PMMA) with PMMA ionomers: Mechanical properties[END_REF].

They studied PMMA-co-PMANa in the same way that the PS-co-NaSPS previously described in III.3.1. by Bellinger et al. [START_REF] Hara | Deformation and fracture behavior of polystyrene ionomer and ionomer blends[END_REF], [START_REF] Bellinger | Tensile Fracture Properties of Sulfonated Polystyrene Ionomers. 1. Effect of Ion Content[END_REF]. They observed damaged samples after tensile tests by electron microscopy. At low ion content (< 6 % mol), the samples are damaged by crazing only.

At higher ion content (between 6 % mol and 12.4 % mol), samples are damaged with crazes and shear bands. Above 12.4% mol, they observed only shear bands. Note that they did not provide quantitative mechanical results and their samples remain brittle in the temperature range studied. As with NaSPS, this study underlines the potential of PMAX moieties to increase the ductility of a brittle amorphous polymers, of high Tg (of around 100 °C).

It would be worthwhile studying the evolution of damages under strain with PMALi moieties. It would be also interesting to perform mechanical studies where the temperature is varied, to observe the influence of ionic groups in the ductile regime.

Figure 91 : Ionic interchain interactions in PMMA-co-PMANa, between two sodium carboxylate moieties

Comparison of the effects of sulfonate and carboxylate moieties in PMMA

The influence of the sulfonate and of the carboxylate moieties on the PMMA properties are compared. The Tg of PMMA increases with carboxylate moieties but not with sulfonate moieties. Indeed, the Tg is not always increased with ionic clusters. It depends on various parameters such as the ionic association size and the ion content. The PTMO containing sodium phthalate sulfonates of Chen and Colby [START_REF] Chen | Ionomer dynamics and the sticky Rouse model[END_REF] does not have an increase in Tg, while the PS-co-NaSPS of Weiss [START_REF] Weiss | Rheological behavior of oligomeric ionomers[END_REF] has. Weiss [START_REF] Weiss | Rheological behavior of oligomeric ionomers[END_REF] showed that sulfonate groups build large clusters in PS.

As a consequence, the Tg increase in a way similar to Eisenberg systems [START_REF] Eisenberg | A new multiplet-cluster model for the morphology of random ionomers[END_REF], [START_REF] Eisenberg | Introduction to Ionomers[END_REF] (see the Chapter I. 3.4.1 for more details). In the model of Eisenberg, clusters induce a large zone of restricted mobility when they are large enough. These clusters may even have their own Tg, once the dimension of overlapping regions of reduce mobility exceeds ~ 50 -100 Å [START_REF] Eisenberg | A new multiplet-cluster model for the morphology of random ionomers[END_REF],

[137]- [START_REF] Kim | Relations between the neutralization level and clustering of amorphous ionomers[END_REF]. The other way to increase Tg is to disperse ionic groups in the matrix and to create many ionic interchain bonds (no clusters). This is the case of the PEO of Chen and Colby [START_REF] Chen | Ionomer dynamics and the sticky Rouse model[END_REF] containing sodium phthalate sulfonates or of the sulfonate polyamides of Martins et al [START_REF] De | Effect of intermolecular interactions on the viscoelastic behavior of polyamides[END_REF].

Martins observed an increase of Tg in the absence of ionic phase segregation by SAXS.

Lundberg [START_REF] Lundberg | A Comparison of Sulfonate and Carboxylate Ionomers[END_REF] introduced NaSPS and PMANa moieties in PS at 3 % and 5 % mol. He measured the Tg shift. The Tg increased with both moieties, but the carboxylate ionomers display a modest increase compared to the sulfonate ionomers. In our PMMA systems it is the contrary: the Tg shift is larger with carboxylates than with sulfonates. In these PS of Lundberg and Weiss, the difference in Tg shift may be due to the fact that carboxylate associations are hindered by the steric hindrance of styrene groups, while the sulfonate associations are distant from the chain and can more easily associate themselves.

In our PMMA systems, the interpretation is that carboxylate moieties built stronger associations than sulfonate moieties. The inductive effect of the CO2 -is stronger than the one of SO3 -. As a consequence, the carboxylate moieties create stronger interactions with their cations, and therefore their counterparts, than sulfonates (Figure 90 and Figure 91). Furthermore, in PMMA there is less steric hindrance for carboxylate moieties than in the PS of Lundberg cited above. Indeed, the carboxylate groups in PMMA backbones are less trapped and more easily accessible to those of neighboring chains. As a consequence they can create more and stronger interactions between them as compared to the carboxylate moieties added in the PS of Lundberg. Note that the sulfonate groups are distant from the polymer chains thanks to the styrene groups, in both PMMA and PS matrix. In our PMMA systems, the sticker activation energy of NaSPS and PMAX are of the same magnitude: of 105 to 125 kJ/mol and of 107 to 116 kJ/mol respectively. It would have expected the interaction between PMAX groups to be stronger than those with NaSPS. This discrepancy is may be a consequence of the fact that NaSPS are less soluble in PMMA with their styrene groups than PMAX. As a consequence, ionic associations may be constituted of a larger number of ionic groups than in carboxylate associations, which contributes to increasing the measured activation energy of stickers.

Finally, the influence of stickers on the viscoelastic properties of ionomers depends on various parameters, and not only on the nature of the ionic groups. First, the dielectric constant is a key parameter. A high dielectric constant reduces the energy barrier of dissociation of stickers and allows for the dispersion of ionic groups. Their interaction in a high dielectric constant polymer is weaker. In the case of unentangled polymers, if the polymer is polar and solvate the ionic species, the master curves shapes are not modified. As in the case of PEO and PA (Table 24), the time τe increases but no rubbery plateau is observed. On the contrary, if the matrix is less polar and has a low solvation ability for ionic species, ionic association occurs and create a rubbery plateau due to long lifetime of stickers (PS and PTMO in Table 24). For entangled polymers, the extension of the rubbery plateau is determined by the number of stickers per entanglement (Ms vs Me), as discussed in Chapter I.3.3.3).

To conclude, there are two possibilities to consider, according to whether the ionic associations are dispersed or in large aggregates. The formation of strong and larger ionic associations are favorable to increase the mechanical properties as mentioned by Bellinger and Sauer [START_REF] Bellinger | Tensile Fracture Properties of Sulfonated Polystyrene Ionomers. 1. Effect of Ion Content[END_REF], [START_REF] Ma | Poly(methyl methacrylate) Ionomers. 2. Deformation Modes under Simple Tension[END_REF], (in regimes where the samples remain fragile though). In this case, the processability may be difficult due to long relaxation times and increased viscosities. A compromise process/properties have to be reached. In PMMA, synthesis conditions need to be carefully chosen to ensure thermal stability at high temperatures for which stickers are dissociated. To obtain the formation of these ionic associations, a low polarizable matrix have to be chosen [START_REF] Chen | Ionomer dynamics and the sticky Rouse model[END_REF], [START_REF] Zhang | Dynamics of associative polymers[END_REF]. On the other hand, in the case of dispersed ionic groups in matrices such as PEO, the Tg can be increased. Processability may be preserved when the terminal flow is achievable at not too high temperatures. The possibility to improve the mechanical properties in this way is not documented. Finally, the most important parameters are ε, Ms and Me. The viscoelastic properties of examples mentioned here from the literature and the one of our results are summarized in Table 24. Table 24 : Viscoelastic properties of ionomers discussed in the Chapter III, from the literature review (made in Chapter I), dielectric constants ε are from [START_REF] Mark | Polymer Data Handbook[END_REF], [START_REF]Dielectric Constant[END_REF]. Eas are determined with the method cited in [START_REF] Chen | Ionomer dynamics and the sticky Rouse model[END_REF], [START_REF] Leibler | Dynamics of reversible networks[END_REF]

Polymers

III.4 Conclusion

In this third chapter, the influence of ionic moieties on the thermal, viscoelastic and mechanical properties up to ultimate properties on PMMA were studied. Sodium styrene sulfonates were added as pendant groups on PMMA up to 3 % mol. The Tg and the mechanical properties at 23 °C were not modified. Sodium styrene sulfonate stickers changed significantly the viscoelastic properties of PMMA. The rubbery plateau is extended by 4 decades in the PMMA-co-NaSPS 60k 3% sample. There is more than one sticker per entanglement, with long lifetime of ionic associations. As a consequence, stickers dominate the terminal relaxation time.

It is suggested that sulfonate moieties form multiplets or clusters in the PMMA matrix. Other ionic moieties that are carboxylates of lithium, sodium or potassium were studied. The Tg increased. The rubbery plateau is extended by 1 decade per mol of stickers. The long lifetime of ionic associations dominates the terminal relaxation. Carboxylate moieties also formed multiplets or clusters in the PMMA matrix. Our interpretations is that carboxylates create stronger interactions than sulfonates, due to inductive effect. On the other hand, carboxylates may create smaller associations due to the steric hindrance as compared to the sulfonates which are distant from polymer chains thanks to the styrene groups. By creating smaller clusters but better dispersed than with sulfonates, the carboxylate moieties allow to increase the Tg of PMMA. We could not study the mechanical properties of the carboxylated PMMA samples because synthesis was insufficiently mastered to produce larger quantities.

Literature suggests that these moieties may allow to increase the mechanical properties by increasing the ductility (transition from crazing to shear banding damages), thanks to the presence of clusters. It would be interesting to study those systems with a higher ion content.

As PMMA have a higher polarizability than PS, a higher ionic content is required to create clusters of equivalent size. In all cases, a higher thermal degradation temperature of PMMA is required, by choosing PMMA synthetized by anionic way. It would be interesting to complete this study with some mechanical analysis at room and high temperatures. SAXS analysis would provide a quantitative analysis of the evolution of the ionic association size with ion content.

IV.1 Screening of the miscibility of ionic salts with PMMA

In the case of polymer / ionic salt blends, high solvation ability of the matrix is necessary to disperse salts and to create "bridge" like interactions between polymer chains (Figure 92).

PMMA has an intermediate polarizability, with a dielectric constant of 3.3, compared to the very polar PEO (~ 10.0) and PA6,6 (4.0) and the non-polar PS (2.5) for example [START_REF] Mark | Polymer Data Handbook[END_REF]. In PMMA, the addition of various salts such as LiSO3CF3, LiClO4, LiBr, LiCl or LiBF4 have been widely studied for lithium electrolyte batteries. In these studies, the complexation of Li + with the oxygen atom of the carbonyl of PMMA has been widely proven by FTIR [START_REF] Ito | Additive Effects of Lithium Salts with Various Anionic Species in Poly (Methyl Methacrylate)[END_REF], [START_REF] Yap | Investigation on dielectric relaxation of PMMA-grafted natural rubber incorporated with LiCF3SO3[END_REF]- [START_REF] Miyagawa | Viscoelastic properties of poly(methyl methacrylate) with high glass transition temperature by lithium salt addition[END_REF],

[108], [START_REF] Singh | FTIR and rheological studies of PMMA-based nanodispersed gel polymer electrolytes incorporated with LiBF4 and SiO2[END_REF]. Thanks to motivated research to find alternatives to lithium batteries, it is also known that sodium salts are miscible with other matrices successfully, like ether oxygen based matrix [START_REF]Electrical conduction mechanism in NaCl complexed PEO/PVP polymer blend electrolytes[END_REF]- [START_REF] Osman | A comparative study of lithium and sodium salts in PAN-based ion conducting polymer electrolytes[END_REF].

Figure 92 : Polymer chains and an ionic salt with "bridge" like ionic interactions

We made a selection of different ionic salts likely miscible with PMMA. Sodium p-toluene sulfonate, as well as sodium p-toluene sulfinate are chosen for this study for their structural similarities with the sodium styrene sulfonate moieties (NaSPS) (Chapter III.1.). Sodium salicylate is chosen since it has also been observed mixed with PVA matrix [START_REF] Ahad | Structural, Thermal, and Electrical Properties of PVA-Sodium Salicylate Solid Composite Polymer Electrolyte[END_REF]. Triflate salts are selected for their stability and thanks to the wide literature made on batteries [START_REF] Kurapati | Novel solid polymer electrolyte based on PMMA:CH3COOLi effect of salt concentration on optical and conductivity studies[END_REF], [START_REF] Miyagawa | Viscoelastic properties of poly(methyl methacrylate) with high glass transition temperature by lithium salt addition[END_REF], [START_REF] Sen | A New High-Temperature Lithium Para-Toluene Sulfonate (LIPTSA) Salt for Rechargeable Batteries[END_REF]. Lithium triflate (LiSO3CF3, denoted LiT here) is known to be miscible with PMMA [START_REF] Ito | Additive Effects of Lithium Salts with Various Anionic Species in Poly (Methyl Methacrylate)[END_REF],

[100], [START_REF] Tsugawa | Effect of lithium salt addition on the structure and optical properties of PMMA/PVB blends[END_REF]. Salt structures are described in Figure 93. The matrix used is the PMMA from Polysciences of Mw = 100 kg/mol.

IV.1.1 Miscibility

The solvent casting method is the method of choice for mixing ionic salts with polymers.

The solvent casting conditions must be well defined. The procedure is detailed in the Chapter II.2.1. Salts are also blended with PMMA by melt extrusion. This method allows to obtain larger quantities of product and to confirm the solubility observed by solvent casting. The melt extrusion process is performed with a micro-compounder extrusion device at 230 °C. The procedure is detailed in the Chapter II.2.2.

The solubility of salts in the PMMA matrix with the two methods is given in Table 25 and in Figure 94. If the matrix remains transparent, salts are considered soluble and if large aggregates are observed it is considered insoluble. Results show that all salts based on an aromatic ring with a sulfonate or a carboxylate group are insoluble in PMMA. These ionic salts build large white aggregates. Sodium benzoate (3 % mol) is here an exception: a white homogeneous disk is obtained. Due to optimized parameter conditions, a well dispersed suspension was obtained but we conclude nevertheless that this salt is insoluble in PMMA. The p-toluene sulfonate salts was miscible at 3 % mol, but not at 5 % mol in our conditions. As expected from literature, lithium triflate salts are found to be miscible with PMMA, at least up to 30 % mol. Sodium and potassium triflate salts are also found miscible with PMMA, up to around 15 % mol and 10 % mol respectively. The dispersion in homogeneous disc is checked by 1 H NMR, with samples taken from different parts of the disc. We conclude that among the studied salts, those with aromatic rings are insoluble in PMMA, and that lithium salts are more soluble than sodium or potassium salts. We measured the increase of Tg as a function of the ion content of the soluble salts.

Ion content

In the Section IV.2, we study in more details the properties of PMMA / pTsNa blends within their solubility range. It allows for comparing their properties to those of similar structure NaSPS added in the copolymers PMMA-co-NaSPS studied in the Chapter III.1. PMMA / LiT or NaT blends will be considered further in the Section IV.3. These systems are prepared in larger quantities with a continuous extrusion process. KT having little effect on the Tg of PMMA is not considered further.

IV. for LiT and NaT respectively (Section IV.1.2.). We assume that this is due to a better dispersion of salts thanks to the extrusion screw mixing elements.

These measurements are consistent with results from the literature where 7 % mol of LiT increases the Tg by 15 °C for Miyagawa [START_REF] Miyagawa | Viscoelastic properties of poly(methyl methacrylate) with high glass transition temperature by lithium salt addition[END_REF]. He found that LiT is miscible up to 60 % mol in PMMA using solvent casting conditions, with no impact on the transparency of the matrix.

IV.3.2 Sensitivity to moisture

Ionic salts are hydrophilic, especially lithium. Prior to experiments, the water absorption kinetics of our samples is measured. Before viscoelastic measurements, the water content is checked on dried samples with a Karl Fisher and is found to be smaller than 500 ppm. Then, tensile specimens are exposed to air at 23 °C and RH 50 % for a few days. It is found that during the first 30 min, the water absorption remains below 0.1 %, which is considered as negligible regarding the effect on mechanical properties. The water uptake is plotted in Figure 99.

IV.3.4 Viscoelastic properties

The viscoelasticity of the PMMA / triflate salts blends are reported in Figure 101 and in Table 27. Master curves regarding the frequency dependence of G' and G" are built using the WLF law at a reference temperature of 170 °C.

With increasing ion content, master curves are shifted to lower frequencies, similarly to the increase of the Rouse time between entanglements τe (see Figure 133 and Figure 134 in Annexes). The rubbery plateau length is reduced by 0.8 decade with 10 % mol of LiT and by 0.5 decade with 10 % mol of NaT. The contrary was observed for the PMMA-co-NaSPS studied in the Chapter III.1, for which the plateau was extended by more than one decade.

While the ionic interactions are strong in the glassy state, they become weaker at high temperatures, allowing the terminal region of the master curves to be clearly detected (τs < τe), contrary to random ionic copolymers studied in the Chapter III (τs > τe). Note that the degradation temperature of the PMMA matrix is higher than in the copolymers of Chapter III.

The narrowing of the rubbery plateau may be due to a decrease of the entanglement density in presence of ionic salts. Since the ratio between τrept and τe scales as (N/Ne) 3 (where N is the number of monomers of the chains and Ne the number of monomers per entanglement), the reduction of the plateau length may be interpreted as a dilution effect due to the presence of the salt. Ito et al. [START_REF] Ito | Rheological and mechanical properties of poly(methyl methacrylate) doped with lithium salts[END_REF] observed similar effects. They interpreted this effect as a consequence of a so-called "pining effect" of lithium triflate salts in PMMA which may prevent the good entanglement of polymer chains.

The plateau modulus GN 0 is determined experimentally with the VGP plot (as described in the Chapter I, with the minimum of the phase angle δ = f(G*) = f( ). It decreases with increasing ion content (Table 27). This may be interpreted as a consequence of the diluting effect just discussed above. Then Me is determined from the plateau modulus with the equation . The molecular weight between entanglements Me of the PMMA of Mw = 100 kg/mol was calculated to be Me = 8,375 kg/mol.

An approximation of the zero-shear viscosity η0 (with ) is reported in Figure 102. The logarithm of the zero shear viscosity η0 increases linearly with the ion content, with a slope of 0.12 Pa.s / mol of LiT and of 0.04 Pa.s / mol of NaT. These slopes are 10 times smaller than in the Chapter III with covalently attached ionic groups (~1 -1.5), which is better for processing.

IV.3.5 Dispersion of ionic triflate salts

The salts dispersion is characterized by X-rays analysis. The SAXS measurements showed no signal, corresponding to the absence of phase segregation at a scale from 1 to 30 nm.

The WAXS pattern gives us more information. In Figure 104, two peaks are observed in the neat PMMA. The scattering vector at q = 1 Å -1 corresponds to the average distance between chains and the one at q = 2 -2.5 Å -1 to the average distance between pendant groups (q = 2πn/d) [START_REF] Al-Muntaser | Enhancement of optical and electrical properties of PVC/PMMA blend films doped with Li4Ti5O12 nanoparticles[END_REF]. For the ionic PMMA's, these peaks are more diffused and shifted to higher scattering vector. The distance between PMMA chains is calculated (with q = 2πn/d) to be 6.25 Å. This interchain distance is reduce to 5.67 Å with 10 % mol of LiT and to 5.62 Å with 10 % mol of NaT. The distance between pendant groups is 3 Å for neat PMMA. This distance is less regular for ionic PMMA blends as the intensity is decreased and the peak is broadened. The absence of a salt crystallization peak suggests that triflate salts are well dispersed in the PMMA matrix. It is observed that with increasing ion content, this band is broadened. This effect is more pronounced with the lithium than with the sodium cation. This confirms that the cation interacts with the carbonyl of the PMMA and that lithium interactions are stronger.

IV.3.7 Discussion

From the X-rays analysis, the infrared spectroscopy as well as with the observation of the increase in Tg, we conclude that ionic interchain interactions are created thanks to ionic salts. Ions create "bridges" like structures between the carbonyl groups of PMMA of adjacent chains. These interchain interactions are exemplified in Figure 106. Each anion is supposed to remain in the vicinity of its cation.

Moreover, the different cations (Li + , Na + and K + ) do not have the same efficiency for modifying the PMMA properties. These differences probably stem from the difference between the cation sizes. The smaller the radius, the larger the polarizability of the cation, the stronger the interaction with the carbonyl group of PMMA. Weiss and his coworkers [START_REF] Weiss | Rheological behavior of oligomeric ionomers[END_REF] made this hypothesis in the case of PS ionomers, for which the viscosity increases with the quantity cq/a, where c is the concentration in ionic species, q the charge and a the cation radius. Binding energies of the triflate salt are determined with the Coulomb's law (see section I.3.3.1 for more details). The corresponding values of the interaction energies are of 122 to 153 kJ/mol and increase with decreasing cation size, as shown in Table 28.

IV.4 Conclusion

In this chapter, the influence of ionic salts on the PMMA properties was studied. The first condition is the solubility of the salts with the polymer matrix. A screening of various ionic salt structures was performed. Among the studied salts, lithium, sodium and potassium triflate salts are miscible with PMMA. On the contrary, ionic salts containing aromatic ring are not soluble.

The dispersion of triflate salts in the matrix was checked by X-rays studies. Then, IR spectroscopy studies show that lithium and sodium cations create strong interactions with the carbonyl groups of PMMA. The triflate anion is miscible with PMMA, as a consequence, triflate salts display a good miscibility leading to a homogeneous dispersion in the polymer matrix. On the contrary, aromatic anions remain bounded with their cation. This prevents the solubilization of these salts in PMMA.

The glass transition temperature of PMMA increases by about 23 °C with 10 % mol of LiT and by 6 °C with 10 % mol NaT. Master curves are shifted to higher temperatures in melt rheology due to the increase in τe (similarly to the increased Tg). The rubbery plateau length and modulus are reduced due to a dilution effect of the salt. Ionic interactions are established between carbonyls of neighboring polymer chains, resulting in an increase of Tg. The effect of ionic interactions is not observable in the terminal relaxation regime which controls the viscosity at higher temperatures, preserving thereby the processability of PMMA. The main drawback is the hydrophilicity of the salts, leading to progressive water uptake of the samples which could reduce the PMMA properties over long period of time. In the next chapter, the mechanical properties of PMMA / ionic triflate salts blends are measured at various temperatures.

V.1 Tensile behavior

Amorphous thermoplastics can exhibit different typical behaviors. For example, the poly(carbonate) is ductile over a wide range of temperatures, while poly(styrene) and poly(methyl methacrylate) are brittle up to high temperatures. Mechanical properties are sensitive to temperature. The transition temperature from a brittle to a ductile behavior is denoted "TBD". Tensile tests were carried out on PMMA and on PMMA / triflate salts blends of lithium and sodium, from 23 °C to 80 °C, with steps of 10 °C, at RH 50%. The strain rate was fixed at 10 -3 s -1 . Parameters studied were the nature of the cation, the ion content and the temperature. The Young's modulus (E), the yield stress (σy), the stress and strain at break (σr and εr) are reported. The Young's modulus is determined with the slope in the elastic domain between 0.1 % and 0.3 % of the true strain. The yield stress is defined as the maximum of the stress after the elastic regime (see Section I.2.3.1 for more details).

V agreement with the results from literature where a typical value of 3.2 GPa is referenced [START_REF] Mark | Polymer Data Handbook[END_REF].

The elongation at break is small (approximatively 2.8 %), in accordance with literature references which suggest values between 2 % to 10 % [START_REF] Mark | Polymer Data Handbook[END_REF]. The Young's modulus and the yield stress decrease linearly upon increasing the temperature. The brittle to ductile transition temperature is between 40 °C and 50 °C. In the ductile regime, a small strain softening is observed. PMMA shows very little, if any, strain hardening. Tg (Tg + 13 °C). Then, over a wide temperature range from 50 °C to 80 °C, the ductility is improved with a higher yield stress and higher plastic flow stress than in neat PMMA. To sum up the results concerning sodium blends, PMMA containing 3 % and 5 % mol of NaT exhibits the same general behavior: the Tg and the TBD increase by the same amount.

Samples are more brittle and stiff than neat PMMA at low temperatures. Then, the ductility is improved in the ductile regime at temperatures just above TBD. The samples at 10 % mol of NaT are also more brittle than neat PMMA at low temperatures. Contrary to the PMMA with 3 % and 5 % mol of NaT, the mechanical properties are lower than that of neat PMMA at higher temperatures, with a low flow stress. The temperatures and ion contents for which plastic properties are improved, regarding the yield stress are gathered in Figure 116.

V.1.2.5 Discussion

Finally, PMMA containing LiT and NaT salts show the same general behavior regarding the ionic concentration and the temperature. While the brittleness and stiffness are increased with the influence of the ion content at low temperatures, the plastic properties are increased in a specific temperature range, just above TBD. This temperature range is broader with 5 % mol of salts. Then with 10 % mol of salts, plastic properties are deteriorated. The ion content reaches an optimum point between 3 % and 10 % mol to improve the plastic properties. The lithium cation is more efficient than sodium cation in improving the PMMA properties, in both fragile and ductile regimes. It would be interesting to explore in more details the ionic concentration of LiT and the temperature range for which plastic properties are improved, e.g. between 3 % and 10 % mol of salt in order to obtain to optimized properties for PMMA.

It is interesting to compare our results with the only comparable system found in the literature. Recently, Yamaguchi et al. [START_REF] Sako | Modulus enhancement of polycarbonate by addition of lithium perchlorate[END_REF] [151]- [START_REF] Genier | Effect of Coordination Behavior in Polymer Electrolytes for Sodium-Ion Conduction: A Molecular Dynamics Study of Poly(ethylene oxide) and Poly(tetrahydrofuran)[END_REF]. In a case of a coordination sphere, typically in water solution, an octahedral pyramidal geometry is adopted.

According to Lewis, Li + and Na + are defined as a hard acid and an oxygen atom as a hard base. Thus, the interactions between cations and oxygen donor atoms are strong. Using the hard and soft base scale, one can predict the preferred donor atoms in Li + or Na + complexes.

The stability of Li + or Na + complexes decreases as the ligand donor atoms are changed as follows: 0 > N > S > F. This means that, in the triflate anion, the CF3 side of the molecule don't interact with the lithium [START_REF] Olsher | Coordination chemistry of lithium ion: a crystal and molecular structure review[END_REF].

For the sake of simplicity, we will consider that the lithium and sodium cations have a coordination sphere of 4 and 6, respectively, as it is frequently assumed.

V.2.1.2 Denticity of the triflate anion

The triflate anion T -can create one or more bonds depending on the location of its negative charge [START_REF] Côté | The supramolecular chemistry of the sulfonate group in extended solids[END_REF], as shown on Figure 119. The dentate character of a ligand (here the triflate anion) represents the number of coordinating atoms [START_REF] Bhatt | Essentials of Coordination Chemistry: A Simplified Approach with 3D Visuals, 1st edition[END_REF]. Triflate may be monodentate, bidentate or even tridentate. dynamics simulations and defined as follows [START_REF] Ito | Enhancement of the glass transition temperature of poly(methyl methacrylate) by salt[END_REF], [START_REF] Miyagawa | Viscoelastic properties of poly(methyl methacrylate) with high glass transition temperature by lithium salt addition[END_REF], [START_REF] Bernson | Coordination and conformation in PEO, PEGM and PEG systems containing lithium or lanthanum triflate[END_REF], [START_REF] Frech | Ionic Transport in Polymer Electrolytes: The Essential Role of Associated Ionic Species[END_REF], [START_REF] Dong | Molecular Dynamics Simulations and Vibrational Spectroscopic Studies of Local Structure in Tetraglyme:Sodium Triflate (CH3O(CH2CH2O)4CH3:NaCF3SO3) Solutions[END_REF], [START_REF] Huang | Molecular structures and normal vibrations of trifluoromethane sulfonate (CF3SO3-) and its lithium ion pairs and aggregates[END_REF], [START_REF] Rhodes | Crystalline Phases of Poly(Ethylene Oxide) Oligomers and Sodium Triflate: Changes in Coordination and Conformation with Chain Length[END_REF],

[156]- [START_REF] Mason | Infrared spectroscopic and conductivity studies of poly(N-methylpropylenimine)/lithium triflate electrolytes[END_REF].

For the lithium triflate, a free anion T -is designed as the state where the salt is fully dissociated, solvated in the solution. Note that after dissociation, the triflate anion T -remains relatively free, near a cation, while the cation is coordinated with some oxygen atom. An ionic pair is the electrically neutral species LiT. A triple cation is Li2T + , a triple anion LiT2 -. Their presence may lead to ill-defined larger aggregates. Ionic species are shown Figure 120. The same definitions are made with the sodium triflate [START_REF] Frech | Ionic Transport in Polymer Electrolytes: The Essential Role of Associated Ionic Species[END_REF]. A free ion T -is designed as the state where the salt is fully dissociated. An ionic pair is NaT. A triple cation is Na2T + .

An isolated triple anion is NaT2 -. There is an additional isolated species which is NaT3 2-. Ionic species are shown in Figure 121. The dispersion of ionic salts may evolve with the ion content. Our hypothesis is that, with increasing ionic concentration, the ratio between the fully dissociated ions and partially associated ions evolves towards a higher share of associated species. That may explain why the system PMMA/LiT 90/10 mol/mol exhibits deteriorated properties: if ionic salts are not fully dissociated and dispersed along the matrix, the lithium cation is neighbored by mostly triflate anions. That is not favorable to the creation of interchain ionic bonds between PMMA chains, as described on the left side of Figure 122, in which we describe some possible structures of ionic complexes. On the contrary, if ionic salts are fully dissociated and dispersed within the matrix, there are many interchain bonds between PMMA chains. In Figure 122, the possible types of ionic interactions between the salt and the matrix are proposed, from the aggregated states to the fully dissociated and solvated states. Infrared analysis are carried out to identify the presence of these complexes. The ionic species identification is made through literature. From the determination of the triflate anion environment made by IR spectroscopy, deductions are made on the cation environment and finally, with the help of the coordination chemistry, on the potential interactions between the PMMA and the ionic salts. In PMMA, Li + tends to complete up to 4 its coordination sphere. As a consequence, if it interacts with 3 carbonyls, the sphere is completed with 1 oxygen from T -.

If it interacts with 2 carbonyls, the coordination sphere is completed by 2 oxygen atoms from T -. And if Li + interacts with only 1 carbonyl, its coordination sphere is completed with 3 oxygen atoms from T -. Note that when LiT is dissociated, T -remains in the vicinity of its cation. The same occurs with NaT in PMMA. Depending on the number of interactions Na + has with carbonyls of PMMA, it will complete its coordination sphere to 6 with triflate oxygen atoms.

Relationships between the ionic microstructures and the mechanical properties are proposed.

V.2.2 Identification of the ionic species in PMMA / ionic triflate salts blends

V.2.2.1 Infrared spectroscopy

Infrared spectroscopy allows to define the close neighborhood of the triflate anion [START_REF] Ito | Enhancement of the glass transition temperature of poly(methyl methacrylate) by salt[END_REF],

[104], [START_REF] Bernson | Coordination and conformation in PEO, PEGM and PEG systems containing lithium or lanthanum triflate[END_REF], [START_REF] Dong | Molecular Dynamics Simulations and Vibrational Spectroscopic Studies of Local Structure in Tetraglyme:Sodium Triflate (CH3O(CH2CH2O)4CH3:NaCF3SO3) Solutions[END_REF], [START_REF] Huang | Molecular structures and normal vibrations of trifluoromethane sulfonate (CF3SO3-) and its lithium ion pairs and aggregates[END_REF], [START_REF] Hyun | Molecular Dynamics Simulations and Spectroscopic Studies of Amorphous Tetraglyme (CH3O(CH2CH2O)4CH3) and Tetraglyme:LiCF3SO3 Structures[END_REF], [START_REF] Sanders | A spectroscopic and conductivity comparison study of linear poly(N-methylethylenimine) with lithium triflate and sodium triflate[END_REF]. As discussed just above in the section V.2.1.3, this is an indirect method to define interactions between ionic salts and PMMA. FTIR-ATR spectroscopy was performed on the ionic salts powder (dried under vacuum at 70 °C / 12h) and on tensile specimens of blends at 23 °C (dried under vacuum at 70 °C / 12h). First, the experimental spectra of our neat lithium and sodium triflate salts are shown in Figure 123 and Figure 124. Their characteristic bands are reported in Table 29.

Resonance bands Attribution

LiT NaT cm - 123 and in Figure 124 from [START_REF] Ito | Enhancement of the glass transition temperature of poly(methyl methacrylate) by salt[END_REF], [START_REF] Miyagawa | Viscoelastic properties of poly(methyl methacrylate) with high glass transition temperature by lithium salt addition[END_REF], [START_REF] Dong | Molecular Dynamics Simulations and Vibrational Spectroscopic Studies of Local Structure in Tetraglyme:Sodium Triflate (CH3O(CH2CH2O)4CH3:NaCF3SO3) Solutions[END_REF], [START_REF] Huang | Molecular structures and normal vibrations of trifluoromethane sulfonate (CF3SO3-) and its lithium ion pairs and aggregates[END_REF], [START_REF] Ramesh | Conductivity, dielectric behavior and FTIR studies of high molecular weight poly(vinylchloride)-lithium triflate polymer electrolytes[END_REF] Figure 123 : FTIR-ATR spectrum of the neat lithium triflate salt (LiT), on a platinum diamond from 4000 to 400 cm -1 with a resolution of 4 cm -1

Figure 124 : FTIR-ATR spectrum of the neat sodium triflate salt (NaT) on a platinum diamond from 4000 to 400 cm -1 with a resolution of 4 cm - In PMMA / ionic triflate salt blends, specific bands of the triflate anion are observed.

We focus first on the bands at 1040 cm -1 corresponding to the symmetric stretching of SO3.

The symmetric vibration bands of SO3 at 1040 cm -1 are reported in Figure 125. The intensity of the band increases with increasing ion content. For the lithium systems, the resonance frequency of the band is at 1041 cm -1 as in the neat LiT. There is an additional band at 1032 cm -1 . Moreover, the band of the PMMA/LiT 90/10 mol/mol sample is broaden to higher frequencies as compared to systems at lower ion content. For the sodium systems, the band is at 1034 cm -1 as in the neat NaT. Sodium samples exhibit only well-defined bands. They are broader in lithium than in sodium systems. It is possible to attribute these bands to some of the ionic species, described above in section V.2.1.3. Wheeler et al. [START_REF] Dong | Molecular Dynamics Simulations and Vibrational Spectroscopic Studies of Local Structure in Tetraglyme:Sodium Triflate (CH3O(CH2CH2O)4CH3:NaCF3SO3) Solutions[END_REF], [START_REF] Huang | Molecular structures and normal vibrations of trifluoromethane sulfonate (CF3SO3-) and its lithium ion pairs and aggregates[END_REF], [START_REF] Hyun | Molecular Dynamics Simulations and Spectroscopic Studies of Amorphous Tetraglyme (CH3O(CH2CH2O)4CH3) and Tetraglyme:LiCF3SO3 Structures[END_REF] have characterized LiT and NaT systems by IR spectroscopy and by molecular dynamic simulations. In their article, Huang and Wheeler [START_REF] Huang | Molecular structures and normal vibrations of trifluoromethane sulfonate (CF3SO3-) and its lithium ion pairs and aggregates[END_REF] added LiT in various solutions showing different polarizability (2-methyltetrahydrofuran and PPO trimer). They attributed the small changes in the resonance frequency to different states of the lithium triflate anion. These frequencies are reported in Table 30. The aggregation of triflate salts shifts resonance bands to higher frequencies. The observed frequency of the S = O bond depends whether the triflate interacts with one or more Li + , disregarding the fact that the Li + interacts with one, two or three carbonyls.

Free T-

Ion pair LiT

Aggregates - [START_REF] Huang | Molecular structures and normal vibrations of trifluoromethane sulfonate (CF3SO3-) and its lithium ion pairs and aggregates[END_REF] If we refer to this publication of Huang and Wheeler [START_REF] Huang | Molecular structures and normal vibrations of trifluoromethane sulfonate (CF3SO3-) and its lithium ion pairs and aggregates[END_REF], the two bands in our lithium systems at 1041 cm -1 and 1032 cm -1 correspond to the presence of ionic pairs LiT and free ions T -. Moreover, the band of the PMMA/LiT 90/10 mol/mol sample, broaden towards high frequencies means that some aggregates are present. Then according to the publication of Duong and Wheeler [START_REF] Dong | Molecular Dynamics Simulations and Vibrational Spectroscopic Studies of Local Structure in Tetraglyme:Sodium Triflate (CH3O(CH2CH2O)4CH3:NaCF3SO3) Solutions[END_REF], the population of ionic species in sodium systems corresponds to the presence of ionic pairs NaT at 1034 cm -1 .

It can be deduced from the 1040 cm -1 bands that LiT is better dissociated than NaT in PMMA: solvated free anions T -are observed by infrared spectroscopy for lithium salts and not for sodium salts. The observation of T -suggests the presence of free Li + resulting from the full LiT dissociation. Li + can be solvated by up to 4 carbonyls from PMMA. On the contrary, Na + remains coordinated to the triflate anion in NaT pairs. Na + may interact with up to 4 carbonyls of PMMA to complete its coordination sphere to 6.

Then, the region between 1210 cm -1 and 1350 cm -1 is observed and reported in Figure 126. The neat LiT possesses bands at 1247 cm -1 and 1290 cm -1 and the neat NaT at 1230 cm -1 and 1254 cm -1 , corresponding to the asymmetric stretching of CF3 and to the asymmetric stretching of SO3 respectively. Unfortunately, these bands are overlapped with those corresponding to the C-O stretching of PMMA at 1237 cm -1 and at 1268 cm -1 , making the analysis difficult. The intensity of these bands increases with the ion content. The lithium samples display an additional band at 1300 cm -1 that is present neither for the neat salt nor for the neat PMMA. According to Huang and Wheeler [START_REF] Huang | Molecular structures and normal vibrations of trifluoromethane sulfonate (CF3SO3-) and its lithium ion pairs and aggregates[END_REF], this band corresponds to aggregates of LiT. It specifies the analysis made above for the band at 1040 cm -1 , all lithium samples have some aggregated ionic salts.

Figure 126 : ATR spectra of PMMA / triflate salts blends with increasing ion content. The dashed lines are the ATR spectra of the neat ionic salts. Bands at 1270 cm -1 correspond to the asymmetric stretching of the SO3 and the band at 1224 cm -1 at asymmetric stretching of CF3.

To conclude on infrared spectroscopy analysis performed at 23 °C, different populations of ionic species are observed in PMMA/triflate salts blends:

-in lithium samples, free anions T -, ionic pairs LiT and some aggregates are identified.

The presence of free anion T -suggests the presence of free cations Li + , increasing the interactions with the carbonyls of PMMA. The aggregated species are present in larger quantities in samples containing 10 % mol of LiT, as the band is broader.

-Only one population is observed in sodium samples corresponding to ionic pairs NaT.

The literature allows us to explain the possible structures in which the ionic species identified by IR spectroscopy are involved, and to present an interpretation about the relationship between the evolution of the microstructure with ion content and temperature, with respect to the mechanical properties.

V.2.2.2 Relationship between the microscopic interactions and the mechanical properties

In a later paper, Hyun and Wheeler [START_REF] Hyun | Molecular Dynamics Simulations and Spectroscopic Studies of Amorphous Tetraglyme (CH3O(CH2CH2O)4CH3) and Tetraglyme:LiCF3SO3 Structures[END_REF] studied an amorphous tetraglyme (H₃CO(CH₂CH₂O)₄CH₃)/LiT blends with an ether O:Li + ratio of 10:1, by molecular dynamics simulations and IR spectroscopy, at 300 K and 400 K. The tetraglyme is used to simulate the behavior of LiT in PEO. They found that, -the population of ion pairs LiT decreases as temperature increases while populations of Li2T + and Li3T 2+ aggregates grow. Structures are shown in Figure 127.

-For the ion pair LiT, two geometries of cation-anion associations were detected. The bidentate geometry predominates at both temperatures (300 K and 400 K), but the monodentate mode fraction increases upon increasing the temperature. Thus, at higher temperatures, the monodenticity allows to accommodate more bridges between two triflate ions in Li2T + and Li3T 2+ complexes, contributing to create bigger aggregating structures. The evolution of the structure of ionic species is shown in Figure 127.

In these aggregates, other structures are possible such as LiT2 -and LiT3 2-(Figure 127).

In the article of Frech [START_REF] Frech | Ionic Transport in Polymer Electrolytes: The Essential Role of Associated Ionic Species[END_REF], they specified that the triple anion LiT2 -is unfortunately not detectable by IR spectroscopy since the T -in the ion pair LiT and in the triple anion LiT2 -vibrate at the same frequency. In a same way, we expect that the ionic species LiT3 2-is not detectable.

Figure 127 : Associated ionic species of lithium triflate (LiT), determined by IR spectroscopy and molecular dynamic simulations in tetraglyme, at low and high temperatures, by Wheeler. The denticity of the ligand with the lithium cation is monodentate or bidentate, according to Wheeler [START_REF] Huang | Molecular structures and normal vibrations of trifluoromethane sulfonate (CF3SO3-) and its lithium ion pairs and aggregates[END_REF], [START_REF] Hyun | Molecular Dynamics Simulations and Spectroscopic Studies of Amorphous Tetraglyme (CH3O(CH2CH2O)4CH3) and Tetraglyme:LiCF3SO3 Structures[END_REF].

The unlinked bonds of the cation are involved with oxygen atoms of the tetraglyme, or with oxygen atoms from triflate anion in bigger ionic associations at high temperatures.

As a reminder, the notation of ionic species includes only triflate anions, which are in the first coordination sphere of the cation. Some of the triflate anions or cations in these species are coordinated to other anions or cations, and therefore exist as part of bigger ionic aggregates rather than as isolated species.

Then, Dong and Wheeler [START_REF] Dong | Molecular Dynamics Simulations and Vibrational Spectroscopic Studies of Local Structure in Tetraglyme:Sodium Triflate (CH3O(CH2CH2O)4CH3:NaCF3SO3) Solutions[END_REF] studied, in the same way as their previous article tetraglyme (H₃CO(CH₂CH₂O)₄CH₃)/NaT blends with an ether O:Na + ratio of 10:1 by molecular dynamics and IR spectroscopy at 300 K and 400 K. They found that:

-as with LiT, aggregation is promoted upon increasing the temperature. The band ratios indicate the presence of mainly free ions (42%) and ion pairs (40%) at 300 K and of more aggregated species at 400 K. The aggregated species Na2T + fraction increases from 15 % to 38 % and the aggregated fraction of NaT3 2-increases from 3 % to 13 %.

-Unlike with Li + , the bidentate coordination of Na + by the triflate remains favorable at higher temperatures (contrary to the monodentate and tridentate coordination for the lithium). For Na + coordinated to 2 triflate anions in NaT2 -, a double-bidentate geometry in which the Na + bridges 4 oxygen atoms, 2 from each triflate anion, is favored at the higher temperatures. In NaT3 2-, cation-anion association through monobi-bidentate and bi-bi-bidentate geometries becomes more prominent with increasing temperature. The evolution of the structure of ionic species is shown in Figure 128. The denticity of the ligand with the sodium cation is bidentate, according to Wheeler [START_REF] Dong | Molecular Dynamics Simulations and Vibrational Spectroscopic Studies of Local Structure in Tetraglyme:Sodium Triflate (CH3O(CH2CH2O)4CH3:NaCF3SO3) Solutions[END_REF]. The unlinked bonds of the cation are involved with oxygen atoms of the tetraglyme, or with oxygen atoms from triflate anion in bigger ionic associations at high temperatures.

Thus, from our observations on the IR spectroscopy and Wheeler's data [START_REF] Dong | Molecular Dynamics Simulations and Vibrational Spectroscopic Studies of Local Structure in Tetraglyme:Sodium Triflate (CH3O(CH2CH2O)4CH3:NaCF3SO3) Solutions[END_REF], [START_REF] Huang | Molecular structures and normal vibrations of trifluoromethane sulfonate (CF3SO3-) and its lithium ion pairs and aggregates[END_REF], [START_REF] Hyun | Molecular Dynamics Simulations and Spectroscopic Studies of Amorphous Tetraglyme (CH3O(CH2CH2O)4CH3) and Tetraglyme:LiCF3SO3 Structures[END_REF], our mechanical results for lithium and sodium systems are interpreted as follows:

-The Tg increased linearly with ion content due to the creation of many ionic interchain bonds. As a consequence, the brittle to ductile transition temperature TBD is increased.

The brittleness, the Young modulus and the stiffness are increased at low temperatures (23 °C -40 ° C). At higher temperatures, and notably just above the TBD, the plastic flow stress is increased as compared to neat PMMA. This is observed between 50 °C and 80 °C for PMMA / LiT 95/5 mol/mol for example.

-When introduced in the polymers, triflate salts are either solubilized and fully dispersed along the PMMA chains, either partially dissociated. We propose that the ratio of the fully dispersed salts is higher at low ion content than at high ion content (10 % mol). It is suggested that the fraction of undissociated salts, present in samples at 10 % mol of salts, plasticized the modified PMMA. Furthermore, the plasticizing effect may be not linear with ion content [START_REF] Mathis | Controlling the Morphology in Epoxy/Thermoplastic Systems[END_REF]. Upon increasing temperatures, or ion content, the ratio of undissociated species increases, increasing the plasticizing effect. As a consequence, the properties of PMMA / triflate salts blends are deteriorated with respect to neat PMMA at high temperature, and even more for the high ion content of 10 % mol of ionic salts.

These interpretations are illustrated in Figure 129 for the lithium systems and in Figure 130 for the sodium systems.

V.3 Conclusion

In this chapter, mechanical properties of PMMA containing 3 % to 10 % mol of lithium and sodium triflate salts have been studied. The brittle to ductile transition temperature TBD increases with ion content, from approximatively 40 °C around to 60 °C, mainly due to a Tg effect (as Tg increased linearly with the ion content). While at low temperatures, the brittleness and the stiffness are enhanced with the ion content, at the beginning of the ductile regime, the plastic properties (yield stress and flow stress) are improved with 3 % and 5 % mol of ionic salts. But with 10 % mol of triflate salts, there is an abrupt transition with a low plastic modulus and properties are deteriorated. It is suggested that the microstructure evolves with the ion content and the temperature.

In PMMA / LiT blends, at low ion content, and at 23 °C, free triflate anions T -, ionic pairs

LiT and some aggregates are identified by IR spectroscopy. LiT are the predominant species.

The presence of T -suggests the presence of fully dissociated Li + interacting with PMMA. This is favorable to increase the mechanical properties. In PMMA / NaT blends, only the ionic pairs NaT was identified. This ionic pairs also interact with the carbonyls of PMMA, for the sodium to complete its coordination sphere.

The lithium cation creates stronger interactions than the sodium cation (Coulomb's law).

The brittle behavior at low temperatures and the plastic properties at high temperatures show the largest modification with lithium.

According to the literature, upon increasing temperatures, aggregates are created (with species such as Li2T + , Li3T 2+ , LiT2 -, LiT3 2-or Na2T + , NaT2 -, NaT3 2-). The cations are interacting preferentially with oxygen atoms from the triflate anions instead of oxygen atoms from PMMA.

So the apparition of bigger associated species reduce the possibility for the lithium or for the sodium cation to interact with the polymer matrix. Moreover, highly associated species may plasticize the system. When introduced in the PMMA, ionic salts are either fully dissociated, either partially associated. It is proposed that, upon increasing ion content or/and temperatures, the ratio of partially associated species increased, and that their plasticizing effect are not linear with the ion content. As a consequence, mechanical properties are deteriorated at high temperatures, and with 10 % mol of ionic salts.

These results highlight the potential of ionic salts to improve the properties of amorphous polymers such as PMMA. For this purpose, the full dissociation of the ionic salts is required, in order to optimize the number of interactions that the cation can make with the matrix. The ability of the ionic salt to be dissociated in the matrix could be modified by changing the anion, with a bigger size (Coulomb's law) for example. It would be interesting to perform vibrational infrared spectroscopy at higher temperatures in order to check the structures of ionic species present in the matrix. Moreover, it would be also interesting to made electronic microscopy to observe the evolution of damages with the ion content and the temperature.

The second type of ionic pendant groups is lithium, sodium or potassium carboxylates.

They were introduced at 1.6 % and 11.4 % mol in PMMA-co-PMAA copolymer of Mw = 34 kg/mol and 235 kg/mol. They allow to increase the Tg of PMMA, up to + 9 °C with 3.3 % of PMALi for example. The viscoelastic behavior is also modified with an extension of the rubbery plateau, in the order of 1 decade per mol of ion. This is explained by the fact that there is one or more stickers per entanglement and that the sticker lifetime is longer than the Rouse time between entanglements (τs > τe).

Finally, ionic sulfonate and carboxylate pendant groups exhibit associative behavior.

They build clusters of strong interactions and long lifetimes. It results in an extension of the rubbery plateau and an increased viscosity. The sticker activation energies were calculated from the extension of the rubbery plateau (and not from the shift of the monomer time). It is in the order of 107 to 125 kJ/mol for NaSPS and 107 to 116 kJ/mol for the PMAX moieties (X = Li, Na, K). Note that, as the synthesis conditions of our PMMA containing carboxylate moieties need to be developed, only small quantities of materials were available. As a result, it was not possible to characterize the mechanical properties of these samples.

Even if the processability may be difficult, the creation of clusters allows the properties to be improved, such as in the PS-co-PMANa of Eisenberg or in our PMMA-co-PMANa where the Tg is increased. Some studies [START_REF] Chen | Ionomer dynamics and the sticky Rouse model[END_REF], [START_REF] Martins | Effect of intermolecular interactions on the viscoelastic behavior of unentangled polyamide melts[END_REF], underline the potential of sulfonate and carboxylate moieties to improve the mechanical properties, by changing the damage mechanism from crazes to shear bands. Clusters may stabilize the growth of crazes, delaying the failure of samples.

Finally, the dielectric constant of the polymer matrix is the first indicator for determining the behavior of ionic moieties. If it is low, the ionic moieties may lead to an associative behavior, while if it is high to a dissociative behavior. In both cases, the Tg may be increased, either by the presence of clusters, either by the presence of many interchain ionic interactions.

A second strong parameter is the comparison between the molecular weight between stickers and between entanglements. Me and Ms determine the extension of the rubbery plateau. For example, the rubbery plateau lenght is increased with increasing ion content. A reptation time delayed to high temperatures (low frequencies) lead to potential difficulties for processing the material.

Polymers/ionic salts blends Another way to add ionic interchain bridges is to directly mix ionic salts in the PMMA matrix. Ionic salts were introduced by solvent casting and by melt extrusion. A good dispersion state has to be achieved. The solubility of the anion is important and the nature of the cation also: for small cation size higher interactions are achieved as a consequence of Coulomb's law.

PMMA / ionic triflate salts blends of lithium and sodium were studies. The Tg of PMMA increases linearly with the ion content. The viscoelastic properties were analyzed. Contrary to random ionic copolymers, the plateau is not extended, but narrowed. Ionic salts reduce chain entanglements by a dilution effect. The non-extension of the rubbery plateau is interesting from a processing point a view because it allows for the reduction of the processing temperature. The mechanical properties of PMMA /triflate salts blends at different temperatures were studied.

At low temperatures the brittleness increases with increasing ion content. At higher temperatures, the toughness increases above the onset of the ductile regime (just after TBD). The mechanical behavior is improved with an ion content between 3 % and 5 % mol and deteriorated at 10 % mol. We identify a domain for mechanical properties improvement in the temperature-ion content phase space.

We proposed that the ionic microstructure evolves with the ion content. At 23 °C, the IR spectroscopy shows the presence of free anions T -in PMMA / LiT blends but not in PMMA / NaT blends. The lithium salts are better solvated in the matrix than sodium salts. Ionic pairs of LiT or NaT are also identified as well as some aggregates for LiT. Upon increasing the ion content, salts create bigger aggregates. These aggregates saturate the environment of the lithium or sodium cation: their coordination sphere are composed mainly of oxygen atoms from the triflate anion. It reduces the possibility to create ionic interchain bonds between PMMA chains. Upon increasing the temperature, these same aggregates appear in larger quantity, even for the low ion content. With 10 % of salts, the properties decrease rapidly upon increasing the temperature. It is proposed that the ratio of partially associated species is predominant on the dissociated species, and that they show a non-linear plasticizing effect, decreasing the mechanical properties.

In all these cases, the lithium cation creates stronger interactions with the PMMA matrix due to its higher charge to radius ratio. A more polarizable matrix is required such as PEO for the use of sodium or even potassium cations. Note that the main limitation of lithium salts is its sensitivity to humidity. As a result, they may plasticize materials.

Perspectives

In perspective, for the random ionic copolymers studied, we propose that it would be interesting to added higher ion content of NaSPS and PMAX pendant groups, up to 10 % mol.

As PMMA has an intermediate polarizability (larger than PS), a higher ion content is required to create similar clusters as in PS for example. A key point is to use anionic synthetized PMMA to have a better thermal stability, as the terminal zone is delayed and the viscosity is increased with ion content. It would be interesting to use lithium groups, to increase the interaction strength. Then, it would be interesting to evaluate the damage mechanism of these systems upon deformation by electronic microscopy and by X-rays analysis. The main goal would be to investigate if the creation of ionic clusters allows to stabilize the crazes.

Concerning the PMMA / LiT blends, the optimized ratio of ionic salts, between 4 % and 8 % mol could be systematically investigated in order to explore the full range of possibilities for improvement of PMMA plastic properties. Mechanical properties after physical ageing under wet atmosphere are necessary since lithium salts are sensible to moisture. To investigate further the properties of PMMA/ ionic triflate salts blends, it would be interesting to perform IR spectroscopy at high temperature to identify quantitatively the presence of the ionic species, or also solid state NMR studies for probing other bonds, in particular those of the cations. As with random ionic copolymers, it would be interesting to investigate the damage mechanisms by electron microscopy and X-rays analysis, to see if the addition of ionic salts in PMMA is a way to control the evolution of damages leading to early failure of polymers. In PMMA / ionic salts blends, a full dispersion and dissociation of the salts is more efficient in improving the mechanical properties. For that, it is possible to explore other anion and cation types, varying their sizes and the dissociation ability of the salt.

V. 3 α

 3 Abbreviations

Figure 2 :

 2 Figure 2 : Polymer chain conformations with different tacticities, adapted from[START_REF] Forte | Is poly(Methyl methacrylate) (PMMA) a suitable substrate for ALD?: A review[END_REF]

Figure 4 :Figure 5 :Figure 6 :Figure 7 :

 4567 Figure 4 : Thermal decomposition of PMMA according to its synthesis mode, under inert atmosphere

Figure 8 :

 8 Figure 8 : Molecular relaxations of PMMA, from[START_REF] Ionita | Viscoelastic behavior of PMMA in relation to deformation mode[END_REF]

Figure 11 :

 11 Figure 11 : Phase shift δ between the applied stress and the measured strain

Figure 14 :

 14 Figure 14 : Typical master curve of entangled polymers, with τrep the reptation time, τe the Rouse relaxation time between entanglements and τ0 the monomer relaxation time.

  by entanglements. Chains create a complex topological constraints schematized by a tube around the one first chain. The tube model describes the one dimensional mobility of a long polymer chain which diffuses along the tube. Relaxation movements along the tube are called reptation as illustrated in Figure 15.

Figure 15 :

 15 Figure 15 : Reptation of polymer chain along a tube. (a) Formation of a loop at the extremity of the chain, (b) propagation of the loop, (c) resulting displacement of the chain from the left to the right of the tube, from [43].

  Influence of the molecular weightThe main parameter controlling the rheological behavior is the molecular weight. It has a strong influence on the length of the rubbery plateau and the zero shear viscosity η0. They both increase when the molecular weight increase. The critical molecular weight Mc is directly linked with Me. Mc can be described as the minimum molecular weight required for a temporary network structure to exist due to the topological constraints created by surrounding chains. Mc is generally slightly larger than Me. At a given temperature, and below a critical molecular weight Mc, η0 increases linearly with M, while above Mc, it increases like M 3,4 (Figure16).

Figure 16 :

 16 Figure 16 : Relationship between the molecular weight Mw and the melt viscosity η0. The change in the slope define the critical molecular weight Mc.

Figure 17 :

 17 Figure 17 : VGP plot of polystyrene of various molecular weights, used to determine the plateau modulus at the minimum of the phase angle δ = f(G*)=f(, from[START_REF] Trinkle | Van Gurp-Palmen-plot: a way to characterize polydispersity of linear polymers[END_REF]

Figure 18 :

 18 Figure 18 : Typical stress -strain curve of a ductile amorphous polymer under tensile or compressive stress

Figure 22 :

 22 Figure 22 : Damage mechanisms of PMMA under tensile stress with: a) Pre-existing impurities, b) Heterogeneous nucleation of cavities, c) The craze growth is blocked by the local strain hardening of the polymer, d-e) Homogeneous nucleation ahead the craze, f) Failure of the specimen when a craze reaches a critical growth rate, from[START_REF] Djukic | Study of Damage Mechanisms of Amorphous and Low Semicrystalline Polymers under Tensile Deformation by Ultrasmall-Angle X-ray Scattering[END_REF]

Figure 23 :

 23 Figure 23 : Change in the micromechanical deformation structures in different cyclic olefin copolymers in relation to cyclic monomer type and content with transition from brittle to ductile behavior, revealed by TEM. The deformation direction is perpendicular and propagation of thedeformation zones is from the left to the right, from[START_REF] Michler | Electron Microscopy of Polymers[END_REF]

Figure 24 :

 24 Figure 24 : Basic interactions in associative polymers with chemical covalent bonds and physical bonds (ionic interactions, hydrogen bonds, hydrophobic interactions and π-π stacking), from[START_REF] Zhang | Dynamics of associative polymers[END_REF]

Figure 26 :

 26 Figure 26 : Mobility restricted region around a multiplet in poly(styrene-co-sodium methacrylate)ionomer, from[START_REF] Eisenberg | A new multiplet-cluster model for the morphology of random ionomers[END_REF]

  corresponding relaxation time is τe = τs(Me 2 /Ms 2 ), and the corresponding reptation time is τrep = τe(M/Me) 3 = τs(M 3 /(MeMs 2 )), which is the same expression as in the first case.In this case, though, a double plateau is observed. The first plateau modulus is GN 0 = ρRT/(1/Me + 1/Ms) the second plateau modulus is the standard GN 0 = ρRT/Me.

Figure 27 :

 27 Figure 27 : Evolution of the storage modulus G' as a function of frequency ω for a linear chain with entanglements (black), and linear chains with stickers and entanglements: Ms > Me (blue line) andMs > Me (red line). The sticker relaxation time τs is much longer than the Rouse time between entanglement τe, from[START_REF] Zhang | Dynamics of associative polymers[END_REF]

Figure 28 :

 28 Figure 28 : Pseudo master curve G' and G" of lithium sulfonate polystyrene (LiSPS) with 4.8 % mol ion, containing 2 stickers/chain, Mw = 4 kg/mol, Ms < Me, adapted from[START_REF] Weiss | Rheological behavior of oligomeric ionomers[END_REF]

Figure 29 :

 29 Figure 29 : General scheme of the ion hopping process allowing melting flow of ionomers, from[START_REF] Vanhoorne | Low-Shear Melt Rheology of Partially-Neutralized Ethylene-Methacrylic Acid Ionomers[END_REF]

Figure 30 :

 30 Figure 30 : G' and G" master curves obtained as function of frequency for PEO and PTMO samples with increasing ionic salts content: (a) PE0600-xNa, and (b) PTMO650-xNa, x indicating the ionic fraction, Tref = 20°C, with model prediction (dark line) from [1].

Figure 31 :

 31 Figure 31 : (a) G' and (b) G" master curves of 4.8 % sulfonate polystyrene with various alkali metal salts (Li, Na, K, Rb, Cs), Tref = Tg + 45 °C, (c) SAXS curves of the corresponding sample (intensitywere not normalized with the electron density contrast), from[START_REF] Weiss | Rheological behavior of oligomeric ionomers[END_REF]

Figure 32 :Figure 33 :I. 3 . 4 . 5

 3233345 Figure 32 : Stress -strain curves of PC, and PC containing 5%wt of LiClO4 or m-terphenyl (m-tPh),from[START_REF] Sako | Modulus enhancement of polycarbonate by addition of lithium perchlorate[END_REF]

( 1 H

 1 NMR, SEC, ATR, SAXS, WAXS…), thermal (TGA, DSC), thermodynamical (DMA, melt rheology…) and mechanical characterizations (tension and compression) are detailed.

Figure 34 :II. 1 MaterialsII. 1 . 1 II. 1 . 1 . 1

 34111111 Figure 34 : a. PMMA-co-NaSPS, b. PMMA-co-PMAX with X=Li, Na, K

Figure 35 :

 35 Figure 35 : Chemical structure of PMMA-co-NaSPS

Figure 36 :

 36 Figure 36 : Reaction of the radical polymerization of PMMA-co-NaSPS

Figure 37 :

 37 Figure 37 : Reaction of the radical polymerization of PMMA

Figure 38 :

 38 Figure 38: Reaction of neutralization of acid functions of PMMA-co-PMAA into PMMA-co-PMAX, with X = Li, Na, K

  MeOH. After 3 h of magnetic stirring, the salts solution was added slowly into the PMMA solution. The final proportion was MEK/MeOH 80/20 wt/wt, with a polymer/solvent ratio of 10/90 wt/wt. The solution was stirred at room temperature overnight before being casted into cylindrical teflon molds of 10 cm in diameter. Solvents evaporated at room temperature at least for 3 days, then at 70 °C for 24 h in vacuum oven, and finally at 130 °C for another 24 h in vacuum oven to complete evaporation of residual solvents. The final thickness of the disk obtain was around 150 μm. The solvent casting method is shown in Figure40.

Figure 40 :

 40 Figure 40 : Schematic illustration of the solvent casting process for the formulation of PMMA with ionic salts

Figure 42 :

 42 Figure 42 : Schematic illustration of the injection molding process

  been dried 12 h at 70 °C. Prior to extrusion, samples were pre-conditioned in individual flasks containing 4.5 g of PMMA and the corresponding amount of ionic salts with dry-mixing, in order to facilitate the insertion and limit the moisture absorption. Flasks were dried overnight at 50 °C in a vacuum oven and sealed under nitrogen atmosphere. The extrusion was performed at 230 °C, with a speed of 200 to 250 rpm. The residence time for the polymer in the device was between 2 min and 5 min.

Figure 43 :

 43 Figure 43 : Extrusion chamber of the micro-compounder Thermo Scientist HAAKE Minilab II Rheometer CTW5, with two interpenetrating co-rotating screws, a recirculation channel and a bypass valve.

Figure 44 :

 44 Figure 44 : Micro injection molding machine HAAKE Minijet Pro

  Injections molding were made by the IPC (Industrial Technical Center of Plastics and Composites, Oyonnax, France) with an electric Fanuc 15T equipped with a 16 mm diameter screw. Pellets were introduced in the sleeve with the help of a dosing device. The screw delivered the pellets to the injection head at a speed of 60 rpm, and with an increasing temperature profile from 215 to 230 °C. The cycle time was 18 s. The injection head moves forward at 50 mm/s to bring the material into the mold and maintains a pressure of 250 bars for 4 s. The mold temperature is 50 °C. After the injection molding, samples were dried during 12 h at 70 °C and stored in hermetic bags.

  SEC analyses were performed using a GPC PL Lab 120 device equipped with four Agilent PLgel Mixed C columns in series and a refractive index detector (RID) (Solvay RICL, Analytical Laboratory, A. Siot, N. Delon-Anik). Columns were calibrated with PMMA standards of narrow polydispersity. Samples were dissolved in DMF with the addition of 5 % wt of lithium bromide (LiBr) to complete dissolution of the functionalized polymer. Toluene was used as internal flow marker. All samples were analyzed with a flow rate of 0.7 mL/min. Results were expressed in PMMA equivalent.

Figure 47 :

 47 Figure 47 : Schematic illustration of the SEC principle

Figure 48 :

 48 Figure 48 : Schematic illustration of a potentiometric titration. Left: experimental set up. Right: Evolution of the pH as a function of the volume of titrant added (purple) with the determination of the equivalent volume VE by the derivative method (orange).

First, the

  concentration of carboxylate functions COO -(carboxylic acid function COOH, neutralized with X = Li, Na, K) was measured by direct determination with HCL 0.1 mol/L.

Figure 49 :

 49 Figure 49 : Schematic illustration of the ATR principle

  setups are described in Figure51. They consist of an X-rays source, which creates a beam of a specific wavelength λ, and devices which focus the rays. The beam goes through the sample and is scattered. A detector placed behind the sample records the intensity of the scattered beam as a function of the scattering angle.Since d is inversely proportional to θ, the larger the angle θ, the smaller the detected distance d between crystal planes. The range of scanned angles is chosen by varying the distance between the sample and the detector. Wide angle X-ray scattering (WAXS) are commonly used to analyze the sample crystalline structure thanks to Bragg peaks. In our study, it is used to check salts crystallinity and the possible aggregation in the PMMA matrices. Small angle Xray scattering (SAXS) is used to probe structures from the nanometer to the micrometer scale by measuring the intensity of the scattered beam at small q values (close to θ = 0°).

Figure 51 :

 51 Figure 51 : Schematic illustration of the X-ray test bench with WAXS and SAXS positions

II. 3 . 2 . 1

 321 Thermogravimetry (TGA) Thermogravimetric analysis (TGA) measures the change in weight of a sample as a function of time and temperature. Weight changes are caused by the material decomposition, oxidation reactions or physical changes (evaporation of water or residual solvent, desorption...).

Figure 52 :

 52 Figure 52 : Schematic illustration of the TGA principle

  The glass transition temperatures Tg was determined on a TA Instruments Q2000 at a heating rate of 10 °C/min in a standard mode at Solvay RICL. A Rapid Cooling System with a N2 flow of 50 mL/min was used. Non-hermetic aluminum pans were filled with 5 -10 mg of polymer samples. A Heat / Cool / Heat cycle was carried out from 35 °C to 200 °C. The first heating ramp allows to erase the history of the sample (physical or thermal ageing, process).The glass transition Tg can be identified by a step in the heat flow curve. Tg was determined during the second heating cycle thanks to the tangent method.

Figure 53 :

 53 Figure 53 : Schematic illustration of the DSC principle

  Time sweeps were first run to check the thermal stability of samples. They were performed during 1 h, at 1 Hz and at a temperature below the degradation of the sample (usually at T = Td -10 °C). Then, strain sweeps were performed from Tg + 10 °C to Tg + 100 °C (or up to the degradation temperature Td -10 °C), by steps of 10 °C in order to identify the limit of the linear regime of deformation. Frequency sweeps were performed in the linear viscoelastic regime, at a constant temperature, from 100 rad/s to 0.1 rad/s. The test procedure of frequency sweeps on a sample is explained in Figure54and detailed as follows: a) Frequency sweeps were performed first at the reference temperature Tref. b) Then, they were performed at temperatures lower than Tref, decreasing temperatures by steps of 10 °C until Tg + 10 °C. c) Then, the test at Tref was repeated. d) Frequency sweeps were performed at temperatures higher than Tref, increasing temperatures by steps of 10 °C until Td -10 °C. e) A final frequency sweep was made at Tref to check the stability of the sample.This method has been adapted from Martins et al.[START_REF] De | Effect of intermolecular interactions on the viscoelastic behavior of polyamides[END_REF]. Each measurement was performed twice to ensure reproducibility.

Figure 54 :

 54 Figure54: Temperature sequence used for the rheological measurements, adapted from[START_REF] De | Effect of intermolecular interactions on the viscoelastic behavior of polyamides[END_REF]

20 mm x 4

 4 mm x 2 mm were cut from tensile specimens. Experiments were carried out in the linear behavior, with a strain of amplitude 0.01 %, by applying a temperature sweep from -50 °C to 130 °C, at 2 °C/min, and at the frequency of 1 Hz. The chosen frequency of 1 Hz allowed to compare the α-relaxation temperature Tα with the Tg measured in DSC.

Figure 55 :II. 3 . 5 . 1

 55351 Figure 55 : Temperature sweep of PMMA (Mw = 100 kg/mol from Polysciences) in DMTA at 1 Hz, 0.01 %. The α-and β-molecular relaxations are identified.

  A video system called Imetrum was used as a non-contact extensometer. Specimens, represented in Figure56, has a dimension described by the ISO527-2-5A standard. Samples were dried 12 h at 60 °C in vacuum prior to experiments and stored in hermetic bags. Two points were drawn at an initial distance of l0 = 30 mm. The evolution of the length l between the 2 points was measured during the applied deformation by a camera from the extensometer Imetrum. Tensile tests were performed at various temperatures from 23 °C to 90 °C, at RH = 50%, at a nominal strain rate of = 10 -3 s -1 . For each test, the specimens were set up between the two jaws in the oven 15 min for reaching thermal equilibrium. A pre-load of 1 to 2 N was applied. Nominal stress -true strain curves were obtained. Five tests are performed for each sample.

Figure 56 :

 56 Figure 56 : Tensile specimen submitted to an uniaxial tensile force F. S0 is the initial section of the sample, l the length of the sample and l0 is the initial length of the sample.

Figure 57 :

 57 Figure 57 : Picture of the installation of the Zwick / Roell Z020 equipped with an oven and Imetrum.

Figure 58 :

 58 Figure 58 : Compression specimen submitted to a compression force F. l is the sample thickness and l0 the initial sample thickness.

III. 1

 1 systems are prepared from commercially available PMMA by Solvay, containing at 1.6 % mol and 11.4 % mol of carboxylic acid moieties. Acid functions were neutralized with alkali metal cations. The influence of ionic moieties on the PMMA properties are analyzed. The thermal stability and the glass transition temperature are determined. The rheological properties are measured, in particular, the activation energy of ionic associations. Then, when it was feasible experimentally, mechanical properties were measured. Various ionic moieties, cations, molecular weights, and ion contents are studied. The influence of the strength of ionic associations are compared. Effect of the introduction of sodium styrene sulfonate moieties III.1.1 Chemical structure Four entangled poly (methyl methacrylate-co-sodium styrene sulfonate) (PMMA-co-NaSPS) were synthetized (see the section II.1.1.1 for more details). For that, ionic stickers of sodium styrene sulfonate (NaSPS) were introduced onto a PMMA backbone, with two ion contents (1.5 and 3 % mol) and two molecular weights (Mw = 60 kg/mol and 200 kg/mol). The polydispersity is close to 2. The chemical structure is shown in Figure 59 and reported in

Figure 60 :Figure 61 :

 6061 Figure 60 : Thermal degradation profile of low molecular weight PMMA and PMMA-co-NaSPS (Mw = 60 kg/mol), with increasing ion contents from 0 to 3 % mol, under N2 at 10 °C/min

Figure 62 in

 62 Figure 62 in the region of 170 to 190 °C (see Chapter I.1.5 for more details). As a consequence, DSC experiments measure lower Tg due to the presence of solvent trapped within the complexes. These complexes can be removed by a drying method at high temperature. Thus to be well dried from residual solvents (presence of DMSO from polymerization), polymers are cryo-ground and dried at temperature close to Tg at 120 °C for 36 h under vacuum.

Figure 62 :

 62 Figure 62 : DSC thermograms of PMMA-co-NaSPS 200k 3%, dried for 24 h at 80 °C under vacuum. The presence of an endotherm observed at 178 °C is characteristic of the presence of a stereocomplex. Heat / Cool / Heat temperature ramps from 35 °C to 200 °C at 10 °C/min, under N2.

DMTA.

  The α-relaxation temperature Tα of PMMA corresponds to the moment where the storage modulus E' drops in the glassy to rubber transition region. It is reflected in the tan δ curve by a peak in the temperature domain from 40 °C to 140 °C for neat PMMA, depending on tacticity. A second smaller peak is observable in tan δ, corresponding to the β-relaxation temperature Tβ. It occurs in the temperature domain of -43 °C to 33 °C and is related to the motion of the side group of PMMA containing the carbonyl function. So Tα and Tβ are taken as the peak maximum of the tan δ curves.

Figure 63 :Table 12 :III. 1 . 5 . 1

 6312151 Figure 63 : Tan δ as function of temperature of PMMA and PMMA-co-NaSPS of (a) low molecular weight samples (Mw = 60 kg/mol) and (b) high molecular weight samples (Mw = 130 to 200 kg/mol), at 1 Hz

Figure 64 :

 64 Figure 64 : Master curves on the G' and G" moduli of PMMA with increasing molecular weights, Tref = 150 °C

Figure 65 :Figure 66 : 36 )

 656636 Figure 65 : Dependence of the horizontal shift factor aT of the WLF law with temperature for PMMA with increasing molecular weights, points are experimental data, lines are WLF fits, Tref = 150 °C

Figure 67 :

 67 Figure 67 : (a) Evolution of the length of the rubbery plateau as function of the molecular weight of PMMA (b) Evolution of the zero shear viscosity η0 as function of the molecular weight of PMMA.

  moieties. Master curves regarding the frequency dependence of G' and G" of PMMA with increasing ion content are shown in Figure 68 and Figure 69. The evolution of tan δ as a function of frequency is displayed in Figure 70 and Figure 71. NaSPS moieties lead to a shift of master curves to lower frequencies, proportionally to the shift of the Rouse time between entanglements τe. A key feature is that the length of the rubbery plateau is extended by 4 decades with 3 % mol of NaSPS for low molecular weight samples, and by 3 decades for the high molecular weight samples. The increase of the plateau length is larger for the low molecular weight ionic PMMA's in Figure 68 than for the large molecular weight ionic PMMA's in Figure 69. The plateau is not a real plateau but since the modulus displays a slow decreasing value towards lower frequencies. The terminal regime cannot be reached, indicating that the degradation of polymers occurs at temperatures (between 165 and 224 °C, Section III.1.2) at which the ionic interactions are still effective.

Figure 68 :Figure 69 :Figure 70 :Figure 71 :Figure 72 :Figure 73 :

 686970717273 Figure 68 : Master curves of low molecular weight PMMA and PMMA-co-NaSPS (Mw = 60 kg/mol) with increasing ion content from 0 to 3 % mol, at Tref = 150 °C

Figure 74 :

 74 Figure 74 : Approximation of the zero-shear viscosity η0 a function of the ion content for PMMA and PMMA-co-NaSPS

Figure 75 :Figure 76 :

 7576 Figure 75 : Dependence of the monomeric relaxation time τ0 with temperature, for low molecular weight PMMA-co-NaSPS (Mw = 60 kg/mol), Tref = 150 °C

Figure 77 :

 77 Figure 77 : Evolution of the activation energy of stickers Eas with temperature of low molecular weight PMMA-co-NaSPS (Mw = 60 kg/mol), determined from the application of the Arrhenius law from the shift of τ0

Figure 78 :

 78 Figure 78 : Evolution of the activation energy of stickers Eas with temperature of high molecular weight PMMA-co-NaSPS (Mw = 200 kg/mol), determined from the application of the Arrhenius law from the shift of τ0

  PMMA -co -NaSPS 200k 1.5% 6.3 x 10 5 * 3,2 x 10 1* 1.1 x 10 -1 117* PMMA -co -NaSPS 200k 3% 1.6 x 10 6 * 2,2 x 10 1* 2.6 x 10 -1

  2.1). The thermocompression was made with a 100 mm x 100 mm x 1.5 mm imprint and a cycle at 150 °C during 7 min. By applying a lower temperature than in extrusion for a longer time, the polymer was able to flow. Resulting sheets are shown in Figure 80. Sheets were cut with a Charlyrobot device as shown in Figure 81. Due to the high brittleness of the low molecular weight samples, many tensile specimen broke directly during the cutting.

Figure 80 :Figure 81 :

 8081 Figure 80 : Pictures of thermocompressed sheets of PMMA and PMMA-co-NaSPS

Table 16 :Figure 82 :

 1682 Figure 82 : Nominal strain -nominal stress curves of PMMA-co-NaSPS in compression tests at = 2.10 -3 s -1 and T = 23 °C

Figure 83 :

 83 Figure 83 : True strain -nominal stress curves of PMMA-co-NaSPS in tension at = 1.10 -3 s -1 and T = 90 °C, preload 1 N, 5 mm/min

  25 %), yield stress and elongation at break of PMMA-co-NaSPS in tension at = 1.10 -3 s -1 and T = 90 °C, preload 1 N, 5 mm/min III.1.8 Partial conclusion The influence of sodium styrene sulfonates (NaSPS) on the PMMA properties was investigated with two molecular weight (Mw = 60 kg/mol and 200 kg/mol) and two ion content (1.5 % and 3 % mol). The Tg of PMMA is not significantly modified. Ionic interactions are strong and have long relaxation lifetime. As a consequence, there is an extension of the rubbery plateau by around 4 decades with 3 % mol of NaSPS. The delay of the terminal zone to higher temperatures is not benefit for the processability. The activation energy of ionic associations are determined from the extension of the rubbery plateau and are in the order of 105 to 125 kJ/mol. Ionic associations are stronger in polymers of low molecular weight and increase with the ion content. Mechanical properties are not modified in compression at 23 °C and deteriorated in tensile mode at 90 °C.

Figure 84 :

 84 Figure 84 : Chemical structure of PMMA-co-PMAX, with X = H, Li, Na, K

Figure 85 :

 85 Figure 85 : DSC curves of PMMA-co-PMAX % mol, with X = Li, Na, K and Mw = 235 kg/mol. 2nd ramp of the Heat / Cool / Heat cycle, 10 °C/min

Figure 86 :Figure 87 :Figure 88 :

 868788 Figure 86 : Master curves of PMMA-co-PMAX % mol, with X = Li, Na, K, Mw = 34 kg/mol, Tref = 150 °C

Figure 89 :

 89 Figure 89 : Dependence of the monomeric relaxation time τ0 with temperature, Tref = 150 °C

Figure 93 :

 93 Figure 93 : Chemical structures of ionic salts: a. sodium p-toluene sulfonate, b. sodium benzoate, c. sodium salicylate, d. sodium p-toluene sulfinate, e. lithium p-toluene sulfinate, f. lithium triflate, g. sodium triflate, h. potassium triflate

Figure 94 :

 94 Figure 94 : Picture of PMMA / ionic salts blend disks made by solvent casting, a. immiscible salts, b. immiscible salts but homogeneously dispersed, c. miscible salts

Figure 95 :

 95 Figure 95 : Evolution of the Tg of PMMA / alkali metal triflate salts blends, as a function of the ionic concentration and of the cation nature (---dash line are linear fits)

First, the thermal

  degradation is measured by TGA and the glass transition temperature Tg by DSC. It is observed that the presence of salts has no impact on the degradation profile and on the Tg of PMMA. The degradation onset temperature Td is close to 370 °C (one step of degradation). Tg is unchanged and remains equal to 109 °C for all systems. This fact is checked by DMTA with a temperature sweep at 1 Hz. The α-and β-relaxations are unchanged with the addition of pTsNa. The viscoelastic moduli G' and G" are measured by melt rheology and are shown in Figure 96. The time-temperature superposition curves are built in order to obtain the corresponding WLF laws. It is observed that with increasing ion content, moduli are slightly increased in all frequency regimes.

Figure 96 :

 96 Figure 96 : Master curves on the moduli G' and G" of PMMA / pTsNa blends, Tref = 150 °C

Above 40 %

 40 mol of salts, films are very brittle. He highlights the fact that at the limit of solubility, the molar ratio of lithium to the carbonyl groups was almost close to 1. There are no data in the literature about the Tg of NaT blended with PMMA. Sodium create weaker interactions with PMMA than lithium.

Figure 98 :

 98 Figure 98 : Evolution of the Tg of PMMA / alkali metal triflate salt blends, as function of the ionic concentration and of the cation nature (---dash line are linear fits)

Figure 99 :

 99 Figure 99 : Water uptake over 15 days in PMMA /alkali metal triflate salt blends, under air, at T = 23 °C and RH 50 %, with a zoom in the first 1 h

Figure 100 :

 100 Figure 100 : Temperature dependence of the storage elastic moduli E', loss elastic moduli E'' and loss tangent (tan δ) for PMMA / triflate salts blends 90/10 mol/mol, at 1 Hz. Influence of the cation.

Figure 101 :

 101 Figure 101 : Master curves of PMMA / alkali metal triflate salt blends, at Tref = 170 °C. Influence of the cation.

Figure 102 :Table 27 :Figure 103 .

 10227103 Figure 102 : Evolution of the zero shear viscosity η0 with the ion content in PMMA / alkali metal triflate salt blends. Influence of the cation.

Figure 103 :

 103 Figure 103 : Evolution of the monomer relaxation times τ0 with temperature for PMMA / alkali metal triflate salt blends. Tref = 170 °C. Influence of the ion content.

Figure 104 :

 104 Figure 104 : WAXS diffractograms of PMMA / alkali metal triflate salts blends 90/10 mol/mol

Figure 105 :

 105 Figure 105 : FTIR-ATR spectra, focused on a band attributed to the symmetric stretching of the carbonyl function of PMMA C=O in PMMA / alkali metal triflate salts 90/10 mol/mol. The intensity was normalized with respect to the band at 1720 cm -1 .

Figure 106 :

 106 Figure 106 : Interchain interaction between the lithium or sodium cation of the triflate salt and the carbonyl of the PMMA polymer chain, with X + = Li + or Na +

. 1 . 1

 11 Tensile behavior of neat PMMA Stress -strain curves of the reference PMMA (Polysciences, Mw = 100 kg/mol) are plotted in Figure 107 at each temperature. The Young's modulus, the yield stress and the elongation at break are plotted in Figure 108 as a function of temperature. As expected [126], the behavior of PMMA is brittle at 23 °C. The measured Young's modulus is in the order of 3,3 GPa, in

Figure 107 :Figure 108 : 2 V. 1 . 2 . 1

 1071082121 Figure 107 : True strain -engineering stress curves of PMMA as function of temperature from 23 °C to 80 °C in uniaxial tensile tests at a strain rate of 10 -3 s -1 .

Figure 109 :

 109 Figure 109 : True strain -engineering stress curves of PMMA/LiT 97/3 mol/mol as compared to neat PMMA, at 23 °C, 60 °C and 80 °C in uniaxial tensile tests at a strain rate of 10 -3 s -1 .

Figure 110 :

 110 Figure 110 : True strain -engineering stress curves of PMMA/LiT 95/5 as compared to neat PMMA, at 23 °C, 60 °C and 80 °C in uniaxial tensile tests at a strain rate of 10 -3 s -1 .

Figure 111 :

 111 Figure 111 : True strain -engineering stress curves of PMMA/LiT 90/10 mol/mol as compared to neat PMMA, at 23 °C, 60 °C and 80 °C in uniaxial tensile tests at a strain rate of 10 -3 s -1 .

Figure 112 :V. 1 . 2 . 2

 112122 Figure 112 : Comparison of the plastic properties (yield stress) as a function of the temperature and ion content in PMMA/LiT blends. The green area highlights the parameters with improved yield stress as compared to neat PMMA.

Figure 113 :

 113 Figure 113: True strain -engineering stress curves of PMMA/NaT 97/3 mol/mol as compared to neat PMMA, at 23 °C, 60 °C and 80 °C in uniaxial tensile tests at a strain rate of 10 -3 s -1 .

Figure 114 :

 114 Figure 114 : True strain -engineering stress curves of PMMA/NaT 95/5 mol/mol as compared to neat PMMA, at 23 °C, 60 °C and 80 °C in tensile tests at a strain rate of 10 -3 s -1 .

Figure 115 :

 115 Figure 115 : True strain -engineering stress curves of PMMA/NaT 90/10 mol/mol as compared to neat PMMA, at 23 °C, 60 °C and 80 °C in uniaxial tensile tests at a strain rate of 10 -3 s -1 .

Figure 116 :V. 1 . 2 . 3

 116123 Figure 116 : Comparison of the plastic properties (yield stress) as a function of the temperature and ionic content in PMMA / NaT blends. The green area highlights the parameters with improved yield stress as compared to neat PMMA.

Figure 117 :

 117 Figure 117 : Evolution of the Young's modulus of PMMA/ionic triflate salts blends according to the temperature Tα -T, from tensile test at 10 -3 s -1 . Tα was measured by DMTA at 1 Hz. Dashed lines are linear fits.

Figure 118 :

 118 Figure 118 : Evolution of the yield stress of PMMA/ionic triflate salts blends according to the temperature Tα -T, from tensile test at 10 -3 s -1 . Tα was measured by DMTA at 1 Hz. Dashed lines are linear fits.

Figure 119 :V. 2 . 1 . 3

 119213 Figure119: Denticity of a sulfonate anion, X + is the metal cation, adapted from[START_REF] Côté | The supramolecular chemistry of the sulfonate group in extended solids[END_REF]

Figure 120 :

 120 Figure 120 : Structures of ionic species of lithium triflate salts (arbitrarily in a bidentate mode)

Figure 121 :

 121 Figure 121 : Structures of ionic species of sodium triflate salts (arbitrarily in a bidentate mode)

Figure 122 :

 122 Figure 122 : Possible structures of ionic species of lithium and sodium triflate salts (LiT and NaT) in PMMA, according to various dissociation states

Figure 125 :

 125 Figure 125 : FTIR-ATR spectra of PMMA / triflate salts blends with increasing ion content. The dashed line is the ATR spectrum of the neat ionic salts. Bands at 1040 cm -1 correspond to the symmetric stretching S=O of the SO3 group.

Figure 128 :

 128 Figure 128 : Associated ionic species of sodium triflate (NaT), determined by IR spectroscopy and molecular dynamics simulations in tetraglyme and present at low and high temperatures by Wheeler.The denticity of the ligand with the sodium cation is bidentate, according to Wheeler[START_REF] Dong | Molecular Dynamics Simulations and Vibrational Spectroscopic Studies of Local Structure in Tetraglyme:Sodium Triflate (CH3O(CH2CH2O)4CH3:NaCF3SO3) Solutions[END_REF]. The unlinked bonds of the cation are involved with oxygen atoms of the tetraglyme, or with oxygen atoms from triflate anion in bigger ionic associations at high temperatures.

Figure 129 :

 129 Figure 129 : Interpretations on the evolution of the structure of ionic species in our PMMA/LiT blends with temperature and ion content.

Figure 130 :

 130 Figure 130 : Interpretations on the evolution of the structure of ionic species in our PMMA/NaT blends with temperature and ion content.

Figure 133 :

 133 Figure 133 : Master curves of PMMA / LiT blends, at Tref = 170°C. Influence of the ion content.

Figure 134 :

 134 Figure 134 : Master curves of PMMA / NaT blends, at Tref = 170°C. Influence of the ion content.

Figure 135 :

 135 Figure 135 : Stress -strain curves of PMMA / triflate salts blends. The temperature is fixed, from 23 °C to 80 °C, with steps of 10 °C. The ion content increases. The strain rate is 10 -3 s -1 .

Figure 136 :

 136 Figure 136 : Stress -strain curves of PMMA / triflate salts blends. The temperature varies from 23 °C to 80 °C, with steps of 10 °C. The ion content is fixed. The strain rate is 10 -3 s -1

properties PMMA PS PC SAN PVC

	Elongation at break (%)	2-10	1-4	50-100	1-3	20-85
	Tensile strength (MPa)	48-76	30-60	60-70	40-80	45-60
	Tensile modulus (GPa)	3.1	3.3	2.4	3.6	3.0

Table 1 :

 1 Basic mechanical properties of amorphous polymer[START_REF] Mark | Polymer Data Handbook[END_REF]

PS SAN PMMA PC

	Elongation at break (%)	1-4	1-3	2-10	50-100
	Tensile strength (MPa)	30-60	40-80	48-76	60-70
	Me	19100	11600	9150	3490
	νe (μm 3 )	3.10 7	6.10 7	8.10 7	29.10 7
	d (nm)	9.6	8.2	7.3	4.4
	Deformation structure	Fibrillar	Coexistence	Coexistence	Homogeneous
	Table 2: Comparison of entanglement molecular weight Me, entanglement density ve, entanglement
	distance and typical deformation for various amorphous polymer from [16], [75]

Table 4 ,

 4 with particular interest on the molten and solid states properties.

	Polymers + salts	Tg	Main observations	Ref
		°C
	PMMA + 7 % mol LiCF3SO3, LiBr	127 to 137 with LiCF3SO3 127 to 133 with LiBr	No change in the overall shape of the TTS τe shifted to lower ω	Ito, Nitta [99]
	PMMA + 0 -72 % mol LiCF3SO3	105 to 120 with 7 % mol 105 to 180 with 50 % mol	η0 increased rapidly No change in the overall τe shifted to lower ω shape of the TTS	Yamaguchi [104]
	PEO + 0 -7 % mol LiCF3SO3	-66 to -60	E and σy decreased in tensile loading at 23 °C	Pumchusak [92]
	PLA + 0 -10 % mol LiCF3SO3	65 to 72	E and σy increased in tensile loading at 23°C, εrupt decreased from 340 to 5 %	Yamaguchi [113]
	PC + 0 -11.6 % mol LiClO4	152°C unchanged	E and toughness, increased, as well as flow stress from 50 to 55 MPa with 6%	Sako, Yamaguchi [112]
	PEO + 0 -20 % mol LiCF3SO3, LiBF4	-	E decreased, from 332 to 23 MPa with 20 % mol of LiCF3SO3

Table 5 :

 5 General properties of the synthetized PMMA and PMMA-co-NaSPS with the molecular weights Mn, Mw and polydispersity PD measured by SEC. The tacticity is measured by1 H NMR.

Table 6 :

 6 commercials PMMA are used as reference materials for the formulation with ionic salts. We characterized their basic properties. The measured molecular weight differs from that expected for the PMMA from Acros Organics. Properties are reported in Table8.

	System	Ion content	Ratio MAX/MMA	Mn	Mw	PD Tacticity
		%mol		kg/mol kg/mol		i:a:s
	Reference
	PMMA -co -PMAA	11.4
	Samples
	PMMA -co -PMALi	12.2	1:9	127	235	1.8	4:37:59
	PMMA -co -PMNa	10.8
	PMMA -co -PMAK	1.14
	Table 7 : General properties of PMMA-co-PMAX, X = acid, Li, Na, K of high ion content
	(11.4 % mol) and high molecular weight (Mw = 235 kg/mol), with the molecular weights Mn, Mw and
	polydispersity PD measured by SEC. The tacticity is measured by 1 H NMR.

General properties of PMMA-co-PMAX, X = acid, Li, Na, K of low ion content (1.6 % mol) and low molecular weight (Mw = 34 kg/mol), with the molecular weights Mn, Mw and polydispersity PD measured by SEC. The tacticity is measured by

1

H NMR.

Two

Table 8 :

 8 General properties of commercial PMMA, with the molecular weights Mn, Mw and polydispersity PD measured by SEC. The tacticity is measured by 1 H NMR. The glass transition temperature Tg is measured by DSC and the onset thermal degradation temperature Td is measured by TGA under N2.

II.1.3 PMMA / ionic salts blends

Various ionic salts were chosen to be blended with PMMA. Lithium triflate (purity > 98 %), sodium triflate (> 98 %), potassium triflate (> 98%) and lithium p-toluene sulfinate (97 %) are purchased from Sigma Aldrich. Sodium salicylate (> 99%), sodium p-toluene sulfonate (95 %) and sodium p-toluene sulfinate (97 %) are purchased from Acros Organics.

Sodium benzoate (99 %) is purchased from Alfa Aesar. Salts are used as received. Structures are shown in Figure

39

. PMMA / ionic salt blends are made by solvent casting or by melt extrusion with the commercial PMMAs described in Table

8

. Figure 39 : Chemical structures of ionic salts: a. sodium p-toluene sulfonate, b. sodium benzoate, c. sodium salicylate, d. sodium p-toluene sulfinate, e. lithium p-toluene sulfinate, f. lithium triflate, g. sodium triflate, h. potassium triflate II.2 Processing II.2.1 Thermocompression PMMA-co-NaSPS samples (detailed above in section in II.1.1) were thermo-compressed to prepare tensile and compressive specimens. During a thermocompression, pressure and temperature are maintained for a specific time on the sample which has been preconditioned in a mold. Pellets or powder flow into the mold and adopt the corresponding shape. A cooling process is finally applied.

Table 9 :

 9 Attribution of the IR characteristic bands of PMMA (Polysciences), from[START_REF] Charvet | Damage Mechanisms of Plasticized Cellulose Acetate under Tensile Deformation Studied by Ultrasmall-Angle X-ray Scattering[END_REF],[START_REF] Djukic | Study of Damage Mechanisms of Amorphous and Low Semicrystalline Polymers under Tensile Deformation by Ultrasmall-Angle X-ray Scattering[END_REF]

II.3.1.6 X-rays scattering (WAXS, SAXS)

Table 10

 10

	System	Ions/chain	Mn	Mw	PD
	% mol		kg/mol kg/mol
	PMMA 60k	-	27	55	2.0
	PMMA -co -NaSPS 60k 1.5%	4	27	54	2.0
	PMMA -co -NaSPS 60k 3%	9	31	60	1.9
	PMMA 130k	-	48	136	2.8
	PMMA 200k	-	94	197	2.1
	PMMA -co -NaSPS 200k 1.5%	12	79	203	2.6
	PMMA -co -NaSPS 200k 3%	17	58	197	3.4

for each sample.

Figure 59 : Chemical structure of PMMA-co-NaSPS

Table 10 :

 10

Chemical structure of PMMA and PMMA-co-NaSPS. Molecular weights were determined by SEC.

Table 11 :

 11 Tacticity and glass transition temperature of PMMA and PMMA-co-NaSPS, measured by

	Tacticity	Tg

1 H NMR and DSC

Table 13 :

 13 Rheological parameters of PMMA with increasing molecular weights, Tref = 150 °C

		C1	C2	GN 0			η0
			K -1	Pa	s	s	Pa.s	kg/mol
	PMMA 60k	4.6	75.9	5.3 x 10 5	2.2 x 10 1 4.9 x 10 -2 1.4 x 10 6	7.8
	PMMA 130k	5.1	76.9	5.3 x 10 5	6.6 x 10 2 3.7 x 10 -2 3.5 x 10 7	7.8
	PMMA 200k	7.5	119.7	4.4 x 10 5	3.1 x 10 3 2.8 x 10 -2 5.3 x 10 7	9.5
	III.1.5.2 Influence of ionic associations in ionic PMMA
	We consider here the viscoelasticity of PMMA containing sodium styrene sulfonate

Table 14 :

 14

	System	C1	C2	GN 0				η0
	% mol		K -1	Pa		s	s	Pa.s
	PMMA 60k	4.6	75.9	5.3 x 10 5	2.2 x 10 1	4.9 x 10 -2	1.4 x 10 6
	PMMA -co -NaSPS 60k 1.5%	8.2	80.7	5.5 x 10 5	3.7 x 10 2	6.3 x 10 -2	7.4 x 10 6
	PMMA -co -NaSPS 60k 3%	9.5	110.6	4.7 x 10 5	6.3 x 10 5 *	1.5 x 10 1	9.3 x 10 9 *
	PMMA 130k	5.1	76.9	5.4 x 10 5	6.6 x 10 2	3.7 x 10 -2	3.5 x 10 7
	PMMA 200k	7.5	119.7	4.4 x 10 5	3.1 x 10 3	2.7 x 10 -2	5.3 x 10 7
	PMMA -co -NaSPS 200k 1.5%	13.5	175.8	3.7 x 10 5	6.3 x 10 5 *	1.1 x 10 -1	8.4 x 10 8 *
	PMMA -co -NaSPS 200k 3%	15.9	196.6	4.7 x 10 5	1.6 x 10 6 *	2.6 x 10 -1	3.9 x 10 10 *
	System		Ion/chain	Ms	Me	Ion/ent
	% mol			kg/mol kg/mol
	PMMA 60k		-		-	7.8	-
	PMMA -co -NaSPS 60k 1.5%	4		6.7	-	1.2
	PMMA -co -NaSPS 60k 3%	9		3.3	-	2.4
	PMMA 130k		-		-	7.8	-
	PMMA 200k		-		-	9.5	-
	PMMA -co -NaSPS 200k 1.5%	12		6.7	-	1.4
	PMMA -co -NaSPS 200k 3%	17		3.3	-	2.9

Rheological parameters of PMMA and PMMA-co-NaSPS, Tref = 150 °C (* estimations of the last crossover modulus, not reached due to thermal degradation of the sample)

Table 17 :

 17 Young modulus (calculated with Imetrum between 0.05 % and 0.

	Sample	tests number	E	σy	εbreak
	% mol		MPa	MPa	%
	PMMA 60k	1	1956	-	1.2
	PMMA-co-NaSPS 1,5% 60k	2	1112	-	1.5
	PMMA 130k	4	1710	35	98.9
	PMMA-co-NaSPS 1,5% 200k	2	1717	33	43.3
	PMMA-co-NaSPS 3% 200k	3	1432	30	78.6

-3 s -1 and T = 90 °C, preload 1 N, 5 mm/min

Table 18 :

 18

	System	Ion / ent	Mn	Mw	PD
	% mol		kg/mol kg/mol
	Reference
	PMMA -co -PMAA 1.6%	0.9
	Samples
	PMMA -co -PMALi 3.3%	2.0	21	34	1.6
	PMMA -co -PMANa 0.5%	0.3
	PMMA -co -PMAK 1.5%	0.8
	System	Ion / ent	Mn	Mw	PD
	% mol		kg/mol	kg/mol
	Reference
	PMMA-co-PMAA 11.4%	15
	Samples
	PMMA-co-PMALi 12.2%	15	127	235	1,8
	PMMA-co-PMANa 10.8%	13
	PMMA-co-PMAK 1.1%	2

Chemical properties of PMMA-co-PMAX, X = H, Li, Na, K of low molecular weight and low ion content. Molecular weights are identical since samples are prepared from the same parent polymer, without chain modifications. The nominal value for the ionic content should be 1.6 % mol and they are observed at 3.3 % mol for Li, 0.5 % mol for Na and 1.5 % mol for K by ICP-AES.

Table 19 :

 19 Chemical properties of PMMA-co-PMAX, X = H, Li, Na, K of high molecular weight and high ion content. Molecular weights are identical since samples are prepared from the same parent

polymer, without chain modifications. The nominal value for the ionic content should be 11.4 % mol and they are observed at 12.2 % mol for Li, 10.8 % mol for Na and 1.1 % mol for K by ICP-AES.

Table 20 :

 20 [START_REF] Fernández-Garcia | Solvent effects on the free-radical polymerization of methyl methacrylate[END_REF] Glass transition temperature of PMMA-co-PMAX, with X = Li, Na, K and Mw = 34 kg/mol and tacticity of 5:40:55

	Samples
	PMMA -co -PMALi 3.3%	125
	PMMA -co -PMANa 0.5%	122
	PMMA -co -PMAK 1.5%	124
	System	Tg
	Ion %mol	°C
	Reference
	PMMA-co-PMAA 11.4%	133
	Samples
	PMMA-co-PMALi 12.2%	152
	PMMA-co-PMANa 10.8%	138
	PMMA-co-PMAK 1.1%	145

Table 21 :

 21

Glass transition temperature of PMMA-co-PMAX, with X = Li, Na, K, and Mw = 235 kg/mol and tacticity of 4:37

:59

Table 22 :

 22

	PMMA -co -PMANa 0.5%	7.5	83.3	7.7 x 10 5	3.1 x 10 1	3.6 x 10 -1 6.6 x 10 6
	PMMA -co -PMAK 1.5%	13.4 159.4 6.0 x 10 5	4.8 x 10 2	3.8 x 10 -1 4.6 x 10 7
	System		Ion/chain	Ion/ent	Me	Ms
	Ion % mol					kg/mol kg/mol
	Reference
	PMMA -co -PMAA 1.6%		3.4		0.9	5.9	6.2
	Samples
	PMMA -co -PMALi 3.3%		6.9		2.0	3.0
	PMMA -co -PMANa 0.5%		1.2		0.3	17.9
	PMMA -co -PMAK 1.5%		2.9		0.8	7.14

Rheological parameters of PMMA-co-PMAX, X = Li, Na, K, Mw = 34 kg/mol, Tref = 150 °C

Table 23 :

 23 Activation energy of stickers in PMMA-co-PMAX, with X = Li, Na, K and Mw = 34kg/mol, calculated from the extension of the rubbery plateau As previously discussed with the sulfonates (Section III.1.5.3), we can compare this activation energy of stickers with those of the systems studied by Chen and Colby[START_REF] Chen | Ionomer dynamics and the sticky Rouse model[END_REF] and of Weiss[START_REF] Weiss | Viscoelastic Behavior of Very Lightly Sulfonated Polystyrene Ionomers[END_REF],[START_REF] Weiss | Rheological behavior of oligomeric ionomers[END_REF]. They used the same method of the extension of the plateau, but with the monomer time τ0 instead of the ballistic time τb in the equation. They found an activation energy for sodium phthalate sulfonate stickers in PEO of 14 kJ/mol and of 58 kJ/mol in PTMO. The activation energy of sodium styrene sulfonate in PS is ~65 kJ/mol. With their method, our Eas would be found to be in the order of 34 to 42 kJ/mol. Regarding the polarisability of the

		τrep	τs	τe	Eas
	Ion % mol	s	s	s	kJ/mol
	PMMA -co -PMALi 3.3%	1.5 x 10 4	2.0 x 10 1	5.0 x 10 -1	116
	PMMA -co -PMANa 0.5%	3.1 x 10 1	1.5 x 10 0	3.6 x 10 -1	107
	PMMA -co -PMAK 1.5%	4.8 x 10 2	3.7 x 10 0	3.8 x 10 -1	110

matrices (2.5 for PS, 2.5 for PTMO, ~ 10 for PEO and 3.3 for PMMA) and as the polarisability of the matrix reduce Eas, our activation energy are, as expected, between the one of PEO and the one of PTMO and PS. Note that we compared here with carboxylate moieties with sulfonate moieties values.

III.2.5 Partial conclusion

PMMA containing lithium, sodium and potassium carboxylate moieties (PMAX, X = Li, Na, K) were studied. The acid salification reaction was sometimes not total, so the ion content differs between samples. A matrix of low ion content and low molecular weight energy is in the order of 110 kJ/mol.

Table 25 :

 25 Miscibility of ionic salts with PMMA blended by solvent casting or by extrusion techniques.

			Miscibility	Miscibility
			by solvent casting	by melt extrusion
		% mol
	Sodium p-toluene sulfonate	1-5	+ at 3 % mol -at 5 % mol	-
	Sodium benzoate	1-3	+/-	-
	Sodium salicylate	1-3	-	-
	Sodium p-toluene sulfinate	1-3	-	-
	Lithium p-toluene sulfinate	1-3	-	-
	Lithium triflate	1-30	+	+
	Sodium triflate	1-15	-	+
	Potassium triflate	1-10	-	+

(+) transparent matrix, (-) presence of aggregates of salts (+/-) matrix homogeneously white.

2 PMMA / sodium p-toluene sulfonate salt blends

  Sodium p-toluene sulfonate (pTsNa) was blended with PMMA by a discontinuous extrusion process on a laboratory device, at 1.5 % and 3 % mol (conditions are detailed in the Chapter II.2.2.). The PMMA used is from Acros Organics with Mw = 90 kg/mol. The extrudate is homogeneously white. It suggests that salts are dispersed but not solvated in PMMA. Tensile specimens are prepared by injection molding.

Table 26 :

 26 α-and β relaxation temperatures of PMMA / alkali metal triflate salt blends, obtained by DMTA with temperature sweeps tests at 1 Hz. tan δ peaks are fitted with a Gaussian function.

	Samples	Tα	Tβ
		°C	°C
	PMMA	104.3	16.8
	PMMA / LiT 97/3 mol/mol	113.0	13.0
	PMMA / LiT 95/5 mol/mol	117.5	11.0
	PMMA / LiT 90/10 mol/mol	126.8	6.7
	PMMA / NaT 97/3 mol/mol	105.7	16.0
	PMMA / NaT 95/5 mol/mol	109.3	10.5
	PMMA / NaT 90/10 mol/mol	112.3	5.5

Table 28 :

 28 Binding energy of the triflate salts: influence of the cation radius, determined with the Coulomb's law (U(r) = e²/4πε0εr, cation and anion charges are +1e and -1e respectively (e is the elementary charge)), the anion size value is from[START_REF] Ito | Enhancement of the glass transition temperature of poly(methyl methacrylate) by salt[END_REF]

	Salts	a+	a-	U	Binding energy
		nm	nm	J	kJ/mol
	LiT	0.073	0.230	2.3 x10 -19	153
	NaT	0.102	0.230	2.1 x10 -19	139
	KT	0.151	0.230	1.8 x10 -19	122

  ~ 3), but PC is ductile at room temperature. Here again, the complexation of the lithium cation with the carbonyl of PC is observed by FTIR. The Tg of PC is close to 152 °C and unaffected by the introduction of LiClO4. The Young's modulus increases at 25 °C with 6 % mol of LiClO4 from 1820 MPa to 1980 MPa, and the toughness increases from 30 to 33 MPa[START_REF] Weiss | Viscoelastic Behavior of Very Lightly Sulfonated Polystyrene Ionomers[END_REF]. The elongation at break is unchanged. Like our results with PMMA, there is Complexed Na + usually exhibit coordination numbers varying between 5 and 7[START_REF] Dong | Molecular Dynamics Simulations and Vibrational Spectroscopic Studies of Local Structure in Tetraglyme:Sodium Triflate (CH3O(CH2CH2O)4CH3:NaCF3SO3) Solutions[END_REF],

	introduced lithium perchlorate (LiClO4) into
	poly(carbonate) (PC). Both PMMA and PC are amorphous and have comparable dielectric
	constant (ε

Table 29 :

 29 Attribution of the resonance bands of the ATR spectra of lithium triflate salts (LiT) and sodium triflate salt (NaT) shown in Figure

Table 30 :

 30 IR resonance bands of the different ionic species of lithium triflate salts, determined by using solution of different polarisability, from

	Attribution

Remerciements

Chapter IV -PMMA / ionic salts blends

In this chapter, the properties of PMMA blended with ionic salts are discussed. First, a selection of salts likely to be soluble with PMMA is made. The solubility is investigated by solvent casting and melt extrusion (on a lab scale discontinuous extrusion process). Then, PMMA / ionic triflate salts systems are prepared in larger quantities with a continuous extrusion process) to prepare specimens for mechanical properties measurements (detailed later in Chapter V). The structure of the salt, the nature of the cation and the influence of the ion content are compared. The thermal and the viscoelastic properties are studied. The interactions between the ionic salts and the polymer matrix are characterized by infrared spectroscopy. During storage for a few weeks, an aggregation of salts was observed. Samples change from homogeneously white to a transparent matrix with white aggregates of salts exhibit a size of 0,1 to 1 mm. We conclude that pTsNa salts are definitively not soluble in PMMA. This is probably the reason why the glass transition temperature are unchanged and the viscoelastic properties only slightly modified. Such ionic groups, which are found insoluble, need to be grafted in order to modify the viscoelastic properties in a controllable way as in Chapter III.

IV.3 PMMA / alkali metal triflate salt blends

Lithium and sodium triflate salts (LiT and NaT) are blended with PMMA up to 10 % mol by melt extrusion on a larger device than that used for pTsNa. The process is described in Section II.2.3.

IV.3.1 Glass transition temperatures

The glass transition temperatures of triflate blends are reported as a function of ion content in Figure 98. As previously observed in the Section IV. when the ion content increases, a change in the ionic dispersion happen, reducing suddenly the mechanical properties. In a following section, we discuss the possible changes in salt dispersion at high ionic fraction.

V.2 Microstructure of ionic associations

Regarding the mechanical properties of PMMA / ionic triflate salts blends, several questions are raised. How do the ionic interactions evolve with temperature and ion content?

Can we understand the microscopic mechanism which controls the improvement of the plastic properties at low ion content in the ductile regime? What is the cause of the deterioration in plastic properties at high ionic concentration? Previous WAXS and SAXS analysis (Chapter IV.3.5.) revealed that ionic salts are well dispersed in PMMA even at 10 % mol. FTIR-ATR analysis at 23 °C proved that Li + and Na + cations interact with the carbonyls of the PMMA (Chapter IV.3.6).

The possible interactions between the cation, the anion and the PMMA will be detailed below. The identification of various states of ionic species will be discussed with the help of reference to the literature (coordination chemistry, electrostatic interactions) and with infrared analysis.

V.2.1 Coordination chemistry and structure of the ionic species

V.2.1.1 Coordination of the cation

Complexed Li + can exhibits coordination numbers varying from 2 to 8, but the most favorable coordination numbers are expected to be 4, 5, and 6. A tetrahedral geometry is adopted for a coordination number of 4, a square pyramidal for a coordination of 5 and an octahedral pyramidal for a coordination of 6 [START_REF] Olsher | Coordination chemistry of lithium ion: a crystal and molecular structure review[END_REF]. The coordination numbers of Li + in some complexes containing carboxylic acids are found to be 4, 5, and 6 [START_REF] Olsher | Coordination chemistry of lithium ion: a crystal and molecular structure review[END_REF].

General conclusion

The main objective of this PhD was to modify the PMMA properties with the introduction of strong ionic interactions. This study, dealing with the development of supramolecular polymers, was carried out in collaboration between Solvay and the CNRS. In this study, ionic salts were added within the polymer chains of PMMA by synthesis or by formulation. Ionic PMMAs were characterized in both molten and solid states. The strength of the ionic interactions was compared according to the structure of the anion, the nature of the cation, the ion content and the molecular weight of PMMA.

A preliminary work consisted in understanding the fundamental characteristics of PMMA. The synthesis conditions determine its degradation profile. The onset degradation temperature is generally above 300 °C for PMMA made by anionic polymerization while it is around 150 °C for PMMA made by radical polymerization. This predispose or not the ability of PMMA for processing. The synthesis conditions also determine the tacticity, which influences significantly the glass transition temperature. We detected the presence of stereocomplexes by DSC, which contained residual solvents. The drying method was therefore readapted to get rid of these complexes.

Random ionic copolymers

Two types of ionic pendant groups were added into the PMMA. First, sodium styrene sulfonate moieties (NaSPS) were introduced at 1.5 % and 3 % mol in PMMA chains of Mw = 60 kg/mol and 200 kg/mol. The Tg was not modified and in the order of 125 °C.

Nevertheless, the viscoelastic behavior was modified, with a rubbery plateau extended by 3 to 4 decades for all samples, exactly by 4 decades for the PMMA-co-NaSPS 3 % mol at Mw = 60 kg/mol. The larger plateau is explained by the fact that there is more than one sticker per entanglement and by the fact that the sticker lifetime is longer than the Rouse time between entanglements (τs > τe). Thus, sticker lifetime dominates the Rouse relaxation between entanglements and rescale the reptation process. As a consequence, viscosity is increased.

However, the mechanical properties of PMMA-co-NaSPS are not improved at 23°C in compression and the toughness is decreased at 90 °C in tensile tests.

Appendix -Chapter IV.