Benjamin Pomes

Emmanuel Richaud

Jean-Franc ¸ois Nguyen

REQUIREMENTS FOR SEVERAL KINDS OF MEDICAL APPLICATIONS

FIGURE 7.3 Some urethane dimethacrylate monomers. Macrofill (10-50 μm) Microfill (40-50 nm) Hybrid (10-50 μm + 40 nm) Midfill (1-10 μm + 40nm) Minifill (0.6-1 μm + 40 nm) Nanofill (5-100 nm) Microhybrid Nanohybrid Nanofill-cluster

A biomaterial is defined, according to the Consensus Conference of Chester (1992), as a material intended to interface with biological systems to evaluate, treat, increase, or replace any tissue, organ, or function of the body. According to the American National Institute of Health, a biomaterial is also described as "any substance or combination of substances, other than drugs, synthetic or natural in origin, which can be used for any period of time, which augments or replaces partially or totally any tissue, organ or function of the body, in order to maintain or improve the quality of life of the individual." Orthodontic brackets and surgical instruments are not included in this definition [START_REF] Bergmann | Dental Ceramics Microstructure, Properties and Degradation[END_REF].

All materials used for replacing human tissues have joint specifications such as biocompatibility and they must also be noncytotoxic, nonallergic, nonimmunogenic, nonthrombogenic, and noncarcinogenic. Their specifications depend on their applications. Biomaterials suitable for dental restoration applications should meet these requirements:

• Nonirritating for the pulp and periodontal tissues.

• Low volumetric variation.

• Thermal insulation to protect the pulp from temperature variations.

• Esthetic and the stability of the different shades.

• Possible and simple repair and replacement. • Easy handling.

• Resistance to water degradation and wear.

• Polishing ability to obtain a surface roughness limiting the adhesion of the plaque and thus to avoid secondary decay and periodontal diseases.

• Be compatible with sealing materials (bond, cement).

• Prevent leakage and saliva contamination and so dentinal hypersensitivity, coronary re-infection of the pulped tooth, secondary carious lesions and marginal dyschromias. • Have mechanical properties adapted to the type of restoration and ideally the closest to the dental tissues:

• Flexural strength greater than or equal to that of enamel ($380 MPa), and dentin (219 MPa). • Modulus of elasticity in the range of 90À98 GPa for enamel and 18À22 GPa for dentin. • Hardness Vickers in the range of ,300 HVN for enamel.

• Toughness in the range of 0.7À0.8 MPa m 1/2 for enamel, 2 MPa m 1/2 for dentin [START_REF] Xu | Indentation damage and mechanical properties of human enamel and dentin[END_REF].

CHEMISTRY OF POLYMETHACRYLATES AND THEIR COMPOSITES

7.2.1 MONOMERS

Methyl methacrylate

Polymethyl methacrylate (PMMA) is the most well-known polymer of the methacrylate family, obtained from the in-chain polymerization of methyl methacrylate. It was developed in the 1930s by Hill and Crawford for Imperial Chemical Industries in England (Perspex), by Ro ¨hm and Haas in Germany (Plexiglas), and by Du Pont de Nemours in the United States (Lucite). It displays several interesting properties such as:

• A higher light transmission than glass (92% of visible light).

• A low density (1.18 g cm 23 ) being about half that of glass.

• Shatter proof • Softer and easier to scratch than glass (however, scratch-resistant coatings may be applied).

Its first applications as aircraft windows took place during World War II. Medical applications came later and include:

• In cardiology in pacemakers.

• For ophthalmology as artificial eye lenses for cataract surgery.

• For prosthetic dentistry in removable total and partial dentures (Fig. 7.1), temporary fixed denture, and restorative dentistry and for orthodontic devices. • As bone cement for orthopedic surgery of the hip, knee, and other joints for the fixation of polymer or metallic prosthetic implants on living bone.

Other methacrylates for dental applications

In the 1950s, composite restorations were made from PMMA. Significant polymerization induced volume shrinkage and heat release as well as the release of methyl methacrylate monomers resulting in marginal discoloration, pulp reactions, and secondary caries. In 1956, Bowen tried to reduce shrinkage by using a bigger monomer: the bisphenol A surrounded by two glycidyl groups. However, moisture tended to inhibit polymerization. Bisphenol A glycidyl methacrylate (Bis-GMA, Fig. 7.2) was obtained by substituting end groups with methacrylate functions and offered an excellent solution to the problem [START_REF] Bowen | Dental Filing Material Comprising Vinyl Silane Treated Fused Silica and a Binder Consisting of the Reaction Product of Bis Phenol and Glycidyl Acrylate[END_REF][START_REF] Soderholm | BIS-GMA--based resins in dentistry: are they safe?[END_REF].

Bis-GMA has several advantages compared to PMMA, such as lower volatility, lower diffusion in dental tissues, and lower polymerization shrinkage because of its larger size, which explains its success. In addition, its tetrafunctional structure (i.e., two double bonds) makes it possible to obtain a crosslink network with better mechanical and physical properties.

However, Bis-GMA shows a high viscosity (1200 Pa s) (Barszczewska-Rybarek, 2009) because of its large size, and rigidity due to the two aromatic rings and especially its hydroxyl groups creating strong hydrogen intermolecular bonds between them which significantly reduces the mobility and make the molecule more hydrophilic. As it will be seen later, this involves a low conversion degree (DC)-39% in the case of photopolymerization and a limited incorporation of fillers as well as difficulty to handle the material [START_REF] Sideridou | Effect of chemical structure on degree of conversion in light-cured dimethacrylate-based dental resins[END_REF].

Consequently, Bis-GMA is always associated with minor monomers such as triethylene glycol dimethacrylate-TEGDMA, with a viscosity of 0.011 Pa s Removable total denture. [START_REF] Ilie | Resin composite restorative materials[END_REF][START_REF] Moszner | New developments of polymeric dental composites[END_REF]-or other derivatives such as bisphenol A ethoxyl dimethacrylate (Bis-EMA) (452 g mol 21 ) and bisphenol A propoxyl dimethacrylate Bis-PMA (480 g mol 21 ) and having a lower viscosity than Bis-GMA (because of its lower molar mass and the absence of hydroxyl groups).

UDMA monomers were developed in the 1970s by Forster and Walker (1974). Those UDMAs constitute a wide family of molecules differing by their molar mass and their structure (Fig. 7.3). The 1,6-bis(methacryloxy-2-ethoxycarbonylamino)-2,4,4-trimethylhexane is by far the most used and has a very low viscosity (23.1 Pa s) [START_REF] Barszczewska-Rybarek | StructureÀproperty relationships in dimethacrylate networks based on Bis-GMA, UDMA and TEGDMA[END_REF].

Composition of the matrix Monomers

Mixtures of several monomers are currently encountered in the literature for model and commercial materials. Usually, UDMA or Bis-GMA are used as major monomers together with minor monomers such as TEGDMA, HEMA, and bis-EMA for lowering the viscosity [START_REF] Ru ¨ttermann | Impact of replacing Bis-GMA and TEGDMA by other commercially available monomers on the properties of resin-based composites[END_REF][START_REF] Rahim | Water sorption characteristics of restorative dental composites immersed in acidic drinks[END_REF][START_REF] Aljabo | Conversion, shrinkage, water sorption, flexural strength and modulus of remineralizing dental composites[END_REF][START_REF] Bhamra | Influence of LED irradiance on flexural properties and Vickers hardness of resin-based composite materials[END_REF][START_REF] Thomaidis | Mechanical properties of contemporary composite resins and their interrelations[END_REF]. The use of minor monomers lowers viscosity which aims at incorporating more fillers to improve the mechanical properties, and to increase the conversion degree [START_REF] Floyd | Network structure of Bis-GMA-and UDMA-based resin systems[END_REF].

Activators and polymerization initiators

The initiation of the polymerization reaction requires the creation of radicals coming from, for example:

• For chemopolymerization: amines (para-amino methyl acetate, paratoluenesulphonic acids, thioureas, and ascorbic acids) and peroxides (benzoyl peroxide as shown in Scheme 7.1, cumene peroxide, and terbutyl hydroperoxide). • For photopolymerization: camphorquinone (Fig. 7.4) in combination with an aromatic amine. The camphorquinone displays an absorption in the range of 400À550 nm with a λ max at 470 nm [START_REF] Leprince | Progress in dimethacrylatebased dental composite technology and curing efficiency[END_REF] leading to radical generation, as illustrated in Scheme 7.2.

Polymerization inhibitors

Phenolic compounds react with free radicals and are used to avoid the possible spontaneous polymerization occurring during monomer storage.

Coupling agents

The coupling agent is an amphiphilic molecule bonding the hydrophilic inorganic filler and the hydrophobic resin. One of the most common molecules is 3-(Trimethoxysilyl)propyl methacrylate (Fig. 7.5).

DENTAL COMPOSITES

Composite material can be defined as a combination of two or more immiscible materials of different chemical natures, leading to better properties than those of the individual components used alone. They are constituted by a matrix and dispersed reinforcements. In the case of an organic matrix, the reinforcement is an inorganic solid (glass, ceramic, metal) in the form of fibers, particles, or flakes. The properties of the composite material depend on the filler volume fraction, shape factor (or length:diameter ratio), and orientation [START_REF] Kardos | Short-fiber-reinforced polymeric composites, structureÀproperty relations[END_REF]. The matrix allows the transmission of the mechanical stresses to the reinforcement, the protection of this later against the external environment, and determines the conditions of use and processing. Their composition has evolved since their introduction in odontology more than 50 years ago. Their clinical success would not have been possible without an understanding of the adhesion phenomena allowing their adhesion to dental tissues: enamel [START_REF] Buonocore | A simple method of increasing the acrylic filling materials to enamel surfaces[END_REF] and dentin [START_REF] Nakabayashi | Hybrid layer as a dentin-bonding mechanism[END_REF].

The inorganic fillers may be silicas (SiO 2 ) in crystalline form such as quartz, or in amorphous form such as borosilicate glass, or heavy metal (Sn, Ba) glasses. Their shape can be angular (obtained by grinding), rounded (obtained by melting), or square with rounded corners [START_REF] Raskin | Les re ´sines composites proprie ´te ´s et indications cliniques[END_REF]. Organomineral fillers are crushed prepolymerized composites and then added to the monomer/filler mixture, which makes it possible to reduce the shrinkage and to adapt the viscosity of the composite. Organoorganic fillers (trimethylolpropane trimethacrylate) and ceramics with grafted methacrylate groups (OrMoCers) [START_REF] Raskin | Les re ´sines composites proprie ´te ´s et indications cliniques[END_REF][START_REF] Raskin | Socie ´te ´Francophone de Biomate ´riaux Dentaires[END_REF] can also be used.

Composites can be classified according to the particle size and distribution of the fillers, the viscosity and the mode of polymerization, as dicussed next. 1. Macrofill: The first macrofill conventional composites presented 10À50 μm fillers, providing excellent mechanical properties, but difficulty in polishing and degradation at the surface by abrasion. 2. Microfill: microfill composites with 40À50 nm fillers were developed to overcome these disadvantages. They have good polishing properties, but low mechanical properties. 3. Hybrid: Hybrid composites are a mix of the particle sizes of the two previous families and, therefore, were used as a compromise between the mechanical, optical, and polishing properties. 4. Midfill: The tendency was then to reduce the size of the fillers to result in the hybrid midfill composites with charges of 1À10 μm and 40 nm. 5. Minifill: The evolution continued with the decrease in the size of the fillers with the minifill composites, with 0.6À1 μm and 40 nm filler, from which microhybrid composites were used for restorations in the anterior and posterior sectors. 6. Nanofill: The most recent innovations concern the development of nanofilled composites with 5À100 nm nanoparticules. However, this filler family has declined because of the difficulty of incorporating nanoparticles, the presence of numerous defects linked to the exponential increase of the matrix/fillers interface, and their high viscosity. To solve these problems, the nanofillers were partially sintered into nanoparticle aggregates (cluster) ranging from 5 to 75 nm in diameter [START_REF] O'brien | Dental Materials and Their Selection[END_REF].

Particle size and distribution of fillers

The size of filler particles incorporated into the resinous matrix of commercial dental composites tends to decrease over the years [START_REF] Ilie | Resin composite restorative materials[END_REF][START_REF] Ferracane | Resin composite À state of the art[END_REF]. Currently, microhybrid composites and nanohybrid composites (i.e., microhybrides with nanoparticles) are commercially available and display relatively close mechanical properties. Fiber-reinforced composites constitute a relatively new class of dental composites and are drawing increasing interest [START_REF] Ballo | Biocompatibility of fiber-reinforced composites for dental applications[END_REF].

Viscosity

According to Einstein's formula, spherical fillers lead to a viscosity increase given by: η 5 η 0 Uð1 1 2:5 3 φÞ (7.1)

η and η 0 being, respectively, the viscosity of filled and unfilled resin, and φ the filler ratio (in volume). Adding c. 50%À60% fillers by weight (i.e., 80% in volume) leads to viscosity almost 30-times higher than for base resin [START_REF] Papakonstantinou | Evaluation of UDMA's potential as a substitute for Bis-GMA in orthodontic adhesives[END_REF] and can reach more than 2000 Pa s.

Reactive mixtures for dental resin composites cover a wide range of viscosities which allow them to meet the requirements of numerous clinical indications. Fluid composites with low viscosity have 0.4À3 μm filler, a V f of 42%À53%, are packaged as syringes (Fig. 7.7), and indicated for cervical restorations or for low-tissue losses. The high viscosity condensable composites have V f of 66%À70% and are indicated for site tissue losses 1 and 2 [START_REF] Sakagushi | Craig's Restorative Dental Materials[END_REF].

Polymerization mode

The composites can also be classified according to their mode of polymerization: photopolymerization (Fig. 7.8), chemopolymerization, dual photo-and chemopolymerization and more recently high-pressure high-temperature polymerization for industrial composite blocks suitable for CADCAM applications, which are discussed further next (Fig. 7.9).

Photopolymerization is usually performed using lamps with 150À600 mW cm 22 irradiance, for 10À60 seconds durations. Photopolymerization of dental resin composites is performed using LED or halogen light curing units with, respectively, an emission peak in the 450À470 nm [START_REF] Issa | Effect of curing light emission spectrum on the nanohardness and elastic modulus of two bulk-fill resin composites[END_REF] and 450À520 nm [START_REF] Bala | Effect of LED and halogen light curing on polymerization of resin-based composites[END_REF] wavelength ranges. The emission spectra and characteristics of some commercial lamps can be found in [START_REF] Haenel | Effect of the irradiance distribution from light curing units on the local micro-hardness of the surface of dental resins[END_REF].

CAD/CAM applications suitable for the manufacture of dental restorations are currently being developed [START_REF] Van Noort | The future of dental devices is digital[END_REF][START_REF] Miyazaki | A review of dental CAD/CAM: current status and future perspectives from 20 years of experience[END_REF] because they obtain a constant quality. Chairside CAD/CAM can be used for prosthesis in dental surgery. In addition, blocks for CADCAM applications are manufactured industrially and so are more homogeneous and have fewer defects than handled materials.

Two types of blocks are currently commercially available: ceramic blocks and composite blocks. Ceramic blocks have superior mechanical properties and their chemical inertia which give them good biocompatibility. However, they are difficult to machine and cannot tolerate plastic deformations, which leads to the risk of fractures at the fine edges during the machining of the dental prosthesis. Thus, reoperation is more delicate. Composite blocks have lower mechanical properties, lower wear resistance and are less biocompatibile due to residual monomer release from incomplete polymerization. Nevertheless, they are easier to set on dental tissues and reoperation is easier. They also have better machinability and polishability. Indeed, the use of composite resin blocks designs for CAD/CAM significantly reduces the machining time and tool wear [START_REF] Mainjot | From artisanal to CAD-CAM blocks: state of the art of indirect composites[END_REF].

New technologies have been developed on polymerization and the methods for producing the blocks in order to increase the mechanical properties of the composites and to increase their strength, longevity, and biocompatibility.

Conventional thermopolymerization and photopolymerization have the disadvantage of being incomplete resulting in a low degree of conversion (56%À67%) FIGURE 7.9

Polymer infiltrated ceramic network block suitable for CADCAM. [START_REF] Ferracane | Wear and marginal breakdown of composites with various degrees of cure[END_REF]. Moreover, it induces internal stresses in the composite resulting from the shrinkage and the differential polymerization between the superficial part close to the source of irradiation and the deeper part [START_REF] Ferracane | Developing a more complete understanding of stresses produced in dental composites during polymerization[END_REF].

To improve the mechanical properties of a composite, the polymerization mode can be enhanced. A previous study has shown that high temperature (180 C) and high pressure (250 MPa) polymerization allowed a significant increase in the mechanical properties of commercial composites compared to conventional photopolymerization [START_REF] Nguyen | Resin composite blocks via high-pressure high-temperature polymerization[END_REF].

Dispersed filler composite blocks are synthesized by thermopolymerizing (under high pressure or not) a mixture of mixed fillers and monomers [START_REF] Mainjot | From artisanal to CAD-CAM blocks: state of the art of indirect composites[END_REF][START_REF] Nguyen | Properties of experimental urethane dimethacrylate-based dental resin composite blocks obtained via thermopolymerization under high pressure[END_REF].

PICN blocks present a particular microstructure as they are synthesized from a sintered glass-ceramic network with a φ f greater than 73.8% in the form of a block, secondarily infiltrated by monomers, and then thermopolymerized under high pressure. Their fundamental characteristic is that they consist of two continuous networks imbricated in one another:

• A sintered glass-ceramic inorganic network with open porosity.

• An organic network constituted by the crosslinking of a dimethacrylic monomer inside the inorganic network.

The PICN microstructure allows for a higher fillers ratio compared to classical dispersion, and results in higher mechanical properties [START_REF] Nguyen | Properties of experimental urethane dimethacrylate-based dental resin composite blocks obtained via thermopolymerization under high pressure[END_REF].

CHALLENGES IN IMPROVING PROPERTIES

Manufacturers try to improve dental composites performance by modifying the formulation of monomers and photoinitiators.

Composites with other monomers such as siloxane, oxirane, or silorane have been developed in order to attenuate the shrinkage, but do not provide significant improvement in the mechanical properties [START_REF] Lien | Physical properties of a new silorane-based restorative system[END_REF].

Alternative photoinitiation systems based on mono-acyl phosphine oxide (MAPO), a bioacyl phosphorine oxide with a better production efficiency of free radicals than camphorquinone, allowing an increase in conversion degree, mechanical properties, and better polymerization in depth. These systems also improve biocompatibility because no tertiary amines are needed to generate free radicals. However, their absorption spectrum corresponds less to commercially available photopolymerization lamps [START_REF] Leprince | Progress in dimethacrylatebased dental composite technology and curing efficiency[END_REF].

Improving composites is a complex process. Several papers have been aimed at comparing the performances of various reactive mixtures [START_REF] Papakonstantinou | Evaluation of UDMA's potential as a substitute for Bis-GMA in orthodontic adhesives[END_REF][START_REF] Fonseca | Effect of monomer type on the C 5 C degree of conversion, water sorption and solubility, and color stability of model dental composites[END_REF]. Indeed, changing the nature or ratio of a given component can induce undesired side effects (sometimes minor). The overall possible effects are summarized in Figs. 7.10À7.12. The anionic polymerization of MMA can be made in the presence of YCl 3 /lithium amide of indoline/nBli [START_REF] Ihara | Anionic polymerization of methyl methacrylate and tert-butyl acrylate initiated with the YCl 3 /lithium amide/nBuLi systems[END_REF]. Despite the interesting features of anionic MMA-polydispersity index close to 1, and possibility to get block Effect increasing the concentration in the major monomer.

METHODS FOR MATERIAL SYNTHESIS

copolymers [START_REF] Baskaran | Anionic vinyl polymerization-50 years after Michael Szwarc[END_REF]-most of the industrial and medical PMMA grades are obtained from radical polymerization [START_REF] O'brien | Dental Materials and Their Selection[END_REF][START_REF] Powers | Craig's Restorative Dental Materials[END_REF]. The first step (initiation) corresponds to the creation of radicals by photo-or thermochemical processes (see Schemes 7.1 and 7.2, respectively):

A 1 heat or UV-A
The free radicals break the CQC bonds of the monomers to form the first elements of the increasing polymer chain (Scheme 7.3). Then, during the propagation phase, polymers are formed by the successive addition of monomers (Scheme 7.4).

The propagation reaction which corresponds to the opening of CQC double bonds is, in essence, exothermic. The heat of polymerization is, thus, given by:

ΔH polym 5 ΔH C5C À ΔH C2C ð Þ monomer À ΔH C2C ð Þ monomer2monomer (7.2)
In PMMA, the hindering effect of acetyl groups make the third term quite low compared to other polymers so that the heat of polymerization is lower than for

+ + + + ↑ φ filler --- --- --- FIGURE 7.12
Effect increasing minor monomers.

CH 3 C H 2 O OMe A°C H 3 CH 2 O OMe A °C CH 3 C H 2 C O OMe A°C CH 3 CH 2 C O OMe A °SCHEME

7.3

Chain initiation of MMA.

other olefins [START_REF] Roberts | Heat of polymerization. A summary of published values and their relation to structure[END_REF]. However, the temperature in the bulk of a PMMA made bone cement polymerizing at room temperature reach about 80 C [START_REF] Khandaker | The effect of nanoparticles and alternative monomer on the exothermic temperature of PMMA bone cement[END_REF]. Finally, the termination phase closes the reaction by coupling two reactive polymers, or a reactive polymer with a reactive monomer, resulting in the formation of a stable covalent bond (Scheme 7.5).

One of the most remarkable properties of PMMA is that it is soluble in its monomer. In the applications of PMMA as bone cement, PMMA powder mixed with an initator (benzoil peroxide) is hence mixed with a MMA monomer containing N,N dimethyl p-toluidine [START_REF] Asgharzadeh Shirazi | A constitutive material model for a commercial PMMA bone cement using a combination of nano-indentation test and finite element analysis[END_REF]. The PMMA is, hence, dissolved in monomer which polymerizes to give a glassy solid.

Kinetic aspects

The polymerization mechanism of MMA can be represented in a simple way as [START_REF] Cardenas | High-conversion polymerization. I. Theory and application to methyl methacrylate[END_REF]:

Initiation: I-2A k d A 1 M-A-M k i Propagation: A-M i -M 1 M-A-M i11 -M k p Termination: A-M i -M 1 A-M j -M -A-M i1j12 -A k t1
It is assumed that the termination rate constants for combination and chain transfer to monomers are insignificant compared to the termination rate constant for disproportionation. Under the assumption of classical chemical kinetics (steady state hypothesis on A , and on the overall concentration in radical species [R ]), it can be shown that:

d½AM dt 5 2k d A ½ 2 k p AM ½ M ½ 2 k t M ½ Á R ½ (7.3) d½R dt 5 2k d A ½ 2 k t R ½ 2 (7.4) r polymerization 5 2 d M ½ dt 5 2k d k p A ½ M ½ k t (7.5) C CH 3 CH 2 C O OMe A C CH 2 CH 2 C O OMe A C CH 3 CH 3 C O OMe C CH 3 C H 2 C O OMe C CH 2 CH 2 C O OMe A C CH 3 CH 3 C O OMe n °°°S CHEME 7.4
Chain propagation of PMMA.

C CH 2 CH 2 C O OMe A C CH 3 CH 3 C O OMe n C CH 2 C O OMe C CH 2 C O OMe A CH 3 C H 3 m C CH 2 CH 2 C O OMe A C CH 3 C O OMe n C CH 2 C O OMe C CH 2 C O OMe A CH 3 m CH 3 CH 3 C CH CH 2 C O OMe A C CH 3 CH 3 C O OMe n C CH 2 C O OMe C CH 2 C O OMe A CH 3 C H 3 m H °°SCHEME 7.5
Chain termination of PMMA.

It can also be shown that the solution of those differential equations fairly represent the early stages of the polymerization reaction. Some values of kinetic parameters are given in Table 7.1 [START_REF] Begum | Modeling methyl methacrylate free radical polymerization: Reaction in hydrophobic nanopores[END_REF].

During polymerization, the molar mass increases, which lowers the mobility of radicals and the termination rate. At a certain stage, it results in observed autoacceleration (i.e., the "Thromsdorff effect"), as illustrated in Fig. 7.13. [START_REF] Cardenas | High-conversion polymerization. I. Theory and application to methyl methacrylate[END_REF] proposed to model autoacceleration by using a termination rate constant for nonentangled growing chains and another for entangled ones. Later, Simon and colleagues [START_REF] Begum | Modeling methyl methacrylate free radical polymerization in nanoporous confinement[END_REF] proposed a more-refined theory taking into account the role of free volume and its consequences on the diffusion rate of radicals. These developments, however, are out of the scope of this chapter.

The most interesting research deals with the copolymerization of several chemically different monomers which is relevant with reactive mixtures presented in Section 7.2.1.3. The theoretical treatment of copolymerization was proposed by [START_REF] Mayo | Copolymerization. I. A basis for comparing the behavior of monomers in copolymerization; the copolymerization of styrene and methyl methacrylate (Review)[END_REF]. To summarize, the growing chain can be terminated either by an A or B site, which reacts either with a free A or B monomer: Monomer conversion versus polymerization time.

-

--A 1 A ----AA k AA ---A 1 B ----AB k AB ---B 1 A ----BA k BA ---B 1 B ----BB k BB
The reactivity ratio k AA /k AB and k BA /k BB together with the composition of the reactive mixture, thus, give a prediction of the polymer composition and microstructure (i.e., random, alternating, or block copolymer). This theory was not, however, applied to methacrylates copolymers to the best of our knowledge.

POLYMERIZATION OF METHACRYLATE NETWORKS

Mechanistic aspects

Networks are used by using a tetrafunctional monomer (i.e., having two double bonds) such as dimethacrylates presented in Section 7.2.1.2. The processes is described in Scheme 7.6 for MMA:

This tetrafunctional behavior makes various kinds of intramolecular cyclization reactions possible together with intermolecular crosslinking as presented in Schemes 7.7 and 7.8 [START_REF] Elliott | Primary cyclization in the polymerization and TEGDMA: a modeling approach to understanding the cure of dental resins[END_REF].

A n A n °°-8 SCHEME 7.8
Mechanism of primary cyclization.

Polymerization kinetics

The polymerization of networks by radical polymerization is often divided into four successive steps as schematized in Fig. 7.14 (Pascault et al. 2002a).

The first step (pregel step) corresponds to the consumption of inhibitors and their reaction with monomers and the first propagations reaction.

The second step ("gel step") corresponds to the appearance of the first insoluble compounds. Growing chains react either with a monomer or by intramolecular primary cyclization. It results in the formation of crosslinked compact molecules very often called microgels, but better defined as crosslinked microparticles. The gel point is defined by a conversion degree at 1% in theory, but is observed in practice to be around 5% due to cyclizations. Despite the decrease in molecular mobility due to the continuous growth of polymer chains. Monomers can still diffuse and react at the periphery of the microgels in formation.

During the third step, the microgels connect to form macrogels which result in an increase in viscosity, so that the mobility of the polymers and monomers is reduced. At the end of this phase, the viscosity is so increased that termination reactions involving macromolecular radicals are inhibited, leading to a sudden autoacceleration of the polymerization rate.

The fourth step ("glassy step") corresponds to the vitrification where polymerization media turn to a glassy state, that is, that polymerization is frozen by lack of macromolecular mobility which explains why the conversion never reaches 100% [START_REF] Dušek | Diffusion control in the kinetics of cross-linking[END_REF]. The polymerization reaction can be completed only by an adequate postcuring step at temperatures higher than the glass transition of the vitrified network.

PARAMETERS INFLUENCING POLYMERIZATION

Intrinsic factors

Polymerization intrinsic factors depend essentially on the chemical composition and method of manufacture of the composite:

1. The viscosity of monomers is an important parameter for the polymerization kinetics and conversion of the dimethacrylate polymers by affecting the mobility and the reactivity of the monomers (Barszczewska-Rybarek, 2009). 2. Fillers decrease the conversion by increasing the overall viscosity of the composite and, locally, by reducing the mobility of the monomers around the fillers. For example, adding 50% fillers leads to a strong increase in viscosity (almost 30-times higher), but only a minor decrease in conversion degree (about 63% vs 61%) [START_REF] Papakonstantinou | Evaluation of UDMA's potential as a substitute for Bis-GMA in orthodontic adhesives[END_REF]. Furthermore, fillers can alter the photopolymerization by dispersing the photons superficially [START_REF] Leprince | Progress in dimethacrylatebased dental composite technology and curing efficiency[END_REF].

Higher concentrations of initiator increases the conversion degree.

Nevertheless, in the case of photopolymerization, when the initiator concentration exceeds an optimum value, the conversion degree decreases due to the excessive absorption of photons in the irradiated surface area and, thus, a decrease in the photon transmission in depth [START_REF] Musanje | Determination of the optimal photoinitiator concentration in dental composites based on essential material properties[END_REF]. 4. Optical properties affect the photon transmission and, therefore, influence the conversion degree and the polymerization depth during photopolymerization.

The photon transmission will be reduced in an opaque composite with a darker and more saturated hue, which increases the difference in degree of polymerization between the surface and at depth [START_REF] Musanje | Curing-light attenuation in filledÀresin restorative materials[END_REF][START_REF] Shortall | Depth of cure of radiation-activated composite restoratives À influence of shade and opacity[END_REF]. This is, for example, illustrated in [START_REF] Aljabo | Conversion, shrinkage, water sorption, flexural strength and modulus of remineralizing dental composites[END_REF] where 40%-filled composites displayed a conversion degree of about 70% at the surface versus c. 40% at a 4 mm depth.

Extrinsic factors

Temperature and pressure conditions influence polymerization. Higher temperature promotes molecular mobility. Higher pressure decreases molecular mobility [START_REF] Murli | Pressure-induced polymerization of acrylic acid: a Raman spectroscopic study[END_REF], but paradoxically has some beneficial effects on the reactivity [START_REF] Schettino | Activation and control of chemical reactions at very high pressure[END_REF].

In the case of photopolymerization, the photon source affects the polymerization by its emission spectrum, irradiation time, irradiation distance, and polymerization protocol [START_REF] Musanje | Determination of the optimal photoinitiator concentration in dental composites based on essential material properties[END_REF]. The effect of curing protocol on the main properties (glass transition, modulus, conversion degree) is developed in [START_REF] Dewaele | Influence of curing protocol on selected properties of light-curing polymers: degree of conversion, volume contraction, elastic modulus, and glass transition temperature[END_REF].

POLYMERIZATION SHRINKAGE AND ITS CONSEQUENCES

The polymerization shrinkage of dental resins composite is inherent to polymerization reactions. This is due to the replacement of the Van der Waals bonds between the monomers by covalent bonds and a decrease in the free volume [START_REF] Kleverlaan | Polymerization shrinkage and contraction stress of dental resin composites[END_REF]. The shrinkage is about 1.5%À5% by volume [START_REF] Floyd | Network structure of Bis-GMA-and UDMA-based resin systems[END_REF][START_REF] Ferracane | Developing a more complete understanding of stresses produced in dental composites during polymerization[END_REF] and depends on the concentration of the CQC of the monomers, the volume fraction of the composite, and the conversion degree.

The polymerization shrinkage is associated with stresses at the interface between the dental tissues and the composite restoration, and induces:

• Stresses on dental structures with fracture risks in enamel and dentine [START_REF] Ferracane | Developing a more complete understanding of stresses produced in dental composites during polymerization[END_REF][START_REF] Park | Residual stress in composites with the thin-ring-slitting approach[END_REF]. • Stresses at the joint between the restorative material and the dental tissues resulting in leakage and postoperative sensitivities, marginal discolorations, bacterial contamination, and secondary caries.

This polymerization shrinkage also provokes contraction in the composite resin inducing internal stresses in the material [START_REF] Ferracane | Developing a more complete understanding of stresses produced in dental composites during polymerization[END_REF]. The commonality of polymethacrylates obtained by radical polymerization is that they are amorphous materials. The main transition is the glass transition T g separating the glassy and the rubbery regimes.

PHYSICOCHEMICAL, BIOLOGICAL AND MECHANICAL PROPERTIES

1. The glass transition of linear polymer (here PMMA) increases with molar mass, as described by the Fox-Flory's equation [START_REF] Fox | Second-order transition temperatures and related properties of polystyrene. I. Influence of molecular weight[END_REF]:

T g 5 T gN 2 K FF M n (7.6)
Some values of T gN and K are given for PMMA in Table 7.2. [START_REF] Gilormini | Radiochemical "degelation" methacrylate networks[END_REF] or other tetrafunctional acrylates [START_REF] Loshaek | Crosslinked polymers.-II. Glass temperatures of copolymers of methyl methacrylate and glycol dimethacrylates[END_REF].

The most general equation linking T g increase with the conversion degree of monomer was proposed by Pascault and Di Benedetto (Pascault and Williams, 1990):

T g 2 T g0 T gN 2 T g0 5 λx 1 2 1 2 λ ð Þx (7.7)
where subscripts "0" and "N" correspond to totally unreacted and totally reacted materials, λ is the ratio of heat capacity jump a T g of cured and uncured materials ΔC pN /ΔC p0 .

The glass transition of a fully cured network (T gN ) is given by DiMarzio's equation [START_REF] Dimarzio | On the second-order transition of a rubber[END_REF]:

T gN 5 T gl 1 2 K DM Fn 0 ð Þ (7.8)
where K DM is the DiMarzio's constant equal to 2.91 for tridimensional networks such as epoxies [START_REF] Bellenger | Effect of structure on glass transition temperature of amine crosslinked epoxies[END_REF], n 0 is the crosslink density (mol kg 21 ) 5 2/M m if network is fully cured (M m is the mass of monomer), T gl is the glass transition of a "virtual" linear polymer (n 0 5 0), F is the flex parameter (kg mol 21 ) related to the molar mass per rotatable bond. The calculation of parameters of DiMarzio's law is illustrated in [START_REF] Bellenger | Effect of structure on glass transition temperature of amine crosslinked epoxies[END_REF] and [START_REF] Ernault | Thermal-oxidation of epoxy/amine followed by glass transition temperature changes[END_REF]. Some results are given in Table 7.3. In the case of UDMA, a good agreement is found with values obtained for materials being almost fully cured (Chi [START_REF] Phan | Optimum pressure for the high-pressure polymerization of urethane dimethacrylate[END_REF].

However, Eqs. (7.7)À(7.8) show that T g decreases dramatically if networks are not totally crosslinked, which is very often the case in networks cured at room temperature in dentistry. This is, for example, illustrated in the case of photocured Bis-GMA-TEGDMA (Table 7.4) [START_REF] Stansbury | Dimethacrylate network formation and polymer property evolution as determined by the selection of monomers and curing conditions[END_REF].

The consequences of undercuring on mechanical properties at room temperature are illustrated, for example, by [START_REF] Ferracane | In vitro aging of dental composites in water--effect of degree of conversion, filler volume, and filler/matrix coupling[END_REF]. The main results are summarized in Table 7.5. β transition corresponds to the activation of local mobility involving the group of atoms belonging to a monomer. It usually corresponds to a decrease in modulus: ΔE β 5 1300 MPa. In the case of PMMA, a relative jump of 20% compared to "modulus at 0 K" (i.e., deduced from Eqs. 7.9À7.11) is reported [START_REF] Gilbert | Modulus-maps for amorphous polymers[END_REF]. This transition is, however, not documented, to the best of our knowledge, for dental composites.

Short deformation properties

Typical stressÀstrain curves of PMMA at several temperatures and strain rates are schematized in Fig. 7.15 [START_REF] Moy | Stress-strain response of PMMA as a function of strain-rate and temperature[END_REF].

In dimethacrylate networks [START_REF] Foroutan | Mechanical properties of dental composite materials reinforced with micro and nano-size Al 2 O 3 filler particles[END_REF], stressÀstrain curves usually do not display any "hook" typical of a plastic deformation, which is why they are quite often characterized by their values of elastic modulus and ultimate strength.

The elastic behavior of a polymer originates from its cohesive energy which continuously decreases due to the thermal expansion increasing the interchain distance, and the activation of motions decreasing elastic modulus by ΔE i at some given temperatures (e.g., β or γ transitions) [START_REF] Gilbert | Modulus-maps for amorphous polymers[END_REF]):

E 5 E 0 Á 1 2 αÁ T T g 2 X ΔE i (7.9)
According to the linear elasticity theory, Young's (E), bulk (K), and shear (G) modulus values at any temperature are interrelated by Eqs. (7.10)À(7.11):

E 5 3UKUð1 2 2vÞ (7.10)

E 5 2ð1 1 vÞUG (7.11)
where v is the Poisson's ratio (see later). Their subglassy values K 0 and E 0 at very low temperature are shown to be correlated the cohesive energy density (CED) according to the formula (Pascault et al., 2002b):

K 0 B11UCED (7.12) CED 5 E coh V m (7.13)
where E coh is the cohesive energy (J mol 21 ), V m is the molar volume (cm 3 mol 21 ), CED is the density of cohesive energy (MPa 1/2 ). E coh and V m can be calculated according to the incremental method based on additive group's contribution proposed by [START_REF] Van Krevelen | Chap 6. Properties of Polymers À Their Correlation with Chemical Structure; Their Numerical Estimation and Prediction from Additive Group Contributions[END_REF], as shown in Table 7.6. If the Poisson's ratio is on the order of 0.3À0.4 (see later), the Young modulus of the matrix is, thus, expected to be close to 5 GPa.

However, experimental values are usually below these maximum values for several reasons, two of these being:

• Firstly, the undercured characteristics of the networks. A good example of modulus increase with conversion degree is given in Stansbury (2012) (see also Table 7.5). The gelation is observed at a conversion degree about 7% at which materials are a visco-elastic solid having an elastic modulus c. 100 Pa.

When the conversion degree reaches c. 20%, the modulus is close to 10 MPa. It exceeds 100 MPa when the conversion degree is more than 0.5. • Secondly, the existence of several thermomechanical transitions increasing the mobility of groups, monomers, and later units made of several monomers (e.g., the β transition presented in Section 7.4.1.1 and decreasing, step-by-step, the modulus.

At room temperature, that is, presumably in the subglassy domain (between T β and T g ), Young's modulus values are, thus, on the order of 1 GPa for some lightcured unfilled dimethacrylates [START_REF] Sideridou | Study of water sorption, solubility and modulus of elasticity of light-cured dimethacrylate-based dental resins[END_REF][START_REF] Bindu | Size-scale effects of silica on bis-GMA/TEGDMA based nanohybrid dental restorative composites[END_REF].

In the case of highly filled commercial materials, several equations describe the effect of fillers on mechanical properties [START_REF] Atai | Nano-porous thermally sintered nano silica as novel fillers for dental composites[END_REF]. One of the most wellknown is the Halpin-Tsai equation in the case of spherical fillers [START_REF] Pal | New models for effective Young's modulus of particulate composites[END_REF]):

E r 5 1 1 5 2 ÁφÁ 2 Ed Em 2 2 2 Ed Em 1 3 2 4 3 5 (7.14)
Despite the modulus of "pure" fully cured matrix is in the order of 5 GPa (see Table 7.7), it is not surprising that the elastic modulus of commercial dental materials increases linearly with filler content (see, e.g., [START_REF] Masouras | Correlation of filler content and elastic properties of resin-composites[END_REF] and can reach values c. 10 GPa [START_REF] Ferracane | In vitro aging of dental composites in water--effect of degree of conversion, filler volume, and filler/matrix coupling[END_REF][START_REF] Papadogiannis | Viscoelastic properties, creep behavior and degree of conversion of bulk fill composite resins[END_REF]Jager et al., 2016b). It can be observed that the filler ratio influences the viscosity of the reactive mixture and later its conversion degree (see Fig. 7.10 and Ferracane et al., 1998) so that predicting the value of composites modulus remains intricate.

Experimentally, as illustrated in the case of PMMA [START_REF] Mott | The bulk modulus and Poisson's ratio of "incompressible" materials[END_REF], the modulus at very low temperatures can be estimated from ultrasonic measurements from a relationship between the longitudinal and the shear wave velocities (V L and V T ) of the sample immersed in water and the density: The Poisson's ratio (ν) in a composite can also be estimated from the volume fraction of fillers (φ), the Poisson's ratio of matrix, and filler ν m and ν f [START_REF] Halpin | The Halpin-Tsai equations: a review[END_REF]:

V L 5 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E u ρ Á 1 2 ν u ð1 1 ν u Þð1 2 2ν u Þ s (7.15) V T 5 ffiffiffiffiffi ffi G u ρ s (7.16)
ν 5 1 2 φ ð ÞÁν m 1 φÁν f (7.17)
Its value for matrices (0.3À0.35) increases at about 0.5 when T reaches T g , that is, when the polymer turns from a glassy to rubbery state at which it is incompressible [START_REF] Mott | The bulk modulus and Poisson's ratio of "incompressible" materials[END_REF]. In the case of filled dental composites [START_REF] Chunga | Measurement of Poisson's ratio of dental composite restorative materials[END_REF], values ranging from 0.3 to 0.4 are recorded at room temperature (Table 7.7).

Higher values are observed for commercial composites. According to several authors, hardness and elastic modulus are well-correlated [START_REF] Thomaidis | Mechanical properties of contemporary composite resins and their interrelations[END_REF][START_REF] Pal | New models for effective Young's modulus of particulate composites[END_REF]. Li et al. (2009a) propose, for example, a linear correlation:

EB0:15 3 Knoop Microhardness (7.18)
E being expressed here in GPa. The positive effect of curing on the microhardness is illustrated in [START_REF] Haenel | Effect of the irradiance distribution from light curing units on the local micro-hardness of the surface of dental resins[END_REF] whereas Li et al [START_REF] Atai | Nano-porous thermally sintered nano silica as novel fillers for dental composites[END_REF] also show a decrease in hardness with polymer thickness.

Ultimate flexural strength has to display a value at least equal to 50 MPa for clinical requirements (as mentioned in [START_REF] Bindu | Size-scale effects of silica on bis-GMA/TEGDMA based nanohybrid dental restorative composites[END_REF]. Typical values for dental composites are given in Table 7.8 (see [START_REF] Barszczewska-Rybarek | StructureÀproperty relationships in dimethacrylate networks based on Bis-GMA, UDMA and TEGDMA[END_REF].

According to Eyring's theory, plasticity originates in the jump of segments. This phenomenon is thermally activated (with a ΔH energy corresponding to the potential barrier) and facilitated by the activation volume v flow and the external stress σ. The yield stress σ Y is, thus, linked to the strain rate _ γ:

σ y 2 5 ΔH v flow 2 kT v flow Uln _ γ 0 _ γ À Á (7.19)
This equation is close to the experimental observations by Kambour, according to which: C ranges from 0.5 to 1 MPa K 21 [START_REF] Cooke | Yielding behaviour in model thermosets À II. Temperature dependence[END_REF][START_REF] Li | Molecular dynamics predictions of thermal and mechanical properties of thermoset polymer EPON862/DETDA[END_REF]. A decrease in glass transition, thus, results in a decrease in yield stress.

σ Y 5 CU T g 2 T À Á 1 σ Y0 (7.20)
At temperatures above the glass transition, thermoset networks are in a rubbery state. Elastic behavior is given by the Flory approach according to which the Young's modulus is proportional to the concentration in elastically active chains n 0 [START_REF] Mark | The rubber elastic state (Chapter 1)[END_REF]:

E 5 3ρRT M C 5 3Án 0 RT (7.21)
where ρ is the density, M C the average molar mass between crosslinks, R the gas constant, and T the absolute temperature. Values of rubbery modulus (measured at 175 C) of several bis-GMA 1 HEMA networks close to 25 MPa are given in [START_REF] Park | Water sorption and dynamic mechanical properties of dentin adhesives with a urethane-based multifunctional methacrylate monomer[END_REF]. This means that the average molar mass between crosslink nodes is c. 400À500 g mol 21 (i.e., n 0 c. 2 mol kg 21 ). This is the expected order of magnitude in these materials (see Table 7.3) since the HEMA comonomer contributes to an increase of the molar mass between crosslinks.

The correlation between rubbery modulus and conversion degree is illustrated in the case UDMA by Sadoun and colleagues (Chi [START_REF] Phan | Optimum pressure for the high-pressure polymerization of urethane dimethacrylate[END_REF]. Identically to glassy modulus, it increases with filler content [START_REF] Munhoz | Effect of nanoclay addition on physical, chemical, optical and biological properties of experimental dental resin composites[END_REF] as described by [START_REF] Guth | Theory of filler reinforcement[END_REF]:

E 5 E 0 :ð1 1 2:5φ 1 14:1φ 2 Þ (7.22)
where 14.1 3 φ 2 expresses the fillerÀfiller interaction effect on elasticity and is particularly relevant for highly filled matrices such as dental composites.

Even if Young's modulus on the rubbery plateau is not itself helpful data for practitioners, it is noteworthy that it allows an estimation of the concentration in elastically active chains, expected to decrease during hydrolytic degradation (see Section 7.5.3).

Ultimate properties

The toughness expresses the ability of a material to absorb energy and plastically deform without fracturing. According to the Griffith's equation, the stress intensity factor in an infinite plate with a crack of 2a length is:

K I 5 yUσUða:πÞ 1=2 (7.23)
that is, that sample fails either if the stress σ, or the size of the crack a, exceed a critical value. PMMA toughness can be easily studied using a common tensile test sample. In the case of dental composites, various methods are proposed, for example, using notched disks [START_REF] Watanabe | Fracture toughness comparison of six resin composites[END_REF] allowing to study failure in mode I or II. The values of toughness are shown to depend on the load rate, but stay close to 1.5 MPa m 1/2 [START_REF] Wada | Determination of dynamic fracture toughness for PMMA[END_REF]. These values are actually very close to unreinforced poly(UDMA) [START_REF] Phan | High-temperature high-pressure polymerized urethane dimethacrylate-mechanical properties and monomer release[END_REF] and, more unexpectedly, in filler reinforced composites [START_REF] Atai | Nano-porous thermally sintered nano silica as novel fillers for dental composites[END_REF][START_REF] Guth | Theory of filler reinforcement[END_REF][START_REF] Ornaghi | Fracture toughness and resistance of resin composites with different filler size distributions[END_REF].

Reversely, the toughness can reach about 2.5 MPa m 1/2 for resins reinforced with 7.5% short glass fibers [START_REF] Bocalon | Replacement of glass particles by multidirectional short glass fibers in experimental composites: Effects on degree of conversion, mechanical properties and polymerization shrinkage[END_REF]. The presence of rubbery fillers has a positive effect on toughness (Mante et al., 2010;[START_REF] Omran Alhareb | Impact strength, fracture toughness and hardness improvement of PMMA denture base through addition of nitrile rubber/ceramic fillers[END_REF].

The impact strength is typically measured using a Charpy impact test on notched or unnotched samples. The typical value for PMMA is about 5 kJ m 22 with possible improvements by reinforcing with various kinds of rubbery particles (NBR [START_REF] Omran Alhareb | Impact strength, fracture toughness and hardness improvement of PMMA denture base through addition of nitrile rubber/ceramic fillers[END_REF] or poly(methyl methacrylate-b-butyl acrylateb-methyl methacrylate) (MAM) [START_REF] Lalande | Microdeformation mechanisms in rubber toughened PMMA and PMMA-based copolymers[END_REF]. In unfilled poly(UDMA), poly(Bis-GMA), poly(TEGDMA), and their mixtures the value is higher and can reach c. 9 kJ m 22 (Barszczewska-Rybarek, 2009).

Lastly, it is noteworthy that the combined effect of fillers and low monomer viscosity lead to porosities [START_REF] Balthazard | High-resolution tomography study of the porosity of three restorative resin composites[END_REF] which are quite detrimental to the ultimate mechanical properties. It must also be highlighted that the difference between the thermal coefficient dilatation of the polymer filler induces stresses at the polymer/filler interface [START_REF] Ferracane | Developing a more complete understanding of stresses produced in dental composites during polymerization[END_REF] which becomes an area of weakness where a crack will easily propagate and reduces the toughness of the material.

7.4.2

The biocompatibility of dental resins may affect both the patient and the dentist.

In the case of samples immersed in water, it can be observed that a part of the mass is lost presumably because of the migration of low molecular mass compounds [START_REF] Sideridou | Sorption of water, ethanol or ethanol/water solutions by light-cured dental dimethacrylate resins[END_REF].

Those phenomena are usually quantified by measuring the soluble fraction, being the relative mass decrease of a composite resin before immersion and after immersion and complete drying. If the results clearly depend on the curing process, it seems that this soluble part can represent from 0.1% to 1% by weight of the polymer mass in common light-cured dimethacrylate matrices [START_REF] Ru ¨ttermann | Impact of replacing Bis-GMA and TEGDMA by other commercially available monomers on the properties of resin-based composites[END_REF][START_REF] Sideridou | Study of water sorption, solubility and modulus of elasticity of light-cured dimethacrylate-based dental resins[END_REF]. This quantity can even be higher if low molecular mass compounds produced from the partial hydrolytic or enzymatic degradation of networks, which will be addressed in the following of this chapter.

As expected with uncompletely cured networks, a great part of soluble (eluted from resins) compounds contains unreacted monomers and photoinitiators [START_REF] Munhoz | Effect of nanoclay addition on physical, chemical, optical and biological properties of experimental dental resin composites[END_REF][START_REF] Ferracane | Hygroscopic and hydrolytic effects in dental polymer networks[END_REF]. The migration of a chemical out of a polymer is, in great part, controlled by its molar mass (expressing the architecture) of compounds so that it is quite likely that dimers or trimers diffusion is slow enough to be neglected in the first approach.

Quite interestingly, it was observed that the fraction of UDMA and Bis-GMA extracted from UDMA-TEGDMA or Bis-GMA/TEGDMA was systematically higher than their fraction in the polymerization mixture. Since their higher molar mass makes them less mobile than TEGDMA monomers, this suggests that Bis-GMA and UDMA are not randomly polymerized with TEGDMA [START_REF] Floyd | Network structure of Bis-GMA-and UDMA-based resin systems[END_REF] (see Section 7.3.1.2).

The toxicity of several kinds of chemicals involved in the formation of dental composites was addressed by [START_REF] Thonemann | Responses of L929 mouse fibroblasts, primary and immortalized bovine dental papilla-derived cell lines to dental resin components[END_REF]. According to TC50 measurements performed on several kinds of cells, Bis-GMA seems by far to display the highest cytotoxicity compared to UDMA and MMA.

Wear debris are produced from attrition and abrasion of resin composite dental restorations [START_REF] Heintze | How to qualify and validate wear simulation devices and methods[END_REF]. Ingestion of filler particles could result in potential harm to the liver, kidney, or intestine [START_REF] Gatti | Biocompatibility of micro-and nanoparticles. Part I: In liver and kidney[END_REF][START_REF] Gatti | Biocompatibility of micro-and nano-particles in the colon[END_REF]. Nevertheless there is no scientific evidence that swallowed particles induce a significant health risk for patients [START_REF] Heintze | How to qualify and validate wear simulation devices and methods[END_REF].

Besides this, polishing, shaping, and grinding composites result in particle dust (,5 μm particles including nanoparticles ,100 nm) which can be inhaled and penetrate the lungs [START_REF] Van Landuyt | Should we be concerned about composite (nano-)dust?[END_REF], provoking cell toxicity in human bronchial epithelial cells [START_REF] Cokic | Cytotoxic effects of composite dust on human bronchial epithelial cells[END_REF]-for exposure under relatively high particle concentrations compared to standard use.

The fiber-reinforced composites were recently introduced and seem to offer a good combination of reinforcement of mechanical properties and low toxicity [START_REF] Ballo | Biocompatibility of fiber-reinforced composites for dental applications[END_REF].

LONG-TERM BEHAVIOR

Let us recall that there are two kinds of ageing phenomena:

• Physical ageing, where the polymer backbone remains unmodified, whereas the free volume is changed by physical relaxation, the ingress of an external penetrant, or the loss of an adjuvant (typically a plasticizer). • Chemical ageing where the polymer backbone or its lateral groups undergo chain scissions or crosslinking induced by any kind of chemical reaction.

In the specific case of polymeric dental materials, the main mechanisms were listed by [START_REF] Ferracane | Hygroscopic and hydrolytic effects in dental polymer networks[END_REF]. The most relevant ones for acrylates will be addressed next.

AGING BY PHYSICAL RELAXATION

This kind of mechanism is common to every glassy polymer. When cooled from elevated temperatures, the specific volume decreases, but the decrease rate is below the T g of the polymer. Lower than this temperature, the polymer can be considered as in an "out-of-equilibrium" state. The primary thermodynamic properties (volume, enthalpy, etc.) decreases slowly during the storage at an ageing temperature (T a ) lower than T g (Fig. 7.16).

Meanwhile, the necessary enthalpy for initiating rubbery phase motions is increased when reheating above T g , generating the enthalpy overshoot commonly observed by DSC [START_REF] Diaz-Calleja | Physical model explaining the effect of physical ageing on dynamic mechanical and calorimetric properties of poly (Methyl Methacrylate)[END_REF] and a slight increase of T g toward a "fictive temperature" (T f ) given by:

T f 5 T g 2 Δh Δc P (7.24)
The enthalpy overshoot tends toward an asymptotical value given by:

Δh N 5 Δc P U T g À T a À Á (7.25)
where Δc P 5 c Pl Àc Pg is the heat capacity jump at T g , and T a is the temperature at which physical ageing occurs.

From a practical point of view, the distance to equilibrium increases with decreasing temperature, but the rate decreases very strongly when temperature decreases, so that this ageing mechanism is typically significant in the temperature range [T g ; T g 2 60 C] [START_REF] Pethrick | Towards a molecular approach to physical ageing in poly(methyl methacrylate)[END_REF].

Physical ageing is described by a distribution of relaxation times:

φ t ð Þ 5 exp 2 t τ β ! (7.26)
The function seems to depend on the experimental technique (e.g., dynamic modulus, dilatometry, calorimetry) used for measuring [START_REF] Pe ´rez | Physical ageing of amorphous polymers. Theoretical analysis and experiments on poly(methyl methacrylate)[END_REF].

τ is the relaxation time that can be predicted by two models [START_REF] Hodge | Enthalpy relaxation and recovery in amorphous materials[END_REF]:

1. ToolÀNarayanaswamyÀMoynihan model predicts the relaxation time from the value of "fictive" temperature [START_REF] Narayanaswamy | A model of structural relaxation in glass[END_REF]:

τ 5 τ 0 Áexp xΔh à RT 1 1 2 x ð ÞΔh à R:T f ! (7.27)
2. KovacsÀAklonisÀHutchinsonÀRamos (KAHR) [START_REF] Grassia | Modeling volume relaxation of amorphous polymers: Modification of the equation for the relaxation time in the KAHR model[END_REF][START_REF] Grassia | Isobaric and isothermal glass transition of PMMA: pressure-volume-temperature experiments and modelling predictions[END_REF]: Mechanism of physical relaxation ageing. T g is the glass transition temperature, T β the highest temperature of subglassy transition, and v is the specific volume [START_REF] Struik | Physical Aging in Amorphous Polymers and Other Materials[END_REF].

τ 5 τ R Áexp θÁ T R 2 T ð Þ ½ Áexp 2
where τ R is the relaxation time at the reference temperature T R , θ is linked to activation energy, x is an adjustable parameter ranging from 0 to 1, η is parameter specific to the value under study (i.e., depending on heat capacity [c P ] for enthalpic relaxation, dilatation coefficient α for volumetric relaxation).

The full description of these models is out of the scope of this chapter. Since ageing by physical relaxation results in a decrease of free volume quantity, all and mechanical properties related to free volume are changed, for example:

• Yield stress is increased, possibly because the activation volume v flow (see Eyring's equation) is linked to the residual free volume. • Creep resistance [START_REF] Hutchinson | The effects of thermal history on the density and mechanical properties of poly(methyl methacrylate)[END_REF] • Toughness [START_REF] Arnold | The effects of physical aging on the brittle fracture behavior of polymers[END_REF], • Loss tangent is decreased in the domain of the subglassy transition (c. 320K in the case of PMMA) [START_REF] Diaz-Calleja | Physical model explaining the effect of physical ageing on dynamic mechanical and calorimetric properties of poly (Methyl Methacrylate)[END_REF][START_REF] Etienne | Physical aging and molecular mobility of amorphous polymers[END_REF] (see Fig. 7.17).

A final consequence is worth being investigated. It seems clear that physical ageing relaxation induces free volume collapse, i.e., a decrease in the size of nanovoids present in the polymer [START_REF] Pethrick | Towards a molecular approach to physical ageing in poly(methyl methacrylate)[END_REF] with possible consequences on the water ingress in the composite.

HUMID AGEING

The penetration of water is an environmental factor that can drastically limit the performance of polymers. Two subcases can be distinguished:

• Water diffuses into the polymer, but does not change the polymer's architecture. • Water diffuses and reacts with the polymer, generating scission of lateral or skeletal bonds (Section 7.5.3).

Water solubility

The mechanism of the polymerÀwater interaction can be, firstly, described by the shape of the sorption isotherm where the ratio of water in the polymerÀwater mixture is plotted by the function of water activity (or partial pressure), as illustrated in Fig. 7.18. Several shapes of sorption isotherms are described for the sorption of gases into polymers. In the case of water penetration, three main cases exist:

1. Henry's law is the simplest theory for water dissolution. It is associated to a very dilute solution behavior in which dissolved water molecules are few and far between. It assumes that maximum (equilibrium) water uptake is directly proportional to the external water partial pressure:

C 5 sUP (7.29)
where C is solubility expressed, for example, in cc(STP)/cc(polymer). s is the solubility coefficient (expressed in mol L 21 Pa 21 ) expected to obey Van't Hoff law:

(5)

(4) (4) (5)
(2)

(3)

(1)

(1) FIGURE 7.17

The effect of physical ageing on PMMA at 363 K after thermal annealing on: (A) loss factor; and (B) specific heat.

Reused with permission of Elsevier.

The apparent activation energy for water equilibrium concentration is, thus, given by:

E S 5 2 ΔH S À ΔH vap (7.32)
ΔH vap is close to 43 kJ mol 21 . In PMMA, ΔH S B 243 kJ mol 21 so that water uptake does not depend on temperature as in the first approach [START_REF] Barrie | Diffusion and association of water in some polyalkylmethacrylates. Part 1 À Equilibrium sorption and steady state permeation[END_REF]).

2. An isotherm which is linear at low activity and displays an upturn at higher water pressures (such as B isotherm in Fig. 7.18) is associated to a type III isotherm in the BET classification and is sometimes called a Flory Huggins isotherm. This upturn has two explanations: a. Due to clustering of solvent molecules. b. Due to plasticization of the polymer matrix induced by solvent sorption. The mathematical description of Flory Huggins isotherms is given by:

ln P=P 0 5 lnð1 2 φ p Þ 1 φ p 1 χφ 2 p (7.33)
where φ p is the volume fraction of the polymer in the waterÀpolymer mixture. is the Flory parameter describing the polymerÀwater affinity, expressed by:

χ 5 V mwater RT Á δ polymer 2δ water À Á 2 (7.34)
where V mwater is the molar volume of water, δ polymer , and δ water are, respectively, the solubility parameters of polymer and water, R the ideal gas constant and T the absolute temperature.

In the case of PMMA-water association, both solubility parameters are known: δ PMMA 5 19.0 MPa 1/2 and δ water 5 47.9 MPa 1/2 . However, the resulting χ parameter seems to be an overestimation (5.91 at 35 C) compared to the value deduced from sorption isotherms (3.48). One possible explanation is that this estimation of χ from the solubility parameter values is not refined enough for taking into account the various kinds of interactions (e.g., dispersive, dipole-dipole, hydrogens, etc.).

Another explanation is the presence of water clusters, which can be observed by dielectric measurements at high water uptake [START_REF] Garden | A dielectric study of water uptake in epoxy resin systems[END_REF]. The clustering function was defined by [START_REF] Zimm | Sorption of vapors by high polymers[END_REF] as:

f ZL 5 G 11 ν 1 5 2 1 2 φ 1 À Á Á @a 1 =φ 1 @a 1 ! T;P 2 1 (7.35)
When f ZL is below a value of À1, no clustering occurs. Means cluster size (MCS) is given by: MCS 5 1 1 φ 1 UG 11 =v 11 (7.36)

It was, hence, shown [START_REF] Davis | Water clustering in glassy polymers[END_REF] that water molecules associate to form "dimers" when water external partial pressure (or activity) exceeds 0.2, which is typically the case when PMMA is immerged in water.

3. The Langmuir isotherm describes the equilibrium between the absorption (rate constant k 1 ) and desorption (rate constant 5 k 21 ) of molecules on a surface; the rate being propositional to water external partial pressure (P) and the concentration of sorbed water (c), as described by:

k 1 UPU 1 À c ð Þ5 k 21 Uc (7.37)
which can be reformulated under the general form:

c 5 AÁp 1 1 BÁp (7.38)
In some cases, the sorption of a penetrant can be modeled by the dual sorption theory, which is the combination of Henry and Langmuir sorptions:

c 5 sÁp 1 AÁp 1 1 BÁp (7.39)
Some cases corresponding to this dual sorption mode are presented in [START_REF] Vieth | Dual sorption theory[END_REF].

There are several values for water-uptake in methacrylates immerged in water [START_REF] Sideridou | Study of water sorption, solubility and modulus of elasticity of light-cured dimethacrylate-based dental resins[END_REF][START_REF] Sideridou | Volumetric dimensional changes of dental light-cured dimethacrylate resins after sorption of water or ethanol[END_REF][START_REF] Gonzales | Evaluation of the effect of water content on the stress optical coefficient in PMMA[END_REF][START_REF] Smith | The effect of water on the glass transition temperature of poly(methyl methacrylate)[END_REF]. Some of these are provided in Table 7.9.

The water affinity of a given polymer can be expressed as the number of water molecules absorbed per monomeric unit [START_REF] Morel | Structure-water absorption relationships for amine-cured epoxy resins[END_REF]:

H 5 w m ÁM 1800 5 X n i H i (7.40)
where M is the molar mass of the repetitive unit, n i is the number of groups able to bind with H i molecules of water.

H i can be estimated from several polymers or chemicals (ideally with only one kind of functional group). For example, data for PMMA (Table 7.8) suggest H ester B 0.1. However, this simple theory can fail for several reasons:

• The contribution of hydroxyl group (H OH ) might be weaker than in linear polymers such as PVOH because of the possibility of intramolecular hydrogen bonds [START_REF] Kalachandra | Comparison of water sorption by methacrylate and dimethacrylate monomers and their corresponding polymers[END_REF] as observed when OH are hydrogenbonded with heteroatoms (nitrogen atoms at the crosslink node for epoxy/ diamine networks [START_REF] Morel | Structure-water absorption relationships for amine-cured epoxy resins[END_REF], oxygen for Bis-GMA. • Water can have a very specific interaction with other water molecules (clustering). • This simple theory considers the presence of polar and apolar groups, but not their molecular arrangements and the subsequent possibility to create "complexes" with water molecules.

Lastly, [START_REF] Kerby | Synthesis and evaluation of modified urethane dimethacrylate resins with reduced water sorption and solubility[END_REF] also observed that the water uptake value is correlated with water contact angle: hydrophilic samples display a lower contact angle than hydrophobic ones.

Water diffusion

The diffusion of water in a polymer is expected to be described by the second Fick's law, provided that diffusivity does not depend on the water concentration:

@c @t 5 D w Á @ 2 c @r 2 (7.41)
This equation was solved analytically by [START_REF] Crank | The Mathematics of Diffusion[END_REF], for example, in the case of an "infinite" plate having a 2e thickness:

m t ð Þ2m 0 m N 2 m 0 5 1 2 8 π 2 • X N n50 1 ð2n11Þ 2 •exp 2 D• 2n11 ð Þ 2 •π 2 •t 4e 2 (7.42)
It is easy to verify that Eq. (7.42) describes fairly the sorption curves displayed in Fig. 7.19A. Increasing the number of terms of the index n allows a better description of the curve in the earliest sorption times. This equation can be simplified into:

• at low penetrant uptake (m/m N , 0,6):

ΔmðtÞ Δm N 5 4 e • ffiffiffiffiffiffiffi D•t π r (7.43)
• at high penetrant uptake:

ΔmðtÞ Δm N 5 1 2 8 π 2 •exp 2
Dπ 2 e 2 t (7.44)

In other words, if mass uptake varies linearly with the square root of time at low mass uptake values, it means that diffusion obeys Fick's law. The initial slope can, thus, be used to estimate the apparent diffusivity. It seems that the water diffusion into methacrylate-based polymers obeys Fick's law [START_REF] Sideridou | Sorption of water, ethanol or ethanol/water solutions by light-cured dental dimethacrylate resins[END_REF][START_REF] Barrie | Diffusion and association of water in some polyalkylmethacrylates. Part 1 À Equilibrium sorption and steady state permeation[END_REF][START_REF] Dhanpal | Effect of temperature on water sorption and solubility of dental adhesive resins[END_REF]FIGURE 7.19 The general shape of mass uptake in a polymer in the presence of water in the case of a: (A) Fick Diffusion model; and (B) Langmuir diffusion model. [START_REF] Sideridou | Water sorption characteristics of light-cured dental resins and composites based on Bis-EMA/PCDMA[END_REF]. Some values are given in Table 7.10 that show differences between experiments performed in sorption mode compared to desorption mode [START_REF] Sideridou | Sorption of water, ethanol or ethanol/water solutions by light-cured dental dimethacrylate resins[END_REF][START_REF] Dhanpal | Effect of temperature on water sorption and solubility of dental adhesive resins[END_REF][START_REF] Sideridou | Water sorption characteristics of light-cured dental resins and composites based on Bis-EMA/PCDMA[END_REF].

Since samples actually differ from plates (length [L] and width [l] are finite values), [START_REF] Shen | Moisture absorption and desorption of composite materials[END_REF] proposed a correction for taking into account the geometry of samples:

D réel 5 D app 11 2e L 1 2e l À Á 2 (7.45)
D is expected to obey to Arrhenius law:

D T ð Þ5 D 0 :exp 2 E D RT (7.46)
In PMMA, E D would be on the order of 45 kJ mol 21 [START_REF] Barrie | Diffusion and association of water in some polyalkylmethacrylates. Part 1 À Equilibrium sorption and steady state permeation[END_REF], which seems to be quite common with other values reported for amorphous polymers in their glassy state (Li et al., 2009b). Values slightly lower (30À35 kJ mol 21 ) are observed in some matrices of dental composites [START_REF] Dhanpal | Effect of temperature on water sorption and solubility of dental adhesive resins[END_REF].

In some cases, the sorption curves display two plateaus which are attributed to the existence of polymeric sites inducing strong interactions with water molecules. Water molecules present in the polymer matrix divide into two parts:

• Free water which diffuses.

• Bound water being in strong interaction with some specific sites of the polymer.

This Langmuir-type diffusion was mathematically described by [START_REF] Carter | Langmuir-type Model anomalous moisture diffusion in composite resins[END_REF] by denoting:

• n(t) the concentration in "free" water.

• N(t) the concentration in "bound" water. • γ the probability that "free" water becomes "bound" water.

• β the probability that "bound" water becomes "free" water.

The equilibrium is described by: γUn N 5 βUN N (7.47)

The system is described via a system of differential equations:

@n @t @N @t 5 DÁ @ 2 n @x 2 (7.48) @N @t 5 γn 2 βN (7.49)

By denoting:

κ 5 π 2 D ð2eÞ 2 (7.50)
Its solution can be approximated:

• at short absorption times:

NðtÞ N 5 4 π 3=2 Á β β 1 γ Á ffiffiffiffi ffi κt p (7.51)
• at high absorption times:

NðtÞ N 5 1 2 γ β 1 γ Áexp 2 βt ð Þ (7.52)
The "pseudo plateau" value can be approximated by:

N pseudo equilibre N 5 β β 1 γ (7.53)
However, such a process has not been reported, to the best of our knowledge, for the case of any methacrylate-based materials.

The rate at which water diffuses is influenced by the penetrant architecture and polymer free volume, as proposed by [START_REF] Cohen | Molecular transport in liquids and glasses[END_REF]:

D 5 D 0 Uexp 2b=V f À Á (7.54)
where, b is related to penetrant size and V f to polymer "empty" space allowing penetrant jumps.

"Free volume" theory is, for example, well-illustrated in the case of epoxy networks when correlating the measured value of diffusivity (determined from the classical gravimetric method) with the volume of nanoholes (expected to be linked to free volume) [START_REF] Frank | Effect of stoichiometry and cure prescription on fluid ingress in epoxy networks[END_REF]. In the case of methacrylate-based polymers, it was observed that the diffusivity values in networks-based tetrafunctional methacrylates was lower than in analogous methacrylates, presumably because of the highly crosslinked nature of the networks and the lower free-volume content [START_REF] Kalachandra | Comparison of water sorption by methacrylate and dimethacrylate monomers and their corresponding polymers[END_REF].

Theories linking diffusivity with the capability of polymer segments to facilitate diffusion are also illustrated in polymers having a subglassy transition (also named β transition) where Halary observed a good correlation between the occurrence of this transition and the diffusivity of water [START_REF] Halary | Structure-property relationships in epoxy-amine networks of wellcontrolled architecture[END_REF].

It seems, also, that the ageing by physical relaxation (see Section 7.5.1) can influence the overall-water ageing process, since the decrease in free volume is accompanied by an overall lower penetration of water, as illustrated by Siu-Wai [START_REF] Kong | Physical Aging in Epoxy Matrices and Composites[END_REF] in the case of epoxies resins.

Contrarily to theories considering diffusion being mainly influenced by the amount of free volume, Verdu and colleagues [START_REF] Merdas | Factors governing water absorption by composite matrices[END_REF] observed that for a family of epoxy resins, diffusivity was inversely correlated with solubility. Since this later mainly originated from polar groups (such as isopropanol in epoxies) inducing a strong interaction with water, they suggested that these later decrease the diffusivity. The following mechanism was proposed: This theory is verified in part by [START_REF] Dhanpal | Effect of temperature on water sorption and solubility of dental adhesive resins[END_REF] for some dental composites, where the differences are few.

Consequences of physical ageing on mechanical properties

Water is a small molecule characterized by a low T g (T g 5 136K for water; [START_REF] Angell | Glass transition temperatures for simple molecular liquids and their binary solutions[END_REF]. It is, thus, not surprising that the main consequence of water penetration in acrylate polymers is a decrease of glass transition temperature [START_REF] Smith | The effect of water on the glass transition temperature of poly(methyl methacrylate)[END_REF], which can be tentatively described by several models, such as:

1. The DiMarzio's equation is the simplest law for describing the T g depletion for a polymer in presence of a plasticizer: where ΔC p is change of heat capacity at T g for each component of the mixture equal to ΔC P1 5 1.94 J (g K) 21 for PMMA and ΔC P2 5 0.318 J (g K) 21 for water. 3. [START_REF] Ellis | Interaction of epoxy resins with water: the depression of glass transition temperature[END_REF]:

T g 5 w 1 ÁΔC p1 ÁT g1 1 w 2 ÁΔC p2 ÁT g2 w 1 ÁΔC p1 1 w 2 ÁΔC p2 (7.57)
4. [START_REF] Kelley | Viscosity and glass temperature relations for polymerdiluent systems[END_REF]:

T g ΔαÁT g2 Áφ 2 1 α 1 ÁT g1 Áφ 1 ΔαÁφ 2 1 α 1 φ 1 (7.58)
where α 1 is the diluent coefficient of cubic expansion, and Δα is the change of coefficient of cubic expansion for the polymer at T g for which it is considered as an universal value close to 4.8 3 10 24 K 21 .

The effect of water absorption in PMMA is illustrated on the depletion of elasticity modulus in the glassy state from 3700 to 3000 MPa when water fraction increases from 0% to 1.4% (Delpino [START_REF] Gonzales | Evaluation of the effect of water content on the stress optical coefficient in PMMA[END_REF].

T g 5 f Áw 1 ÁΔC p1 ÁT g1 1 w 2 ÁΔC p2 ÁT g2 f Áw 1 ÁΔC p1 1 w 2 ÁΔC p2 (7.59)
where f is considered as the fraction of water active for reducing T g (i.e., 1 À f is the fraction of water absorbed in microvoids).

In fully cured networks, water plasticization results in a decrease in compressive strength and microhardness [START_REF] Ferracane | In vitro aging of dental composites in water--effect of degree of conversion, filler volume, and filler/matrix coupling[END_REF][START_REF] Kalliyana Krishnan | Effect of diluent upon the properties of a visiblelight-cured dental composite[END_REF]. A good illustration is given in the case of Bis-GMA 1 HEMA networks in [START_REF] Park | Water sorption and dynamic mechanical properties of dentin adhesives with a urethane-based multifunctional methacrylate monomer[END_REF], the results of which are schematized in Fig. 7.20.

According to the Kambour's theory, yield stress depends on the value of T g (see Section 7.4.1). A decrease in glass transition results in a decrease in yield stress as illustrated by [START_REF] Leger | A study of the impact of humid aging on the strength of industrial adhesive joints[END_REF]: according to these authors, changes in mechanical properties induced by solvent ingress leading to a given temperature decrease (e.g., 20 C) are equivalent to the mechanical properties decrease induced by the same temperature increase (i.e. 20 C). It is worth noting that physical ageing in principle, characterized by an equilibrium state, i.e., physical properties are expected to plateau after a longexposure time. However, since dental composites are sometimes undercured, the decrease in T g and subsequent macromolecular mobility increase may also induce an increase in conversion degree and later in some mechanical properties [START_REF] Ferracane | In vitro aging of dental composites in water--effect of degree of conversion, filler volume, and filler/matrix coupling[END_REF][START_REF] Malacarne-Zanon | Effects of ethanol addition on the water sorption/solubility and percent conversion of comonomers in model dental adhesives[END_REF].

Role of the interface

A supplementary level of complexification is observed in composites. It was also observed that the polymer/fillers interface displays usually weaker properties than the "bulky" polymer matrix, as illustrated in numerous papers dealing with T g measurements of organic matrices at the boundary with the interface [START_REF] Tillman | Examination of interphase thermal property variance in glass fiber composites[END_REF][START_REF] Joliff | Modified water diffusion kinetics in an unidirectional glass/fibre composite due to the interphase area: Experimental, analytical and numerical approach[END_REF]. It is, thus, observed that water solubility and diffusivity in composites are higher than those predicted by a simple mixture law (i.e., assuming that water does not diffuse into the filler) as observed by [START_REF] Chateauminois | Study of the interfacial degradation of a glass-epoxy composite during hygrothermal ageing using water diffusion measurements and dynamic mechanical thermal analysis[END_REF] in the case of reinforced epoxies.

This was also illustrated by [START_REF] Kalachandra | Influence of fillers on the water sorption of composites[END_REF] in the case of PMMA filled with barium-based particles (Table 7.11). The detrimental effects of the interface can be partially attenuated by the use of proper coupling agents (such as 4-methacryloxyethyl trimellitic anhydride).

Other examples are reported for the case of dimethacrylates used in dentistry where:

• Water solubility reaches 1.2%À1.7% even for composites with c. 75% weight fillers [START_REF] Wei | Diffusion and concurrent solubility of self-adhering and new resinÀmatrix composites during water sorption/desorption cycles[END_REF], that is, higher than expected from the water-uptake value for pure resin (see Table 7.8). • The diffusivity is observed to be higher in composites than in the pure matrix [START_REF] Dhanpal | Effect of temperature on water sorption and solubility of dental adhesive resins[END_REF]. The water solubility and/or diffusivity are higher in the pure matrix, thus, needing much more complex modeling [START_REF] Joliff | Study of the moisture/stress effects on glass fibre/epoxy composite and the impact of the interphase area[END_REF].

In terms of mechanical properties, these observations are consistent with the results obtained by Jager et al. (2016a) who found highly filled matrices to be the most sensitive to water permeation.

Effect of penetrant composition mixture

It seems that, in a first approach, water has almost the same effect than various artificial salivas, as illustrated by [START_REF] Al-Mulla | Effect of water and artificial saliva on mechanical properties of some denture-base materials[END_REF].

Ethanol is also more soluble in dimethacrylates than water [START_REF] Malacarne-Zanon | Effects of ethanol addition on the water sorption/solubility and percent conversion of comonomers in model dental adhesives[END_REF], consistent with its lower solubility parameter (26.5 MPa 1/2 ) than water.

The effect of water and more acidic media (coke, orange juice) was compared by [START_REF] Rahim | Water sorption characteristics of restorative dental composites immersed in acidic drinks[END_REF] showing that:

• Diffusion mechanism remains Fickian in every case.

• The water diffusion coefficient remains about constant.

• The maximum fluid uptake and the fraction of solubilized compounds increases.

This last result can be explained due to better leaching of unreacted monomers and soluble materials and/or a possible hydrolysis reaction, which will be next.

CHEMICAL AGEING BY HYDROLYSIS

A supplementary effect of water penetration is the possible hydrolysis of ester groups. In the case of biomaterials, these reactions were proposed:

1. In the case of PMMA where chain scission occur on side chains [START_REF] Ayre | Ageing and moisture uptake in (PMMA) bone cements[END_REF][START_REF] Ali | A review of the properties and applications of poly (methylmethacrylate) (PMMA)[END_REF][START_REF] Semen | The acid hydrolysis of isotactic and syndiotactic poly(methyl methacrylate)[END_REF][START_REF] Du | Complete UV emission of ZnO nanoparticles in a PMMA matrix[END_REF]) (Scheme 7.9). The hydrolytic degradation is, thus, expected to firstly modify the polarity of the material (since each elementary reaction converts one ester group into a carboxylic acid group). 2. In the case of TEGDMA in the presence of enzymes such as cholesterol esterase [START_REF] Ferracane | Hygroscopic and hydrolytic effects in dental polymer networks[END_REF][START_REF] Finer | Salivary esterase activity and its association with the biodegradation of dental composites[END_REF]) (Scheme 7.10).

In ideal networks (no dangling chains or loops), one has:

n 5 n 0 À 3s (7.60) CH 2 C CH 3 C O OMe n CH 2 C CH 3 C O OH n + CH 3 OH SCHEME 7.9
Mechanism of PMMA hydrolysis.

But, this relation is no longer valid differ from the ideal (since each chain scission generates two dangling chains). The complete mathematical treatment is proposed in [START_REF] Richaud | Crosslink density changes during the hydrolysis of tridimensional polyesters[END_REF].

In networks such as Bis-GMA, the ratio of ester bond needed for the "degelation" of the network (i.e., the total disappearance of elastically active chains and the possible solubilization of the material in a good solvent) is given by [START_REF] Gilormini | A statistical theory of polymer network degradation[END_REF]:

x d 5 1 2 1 ffiffiffiffiffiffiffiffiffiffiffi 1 1 2 L q (7.61)
L being the number of reactive units (here hydrolysable ester groups) per elastic chain.

Since carboxylic acids are efficient catalysts of the hydrolysis reaction, the hydrolysis degradation can display a certain autoaccelerated behavior [START_REF] Richaud | Crosslink density changes during the hydrolysis of tridimensional polyesters[END_REF]. The kinetic aspects of ageing are depicted in Fig. 7.21. Lastly, it must be mentioned that the kinetics of water ageing may be by the rate of water diffusion from the edge to the bulk [START_REF] El Yagoubi | A fully coupled diffusion-reaction scheme for moisture sorptionedesorption in an anhydride-cured epoxy resin[END_REF]. This means that the general equation for water consumption in any layer of the polymer is given by [START_REF] Jacques | Hydrolytic ageing of polyamide 11. 1. Hydrolysis kinetics in water[END_REF]: @w @t 5 D w Á @ 2 w @x 2 2 k h ÁwÁe (7.62)

where D w is the water diffusivity, k h is the rate constant for hydrolysis, e and w are, respectively, the concentrations in water and in hydrolysable groups (namely ester). This equation can be adapted for several practical cases (e.g., the existence of several kinds of reactive groups, or the possibility of noncatalyzed and catalyzed hydrolysis), but in the simplest case, the thickness of degraded layer can be approximated by: In other words, the final properties of the polymer correspond to the average of the undegraded bulk and the degraded edges.

CHEMICAL AGEING BY RADIOLYSIS

Radiolytic processes are involved in the sterilization of some polymers before implantation [START_REF] Barton | The effects of gamma irradiation on medical grade poly(methyl methacrylate)[END_REF]. Results obtained on PMMA unambiguously show the decrease of molar mass, which is ascribed to the mechanisms shown in Scheme 7.11.

The number of scissions induced by an irradiation dose D per unit mass is given by: (7.64) where G(s) denotes the radiochemical yield of PMMA (in mol J 21 ). The radiochemical yield G(s) should be close to 1À2 3 10 27 mol J 21 in PMMA [START_REF] Schnabel | Aspects of Polymer Degradation and Stabilization[END_REF][START_REF] Thominette | Effect of radiolysis on the glass transition temperature of poly (methyl methacrylate)[END_REF][START_REF] Babu | Radiolysis of resist polymers. 1. Poly(methyl α-haloacrylates) and copolymers with methyl methacrylate[END_REF][START_REF] Charlesby | Comparison of gamma and ultra-violet radiation effects in polymethyl methacrylate at higher temperatures[END_REF]. Even if it is not of clinical interest, the case of the radiolysis of networks obtained from dimethacrylate remains an open question since the reactivity of esters (i.e., the radiochemical yield for chain scission) present in dimethacrylate might differ from the reactivity of esters present in PMMA [START_REF] Gilormini | Radiochemical "degelation" methacrylate networks[END_REF]. The mechanisms of chain scission in PMMA.

s 5 G s ð ÞÁD

CREEP AND FATIGUE

Let us first recall are two kinds of fatigue experiments:

1. Those made on unnotched samples: they lead to Wohler curves where mechanical stress is plotted versus the number of cycles. The Wohler curves of bulk-and reinforced-PMMA are compared in [START_REF] Baleani | Fatigue strength of PMMA bone cement mixed with gentamicin and barium sulphate vs pure PMMA[END_REF]. The report shows that filler would have a detrimental effect on fatigue resistance. 2. Those made on notched samples (fatigue crack propagation): they lead to the plot of crack growth rate (da/dN) versus the intensity factor (ΔK 5 ΔσÁaÁπ 1/2 Áf 5 K max 2 K min , K max , and K min are defined as the maximum and minimum stress intensity experienced by the crack and f being a geometric factor). The classical curve for fatigue crack propagation is depicted in Fig. 7.22.

The left side of the curve leads to the minimal value of stress intensity factor (also named fatigue crack inception or threshold ΔK i or ΔK th ) leading to crack propagation. Higher values of ΔK i correspond to tougher samples. ΔK i is slightly higher than 0.1 MPa m 1/2 in PMMA [START_REF] Ramsteiner | Fatigue crack growth in polymers[END_REF]) and c. five-times higher for composites used in dental restoration [START_REF] Shah | Mechanistic aspects of fatigue crack growth behavior in resin based dental restorative composites[END_REF].

The right side of the curve is a vertical asymptote reached at a stress intensity value K C close to the sample toughness (see Section 7.4.1) and linked to the critical size of a defect leading to brittle failure: In the intermediary domain, a linear dependence between crack growth rate and factor is observed, which is described by the Paris law [START_REF] Paris | A rational analytic theory of fatigue[END_REF]:

da dN
5 CÁΔK m (7.66)

In the case of thermoplastic polymers, the positive effect of average molar mass is illustrated in [START_REF] Skibo | On the generality of discontinuous fatigue crack growth in glassy polymers[END_REF]. The most probable explanation is that longer polymer chains produce effective entanglements and better fatigue resistance of the crazes. Fig. 7.23 illustrates a comparison of crack growth rate on PMMA aged in air and that grown in a Ringer solution [START_REF] Ayre | Ageing and moisture uptake in (PMMA) bone cements[END_REF] and illustrates the complexities of the effect of ageing on fatigue properties. m would be on the order of 5 for hydrolytically aged dental composites made of Bis-GMA, UDMA, Bis-EMA, and a small amount of TEGDMA, together with 60% of silica and zirconia fillers. Moreover, SEM observations show that the cracks propagate at the particle matrix interface and cause possible matrix-filler debonding [START_REF] Shah | Mechanistic aspects of fatigue crack growth behavior in resin based dental restorative composites[END_REF].

From a practical point of view, it is noteworthy that polymers are bad thermal conductive materials and that a high frequency for fatigue test can induce significant self-heating. Temperature can for example exceed 100 C in a PMMA submitted to a 50 Hz cyclic stress, meaning that sample reaches is rubbery domain and sample fails at a very low number of cycles [START_REF] Justice | Enhancement of the fatigue life of PMMA through prior crazing[END_REF]. Crack growth rate of a PMMA bone cement aged in air or in Ringer's solution

CONCLUSION AND PROSPECTS FOR THE FUTURE OF THESE

and methacrylates polymers are easily obtained by radical in-chain polymerization which makes composites easy to use for surgeons and dentists as biomaterials and matrices.

In this chapter, we presented various methods for synthesis and the structureproperties relationships aimed for designing materials.

However, they are sensitive, in particular, to water resulting that the initial properties cannot be maintained in vivo. The main degradation mechanisms expected to occur at moderate temperature, during use or sterilization by irradiation were presented and might be helpful to avoid complications induced by longterm ageing. One of the scientific challenges remains to take into account the presence of fillers complicating the lifetime prediction.

In the future, researches should pursue improving the dispersion of fillers and the development of materials that offer a good compromise between low viscosity and improved mechanical properties. The properties could also be improved by new polymerization strategies involving, for example, enhanced hydrostatic pressure to limit the presence of porosities which are known to dramatically decrease the mechanical properties of composites and increasing composites' water uptake [START_REF] Soles | Contributions of the nanovoid structure to the kinetics moisture transport in epoxy resins[END_REF].

FIGURE

  FIGURE 7.1

Ferracane ( 2011

 2011 ) proposed to classify dental composites according to the fillers size (Fig.7.6).

FIGURE

  FIGURE 7.7Resin composite in syringe.

FIGURE

  FIGURE 7.8 Polymerization lamp.

  FIGURE 7.10Effect of increasing the filler ratio (φ f ).

  Initiation step for network polymerization.

  FIGURE 7.14Kinetics aspects of network formation.

  7.4.1 STRUCTUREÀPROPERTIES RELATIONSHIPS AND LINK WITH CLINICAL APPLICATIONS7.4.1.1 Glass transition temperature and other transitions

FIGURE 7. 15

 15 FIGURE 7.15 Typical stressÀstrain curves in PMMA.

P

  is the water partial pressure (expressed in Pa) obeying Clapeyron's law:

FIGURE 7

 7 FIGURE 7.18Shape of sorption isotherms in polymers.

FIGURE 7. 20

 20 FIGURE 7.20Schematic thermomechanical behavior of virgin (full line) and water-aged (dashed line) bis-GMA 1 HEMA resin (in the case of physical ageing without chemical reactions).

  SCHEME 7.10Mechanism of TEGDMA hydrolysis.

FIGURE 7. 21

 21 FIGURE 7.21Typical kinetic curves for various ageing processes involving water.

  FIGURE 7.22Schematic results of fatigue crack propagation experiment.

  FIGURE 7.23

Table 7 .

 7 1 Approximate Values of Kinetic Parameters for Polymerization (Initiation by AIBN)

k d s 21 10 15 Áexp(261,000/RT) k p I mol 21 s 21 2.7 3 10 6 Áexp(210,600/RT) k t I mol 21 s 21 10 8 Áexp(21400/RT) FIGURE 7.13

Table 7

 7 The glass transition of thermoset networks increases with crosslinking density as, for example, illustrated in polymethylmecrylate networks crosslinked with ethylene glycol methacrylate

	.2 Flox-Flory Parameters for PMMA (Cardenas and
	O'Driscoll, 1976; Lu and Jiang, 1991)
		T gN (K)	K FF (K kg mol 21 )
	a-PMMA	387	2.10 5
	a-PMMA	388	21.10 4
	i-PMMA	318	11.10 4
	s-PMMA	405	20.10 4

Table 7 .

 7 3 Theoretical Maximum Glass Transition Temperature of Fully Cured Methacrylate Networks Used for Dental Applications

		T gl (K)	F (g mol 21 )	n 0 (mol g 21 )	T gN (K)
	BisGMA	327.4	18.3	0.0039	413.2
	UDMA	320.6	15.4	0.00425	399
	BisEMA	320.7	17.2	0.0037	394
	TEGDMA	268.4	14.7	0.00699	382.9

Table 7 .

 7 4 Characteristics of Photocured Bis-GMA-TEGDMA Networks

	Curing time (s)		25	45	60	15
	Conversion degree (%)	36.3	47.5	55.1	68.3
	Approximative T g ( C)	15	25	50	90
	Table 7.5 Effect of Curing Degree in a Bis-GMA-TEGDMA (50/50) Matrix
	Reinforced with 62% Fillers
	Conversion Degree (%)	E (GPa)	K IC (MPa m 1/2 )	σ f (MPa)	Hardness (kg mm 22 )
	55	6.38	1.29	88.7		63.5
	60	8.94	1.61	109.2		73.2
	61	10.35	1.79	115.2		77.0
	64	11.41	1.89	117.1		86.3
	66	14.27	2.19	155.4		93.4

Table 7

 7

	TEGDMA	89,640	184.9	485	5.3
	UDMA	169,530	342.9	494	5.4
	Bis-GMA	225,930	339.4	666	7.3
	Bis-EMA	185,930	393.4	473	5.2
	PMMA	33,830	81.9	413	4.5

.6 Estimation of Cohesive Energy and Compression Modulus E coh (J mol 21 )

V m (cm 3 cm 21 ) CED (MPa) K (GPa)

Table 7 .

 7 7 Poisson's Ratio of Polymethacrylates Used for Dental Applications

	Resin	Filler		Poisson's Ratio
	BisGMA 1 TEGDMA	40%	Colloidal silica 0.01À0.09 μm	0.372
	BisGMA 1 TEGDMA	66%	Zircone 1 silica 0.01À3.5 μm	0.302
	BisGMA 1 UDMA 1 BisEMA	60%	Zircone 1 silica 0.01À3.5 μm	0.308
	BisGMA 1 TEGDMA	47%	Zircone 1 silica 0.01À6 μm	0.393

Table 7

 7

	.8 Flexural Strength, Elastic Modulus, and Brinell Hardness for Some
	Unfilled Polymethacrylates Used for Dental Applications (Barszczewska-
	Rybarek, 2009)
	Resin	σ f (MPa)	E (MPa)	HB (N mm 22 )
	Poly(bis GMA)	115	3800	75
	Poly(TEGDMA)	85	3900	135
	Poly(UDMA)	140	3500	165
	Poly(bisGMA-co-TEGDMA)	95	4100	90
	Poly(bisGMA-co-TEGDMA-co-UDMA)	105	2800	190

Table 7 .

 7 9 Water Equilibrium Mass Uptake in Several Methacrylate Polymers

			w/w	Reference
	PMMA	23 C	1.90%	Smith and Schmitz (1988)
	BisGMA	37 C	3.57%À3.86%	Sideridou et al. (2008)
	TEGDMA	37 C	5.74% 2 6.25%	Sideridou et al. (2008)
	UDMA	37 C	2.39%À3.10%	Sideridou et al. (2008)
	BisEMA	37 C	1.92%À2.11%	Sideridou et al. (2008)
	D3MA	37 C	0.65%À0.66%	Sideridou et al. (2008)

Table 7 .

 7 10 Values of Diffusion Coefficient in Several Resins[START_REF] Sideridou | Sorption of water, ethanol or ethanol/water solutions by light-cured dental dimethacrylate resins[END_REF][START_REF] Barrie | Diffusion and association of water in some polyalkylmethacrylates. Part 1 À Equilibrium sorption and steady state permeation[END_REF]

		T (K)	D (cm 2 s 21 )	Reference
	PMMA	313.7	5.2 3 10 28	Barrie and Machin (1971)
		323.4	8.9 3 10 28	Barrie and Machin (1971)
		333	1.5 3 10 27	Barrie and Machin (1971)
		343.2	2.4 3 10 27	Barrie and Machin (1971)
	BisGMA	310	1.1 3 10 27	Sideridou and Karabela (2011)
	BisEMA	310	0.74 3 10 27	Sideridou and Karabela (2011)
	UDMA	310	0.69 3 10 27	Sideridou and Karabela (2011)
	TEGDMA	310	0.15 3 10 27	Sideridou and Karabela (2011)
	D3MA	310	0.62 3 10 27	Sideridou and Karabela (2011)

Table 7 .

 7 11 Water Sorption Parameter at 37 C in PMMA and Its Composites

			Diffusion	% Water Uptake
		%	Coefficient
	Material	Polymer	( 3 10 8 cm 2 s 21 )	Calulated Experimental
	PMMA	100	2.26		2.28
	PMMA 1 barium sulfate	31	33.18	0.71	1.23
	PMMA 1 barium	30	10.08	0.68	1.27
	sulfate 1 coupling agent
	PMMA 1 barium glass	25	10.55	0.57	1.23
	silance coated
	PMMA 1 barium glass	23	9.42	0.52	1.04
	silance coated 1 coupling
	agent