1 Introduction 1.1 THERMOPLASTIC AND THERMOSETTING POLYMERS Based on their response to temperature, plastic materials may be classified into two main categories: thermoplastics and thermosets. A thermoplastic behaves like a fluid above a certain temperature level, but the heating of a thermoset leads to its degradation without its going through a fluid state. In fact, this reflects the behavior of plastic materials under the action of fire, providing the simplest identification test. This classification is not restricted to plastic materials but may also be extended to the behavior of coatings, adhesives, and several other categories. This is why we find it better to use the term thermosetting polymers, which implies the different ways in which these materials are used and adds the fact that a constitutional repeating unit (CRU) is present in their chemical structures. These materials are also referred to as thermosetting resins, which is a vaguer definition that may be applied to the starting monomers or oligomeric precursors, as well as to the final materials. Typical examples of thermosetting polymers are phenolic and urea– formaldehyde resins, unsaturated polyesters, and epoxy resins. Typical ther- moplastics are polyethylene, polypropylene, polystyrene, and poly(vinyl chloride). The thermoplastic or thermosetting character of a polymer depends on whether it can reach a fluid state by heating. This state can be attained only if individual macromolecules separate to produce flow. This is in principle possible for materials composed of linear or branched macro- molecules held together by secondary forces (van der Waals, dipole–dipole, hydrogen bonding). These materials may be either amorphous (e.g., atactic polystyrene) or semicrystalline (e.g., polyethylene, polypropylene). For amorphous thermoplastics, flow will take place by heating beyond the glass transition temperature (after devitrification). For semicrystalline thermoplastics, it is necessary to heat beyond the melting temperature to reach a fluid state. For high-molar-mass thermoplastics (with molar masses much higher than the entanglement limit), the fluid state is characterized by very large relaxation times so that processing by conventional methods is not possible. In some cases the synthesis and shaping of a thermoplastic polymer is produced in the same process as for thermosetting polymers (reactive pro- cessing). For example, some poly(amide-imides) are processed by combining the injection molding of prepolymers with reactive chain ends, with the subsequent cure in a heated mold, to obtain a part made of a high-molar- mass linear polymer that cannot be processed by conventional methods. Cast poly(methyl methacrylate) sheets are produced from a solution of the final polymer in methyl methacrylate. The dilution of the initial mono- mer with the polymerization product is required to reduce both the tem- perature increase due to the heat of reaction and the final shrinkage of the part. In poly(tetrafluoroethylene) or poly(acrylonitrile), the density of sec- ondary forces is so high that degradation of the chemical structure takes place before a fluid state is reached. All these materials are classified as thermoplastics because individual molecules can in principle be separated by flow (even though unrealistic times are required) or through the action of an adequate solvent. A distinctive characteristic of a thermosetting polymer is that one giant macromolecule consisting of covalently bonded repeating units is formed during the polymerization process. This giant macromolecule that percolates throughout the sample is called a gel. Unless the covalent bonds present in the gel are destroyed by the action of temperature or a reactive solvent, the thermosetting polymer will not flow. Therefore, the thermoset- ting nature of a polymer is due to the presence of a network formed by covalent bonds. A good solvent will swell the polymer but will not dissolve it. However, not every polymer network is a thermosetting polymer, because networks may be also be produced by physical crosslinks among individual chains, as in gelatin. In this case, heating dissociates the individual polymer molecules and converts the material from a gel to a fluid state (a sol). And the gel may be reversibly regenerated during a subsequent cooling step. 2 Chapter 1 Therefore, from a more fundamental point of view, thermosetting polymers may be defined as polymer networks formed by the chemical reaction of monomers, at least one of which has 3 or more reactive groups per molecule (a functionality equal to or higher than 3), and that are present in relative amounts such that a gel is formed at a particular conversion during the synthesis. In a symbolic form, it may be stated that a thermo- setting polymer is obtained by the homopolymerization of an A f molecule ðf ! 3 is the number of functional groups per molecule), or the polymeriza- tion of A f by reaction with B g (where f and/or g are ! 3) and they are present in a particular ratio such that a gel will be formed. In commercial formulations, mixtures of several monomers differing in chemical structure and functionality may be used and the gel may be formed through com- petitive reactions among the different monomers. Because the polymer network is produced in an irreversible way, the synthesis of a thermosetting polymer is carried out to produce the final material with the desired shape. Therefore, polymerization and final shap- ing are performed in the same process. The situation is completely dif- ferent for most of the thermoplastic polymers. The processor gets the final part by heating (to provide flow) and cooling (to set the final shape) in an injection machine, an extruder, etc. The mold used to obtain a part made of a thermosetting polymer is a true chemical reactor, while the machine used to obtain a similar part made of a thermoplastic poly- mer acts as a heat exchanger (part of the necessary heat may be gener- ated by viscous dissipation). In thermosetting polymers incorrect processing leads to the irreversible loss of the material (it may be reused for other purposes, e.g., as a filler); in thermoplastics the material may be reused many times (although a continuous decrease in the average molar mass is produced by the relatively high temperatures used in the proces- sing machines). The synthesis of a thermosetting polymer starts from monomers (a sol phase). At a particular conversion of functional groups, gelation takes place, meaning that a giant macromolecule that percolates through the sample appears in the system. This sol–gel critical transition is a distinctive feature of thermosetting polymers. Before gelation the material is a sol with a finite value of viscosity. At gelation, viscosity increases to infinite. After gelation an insoluble fraction (the gel fraction) is present in the system. Eventually, at full conversion of functional groups, in stoichiometric formulations, the sol fraction disappears and the final thermosetting polymer is composed of one giant molecule of a gel. Although a sol–gel transformation is present in the synthesis of any thermosetting polymer, in some fields it is used in a rather restrictive way. For example, ceramists associate sol–gel processes with the hydrolytic con- Introduction 3 densation of precursors to obtain inorganic polymer networks (SiO 2 , TiO 2 , etc.) or hybrid inorganic–organic polymer networks. Thermosetting polymers are usually amorphous because there is no possibility of ordering portions of the network structure due to the restric- tions imposed by the presence of crosslinks. Exceptions are networks obtained from rigid monomers exhibiting a nematic–isotropic transition. In these cases, a polymer network presenting a nematic–isotropic transition may be obtained, provided that the concentration of crosslinks is kept at a low value. One of the most important parameters characterizing a thermosetting polymer is the location of its glass transition temperature (T g ) with respect to the temperature at which it is used (T use ). Most thermosetting polymers are formulated and selected so that their T g is higher than T use ; therefore, they behave as glasses during their use. Materials exhibiting a T g lower than T use are classified as rubbers, but they can also be regarded as thermosetting polymers operating in the rubbery state and are thus included within the scope of the book. Thermosetting polymers are well established in areas where thermo- plastics cannot compete because of either properties or costs. For example, phenolics constitute a first option when fire resistance is required because they are self-extinguishing and exhibit low smoke emission. Urea–formalde- hyde polymers for wood agglomerates and melamine–formaldehyde for furniture coatings give products of excellent quality at low costs. Unsaturated polyesters are extensively used to produce structural parts with a glass-fiber reinforcement. In addition, epoxies, cyanate esters, and polyimides are employed for aeronautical and electronic applications where their excellent properties cannot be matched by thermoplastics. The average percent annual growth in the United States during the decade from 1989 to 1999 was 2% for synthetic rubbers, 4% for thermosetting polymers, and 5% for thermoplastics. 1.2 ORGANIZATION OF THE BOOK Every chapter has been prepared in a self-consistent form and includes a particular notation that is given at its end (although the most frequently occurring variables and parameters have the same notation throughout the book). Thus, a reader with a preliminary knowledge of the subject can go directly to any of the chapters. However, for a reader approaching the subject for the first time, it will be much more convenient to follow the order in which the book is organized. 4 Chapter 1 Different chemistries for the synthesis of thermosetting polymers are described in Chapter 2. The distinction between step-growth and chain polymerizations is clearly established, and several examples of both types of reaction are presented. The buildup of the network is discussed in Chapter 3 for both types of polymerization reactions. Equations derived from mean-field models or from combinations of kinetic and recursive pro- cedures (fragment approach) enable us to calculate statistical parameters of the network as a function of the conversion of functional groups. In parti- cular, the gel conversion may be predicted and stoichiometric ratios neces- sary to avoid gelation may be obtained. The evolution of the glass transition temperature with conversion is discussed in Chapter 4. This information, together with the gel conversion, is used to develop transformation diagrams that may be employed to predict the different transitions that will take place during a cure cycle. Chapter 5 presents different equations, either phenom- enological or based on reaction mechanisms, used to describe the kinetics of network formation. Some incorrect ways of presenting kinetic results are discussed and examples are provided; the influence of diffusion limitations is analyzed. Both rheologic and dielectric monitoring of network formation are discussed in Chapter 6, while Chapter 7 tries to answer the question con- cerning the inhomogeneity of some polymer networks (a controversial sub- ject). Chapter 8 deals with the preparation of rubber-modified thermosets and thermoset–thermoplastic blends, which are frequently used to improve some properties of the neat thermosetting polymer. An introduction to the processing of thermosetting polymers is developed in Chapter 9, with the main emphasis placed on the estimation of temperature and conversion profiles generated during the cure process. The effect (or lack of effect) of crosslinks on basic physical properties of thermosetting polymers is discussed in Chapter 10, while the effect on elastic and viscoelastic properties is analyzed in Chapter 11. Yielding and fracture of neat and modified thermosetting polymers are discussed in Chapters 12 and 13. Finally, the very important problem of the durability of polymer networks is presented in Chapter 14. Introduction 5 . thermosetting polymers is discussed in Chapter 10 , while the effect on elastic and viscoelastic properties is analyzed in Chapter 11 . Yielding and fracture of neat and modified thermosetting polymers. growth in the United States during the decade from 19 89 to 19 99 was 2% for synthetic rubbers, 4% for thermosetting polymers, and 5% for thermoplastics. 1. 2 ORGANIZATION OF THE BOOK Every chapter has. 1 Introduction 1. 1 THERMOPLASTIC AND THERMOSETTING POLYMERS Based on their response to temperature, plastic materials may