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The two monomers enter into the copolymer in overall amounts determined by their relative concentrations and reactivities. The simultaneous chain polymerization of different monomers can also be carried out with mixtures of three or more monomers. Such polymerizations are generally referred to as multicomponent copolymerizations; the term terpolymerization is speci cally used for systems of three monomers. Copolymerization is also important in step polymerization. Relatively few studies on step copolymerization have been carried out, although there are considerable commercial applications. Unlike the situation in chain copolymerization, the overall composition of the copolymer obtained in a step copolymerization is usually the same as the feed composition since step reactions must be carried out to close to 100% conversion for the synthesis of



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(6.1)

Principles of Polymerization, Fourth Edition. By George Odian ISBN 0-471-27400-3 Copyright # 2004 John Wiley & Sons, Inc.

high-molecular-weight polymers. Further, most step polymerizations are equilibrium reactions and the initially formed copolymer composition is rapidly changed by equilibration. This chapter is concerned entirely with chain copolymerization. The main features of step copolymerization have been covered in Sec. 2-13.

(6.3)





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Chain copolymerization is important from several considerations. Much of our knowledge of the reactivities of monomers, free radicals, carbocations, and carbanions in chain polymerization comes from copolymerization studies. The behavior of monomers in copolymerization reactions is especially useful for studying the effect of chemical structure on reactivity. Copolymerization is also very important from the technological viewpoint. It greatly increases the ability of the polymer scientist to tailor-make a polymer product with speci cally desired properties. Polymerization of a single monomer is relatively limited as to the number of different products that are possible. The term homopolymerization is often used to distinguish the polymerization of a single monomer from the copolymerization process. Copolymerization allows the synthesis of an almost unlimited number of different products by variations in the nature and relative amounts of the two monomer units in the copolymer product. A prime example of the versatility of the copolymerization process is the case of polystyrene. More than 11 billion pounds per year of polystyrene products are produced annually in the United States. Only about one-third of the total is styrene homopolymer. Polystyrene is a brittle plastic with low impact strength and low solvent resistance (Sec. 3-14b). Copolymerization as well as blending greatly increase the usefulness of polystyrene. Styrene copolymers and blends of copolymers are useful not only as plastics but also as elastomers. Thus copolymerization of styrene with acrylonitrile leads to increased impact and solvent resistance, while copolymerization with 1,3-butadiene leads to elastomeric properties. Combinations of styrene, acrylonitrile, and 1,3-butadiene improve all three properties simultaneously. This and other technological applications of copolymerization are discussed further in Sec. 6-8. 6-1b Types of Copolymers

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As can be seen from (6.3), we have neglected the constant self-energy contribution to the Coulomb energy. This term leads to a shift in the mass of the bare particle. It is the same mass renormalization as that present in classical theory [131]. The linear size of a typical hydrogen atom is on the order of 1A. Only x-rays have wavelengths of that magnitude. The wavelengths of electromagnetic radiation emitted and absorbed by electronic transitions are usually much longer than this. When such radiation interacts with the atom, the field experienced by the electron is, to a very good approximation, the same experienced by the nucleus. So in equation (6.1) we can replace the position operator of the electron, r, in the argument of A by the position of the proton, which we assume fixed at the origin. This is called the dipole approximation (see Sec. 5.1). In the electric dipole approximation, the electron is insensitive to the magnetic field and the Heisenberg equation for the Cartesian momentum 7r= p + (qj c)A(O) together with the Heisenberg equation for the position of the electron (i.e., r =7r jm) yields the Newton-Lorentz equation without the magnetic force term

The copolymer described by Eq. 6-1, referred to as a statistical copolymer, has a distribution of the two monomer units along the copolymer chain that follows some statistical law, for example, Bernoullian (zero-order Markov) or rst- or second-order Markov. Copolymers formed via Bernoullian processes have the two monomer units distributed randomly and are referred to as random copolymers. The reader is cautioned that the distinction between the terms statistical and random, recommended by IUPAC [IUPAC, 1991, in press], has often not been followed in the literature. Most references use the term random copolymer independent of the type of statistical process involved in synthesizing the copolymer. There are three other types of copolymer structures alternating, block, and graft. The alternating copolymer contains the two monomer units in equimolar amounts in a regular alternating distribution:

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