The Kinetics of Chain Polymerizations

We have seen that the rate of step-growth or condensation polymerization is relatively slow and macromolecules are only produced at high degrees of conversion. In contrast, chain or addition polymerizations occur rapidly and polymer is produced in the initial stages of the reaction. Instead of having monomers going to oligomers and then to polymers, with essentially all the molecules 

FIGURE 4-13 The main steps of free radical polymerization. 

In some treatments of the kinetics of polymerization this step alone is considered initiation. Others consider initiation to also include a second step the reaction of this very reactive radical (because of the unshared electron left hanging out ) with the first monomer (Equation 4-22). 

This is the way we were taught, so that s what you re going to get However, it doesn t make a lot of difference, because the decomposition of the initiator is much slower than 

Note that we have written r, in terms of both the rate of formation of M] species and rate of disappearance of monomer and then substituted to get the final equation. The factor 2 appears because each initiator molecule (in this case peroxide) gives two radicals and can start two chains. One could also fold the constant factor 2 into the rate constant, if one were of a mind to do so. However, not all of the so-called primary radicals formed by decomposition of initiator react with the first monomer. Several other reactions can occur, some of which are shown below in 

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Bamford43,59 63 has proposed a general treatment for solving polymerization kinetics with chain length dependent kt and considered in some detail the ramifications with respect to molecular weight distributions and the kinetics of chain transfer, retardation, etc. 

Why are the kinetics of chain growth polymerization more difficult to study than those of step growth polymerization What simplification do we use to treat the kinetics of the chain growth process How does this simplification reduce the complexity of the problem and what are the limitations of this method ... 

The largest-volume polymers are polyolefins, and the kinetics of olefin polymerization are fairly similar to the ideal addition process just considered. All these olefins form condensation products to form a very long-chain alkane such as... 

The kinetics of template polymerization depends, in the first place, on the type of polyreaction involved in polymer formation. The polycondensation process description is based on the Flory s assumptions which lead to a simple (in most cases of the second order), classic equation. The kinetics of addition polymerization is based on a well known scheme, in which classical rate equations are applied to the elementary processes (initiation, propagation, and termination), according to the general concept of chain reactions. 

The dependence of the propagation rate on the concentration of growing chains is illustrated in Figures 6 and 7, and is listed in Table II. The first-order rate constant from Table II are plotted as a function of the initiator concentration. Although the kinetics of organolithium polymerization in nonpolar solvents have been subjected for intensive studies, the results were still somewhat controversial. In view of the strong experimental evidence for association between the organolithium species, the kinetic order ascribed to this phenomenon was postulated (30,31) as shown in Equations (5) and (6). 

A similar phenomenon was postulated by Thomas and Pellon (10) to account for data obtained in the kinetics of acrylonitrile polymerization. They felt that it was possible to obtain unimolecular chain termination by a process of burial. This was conceived as a mechanism by which the growing chain became shielded from further growth by coiling or by embedding itself in the solid phase. At room temperatures we feel the... 

Nomura (25) investigated the effect of carbon tetrabromide, carbon tetrachloride and long chain mercaptans on the kinetics of emulsion polymerization of styrene. In the case of CBr and CCl the effect on the polymerization was attributed to desorption of the small chain transferred radicals. Similar results were obtained by Napper et al (26). Nomura also observed that the long chain mercaptan (n- dodecyl mercaptan) did not affect the number of particles and the rate, presumably due to the water-insolubility of the chain transferred radicals. 

The subject of the kinetics of vinyl polymerization by radical mechanisms is treated exhaustively in a book by Bamford, et al. (4) and more briefly in many textbooks of polymer chemistry. The polymerization of vinyl monomers is a chain reaction in which the primary reactions are ... 

After the nucleation period, three types of kinetic processes determine the kinetics of emulsion polymerization radical entry, radical desorption, and polymer chain formation in the polymer particles. The kinetics of emulsion polymerization are fully described by the following five dimensionless parameters ... 

The kinetics of olefin polymerization are the subject of several studles>104,153-156,162,182,221,226,240,241,246,252,255,266,28 12 and of an excellent book by Keii.17 The most relevant studies will be discussed below. However, we first note that the precise description of the kinetics of catalytic olefin polymerization under industrially relevant polymerization conditions has proved to be very difficult. For a given catalytic system, one has to identify all possible insertion, chain-release, and chain-isomerization reactions, and their dependence on the polymerization parameters (most importantly, temperature and monomer concentration). Once the kinetic laws for each elementary step have been determined, they have to be combined in one model in order to be able to predict the catalyst performance. This has been attempted for both ethylene and propylene polymerizations. The case of propylene polymerization with a chiral, isospecific zirconocene is shown in Figure 14.162... 

The kinetics of emulsion polymerization is complex, involving a large number of species and at least two phases. The first quantitative approach to emulsion polymerization kinetics led to extensions by many others.The important events to consider are 1) the free-radical reactions of chain formation initiation, propagation, chain transfer, and termination and 2) the phase transfer events that control particle formation radical entry into particles from the aqueous phase, radical exit into the aqueous phase, radical entry into micelles, and the aqueous phase coil-globule transition. In free-radical emulsion polymerization, the fundamental steps are shown schematically in Fig. 1... 

Though ionic polymerization resembles free-radical polymerization in terms of initiation, propagation, transfer, and termination reactions, the kinetics of ionic polymerizations are significantly diflFerent from free-radical polymerizations. In sharp contrast to free-radical polymerizations, the initiation reactions in ionic polymerizations have very low activation energies, chain termination by mutual destruction of growing species is nonexistent, and solvent effects are much more pronounced, as the nature of solvent determines whether the chain centers are ion pairs, free ions, or both. No such solvent role is encountered in free-radical polymerization. The overall result of these features is to make the kinetics of ionic polymerization much more complex than the kinetics of free-radical polymerization. 

Even when conditions are scrupulously controlled, the kinetics of cationic polymerization are rarely simple. Water is highly reactive towards organic cations and if present as initiator, any excess will terminate polymer chains. Excess water may also destroy the coinitiator in some cases, or compete successfully with monomer for the initiator-coinitiator complex (see later). The kinetic influence of water is thus complicated. In some systems, the initial rate of polymerization increases with concentration of water at low concentrations and becomes independent as this concentration increases. Such behavior has been reported for the polymerization of isobutene in dichloromethane initiated by titanium tetrachloride and water [21]. In other systems, the initial rate of polymerization may rise to a maximum and then decline with increasing concentrations of water. Such behavior has been observed in the SnCl4/H20 initiated polymerization of styrene in carbon tetrachloride [22]. 

Nonpolar Media. Because organolithium initiators are soluble in hydrocarbons, the kinetics of these polymerizations have also been studied in these nonsolvating media. A large number of such studies have been carried out (3, 41) mainly on styrene and the dienes. Again the propagation rate is first order with respect to monomer, in accordance with Reaction 13. However, the rate dependence on growing chain concentration has been found to show marked variation from one system to another with the orders varying from one half to much lower values (3, 41). These systems pose... 

An interesting analysis of the influence of thermodynamics on the kinetics of TXN polymerization is given in a series of papers by Enikolopyan et al. 96-98). These authors consider polymerization to be homogeneous (in the kinetic sense) in contrast to the above-discussed polymerization in the crystalline state. The equilibrium between crystalline and dissolved polymer is considered (only the fragment of the chain that carries the active end needs to be dissolved) and on this basis some kinetic peculiarities of TXN polymerization are explained. 

For simultaneous interpenetrating networks (SINs), two independent, non-interfering reactions are required. Thus, a chain and a step polymerization have been the method of choice for many such polymerizations. Typical examples have involved PS and polyurethanes [Hourston and Schafer, 1996 Mishra et ai, 1995], and PMMA. A key factor in the kinetics of such polymerizations is to keep the system above the glass transition temperature of both components. If the glass transition of either the polymer network I or polymer network II rich phase vitrifies, the polymerization in that phase may slow dramatically. 

Ionic-polymerization Kinetics. The kinetics of ionic polymerization share some common principles with that of the free-radical reaction. Both are based on the basic steps of initiation, propagation, termination, and chain transfer, and in both the ultimate average molecular weight depends on the ratio of the reaction rates of propagation and termination. There are, however, important differences. In ionic polymerization the termination step appears to be unimolecular, while it is bimolecular in free-radical type polymerization. The dependence of the kinetic scheme of the reaction on the various parameters is therefore different in the two reactions. Likewise, the fact that a cocatalyst has to be brought into the ionic reaction scheme has to be taken into account. 

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