Kinetic chain

As with the rate of polymerization, we see from Eq. (6.37) that the kinetic chain length depends on the monomer and initiator concentrations and on the constants for the three different kinds of kinetic processes that constitute the mechanism. When the initial monomer and initiator concentrations are used, Eq. (6.37) describes the initial polymer formed. The initial degree of polymerization is a measurable quantity, so Eq. (6.37) provides a second functional relationship, different from Eq. (6.26), between experimentally available quantities-n, [M], and [1]-and theoretically important parameters—kp, k, and k. Note that the mode of termination which establishes the connection between u and hj, and the value of f are both accessible through end group characterization. Thus we have a second equation with three unknowns one more and the evaluation of the individual kinetic constants from experimental results will be feasible. 

The degree of polymerization in Eq. (6.41) can be replaced with the kinetic chain length, and the resulting expression simplified. To proceed, however, we must choose between the possibilities described by Eqs. (6.34) and (6.35). Assuming termination by disproportionation, we replace n, by v, using Eq. (6.37) ... 

The kinetic chain length u may also be viewed as merely a cluster of kinetic constants and concentrations which was introduced into Eq. (6.54) to simplify the notation. As an alternative, suppose we define for the purposes of this chapter a fraction p such that... 

The three-step mechanism for free-radical polymerization represented by reactions (6.A)-(6.C) does not tell the whole story. Another type of free-radical reaction, called chain transfer, may also occur. This is unfortunate in the sense that it complicates the neat picture presented until now. On the other hand, this additional reaction can be turned into an asset in actual polymer practice. One of the consequences of chain transfer reactions is a lowering of the kinetic chain length and hence the molecular weight of the polymer without necessarily affecting the rate of polymerization. 

The kinetic chain length has a slightly different definition in the presence of chain transfer. Instead of being simply the ratio Rp/R, it is redefined to be the rate of propagation relative to the rates of all other steps that compete with propagation specifically, termination and transfer (subscript tr) ... 

We shall consider these points below. The mechanism for cationic polymerization continues to include initiation, propagation, transfer, and termination steps, and the rate of polymerization and the kinetic chain length are the principal quantities of interest. 

Chain transfer reactions to monomer and/or solvent also occur and lower the kinetic chain length without affecting the rate of polymerization ... 

The overall effect, aside from the change in the polymer composition, is a decrease in the rate of monomer reaction, the kinetic chain length, and the polymer molecular weight (83). 

An important descriptor of a chain reaction is the kinetic chain length, ie, the number of cycles of the propagation steps (eqs. 2 and 3) for each new radical introduced into the system. The chain length for a hydroperoxide reaction is given by equation (10) where HPE = efficiency to hydroperoxide, %, and 2/ = number of effective radicals generated per mol of hydroperoxide decomposed. For 100% radical generation efficiency, / = 1. For 90% efficiency to hydroperoxide, the minimum chain length (/ = 1) is 14. 

The main reason that the decreases as the polymerization temperature increases is the increase in the initiation and termination reactions, which leads to a decrease in the kinetic chain length (Fig. 17). At low temperature, the main termination mechanism is polystyryl radical coupling, but as the temperature increases, radical disproportionation becomes increasingly important. Termination by coupling results in higher PS than any of the other termination modes. 

For example, at 60°C, = 2300 and = 2.9 x 10. An estimate of kinetic chain lifetime, ie, the time from initiation to termination by reaction with... 

Termination. The conversion of peroxy and alkyl radicals to nonradical species terminates the propagation reactions, thus decreasing the kinetic chain length. Termination reactions (eqs. 7 and 8) are significant when the oxygen concentration is very low, as in polymers with thick cross-sections where the oxidation rate is controlled by the diffusion of oxygen, or in a closed extmder. The combination of alkyl radicals (eq. 7) leads to cross-linking, which causes an undesirable increase in melt viscosity. 

Radical Scavengers Hydrogen-donating antioxidants (AH), such as hindered phenols and secondary aromatic amines, inhibit oxidation by competing with the organic substrate (RH) for peroxy radicals. This shortens the kinetic chain length of the propagation reactions. 

The average kinetic chain length r is defined as the number of monomer units consumed per active centre formed and is given by R fV (or R tV ). 

Destruction of macroradicals—scission of kinetic chains. A disproportionation reaction is most common at this stage ... 

At present, high-temperature stabilization of polyolefins is still misunderstood besides, this problem presents serious difficulties. Stabilization of thermal oxidation and photoinduced destruction with the use of stabilizers in this case is inefficient, since at high temperatures these stabilizers are easily evaporated out of the polyolefin melt and decomposed with the formation of radicals capable of initiating additional kinetic chains of destruction. 

The block copolymer produced by Bamford s metal carbonyl/halide-terminated polymers photoinitiating systems are, therefore, more versatile than those based on anionic polymerization, since a wide range of monomers may be incorporated into the block. Although the mean block length is controllable through the parameters that normally determine the mean kinetic chain length in a free radical polymerization, the molecular weight distributions are, of course, much broader than with ionic polymerization and the polymers are, therefore, less well defined,... 

Such a reciprocal motion of the kinetic chain (or back reaction) results in the decomposition of hydroperoxide groups without any interruption of kinetic chains and leads to the decrease in hydroperoxy groups. It has... 

In the process of radical polymerization a monomolecular short stop of the kinetic chain arises from the delocalization of the unpaired electron along the conjugated chain and from the competition of the developing polyconjugated system with the monomer for the delivery of rr-electrons to the nf-orbitals of a transition metal catalyst in the ionic coordination process. Such a deactivation of the active center may also be due to an interaction with the conjugated bonds of systems which have already been formed. 

If the amount of termination by radical-radical reaction is neglected the degree of polymerization and the kinetic chain length are given by eq. 29 ... 

Thus with aMeSt, the kinetic chain is relatively short, monomer is consumed mainly by initiation and propagation, and chain transfer by the HSiCCHj CH H C Q initiator is unfavorable (see Sect. III.B.3.b.i.). In contrast, with isobutylene the kinetic chain may live longer because it is sustained by thermodynamically favorable chain transfer by the initiator. Scheme 5 illustrates the mechanism of isobutylene polymerization by the HSi(CH3)2CH2CH29>CH2Cl/Me3Al system. The kinetic chain is sustained by chain transfer loops shown on the left margin of the Scheme. 

This is equivalent to the steady-state approximation. Provided the kinetic chains are long,... 

It Is well known that low values of Tq and [ ]q lead to high DPs. This Is accurately reflected by parameter (v )q, the Initial kinetic chain length (Table XIll), which Is a quotient of feed composition ratio Xq and dimensionless parameter a. Thus,... 

Figures 1-4 show that when polymerizations were carried out at low concentrations of initiator and/or at low temperatures, the agreement between the model predictions and the experimental data is not so good. This is due to the fact that under those reaction conditions where R is low a large kinetic chain length is expected. When this is so, chain transfer to monomer becomes a reaction to be taken into account, since it markedly influences the chain length of the polymer being formed. A decrease in the instantaneous degree of polymerization, due to chain transfer to monomer, will reduce the concentration of the entangled radicals and, consequently, a decrease in the rate of polymerization is expected.

Support for the involvement of Fe comes from the observation that the kinetic chain length of the dimethyl ester increases with increasing concentration of added Fe together with a fourfold increase in the yield of 262 (216). However, as a vinyl cation bearing carbonyl substituents may be energetically unfavorable, an alternative mechanism, involving a ligand transfer from hydrated Fe ions followed by an acid-catalyzed cyclization, may be a more likely pathway ... 

Any polymer contains some inner free space free volume distributed in a dynamic manner between its molecular chains (see Section 23.2). When it is exposed to a fluid (liquid or gas) the physical possibility exists for fluid absorption by the polymer, if the fluid molecules or atoms are small enough to fit into local regions of this distributed space during kinetic movements. As this happens, subsequent kinetic chain motion must allow for the newly absorbed fluid molecules and, hence, the polymer s overall volume will adjust accordingly this action will coincide with the formation of more free space around these fluid molecules—so the polymer will swell a little. This process will be continued until an equilibrium is reached ( equilibrium swelling ), by which time the extent of swelling can be considerable. The amount of fluid taken up and the rate at which this happens are both important, and are discussed in this and following sections. 

Eqs. (26) and (27) apply irrespective of the nature of the initiation process it is required merely that the propagation and termination processes be of the second order. They emphasize the very general inverse dependence of the kinetic chain length on the radical concentration and therefore on the rate of polymerization. The kinetic chain length may be calculated from the ratios k /kt as given in Table XI and the rate of polymerization. Thus, for pure styrene at 60°C... 

At the same rate of polymerization, the kinetic chain length for vinyl acetate is over a hundred times that for styrene on account of the greater speed of propagation relative to termination for vinyl acetate. At a convenient rate of 10 moles/liter/sec., for example, each radical chain generated consumes on the average about 5X10 vinyl acetate units under the conditions stated. 

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