Free radical polymerization kinetic chain length

Computational Aspects of Free Radical Polymerization Kinetics with Chain Length Dependent Termination... 

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 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,... 

Unlike ionic polymerizations, the termination of the growing free radical chains usually occurs by coupling of two macroradicals. Thus, the kinetic chain length (v) is equal to DP/2. The chemical and kinetic equations for bimolecular termination are shown below (Equations 6.17 and 6.18). 

Photoinitiated free radical polymerization is a typical chain reaction. Oster and Nang (8) and Ledwith (9) have described the kinetics and the mechanisms for such photopolymerization reactions. The rate of polymerization depends on the intensity of incident light (/ ), the quantum yield for production of radicals ( ), the molar extinction coefficient of the initiator at the wavelength employed ( ), the initiator concentration [5], and the path length (/) of the light through the sample. Assuming the usual radical termination processes at steady state, the rate of photopolymerization is often approximated by... 

The analysis of Talamini et al. [3, 4] is presented below. In the case of free-radical homogeneous polymerization the kinetic chain length is given by the relation ... 

The molecular weight distribution and the average molecular weight in a free-radical polymerization can be calculated from kinetics. The kinetic chain length v is defined as the average number of monomers consumed per number of chains initiated during the polymerization. It is the ratio of the propagation rate to the initiation rate (or the termination rate with a steady-state approximation) ... 

The bimolecular termination reaction in free-radical polymerization is a typical example of a diffusion controlled reaction, and is chain-length-depen-dent [282-288]. When pseudobulk kinetics appUes, the MWD formed can be approximated by that resulting from bulk polymerization, and it can be solved numerically [289-291]. As in the other extreme case where no polymer particle contains more than one radical, the so-caUed zero-one system, the bimolecular termination reactions occur immediately after the entrance of second radical, so unique features of chain-length-dependence cannot be found. Assuming that the average time interval between radical entries is the same for all particles and that the weight contribution from ohgomeric chains formed... 

Reactions (1) and (4) are essentially the same as the addition of reactive species to the monomer, which is the same as the initiation and propagation reactions in the free radical chain growth polymerization. However, the kinetic chain length in vacuum is very short, and in a practical sense these reactions can be considered to be stepwise reactions. Cycle I consists of reactions of reactive species with a single reactive site, and cycle II is based on divalent reactive species. Reaction (3) is a cross-cycle reaction from cycle II to cycle I. The growth via cycle I requires the reactivation of the product species, whereas cycle II can proceed without reactivation as long as divalent reactive species or monomers with double bond or triple bond exist. 

For the free-radical polymerization in which termination is by transfer to the monomer or a chain transfer agent and by addition, the kinetic chain length is... 

This relation is of fundamental importance in free-radical polymerization since the kinetic chain length decreases with an increase in the rate of initiation. Thus an attempt to accelerate polymerization by adding more initiator will produce a faster reaction but the polymer will have shorter chains. This can also be seen as a consequence of the steady-state approximation in a linear chain reaction since the rate of termination is equal to the rate of initiation and, if the rate of termination increases to match the rate of initiation, the chains must necessarily be shorter. 

The specificity of the reaction mechanism to the chemistry of the initiator, co-initiator and monomer as well as to the termination mechanism means that a totally general kinetic scheme as has been possible for free-radical addition polymerization is inappropriate. However, the general principles of the steady-state approximation to the reactive intermediate may still be applied (with some limitations) to obtain the rate of polymerization and the kinetic chain length for this living polymerization. Using a simplified set of reactions (Allcock and Lampe, 1981) for a system consisting of the initiator, I, and co-initiator, RX, added to the monomer, M, the following elementary reactions and their rates may be... 

Problem 6.44 Consider a case of free-radical polymerization where termination involves both disproportionation and coupling of chain radicals but chain transfer reactions can be neglected. Derive an expression for the distribution function for the degree of polymerization of polymer in terms of the kinetic chain length and the ratio of termination by disproportionation to that by coupling [65]. Simplify the expression for two limiting cases where (a) termination is solely by coupling and (b) termination is solely by disproportionation. 

Equation (P6.44.23) shows that the distribution function for the degree of polymerization of polymer formed by a free-radical chain mechanism, in which chain transfer is absent, depends only on the kinetic chain length and the ratio of disproportionation to coupling. The plot of vs. x according to Eq. (P6.44.23) gives the... 

The kinetic chain length of a free-radical polymerization process is the ratio of kp/kr, where kp is the rate of propagation and ky is the rate of termination. Since allylic hydrogens are not involved in the propagation step, substitution of deuterium for these hydrogens was expected to affect the termination process. When this indeed was found to be the case, as evinced by the increase in the kinetic chain length and the MW of the polymer, it was considered reasonable evidence that the allylic hydrogens were the cause of the characteristic behavior of allyl esters [15]. 

Since the degree of polymerization is proportional to the kinetic chain length, an increased rate of polymerization should also mean an increased degree of polymerization X. In fact, this behavior is also observed in the region of the gel effect. Before the gel effect is observed (low conversions), however, X does not decrease with the yield w, but first remains constant (Figure 20-4). The effect is probably brought about by a transfer of polymer free radicals to monomer. 

A polymer may be formed by hundreds, thousands, or even tens of thousands of monomeric units. This material can also be present in natural form, for example, cellulose and rubber. The characteristics of these macromolecules depend on the monomer, chain length, and composition of the mixture. The mechanism and kinetics have been presented. We present the free radical polymerization of styrene (solution polymerization) as an example. 

The kinetics of chain-reaction polymerization is illustrated in Fig. 3.28 for a free radical process. Analogous equations, except for termination, can be written for ionic polymerizations. Coordination reactions are more difficult to describe since they may involve solid surfaces, adsorption, and desorption. Even the crystallization of the macromolecule after polymerization may be able to influence the reaction kinetics. The rate expressions, as given in Appendix 7, Fig. A7.1, are easily written under the assumption that the chemical equations represent the actual reaction path. Most important is to derive an equation for the kinetic chain length, v, which is equal to the ratio of propagation to termination-reaction rates. This equation permits computation of the molar mass distribution (see also Sect. 1.3). The concentration of the active species is very small and usually not known. First one must, thus, ehminate [M ] from the rate expression, as shown in the figure. The boxed equation is the important equation for v. 

For free radical polymerization, the kinetic chain length will vary over the batch polymerization cycle as a function of monomer and polymer concentrations ... 

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