Polymerization kinetic treatment

Not all initiating radicals (/ ) succeed in initiating polymerization, recombination of these radicals in the solvent can decrease the efficiency (/) to a value lower than 1. Detailed kinetic treatment of photoinitiation processes are discussed by Oster and Yang [3]. 

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. 

General features of the polymerization kinetics for polymerizations with deactivation by reversible coupling have already been mentioned. Detailed treatments appear in reviews by Fischer," Fukuda et ai and Goto and I vikuda" and will not be repeated here. 

In this paper, the pseudo-kinetic rate constant method in which the kinetic treatment of a multicomponent polymerization reduces to that of a hcmopolymerization is extensively applied for the statistical copolymerization of vinyl/divinyl monomers and applications to the pre- and post-gelation periods are illustrated. 

A generalized kinetic treatment of the array of processes occurring in condensation polymerization might appear hopelessly complex. In the polyesterification of a hydroxy acid, for example, the first step is intermolecular esterification between two monomers, with the production of a dimer... 

Eqs. (3), (4), (5), and (7) describe the mechanism of an initiated free radical polymerization in a form amenable to general kinetic treatment. The rate of initiation of chain radicals according to Eqs. (3) and (4) may be written... 

Since the depolymerization process is the opposite of the polymerization process, the kinetic treatment of the degradation process is, in general, the opposite of that for polymerization. Additional considerations result from the way in which radicals interact with a polymer chain. In addition to the previously described initiation, propagation, branching and termination steps, and their associated rate constants, the kinetic treatment requires that chain transfer processes be included. To do this, a term is added to the mathematical rate function. This term describes the probability of a transfer event as a function of how likely initiation is. Also, since a polymer s chain length will affect the kinetics of its degradation, a kinetic chain length is also included in the model. 

Tanford presented a cogent kinetic treatment of random scission of a polymer, and the complete analysis is beyond the scope of this Handbook. The basic idea is that a molecule M, can yield a molecule (where x and y indicate the degree of polymerization, and where y > x) in two different ways. The x-mer formation rate from y-mers is twice the rate of bond scission at the concentration of the y-mer thus,... 

A similar kinetic treatment has been utilized by Fontana and Kidder (/6) to explain the details of the cationic polymerization of propylene. 

In many binary copolymerizations, there is a pronounced tendency for the two types of monomer unit to alternate along the copolymer chain. In extreme cases, there is almost perfect alteration, notably for pairs of monomers, e.g, maleic anhydride and stilbene, which do not polymerize on their own. Ternary copolymenzations are of practical importance die kinetic treatments developed for binary copolymerizations can be extended to diese systems. 

The kinetic treatment of a simple polymerization is readily extended to nonpolymerization chain reactions such as that of Scheme 9. Here we again... 

Utilizing the seed latex polymerization method to avoid the occurance of new particle formation, the kinetic treatment of an emulsion polymerization is quite straight forward. Assuming that all the particles are the same size, the rate of polymerization,... 

Many chain-growth copolymerizations include dienes such as divinyl benzene or divinyl adipate that act as crosslinking agents and lead to gel formation. Polymerization kinetics in such cases are complex and are beyond the scope of a book on homogeneous reactions. Here, only binary copolymerization of monofunctional monomers will be examined. For an excellent and extensive treatment that includes copolymerization of more than two monomers as well as crosslinking by bifunctional monomers, the reader is refer to Odian s book [123]. 

Recently, a series of works have been published on the cationic po merization of lactones (e.g. p-propiolactone and e-caprolactone ) and various ionic ecies have been reported together with elaborate kinetic treatments and some electrochemical measurements. In our opnion the chemical structure of the growing species in the cationic polymerization of lactones has not yet firmly been established (see also Ref. 190) and, therefore, a more detailed discussion of the% interesting and important systems must wait until these structures are known. 

The first complete kinetic treatment of an intermolecular interaction was given in the studies of the polymerization of 3,3-bis-(chloromethyl)oxetane % The following kinetic scheme describes the nothstationary process in which termination on polymer competes with drain propagation (initiation is assumed to be fast) ... 

The kinetic treatment revealed that the reactivity of pendant allyl groups of the prepolymer is approximately equal to that of the monomer. The ratios ri = kii/kii and r2 = kn/kn have been estimated to be 1.0 and 0.9, respectively [67]. A similar result was also observed for the post-copolymerization of DAI prepolymer with ABz [68]. Now, we can conclude that the concept of equal reactivity of functional groups belonging to the monomer and polymer is valid for the radical polymerization of diallyl aromatic dicarboxylates at an early stage of polymerization, at least up to the theoretical gel point. However, in the case of the highly branched prepolymer formed at a late stage of polymerization, i.e. far beyond the theoretical gel point, the reactivity of pendant allyl groups may be reduced by steric hindrance. 

More detailed information on the activation pathway, which distinguishes the polymeric photoinitiators from the corresponding low-molecular-weight structural models, has been obtained by photophysical measurements [22,27,28] in terms of quantum yield and average lifetime of the triplet excited state of benzophenone moieties in the above systems. However, in order to get a better comprehension of this point, it is necessary to introduce some basic concepts about the kinetic treatment of a photoinitiated chain polymerization. 

Rates of radiation induced polymerizations are normally determined by dilatometric [85] or gravimetric [84] experiments. Some of the first quantitative results from cyclopentadiene [86] and a-methylstyrene [87] were obtained by competitive kinetic methods, based on the retarding effect of ammonia and amines. This approach tends to yield maximum values for Rp. More recently, however, a procedure combining stationary state kinetic and conductance measurements has been described [88, 89], and further refined [85]. Because the ions generated by 7-ray irradiation have a transient existence, the kinetic treatment leads to expressions which are very similar to those derived for homogeneous free radical polymerizations [90]. A simplified version of the kinetic scheme is as follows ... 

There is no adequate kinetic treatment for this aspect of coordination polymerization although many compounds have a major influence on the reactions. Some have a retarding effect, e.g., water, alcohols, carbon dioxide [101], while others accelerate polymerization. Examples of the... 

In homogenous media, most of the transacylation reactions are reversible and as soon as the first polymer amide groups are formed, the same kind of reactions can occur both at the monomer and at the polymer amide groups. Unless the active species are steadily formed or consumed by some side reaction, a set of thermodynamically controlled equilibria is established between monomer, cyclic as well as linear oligomers and polydisperse linear polymer. The existence of these equilibria is a characteristic feature of lactam polymerizations and has to be taken into account in any kinetic treatment of the polymerization and analysis of polymerization products. The equilibrium fraction of each component depends on the size of the lactam ring, substitution and dilution, as well as on temperature and catalyst concentration. 

The kinetic treatment of the adiabatic polymerization is very complicated with respect to the variation with increasing temperature of rate coefficients and equilibrium constants. Equations derived with a series of simplifying assumptions (e.g. heat capacity of the monomer (Cp m ) = heat capacity of the amorphous polymer (Cp p) = constant = Cp) lead to [2]... 

Kinetic treatment of the whole course of the cationic polymerization is not yet possible because of the fast side reactions which change the concentration of all active species. So far, only the initial (maximum) rates of polymerization with various kinds of initiators (I) have been described by the following empirical equation [176, 182, 183, 191—193] ... 

The process of polymerization consists in general of three steps initiation, propagation, and termination. In radical polymerization, a catalyst is usually employed as a source of free radicals, the primary radicals. A fraction of these initiate a rapid sequence of reactions with monomer molecules, the primary radical thus growing into a polymer radical. Radical activity is destroyed by reaction of two radicals to form one or two molecules. This termination reaction is called mutual recombination, if only one molecule is formed. Termination by disproportionation results in two molecules. For many common monomers, recombination is the normal mode of termination and the kinetic treatment here is based on this termination reaction. Only slight modifications are required for polymerizations in which termination occurs by disproportionation. If both termination processes occur, another variable must be introduced to describe the kinetics of the system fully. 

Quantitative theoretical treatment of emulsion polymerization kinetics... 

Comprehensive Models. This class of detailed deterministic models for copolymerization are able to describe the MWD and the CCD as functions of the polymerization rate and the relative rate of addition of the monomers to the propagating chain. Simha and Branson (3) published a very extensive and rather complete treatment of the copolymerization reactions under the usual assumptions of free radical polymerization kinetics, namely, ultimate effects SSH, LCA and the absence of gel effect. They did consider, however, the possible variation of the rate constants with respect to composition. Unfortunately, some of their results are stated in such complex formulations that they are difficult to apply directly (10). Stockmeyer (24) simplified the model proposed by Simha and analyzed some limiting cases. More recently, Ray et al (10) completed the work of Simha and Branson by including chain transfer reactions, a correction factor for the gel effect and proposing an algorithm for the numerical calculation of the equations. Such comprehensive models have not been experimentally verified. 

Using the much more reactive acid chloride monomer allows polyester production at much lower temperatures than when using the ester, or free acid. Even under ambient conditions it is so vigorous that interfacial polymerization of diluted solutions of the monomers in an appropriate, immiscible solvent pair may be needed to control the rate. However, the high cost of the acid chloride as compared to terephthalic acid or the ester makes this route commercially unattractive. Also with this monomer pair the kinetic treatment and molecular weight distributions will differ from the general cases outlined in Chapter 20. 

More recently, quantitative treatments of plasma polymerization kinetics have become available. 

The value of n in Eq. (6.230) is of critical importance in determining the rate of polymerization in stage II. Three cases — designated 1, 2, 3 — corresponding, respectively, to n < 0.5, n = 0.5, and n > 0.5 can be distinguished based on the work of Smith and Ewart [69] and others [70-74]. The kinetic treatment given above conforms to Case 2 (n = 0.5), which is the predominant behavior for emulsion polymerizations. It occurs when desorption of radicals does not occur or is negligible compared to the... 

Cr/alumina exhibits a "fast" kinetics profile that is quite different from that of Cr/silica. The polymerization rate develops rapidly, especially when the alumina has been acidified by treatment with silica, fluoride, phosphate, or sulfate. Cr/alumina exhibits polymerization kinetics similar to that of Cr/AlP04, a topic that is discussed in Section 15. The polymerization rate rises quickly when ethylene is added, but later it tends to decay slowly. The rapid initial rise indicates that reduction of Cr(VI), or desorption of redox by-products, and/or alkylation of the chromium, may be more facile on alumina than on silica. Alumina is known as a strong adsorbent in its own right, so that adsorption of by-products from chromium onto the neighboring surface is one possible contributing cause of the rapid development of polymerization rate. 

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