Treatment of Polymerization Kinetics

In Section 5.2.1.1 we provide an overview of the classical treatment of polymerization kinetics. Some aspects of termination kinetics are not well understood and no wholly satisfactory unified description is in place, Nonetheless, it remains a fact that many features of the kinetics of radical polymerization can be predicted using a very simple model in which radical-radical termination is characterized by a single rale constant. The termination process determines the molecular weight and molecular weight distribution of the polymer. In section... 

Gilbert [70] in a recent book has incorporated many of these basic ideas into a treatment of polymerization kinetics. 

A major objective of the current research programme is to extend the treatment of polymerization kinetics based on direct measurements of monomer and radical concentrations to crosslinking systems. Conventional methods for measurement of monomer concentrations are not suitable, as they require soluble polymer. We have been able to apply our procedure for utilizing the near-infrared spectrum of the C=C bond in methyl methacrylate to systems containing ethylene glycol dimethacrylate (EGDMA) [14]. 

The structure of a polymeric network Is ultimately determined by the method of synthesis. The monomer and crosslinker concentrations, the initiator type and concentrations, the relative reactivities of the monomers, the specific solvent and reaction temperature are all significant. Commercially, the rate of the polymerization reaction Is also important, since it directly affects the volumetric efficiency of the production equipment. Many of the important structural parameters are determined by the polymerization kinetics and by the various stoichiometries of the reaction. For acrylic acid and sodium acrylate, several studies of the polymerization kinetics reveal that these monomers behave consistently with the standard treatment of polymerization kinetics, with polymerization rate generally first order in monomer concentration except when specific initiator effects occur. 

In traditional treatments of copolymerizaiion kinetics, the values of the ratios sA and % are implicitly set equal to unity (Section 7.3.1.2.2). Since they contain no terms from cross propagation, these parameters have no direct influence on either the overall copolymer composition or the monomer sequence distribution they only influence the rate of polymerization. 

The treatment of batch polymerizations is in principle more difficult than that of continuous polymerizations in the latter, it may be permissible to assume steady-state conditions, though this has been questioned as indicated above but in the former it can never be permissible. It may, however, be permissible to make the assumption usual in treatments of the kinetics of radical polymerizations that the time-derivatives of radical concentrations may be neglected, though Kuchanov and Pismen (94) have questioned this assumption but the time-dependence of the polymer concentration must always be taken into account. 

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). 

The kinetics of emulsion polymerization reactions are complex because of the numerous chemical and physical phenomena that can occur in the multicomponent, multiphase mixture. A large amount of literature exists on kinetics problems. The general references listed at the end of this chapter contain many important papers. The review paper by Ugelstad and Hansen (11) is a comprehensive treatment of batch kinetics. The purpose of the remainder of this chapter is to present the general kinetics problems and some of the published results. The reader should use the references cited earlier for a more detailed study. 

The addition of a monomer unit results in a radical structurally similar to the radical before the addition therefore, there is no alteration in the stability of the growing radical. The group substituent (G in Scheme 4.3) has an effect on the stability of both the double bond and the resulting radical. An increase in the stabilizing effect of G produces a reduction of k, the rate constant of the propagation reaction, as indicated in Table 4.1. To simplify the mathematical treatment of the kinetics in the radical polymerization, it is assumed that is independent of the size of the propagating radical. Nevertheless, it is known that the diffusivity of species affects the rate constant, a fact that is more evident at low molecular weights (MWs). 

A model was developed for a unified treatment of the kinetics of both cationic and anionic polymerizations.It is based on a system of kinetic models that cover various initiation and... 

In the quantitative treatment of polymerization reactions, we must, therefore, seek further quantities accessible experimentally which may give us additional information concerning the process the average degree of polymerization of. the resulting product is one of these. Its kinetic evalu-... 

The generating function as a tool for the analysis of polymerization kinetics was introduced by Howe [35] in the treatment of radical chain growth... 

The kinetic treatment of polymerizations becomes much simpler if it is assumed that the reactivity of a group is unaffected by the size of the molecule to which it is attached (principle of equal chemical reactivity). This... 

As has been explained in Sect. 2.2, a complete description of the kinetics of the bulk photopolymerization of diacrylates cannot be given at the present time, however. In this section, we will describe a few typical side reactions during the bulk polymerization of diacrylates as well as a preliminary approach for the treatment of the kinetics during vitrification of the system. 

Hydrolysis and Polycondensation. As shown in Figure 1, at gel time (step C), events related to the growth of polymeric chains and interaction between coUoids slow down considerably and the stmcture of the material is frozen. Post-gelation treatments, ie, steps D—G (aging, drying, stabilization, and densification), alter the stmcture of the original gel but the resultant stmctures aU depend on the initial stmcture. Relative rates, of hydrolysis, (eq. 2), and condensation, (eq. 3), determine the stmcture of the gel. Many factors influence the kinetics of hydrolysis and... 

The kinetic mechanism of emulsion polymerization was developed by Smith and Ewart [10]. The quantitative treatment of this mechanism was made by using Har-kin s Micellar Theory [18,19]. By means of quantitative treatment, the researchers obtained an expression in which the particle number was expressed as a function of emulsifier concentration, initiation, and polymerization rates. This expression was derived for the systems including the monomers with low water solubility and partly solubilized within the micelles formed by emulsifiers having low critical micelle concentration (CMC) values [10]. 

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... 

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. 

Study of the kinetics of the oxidation of asymmetric secondary hydroxylamines to nitrones with H2O2, catalyzed by methylrhenium trioxide, has led to the elucidation of the mechanism of the reaction (104). Full transformation of N,N -disubstituted hydroxylamines into nitrones upon treatment with H2O2 occurs on using polymeric heterogeneous catalysts such as polymer-supported methylrhenium trioxide systems (105). 

NUCLEATION. The polymer self-assembly theory of Oosawa and KasaP treats nucleation as a highly cooperative and unfavorable event. Their kinetic theory for nucleation permits one to obtain information about the size of the polymerization nuclei, provided that two basic assumptions can be satisfied experimentally. First, the rate of nuclei formation is assumed to be proportional to the ioth power of the protomer concentration, with io representing the number of protomers required to create the nucleus. Second, the treatment deals only with that period during which the polymerization rate greatly exceeds the rate of protomer loss from the polymers (i.e., the initial stage of polymerization when the protomer concentration is the highest). 

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,... 

Adsorption phenomena are important in most Ziegler-Natta polymerizations, and this requires treatment by heterogeneous kinetics [Bohm, 1978 Boor, 1979 Chien and Ang, 1987 Chien and Hu, 1987 Cooper, 1976 Keii, 1972 Tait and Watkins, 1989]. The exact form of the resulting kinetic expressions differs depending on the specific adsorption... 

Another additional chemical complication can arise from the presence of quenching reagents which deactivate the reactive polymers. This kinetic quenching mechanism may also be included in the formalism through the addition of an additional differential equation. A more thorough treatment of these extensions and their applications to polymerization reactions is currently in progress. 

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