Chemical Control Model

More recent wmrk has shown that the observed variation in propagation rate constants with composition is not sufficient to define the polymerization rates. There remains some dependence of the termination rate constant on the composition of the propagating chain. Thus, the chemical control (Section 

1) and the various diffusion control models (Section 7.4.2) have seen new life and have been adapted by substiluling the terminal model propagation rale constants (Apxv) with implicit penultimate model propagation rate constants ( y Section 7.3.1.2.2). 

The chain length dependence of termination rate constants (Section 5.2.1.4) should not be ignored when considering copolymerization kinetics. It has been pointed out that average chain lengths in copolymerization will be a function of the monomer feed composition especially in copolymerizations with disparate propagation rate constants. Factors determining the rate of copolymerizalion are not fully resolved and copolymerization kinetics remains a topic of discussion and an area in need of further study. 

The rate of copolymerization often shows a strong dependence on the monomer feed composition. Many theories have been developed to predict the rate of copolymerization based on the terminal model for chain propagation (Section 7.3.1.1). This usually requires an overall rate constant for termination in copolymerization that is substantially different from that observed in homopolymerization of any of the component monomers. 

The instantaneous rate of monomer consumption in binary copolymerization is then given by eq. 62  

More recent work has shown that the observed variation in propagation rate constants with composition is not sufficient to define the polymerization rates.5 161,1152 There remains some dependence of the termination rate constant on the composition of the propagating chain. Thus, the chemical control (Section 7.4.1) and the various diffusion control models (Section 7.4.2) have seen new life and have been adapted by substituting the terminal model propagation rate constants (ApXv) with implicit penultimate model propagation rate constants (kpKY -Section 7.3.1.2.2). 

In evaluating the kinetics of copolymerization according to the chemical control model, it is assumed that the termination rate constants k,AA and A,Br are known from studies on homopolymerization. The only unknown in the above expression is the rate constant for cross termination (AtAB)- The rate constant for this reaction in relation to klAA and kmB is given by the parameter j . 

Values of 0 required to fit the rate of copolymerization by the chemical control model were typically in the range 5-50 though values 1 are also known. In the case of S-MMA copolymerization, the model requires 0 to be in the range 5-14 depending on the monomer feed ratio. This chemical control model generally fell from favor wfith the recognition that chain diffusion should be the rate determining step in termination. 

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In eq. 68, is defined as in the chemical control model but this expression is cast in terms of the monomer feed composition rather than the radical chain end population. 

A better fit is often provided by a combined model [29] which uses the parameter

copolymer composition. The empirical formulation is derived by substituting mole fractions of each monomer for the radical mole fractions n and ri2 in Eq. (7.62)... 

Equations (7.58) and (7.68) yield the rate of copolymerization, and may be taken from previous studies of the chemical control model, or from an empirical correlation between this parameter and the r T2 product [27] which is based on the fact that cross-termination over homo-termination. Direct measurements of have been obtained [26] by measuring the absolute values of the rates of propagation and termination in pure monomers and in mixtures of various compositions. In the case of styrene-/7-metho)q styrene, = 1, indicating that no polar or other influences favor cross-termination. In most cases, however, cross-termination is... 

Exptl. Chemical control model with (f) — 15 Diffusion control model (no parameter) Combined model with ( = 15... 

Equations (7.46) and (7.56) yield the rate of copolymeiization, and 0 may be taken from previous studies of the chemical control model. 

Chemical Control Model For copolymeriization, Eq. (7.52) for chemical control model is conveniently written (Rudin, 1982) as... 

Chemical control model Diffusion control model Combined model... 

The kinetics of diffusion-controlled termination in copolymerization is difficult to study. The original interpretation of low-conversion rate data was based on a chemically controlled model utilizing a cross-termination factor ... 

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