Brief History of Step Reaction Kinetic Modeling

Brief History of Step Reaction Kinetic Modeling 

Flory [34] was one of the pioneers in the development of models to predict the kinetics of polyester formation. Simple equations derived to predict the kinetics of synthesis of linear polyesters, which can be found in excellent polymer textbooks, are briefly overviewed next [35-37]. 

The rate of a step polymerization is conveniently expressed in terms of the concentrations of the reacting functional groups. In the case of polyester formation, two such groups appear, namely, carboxyl, -COOH, and hydroxyl, -OH. The rate of polymerization can then be expressed as the rate of disappearance of carboxyl groups -d[-COOH]/df given by 

Two quite different kinetic situations arise from Equation 4.1 depending on the identity of HA, that is, on whether a strong acid is added as an external catalyst providing two different modeling approaches, that of self- and external-catalyzed polymerization. 

In the absence of an externally added strong acid, the diacid monomer acts as its own catalyst for the esterification reaction. For this case, [HA] is replaced by [-COOH] in Equation 4.1. Assuming that the two functional groups are nearly stoichiometric, and setting [-COOH] = N, the final equations expressing the variation of reaction extent,/ and polymer number average degree of polymerization (NADP), DP,j with time can be written as [34, 35] 

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