Kinetic Modeling of Irreversible Polycondensations

In his pioneering study of nonlinear polycondensation [7], Stockmayer has already checked his statistical solution [Eq. (5)] by solving the mass balance equations in a batch reactor for the concentrations of functional groups A and the set of isomeric polymer molecules P with x repeating units X [Eqs. (122)]. 

The two solutions are identical. Hence, for a long time no importance was attributed to the use of a kinetic approach for describing batch polycondensations starting from monomers, and the statistical approach was preferred. Of course, chemical engineers had to deal with semi-batch and continuous stirred tank reactors where the statistical approach, although possible, is cumbersome and error-prone, so a few papers appeared in the 1960s dealing with kinetically controlled linear polycondensations [274—276]. 

It is possible to obtain a rate equation for the members of each dass by adding the contributions of the various condensation reactions, leading to a version of Smoluchowski s coagulation equation. 

The rate of formation of groups requires a modification of Eq. (68), since it is no longer possible to include breakage or exchange reactions. Adding the unimolecular reactions defined above, the new general rate equation becomes Eq. (124). 

The multiple sums in the rate of formation of P(x), which will not be presented, are simplified through consideration of its generating function [Eqs. (125), (126)] 

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