Kinetic Modeling of Linear Reversible Polycondensations

The reversible alternating polycondensation with FSSEs in both monomers (see Section 3.1.5), disregarding exchange reactions, is a convenient case study for discussing problems of modeling this kind of systems. It can be described by the rate laws of Eqs. (132) and (133). 

It may be observed from these expressions that, in general, it is not possible to obtain a closed finite set of rate equations for the first oligomers - rate equations for oligomers with chain length n always depend on concentrations of oligomers with chain length n + l. Only when the rate constants of reverse equations are equal do the above expressions simplify (FSSE for reverse reaction), and the above-mentioned difficulty disappears. 

On introduction of generating functions of the CLD, defined in Eq. (134), the concentrations of end groups, trimers, and tetramers conform with Eqs. (134) and (135). 

The rate equations in terms of those generating functions become Eqs, (136). 

Insertion of these rate laws in mass balances of ideal reactors (batch/plug flow or transient CSTR) leads to systems of semi-linear, first-order, partial differential equations, with a single family of characteristics [Eq. (139)]. 

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