Calculation of molecular weight distribution of products of non-equilibrium polycondensation, considering the “substitution effect”

Abstract

A general algorithm was formulated for calculating MWD of non-ideal polycondensation systems with consideration of the “substitution effect”. This algorithm enables the cost of machine time to be reduced considerably when calculating MWD; this is illustrated in detail for linear irreversible homopolycondensation. It was shown that all reactive systems, according to kinetic constants and values of conversion, within the framework of the model examined may have three different types of MWD function. Systems of the first type with conversion p close to one, are described with fair accuracy for all products by a most probable exponential Flory distribution with a parameter practically coinciding with the number average degree of polymerization P N = (1− p) −1 and coefficient of polydispersion K P = 2. Systems of the second type are characterized by a bimodal form of gravimetric MWD with a second maximum in the range of low molecular weight oligomers and K P values noticeably higher than two. In systems of the third type MWD is described by exponential distribution and K P = 2, but the P N value for these markedly exceeds the value of (1 − p) −1 derived in the Flory distribution. The formation of systems with bimodal MWD and values of K P > 2 distinguishes qualitatively non-equilibrium reaction conditions from equilibrium conditions, while for ideal polycondensation without the “substitution effect” there is no such distinction.