Semiempirical rate equation for solid state polymerization of poly(ethylene terephthalate)

Solid-state polymerization (SSP) of poly(ethylene terephthalate) (PET) is characterized by two distinct features. First, there exists an ultimate or limiting intrinsic viscosity (IV), Second, the SSP rate varies with the prepolymer IV Although there are several existing empirical rate equations and numerous published models for the SSP of PET, none can adequately describe these features. In this article, a simple semiempirical rate equation that aptly describes the behaviors of the SSP of PET is proposed. It is based on the assumptions that there are two categories of functional end groups, active and inactive end groups, and that the overall SSP follows a second order kinetics. Thus, the overall SSP rate is expressed as -dC/dt = 2 k(a) (C - C-ai)(2), where C is the total end group concentration, t, the SSP time, k(a), the apparent reaction rate constant, and C-ai, the apparent inactive end group concentration. With this rate equation, the effects of all factors that influence the SSP rate are implicitly and conveniently accounted for by the two parameters, k(a) and C-ai. For example, k(a) increases, while C-ai decreases, with increasing SSP temperature, increasing prepolymer IV, and decreasing particle size. The proposed rate equation fits the IV or molecular weight build-up curves for the SSP of PET under various conditions very well, and can be extrapolated beyond data with reasonable accuracy. (C) 2002 John Wiley Sons, Inc.