Relationship between the autoacceleration of polymerization rate and conversion in radical polymerization

By using a simple treatment for the kinetics of radical polymerization with primary radical termination, the ratio k_ty/k_tx of chain termination rate constant k_ty at conversion y to that k_tx at conversion x and the ratio k_tiy/k_tix of the primary radical termination rate constant k_tiy at conversion y to k_tix at conversion x were calculated for the polymerizations of methyl methacrylate and ethyl acrylate in the conversion range 0 to 0.4. k_ty/k_tx and k_tiy/k_tix were treated by using the following equations based on the variation of conversion: where g(T,y) is the average fractional free volume of radical chain end at conversion y and absolute temperature and β(T) is a function depending on T, and where g_i(T,y) is the average fractional free volume of primary radical at conversion y and T and β_i(T) is a function depending on T. The autoacceleration for the above monomers was successfully interpreted by the above treatment.