Modeling the Effects of Primary Radicals in Free-Radical Polymerization

The effects of non‐ideal initiator decomposition, i.e., decomposition into two primary radicals of different reactivity toward the monomer, and of primary radical termination, on the kinetics of steady‐state free‐radical polymerization are considered. Analytical expressions for the exponent n in the power‐law dependence of polymerization rate on initiation rate are derived for these two situations. Theory predicts that n should be below the classical value of 1/2. In the case of non‐ideal initiator decomposition, n decreases with the size of the dimensionless parameter α ≡ (ktz /kdz) √rinkt, where ktz is the termination rate coefficient for the reaction of a non‐propagating primary radical with a macroradical, kdz is the first‐order decomposition rate coefficient of non‐propagating (passive) radicals, rin is initiation rate, and kt is the termination rate coefficient of two active radicals. In the case of primary radical termination, n decreases with the size of the dimensionless parameter β ≡ kt,s rin1/2/kp,s M rt,l1/2, where kt,s is the termination rate coefficients for the reaction of a primary (“short”) radical with a macroradical, kt,l is the termination rate coefficients of two large radicals, kp,s is the propagation rate coefficient of primary radicals and M is monomer concentration. As kt is deduced from coupled parameters such as kt /kp, the dependence of kp on chain length is also briefly discussed. This dependence is particularly pronounced at small chain lengths. Moreover, effects of chain transfer to monomer on n are discussed.