Modeling the Effects of Primary Radicals in Free-Radical Polymerization

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The effect of non-ideal initiator decomposi tion, 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 a ≡(k t2 /k d2 )t m /k t , where k a is the termination rate coefficient for the reaction of a non-propagating primary radical with a macroradical, k dz is the first-order decomposition rate coefficient of non-propagating (passive) radicals, r in is initiation rate, and k t is the termination rate coefficient of the active radicals. In the case of primary radical termination, n decreases with the size of the dimensionless parameter β ≡ k 1,s r 1/2 in /k ps Mk 1/2 t.1 , where k t,s is the termination rate coefficients for the reaction of a primary (short) radical with a macroradical, k t,1 is the termination rate coefficients of two large radicals, k r,s is the propagation rate coefficient of primary radicals and M is monomer concentration. As k t is deduced from coupled parameters such as k t /k p , the dependence of k p 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.