Kinetics of free-radical polymerization with chain-length-dependent constants under initiation by laser pulses: Effect of chain length dependence of propagation

Abstract

A numerical procedure is developed which allows taking into account the chain length dependence of the termination and propagation constants for calculating molecular weight distributions (MWDs) formed under free-radical polymerization initiated by an arbitrary sequence of laser pulses. The law kpL = kp0 L + (kp1 - kp0)L (where kp0 is a constant close to the experimentally determined propagation rate constant, kp1 is the constant of the propagation of radicals with unity degree of polymerization, β1 and β2 are constants reflecting the chain length dependences of the propagation of long-chain and ultra-short radicals, respectively) is considered for description of the chain length dependence of the propagation constant. The effect of this dependence on MWDs is considered in detail. It is shown that the time dependence of the chain length of growing radicals, ψ(t), can be used for model-independent determination of chain-length-dependent propagation constants kpL. Theoretically the well-known pulsed laser polymerization (PLP) method for evaluation of the propagation constant can be used for determination of ψ(t), but this determination is questionable in practice. Direct application of this method gives L/∫0L dL′/kpL′ instead of kpL. The consideration of methyl methacrylate polymerization at 25°C as an example shows that the weak chain length dependence of the long-chain kp value with β1 < 0.01 can not be revealed by the PLP method. The effect of the chain length dependence of the propagation constant on model-independent determination of termination constants by time-resolved single-pulse pulsed laser polymerization (TR-SP-PLP) technique is investigated. It is shown that for the methyl methacrylate polymerization at 25°C this technique gives ktL,L values of long-chain radicals with uncertainty ≥10% for β1 > 0.01 (if the propagation constant is assumed to be equal to a constant value) and ktL,L/kpL values of these radicals with uncertainty < 6% for β1 < 0.05. It is shown that the accuracy of determination of both ktL,L and ktL,L/kpL values of short-chain radicals by TR-SP-PLP technique is very low, and that the increase of used laser intensity leads to a considerable improvement of this accuracy.