Chain‐length‐dependent termination rate constant: Effect on molecular weight distributions formed by pulsed laser radical polymerization

Abstract

For polymerization initiated by an arbitrary sequence of laser pulses a numerical technique for calculating molecular weight distributions (MWDs) is developed, which takes into consideration the chain length dependence of the termination rate constant kt. The MWDs for methyl methacrylate and styrene are calculated by use of α and k0 values (for the law k titalici,j = k0(i)−α of termination of radicals with chain length i) and averages \documentclass{article}\pagestyle{empty}\begin{document}$ \overline {(i,{\rm }j)} $\end{document} (for rate constants k titalici,j = k0\documentclass{article}\pagestyle{empty}\begin{document}$ \overline {(i,{\rm }j)} $\end{document} of termination of radicals with different degrees of polymerization) taken from the literature. The dependences of the overall termination constant 〈kt〉 on initiation parameters (pulse repetition rate (v) and pulse intensity for initiation by periodic laser pulses) are presented. Two methods are proposed for α and k0 determination: (a) by experiments on polymerization with periodic laser pulses where monomer‐to‐polymer conversions per pulse are determined for different v; (b) by experiments on polymerization with packets of pulses where the constant kp (the rate constant of propagation), α and k0 can be determined simultaneously from MWD. For both methods simple analytical equations are derived for evaluation of the constants. The limits of application of the methods are determined by use of the numerical technique for MWD calculation.

Pulsed Laser Polymerization at Low Conversions: Broadening and Chain Transfer Effects

“…Hence Equation (33) follows immediately as one may check after replacing f from Equation (A2) into Equation (33) and checking that Equation (G2) is recovered.…”

Bimolecular Free-Radical Termination at Low Conversion

“…Some have used Russell's model (180,181,(214)(215)(216)(217)(218)(219)(220); others have used the same functional form of the chain-length dependence (Eqs. Some have used Russell's model (180,181,(214)(215)(216)(217)(218)(219)(220); others have used the same functional form of the chain-length dependence (Eqs.…”

“…They have performed a number of simulations of PLP, using both chain-length-independent termination rate coefficients, employing generating functions (232)(233)(234)(235), as well as chain-length-dependent termination rate coefficients (220 posed two new methods for the recovery of chain-length-dependent k t information, one based on rate measurements and the other on MWD measurements (220). They have performed a number of simulations of PLP, using both chain-length-independent termination rate coefficients, employing generating functions (232)(233)(234)(235), as well as chain-length-dependent termination rate coefficients (220 posed two new methods for the recovery of chain-length-dependent k t information, one based on rate measurements and the other on MWD measurements (220).…”

Chain-length dependence of free-radical termination rate deduced from laser single-pulse experiments

“…[18] Investigations into the chain-length dependence of the termination rate coefficient are very attractive and several groups have thoroughly addressed this issue during recent years. [19][20][21][22][23][24][25][26] An excellent survey on the relevant literature has recently been provided by de Kock. [27] SP-PLP experiments are particularly well suited for such studies.…”