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

TL;DR

This paper derives an analytical solution for the dead chain molecular weight distribution in pulsed laser polymerization at low conversions, accounting for chain transfer and broadening effects, enhancing understanding of PLP measurements.

Contribution

It provides the most general analytical expression for dead MWD in PLP, including chain transfer effects and broadening, extending previous numerical and analytical results.

Findings

Chain transfer reduces MWD discontinuity amplitudes exponentially.

Transfer introduces a small continuous MWD component.

Optimal k_p inference requires GPC resolution better than n_0^{1/2}.

Abstract

Pulsed laser polymerization (PLP) is widely employed to measure propagation rate coefficients k_p in free radical polymerization. Various properties of PLP have been established in previous works, mainly using numerical methods. The objective of this paper is to obtain analytical results. We obtain the most general analytical solution for the dead chain molecular weight distribution (MWD) under low conversion conditions which has been hitherto obtained. Simultaneous disproportionation and combination termination processes are treated. The hallmarks of PLP are the dead MWD discontinuities located at integer multiples of n_0 = k_p t_0 C_M, where t_0 is the laser period and C_M is the monomer concentration. We show that chain transfer reduces their amplitude by factors e^{-c_{tr} L n_0}, consistent with numerical results obtained by other workers. Here c_{tr} is the chain transfer coefficient and L is an integer. Additionally, transfer generates a small amplitude continuous contribution to the MWD. These results generalize earlier analytical results obtained for the case of disproportionation only. We also considered 2 classes of broadening: (i) Poisson broadening of growing living chains and (ii) intrinsic broadening by the MWD measuring equipment (typically gel permeation chromatography, GPC). Broadening smoothes the MWD discontinuities. Under typical PLP experimental conditions, the associated inflection points are very close to the discontinuities of the unbroadened MWD. Previous numerical works have indicated that the optimal procedure is to use the inflection point to infer k_p. We prove that this is a correct procedure provided the GPC resolution \sigma is better than n_0^{1/2}. Otherwise this underestimates L n_0 by an amount of order \sigma^2/n_0.