Pulsed laser polymerization (PLP) is widely employed to measure propagation rate coefficients kp 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 n0 = kpt0CM, where t0 is the laser period and CM is the monomer concentration. We show that chain transfer reduces their amplitude by factors , consistent with numerical results obtained by other workers. Here ctr is the chain transfer coefficient and Ln0 (L = integer) are the discontinuity locations. Additionally, transfer generates a small amplitude continuous contribution to the MWD. These results generalize earlier analytical results which were obtained for the case of disproportionation only. We also considered two 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 kp. We prove that this is a correct procedure provided the GPC resolution σ is better than nequation/tex2gif-stack-1.gif. Otherwise this underestimates Ln0 by an amount of order σ2/n0.
Schematic of a chain transfer reaction with monomer as the transfer agent.
