  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.
