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

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 −ctrLn0 , consistent with numerical results obtained by other workers. Here c tr is the chain transfer coefficient and Ln 0 (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 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 σ is better than n 1/2 0 . Otherwise this underestimates Ln 0 by an amount of order σ 2 /n 0 .

Fabrication of pH-Responsive Polyimide Polyacrylic Acid Smart Gating Membranes: Ultrafast Method Using 248 nm Krypton Fluoride Excimer Laser

“…PLP is widely used technique to find the propagation rate coefficient in free radical polymerization. 38 With each incoming pulse, free radicals form and propagate until the next pulse comes. If radical is formed and survives until the next pulse, it will continue to propagate and will form a chain of length L 1 given by equation 39…”

“…Such studies have been carried out on various polymers like acrylamide, acrylic acid, methyl methacrylate, butyl acrylate, etc. 38,39,41,42 The chain length depends on laser frequency as propagation occurs in a dark time. The important thing here is to take care that the fluence does not go above 36 mJ/cm 2 , the ablation threshold for PI.…”

“…Grafting occurs by pulsed laser polymerization (PLP) mechanism. PLP is widely used technique to find the propagation rate coefficient in free radical polymerization . With each incoming pulse, free radicals form and propagate until the next pulse comes.…”

“…If radical is formed and survives until the next pulse, it will continue to propagate and will form a chain of length L 1 given by equation where [ M ] is monomer concentration, k p is the propagation rate coefficient and t 0 is the time between two consecutive pulses (frequency –1 ). Therefore, the chain length after n number of pulses L n is be given as Such studies have been carried out on various polymers like acrylamide, acrylic acid, methyl methacrylate, butyl acrylate, etc. ,,, The chain length depends on laser frequency as propagation occurs in a dark time. The important thing here is to take care that the fluence does not go above 36 mJ/cm 2 , the ablation threshold for PI.…”

Modeling of Emulsion Polymerization, Will It Ever be Possible ? Part‐2: Determination of Basic Kinetic Data Over the Last Ten Years

“…Also other authors used a constant broadening factor for correction of PLP data. [27,28] It has to be noted that the extend of column broadening depends on the quality of the SEC equipment and in particular the quality of the column or column set. The frequency dependence of k p was noted in many laboratories but the extend may differ because of the use of different columns.…”