Free radical polymerization in a confined system: An analysis based on a kinetic growth model on regular graphs

With a stochastic model based on self-avoiding walk of multi walkers, free radical polymerization in a confined system is numerically investigated. As a reaction field, we consider not a confined lattice but a graph to represent interactions between polymerizable molecules and possible networks. The result of calculation visualized how the individual polymer chains should grow from moment to moment, which can hardly be tracked by other statistic methods such as Monte Carlo simulation. The calculation also provided the effective chain length of polymers and the average polymerization time, both of which followed a log-normal distribution. With respect to the initial radical density, the effective polymer length monotonically decreased, while the average polymerization time exhibited a single maximum. Considering the probabilities for the multiple radicals to encounter, we derived an inequality that well explained these behaviors. The stochastic model combined with graphs can be a useful tool for analyzing confined polymerization system.