Simulation time analysis of kinetic Monte Carlo algorithmic steps for basic radical (de)polymerization kinetics of linear polymers

Abstract

The relevance of kinetic Monte Carlo (kMC) algorithms and modeling to obtain and tune detailed molecular information for (bio)chemical kinetic systems is growing. A bottleneck remains however the correct representation of time-dependent variations involving distributed species, specifically their reliable sampling with a minimization of the computational cost. The present work compares the performance of leading search methods as already studied at the level of an isolated propagation reaction, i.e. linear search, bisection, tetrasection, binary search tree, and quaternary tree, at the actual process level, complemented by the coupled array method and a direct linear search with no search over the cumulative sum of elements. Emphasis is on three (de)polymerization processes, namely free radical polymerization (FRP), nitroxide mediated polymerization (NMP), and depolymerization via radical unzipping in the context of chemical recycling. For illustration purposes, simplified reaction schemes are used only considering linear chains and constant average rate coefficients. Guidelines are formulated regarding the preference of a given search method depending on the maximal chain length and reaction conditions. For NMP, the most suitable method is the linear search, and for FRP, the quaternary tree. For depolymerization, the fastest method relies on the coupled array, offering an interesting trade-off between code complexity and performance gain. The present work allows researchers to better select the best data structures and best algorithms for studying the (bio)chemical processes of their interest with stochastic solvers.