Scaling Acceleration Algorithm for Hybrid Kinetic Monte Carlo Simulation of Linear Radical Polymerization

Polymer materials design is essential in a wide range of industries, and the simulation of polymerization reactions provides a promising approach to the efficient design of synthesis recipes for desired property targets. The kinetic Monte Carlo (KMC) algorithm has been widely used in the simulation of polymerization reactions due to its ability to track the most delicate details of individual molecular sequences. However, the disadvantage of high computational cost has limited its broader applications, primarily caused by the large number of molecules that must be sampled in KMC simulations. This work proposes a novel scaling acceleration algorithm (SAA) specifically designed for hybrid KMC simulations of linear radical polymerization, which can significantly reduce the number of molecules in KMC simulations of radical polymerization, thus greatly accelerating the simulations. The algorithm can be used in radical reaction systems (currently limited to simple kinetic schemes) with species concentrations on significantly different scales, thus presenting a novel method for simulating polymerization reactions for efficient polymer materials design. To be more specific, this was achieved by solving a continuum model in parallel with the KMC simulation to provide an accurate value of radical concentrations for calculating a scaling factor (SF), which was then used to recover the correct results in KMC simulations when using an insufficient number of molecules. The algorithm was tested on three case studies: (1) free-radical polymerization, copolymerization, (2) atom-transfer radical polymerization (ATRP), homopolymerization, and (3) ATRP, copolymerization. The results showed that SAA simulates the system with at least 100 times fewer molecules than what would have been required for an accurate KMC simulation while achieving acceptable accuracy in the key characteristics of the polymerization system (including conversion, molecular weight distribution, and sequence distribution). In addition, sensitivity analysis of the ATRP model showed that the algorithm can be adequately applied to a wide range of cases with extreme rate constants. While SAA offers a speedier approach to simulate radical polymerization reactions, it is crucial to note that this acceleration process incurs a minor compromise in accuracy, particularly in the calculation of z-average molecular weight (M_z). The algorithm currently accounts for basic polymerization reaction schemes, assuming rapid ordinary differential equation solving and omitting chain-length dependencies.