A Signal-To-Noise-Ratio-Based Automated Algorithm to accelerate Kinetic Monte Carlo Convergence in Basic Polymerizations

Kinetic Monte Carlo (kMC) modelling is ubiquitous to simulate the time evolution of (bio)chemical processes, specifically if populations are involved. A recurring task is the selection of the smallest control volume that leads to convergence, which means that the model outputs are accurate and sufficiently free from stochastic noise and do not significantly change upon further increasing this volume. Selecting a too high (safe) control volume leads to an excessive simulation time, while many small incremental control volume increases are inefficient. This work therefore presents an automated tool to determine the smallest control volume leading to convergence. The tool is illustrated for (intrinsic) free radical and nitroxide mediated polymerization (FRP/NMP), in which the chain length distribution (CLD) is a crucial output. The algorithm starts with a very low volume to then check if the desired (monomer) conversion can be reached, the number average chain length is accurate, and finally the signal-to-noise (SNR) ratio at the CLD level is below a threshold. The execution time of the algorithm is less than twice the time of running the converged simulation directly, hence, saving tremendous time in setting up a kMC simulation and facilitating benchmark studies even beyond polymer reaction engineering applications. A signal-to-noise ratio (SNR) based method to find the control volume that guarantees converged results for kinetic Monte Carlo (kMC) simulations is highlighted and applied in the field of polymer reaction engineering. The application of the algorithm employs less than twice the simulation time compared to the time needed to simulate with a converged volume.image

Automated summary

This study presents an automated tool to determine the smallest control volume leading to convergence in kinetic Monte Carlo (kMC) simulations. The tool saves tremendous time in setting up a kMC simulation, making it useful for benchmark studies in polymer reaction engineering applications.