Development and Application of Refined Monte Carlo Algorithms for Understanding the Nucleation and Growth of Silicate Polymers under Varying Reaction Conditions

Abstract

The exploration of silicate polymerization processes under diverse reaction conditions requires robust computational methods capable of capturing the intricacies of molecular association, oligomer formation, and extended network growth. Recent advances in stochastic algorithms, particularly those based on Monte Carlo principles, have enabled more predictive modeling of the nucleation and subsequent evolution of silicate-based frameworks. A refined treatment of monomer addition and oligomer reorganization steps—alongside an appropriate representation of reaction free energies and configurational states—provides deeper insight into emergent structural motifs. By incorporating systematic updates to conventional acceptance criteria and improving the sampling of intermediate chemical states, it is possible to more accurately monitor species size distributions and branching patterns during polymer growth. This paper presents an integrated approach that synthesizes established stochastic dynamics with new, condition-specific adaptions. Within this approach, the control of partial charge distributions, explicit tracking of steric constraints, and careful calibration of reaction probabilities allow for consistent agreement with experimentally inferred polymerization trends. The method is demonstrated across a range of supersaturation levels and pH values, leading to enhanced clarity on the mechanistic interplay of molecular assembling forces. Crucially, these results emphasize the necessity for algorithms that robustly adapt to the complexities inherent in inorganic polymerization, paving the way for targeted design and prediction of novel silicate materials.