Integrating Multi-Scale Reaction Kinetics and Experimental Validation to Improve Predictive Accuracy of Silica Gelation Simulations

Abstract

Monte Carlo (MC) simulations have become indispensable for modeling silica gelation, yet persistent discrepancies between simulated and experimental results undermine their predictive utility. This study systematically addresses these inconsistencies by integrating atomistically informed reaction kinetics with mesoscale computational models, while establishing rigorous validation protocols. A hybrid stochastic-deterministic framework is developed, coupling discrete silicate tetrahedron polymerization events with continuum solvation effects via a modified Smoluchowski approach. Key parameters include hydrolysis rate constants khyd = Ahyd exp(−Ehyd/RT ) and condensation probabilities Pcond = α[SiOH]2, where α incorporates pH-dependent deprotonation equilibria. Benchmarking against experimental SAXS data (ESRF Beamline ID02) revealed that conventional MC models overestimate gelation times by 38±12% due to inadequate treatment of cyclization barriers. Introducing topological constraints via persistence length corrections (lp = 0.8 nm) reduced this discrepancy to 9±5%. Dynamic light scattering comparisons demonstrated that cluster growth exponents β in ⟨Rh⟩ ∝ tβ shifted from 0.31±0.02 (simulation) to 0.28±0.03 (experiment) upon implementing directional attachment preferences. A novel multi-fidelity validation metric Φ = P i wi|ysim i − yexp i |/σi was developed, weighting critical observables (gel time tg , storage modulus G′, and pore size distribution P (d)) by experimental uncertainty σi. This approach reduced Φ by 62% compared to conventional least-squares fitting, primarily through improved treatment of sol-gel transition dynamics. The framework enables predictive modeling of silica networks across length scales (1-100 nm) with ¡15% error in mechanical properties.