Bridging Nanoscopic Surface Heterogeneity and Macroscopic Nucleation Rates: A Perspective on Probabilistic Approaches

Abstract

Predicting the number of newly formed crystals and their spatial distribution on surfaces or within pore spaces matters across many fields, from structural biology to coupled fluid flow and reactive transport in porous media to atmospheric physics. Nucleation occurs at molecular and nanoscopic scales, yet classical nucleation theory (CNT) provides an averaged, macroscopic description, and a growing body of experimental observations is inconsistent with CNT predictions. Probabilistic nucleation models have been developed to predict mineral formation in reactive porous geochemical systems and to generate uncertainty estimates, for example, of how mineral growth affects fluid flow. However, the probability density functions of nucleation rates or induction times that underlie these models remain poorly constrained and are not grounded in the intrinsic nanoscopic physicochemical mechanisms underlying the observed macroscopic behavior. This perspective reviews recent advances in mineral nucleation research, focusing on modeling in coupled reactive transport systems, and examines how the large uncertainties reported for macroscopic nucleation rates may be linked to the extent and spatial distribution of surface sites with contrasting reactivity, such as kinks, steps, and terraces. Building on this, we propose a framework that integrates site-specific nucleation probabilities and explicitly accounts for polymorph selection to enable deterministic prediction of macroscopic nucleation rates from intrinsic surface properties. While the resulting parameter space is extensive, recent advances in machine learning, combined with high-throughput experimentation and simulation, suggest that such predictive, multiscale models are now within reach.