Computing Nucleation Rates from Confined Equilibria: The Critical Cluster Equivalence Principle

Abstract

Nucleation is a fundamental step in the formation of new materials, with nucleation rates governing phase-transition pathways and outcomes that influence material properties across chemistry, physics, and biology. Nevertheless, extracting nucleation rates remains challenging: experiments are limited by the microscopic length scales involved, while molecular simulations are hindered by the rare-event nature of nucleation and the large system sizes required to sample low-supersaturation regimes typical of experiments and industrial processing. Here, we build on the established thermodynamic correspondence between stable clusters in small, closed systems and critical clusters in open systems and develop a multicomponent extension, the Critical Cluster Equivalence Principle, that transforms this correspondence into a practical workflow for calculating nucleation rates. We employ this equivalence to determine solvent-mediated NaCl crystal nucleation driving forces and rates over a wide range of supersaturations (SNaCl ∈ [1.5, 4]) and further validate the framework by benchmarking against curvature-corrected homogeneous nucleation rates for argon vapor condensation. This has been achieved using a small number of brute-force, finite-size simulations in which cluster-size statistics and monomer-exchange dynamics in the steady-state map directly onto critical clusters in macroscopic systems. By combining this multicomponent correspondence with the computational approach developed here, the current investigation has obtained nucleation rates in excellent agreement with experiments and enhanced sampling simulations. This approach provides a unified and generalizable tool for predicting nucleation rates with minimal computational effort, enabling routine application across a wide range of material systems.