On the Gibbs-Thomson equation for the crystallization of confined fluids

TL;DR

This paper revisits the derivation of the Gibbs-Thomson equation for confined fluid crystallization, clarifies its assumptions, and uses simulations to validate its predictions for melting temperatures in nanopores.

Contribution

It provides a rigorous derivation of the Gibbs-Thomson equation, clarifies the assumptions involved, and demonstrates its application through molecular simulations for confined fluids.

Findings

The Gibbs-Thomson equation can predict melting temperatures in large pores.

Simulations highlight challenges in sampling crystallization under confinement.

The approach offers a potential method to study nanoscale capillary freezing.

Abstract

The Gibbs-Thomson (GT) equation describes the shift of the crystallization temperature for a confined fluid with respect to the bulk as a function of pore size. While this century old relation is successfully used to analyze experiments, its derivations found in the literature often rely on nucleation theory arguments (i.e. kinetics instead of thermodynamics) or fail to state their assumptions, therefore leading to similar but different expressions. Here, we revisit the derivation of the GT equation to clarify the system definition, corresponding thermodynamic ensemble, and assumptions made along the way. We also discuss the role of the thermodynamic conditions in the external reservoir on the final result. We then turn to numerical simulations of a model system to compute independently the various terms entering in the GT equation, and compare the predictions of the latter with the melting temperatures determined under confinement by means of hyper-parallel tempering grand canonical Monte Carlo simulations. We highlight some difficulties related to the sampling of crystallization under confinement in simulations. Overall, despite its limitations, the GT equation may provide an interesting alternative route to predict the melting temperature in large pores, using molecular simulations to evaluate the relevant quantities entering in this equation. This approach could for example be used to investigate the nanoscale capillary freezing of ionic liquids recently observed experimentally between the tip of an Atomic Force Microscope and a substrate.