Freezing water at constant volume and under confinement

Abstract

Water expands upon freezing. What happens when water is cooled below 0 °C in an undeformable, constant-volume container? This is a fundamental question in materials thermodynamics, and is also relevant in biological, geological, and technological applications in which ice forms under nano-, meso-, or macroscale confinement. Here, we analyze the phase-equilibria and kinetic behaviors of water and ice-1h in an isochoric (constant-volume) system. By making use of the Helmholtz potential F (temperature, volume), in contrast to the Gibbs potential G (temperature, pressure), we demonstrate significant changes in phase behavior when the specific volume of the container is constrained below that of ice-1h. We construct a T–V (temperature–volume) phase diagram for water and ice that features a broad two-phase equilibrium region, and we further derive an isochoric nucleation theory that reveals the existence of a critical confinement volume, on the order of microns, below which ice-1h is kinetically prohibited from forming.