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.

Calculation of a temperature–volume phase diagram of water to inform the study of isochoric freezing down to cryogenic temperatures

“…Phase diagrams, which map material equilibrium, may be constructed to reect a wide variety of natural thermodynamic variables. 5,[8][9][10][11][12] Amongst the most common diagrams for pure substances and binary substances respectively are the temperature-pressure and temperature-concentration diagrams, which have been deployed widely since the turn of the 20 th century. These two diagrams exhibit markedly different geometry, and are characterized by markedly different features.…”

“…This temperature range was chosen based on the phases for which mutually-consistent equations of state were available. To construct this phase diagram, we extend the basic method of Powell-Palm, Rubinsky & Sun: 5 the 2D convex hulls enclosing the Helmholtz free energy surfaces F ( T , V ) of all of the aforementioned phases were calculated at discrete temperatures within the stated range ( Fig. 1a ), with an increment of 0.0654 K; single-phase points on the lower convex hull ( Fig.…”

“…[5][6][7] By controlling the volume of the system rather than the pressure, the thermodynamic path the system takes as it is cools is altered fundamentally, with the system occupying various two-phase equilibrium states instead of the single-phase equilibrium states encountered when cooling under constant pressure. This process has been well characterized for the temperature range 0 to À22 C, 5,6 wherein an aqueous isochoric system will exist in stable two-phase equilibrium between ice Ih (the hexagonal ice phase most commonly found on Earth) and liquid water. However, the process of isochoric freezing down to lower temperatures, which will involve multiphase equilibria comprised of multiple forms of ice, has not been rigorously examined in the modern era.…”

Interfacial and Confinement-Mediated Organization of Gas Hydrates, Water, Organic Fluids, and Nanoparticles for the Utilization of Subsurface Energy and Geological Resources

“…Calibrated insights into the fate of fluids in subsurface porous environments are needed. In this context, assessing the influence of pore sizes, shapes, geometries, surface chemistry on the structures, − dynamics, − ,− phase transitions, − rheology, − assembly, ,− and flow of confined fluids , is essential. Among these properties, there have been limited efforts to link the structures of confined fluids or assembly of molecules to the observed properties and the efficacy of fluid storage and recovery activities.…”

Isochoric supercooled preservation and revival of human cardiac microtissues

“…e. Isochoric supercooling enables preservation of biological matter in a metastable ice-free condition at temperatures below the freezing point of water / physiological saline. Isochoric conditions are achieved by confining the preservation solution in a high-rigidity container totally absent of bulk gas phase and denying it access to the atmospheric pressure reservoir, which alters both equilibrium thermodynamics and ice nucleation kinetics of the system 23,24 . f. Temperature-time schematic of the isochoric supercooling preservation protocol.…”