A Thermodynamic Analysis of Enhanced Metastability in Isochoric Supercooled Liquids

Abstract

Experiments show that isochoric (constant-volume) conditions enhance supercooling stability relative to isobaric (constant-pressure) conditions. Here, combining Helmholtz equilibrium thermodynamics with a first-order perturbation methodology, we derive an inequality governing nucleation stability under volumetric constraint. The derivation provides a general thermodynamic proof that for any substance undergoing phase transformation in which the solid is less dense than the liquid, the Helmholtz driving force for solidification in isochoric systems is smaller than the Gibbs driving force in isobaric systems. Since nucleation rates depend exponentially on the inverse square of the driving force, this provides a thermodynamic basis for the observed suppression of nucleation rates. While a full stochastic treatment is beyond the scope of this work, the reduction in driving force implies a weakening of the bias toward growth of pre-critical fluctuations, increasing their probability of thermal dissolution. The analysis yields a dimensionless isochoric stability number. This number is computable from bulk thermodynamic data alone and provides a geometry-independent criterion for comparing metastable liquid stability across materials and conditions.