A Thermodynamic Analysis of Enhanced Metastability in Isochoric Supercooled Liquids

Supercooled liquids with negative Clapeyron slopes are more stable at constant volume than at constant pressure. We compare the isochoric and isobaric driving forces for incipient solidification via a first-order perturbation expansion of the thermodynamic potentials in the solid mass fraction. The analysis yields a geometry-independent inequality: the isochoric Helmholtz driving force is strictly smaller than the isobaric Gibbs driving force. It also introduces a dimensionless stability number Π₀ =  ${\left(v_s-v_l\right)}^2/\left(L_f·{\kappa }_l·v_l\right)$ , where $v_s$ and $v_l$ are the solid and liquid specific volumes, $L_f$ is the latent heat of fusion, and κ_l is the liquid isothermal compressibility. ${\Pi }_0$ ranks materials and guides supercooling design for negative-Clapeyron-slope substances. For water, ${\Pi }_0$  ≈ 0.048. Cryoprotectants increase it several-fold, suppressing nucleation beyond colligative freezing-point depression.