Curvature-dependent metastability of the solid phase and the freezing-melting hysteresis in pores

Abstract

We recapitulate and generalize the concept of the freezing-melting hysteresis that attributes this phenomenon to a free-energy barrier between metastable and stable states of pore-filling material. In a phenomenological description, we show that under commonly encountered conditions, this renders the freezing-point depression $\Delta T_f$ defined by the surface-to-volume ratio $S∕V$, whereas the melting-point depression $\Delta T_m$ by the mean curvature $\kappa$ of the pore surface, with $\Delta T_m∕\Delta T_f=2\kappa (V∕S)$. Employing ${}^1\mathrm{H}$ NMR cryoporometry, we experimentally demonstrate the linear correlation between $\Delta T_m$ and $\Delta T_f$ for several liquids with different $\Delta T_{f,m}$ imbibed in controlled pore glasses. The results compare favorably to the morphological properties of the glasses determined by other techniques. Our findings suggest a simple method for analyzing the pore morphology from the observed phase transition temperatures.