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

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 H-1 NMR cryoporometry, we experimentally demonstrate the linear correlation between Delta T-m and Delta T-f for several liquids with different Delta T-f,T-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.