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 DeltaTf defined by the surface-to-volume ratio S/V, whereas the melting-point depression DeltaTm, by the mean curvature kappa of the pore surface, with DeltaTm/DeltaTf =2kappa(V/S). Employing 1H NMR cryoporometry, we experimentally demonstrate the linear correlation between DeltaTm and DeltaTf for several liquids with different DeltaTf,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.