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 ΔT_f defined by the surface-to-volume ratio S/V , whereas the melting-point depression ΔT_m by the mean curvature κ of the pore surface, with ΔT_m/ΔT_f=2κ(V/S) . Employing H1 NMR cryoporometry, we experimentally demonstrate the linear correlation between ΔT_m and ΔT_f for several liquids with different ΔT_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.