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

Oleg Petrov and István Furó

Phys. Rev. E 73, 011608 – Published 31 January 2006

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 $Δ T_{f}$ defined by the surface-to-volume ratio $S ∕ V$ , whereas the melting-point depression $Δ T_{m}$ by the mean curvature $κ$ of the pore surface, with $Δ T_{m} ∕ Δ T_{f} = 2 κ (V ∕ S)$ . Employing ${}^{1}H$ NMR cryoporometry, we experimentally demonstrate the linear correlation between $Δ T_{m}$ and $Δ T_{f}$ for several liquids with different $Δ T_{f, m}$ 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.