Theoretical Considerations on the Anomalous Heat Capacity of the Capillary Condensate in Fine Pores

Abstract

Among a number of theoretical formulae Eq. (4)∼(7') proposed hitherto for the freezing-point depression of capillary liquid, the authors' formula Eq. (6) is the most general one because the contact angle is taken into account. All the formulae cited here, however, give only the limiting temperature T_f, at which the meniscus surface of the capillary liquid condensing in pores of radius r_f commences to freeze (Fig.3-b).
The effective contact angle Θ as well as the radius of conical pore has been defined with relation to the radius of curvature of menisci by Eqs. (2) and (3). The conical-pore model presented here may be generalized for any type of pores in porous materials. By using these new concepts, a model of freezing phenomenon has been proposed. Frozen layer formed initially in gas-liquid interface, with non-zero value of Θ_SG, is thickened keeping Θ_SG constant, as the temperature decreases (Fig.3-c). On the basis of Laplace's and thermodynamical equations in the three phase equilibrium of the sorbate in pores, a theoretical formula Eq. (18) has been derived. The formula relates the radius of curvature of solid-liquid interface to temperature T, and is easily applicable to the calculation of the amount of the sorbate melted during temperature rise, if the distribution of the pore size is known. Heat capacity curves calculated (Figs.4, 6, 7, 8, 10 and 11) are in fair agreement with the experimental results of Morrison et al. or Antoniou. The values of solid-gas or solid-liquid interfacial tensions and effective contact angles have also reasonably been determined (Tables 1, 2 and 3).
Anomalous excess heat capacity of the condensate, which remained so far without a reasonable explanation, is satisfactorily interpreted by the, capillary condensation theory.