Frenkel−Halsey−Hill Equation, Dimensionality of Adsorption, and Pore Anisotropy

Abstract

The Frenkel-Halsey-Hill (FHH) equation V/V(m) approximately [log(P(0)/P)](-1/s) is revisited in relation to the meaning of its exponent in a specific intermediate range of pressure where capillary condensation occurs. It has been suggested in the past that plots of the form log V = constant - (D - 3)[loglog(P(0)/P)], or its equivalent log S = const - (D - 2) log r, can be used for the estimation of the dimensionality D of the adsorbing surface from those parts of the slopes at low pressure corresponding to straight lines. In the present study it is shown that, for pores of cylindrical geometry and at a specific range of pressure where those pores are filled-up during the process of capillary condensation, the local slopes d log V/d loglog[(P(0)/P)] or d log S/d log r, of plots similar to the above, may be used to estimate the pore anisotropy b of the adsorbing space from the relationships log b = [[d log V/d loglog[(P(0)/P)] - 3] log(0.5r) or log b = [[d log S/d log r] - 2] log(0.5r). These observations lead to the physicogeometrical conjunction that, during capillary condensation in cylindrical pores, usually assumed in nitrogen porosimetry, the scaling dimension of pore anisotropy b, scaled in units of radius r, is related to the dimensionality D of the process.