Corrected Horvath-Kawazoe equations for pore-size distribution

The Horvath-Kawazoe (HK) model is a widely used method for determining pore-size distribution in a microporous material from a single adsorption isotherm. The original model, however, suffers from conceptual flaws. The total interaction energy of the adsorbate is underestimated since the adsorbate-adsorbate interaction is incorrectly calculated. New corrected HK models proposed here for three pore geometries (slit, cylindrical, and spherical) can overcome these defects. Two other improvements have also been made in the new models. These assume that a filled micropore is composed of layers of adsorbate molecules which interact only with the molecular layers in the immediate vicinity. A better estimate of adsorbate-adsorbate-adsorbent interaction is obtained by utilizing actual distances between interacting molecules. The average interaction energy is calculated by a population-weighted average of the energy potential of the layers rather than by integration. This average potential approaches a nonzero value at large pore size, unlike that in the original model. Pore-size distributions predicted by the corrected HK models agreed significantly better with crystallographic data compared to the original model for both microporous and mesoporous sorbents.