Improved Horvath-Kawazoe equations including spherical pore models for calculating micropore size distribution

Since its publication, the Horvath-Kawazoe (H-K) equation has been rapidly and widely adopted for calculating the micropore size distribution from a single adsorption isotherm measured at a subcritical temperature (e.g. N₂ at 77 K or Ar at 87 K). In the H-K formulation, the ideal Henry's law (linearity) is assumed for the isotherm, even though the actual isotherms invariably follow the typical type I behavior, which is well represented by the Langmuir isotherm. The H-K formulation is modified by including the nonlinearity of the isotherm. Inclusion of nonlinearity results in sharpening of the pore size distribution and shifting of its peak position to a smaller size. Furthermore, the H-K equation is extended to spherical pores, and the improved H-K equation for spherical pores by including isotherm nonlinearity is also given. It is shown that the spherical-pore model is particularly useful for zeolites with cavities. Using the literature isotherm data, the improved H-K equations for three pore geometries (slit shape, cylinder and sphere) are compared with the original H-K equations. Clear improvements are seen in the calculated micropore size distributions by using the improved H-K equations.