Derivation of the Expanded Form of the BJH Equation and its Application to the Pore Structure Analysis of Mesoporous Adsorbents

Abstract

The BJH equation, ${\mathrm{v}}_{\mathrm{n}}={\mathrm{R}}_{\mathrm{n}}{\left(\Delta \mathrm{V}\right)}_{\mathrm{n}}-{\mathrm{R}}_{\mathrm{n}}\Delta {\mathrm{t}}_{\mathrm{n}}\sum _{\mathrm{i}=1}^{\mathrm{n}-1}{\mathrm{c}}_{\mathrm{i}}{\mathrm{A}}_{\mathrm{i}}$ , used for pore structure analyses via its application to the N₂ desorption isotherms at 78 K of porous materials, has been modified by substituting the value of c_i and expanding the last term. The quantity v_n is the volume of the pores involved in the nth desorption step and is given in terms of the volume of N₂, (ΔV)_n, exuded from the porous material, the constants R_n and c_i which depend on the average pore size and average thickness of the physically adsorbed multilayer, Δt_n being the decrease in thickness of the multilayer as a result of the nth desorption step and A_i the surface area of the set of pores involved in the ith desorption step. A derivation of the modified equation is presented. It has been applied to the N₂ desorption data of bone char used by Barrett, Joyner and Halenda (BJH). The effect of the multilayer thickness (t) values given by Pierce and de Boer on the pore size distribution of bone char has been studied. The pore size distribution data are compared with those obtained by the original BJH and Pierce methods. The pore system conforms very well with the idealised open-ended cylindrical pore model.

The expanded BJH equation has also been applied to the desorption isotherms of fresh and sintered silica-alumina cracking catalysts over the entire range of silica/alumina ratios. The multilayer thickness (t) values given by de Boer have been used in the calculations. The pore systems of the catalysts, vacuum-dried at 400°C, are observed to conform to the cylindrical pore model as revealed by the excellent agreement between the cumulative surface areas obtained in P.S.D. calculations and the BET surface areas. The pore systems of the catalysts, sintered at different temperatures in a dry oxygen stream, deviate considerably from the cylindrical pore model. Enlargement of the pores and their nonconformity with the ideal pore model are attributed to modifications of the pore structures brought about by the phenomenon known as ‘self-steaming’ with the water vapour released from the catalysts.