Critical discussion of simple adsorption methods used to evaluate the micropore size distribution

The well-known simple adsorption methods used to evaluate the micropore size distribution from low pressure adsorption isotherms were examined by employing model isotherms for slit-like graphite micropores obtained from nonlocal density functional theory. It was shown that in the range of pore sizes from about 0.4 to 0.9 nm, the Horvath Kawazoe (HK) method satisfactorily reproduces the shape of the micropore size distribution, but the pore sizes are underestimated. In the case of micropores wider than 0.9 nm, the method fails as the formation of the monolayer on the pore walls produces a peak corresponding to 0.6 nm micropores on the HK pore size distribution. Therefore, the HK method indicates the presence of microporosity even for nonporous samples. The Dubinin-Astakhov adsorption isotherms were also examined and it was shown that their application to represent local adsorption isotherms for homogeneous pores is questionable. However, the adsorption potential distributions seem to be promising for micropore analysis.Nomenclature A Adsorption potential kJ/mol - C₁ Constant in Eq. 3 and 4 kJ * nm/mol - C₂ Constant in Eq. 3 and 4 nm³ - C₃ Constant in Eq. 3 and 4 nm⁹ - C₄ Constant in Eq. 3 and 4 - d Adsorbate molecule diameter nm - d_A Adsorbent atom diameter nm - G Change in the Gibbs free energy kJ/mol - J Pore size distribution cm³/(g*nm) - R The universal gas constant = 8.31431 J/(mol * K) - T Absolute temperature K - V Amount adsorbed expressed in cm³ of liquid adsorbate per 1 g of the adsorbent = 0.0015468 * amount adsorbed expressed in cm³ STP/g cm³/g - x Pore width nm - X Differential adsorption potential distribution cm³ * mol/(g*kJ) - Constant defined as nm - p Pressure Pa - p₀ Saturated pressure = 760 torr = 101325 Pa Pa - P_c Condensation pressure Pa - Degree of pore filling - S_BET BET specific surface area m²/g - S_ex External surface area obtained fromt-plot method m²/g - V_mi Micropore volume obtained fromt-plot method cm³/g - V₁ Total pore volume cm³/g - E Characteristic energy in the Dubinin-Astakhov equation kJ/mol - n Exponent in the Dubinin-Astakhov equation