Modeling of N2 adsorption in MCM-41 materials: hexagonal pores versus cylindrical pores

Low-temperature nitrogen adsorption in hexagonal pores and equivalent cylindrical pores is analyzed using nonlocal density functional theory extended to amorphous solids (NLDFT-AS). It is found that, despite significant difference of the density distribution over the cross-section of the pore, the capillary condensation/evaporation pressure is not considerably affected by the pore shape being slightly lower in the case of hexagonal geometry. However, the condensation/evaporation step in the hexagonal pore is slightly larger than that in the equivalent cylindrical pore because in the latter case the pore wall surface area and, hence, the amount adsorbed at pressures below the evaporation pressure are underestimated by 5%. We show that a dimensionless parameter defined as the ratio of the condensation/evaporation step and the upper value of the amount adsorbed at the condensation/evaporation pressure can be used as an additional criterion of the correct choice of the gas-solid molecular parameters along with the dependence of condensation/evaporation pressure on the pore diameter. Application of the criteria to experimental data on nitrogen adsorption on a series of MCM-41 silica at 77 K corroborates some evidence that the capillary condensation occurs at equilibrium conditions.