Density functional theory models have been very successful in describing main qualitative features of adsorption in pores of simple geometries. In our previous works we demonstrated that the non-local density functional theory (NLDFT) with suitably chosen parameters of fluid-fluid and fluid-solid interactions quantitatively predicts the positions of capillary condensation and desorption transitions of argon and nitrogen in cylindrical and spherical pores of ordered MCM-41, SBA-15, SBA-16 and related silica materials. However, introduction of pore wall roughness and heterogeneity effects has proved difficult without using expensive two- or three dimensional density distributions.

Here we present computationally efficient model of adsorption in silica nanopores, which accounts for the effects of surface roughness and microporosity. In this model, called the quenched solid density functional theory (QSDFT), we consider solid atoms as quenched component(s) of the solid-fluid system, with given density distribution(s), rather than the source of an external potential. All interactions are split into hard sphere repulsive and mean-field attractive interactions. The former are treated using the fundamental measure density functional. We demonstrate that, using a realistic model for silica structure and established parameters for intermolecular interactions with bridging and nonbridging oxygens, the QSDFT model quantitatively describes adsorption isotherms and isosteric heats of adsorption of Ar and Kr on reference MCM-41 and amorphous silica materials in a wide range of relative pressures. The effects of surface roughness in low-density silica materials of SBA-15 type have been modeled, and the results were found to be in excellent agreement with recently reported x-ray diffraction modeling of multilayer adsorption in SBA-15. QSDFT offers a systematic approach to the practical problems of characterization of micro- mesoporous amorphous silica materials.