Theoretical Approach to Rough Surface Characterization for Silica Materials

We propose a new theoretical approach to obtain the nanoscale morphology of rough surfaces from low-temperature adsorption experiments. Our method is based on one of the most realistic models of rough surfaces formulated in terms of random correlated processes. In our study, the adsorption on the rough surfaces is theoretically described by random surface density functional theory (RS-DFT), which allows us to take into account both the roughness in the normal direction and the correlation length of the lateral surface. Varying geometrical parameters of RS-DFT, we fit the experimental data in the low-pressure range, where the influence of the surface geometry is the most crucial. From this procedure, we obtained best-fit detailed geometry of rough surfaces, which provides full information for further atomistic modeling. Also, the developed approach allows the calculation of the surface fractal dimension from the experimental isotherms. It demonstrates that the surface fractal dimension observed in many experiments is natural for the correlated random surface model. We investigated the surface geometry of popular silica materials synthesized at different conditions. The obtained roughness parameters and fractal dimensions coincide well with the published experimental data and correctly reflects how the nanoroughness of silica materials depends on the synthesis conditions. Analysis of the best-fit specific surface area reveals the mechanism of adsorption on rough surfaces and provides a new strategy for the search of optimal storage materials.