Density Functional Theory Formulation for Fluid Adsorption on Correlated Random Surfaces

We provide novel random surface density functional theory (RSDFT) formulation in the case of geometric heterogeneous surface of solid media which is essential for description of thermodynamic properties of confined fluids. The major difference of our theoretical approach from existing ones is stochastic model of solid surface which takes into account the correlation properties of geometry. The main building blocks are effective fluid-solid potential developed in work (J. Stat. Phys, 2017,167(6), 1519-1545) and geometry based modification of Helmholtz free energy for Lennard-Jones fluids. Efficiency of RSDFT is demonstrated in calculation of argon and nitrogen low temperature adsorption on real heterogeneous surfaces (BP280 carbon black). These results are in good agreement with experimental data published in the literature. Also several models of corrugated materials are developed in the framework of RSDFT. Numerical analysis demonstrates strong influence of surface roughness characteristics on adsorption isotherms. Thus developed formalism provides connection between rigorous description of stochastic surface and confined fluids thermodynamics.