  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.
