We provide novel random surface density functional theory (RSDFT) formulationin the case of geometric heterogeneous surface of solid media which isessential for description of thermodynamic properties of confined fluids. Themajor difference of our theoretical approach from existing ones is stochasticmodel of solid surface which takes into account the correlation properties ofgeometry. The main building blocks are effective fluid-solid potentialdeveloped in work (J. Stat. Phys, 2017,167(6), 1519-1545) and geometry basedmodification of Helmholtz free energy for Lennard-Jones fluids. Efficiency ofRSDFT is demonstrated in calculation of argon and nitrogen low temperatureadsorption on real heterogeneous surfaces (BP280 carbon black). These resultsare in good agreement with experimental data published in the literature. Alsoseveral models of corrugated materials are developed in the framework of RSDFT.Numerical analysis demonstrates strong influence of surface roughnesscharacteristics on adsorption isotherms. Thus developed formalism providesconnection between rigorous description of stochastic surface and confinedfluids thermodynamics.
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