Random Process Theory Approach to Geometric Heterogeneous Surfaces: Effective Fluid–Solid Interaction

Abstract

Realistic fluid-solid interaction potentials are essential in description of confined fluids especially in the case of geometric heterogeneous surfaces. Correlated random field is considered as a model of random surface with high geometric roughness. We provide the general theory of effective coarsegrained fluid-solid potential by proper averaging of the free energy of fluid molecules which interact with the solid media. This procedure is largely based on the theory of random processes. We apply first passage time probability problem and assume the local Markov properties of random surfaces. General expression of effective fluid-solid potential is obtained. In the case of small surface irregularities analytical approximation for effective potential is proposed. Both amorphous materials with large surface roughness and crystalline solids with several types of fcc lattices are considered. It is shown that the wider the lattice spacing in terms of molecular diameter of the fluid, the more obtained potentials differ from classical ones. A comparison with published Monte-Carlo simulations shows good qualitative agreement with the theory predictions. The work provides a promising approach to explore how the random geometric heterogeneity affects on thermodynamic properties of the fluids.

Random surface statistical associating fluid theory: Adsorption of n-alkanes on rough surface

“…as was demonstrated in work [6] in the case when terms of F mono and F chain are depended on segment density ρ solution of (8) can be written as function of r. In assumption of surface radial symmetry external potential can be represented as function of one spatial coordinate only U f s (z), where z is the distance between the chain-segment and the surface [18].…”

“…Our approach is based on Free Energy Averaging Technique presented in the work [20]. Also advanced theory of Markovian random processes and the first passage time probability problem were applied as part of averaging procedure (see work [18]…”

“…Adsorption isotherm in the case of rough surface with known parameters δ, τ can be calculated using external potential U f s (z) [18] and expression (13):…”

Adaptive intermolecular interaction parameters for accurate Mixture Density Functional Theory calculations

“…The mixture of Lennard -Jones (LJ) fluids in terms of DFT, FMT, and MFA was first investigated by Kierlik and Rosenberg in 1991 [37]. Furthermore, the classical DFT was extended for solving particular problems: Statistical Associating Fluid Theory (SAFT) for modeling polymers [38], Quenched Solid Density Functional Theory (QSDFT) [39], and Random Surface Density Functional Theory (RSDFT) [40] to take into account the effect of rough surfaces on fluid behavior, and Random Surface Statistical Associating Fluid Theory (RS-SAFT) to study the impact of rough surface on the adsorption of n-alkanes [41]. However, molecular DFT is not widely used for the prediction of fluid mixture behavior.…”

Electrolytes structure near electrodes with molecular size roughness

“…This starting points z i may be negative for extremely rough surfaces and tends to hard walls value d i /2 as the roughness becomes insignificant. Considering the rough surface as the Gauss correlated process the contact conditions can be calculated as functions of the relative roughness parameters z i (δ/d i , λ/d i ) [25]. The details of the dependence of ions penetration into solid media on the surface roughness and the diameter of molecules can be found in Appendix B.…”