Free-Energy-Averaged Potentials for Adsorption in Heterogeneous Slit Pores Using PC-SAFT Classical Density Functional Theory

Abstract

This study analyzes the adsorption behavior in two-dimensional heterogeneous slit pores using nonlocal density functional theory based on the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state. Both chemical heterogeneity and surface roughness on small atomistic scales are investigated. The solid structure is considered as individual solid interaction sites whereby chemical heterogeneity is introduced through the presence of different solid–fluid sites and molecular roughness by varying the position of the interaction sites in the first solid layers. The effect of both forms of heterogeneity on the adsorption behavior is assessed individually. Effective one-dimensional solid–fluid potentials provide a way to reduce the dimensionality and computational demand of the density functional theory (DFT) calculations. We determine one-dimensional free-energy-averaged (FEA) solid–fluid potentials of methane and n-butane in the low-density limit for solid systems with molecular roughness and chemical heterogeneity. Using this effective one-dimensional solid–fluid potential at any density, we find excellent agreement of adsorption isotherms for both solid descriptions in systems with homogeneous slit pores. Subcritical adsorption isotherms of n-butane in slit pores with surface roughness show deviations at higher pressures due to the formation of fluid layers in the one-dimensional FEA potential. Chemical heterogeneity introduces a shift of the capillary condensation pressure below the saturation pressure of the bulk liquid, which is well described by the free-energy-averaged system.

Ultrananoporous supercapacitor with ionic liquid comprised of two-site cation: an Ising model study (II)

“…For fluid thermodynamic systems, great progress [11][12][13][14][15] has been made for theoretical approaches based on continuous model in recent decades. Systematic liquid theories include Ornstein-Zernike integral equation theory [16][17][18][19], thermodynamic perturbation theory [20][21][22], and classical density functional theory (CDFT) [23][24][25][26][27][28]. The CDFT is originally designed for thermodynamic systems under external field(s), among which includes electrical double layer (EDL) system, which underlies much of the EDLSC.…”

Two-Dimensional PC-SAFT-DFT Adsorption Models for Carbon Slit-Shaped Pores with Surface Energetical Heterogeneity and Geometrical Corrugation

“…Adsorption in porous systems is of considerable importance in research and technical applications such as catalysis, separation processes, and energy storage. , Numerous research studies have been addressed to investigate the inhomogeneous behavior of nanoporous adsorption, − while a promising approach to study the inhomogeneous behavior of confined fluids is the classical density functional theory (DFT). , …”

Thermodynamic Properties of Binary Mixtures Containing Ionic Liquid 1-Butyl-3-methylimidazolium Thiocyanate and Ethanolamines at Different Temperatures: Measurement and PC-SAFT Modeling

“…The PC-SAFT equation of state included perturbation theory that implied to an ensemble of hard spherical segments to form hard chain. , The dispersion of these chains implies the second-degree thermodynamic perturbation, while it could be extended for the associated systems such as self-association through hydrogen bonding . Since a canonical ensemble is considered, the Helmholtz free energy relation is the easiest way to derive thermodynamic relations: where superscripts hc and disp terms are used for the hard chain and dispersion, respectively, which are given in the original version of PC-SAFT. , The symbol assoc was used for association contribution that uses the original SAFT equations. , The components of the equations have been described in the original article as presented in these equations .…”

“…The PC-SAFT equation of state included perturbation theory that implied to an ensemble of hard spherical segments to form hard chain. , The dispersion of these chains implies the second-degree thermodynamic perturbation, while it could be extended for the associated systems such as self-association through hydrogen bonding . Since a canonical ensemble is considered, the Helmholtz free energy relation is the easiest way to derive thermodynamic relations: a = a h c + a d i s p + a a s s o c a h c = m a h s − prefix∑ i x i ( m i − 1 ) ln ( g h s false( σ false) ) a d i s p = prefix− 2 π I 1 m 2 ε σ 3 0.25em ̅ − π ρ m C 1 I 2 m 2 ε 2 σ 3 0.25em ̅ …”