Weighted density functional theory for simple fluids: supercritical adsorption of a Lennard-Jones fluid in an ideal slit pore

Prediction of Adsorption Isotherms and Selectivities: Comparison between Classical Density Functional Theory Based on the Perturbed-Chain Statistical Associating Fluid Theory Equation of State and Ideal Adsorbed Solution Theory

This study gives an assessment of the predictive capability of classical density functional theory (DFT) for adsorption processes of pure substances and mixtures of spherical and nonspherical molecular species. A Helmholtz energy functional based on the perturbed-chain statistical associating fluid theory (PC-SAFT) is applied to calculate isotherms and selectivities of multicomponent adsorption. In order to unambiguously assess the accuracy of the DFT model, we conduct molecular simulations. Monte Carlo (MC) simulations are performed in the grand canonical ensemble using the transition matrix. Two types of systems are studied: a model system, where fluid-fluid and solid-fluid interactions are defined as (single-site) Lennard-Jones interactions, and a more realistic methane-n-butane mixture in a graphite-like pore. Differences between a slit-shaped and a cylindrical pore geometry are examined for the model system. Adsorption isotherms and selectivities obtained from DFT calculations and MC simulations are found in very good agreement, particularly at high pressures. Capillary condensation observed along adsorption isotherms containing n-butane was accurately predicted, both, in equilibrium pressure and in density-increase. Comparisons with results from the ideal adsorbed solution theory are presented, confirming powerful predictions of the DFT approach.

Modeling of bubble nucleation of an air-water mixture near hydrophobic walls

In this work, a density functional approach is applied to calculate the interfacial thermodynamic properties of an air-water mixture in the presence of a hydrophobic wall. Without any mixing parameter, the theoretical model can correctly reproduce the measured interfacial tensions of a nitrogen-water binary mixture. The density profiles of the dissolved air and water near the hydrophobic walls are predicted using the validated model. It is shown clearly that a hydrophobic wall leads to air enrichment and water depletion. According to the extent of air enrichment, the free energy barriers and critical radii of bubble nucleation at different hydrophobic interfaces are calculated to evaluate the possibility of spontaneous bubble nucleation.

Free energy density functional for adsorption of fluids in nanopores

A classical free energy density functional, which is isomorphic to a usual effective hard sphere model + mean field approximation for tail contribution, is proposed for treatment of real fluids in inhomogeneous states. In the framework of the classical density functional theory (DFT), the present functional is applied to two representative model fluids, namely, a Lennard-Jones fluid and a hard core attractive Yukawa fluid, subject to influence of various external fields. A comprehensive comparison with simulation results and a detailed analysis show that the present functional holds simultaneously all of the desirable properties inherent in an excellent functional, such as high accuracy, computational simplicity, consistency with a hard wall sum rule, nonrecourse to use of adjustable parameter(s) and weighted densities, reproduction of bulk second-order direct correlation function (DCF) in bulk limit, and applicability to subcritical fluid phenomena.

Survey of classical density functionals for modelling hydrogen physisorption at 77K

This work surveys techniques based on classical density functionals for modeling the quantum dispersion of physisorbed hydrogen at 77K. Two such techniques are examined in detail. The first is based on the "open ring approximation" (ORA) of Broukhno et al., and it is compared with a technique based on the semiclassical approximation of Feynman and Hibbs (FH). For both techniques, a standard classical density functional is used to model hydrogen molecule-hydrogen molecule (i.e., excess) interactions. The three-dimensional (3D) quantum harmonic oscillator (QHO) system and a model of molecular hydrogen adsorption into a graphitic slit pore at 77K are used as benchmarks. Density functional results are compared with path-integral Monte Carlo simulations and with exact solutions for the 3D QHO system. It is found that neither of the density functional treatments are entirely satisfactory. However, for hydrogen physisorption studies at 77K the ORA based technique is generally superior to the FH based technique due to a fortunate cancellation of errors in the density functionals used. But, if more accurate excess functionals are used, the FH technique would be superior.

Investigation of excess adsorption, solvation force, and plate-fluid interfacial tension for Lennard-Jones fluid confined in slit pores

The excess Helmholtz free energy functional is formulated in terms of a modified fundamental measure theory [Y. X. Yu and J. Z. Wu, J. Chem. Phys. 117, 10156 (2002)] for a short ranged repulsion and a first-order mean-spherical approximation theory [Y. P. Tang, J. Chem. Phys. 118, 4140 (2003)] for a long ranged attraction. Within the framework of the density functional theory, the density profile, excess adsorption, solvation force, and plate-fluid interfacial tension of a Lennard-Jones fluid confined in slit pores are predicted, and the results agree well with the simulation data. The phase equilibria inside the slit pores are determined according to the requirement that temperature, chemical potential, and grand potential in coexistence phases should be equal, and the plate-fluid interfacial tensions at equilibrium states are predicted consequently.

Potential of mean force in confined colloids: Integral equations with fundamental measure bridge functions

The potential of mean force for uncharged macroparticles suspended in a fluid confined by a wall or a narrow pore is computed for solvent-wall and solvent-macroparticle interactions with attractive forces. Bridge functions taken from Rosenfeld's density-functional theory are used in the reference hypernetted chain closure of the Ornstein-Zernike integral equations. The quality of this closure is assessed by comparison with simulation. As an illustration, the role of solvation forces is investigated. When the "residual" attractive tails are given a range appropriate to "hard sphere-like" colloids, the unexpected role of solvation forces previously observed in bulk colloids is confirmed in the confinement situation.

Structure of Lennard-Jones fluids confined in square nanoscale channels from density functional theory

The density distribution of Lennard-Jones fluids confined in square nanoscale channels with Lennard-Jones walls has been studied using the nonlocal density functional theory (DFT) based on the Tarazona model. The effect of channel lengths on the density profiles with various chemical potentials was discussed. It was found that there is an apparent layering phenomenon for the confined fluids due to the combining influences of the enhancing solid-fluid interaction and the excluded volume effect. The pronounced density peaks were observed at the corners of square channels due to the strong fluid-solid interactions. The grand canonical ensemble Monte Carlo simulation (GCEMC) was applied to test the nonlocal DFT results. The DFT calculations are in relatively good agreement with the GCEMC simulations. The adsorption isotherms in a series of square channels were evaluated based on the obtained density distributions. The adsorption mechanism within the square pores was investigated. A comparison between the adsorptions of the square pores with those of the corresponding slit-size pores has been given.

Structure of a soft-sphere fluid at a soft repulsive wall: a comparison of weighted density-functional theories

Density-functional theory is used to investigate the structure of a soft-sphere fluid at a soft wall. The fluid is modeled by an inverse sixth-power repulsive pair potential and the fluid particles interact with a flat stationary wall defined by an inverse-twelth power repulsive external potential. For comparison we examine results using three weighted density approximations (WDA), namely those due to Phys. Rev. A 32, 2909 (1985)]], Phys. Rev. A 39, 426 (1989)]], and the partitioned WDA of Mol. Phys. 90, 951 (1997)]]. The degree to which each of these approximations can accurately predict the structure of the fluid at the wall is evaluated for several densities through comparison with Monte Carlo simulation data.

Modeling inhomogeneous van der Waals fluids using an analytical direct correlation function

Rosenfeld's perturbative method [J. Chem. Phys. 98, 8126 (1993)]] for constructing the Helmholtz energy functional of classical systems is applied to studying inhomogeneous Lennard-Jones fluids, in which the key input-the bulk direct correlation function-is obtained from the first-order mean-spherical approximation (FMSA) [J. Chem. Phys. 118, 4140 (2003)]]. Preserving its high fidelity at the bulk limit, the FMSA shows stable and satisfactory performance for a variety of inhomogeneous Lennard-Jones fluids including those near hard walls, inside slit pores, and around colloidal particles. In addition, the inhomogeneous FMSA reproduces reliably the radial distribution function at its bulk limit. The FMSA is found, in particular, much better than the mean-field theory for fluids near hard surfaces. Unlike alternative non-mean-field approaches, the FMSA is computationally as efficient as the mean-field theory, free of any numerical determination of structure information, weight functions, or empirical parameters.

Weighted density-functional theory for simple fluids: prewetting of a Lennard-Jones fluid

The prewetting of a Lennard-Jones fluid is studied using weighted density-functional theory. The intrinsic Helmholtz free-energy functional is separated into repulsive and attractive contributions. An accurate functional for hard spheres is used for the repulsive functional and a weighted density-functional method is used for the attractive part. The results for this theory are compared against mean-field density-functional theory, the theory of Velasco and Tarazona [E. Velasco and P. Tarazona, J. Chem. Phys. 91, 7916 (1989)] and grand canonical ensemble simulation results. The results demonstrate that the weighted density functional for attractive forces may offer a significant increase in accuracy over the other theories. The density-functional and simulation results also indicate that a previous estimate of the wetting temperature for a model of the interaction of argon with solid carbon dioxide, obtained from simulations [J. E. Finn and P. A. Monson, Phys. Rev. A, 39, 6402 (1989)], is incorrect. The weighted density-functional method indicates that triple-point prewetting is observed for this model potential.

Adsorption of Lennard-Jones fluid mixture in a planar slit: a perturbative density functional approach

A simple perturbative density functional approach is employed to investigate the adsorption behavior of a model Lennard-Jones fluid confined in a slitlike pore. Adsorption of one-component fluid as well as two-component fluid mixtures in varying pore sizes has been investigated. The results on the density profiles and the excess adsorption obtained from this theory are found to be in overall good agreement with the available computer simulation results. The results are also compared with the same from some recent weighted density based calculations.