A Density Functional Theory with a Mean-field Weight Function: Applications to Surface Tension, Adsorption, and Phase Transition of a Lennard-Jones Fluid in a Slit-like Pore

Abstract

A new density functional theory (DFT) for an inhomogeneous 12-6 Lennard-Jones fluid is proposed based on the modified fundamental measure theory for repulsive interaction and a weighted density functional for attractive interaction. The Helmholtz free energy functional for the attractive part is constructed using the modified Benedict-Webb-Rubin equation of state with a mean-field weight function. Comparisons of the theoretical results with molecular simulation data suggest that the new DFT yields accurate bulk surface tension, density distributions, adsorption-desorption isotherms, pore pressures, and capillary phase transitions for the Lennard-Jones fluid confined in slitlike pores with different widths and solid-fluid interactions. The new DFT reproduces well the vapor-liquid critical temperatures of the confined Lennard-Jones fluid, whereas the mean-field theory always overestimates the critical temperatures. Because the new DFT is computationally as simple and efficient as the mean-field theory, it will provide a good reference for further development of a statistical-thermodynamic theory of complex fluid under both homogeneous and inhomogeneous conditions when disperse force has to be considered.

A grand canonical Monte Carlo simulation study of argon and krypton confined inside weakly attractive slit pores

“…In the larger pore (h ¼ 15 Å ), at 300 K, the uniform density profile at 50 atm is contrasted with the incipient appearance, at 200 atm, of the depletion region near the walls and the sticking of argon molecules near the centre (which is less prominent than that at 246 K, due to the reduced amount adsorbed at the higher temperature). Figure 4(a),(b) shows that the pore density values in pure confinement are below the corresponding bulk density as also noted by Hamada et al [1] and Peng and Yu [52] for the LJ argon confined inside a hard wall slit pore. …”

“…At a given temperature, pore density increases with increase in slit height and for a given slit height, the pore density decreases with increase in temperature. These trends have been noted in literature [1,52] also. The isotherms are continuous and indicate no phase transition in the pressure range studied.…”

“…The pressure (and hence, the corresponding bulk density) at which this phase transition occurs in the weakly attractive pores decreases with increase of the strength of attraction in the pore at a given height and, also, with increase in slit height at a given uniform potential. These trends have also been noted by Hamada et al [1] and Peng and Yu [52] in their study of confined argon (modelled as a Lennard-Jones fluid) in attractive pores. These authors note that in a relatively weakly attractive pore the phase transition occurs at densities below the bulk densities, which is not observed in our case, where the fluid -fluid interactions are modelled using the hard core TW model instead of the LJ potential in Refs [1], [52], and the values of the uniform attractive potential for the pores are also different.…”

Compressibility of Thin Film Lubricants Characterized Using Atomistic Simulation

“…Density layering, fluid atoms tending to form layers parallel to confining walls, has been observed using Monte Carlo simulation [21], Density Functional Theory [22], all-atom [23], and united-atom [24] MD simulations, as well as experimentally [25]. This phenomenon has been observed using MD for spherical, linear, and branched chain molecules [24].…”

A hybrid perturbed-chain SAFT density functional theory for representing fluid behavior in nanopores: Mixtures

“…If the second version of PC-SAFT is assumed as a LJ potential, there are several ways to calculate the weight function, i.e., the normalized mean field weight function, 23, 24 the step function with a temperature-dependent diameter 25 or the normalized weight function calculated from direct correlation function. 26 In this work, we chose a common normalized mean field weight function due to its simplicity and known performance, and then the weighted density is an integral within the range of attraction, 23,24 i.e.,…”