Lennard-Jones fluids in cylindrical pores: Nonlocal theory and computer simulation

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Abstract
We present adsorption isotherms, phase diagrams, and density profiles for a Lennard‐Jones fluid confined to a cylindrical pore. In particular, we concentrate on the gas–liquid transition in the pore (capillary condensation). We compare simulations for a series of radii and different temperatures with mean fielddensity functional theory (MFT). Two forms of MFT are considered, the simple local density approximation(LDA) and Tarazona’s nonlocal or smoothed density approximation (SDA). We find that the SDA provides a quite accurate description of fluid structure in the pore and that it produces phase diagrams in good agreement with the simulation data. For larger radii and temperatures T/T c ≳0.6 the SDA shows steep rises in adsorption close to the transition. This strongly affects the shape of the coexistence curve in the T, ρ̄ plane. Here ρ̄ is defined as the average density inside the pore. This behavior is confirmed by the simulation. In contrast, LDA gives a poor representation of the fluid structure and this underlies the failure to reproduce the phase diagrams and adsorption isotherms found with SDA or simulation. For extremely small radii (R*≈1) the simulation adsorption isotherms are smooth, and for not too low a temperature they are accurately described by an approach which starts from the potential distribution theorem and uses perturbation theory for the true one‐dimensional fluid.