P. Tarazona

Fluids in narrow pores: Adsorption, capillary condensation, and critical points

By means of a density functional approach the phase equilibria of a simple fluid confined by two adsorbing walls have been investigated as a function of wall separation H and chemical potential μ for temperature T corresponding to both partial and complete wetting situations. For large values of H and small undersaturations Δμ ≡ μsat−μ, we recover the macroscopic formulas for the undersaturation at which a first‐ order phase transition (capillary condensation) from dilute ‘‘gas’’ to a dense ‘‘liquid’’ occurs in a single, infinitely long slit. For smaller H we compute the lines of coexistence between gas and liquid in the (Δμ, 1/H) plane at fixed values of T. The adsorption Γ(Δμ), at fixed T and H, is characterized by a loop. At the first order transition Γ jumps discontinuously by a finite amount; however metastable states exist and these could give rise to hysteresis of the adsorption isotherms obtained for the single slit. The loop disappears at a capillary critical point (Δμc, 1/Hc) at each T. For H

Dynamic density functional theory of fluids

We present a new time-dependent density functional approach to study the relaxational dynamics of an assembly of interacting particles subject to thermal noise. Starting from the Langevin stochastic equations of motion for the velocities of the particles we are able by means of an approximated closure to derive a self-consistent deterministic equation for the temporal evolution of the average particle density. The closure is equivalent to assuming that the equal-time two-point correlation function out of equilibrium has the same properties as its equilibrium version. The changes in time of the density depend on the functional derivatives of the grand canonical free energy functional F[ρ] of the system. In particular the static solutions of the equation for the density correspond to the exact equilibrium profiles provided one is able to determine the exact form of F[ρ]. In order to assess the validity of our approach we performed a comparison between the Langevin dynamics and the dynamic density functional...

A simple density functional theory for inhomogeneous liquids

A simple free energy functional, which incorporates both ‘local’ thermodynamics and short ranged correlations, is formulated and applied to the calculation of the density profile of fluids near hard walls. For hard sphere fluids the calculated profiles are in reasonable agreement with Monte Carlo results. For a Lennard-Jones liquid the profiles exhibit the phenomenon of wetting by gas; the oscillations in the density profiles become much less pronounced and a layer of gas develops near the wall as the bulk density approaches its value at coexistence. Such behaviour was found earlier in Monte Carlo simulations but is not accounted for by existing integral equation theories based on closures of the wall-particle Ornstein-Zernike equation.

Capillary condensation and adsorption in cylindrical and slit-like pores

The nature of adsorption of simple fluids confined in model pores is investigated by means of a density functional approach. For temperatures T corresponding to a partial wetting situation a first-order phase transition (capillary condensation) from dilute ‘gas’ to dense ‘liquid’ occurs at relative pressures p/psat close to those predicted by the macroscopic Kelvin equation, even for radii Rc or wall separations H as small as 10 molecular diameters. In a complete wetting situation, where thick films develop, the Kelvin equation is, in general, not accurate. At fixed T the adsorption Γm(p) exhibits a loop; Γm jumps discontinuously at the first-order transition, but the accompanying metastable portions of the loop could produce hysteresis similar to that observed in adsorption measurements on mesoporous solids. Metastable thick films persist to larger p/psat in slits than in cylinders and this has repercussions for the shape of hysteresis loops. For a given pore size the loop in Γm shrinks with increasing T and disappears at a capillary critical temperature Tcapc( Tcapc condensation no longer occurs and hysteresis of Γm will not be observed. Such behaviour is found in experiments. A prewetting (thick–thin film) transition can occur for confined fluids. The transition is shifted to a smaller value of p/psat than that appropriate to prewetting at a single planar wall. Whereas the magnitude of the shift is very small for slits, it is substantial for cylinders and this leads to the possibility of finding a triple point, where ‘liquid’ and thick and thin films coexist, in cylindrical pores whose radii may not be too large for investigation by experiment or computer simulation. Adsorption of supercritical fluids (T > Tc, the bulk critical temperature) in cylinders is mentioned briefly.

Density functional theory and the asymptotic high density expansion of the free energy of classical solids and fluids

On the basis of the fundamental-measure free energy functional for hard spheres and thermodynamic perturbation theory, a unified analytical description of classical bulk solids and fluids is obtained, predicting correctly the major features of their equations of state and freezing parameters as obtained by simulations. The fundamentally different fluid and solid asymptotic high density expansions for the potential energy, featuring a static-lattice Madelung term and the harmonic 3/2k B T correction, on one hand, and a fluid Madelung energy with a ˜T 3/5 thermal energy correction, on the other, both originate from the same singularity in the hard sphere free energy functional.

Density functional approximation for hard‐body liquid crystals

We present a density functional approximation for the free energy of a system of hard bodies with arbitrary shape and orientational distribution. For systems with homogeneous density it reduces to existing treatments, which describe the isotropic liquid and the nematic liquid crystal. The treatment of the inhomogeneous density allows the study of smectic and crystal phases. We applied the approximation to a system of parallel hard spherocylinders, for which we compare the nematic to smectic‐A phase transition with recent computer simulation data. We also study a system of oblique cylinders and show that smectic‐C phase may appear as the result of packing effects in systems of hard bodies.

Dimensional crossover and the freezing transition in density functional theory

A modified geometrically based free-energy functional for hard spheres is proposed which gives reliable results even for situations of extreme confinements that reduce the effective dimensionality D. It is accurate for hard spheres between narrow plates .D D 2/, inside narrow cylindrical pores .D D 1/, and is exact in the 0D limit (a cavity that cannot hold more than one particle). This functional also predicts the hard-sphere fluid-solid transition in excellent agreement with the simulations.

Capillary condensation in structured pores

We investigate capillary condensation in slit‐like pores with structured walls, described by a simple lattice gas model based on the mean‐field approximation. Most theoretical workers did not go beyond very simple capillary models with perfect symmetry, thus being unable to map experiments in real pores with rather complex structure. In this paper we deal with chemical inhomogeneity, produced by a periodic wall potential, that causes fluid attraction and repulsion altering along the walls. We observe a new mechanism of capillary condensation, characterized by a splitting of the equilibrium ‘‘gas–liquid’’ transition, and we concentrate on the crucial role the typical length for the wall inhomogeneity, λ, plays compared with the pore width, H. Our microscopic results are confirmed by a macroscopic analysis that leads to a modified Kelvin equation, giving a quantitative prediction of capillary condensation in structured pores. Furthermore our model explains the nature of the critical isochore as measured in ...

The intrinsic structure of the water surface

An operational procedure to obtain the intrinsic structure of liquid surfaces is applied here to a molecular dynamics simulation of water, with a model of point charges for the molecular interactions. The method, which had been recently proposed and used for simple fluids, is successfully extended to a molecular liquid with the complex bond structure of water. The elimination of the capillary wave fluctuations, in the intrinsic density and orientation profiles, gives a new overall view of the water surface, at the sharpest molecular level, and without the size-dependent broadening observed in the mean profiles. The molecules belonging to the outer liquid layer are clearly identified, and we find that only these molecules exhibit a clear preferential orientation to lie flat on the surface. Moreover, there is a strong correlation between the dipolar structure and the local curvatures of the intrinsic surface, so that at the extrusions of the intrinsic surface the molecular dipoles point preferentially toward the vapor side of the interface. Finally, we have found an intrinsic density layering structure, although the inner structure is strongly damped beyond the second layer.

Two-stage capillary condensation in pores with structured walls: A nonlocal density functional study

We present phase diagrams for capillary condensation in chemically structured slit pores characterized by two first-order transitions from the confined “gas” over “liquid bridges” to “liquid.” The split adsorption is produced by a complex periodic wall potential in one of the lateral directions that mimics inhomogeneities in real materials. After the previous condensation of liquid drops at the most attractive adsorption sites these may combine to form liquid bridges between opposite walls, separated between them by “gas gaps.” Nonlocal density functional theory is employed to investigate this stepwise mechanism and the stability of the liquid bridges phase in function of the thermodynamic conditions and the pore structure, especially the ratio of the two typical lengths, the corrugation period λ and the pore width H. Macroscopic predictions for the subcritical phase equilibria and the critical limit complete the study. The calculations confirm our previous results [P. Rocken and P. Tarazona, J. Chem. Phy...