The role of attractive intermolecular forces in the density functional theory of inhomogeneous fluids

Liquid-liquid phase separation in an inhomogeneous ternary colloid-polymer mixture

Suspended colloids are often considered as models for molecules, which are sufficiently big so that they can be observed directly in (light) microscopes and for which the effective interaction among each other can be tailored. The Asakura-Oosawa model of ideal colloid-polymer mixtures captures the idea of tuning the interaction between the colloids via a potential, which possesses a range set by the size of the polymers and an attractive strength characterized by the (reservoir) number density of the polymers, which plays the role of an inverse temperature. The celebrated Asakura-Oosawa depletion potential allows one to recreate the bulk phase diagram of a simple fluid by employing a colloid-polymer mixture. This has been verified in theory, by computer simulations, and via experiments. Here, we study the phase behavior of a confined colloid-polymer mixture with two polymer species. The sizes and densities are chosen such that the resulting bulk phase diagram exhibits a second stable critical point within the framework of the classical density functional theory. Our results suggest that a suitably tuned colloid-polymer mixture can be an interesting model system to study fluids with two critical points.

Toward a density-functional theory for the Jagla fluid

The so-called Jagla fluid is well known to exhibit, in addition to the usual gas-liquid critical point, also a liquid-liquid critical point, as well as a density anomaly. This makes it an interesting toy model for water, for which a liquid-liquid critical point is considered to exist but so far eludes experimental verification due to crystallization occurring in the corresponding metastable, deeply supercooled state. With the Jagla fluid being understood quite well in bulk-mostly via simulation studies-the focus of the present study is to describe the spatially inhomogeneous fluid in terms of classical density-functional theory (DFT) with the aim to be able to control its phase behavior on changing the shape or the nature of the confinement of the fluid. This information might contribute to guide potential experimental tests of the liquid-liquid critical point of actual water. We first determine the bulk phase diagram for the Jagla fluid by using thermodynamical perturbation theory. In doing so we explain why the perturbation theories of Barker and Henderson as well as of Weeks, Chandler, and Anderson fail to describe the Jagla fluid. We then continue to construct a perturbative DFT based on our bulk model, which shows significant improvement over the standard mean-field DFT valid at high temperatures. But ultimately the perturbative DFT breaks down at state points close to the binodal line and at low temperatures. This prevents us from achieving the original aim to study a highly confined, inhomogeneous Jagla fluid close to its liquid-liquid binodal.

Mean-field theory of inhomogeneous fluids

The Barker-Henderson perturbation theory is a bedrock of liquid-state physics, providing quantitative predictions for the bulk thermodynamic properties of realistic model systems. However, this successful method has not been exploited for the study of inhomogeneous systems. We develop and implement a first-principles "Barker-Henderson density functional," thus providing a robust and quantitatively accurate theory for classical fluids in external fields. Numerical results are presented for the hard-core Yukawa model in three dimensions. Our predictions for the density around a fixed test particle and between planar walls are in very good agreement with simulation data. The density profiles for the free liquid vapor interface show the expected oscillatory decay into the bulk liquid as the temperature is reduced toward the triple point, but with an amplitude much smaller than that predicted by the standard mean-field density functional.

Excess pressure and electric fields in nonideal plasma hydrodynamics

Nonideal plasmas have nontrivial space and time correlations, which simultaneously impact both the excess thermodynamic quantities as well as the collision processes. However, hydrodynamics models for designing and interpreting nonideal plasma experiments, such as inertial-confinement fusion experiments, typically neglect electrodynamics, although some models include electric fields indirectly through a generalized Fick's law. However, because most transport models are not computed self-consistently with the equation of state, there is double counting of the forces in the excess thermodynamic quantities and the collision terms. Here we employ the statistical mechanical hydrodynamic theory of Irving and Kirkwood [J. Chem. Phys. 18, 817 (1950)JCPSA60021-960610.1063/1.1747782] to examine inhomogeneous, nonideal plasmas that contain electric fields. We show that it is not possible to simultaneously separate terms that correspond to electric fields and excess pressure; rather, these quantities arise from the same interparticle Coulomb forces. Moreover, new terms associated with nonlocality appear in the presence of strong inhomogeneities.

Long-ranged contributions to solvation free energies from theory and short-ranged models

Long-standing problems associated with long-ranged electrostatic interactions have plagued theory and simulation alike. Traditional lattice sum (Ewald-like) treatments of Coulomb interactions add significant overhead to computer simulations and can produce artifacts from spurious interactions between simulation cell images. These subtle issues become particularly apparent when estimating thermodynamic quantities, such as free energies of solvation in charged and polar systems, to which long-ranged Coulomb interactions typically make a large contribution. In this paper, we develop a framework for determining very accurate solvation free energies of systems with long-ranged interactions from models that interact with purely short-ranged potentials. Our approach is generally applicable and can be combined with existing computational and theoretical techniques for estimating solvation thermodynamics. We demonstrate the utility of our approach by examining the hydration thermodynamics of hydrophobic and ionic solutes and the solvation of a large, highly charged colloid that exhibits overcharging, a complex nonlinear electrostatic phenomenon whereby counterions from the solvent effectively overscreen and locally invert the integrated charge of the solvated object.

Approach to approximating the pair distribution function of inhomogeneous hard-sphere fluids

We introduce an approximation for the pair distribution function of the inhomogeneous hard sphere fluid. Our approximation makes use of our recently published averaged pair distribution function at contact, which has been shown to accurately reproduce the averaged pair distribution function at contact for inhomogeneous density distributions. This approach achieves greater computational efficiency than previous approaches by enabling the use of exclusively fixed-kernel convolutions and thus allowing an implementation using fast Fourier transforms. We compare results for our pair distribution approximation with two previously published works and Monte Carlo simulation, showing favorable results.

Wetting behavior of spherical nanoparticles at a vapor-liquid interface: a density functional theory study

The wetting behavior of spherical nanoparticles at a vapor-liquid interface is investigated by using density functional theory, and the line tension calculation method is modified by analyzing the total energy of the vapor-liquid-particle equilibrium. Compared with the direct measurement data from simulation, the results reveal that the thermodynamically consistent Young's equation for planar interfaces is still applicable for high curvature surfaces in predicting a wide range of contact angles. The effect of the line tension on the contact angle is further explored, showing that the contact angles given by the original and modified Young's equations are nearly the same within the region of 60° < θ < 120°. Whereas the effect is considerable when the contact angle deviates from the region. The wetting property of nanoparticles in terms of the fluid-particle interaction strength, particle size, and temperature is also discussed. It is found that, for a certain particle, a moderate fluid-particle interaction strength would keep the particle stable at the interface in a wide temperature range.

Simple density functional approach to adsorption of biomolecules on solid surfaces

A simple density functional approach for modeling the adsorption of biomolecules is considered. The model comprises a three-component mixture consisting of spherical and differently charged ions and chain molecules. Spherical ions can form associative bonds with selected segments of a chain. To enable the formation of bonds between chain segments and spherical ions, the statistical associating fluid theory is applied. The present theory is used to study the structure of adsorbed layers, the excess adsorption isotherms, and the capacitance of the double layer.

Some estimates of the surface tension of curved surfaces using density functional theory

Density functional theory is used to calculate the surface tension of planar and slightly curved surfaces, which can be written as gamma(R)=gamma(infinity)(1-2delta(infinity)R), where R is the radius of curvature of the surface. Calculations are performed for a Lennard-Jones fluid, split into a hard-sphere repulsive potential and an attractive part. The repulsive part is treated using the local density approximation. The attractive part is treated using a high temperature approximation (HTA) in which the pair correlation function is approximated by the Percus-Yevick pair correlation function of a uniform hard-sphere fluid evaluated at a position-dependent average density. An expression relating the Tolman length delta(infinity) to the density profile of the planar surface is derived. Numerical results are presented for the planar surface tension gamma(infinity) and for delta(infinity) and are compared with those using mean field theory (MFT) and with those using the square-gradient approximation. Values for gamma(infinity) using the HTA are 30%-40% higher than those using MFT. Values for delta(infinity) using the HTA are around -0.1 (in units of the Lennard-Jones parameter sigma) and only weakly dependent on temperature. These values are less negative than the values from MFT. The square-gradient approximation gives reasonable estimates of the more accurate nonlocal results for both the MFT and the HTA.

Layered interfaces between immiscible liquids studied by density-functional theory and molecular-dynamics simulations

We present a study of the structure in the interface between two immiscible liquids by density-functional theory and molecular-dynamics calculations. The liquids are modeled by Lennard-Jones potentials, which achieve immiscibility by suppressing the attractive interaction between unlike particles. The density profiles of the liquids display oscillations only in a limited part of the simple liquid-phase diagram (rho,T). When approaching the liquid-vapor coexistence, a significant depletion appears while the layering behavior of the density profile vanishes. By analogy with the liquid-vapor interface and the analysis of the adsorption this behavior is suggested to be strongly related to the drying transition.

Density-functional study of interfacial properties of colloid-polymer mixtures

Interfacial properties of colloid-polymer mixtures are examined within an effective one-component representation, where the polymer degrees of freedom are traced out, leaving a fluid of colloidal particles interacting via polymer-induced depletion forces. Restriction is made to zero-, one-, and two-body effective potentials, and a free energy functional is used that treats colloid excluded volume correlations within Rosenfeld's fundamental measure theory, and depletion-induced attraction within first-order perturbation theory. This functional allows a consistent treatment of both ideal and interacting polymers. The theory is applied to surface properties near a hard wall, to the depletion interaction between two walls, and to the fluid-fluid interface of demixed colloid-polymer mixtures. The results of the present theory compare well with predictions of a fully two-component representation of mixtures of colloids and ideal polymers (the Asakura-Oosawa model) and allow a systematic investigation of the effects of polymer-polymer interactions on interfacial properties. In particular, the wall surface tension is found to be significantly larger for interacting than for ideal polymers, whereas the opposite trend is predicted for the fluid-fluid interfacial tension.

An accurate density functional theory for the vapor-liquid interface of associating chain molecules based on the statistical associating fluid theory for potentials of variable range

A Helmholtz free energy density functional is developed to describe the vapor-liquid interface of associating chain molecules. The functional is based on the statistical associating fluid theory with attractive potentials of variable range (SAFT-VR) for the homogenous fluid [A. Gil-Villegas, A. Galindo, P. J. Whitehead, S. J. Mills, G. Jackson, and A. N. Burgess, J. Chem. Phys. 106, 4168 (1997)]. A standard perturbative density functional theory (DFT) is constructed by partitioning the free energy density into a reference term (which incorporates all of the short-range interactions, and is treated locally) and an attractive perturbation (which incorporates the long-range dispersion interactions). In our previous work [F. J. Blas, E. Martin del Rio, E. de Miguel, and G. Jackson, Mol. Phys. 99, 1851 (2001); G. J. Gloor, F. J. Blas, E. Martin del Rio, E. de Miguel, and G. Jackson, Fluid Phase Equil. 194, 521 (2002)] we used a mean-field version of the theory (SAFT-HS) in which the pair correlations were neglected in the attractive term. This provides only a qualitative description of the vapor-liquid interface, due to the inadequate mean-field treatment of the vapor-liquid equilibria. Two different approaches are used to include the correlations in the attractive term: in the first, the free energy of the homogeneous fluid is partitioned such that the effect of correlations are incorporated in the local reference term; in the second, a density averaged correlation function is incorporated into the perturbative term in a similar way to that proposed by Toxvaerd [S. Toxvaerd, J. Chem. Phys. 64, 2863 (1976)]. The latter is found to provide the most accurate description of the vapor-liquid surface tension on comparison with new simulation data for a square-well fluid of variable range. The SAFT-VR DFT is used to examine the effect of molecular chain length and association on the surface tension. Different association schemes (dimerization, straight and branched chain formation, and network structures) are examined separately. The surface tension of the associating fluid is found to be bounded between the nonassociating and fully associated limits (both of which correspond to equivalent nonassociating systems). The temperature dependence of the surface tension is found to depend strongly on the balance between the strength and range of the association, and on the particular association scheme. In the case of a system with a strong but very localized association interaction, the surface tension exhibits the characteristic "s shaped" behavior with temperature observed in fluids such as water and alkanols. The various types of curves observed in real substances can be reproduced by the theory. It is very gratifying that a DFT based on SAFT-VR free energy can provide an accurate quantitative description of the surface tension of both the model and experimental systems.

Transformation from Rogers-Young approximation to the density functional approach for nonuniform fluids: numerical recipe

A numerical recipe is devised to extend the methodology [J. Chem. Phys. 112, 8079 (2000)] to nonhard-sphere nonuniform fluids where analytical expressions for the functional relationship of the bridge function as a function of indirect correlation function do not exist, the numerical recipe is also based on the universality of the free-energy density functional. As an example, the recipe is employed to calculate the density profile of a colloidal suspension near a single charged hard wall and the hard-sphere Yukawa fluid near a single hard wall and a single hard wall with an attractive tail, the agreement of the predictions of the theory with the simulation data is good. The difference of the present methodology from that of the weighted density approximation is discussed.

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

The adsorption of a Lennard-Jones fluid in an ideal slit pore is studied using weighted density functional theory. The intrinsic Helmholtz free-energy functional is separated into repulsive and attractive contributions. Rosenfeld's accurate fundamental measure functional is employed for the repulsive functional while another weighted density functional method is employed for the attractive functional. This other method requires an accurate equation of state for the bulk fluid and an accurate pair-direct correlation function for a uniform fluid, determined analytically or numerically. The results for this theory are compared against mean-field density functional theory and grand canonical ensemble simulation results, modeling the adsorption of ethane in a graphite slit. The results indicate that the weighted density functional method applied to the attractive functional can offer a significant increase in accuracy over the mean-field theory.