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

Closure-based density functional theory applied to interfacial colloidal fluids

The behavior of dense colloidal fluids near surfaces can now be probed in great detail with experimental techniques like confocal microscopy. In fact, we are approaching a point where quantitative comparisons of experiment with particle-level theory, such as classical density functional theory (DFT), are appropriate. In a forward sense, we may use a known surface potential to predict a particle density distribution function from DFT; in an inverse sense, we may use an experimentally measured particle density distribution function to predict the underlying surface potential from DFT. In this paper, we tested the ability of the closure-based DFT of Zhou and Ruckenstein (J. Chem. Phys. 2000, 112, 8079-8082) to perform forward and inverse calculations on potential models commonly employed for colloidal particles and surfaces. To reduce sources of uncertainty in this initial study, Monte Carlo simulation results played the role of experimental data. The combination of Rogers-Young and modified-Verlet closures consistently performed well across the different potential models. For a reasonable range of choices of the density, temperature, and potential parameters, the inversion procedure yielded particle-surface potentials to an accuracy on the order of 0.1kT.

How to extend hard sphere density functional approximation to nonuniform nonhard sphere fluids: Applicable to both subcritical and supercritical temperature regions

A methodology for the formulation of density functional approximation (DFA) for nonuniform nonhard sphere fluids is proposed by following the spirit of a partitioned density functional approximation [Zhou, Phys. Rev. E 68, 061201 (2003)] and mapping the hard core part onto an effective hard sphere whose high order part of the functional perturbation expansion is treated by existing hard sphere DFAs. The resultant density functional theory (DFT) formalism only needs a second order direct correlation function and pressure of the corresponding coexistence bulk fluid as inputs and therefore can be applicable to both supercritical and subcritical temperature cases. As an example, an adjustable parameter-free version of a recently proposed Lagrangian theorem-based DFA is imported into the present methodology; the resultant DFA is applied to Lennard-Jones fluid under the influence of external fields due to a single hard wall, two hard walls separated by a small distance, a large hard sphere, and a spherical cavity with a hard wall. By comparing theoretical predictions with previous simulation data and those recently supplied for coexistence bulk fluid situated at "dangerous" regions, it was found that the present DFA can predict subtle structure change of the density profile and therefore is the most accurate among all existing DFT approaches. A detailed discussion is given as to why so excellent DFA for nonhard sphere fluids can be drawn forth from the present methodology and how the present methodology differs from previous ones. The methodology can be universal, i.e., it can be combined with any other hard sphere DFAs to construct DFA for other nonhard sphere fluids with a repulsive core.

Inverse density-functional theory as an interpretive tool for measuring colloid-surface interactions in dense systems

Recent advances in optical microscopy, such as total internal reflection and confocal scanning laser techniques, now permit the direct three-dimensional tracking of large numbers of colloidal particles both near and far from interfaces. A novel application of this technology, currently being developed by one of the authors under the name of diffusing colloidal probe microscopy (DCPM), is to use colloidal particles as probes of the energetic characteristics of a surface. A major theoretical challenge in implementing DCPM is to obtain the potential energy of a single particle in the external field created by the surface, from the measured particle trajectories in a dense colloidal system. In this paper we develop an approach based on an inversion of density-functional theory (DFT), where we calculate the single-particle-surface potential from the experimentally measured equilibrium density profile in a nondilute colloidal fluid. The underlying DFT formulation is based on the recent work of Zhou and Ruckenstein [Zhou and Ruckenstein, J. Chem. Phys. 112, 8079 (2000)]. For model hard-sphere and Lennard-Jones systems, using Monte Carlo simulation to provide the "experimental" density profiles, we found that the inversion procedure reproduces the true particle-surface-potential energy to an accuracy within typical DCPM experimental limitations (approximately 0.1 kT) at low to moderate colloidal densities. The choice of DFT closures also significantly affects the accuracy.

Analysis of the validity of perturbation density functional theory: Based on extensive simulation for simple fluid at supercritical and subcritical temperature under various external potentials

Because of the scarcity of available simulation data for confined hard-core attractive Yukawa model fluid, extensive Monte Carlo (MC) simulation research for this fluid under the influence of various external potentials were carried out. The present MC simulation results were employed to test a performance of the third-order perturbation density functional theory (DFT) based on a high order direct correlation function (DCF) [S. Zhou and E. Ruckenstein, Phys. Rev. E. 61, 2704 (2000)]. It was found that the present perturbation DFT formalism is soundly structured only if the imported second-order DCF is reliable. In this case, the accuracy of the results can be satisfactory or even very high for various types of external potentials. Further, the associated adjustable parameter can be universal, i.e., independent of the particular external field responsible for the generation of a nonuniform density profile. Dependence of both the maintenance of the reliability of the formalism and holding of the universality of the adjustable parameter on the accuracy of the imported bulk second-order DCF can be strengthened by the large difference between the external field investigated and that caused by a single hard wall used for specification of the adjustable parameter. In case the gaseous density in the subcritical region is below the coexistence density, an excellent performance of the present formalism is observed even for the mean spherical approximation's second-order DCF as an input. This advantageous property, combined with the fact that the present formalism needs only the second-order DCF of fluid at the coexistence state as an input, enables the present formalism to be a very good theoretical tool for the investigations of wetting and prewetting transitions.

Reformulation of density functional theory for generation of the nonuniform density distribution

The concept of universality of the free energy density functional and the weighted density approximation are combined to provide the density distribution profile of nonuniform fluids from the predictions of integral equation theory for the corresponding uniform fluids. To obtain the expression for the free energy as a function of the density distribution, the present formalism expresses the difference of the first order direct correlation function of a nonuniform fluid with respect to its uniform fluid counterpart as a function of the weighted density, which is also a function of the space position. The input parameters used in the present approach are the radial distribution function and the second order direct correlation function of the corresponding uniform fluid. All of these parameters can be easily obtained from numerical solution of Ornstein-Zernike integral equation theory. The present approach is based on the formalism of classical density functional theory (DFT) and its application to two kinds of fluid under different external potentials is presented. The agreement of the theoretical predictions with the corresponding computer simulation data is good. The present formulation of DFT can treat fluids of different interaction potential under nonzero external fields in a unified way.