Statistical Mechanics Approach for Uniform and Non-uniform Fluid with Hard Core and Interaction Tail

One recently proposed self-consistent hard sphere bridge functional was combined with an exponential function exp(-cr) and a re-normalized indirect correlation function to construct the bridge function for fluid with hard core and interaction tail. In the present approach, the adjustable parameter α was determined by the thermodynamic consistency realized on the compressibility modulus, the re-normalization of the indirect correlation function was realized by a modified Mayer function with the interaction potential replaced by the perturbative part of the interaction potential. As an example, the present bridge function was combined with the Ornstein-Zernike (OZ) equation to predict structure and thermodynamics properties in very good agreement with the simulation data available for Lennard-Jones (L J). Based on the universality principle of the free energy density functional and the test particle trick, the numerical solution of the OZ equation was employed to construct the first order direct correlation function of the non-uniform fluid as a functional of the density distribution by means of the indirect correlation function. In the framework of the density functional theory, the numerically obtained functional predicted the density distribution of LJ fluid confined in two planar hard walls that is in good agreement with the simulation data.     

方阱链流体在固液界面分布的密度泛函理论研究

应用Yethiraj的加权密度近似泛函理论研究平板狭缝中方阱链流体的密度分布，系统的Helm holtz自由能泛函分为理想气体的贡献利剩余贡献两部分，其中剩余贡献部分分别采用刘洪 来等人建立的基于空穴相关函数的方阱链流体状态方程和Gil-Villegas等人提出的统计缔合 流体理论状态方程(SAFT-VR)结合简单加权密度近似计算.考察了不同链长、温度、系统密度 和壁面吸引强度下平板狭缝中方阱链流体的密度分布，并与Monte Carlo(MC)模拟结果进行 了比较.结果表明采用不同的状态方程对密度分布的计算有明显的影响，对于受限于硬壁狭 缝中的方阱链流体，温度和密度比较高时，两种状态方程计算的结果均与MC模拟符合得比较 好，在低温和低密度下效果变差，SAFT-VR方程的计算结果更接近于MC模拟结果.对于受限于 方阱壁狭缝中的方阱链流体，由于系统密度分布的非均匀性加强，采用两种状态方程计算的 结果均与MC模拟结果有一定偏差，寻找更合适的权重函数是进一步改进的关键. 关键词： 密度泛函理论 非均匀流体 密度分布 固液界面 方阱链     

An integral equation theory for the dense dipolar hard-sphere fluid

An integral equation theory based upon a simple linearization of the hypernetted-chain closure approximation is solved numerically for dipolar hard spheres. The pair-correlation function and thermodynamic properties are found to be in excellent agreement with Monte Carlo results. The dielectric constant in this approximation is larger than that predicted by previous theories.     

Binary fluid mixture of hard ellipses: Integral equation and weighted density functional theory

We study a two-dimensional (2D) classical fluid mixture of hard convex shapes. The components of the mixture are two kinds of hard ellipses with different aspect ratios. Two different approaches are used to calculate the direct, pair and total correlation functions of this fluid and results are compared. We first use a formalism based on the weighted density functional theory (WDFT), introduced by Chamoux and Perera [Phys. Rev. E 58 (1998) 1933]. Second, in general the Percus-Yevick (PY) and the hypernetted chain (HNC) integral equations are solved numerically for the 2D fluid mixtures of hard noncircular particles. Explicit results are obtained for the fluid mixtures of hard ellipses and comparisons are made by the two approaches. Also, the results are compared with the recent Monte Carlo simulation for the one-component fluids of hard ellipses. Finally we obtained the equation of state of hard ellipses for the aspect ratio sufficiently close to 1 and compared our results with the simulations of the fluid mixtures of hard disks.     

Adsorption effects and NMR properties: Continuous chain approach

The NMR properties of nuclei linked to long linear polymer molecules are sensitive to the influence of hard walls. In this context, the residual energy of tensorial spin-spin interactions is calculated using a path integral approach. Several thermodynamic quantities of the polymer system (free energy, equation of state,...) are also expressed, taking chain stiffness effects and the presence of two repulsive walls into consideration.     

Integral equation theory of a one dimensional hard-ellipse fluid between hard walls

Density functional theory is used to study the structure of a one dimensional fluid model of hard-ellipse molecules with their axes freely rotating in a plane, confined between hard walls. A simple Hypernetted chain (HNC) approximation is used for the density functional of the fluid and the integral equation for the density is obtained from the grand potential. The only required input is the direct correlation function of the one dimensional hard-ellipse fluid. For this model, the pressure, sum rule and the density at the walls are obtained. The Percus Yevick (PY), for lower density, and HNC, for higher density, integral equations are also solved to obtain the direct correlation function of hard-ellipse model introduced here. We obtain the average density at the wall as well as the radial density profile. We compare these with Monte Carlo simulations of the same model and find reasonable agreement.     

Density functional for ternary non-additive hard sphere mixtures

Based on fundamental measure theory, a Helmholtz free energy density functional for three-component mixtures of hard spheres with general, non-additive interaction distances is constructed. The functional constitutes a generalization of the previously given theory for binary non-additive mixtures. The diagrammatic structure of the spatial integrals in both functionals is of star-like (or tree-like) topology. The ternary diagrams possess a higher degree of complexity than the binary diagrams. Results for partial pair correlation functions, obtained via the Ornstein-Zernike route from the second functional derivatives of the excess free energy functional, agree well with Monte Carlo simulation data.     

Density functional theory for Baxter's sticky hard spheres in confinement

It has recently been shown that a free energy for Baxter's sticky hard-sphere fluid is uniquely defined within the framework of fundamental measure theory (FMT) for the inhomogeneous hard-sphere fluid, provided that it obeys scaled-particle theory and the Percus-Yevick (PY) result for the direct correlation function [H. Hansen-Goos and J. S. Wettlaufer, J. Chem. Phys. 134, 014506 (2011)]. Here, combining FMT weighted densities with a new vectorial weighted density, we regularize the divergences of the associated strongly confined limit. The free energy that emerges is exact in the zero-dimensional limit, leaves the underlying equation of state unaffected, and yields a direct correlation function distinct from that of PY. Comparison with simulation data for both the bulk pair-correlation function and the density profiles in confinement shows that the new theory is significantly more accurate than the PY-based results.     

A self-consistent density-functional approach to the structure of electric double layer: charge-asymmetric electrolytes

A self-consistent density-functional approach has been employed to study the structure of an electric double layer formed from a charge-asymmetric (2:l) electrolyte within the restricted primitive model which corresponds to charged hard sphere ions and a continuum solvent. The particle correlation due to hard-core exclusions is evaluated by making use of the universality of the density functionals and the correlation function of the uniform hard sphere fluid obtained through the integral equation theory with an accurate closure relation whereas mean spherical approximation is employed for the electrical contribution. Numerical results on the diffuse layer potential drop, ionic density profile, and the mean electrostatic potential near the electrode surface at several surface charge densities are found to be in quantitative agreement with the available simulation data.     

Density Functional Approach Based on Numerically Obtained Bridge Functional

The Ornstein Zernike equation is solved with the Rogers Young approximation for bulk hard sphere fluidand Lennard-Jones fluid for several state points. Then the resulted bulk fluid radial distribution function combinedwith the test particle method is employed to determine numerically the function relationship of bridge functional as afunction of indirect correlation function. It is found that all of the calculated points from different phase space statepoints for a same type of fluid collapse onto a same smooth curve. Then the numerically obtained curve is used tosubstitute the analytic expression of the bridge functional as a function of indirect correlation function required in themethodology [J. Chem. Phys. 112 (2000) 8079] to deterrnine the density distribution of non-uniform hard spherefluid and Lennard Jones fluid. The good agreement of theoretical predictions with the computer simulation data isobtained. The present numerical procedure incorporates the knowledge of bulk fluid radial distribution function intothe constructing of the density functional approximation and makes the original methodology more accurate and moreflexible for various interaction potential fluid.     

On the relationship between the density functional formalism and the potential distribution theory for nonuniform fluids

It is shown that the variational principle for the grand potential of a nonuniform fluid as a functional of the singlet density yields the potential distribution theory for the equilibrium density. We derive the explicit form that the functional takes for a system of hard rods, and propose an approximate one for hard spheres. Attractive interactions are also considered in mean-field approximation. In all cases the pair direct correlation function of the nonuniform system is obtained and the density gradient expansion of the free energy is investigated.     

Augmented Kierlik-Rosinberg Fundamental Measure Functional andExtension of Fundamental Measure Functional to Inhomogeneous Non-hard Sphere Fluids

From point of view of weighted density procedure, it isguessed that a Percus-Yevick (PY) compressibility excess free energydensity, appearing in the Kierlik--Rosinberg type fundamentalmeasure functional (KR-FMF) and expressed in terms of scaledparticle variables, can be substituted by a corresponding expressiondictated by a more accurate Mansoori-Carnahan-Starling-Leland(MCSL) equation of state, while retaining the original weightingfunctions; it is numerically indicated that the resultantundesirable non-self-consistency between the PY type weightingfunction and MCSL type excess free energy density had no bad effecton the performance of the resultant augmented KR-FMF which, on theone hand, preserves the exact low-density limit of the originalKR-FMF and holds a high degree of pressure self-consistency, on theother hand, improves significantly, as expected, the predictions ofdensity profile of hard sphere fluid at single hard wall contactlocation and its vicinity, and of the bulk hard sphere second orderdirect correlation function (DCF), obtained from functionaldifferentiation. The FMF is made applicable to inhomogeneousnon-hard sphere fluids by supplementing a functional perturbationexpansion approximation truncated at the lowest order with summationof higher order terms beyond the lowest term calculated by the FMFfor an effective hard sphere fluid; the resultant extended FMF onlyneeds second order DCF and pressure of the fluid considered atcoexistence state as inputs, consequently is applicable whether theconsidered temperature is above critical point or below criticalpoint. The extended MCSL-augmented KR-FMF is found to be endowedwith an excellent performance for predictions of density profile andsurface tension by comparing the present predictions of these twoquantities with available computer simulation data for inhomogeneoushard core attractive Yukawa fluid and Lennard-Jones fluid.     

Associating fluids with four bonding sites against a hard wall: density functional theory

We present two new perturbation density functional theories to investigate non-uniform fluids of associating molecules. Each fluid molecule is modelled as a spherical hard core with four highly anisotropic square well sites placed in tetrahedral symmetry on the hard core surface. In one theory we apply the weighting from Tarazona's hard sphere density functional theory to Wertheim's bulk first-order perturbation theory. The other theory uses the inhomogeneous form of Wertheim's theory as a perturbation to Tarazona's hard-sphere density functional theory. Each theory approaches Tarazona's theory in the limit of zero association. We compare results from theory and simulation for density profiles, fraction of monomers, and adsorption of an associating fluid against a hard, smooth wall over a range of temperatures and densities. The non-uniform fluid theory which uses Tarazona's weighting of Wertheim's theory in the bulk is in good agreement with computer simulation results.     

Specification of Density Functional Approximation by Radial Distribution Function of Bulk Fluid

A systematic methodology is proposed to deal with the weighted density approximation version of classical density functional theory by employing the knowledge of radial distribution function of bulk fluid.The present methodology results from the concept of universality of the free energy density functional combined with the test particle method.It is shown that the new method is very accurate for the predictions of density distribution of a hard sphere fluid at different confining geometries.The physical foundation of the present methodology is also applied to the quantum density functional theory.     

Theoretical Investigation of Uniform and Non-uniform Penetrable Sphere Fluid

A bridge function approximation is proposed for a single-component fluid consisting of penetrable sphere interacting via a potential that remains finite and constant for center-center distance smaller than the particle diameter and is zero otherwise. The radial distribution function from the Ornstein-Zernike integral equation combined with the present bridge function approximation is in satisfactory agreement with the corresponding simulation data for all of the investigated state points. The presently calculated excess Helmholtz free energy respectively based on virial route and compressibility route is highly self-consistent, and is in very good agreement with simulational results for the case of low temperatures. The present bridge function approximation, combined with the bridge density functional approximation,can reproduce very accurately density profiles of the penetrable sphere fluid confined in a hard spherical cavity for all the cases where simulational results are available.     

Theoretical Investigation of Uniform and Non-uniform Penetrable Sphere Fluid

A bridge function approximation is proposed for a single-component fluid consisting of penetrable sphere interacting via a potential that remains finite and constant for center-center distance smaller than the particle diameter and is zero otherwise. The radial distribution function from the Ornstein-Zernike integral equation combined with the present bridge function approximation is in satisfactory agreement with the corresponding simulation data for all of the investigated state points. The presently calculated excess Helmholtz free energy respectively based on virial route and compressibility route is highly self-consistent, and is in very good agreement with simulational results for the case of low temperatures. The present bridge function approximation, combined with the bridge density functional approximation, can reproduce very accurately density profiles of the penetrable sphere fluid confined in a hard spherical cavity for all the cases where simulational results are available.     

A phase-field model for simulating various spherulite morphologies of semi-crystalline polymers

A modified phase-field model is proposed for simulating the isothermal crystallization of polymer melts. The model consists of a second-order phase-field equation and a heat conduction equation. It obtains its model parameters from the real material parameters and is easy to use with tolerable computational cost. Due to the use of a new free energy functional form, the model can reproduce various single crystal morphologies of polymer melts under quiescent conditions, including dendritic, lamellar branching, ring-banded, breakup of ring-banded, faceted hexagonal, and spherulitic structures. Simulation results of isotactic polystyrene crystals demonstrate that the present phase-field model has the ability to give qualitative predictions of polymer crystallization under isothermal and quiescent conditions.