Hard Core Attractive Yukawa Fluid Research Articles

Parameters of the Liquid-Gas-State Triangle for Hard-Core Attractive Yukawa Fluids.

We discuss the triangle of the liquid-gas concept within the fluid-lattice gas isomorphism approach and the Zeno-element, taking the hard-core Yukawa fluid (HCAYF) as an example. The applicability of such an isomorphism is demonstrated by the symmetrization of binodals with mapping onto the Ising model coexistence curve. We show that the parameters of the isomorphism transformation reflect the liquid-phase instability for hard-core Yukawa potential and its generalization. We also provide a simple mean-field estimate for the parameter z of the fluid-lattice gas transformation and use it to obtain the locus of the critical point.

Hard-core attractive Yukawa fluid global isomorphism with the lattice gas model.

In this work, we study the global isomorphism between the liquid-vapor equilibrium of the hardcore attractive Yukawa fluid (HCAYF) and that of the Lattice Gas (LG) model of the Ising-like type. The applicability of the global isomorphism transformation and the dependence of its parameters on the screening length of the Yukawa potential are discussed. These parameters determine both the slope of the rectilinear diameter of the liquid-vapor binodal and the Zeno-element, which are the core ingredients of the fluid-LG isomorphism. We compare the Zeno-element parameters with the virial Zeno-line parameters, which are commonly used in the literature for the formulation of generalized law of the correspondent states. It is demonstrated that the Zeno-element parameters appear to be sensitive to the liquid state instability when the interaction potential becomes too short-ranged, while the virial ones do not show any peculiarities connected with this specific of the HCAYF.

Thermodynamic properties of hard-core attractive Yukawa fluids: Single-component monomers, binary mixtures and chains

The first three perturbation terms in the inverse temperature expansion of the Helmholtz free energy of hard-core attractive Yukawa (HCAY) monomer fluids have been determined from computer simulation for several values of the range parameter. The predictions of the resulting perturbation theory for the equation of state and the excess energy are shown to be in excellent agreement with simulation data that are also reported. The theory accurately predicts also the simulation data for the liquid–vapour coexistence densities reported in the literature. Extension of the theory to HCAY binary mixtures is achieved by mapping the mixture to an effective single-component fluid and successfully compared with the simulation data reported in this work. The combination of the theory for the single-component fluid of monomers with a version of the Wertheim thermodynamic perturbation theory (TPT) also provides satisfactory results for HCAY chain fluids.

Virial expansions and augmented van der Waals approach: Application to Lennard-Jones-like Yukawa fluid

We argue that recently proposed [Melnyk et al., Fluid Phase Equilibr., 2009, Vol. 279, 1] a criterion to split the pair interaction energy into two parts, one of which is forced to be responsible the most accurate as possible for excluded volume energy in the system, results in expressions for the virial coefficients that improve the performance of the virial equation of state in general, and at subcritical temperatures, in particular. As an example, application to the Lennard-Jones-like hard-core attractive Yukawa fluid is discussed.

Phase behavior of the modified-Yukawa fluid and its sticky limit

Simple model systems with short-range attractive potentials have turned out to play a crucial role in determining theoretically the phase behavior of proteins or colloids. However, as pointed out by D. Gazzillo [J. Chem. Phys. 134, 124504 (2011)], one of these widely used model potentials, namely, the attractive hard-core Yukawa potential, shows an unphysical behavior when one approaches its sticky limit, since the second virial coefficient is diverging. However, it is exactly this second virial coefficient that is typically used to depict the experimental phase diagram for a large variety of complex fluids and that, in addition, plays an important role in the Noro-Frenkel scaling law [J. Chem. Phys. 113, 2941 (2000)], which is thus not applicable to the Yukawa fluid. To overcome this deficiency of the attractive Yukawa potential, D. Gazzillo has proposed the so-called modified hard-core attractive Yukawa fluid, which allows one to correctly obtain the second and third virial coefficients of adhesive hard-spheres starting from a system with an attractive logarithmic Yukawa-like interaction. In this work we present liquid-vapor coexistence curves for this system and investigate its behavior close to the sticky limit. Results have been obtained with the self-consistent Ornstein-Zernike approximation (SCOZA) for values of the reduced inverse screening length parameter up to 18. The accuracy of SCOZA has been assessed by comparison with Monte Carlo simulations.

Non-hard sphere thermodynamic perturbation theory

A non-hard sphere (HS) perturbation scheme, recently advanced by the present author, is elaborated for several technical matters, which are key mathematical details for implementation of the non-HS perturbation scheme in a coupling parameter expansion (CPE) thermodynamic perturbation framework. NVT-Monte Carlo simulation is carried out for a generalized Lennard-Jones (LJ) 2n-n potential to obtain routine thermodynamic quantities such as excess internal energy, pressure, excess chemical potential, excess Helmholtz free energy, and excess constant volume heat capacity. Then, these new simulation data, and available simulation data in literatures about a hard core attractive Yukawa fluid and a Sutherland fluid, are used to test the non-HS CPE 3rd-order thermodynamic perturbation theory (TPT) and give a comparison between the non-HS CPE 3rd-order TPT and other theoretical approaches. It is indicated that the non-HS CPE 3rd-order TPT is superior to other traditional TPT such as van der Waals/HS (vdW/HS), perturbation theory 2 (PT2)/HS, and vdW/Yukawa (vdW/Y) theory or analytical equation of state such as mean spherical approximation (MSA)-equation of state and is at least comparable to several currently the most accurate Ornstein-Zernike integral equation theories. It is discovered that three technical issues, i.e., opening up new bridge function approximation for the reference potential, choosing proper reference potential, and/or using proper thermodynamic route for calculation of f(ex-ref), chiefly decide the quality of the non-HS CPE TPT. Considering that the non-HS perturbation scheme applies for a wide variety of model fluids, and its implementation in the CPE thermodynamic perturbation framework is amenable to high-order truncation, the non-HS CPE 3rd-order or higher order TPT will be more promising once the above-mentioned three technological advances are established.

Augmented Kierlik—Rosinberg Fundamental Measure Functional and Extension of Fundamental Measure Functional to Inhomogeneous Non-hard Sphere Fluids

From point of view of weighted density procedure, it is guessed that a Percus-Yevick (PY) compressibility excess free energy density, appearing in the Kierlik—Rosinberg type fundamental measure functional (KR-FMF) and expressed in terms of scaled particle variables, can be substituted by a corresponding expression dictated by a more accurate Mansoori—Carnahan—Starling—Leland (MCSL) equation of state, while retaining the original weighting functions; it is numerically indicated that the resultant undesirable non-self-consistency between the PY type weighting function and MCSL type excess free energy density had no bad effect on the performance of the resultant augmented KR-FMF which, on the one hand, preserves the exact low-density limit of the original KR-FMF and holds a high degree of pressure self-consistency, on the other hand, improves significantly, as expected, the predictions of density profile of hard sphere fluid at single hard wall contact location and its vicinity, and of the bulk hard sphere second order direct correlation function (DCF), obtained from functional differentiation. The FMF is made applicable to inhomogeneous non-hard sphere fluids by supplementing a functional perturbation expansion approximation truncated at the lowest order with summation of higher order terms beyond the lowest term calculated by the FMF for an effective hard sphere fluid; the resultant extended FMF only needs second order DCF and pressure of the fluid considered at coexistence state as inputs, consequently is applicable whether the considered temperature is above critical point or below critical point. The extended MCSL-augmented KR-FMF is found to be endowed with an excellent performance for predictions of density profile and surface tension by comparing the present predictions of these two quantities with available computer simulation data for inhomogeneous hard core attractive Yukawa fluid and Lennard—Jones fluid.

Effect of critical fluctuations on adsorption of van der Waals fluid in a spherical cavity

A recently proposed non-uniform fifth-order thermodynamic perturbation theory (TPT) is employed to investigate the adsorption of a hard core attractive Yukawa (HCAY) fluid in a spherical cavity. Extensive comparison with available simulation data indicate that the non-uniform fifth-order TPT is sufficiently reliable in calculating the density profiles of the HCAY fluid in the highly confining geometry, and generally is more accurate than a previous third-order + second-order perturbation density functional theory. The non-uniform fifth-order TPT is free from numerically solving an Ornstein–Zernike integral equation, and also free of any adjustable parameter; consequently, it can be applied to both supercritical and subcritical temperature regions. The non-uniform fifth-order TPT is employed to investigate critical adsorption of the HCYA fluid in a single spherical cavity – it is disclosed that the critical fluctuations near the critical point induce depletion adsorption – quantitative theoretical calculation on relationship between the critical depletion adsorption, parameters of coexistence bulk phase and the responsible external field is in agreement with qualitative physical analysis.

Free Energy Density Functional for Adsorption of Fluids in Nanopores

A classical free energy density functional, which is isomorphic to a usual effective hard sphere model + mean field approximation for tail contribution, is proposed for treatment of real fluids in inhomogeneous states. In the framework of the classical density functional theory (DFT), the present functional is applied to two representative model fluids, namely, a Lennard-Jones fluid and a hard core attractive Yukawa fluid, subject to influence of various external fields. A comprehensive comparison with simulation results and a detailed analysis show that the present functional holds simultaneously all of the desirable properties inherent in an excellent functional, such as high accuracy, computational simplicity, consistency with a hard wall sum rule, nonrecourse to use of adjustable parameter(s) and weighted densities, reproduction of bulk second-order direct correlation function (DCF) in bulk limit, and applicability to subcritical fluid phenomena.

Surface tension and vapour–liquid phase coexistence of variable-range hard-core attractive Yukawa fluids

The vapour–liquid phase coexistence and surface tension of hard-core Yukawa fluids with short attraction range, λ = 8.0, 9.0 and 10.0, are reported using grand-canonical transition-matrix Monte Carlo (GC-TMMC) with the histogram reweighting method. Surface tension is calculated using finite-size scaling approach of Binder. We also compare GC-TMMC results with the available literature data for Yukawa fluids with λ = 1.8, 3.0 and 4.0. Critical properties obtained from rectilinear diameter approach and least square-technique are also reported. GC-TMMC results are found to be more precise than the previous reported values. We also present the corresponding state of surface tension for extremely short-range attractive Yukawa fluids.

Virial coefficients of hard-core attractive Yukawa fluids

We used Mayer sampling technique—a method based on free energy perturbation, to calculate virial coefficients B 2– B 6 for hard-core Yukawa fluids with interaction range parameter, λ = 1.8, 3.0, 4.0, 5.0, 8.0, 9.0, and 10. We used these coefficients in the virial equation of state (VEOS) to obtain compressibility factor, Z, at super critical temperatures and found to be in excellent agreement with the predictions of equations of state based on mean spherical approximation (EOS-MSA) for Yukawa fluids up to a reduced density, ρ * , of 0.5. We inspected virial coefficients in representing the PVT behavior along the saturated vapor line of Yukawa fluids. VEOS4, VEOS5 and VEOS6 describe the PVT behavior along the saturated vapor line reasonably good for λ = 1.8, 3.0 and 4.0; and at higher λ, VEOS4 and VEOS5 represent the PVT behavior better than the series that includes B 6. We also report critical properties of Yukawa fluids based on VEOS and compared with the literature values.

On the corresponding states law of the Yukawa fluid

We have analyzed the currently available simulation results as well as performed some additional Monte Carlo simulation for the hard-core attractive Yukawa fluid in order to study its corresponding state behavior. We show that the values of reduced surface tension map onto the master curve and a universal equation of state can be obtained in the wide range of the attractive Yukawa tail length after a certain rescaling of the number density. Some comparisons with other nonconformal potentials are presented and discussed.

Liquid–vapor interfacial properties of attractive Yukawa fluids

Canonical Monte Carlo (MC) simulations have been performed to calculate thermodynamic properties of hard-core attractive Yukawa fluid (HCAYF) with screening length κ = 1.8, 2.0, 2.5 and 3.0. The obtained coexistence and surface tension curves are compared to molecular dynamics (MD) simulations of hard-core and soft attractive Yukawa fluids previously reported in the literature. We show that the properties of both potentials are different, which is in disagreement to a previous statement. For n = 1.8 we find that the cutoff radius must be at least 5.0 to obtain the correct values of the interfacial properties.

Solid phase thermodynamic perturbation theory: Test and application to multiple solid phases

A simple procedure for the determination of hard sphere (HS) solid phase radial distribution function (rdf) is proposed, which, thanks to its physical foundation, allows for extension to other crystal structures besides the fcc structure. The validity of the procedure is confirmed by comparing (1) the predicted HS solid phase rdf's with corresponding simulation data and (2) the predicted non-HS solid phase Helmholtz free energy by the present solid phase first-order thermodynamic perturbation theory (TPT) whose numerical implementation depends on the HS solid phase rdf's as input, with the corresponding predictions also by the first-order TPT but the required HS solid phase rdf is given by an "exact" empirical simulation-fitted formula. The present solid phase first-order TPT predicts isostructural fcc-fcc transition of a hard core attractive Yukawa fluid, in very satisfactory agreement with the corresponding simulation data and is far more accurate than a recent thermodynamically consistent density functional perturbation theory. The present solid phase first-order TPT is employed to investigate multiple solid phases. It is found that a short-ranged potential, even if it is continuous and differentiable or is superimposed over a long-ranged potential, is sufficient to induce the multiple solid phases. When the potential range is short enough, not only isostructural fcc-fcc transition but also isostructural bcc-bcc transition, simple cubic (sc)-sc transition, or even fcc-bcc, fcc-sc, and bcc-sc transitions can be induced. Even triple point involving three solid phases becomes possible. The multiple solid phases can be stable or metastable depending on the potential parameters.

MODELING OF ADSORPTION IN PORES BY MEANS OF THIRD ORDER + SECOND ORDER PERTURBATION DENSITY FUNCTIONAL THEORY AND MONTE CARLO SIMULATION

Results for the inhomogeneous structure of the hard-core repulsive Yukawa (HCRY) fluid and of the hard-core attractive Yukawa (HCAY) fluid in planar and in spherical micropores are presented. The density profiles are obtained by the recently proposed third order + second order perturbation density functional approximation (DFA) and compared with the results of open ensemble Monte Carlo simulation. As known from other recent studies, the reliability of the DFA theory considered in this work is very sensitive to the accuracy of the required bulk direct correlation function (DCF) obtained by the solution of the Ornstein–Zernike (OZ) equation combined by a suitable closure relation. Comparison between the DFA results and simulation data shows that for the HCRY fluid, the DFA theory utilizing the DCF obtained by the OZ equation supplemented by Malijevsky–Labik approximation satisfies the required accuracy for a broad range of conditions. The results for the nonuniform HCAY fluid obtained in our previous work via the mean spherical approximation (MSA)/OZ DCF showed larger disagreement in some cases. In addition, the MSA/OZ equation for the HCAY model failed to have a physical solution at subcritical temperatures when approaching the vapor–liquid coexistence curve. For this reason, an improved version of the theory incorporating nonlinear optimized random phase approximation (ORPA) in the OZ equation for the RDF calculation of the HCAY fluid is applied. This leads to much better agreement of the DFA predictions with the simulation data. In addition, the calculations can also be performed at the conditions at which the MSA/OZ equation has no physical solution.

Improvement on macroscopic compressibility approximation and beyond

A numerical procedure is proposed to extend the thermodynamic perturbation expansion (TPE) to a higher order. It is shown that the present second order term is superior to that due to a macroscopic compressibility approximation (MCA), a local compressibility approximation, and a superposition approximation by Barker and Henderson [Rev. Mod. Phys. 48, 587 (1976)]. Extensive model calculation and comparison with simulation data available in literature and supplied in the present report indicate that the present third order TPE is superior to a previous second order TPE based on the MCA, two previous perturbation theories, which are respectively based on an analytical mean spherical approximation for an Ornstein-Zernike equation, and an assumed explicit functional form for the Laplace transform of radial distribution function multiplied by radial distance, and a recent generalized van der Waals theory. The present critical temperature for a hard core attractive Yukawa fluid of varying range is in very good agreement with that due to a hierarchical reference theory. The present third order TPE is computationally far more modest than the self-consistent integral equation theory, and therefore is a viable alternative to use of the latter.

Structure of inhomogeneous Lennard-Jones fluid near the critical region and close to the vapor-liquid coexistence curve: Monte Carlo and density-functional theory studies

Results for the density profiles of the Lennard-Jones (LJ) fluid subjected to diverse external fields are presented for the Monte Carlo simulations within the grand canonical ensemble and for the third order and second order perturbation density-functional approximation (DFA). In all cases, the bulk LJ fluid in the particle reservoir to which the nonuniform fluid under consideration is connected, is at the conditions situated at "dangerous" regions of the phase diagram, i.e., near the critical temperature or close to the gas-liquid coexistence curve. It is found that the previously investigated third order and second order perturbation DFA for hard core attractive Yukawa fluid [J. Chem. Phys. 122, 064503 (2005)] can perform successfully also for the nonuniform LJ fluid only on the condition of high accuracy of the required bulk second order direct correlation function. The present report further indicates that the proposed third order and second order perturbation DFA is efficient and suitable for both supercritical and subcritical temperatures.