Hard-core Attractive Yukawa 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.

Generalized equation of state for fluids: From molecular liquids to colloidal dispersions

In this work, a new parameterization for the Statistical Association Fluid Theory for potentials of Variable Range (SAFT-VR) is coupled to the discrete potential theory to represent the thermodynamic properties of several fluids, ranging from molecular liquids to colloidal-like dispersions. In this way, this version of the SAFT-VR approach can be straightforwardly applied to any kind of either simple or complex fluid. In particular, two interaction potentials, namely, the Lennard-Jones and the hard-core attractive Yukawa potentials, are discretized to study the vapor-liquid equilibrium properties of both molecular and complex liquids, respectively. Our results are assessed with Monte Carlo computer simulations and available and accurate theoretical results based on the self-consistent Ornstein-Zernike approximation.

Kirkwood-Buff integrals for hard-core Yukawa fluids.

The Kirkwood-Buff (KB) theory of solution is employed to investigate several macroscopic properties of the one-component hard-core Yukawa (HCY) fluid, where the key physical quantities are the KB integrals (KBIs). For both repulsive and attractive HCY fluids, the radial distribution functions are calculated by using the classical density functional theory, and then the corresponding KBIs are carried out. Since the local structure and global properties of a fluid can be related by KBI, we presented the isothermal compressibility and the derivative of the chemical potential with respect to bulk density for both repulsive and attractive HCY fluids. It is found that a transition of the affinity of particles in an attractive HCY fluid exists. The corresponding phase diagrams on the affinity are illustrated, which consist of repulsive and attractive regions with the boundary line of KBIs being zero. These results show that the aggregated structure of a HCY fluid can be effectively regulated by the screening parameter, bulk density and interaction energy, while KBIs can provide a quantitative reliable description on the properties of HCY fluids.

Determination of structure factor and effective intermolecular parameters of liquid alkali metals using mean spherical approximation theory

The structural properties of liquid cesium (Cs) were investigated in the temperature range of 400–2000 K by application of the effective hard-core attractive Yukawa (H-Y) potential function to the mean spherical approximation (MSA) theory. An analytical equation of state was applied to calculate the molecular parameters of a potential function at any thermodynamic state. The proposed approach was used to predict the behavior of the structure factor, S(k), at a wide range of wave vectors (k). The results obtained were compared with the available experimental measurements, which revealed a good agreement over the whole liquid range for Cs. The structure factor at a long wavelength limit, S(0), was also calculated and compared with the experimental data, which showed the accuracy of the Ornstein-Zernike (OZ) behavior of S(k) at the thermodynamic states below the boiling temperature (Tb). For the case of Cs, the presented intermolecular potential model was very much responsive to the thermodynamic states and led to the indication of the two distinct isotherm ranges T <Tb and T >Tb. Two analytical expressions were obtained for the temperature dependency of the potential well-depth (Keff) over the temperature ranges of T <Tb and T >Tb. Furthermore, the proposed approach showed several metal-nonmetal transitions for Cs at about 500, 1100, 1350, and 1650 K. Using the Keff relations for the other liquid alkali metals Na, K, and Rb provided the S(k) results that were more accurate in comparison with the experimental data.

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.

Normal-stress coefficients and rod climbing in colloidal dispersions

We calculate tractable microscopic expressions for the low-shear normal-stress coefficients of colloidal dispersions. Although restricted to the low rate regime, the presented formulas are valid for all volume fractions below the glass transition and for any interaction potential. Numerical results are presented for a system of colloids interacting via a hard-core attractive Yukawa potential, for which we explore the interplay between attraction strength and volume fraction. We show that the normal-stress coefficients exhibit nontrivial features close to the critical point and at high volume fractions in the vicinity of the reentrant glass transition. Finally, we exploit our formulas to make predictions about rod-climbing effects in attractive colloidal dispersions.

Use of the Attractive Hard-Core Yukawa Interaction for Predicting of the Small-kBehavior of the Structure Factor for Simple Fluids

A definition of the direct correlation function (DCF) is applied to monatomic fluids modeled by spherical particles with a pair potential given by a hard-core repulsion and a Yukawa attractive tail. This potential allows one to take advantage of the known analytical properties of the solution to the Ornstein–Zernike (OZ) equation for the case in which the DCF outside the repulsive core is improved by a linear combination of two Yukawa tails. Predictions for the structure factor, \(S(k)\), at low-wave factor are studied and compared with other liquid-state theories and experimental data available in the literature. It was found that the closure considered here provided very well the OZ behavior of \(S(k)\) at low-\(k\) for the near critical point and coexistence curve regions. For the interaction range considered here, one can realize the remarkably accurate divergence of \(S(0)\) at the near critical point, which is related to the fluctuation phenomena.

Comparative study of a universal theoretical way and 3rd + 2nd-order perturbation density functional theory

A universal theoretical way, proposed recently by Zhou, provides a general scheme which transforms any one of hard sphere density functional approximations (DFAs) into a DFA workable for non-hard sphere fluids. In this article, the universal theoretical way is combined with a hard sphere DFA as a Lagrangian theorem-based DFA to perform calculations for density profiles of a hard core attractive Yukawa model fluid influenced by diverse external fields, and the calculation results are compared with corresponding results due to a 3rd + 2nd-order perturbation density functional theory (DFT) and computer simulation previously reported. Several conclusions are drawn from a detailed analysis on the degree of accuracy of the two approximations relative to the computer simulation and described below. (i) Correspondence between the change of relative performance of the two DFAs and the change of the performance of the bulk 2nd-order direct correlation function (DCF) used as an input as a function of bulk state indicates that the bulk 2nd-order DCF is a key input information determining the accuracy of the approximations using them. (ii) For large inhomogeneity, non-perturbation approximation is evidently more successful than a 3rd-order truncation on the functional perturbation expansion series. (iii) The universal theoretical way is very promising given that a successful hard sphere DFA and accurate bulk 2nd-order DCF are incorporated. Under the present conditions, the universal theoretical way gives an excellent account of the density profiles even if the ‘dangerous’ coexistence bulk states are being under consideration. (iv) The present study helps in formulating new approximations for the inhomogeneous excess Helmholtz free energy functional.

Phase behavior of colloids and proteins in aqueous suspensions: Theory and computer simulations

The fluid phase behavior of colloidal suspensions with short-range attractive interactions is studied by means of Monte Carlo computer simulations and two theoretical approximations, namely, the discrete perturbation theory and the so-called self-consistent Ornstein-Zernike approximation. The suspensions are modeled as hard-core attractive Yukawa (HCAY) and Asakura-Oosawa (AO) fluids. A detailed comparison of the liquid-vapor phase diagrams obtained through different routes is presented. We confirm Noro-Frenkel's extended law of scaling according to which the properties of a short-ranged fluid at a given temperature and density are independent of the detailed form of the interaction, but just depend on the value of the second virial coefficient. By mapping the HCAY and AO fluids onto an equivalent square-well fluid of appropriate range at the critical point we show that the critical temperature as a function of the effective range is independent of the interaction potential, i.e., all curves fall in a master curve. Our findings are corroborated with recent experimental data for lysozyme proteins.

Attractive hard-core Yukawa fluids in the nanosized pores: Structure and phase behaviors

A density functional perturbation theory has been developed for studying the structure and phase behaviors of an attractive hard-core Yukawa fluid in the nanosized slit and spherical pores at the subcritical temperature. The calculated results show that the pore geometry and size strongly affect on the liquid–vapor coexistence curve and critical point of a confined attractive hard-sphere Yukawa fluid. For the value of the chemical potential corresponding to a stable liquid phase in the bulk system and a metastable vapor phase, an attractive hard-core Yukawa fluid undergoes a phase transition as the slit width (or the pore radius) is reduced whereby the vapor phase becomes the preferred state at the narrow slit pores (or the small volumes), whereas the liquid is the stable phase at the wide slit pores (or the large volumes). The wide adsorption/desorption curve, which implies the wide range of metastable liquid–vapor states, is observed at a low temperature. The increase of the slit width (or the pore radius) leads to a wider adsorption/desorption curve, whereas the increase of the temperature leads to a narrower liquid–vapor coexistence curve. The critical point in a slit pore is shifted towards a lower temperature compared with that of the bulk phase, i.e., the confinement moves the transition towards a higher chemical potential. The critical point in a spherical pore occurs at a lower temperature compared with that of a slit pore.

Interfacial and coexistence properties of soft spheres with a short-range attractive Yukawa fluid: Molecular dynamics simulations

Molecular dynamics simulations have been carried out to obtain the interfacial and coexistence properties of soft-sphere attractive Yukawa (SAY) fluids with short attraction range, κ = 10, 9, 8, 7, 6, and 5. All our simulation results are new. These data are also compared with the recently reported results in the literature of hard-core attractive Yukawa (HAY) fluids. We show that the interfacial and coexistence properties of both potentials are different. For the surveyed systems, here we show that all coexistence curves collapse into a master curve when we rescale with their respective critical points and the surface tension curves form a single master curve when we plot γ* vs. T/T(c).

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.

Structure of attractive and repulsive hard-core Yukawa fluids: Density functional perturbation theory

Abstract A density functional perturbation theory, which is based on the modified fundamental-measure theory to the hard-sphere repulsion and the first-order mean-filed approximation to the long-range attractive or repulsive contributions, has been proposed in order to study the structural properties of hard-core Yukawa (HCY) fluids. The advantage of the present theory is the simplicity of the calculation of the long-range attractive or repulsive interaction. The calculation shows that the present theory excellently describes the density behaviors of the attractive and repulsive HCY fluids near a planar slit pore. However, at low temperature the accuracy for the attractive HCY fluids slightly deteriorates when increasing the bulk density. The test particle method has been applied to calculate the radial distribution function of the uniform HCY fluids. The present theory predicts an accurate radial distribution function of the attractive and repulsive HCY fluid even for the high density. The phase behaviors of an attractive HCY fluid restricted to the nanosized slit pores have been studied at the subcritical temperature. The results show that the vapor is the stable phase at the narrow slit pores and the liquid is the stable phase at the wide slit pores. The wide liquid–vapor coexistence curve, which implies the wide range of metastable liquid–vapor states, is observed at wide slit pores. The increase of slit width leads to a shift of the liquid–vapor coexistence curve towards lower value of chemical potential.

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.

Thermodynamic properties of short-range attractive Yukawa fluid: Simulation and theory

Coexistence properties of the hard-core attractive Yukawa potential with inverse-range parameter kappa=9, 10, 12, and 15 are calculated by applying canonical Monte Carlo simulation. As previously shown for longer ranges, we show that also for the ranges considered here the coexistence curves scaled by the critical density and temperature obey the law of corresponding states, and that a linear relationship between the critical density and the reciprocal of the critical temperature holds. The simulation results are compared to the predictions of the self-consistent Ornstein-Zernike approximation, and a good agreement is found for both the critical points and the coexistence curves, although some slight discrepancies are present.