Hard-core 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.

A self-consistent perturbative density functional theory for hard-core fluids: phase diagrams, structural and interfacial properties

The classical Density functional theory (DFT) has become a powerful tool to describe the microscopic structure of fluids as the radial distribution function. One of its particular capabilities is to express the thermodynamic properties of those fluids even under the influence of external potentials, such as fluid-solid interaction. However, good models for the Helmholtz free-energy functionals are necessary to improve the results. In this work, we present a self-consistent thermodynamic perturbation theory for the excess Helmholtz free-energy from the DFT applied to hard-core fluids. The new perturbation theory is solved self-consistently without any closure relation to solving the Ornstein-Zernike equation explicitly. We compare the performance of our self-consistent perturbation theory with the results obtained with the well-known second-order Barker-Henderson perturbation theory for the hard-core Yukawa and square-well fluids. Moreover, we propose two versions of the DFT to describe the perturbative contribution: one based on the weighted density approximation theory and another from a modified mean-field theory. The present results confirm the modified mean-field theory as a better option to calculate the thermodynamic and structural properties of hard-core fluids.

Augmentation of the Optimised random phase approximation by use of mayer function as a new perturbation theory of simple fluids

ABSTRACT The Optimised Random Phase Approximation in the thermodynamic perturbation theory of liquids is augmented by use of Mayer function. The direct correlation function of a hardcore potential is assumed to be represented by A Mayer function instead of THE one used in the Random Phase Approximation and Mean Spherical Approximation. Correcting the unphysical behaviour of the corresponding pair correlation function in the hardcore region will give rise to a new perturbation theory as a natural generalisation of the Optimised Random Phase Approximation. To assess its accuracy and reliability, the theory is used to find the structure and thermodynamics of hard-core Yukawa fluids. The new-resulted theory is shown to be more accurate than the Optimised Random Phase Approximation both in predicting the thermodynamic and structure functions of hard-core Yukawa potentials.

On the liquid–vapour coexistence curve in a Lennard–Jones fluid

A hard-core double Yukawa potential is taken as an approximation of the Lennard–Jones (LJ) potential. Using first-order thermodynamic perturbation theory with a hard-sphere fluid as the reference system, the equation of state of the hard-core double Yukawa fluid is derived analytically. Adjusting the hard-core diameter with the Barker and Henderson prescription to account for the repulsive part of the LJ potential, the liquid–vapour coexistence curve of the LJ fluid is computed with such equation of state. The results are compared with simulation data for the LJ fluid and very good agreement is observed.

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.

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.

Adsorption of Yukawa fluids on a hard wall

We construct a closure theory for the bridge functional based on the third-order Ornstein–Zernike (OZ3) equation. The new closure is tested on the adsorption of the hard-core Yukawa fluid on a planar hard wall and its results are compared with Monte Carlo computer simulation. We show that in the particularly challenging cases of depletive adsorption, the density profiles near the wall obtained from the OZ3 theory improve considerably over conventional liquid-state theories, such as the hypernetted-chain and the Percus–Yevick equations. Some technical details of the implementation of the procedure of re-normalisation of the non-uniform indirect correlation function are also provided.

A generalization of random phase approximation as a new theory in the thermodynamic perturbation theory of simple fluids

A generalization of the optimized random phase approximation in the thermodynamic perturbation theory of liquids is proposed. By introducing a new method, we can derive an approximate analytical expression for the free energy of simple liquids. This is achieved by invoking a direct correlation function more general than the mean spherical approximation. By correcting the unphysical behavior of the corresponding radial distribution function in the hard core region, we attain a new perturbation expansion as a natural generalization of the optimized random phase approximation. In order to assess its accuracy and reliability, the theory is employed to find the structure and thermodynamics of hard-core Yukawa fluids. The new resulted optimized second order random phase approximation (OSORPA) is shown to be a little more accurate than the optimized random phase approximation in finding the thermodynamic properties, but it performs much better in predicting the static structure factor of hard-core Yukawa potentials.

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.

Critical asymmetry in renormalization group theory for fluids

The renormalization-group (RG) approaches for fluids are employed to investigate critical asymmetry of vapour-liquid equilibrium (VLE) of fluids. Three different approaches based on RG theory for fluids are reviewed and compared. RG approaches are applied to various fluid systems: hard-core square-well fluids of variable ranges, hard-core Yukawa fluids, and square-well dimer fluids and modelling VLE of n-alkane molecules. Phase diagrams of simple model fluids and alkanes described by RG approaches are analyzed to assess the capability of describing the VLE critical asymmetry which is suggested in complete scaling theory. Results of thermodynamic properties obtained by RG theory for fluids agree with the simulation and experimental data. Coexistence diameters, which are smaller than the critical densities, are found in the RG descriptions of critical asymmetries of several fluids. Our calculation and analysis show that the approach coupling local free energy with White's RG iteration which aims to incorporate density fluctuations into free energy is not adequate for VLE critical asymmetry due to the inadequate order parameter and the local free energy functional used in the partition function.

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.

Structural theory of liquid–vapour critical point with application to hard-core Yukawa fluids

March, Perrot and Tosi [Mol. Phys. 93, 355 (1998)] proposed three structural integrals I 0, I 1 and I 2 to account for the liquid–vapour critical point (LVCP) based on the virial expression for the pressure. The interrelations between these integrals are obtained from the universality of LVCP. We extend the work of March et al. and suggest another structural integral I 3. We also provide analytical expressions for In (n = 0, 1, 2, 3) for hard-core Yukawa fluids based on the series mean spherical approximation. The location of LVCP parameters versus the intermolecular potential range parameter is accurately calculated for three different equations of states. We find good agreement when compared with computer simulation results only for the compressibility equation of state within the mean density approximation. The universality of the critical compressibility ratio at the LVCP is discussed in detail.

Simplified exponential approximation for thermodynamics of a hard-core repulsive Yukawa fluid

Exponential approximation based on the first order mean spherical approximation (FMSA) is applied to the study of the structure and thermodynamics of hard-core repulsive Yukawa fluids. The proposed theory utilizes an exponential enhancement of the analytical solution of the FMSA due to Tang and Lu [J. Chem. Phys., 1993, 99, 9828] for the radial distribution function. From comparison with computer simulation data we have shown that at low density and low temperature conditions, where original FMSA theory fails, the FMSA-based exponential theory predicts a significant improvement.

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).

Critical parameters of hard-core Yukawa fluids within the structural theory

A purely statistical mechanical approach is proposed to account for the liquid–vapor critical point based on the mean density approximation (MDA) of the direct correlation function. The application to hard-core Yukawa (HCY) fluids facilitates the use of the series mean spherical approximation (SMSA). The location of the critical parameters for HCY fluid with variable intermolecular range is accurately calculated. Good agreement is observed with computer simulation results and with the inverse temperature expansion (ITE) predictions. The influence of the potential range on the critical parameters is demonstrated and the universality of the critical compressibility ratio is discussed. The behavior of the isochoric and isobaric heat capacities along the equilibrium line and the near vicinity of the critical point is discussed in details.

Comment on “Structure and thermodynamics of hard-core Yukawa fluids: Thermodynamic perturbation approaches” [J. Chem. Phys, 135, 034505 (2011)

We would like to show that what has been presented in the paper by Kim, Kim, and Seong [J. Chem. Phys, 135, 034505 (2011)] is nothing but an unnecessarily complicated version of (optimized) random phase approximation.

Structure and thermodynamics of hard-core Yukawa fluids: Thermodynamic perturbation approaches

The thermodynamic perturbation theories, which are based on the power series of a coupling constant (λ-expansion), have been proposed for studying the structural and thermodynamic properties of a hard-core Yukawa (HCY) fluid: one (A1-approximation) is the perturbation theory based on the hard-sphere repulsion as a reference system. The other (A2-approximation) is the perturbation theory based on the reference system which incorporates both the repulsive and short-range attractive interactions. The first-order mean-spherical approximation (FMSA) provided by Tang and Lu [J. Chem. Phys. 99, 9828 (1993)] has been employed for investigating the thermodynamic properties of a HCY fluid using the alternative method via the direct correlation function. The calculated results show that (i) the A1 and A2 approximations are in excellent agreements with previous computer simulation results in the literature and compare with the semi-empirical works of Shukla including the higher-order free energy terms, (ii) the A1 and A2 approximations are better than the FMSA and the mean-spherical approximation, (iii) the A2-approximation compares with the A1-approximation, even though the perturbation effect of an A2-approximation is much smaller than that of an A1-approximation, and that (iv) the FMSA study is particularly of advantage in providing the structure and thermodynamics in a simple and analytic manner.