Hard-core Yukawa Research Articles

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.

Thermodynamic Perturbation Theory and Phase Diagram in Simple Fluids

Using the lowest-order liquid-state thermodynamic perturbation theory and the hard-sphere fluid as the reference system, the phase diagram of attractive hard-core Yukawa fluids is computed. The results are presented in the reduced temperature versus reduced density, reduced pressure versus reduced temperature, and reduced pressure versus reduced density planes. A comparison with available simulation data and a discussion of the merits and limitations of this approach are also provided.

Novel perturbation approach for the structure factor of the attractive hard-core Yukawa fluid

A novel perturbation approach for the structure factor S(k) of the Lennard-Jones-type Yukawa fluid with z=1.8 is presented. An approach is based on a new reference system, that is, the short-range Yukawa model with z0>z=1.8. By choosing for the reference system the value z0=6, it is shown that (i) the proposed approach for S(k) performs much better than the traditional hard-sphere reference perturbation method does; (ii) the use of an approximate mean spherical (MSA) description of the reference structure factor provides the results for S(k) that are more accurate as those obtained from the direct MSA computations; and (iii) the results obtained for S(k) tend to reproduce "exact" simulation results when accurate simulation data for the reference system are used.

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.

Liquid–vapour transition of the long range Yukawa fluid

Two liquid state theories, the self-consistent Ornstein–Zernike equation (SCOZA) and the hierarchical reference theory (HRT) are shown, by comparison with Monte Carlo simulations, to perform extremely well in predicting the liquid–vapour coexistence of the hard-core Yukawa (HCY) fluid when the interaction is long range. The long range of the potential is treated in the simulations using both an Ewald sum and hyperspherical boundary conditions. In addition, we present an analytical optimized mean field theory which is exact in the limit of an infinitely long-range interaction. The work extends a previous one by C. Caccamo, G. Pellicane, D. Costa, D. Pini, and G. Stell, Phys. Rev. E 60, 5533 (1999) for short-range interactions.

Possibility of Fisher renormalization of the critical exponents in an Ising fluid

Using Monte Carlo simulation techniques, we study the ferromagnetic order-disorder phase transition in Ising spin fluids with hard-core Yukawa interaction truncated at various cutoff radii r{c}. We focus our interest on the dependence of critical quantities such as the Binder cumulant and various exponent ratios on the value of r{c}, and on the question whether the Fisher-renormalized exponents expected for such systems can be observed in the simulations. It turns out that the corrections to scaling decaying with a rather small exponent prevent reaching the asymptotic region with the computational power available. Thus, we observe only effective exponents, with different (nonuniversal) values depending on the cutoff radius. The same behavior is also found for the critical Binder cumulant. Nevertheless, an exact investigation of the effective susceptibility exponent gamma{eff} as a function of temperature seems to point towards a Fisher-renormalized value. For two selected cutoff radii, the critical temperature is determined more accurately using, in addition to the cumulant crossing technique, the scanning technique and the shifting technique, taking into account corrections to scaling. Simulations of Ising fluids with constant cutoff radius and varying Yukawa-tail screening lengths lambda also show a nonuniversal dependence of U{c} on lambda. Finally, we have performed simulations of the Ising lattice model with increasing number of couplings which show the expected asymptotic behavior, independent of the range of interactions.

Phase diagram and surface tension of the hard-core attractive Yukawa model of variable range: Monte Carlo simulations

The liquid-vapor phase diagram and surface tension for hard-core Yukawa potential with 4<or=kappa<or=7 are calculated by applying canonical Monte Carlo simulation. The authors' new simulation results are more precise than those reported before, which allows them to affirm the accuracy of the previously reported self-consistent Ornstein-Zernike approximation calculations for kappa=5 and 7.

Solvent density inhomogeneities and solvation free energies in supercritical diatomic fluids: A density functional approach

Density functional theory is used to explore the solvation properties of a spherical solute immersed in a supercritical diatomic fluid. The solute is modeled as a hard core Yukawa particle surrounded by a diatomic Lennard-Jones fluid represented by two fused tangent spheres using an interaction site approximation. The authors' approach is particularly suitable for thoroughly exploring the effect of different interaction parameters, such as solute-solvent interaction strength and range, solvent-solvent long-range interactions, and particle size, on the local solvent structure and the solvation free energy under supercritical conditions. Their results indicate that the behavior of the local coordination number in homonuclear diatomic fluids follows trends similar to those reported in previous studies for monatomic fluids. The local density augmentation is particularly sensitive to changes in solute size and is affected to a lesser degree by variations in the solute-solvent interaction strength and range. The associated solvation free energies exhibit a nonmonotonous behavior as a function of density for systems with weak solute-solvent interactions. The authors' results suggest that solute-solvent interaction anisotropies have a major influence on the nature and extent of local solvent density inhomogeneities and on the value of the solvation free energies in supercritical solutions of heteronuclear molecules.

Application of the optimized Baxter model to the hard-core attractive Yukawa system

We perform Monte Carlo simulations on the hard-core attractive Yukawa system to test the optimized Baxter model that was introduced by Prinsen and Odijk [J. Chem. Phys. 121, 6525 (2004)] to study a fluid phase of spherical particles interacting through a short-range pair potential. We compare the chemical potentials and pressures from the simulations with analytical predictions from the optimized Baxter model. We show that the model is accurate to within 10% over a range of volume fractions from 0.1 to 0.4, interaction strengths up to three times the thermal energy, and interaction ranges from 6% to 20% of the particle diameter, and performs even better in most cases. We furthermore establish the consistency of the model by showing that the thermodynamic properties of the Yukawa fluid computed via simulations may be understood on the basis of one similarity variable, the stickiness parameter defined within the optimized Baxter model. Finally, we show that the optimized Baxter model works significantly better than an often used, naive method determining the stickiness parameter by equating the respective second virial coefficients based on the attractive Yukawa and Baxter potentials.

Phase diagram of the hard-core Yukawa fluid within the integral equation method

In this study, the integral equation method proposed recently by Sarkisov [J. Chem. Phys. 114, 9496 (2001).], which has proved accurate for continuous potentials, is extended successfully to the hard sphere potential plus an attractive Yukawa tail. By comparing the results of thermodynamic properties, including the liquid-vapor phase diagram, with available simulation data, it is found that this method remains reliable for this class of models of interaction often used in colloid science.

Critical Endpoint and Analytical Phase Diagram of Attractive Hard-Core Yukawa Spheres

We analytically calculate the gas-liquid critical endpoint (cep) for hard spheres with a Yukawa attraction. This cep is a boundary condition for the existence of a liquid. We use an analytical Helmholtz energy expression for the attractive Yukawa (hard) spheres based on the first-order mean spherical approximation to the attractive Yukawa potential by Tang and Lu (J. Chem. Phys. 1993, 99, 9828). This theory and our analytical simplification of it predict the gas-liquid and fluid-solid phase behavior, as found from computer simulations, very accurately as long as the range 1/kappa of attraction is not too short. We find that the cep is situated at kappasigma approximately 6 and at a contact potential around 2 kT. It follows that a liquid state is only possible when the attraction range is longer than (1/6) of the particle diameter sigma, and the attraction strength is smaller than 2 kT. The liquid region does not span more than 0.6 kT in strength, and there is also a relatively narrow window for the attraction range.

Thermodynamic perturbation theory and glass transition in simple fluids

Using the liquid state thermodynamic perturbation theory and the hard-sphere fluid as the reference system, the liquid–glass transition line of Lennard–Jones and hard-core Yukawa fluids is computed. The results are presented both in the reduced density vs. reduced temperature and in the reduced pressure vs. reduced temperature planes. A comparison with available simulation data and a discussion of the merits and limitations of this approach are also provided.

Further Test of Third Order + Second-Order Perturbation DFT Approach: Hard Core Repulsive Yukawa Fluid Subjected to Diverse External Fields

Grand canonical Monte Carlo simulation is used to investigate density profiles of hard-core repulsive Yukawa (HCRY) model fluid under the influence of various external fields and radial distribution function (RDF) of the bulk HCRY system. The aim of these extensive simulations is to provide exact data for purely repulsive interaction potential against which the validity of a third order + second-order perturbation DFT approach can be tested. It is found that a semiempirical parametrized bridge function due to Malijevsky and Labik performs very well for the RDF of the bulk HCRY fluid. Incorporation of a bulk second-order direct correlation function (DCF) of the HCRY fluid based on the Malijevsky-Labik bridge function into the third order + second-order perturbation DFT approach yields the resulting theoretical predictions for the density profiles of inhomogeneous HCRY fluid that are in a very good agreement with the simulation data, an exception being somewhat larger deviations appearing for the structure of the fluid around the center of a hard spherical cavity. Both theory and simulation predict layering transition and gas-liquid coexistence phenomena occurring with the HCRY model fluid under confined conditions. For the case of an inverse sixth-power repulsive potential under the influence of a flat stationary wall defined by an inverse twelfth-power repulsive potential, the present third order + second-order perturbation DFT approach is found to be superior to several existing weighted density approximations (WDA) and partitioned WDA.

A self-consistent density-functional approach to the structure of nonuniform binary hard-core Yukawa mixtures

A self-consistent density-functional approach has been employed to study the structure of nonuniform binary hard-core Yukawa mixtures as well as the structure of its uniform counterpart. The second-order direct correlation function and the bridge function of the corresponding uniform fluid mixture required as input in the self-consistent theory are obtained from integral equation theory using an accurate closure relation. The calculated density and concentration profiles of the nonuniform mixtures as well as the radial distribution function profiles of the uniform fluid mixtures are shown to compare well with available simulation results.

Structures of Binary Hard-core Repulsive Yukawa Mixtures Near Solid Surfaces from DFT

Structures of Binary Hard-core Repulsive Yukawa Mixtures Near Solid Surfaces from DFT

Phase behavior of dipolar hard and soft spheres

We study the phase behavior of hard and soft spheres with a fixed dipole moment using Monte Carlo simulations. The spheres interact via a pair potential that is a sum of a hard-core Yukawa (or screened-Coulomb) repulsion and a dipole-dipole interaction. The system can be used to model colloids in an external electric or magnetic field. Two cases are considered: (i) colloids without charge (or dipolar hard spheres) and (ii) colloids with charge (or dipolar soft spheres). The phase diagram of dipolar hard spheres shows fluid, face-centered-cubic (fcc), hexagonal-close-packed (hcp), and body-centered-tetragonal (bct) phases. The phase diagram of dipolar soft spheres shows, in addition to the above mentioned phases, a body-centered-orthorhombic (bco) phase, and is in agreement with the experimental phase diagram [Nature (London) 421, 513 (2003)]. In both cases, the fluid phase is inhomogeneous but we find no evidence of a gas-liquid phase separation. The validity of the dipole approximation is verified by a multipole moment expansion.

Phase and interfacial behavior of partially miscible symmetric Lennard-Jones binary mixtures

We have carried out extensive equilibrium molecular-dynamics simulations to study quantitatively the topology of the temperature versus density phase diagrams and related interfacial phenomena in a partially miscible symmetric Lennard-Jones binary mixture. The topological features are studied as a function of miscibility parameter, alpha = epsilonAB/epsilonAA. Here epsilonAA = epsilonBB and epsilonAB stand for the parameters related to the attractive part of the intermolecular interactions for similar and dissimilar particles, respectively. When the miscibility varies in the range 0 < alpha < 1, a continuous critical line of consolute points Tcons(rho)--critical demixing transition line--appears. This line intersects the liquid-vapor coexistence curve at different positions depending on the values of alpha, yielding mainly three different topologies for the phase diagrams. These results are in qualitative agreement to those found previously for square-well and hard-core Yukawa binary mixtures. The main contributions of the present paper are (i) a quantitative analysis of the phase behavior and (ii) a detailed study of the liquid-liquid interfacial and liquid-vapor surface tensions, as function of temperature and miscibility as well as its relationship to the topological features of the phase diagrams.

Density functional for structures of colloids confined in a slit-like pore

A density functional theory is applied to calculating the local density profiles of colloids confined in a slit-like pore as well as the radial distribution functions of bulk colloids. The interaction between the colloidal particles is described using a hard-core Yukawa model. The excess Helmholtz energy functional is a combination of the modified fundamental measure theory of Yu and Wu (2002) for the hard-core contribution and a corrected mean-field theory for the attractive contribution. Comparison with the results from the Monte Carlo simulations shows that the corrected theory improves the density profiles of colloids in the vicinity of contact over the original mean-field theory. Both the present corrected theory and simulations suggest that there are depletion and desorption for the colloid with strong attraction between particles at low temperature.

Structures and adsorption of binary hard-core Yukawa mixtures in a slitlike pore: Grand canonical Monte Carlo simulation and density-functional study

The grand canonical ensemble Monte Carlo simulation and density-functional theory are applied to calculate the structures, local mole fractions, and adsorption isotherms of binary hard-core Yukawa mixtures in a slitlike pore as well as the radial distribution functions of bulk mixtures. The excess Helmholtz energy functional is a combination of the modified fundamental measure theory of Yu and Wu [J. Chem. Phys. 117, 10156 (2002)] for the hard-core contribution and a corrected mean-field theory for the attractive contribution. A comparison of the theoretical results with the results from the Monte Carlo simulations shows that the corrected theory improves the density profiles of binary hard-core Yukawa mixtures in the vicinity of contact over the original mean-field theory. Both the present corrected theory and the simulations suggest that depletion and desorption occur at low temperature, and the local segregation can be observed in most cases. For binary mixtures in the hard slitlike pore, the present corrected theory predicts more accurate surface excesses than the original one does, while in the case of the attractive pore, no improvement is found in the prediction of a surface excess of the smaller molecule.

Local Solvent Density Augmentation around a Solute in Supercritical Solvent Bath: 1. A Mechanism Explanation and a New Phenomenon

A recently proposed partitioned density functional (DF) approximation (Phys. Rev. E 2003, 68, 061201) and an adjustable parameter-free version of a Lagrangian theorem-based DF approximation (LTDFA: Phys. Lett. A 2003, 319, 279) are combined to propose a DF approximation for nonuniform Lennard-Jones (LJ) fluid. Predictions of the present DF approximation for local LJ solvent density inhomogeneity around a large LJ solute particle or hard core Yukawa particle are in good agreement with existing simulation data. An extensive investigation about the effect of solvent bath temperature, solvent-solute interaction range, solvent-solute interaction magnitude, and solute size on the local solvent density inhomogeneity is carried out with the present DF approximation. It is found that a plateau of solvent accumulation number as a function of solvent bath bulk density is due to a coupling between the solvent-solute interaction and solvent correlation whose mathematical expression is a convolution integral appearing in the density profile equation of the DF theory formalism. The coupling becomes stronger as the increasing of the whole solvent-solute interaction strength, solute size relative to solvent size, and the closeness to the critical density and temperature of the solvent bath. When the attractive solvent-solute interaction becomes large enough and the bulk state moves close enough to the critical temperature of the solvent bath, the maximum solvent accumulation number as a function of solvent bath bulk density appears near the solvent bath critical density; the appearance of this maximum is in contrast with a conclusion drawn by a previous investigation based on an inhomogeneous version of Ornstein-Zernike integral equation carried out only for a smaller parameter space than that in the present paper. Advantage of the DFT approach over the integral equation is discussed.