Hard-core Yukawa Potential 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.

Convergence of Coupling-Parameter Expansion-Based Solutions to Ornstein–Zernike Equation in Liquid State Theory

The objective of this paper is to investigate the convergence of coupling-parameter expansion-based solutions to the Ornstein–Zernike equation in liquid state theory. The analytically solved Baxter’s adhesive hard sphere model is analyzed first by using coupling-parameter expansion. It was found that the expansion provides accurate approximations to solutions—including the liquid-vapor phase diagram—in most parts of the phase plane. However, it fails to converge in the region where the model has only complex solutions. Similar analysis and results are obtained using analytical solutions within the mean spherical approximation for the hardcore Yukawa potential. However, numerical results indicate that the expansion converges in all regions in this model. Next, the convergence of the expansion is analyzed for the Lennard-Jones potential by using an accurate density-dependent bridge function in the closure relation. Numerical results are presented which show convergence of correlation functions, compressibility versus density profiles, etc., in the single as well as two-phase regions. Computed liquid-vapor phase diagrams, using two independent schemes employing the converged profiles, compare excellently with simulation data. The results obtained for the generalized Lennard-Jones potential, with varying repulsive exponent, also compare well with the simulation data. Solution-spaces and the bifurcation of the solutions of the Ornstein–Zernike equation that are relevant to coupling-parameter expansion are also briefly discussed. All of these results taken together establish the coupling-parameter expansion as a practical tool for studying single component fluid phases modeled via general pair-potentials.

Self-consistent construction of bridge functional based on the weighted density approximation.

A parameter-free bridge functional is presented using a weighted density approximation (WDA). The key point of this scheme is the utilization of Baxter's relation connecting the second-order direct correlation function (DCF) to the higher-order DCF with the density derivative. The free energy density required for the WDA is determined in a self-consistent manner using Baxter's relation and Percus's test particle method. This self-consistent scheme enables us to employ any type of potential model for simple liquids. The new functional is applied to calculate density distribution functions for the inhomogeneous fluids interacting via the hard-sphere, Lennard-Jones, and hard-core Yukawa potentials under an external field from a planar wall and a slit pore.

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.

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.

Inverse design of charged colloidal particle interactions for self assembly into specified crystal structures.

We study the inverse problem of tuning interaction parameters between charged colloidal particles interacting with a hard-core repulsive Yukawa potential, so that they assemble into specified crystal structures. Here, we target the body-centered-cubic (bcc) structure which is only stable in a small region in the phase diagram of charged colloids and is, therefore, challenging to find. In order to achieve this goal, we use the statistical fluctuations in the bond orientational order parameters to tune the interaction parameters for the bcc structure, while initializing the system in the fluid phase, using the Statistical Physics-inspired Inverse Design algorithm. We also find that this optimization algorithm correctly senses the fluid-solid phase boundaries for charged colloids. Finally, we repeat the procedure employing the covariance matrix adaptation-evolution strategy, a cutting edge optimization technique, and compare the relative efficacy of the two methods.

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.

Partial summation of various subsets of low-temperature terms to all orders in the direct correlation function based thermodynamic perturbation theory of simple liquids

ABSTRACTVarious subsets of a new thermodynamic perturbation expansion for simple liquids [PHYSICAL REVIEW E 83, 021203 (2011)] is summed up by a new method to all orders which yield explicit formulas for the structure and thermodynamic of simple fluids. The formulas then have been tested successfully against computer simulations results for hard-core Yukawa potential.

Brownian Dynamics Simulations of Magnetic Nanoparticles Captured in Strong Magnetic Field Gradients

The behavior of spherical single-domain magnetic nanoparticles in strong inhomogeneous magnetic fields is investigated through Brownian dynamics simulations, taking into account magnetic dipole–dipole interactions, repulsive hard-core Yukawa potential, hydrodynamic particle-wall interactions, and the mechanism of magnetic dipole rotation in the presence of a magnetic field. The magnetic capture process of nanoparticles in prototypical magnetic field gradients generated by a sudden reversal in perpendicular magnetization of a flat substrate (defining a “capture line”) is studied as a function of strength of the magnetic field and volume fraction of the magnetic nanoparticles. Capture curves show a regime where capture follows a power law model and suggest that particles with the Brownian relaxation mechanism are captured at a slightly faster rate than particles with the Néel relaxation mechanism under similar conditions of the field gradient. Additionally, evaluation of the shape of the aggregates of captured particles suggests that greater dipole–dipole interactions result in aggregate structures that are flatter/wider than in the case of negligible dipole–dipole interactions. These results can help guide the design of systems for magnetically directed assembly of nanoparticles into complex shapes at a substrate.

Correlation of isothermal compressibility coefficient and reduced bulk modulus of dense fluids using perturbed linear Yukawa isotherm regularity

ABSTRACTA new simple analytical expression has been derived for predicting the reduced bulk modulus () and isothermal compressibility coefficient () of dense fluids using a new proposed equation of state (EoS) known as the linear Yukawa isotherm regularity (LYIR). The advantage of the derived expressions is that the variation of Br and with the changes of the parameters of Yukawa effective pair potentials (εeff, σeff and λeff) can be investigated. The calculated isotherms of Br and obtained from the derived expression show a good agreement with the literature data for some selected dense fluids. The variation of Br with σeff of effective pair Yukawa potential was studied and it was observed that the increase in the value of σeff accompanied by the increase of Br. The ability of the derived expressions for predicting Br and was compared with the corresponding expressions obtained from the linear isotherm regularity (LIR) and Goharshadi–Morsali–Abbaspour (GMA) EoSs, which are based on an average effective near neighbour pair interaction. It was found that the ability of LYIR EoS in predicting Br is comparable with LIR and GMA EoSs. This comparison also showed that the LYIR EoS can be successfully used to predict and correlate the Br and of dense fluids and the hard-core Yukawa potential can be adequately used in the modelling of the thermodynamical and thermo-physical properties of the dense systems. Finally, the derived expression for Br predicted the common bulk modulus region at which the different isotherms of Br vs. density intersect each other in a density region.

Prediction of fluid-phase behavior of symmetrical binary Yukawa fluids using transition matrix Monte Carlo

Binary fluid mixtures display a wide array of fluid phase behavior ranging from simple vapor-liquid equilibrium diagrams to more complicated topology like azeotropy and heteroazeotropy. As a first step towards understanding the phenomena of equilibrium of binary molecular systems, the properties of binary monoatomic fluids have been studied in this work. An additional simplification made in this work is that of a symmetrical binary system where all similar molecules interact via the hard-core Yukawa (HCY) potential, u(r), while the dissimilar molecules interact via a potential, δu(r) where δ is a scalar parameter. The value of δ here is 0.75, which leads to the dissimilar molecules showing a tendency to dislike one another and the resulting phase diagram is such that the mixing-demixing line intersects the vapor-liquid equilibrium curve away from the vapor-liquid critical point. The effect of the variable potential range parameter of the HCY potential on the topology of the phase diagrams is investigated using grand canonical transition matrix Monte Carlo simulations and the conditions of temperature and pressure at which the system exhibits azeotropy and heteroazeotropy are ascertained. We find that the densities of the mixtures, as predicted by our simulation at equimolar concentrations, are in close agreement with the self-consistent Ornstein-Zernike approximation results of Schöll-Paschinger and co-workers.

Studying structural properties of rubidium and cesium liquid metals using an effective hard-core Yukawa potential

In this work, we investigate the applicability of a modification of the random phase approximation (RPA) theory with an effective hard-core Yukawa potential to the static structure factor for the rubidium and cesium liquid metals. Based upon the perturbation theory, we assume that the core contribution of the direct correlation function is related to the geometric effects via a linear form for a hard-sphere fluid, in which the molecular diameter is obtained at any temperature and, its tail contribution is related to the long-range intermolecular interactions of the system via a linear form. We use the long-range Yukawa potential in the modeling of liquid alkali metals (LAMs) with the decay parameter λ = 1.8 and a well depth potential that is state-dependent. The linear isotherm regularity (LIR) equation of state (EOS) is applied to obtain the long-range interactions. The results obtained show that the proposed approach for LAMs can predict the behavior of the structure factor, S(k), at a wide range of k values with a good accuracy, as compared to the experimental data, over the whole liquid states. The interaction model used is also successful in the presentation of the Ornstein–Zernike (OZ) behavior of S(k) at the low-k region including the S(0) values.

Polymorph selection in the crystallization of hard-core Yukawa system

Colloid-colloid interactions in charge-stabilized dispersions can to some extent be represented by the hard-core Yukawa model. The crystallization process and polymorph selection of hard-core Yukawa model are studied by means of smart Monte Carlo simulations in the region of face-centered-cubic (fcc) phase. The contact value of hard-core Yukawa potential and the volume fraction of the colloids are fixed, while the Debye screening length can be varied. In the early stage of the crystallization, the precursors with relatively ordered liquid structure have been observed. Although the crystal structure of thermodynamically stable phase is fcc, the system crystallizes into a mixture of fcc and hexagonal close-packed (hcp) structures under small Debye screening length since the colloidal particles act as effective hard spheres. In the intermediate range of Debye screening length, the system crystallizes into a mixture of fcc, hcp, and body-centered-cubic (bcc). The existence of metastable hcp and bcc structures can be interpreted as a manifestation of the Ostwald's step rule. Until the Debye screening length is large enough, the crystal structure obtained is almost a complete fcc suggesting the system eventually reaches to a thermodynamically stable state.

Linear Yukawa Isotherm Regularity for dense fluids derived based on the perturbation theory

In the present work, the thermodynamic of dense fluids, both compressed liquids and dense supercritical fluids, has been modeled, solely, based on the contribution of attraction of effective pair potential. The intermolecular interaction is modeled by the hard-core Yukawa potential (HCY) as an effective pair potential (EPP) with temperature dependent hard-core diameter. Using this EPP in the exact thermodynamic relations, an equation of state (EoS) for the compressibility factor of dense fluid has been derived. This EoS shows that (Z − ZCS) as function of ρ1/3 must be linear for each isotherm of fluid where ZCS is the compressibility factor of the reference fluid (Carnahan-Starling (CS) EoS) with temperature-dependent hard-core diameter and Z is the experimental compressibility factor of fluid. To our knowledge, this is the first report on this new regularity for dense fluids only based on the perturbation theory in literature. The validity of this regularity has been tested for different fluids including Ar, Kr, Ne, H2, N2, NH3, NF3, CH4, C2H2, C3H8, C2H6, C2H4 and CH3OH. This regularity is valid for densities greater than ρB, where ρB is the Boyle density. Finally, using the proposed regularity, the values of the EPP parameters for the mentioned fluids were obtained at different temperatures.

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.

A theory based on the RPA to calculate the static structure factor for argon-like fluids using LIR equation of state

In this work, the random phase approximation theory is applied to generate an expression for the direct correlation function based on the linear isotherm regularity equation of state. We use the hard-core Yukawa potential in the modelling of real fluids, in which the molecular parameters are state-dependent. We use this model to predict the behaviour of the structure factor S(k) in a wide range of states for the argon, krypton and xenon liquids. Finally, we compare our results with the experimental and theoretical data available in the literature. Our calculations are capable of showing the behaviour of S(k) at a wide range of k values with good accuracy, as compared to the experimental data for simple fluids at near and far from their triple points. The Ornstein–Zernike behaviour of S(k) observed at the supercritical region was in satisfactory agreement with experiment.

Auxetic Materials and Related Systems

to mechanical metamaterials and related systems with particular emphasis on auxetic systems. Such materials show counter-intuitive, negative behaviours. For example, auxetic materials exhibit negative Poisson’s ratios which mean that these systems get fatter rather than thinner when stretched. Due to the superior properties exhibited by these systems, their study and characterisation has experienced a signifi cant increase, particularly in the last decade, something which may be perceived from the always increasing number of publications and patents in these areas. In fact, this issue is the seventh in a series of special issues published in physica status solidi (b) dedicated to auxetic materials and related systems (see [1–6]).

A new analytical approximation for the second term in the thermodynamic perturbation theory of simple hard-core fluids

An analytical expression for the second term in the thermodynamic perturbation theory of liquids is proposed. The expression is derived by invoking the mean spherical approximation for the direct correlation function of the whole system. We have made then another simplifying approximation to reach an entirely analytical expression for the second term in the thermodynamic perturbation theory. The new resulted second order term in the perturbation theory, although simple and analytical, is shown to be as nearly accurate as the Barker–Henderson second order term for the case of moderate- to long-ranged hard-core Yukawa potentials and the Sutherland potential.

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.