Hard-core Yukawa Research Articles

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.

Modeling the p–v–T behavior of furfural compounds using perturbed linear Yukawa isotherm regularity

The p–v–T behavior of furfural compounds (FCs) such as 5–methylfurfural (5–MF) and tetrahydrofurfuryl alcohol (THF–A) by using the perturbation-based linear Yukawa isotherm regularity (LYIR) were modeled. The LYIR is a perturbation–based equation of state (EoS) which was recently derived by making use of the attraction part of hard–core Yukawa (HCY) potential as perturbation average effective pair potential (AEPP) in the framework of liquid's thermodynamic perturbation theory. To use the LYIR EoS for modeling FCs, each molecule of the FC was considered as an one–center spherical united atom with temperature–dependent effective diameter. The results showed that the LYIR model can predict the p–v–T behavior of the selected FCs very well and the reproduced densities obtained by the LYIR EoS are in very good agreements with the available experimental densities. The range of the relative deviations percentage between the experimental and calculated density are from −0.006% to 0.02% for 5–MF and 0.009% to −0.01% for THF–A. In addition, the parameters of the HCY potential (σeff, λeff), as AEPP, were obtained for the selected FCs using the LYIR model and provided valuable information on the structure, intermolecular interactions, and the role of substitution groups on the p–v–T behavior of this class of green fluids. Moreover, the results of the study mirror the effect of the hydrogenation and the dehydrogenation processes on the value of σeff. Additionally, the contribution of internal pressure in compression factor and also the effect of both pressure and temperature on the internal compression factor were investigated.

Auxeticity enhancement due to size polydispersity in fcc crystals of hard-core repulsive Yukawa particles.

The Poisson's ratio of the fcc hard-core repulsive Yukawa crystals with size polydispersity was determined by Monte Carlo simulations in the isothermal-isobaric ensemble. The effect of size polydispersity on the auxetic properties of Yukawa crystals has been studied. It has been found that an increase of particle size polydispersity causes a decrease of the Poisson's ratio in auxetic directions as well as appearance of a negative Poisson's ratio in formerly non-auxetic directions. A measure of auxeticity was introduced to estimate quantitatively an enhancement of auxetic properties in polydisperse Yukawa crystals. The proposed measure of auxeticity can be applied to appraise the auxeticity of any studied system.

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.

Solvent-mediated forces in critical fluids.

The effective interaction between two planar walls immersed in a fluid is investigated by use of density functional theory in the supercritical region of the phase diagram. A hard core Yukawa model of fluid is studied with special attention to the critical region. To achieve this goal a formulation of the weighted density approximation coupled with the hierarchical reference theory, able to deal with critical long wavelength fluctuations, is put forward and compared with other approaches. The effective interaction between the walls is seen to change character on lowering the temperature: The strong oscillations induced by layering of the molecules, typical of the depletion mechanism in hard core systems, are gradually smoothed and, close to the critical point, a long range attractive tail emerges leading to a scaling form which agrees with the expectations based on the critical Casimir effect. Strong corrections to scaling are seen to affect the results up to very small reduced temperatures. By use of the Derjaguin approximation, this investigation has natural implications for the aggregation of colloidal particles in critical solvents.

A thermodynamic self-consistent theory of asymmetric hard-core Yukawa mixtures

We perform structural and thermodynamic calculations in the framework of the modified hypernetted chain (MHNC) integral equation closure to the Ornstein–Zernike equation for binary mixtures of size-different particles interacting with hard-core Yukawa pair potentials. We use the Percus–Yevick (PY) bridge functions of a binary mixture of hard-sphere (HSM) particles. The hard-sphere diameters of the PY bridge functions of the HSM system are adjusted so to achieve thermodynamic consistency between the virial and compressibility equations of state. We show the benefit of thermodynamic consistency by comparing the MHNC results with the available computer simulation data reported in the literature, and we demonstrate that the self-consistent thermodynamic theory provides a better reproduction of the simulation data over other microscopic theories.

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.

A Hard Convex Core Yukawa Equation of State for Nonassociated Chain Molecules

The compressibility factor of nonassociated chain molecules composed of hard convex core Yukawa segments was derived with SAFT-VR and an extension of the Barker-Henderson perturbation theory for convex bodies. The temperature-dependent chain and dispersion compressibility factors were derived using the Yukawa potential. The effects of temperature, packing fraction, and segment number on the compressibility factor were investigated for chains of the prolate sphereocylinder segments. A comparison of hard core Yukawa chain compressibility factor values and hard chain compressibility factor values showed that the type of interaction potential has more effect on those chain molecules with higher segment numbers. The results demonstrated that in reduced temperatures 1.4 and 2.4, the Yukawa chain of the compressibility factor is insensitive to temperature, while the dispersion term of the compressibility factor changes remarkably with the temperature. The derived equation of state can fairly predict the SAFT-VR results of the hard sphere core chain molecules in the limit of α = 1.

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.

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.

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.