Hard-core 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.

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.

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.

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.

Mean-field theory of inhomogeneous fluids.

The Barker-Henderson perturbation theory is a bedrock of liquid-state physics, providing quantitative predictions for the bulk thermodynamic properties of realistic model systems. However, this successful method has not been exploited for the study of inhomogeneous systems. We develop and implement a first-principles "Barker-Henderson density functional," thus providing a robust and quantitatively accurate theory for classical fluids in external fields. Numerical results are presented for the hard-core Yukawa model in three dimensions. Our predictions for the density around a fixed test particle and between planar walls are in very good agreement with simulation data. The density profiles for the free liquid vapor interface show the expected oscillatory decay into the bulk liquid as the temperature is reduced toward the triple point, but with an amplitude much smaller than that predicted by the standard mean-field density functional.

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.

R -crossing method applied to fluids interacting through variable range potentials

The R-crossing method of thermodynamic geometry is applied to reproduce the coexistence curves of fluid systems described by hard-core Yukawa and hard-core Mye-Type interactions whose range can be varied. Connection between the range of the potential and the validity of the method is studied. Even when scaling relations suggest a dependence on the range, we found explicitly the quantitative dependence for two varying range potentials. Using the saturation pressures, it is possible to assign a percentage P(λ) of measuring how far we can go below the critical point when reproducing the coexistence curve. It is found that there is a close relation between the range of the potential and P(λ). Such relation assures that the larger the range of the potential, the deeper we can go below the critical point. Our results, together with the known low |R| limit, represent two independent criteria to restrict the applicability of the R-crossing method. Namely, at what extent we can accurately reproduce the coexistence curve when we know the range of the intermolecular potential of the thermodynamic system involved.

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.

Capacitance of electrolytes with hydration-mediated interaction in planar electric double layers

ABSTRACTThe theoretical model, which is based on the density functional approach, has been developed for studying the electrostatic properties of electrolytes with the soft, hydration-mediated ion–ion and ion–surface interactions. The theory approximates the hydration-mediated ion–ion interaction through the mean-field approximation. The results show that the theory leads to a good agreement with the simulation results and predicts the camel-to-bell shape transition for the charged hard-core Yukawa ions with the hydration-mediated interaction. The high is observed at a low bulk concentration of ions and the camel-to-bell shape transition occurs when the bulk concentration rises to an appropriate value. The increase of an ion size shifts the maximum differential capacitance () to a low surface charge density. The addition of a repulsive hydration interaction reduces the , whereas the attractive hydration interaction enhances the . The increase of ion–surface and ion–ion interactions decreases the and shifts the maximum to a higher surface charge density. The increase of hydration anion–anion repulsion decreases the of a positively charged electrode and shifts its maximum to more positively charged surfaces.

Polymorph selection during crystallization of a model colloidal fluid with a free energy landscape containing a metastable solid

The free energy landscape responsible for crystallization can be complex even for relatively simple systems like hard sphere and charged stabilized colloids. In this work, using hard-core repulsive Yukawa model, which is known to show complex phase behavior consisting of fluid, FCC and BCC phases, we studied the interplay between the free energy landscape and polymorph selection during crystallization. When the stability of the BCC phase with respect to the fluid phase is gradually increased by changing the temperature and pressure at a fixed fluid-FCC stability, the final phase formed by crystallization is found to undergo a switch from the FCC to the BCC phase, even though FCC remains thermodynamically the most stable phase. We further show that the nature of local bond-orientational order parameter fluctuations in the metastable fluid phase as well as the composition of the critical cluster depend delicately on the free energy landscape, and play a decisive role in the polymorph selection during crystallization.

Molecular dynamics simulation of charged colloids confined between hard walls: pre-melting and pre-freezing across the BCC–fluid coexistence

Molecular dynamics (MD) computer simulations are used to study the structure of hard-core Yukawa systems confined between two parallel hard walls. States around the coexistence between a fluid and a body-centered cubic (BCC) crystal are considered. In all cases a pronounced layering in the vicinity of the walls is observed. Using a thermodynamic integration scheme, we determine the wall-fluid interfacial free energy γ which is negative and monotonically decreasing with increasing bulk density of the fluid. In the case of the fluid, the layers next to the walls undergo a transition from a fluid to a hexagonal structure. This pre-freezing transition occurs well below the coexistence bulk density of the fluid. The confined BCC crystal in (111) orientation shows melted regions between crystalline face-centered cubic (FCC) layers close to the wall and the BCC bulk region.

Auxeticity of Yukawa Systems with Nanolayers in the (111) Crystallographic Plane.

Elastic properties of model crystalline systems, in which the particles interact via the hard potential (infinite when any particles overlap and zero otherwise) and the hard-core repulsive Yukawa interaction, were determined by Monte Carlo simulations. The influence of structural modifications, in the form of periodic nanolayers being perpendicular to the crystallographic axis [111], on auxetic properties of the crystal was investigated. It has been shown that the hard sphere nanolayers introduced into Yukawa crystals allow one to control the elastic properties of the system. It has been also found that the introduction of the Yukawa monolayers to the hard sphere crystal induces auxeticity in the -direction, while maintaining the negative Poisson’s ratio in the -direction, thus expanding the partial auxeticity of the system to an additional important crystallographic direction.

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.

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.

Modeling of the n–alkane homologous series in the range of C6 to C20 using linear Yukawa isotherm regularity (LYIR)

The linear Yukawa isotherm regularity (LYIR) equation of state (EoS) was used to model the p–v–T behavior of n–alkane homologous series CnH2n+2 (6≤n≤20) in the dense fluid region. A molecular model was proposed and the LYIR EoS was modified based on this model to take the effects of segments of the chain molecule into account. In the proposed model, each n–alkane molecule was assumed as an n–fold tangentially one–center spherical segments. In the other word, the n–alkane fluid was considered as a hypothetical mixture of methyl and methylene groups. The average effective pair potential (AEPP) between two segments was modeled by the hard–core Yukawa (HCY) potential in the framework of liquid's thermodynamic perturbation theory (TPT). The experimental p–v–T data of the selected n–alkanes were used to evaluate the validity of the modified LYIR EoS (MLYIR). Four important conclusions were obtained in this work: (a) The average coordination number (z) in the hypothetical mixture depends on n as well as temperature (T) and molar density (ρ) so that its value increases and decreases for the odd and even values of n, respectively. (b) the effective HS diameter (σeff) of segment increases and decreases with the chain length for the n–alkanes with odd and even value of n, respectively, and become independent of the chain length for n>20. (c) The σeff of the n–alkanes with the even number of carbon atoms is greater than that of the molecules with the odd value of n for n<18. (d) The MLYIR EoS showed that the εeff and λeff of Yukawa AEPP for the segment–segment interaction are independent of the chain length. Moreover, the results demonstrated the relationship between the symmetry of chain structure and the value of σeff.

Theory and computer simulation of hard-core Yukawa mixtures: thermodynamical, structural and phase coexistence properties

We report extensive calculations, based on the modified hypernetted chain (MHNC) theory, on the hierarchical reference theory (HRT), and on Monte Carlo simulations, of thermodynamical, structural and phase coexistence properties of symmetric binary hard-core Yukawa mixtures (HCYM) with attractive interactions at equal species concentration. The obtained results are throughout compared with those available in the literature for the same systems. It turns out that the MHNC predictions for thermodynamic and structural quantities are quite accurate in comparison with the MC data. The HRT is equally accurate for thermodynamics, and slightly less accurate for structure. Liquid-vapor (LV) and liquid–liquid (LL) consolute coexistence conditions as emerging from simulations, are also highly satisfactorily reproduced by both the MHNC and HRT for relatively long ranged potentials. When the potential range reduces, the MHNC faces problems in determining the LV binodal line; however, the LL consolute line and the critical end point (CEP) temperature and density turn out to be still satisfactorily predicted within this theory. The HRT also predicts with good accuracy the CEP position.The possibility of employing liquid state theories HCYM for the purpose of reliably determining phase equilibria in multicomponent colloidal fluids of current technological interest, is discussed.