Hybridized Mean Spherical Approximation Research Articles

Structural study of emulsions stabilized by charged nanoparticles

The aim is a quantitative study of the structure of the Pickering emulsionsthat are stabilized by charged nanoparticles. We assume that the interaction potential between droplets is of Sogami type. First, we compute the structural properties using the Integral Equation Method with the so-called hybridized-mean spherical approximation (HMSA). Finally, the validity of this method is tested by confronting the results of the correlation functions found by HMSA integral equation with those from Molecular Dynamics (MD) simulations.

Structure and thermodynamics of Pickering emulsions stabilized by adsorbed charged particles

In this work, we reexamine the problem of the stabilization of the Pickering emulsions by an adsorption of small charged particles on the surfaces of droplets of some liquid dispersed in another unlike liquid. Quantitatively, such a problem is naturally studied through the determination of the structure and thermodynamics of these emulsions. To this end, we first regard droplets as monodisperse small spheres assimilated to charged soft-colloids. For the sake of simplicity, the adsorbed particles are assumed to be point-like. When the temperature of the considered emulsions is fixed (room temperature), the only remaining parameters of discussion are the droplet number density, their size and surface charge, and the concentrations of counterions and ions (in the presence of a salt or an electrolyte). For the study, we adopt the Sogami-Ise pair-potential between anchored droplets that reproduces well the features of the real DLVO’s one. The structure (through the structure factor and spatial correlation-function) and thermodynamics (through the pressure, internal energy and thermal compressibility) are computed using, first, Integral Equation Method, with Hybridized Mean Spherical Approximation, and second, the Molecular Dynamic Simulation. The structure factor and the correlation-function and thermodynamical quantities are discussed in terms of the droplet density, their size and surface charge. Finally, we compare the results from these two methods, and find that they are in good agreement.

Structure and Thermodynamics of Solutions of Colloids Interacting Through Yukawa or Sogami Potentials

The aim of the present work is the determination of the structure and thermodynamics of a monodisperse colloidal solution. We assume that the interaction potential between colloids is of Yukawa or Sogami types. The former is purely repulsive, while the second, it involves, in addition to a repulsive part, a Van der Waals attractive tail. We compute the structure factor and thermodynamics properties, using, the integral equation one with the hybridized mean spherical approximation. We first compare the results relative to this theory, and with this obtained within Monte Carlo simulation. We show that results from integral equation method with a Sogami potential and those of simulation are in good quantitative agreement. Finally, our theoretical results are compared to those of experiment by Tata and coworkers. We find that integral equation theory with Sogami potential agrees well with experiment.

Numerical Study of the Structure and Thermodynamics of Colloidal Suspensions by Variational Method

In this paper, we present the results of calculation of the structure and thermodynamics properties of the dispersions colloidal solution ended using the variational method with the scaling process. We assume that the interaction potential between colloids is of Yukawa or Sogami types. The former is purely repulsive, while the second, it involves, in addition to a repulsive part, a Van der Waals attractive tail. We compute the structure factor and thermodynamics properties, using, first, the variational method with the rescaling technique, and second, the integral equation one with the hybridized mean spherical approximation. We first compare the results relative to these theories, and with those obtained within Monte Carlo simulation. We show that results from integral equation method with a Sogami potential and those of simulation are in good quantitative agreement. Finally, our theoretical results are compared to those of experiment by Tata and coworkers. We find that integral equation theory with Sogami potential agrees well with experiment.

Structure and Electrical Resistivities of Liquid Al and Ga Metals and Their Binary Alloys

The ionic and electronic properties of liquid Al and Ga metals and Al1-xGax alloys have been investigated self-consistently. Partial structure factors have been calculated from the solution of the Ornstein–Zernike equation with the hybridized mean spherical approximation closure, and the transferable electron–ion potential of Fiolhais et al. has been used as the input pseudopotential. Two different formulas are used in the electrical resistivity calculation, namely, the Faber–Ziman formula and the modified Ziman’s formula suggested by Ferraz–March. The results are compared with each other and experimental values.

Direct correlation function for complex square barrier-square well potentials in the first-order mean spherical approximation

The direct correlation function of the complex discrete potential model fluids is obtained as a linear combination of the first-order mean spherical approximation (FMSA) solution for the simple square well model that has been reported recently [Hlushak et al., J. Chem. Phys. 130, 234511 (2009)]. The theory is employed to evaluate the structure and thermodynamics of complex fluids based on the square well-barrier and square well-barrier-well discrete potential models. Obtained results are compared with theoretical predictions of the hybrid mean spherical approximation, already reported in the literature [Guillen-Escamilla et al., J. Phys.: Condens. Matter 19, 086224 (2007)], and with computer simulation data of this study. The compressibility route to thermodynamics is then used to check whether the FMSA theory is able to predict multiple fluid-fluid transitions for the square barrier-well model fluids.

Structure and electrical resistivity of liquid In–Sn alloy

A comparative study is presented for the electrical resistivity of liquid In 1− x Sn x metal alloys. In the electrical resistivity calculation, Faber–Ziman formula and modified Ziman’s formula suggested by Ferraz–March are used. Partial structure factors have been calculated from the solution of Ornstein–Zernike (O–Z) equation with the Hybridized Mean Spherical Approximation (HMSA) closure and the transferable electron–ion potential of Fiolhais et al. has been used as the input pseudopotential. Two different screening functions are used in calculation of form factors which are necessary for the calculation of resistivity. The results are compared with experimental ones and the effect of screening function on resistivity is discussed.

Structure and thermodynamics of discrete potential fluids in the OZ–HMSA formalism

We study the structural and thermodynamic properties of three discrete potentialfluids: the square well (SW), the square well–barrier (SWB), and the squarewell–barrier–well (SWBW) fluids by means of the Ornstein–Zernike (OZ) integralequation and the HMSA (hybrid mean spherical approximation) closure relation.The radial distribution functions, structure factors, and pressure of the systemsare calculated as a function of the strength of the attractive and repulsive partsof the potential in an extended range of densities, mainly covering the range0.1 ≤ ρ* ≤ 0.9. We find that far away from the liquid–vapour coexistence region the HMSA theory is anaccurate approach that compares well with Monte Carlo simulations. We also find that when theattractive parts of the potential dominate over the repulsive part the structure factor at lowq values shows a considerable increase, which suggests the formation of large-scale domainsthat locally exhibit fluid-like structure.

Bridge functions near the liquid-vapor coexistence curve in binary Lennard-Jones mixtures

We have carried out extensive molecular-dynamics simulation studies of binary Lennard-Jones mixtures to calculate directly the bridge function at state points lying in a very narrow single fluid phase region between the vapor-liquid and solid-liquid coexistence lines [Lamm and Hall, Fluid Phase Equilib. 182, 37 (2001); 194-197, 197 (2002)]. By varying the density close to the liquid-vapor coexistence line, significant deviations are observed at intermediate distances between the simulated bridge function and two widely used approximate closures in the integral equation theory of liquids, viz. the hybrid mean spherical approximation and the Duh-Henderson closures. The overall qualitative agreement remains the same with small variation in temperature that brings the system closer to either the liquid-vapor or liquid-solid coexistence curve. We also report a comparison of the direct and indirect correlation functions obtained from our simulation studies as well as from the integral equation theory of liquids. Our results emphasize the need for developing new closures applicable to binary fluid mixtures over a wide range of thermodynamic parameters.

Structure and thermodynamic modelling of Pluronic L64 solutions

AbstractThe aim of the present work is to model structure and thermodynamic properties of Pluronic L64 solutions (triblock copolymer with hydrophilic ends and a hydrophobic middle). We first determined the micelle size by dynamic light scattering at various temperatures. This helps to understand the particle formation mechanism in solution and the interparticle interactions by following the virial coefficient as well as its temperature dependence. Two semi-empirical intermolecular potentials were tested to predict sample properties. First, we used a pure Lennard- Jones pair potential and then we introduced the Lu and Marlow (LM) contribution in its repulsive part. All quantities of interest were computed using the integral equation scheme with hybridized mean spherical approximation. We found that the LM contribution corrects structure and thermodynamic properties of the system by taking into account the effect of particle size.

Molecular dynamics study of the density and temperature dependence of bridge functions in normal and supercritical Lennard-Jones fluids

A systematic study of the density and temperature dependence of bridge functions has been carried out using molecular dynamics simulation studies in one-component Lennard-Jones fluids. In deriving the liquid structure, approximate closures are generally used in integral equation theories of liquids to obtain static density correlations. In the present work, we have directly compared the simulated bridge function to two such commonly used closures, viz., hybrid mean spherical approximation (HMSA) [J. Chem. Phys. 84, 2336 (1986)] and Duh-Henderson [J. Chem. Phys. 104, 6742 (1996)] closures with thermodynamic parameters varying from the normal liquid to the supercritical fluid phase far from and near the critical point. In the normal liquid region, both closures show a qualitative agreement with the simulated bridge function, although the extent of correlation at distances sigma < r < or = 2.5sigma is generally underestimated. A similar behavior is obtained in supercritical fluids far from the critical point where critical fluctuations are no longer important. In contrast, significant deviations are observed in the bridge functions in supercritical fluids near the critical point even at densities as small as 25% or 50% of the critical density. Such behavior appears to have resulted from competing contributions to the bridge function from decreasing indirect correlations and small yet significant cavity correlations persistent even at very low densities.

Microscopic theories of model macromolecular fluids and fullerenes: The role of thermodynamic consistency

We investigate the accuracy of two well-known integral equation theories (IETs) of the fluid state, namely, the modified hypernetted chain (MHNC) approximation and the hybridized mean spherical approximation (HMSA), as applied to systems characterized by short-range interactions. The theoretical approaches are implemented by enforcing their thermodynamic consistency according to two different strategies: in one case the equality of the isothermal compressibility, as calculated via the virial and fluctuation routes from structure to thermodynamics, is imposed [“local” consistency (LC)]; in the other case the equality of the pressure as calculated either via the two previous routes, or via the virial and the energy routes, is imposed [“global” consistency (GC)]. We show that for the class of potentials at issue the GC is in general considerably more accurate than the LC. We document this result by investigating the performances of the MHNC and the HMSA, as applied to the calculation of the thermodynamic and structural properties of the hard-core Yukawa (HCY) potential, the Derjaguin–Landau–Vervey–Overbeek (DLVO) potential and the Girifalco potential for fullerenes. The obtained results are then compared with Monte Carlo simulation data, that we also produce for the same model systems. As far as the HCY potential is concerned, the investigation covers a range of the Yukawa inverse decay length, z, spanning from z=1.8 when the interaction mimics the Lennard-Jones 12-6 potential, to z=7 when the potential mimics the “effective” short range interaction between globular proteins in a highly charge-screened aqueous solution. IETs are then applied to the DLVO potential with charge and Hamaker constant values which fit the dynamical interaction factor of lysozyme in a solution of high ionic strength, and to the Girifalco potential with parameters appropriate to model C60 and C70. It emerges from the present study that the GC is able to provide Helmholtz free energies and chemical potentials which compare quite favorably with the simulation data. As a consequence, we are able to show that the GC estimates of the phase coexistence densities for the HCY and Girifalco potential agree almost quantitatively with the Monte Carlo ones, by thus definitely improving upon previous results obtained within the LC. We also comment on the relevance of confident phase diagram determinations from IETs, in connection with the prediction of protein crystallization. Possible extensions of the present thermodynamic consistency strategies to more sophisticated theories and realistic models of protein solutions and fullerenes are finally suggested.

Comparison between integral equation method and molecular dynamics simulation for three-body forces: Application to supercritical argon

The prediction of the structural and thermodynamic properties of supercritical argon has been carried out by two independent routes: semianalytical calculations and numerical simulations. The first one is based on the hybridized mean spherical approximation (HMSA) conjugated with an effective pair potential that incorporates multipole dispersion interactions. The second one uses a very recent numerical simulation technique, inspired by the Car–Parrinello method [van der Hoef et al., J. Chem. Phys. 111, 1520 (1999)], which contains an effective quantum-mechanical representation of the underlying electronic structure. The latter approach allows us to treat the contribution of the three-body effects as well, and to validate the use of an effective pair potential for them in the framework of the self-consistent integral equation method. For all the supercritical argon states studied, the results obtained with the semianalytical approach are in good agreement with the predictions of the numerical simulation. Here it is shown that HMSA remains competitive with molecular dynamics simulation when the triple-dipole and the dipole–dipole–quadrupole three-body terms are taken into account.

Renormalization of the indirect correlation function to extract the bridge function of simple fluids

The standard integral equation approach is used to extract the bridge function and other correlation functions of simple fluids. To do this, we firstly use the hybridized mean spherical approximation (HMSA), which involves a renormalization of the indirect correlation function. Secondly, we propose a new division scheme for the pair potential founded on the merging process of a test particle into the system. Thirdly, we take advantage of the thermodynamic consistent condition put forward in the HMSA to optimize the depth of the long-range part of the pair potential inside the core, making the procedure autonomous and state dependent. The method is tested on the pure Lennard-Jones fluid in supercritical conditions. Very good agreement is obtained for structural quantities and thermodynamic properties as compared to the Monte Carlo (MC) results for the bridge function and to the molecular dynamics (MD) results for the thermodynamic properties.

A State-dependent Division Scheme for the Potential of Simple Fluids

A new division scheme for the pair potential into long-range and short-range parts is presented, which takes account of the dependence on the density and makes possible the extraction of the bridge function B(r) in the core region. The calculation of the correlation functions is carried out with the hybridized mean spherical approximation (HMSA). As attested by the comparison with the simulation results, HMSA used with this potential separation is suitable to produce accurate bridge function and pair correlation function for the Lennard-Jones fluid.

Effects of dispersion forces on the structure and thermodynamics of fluid krypton

Semianalytical and numerical calculations are performed to predict the structural and thermodynamic properties of low-density Kr fluid. Assuming that the interatomic forces can be modelled by a pairwise potential plus the three-body Axilrod-Teller potential, two different routes are explored. The first one is based on the hybridized mean spherical approximation integral equation of the theory of liquids and the second one uses large-scale molecular dynamics (MD). Algorithms for MD simulation are constructed on parallel machines to reduce the amount of computer time induced by the calculations of the three-body forces and the pair-correlation function. Our results obtained with the two methods mentioned above are in quite good agreement with the recent small-angle neutron-scattering experiments [Formisano et al., Phys. Rev. Lett. 79, 221 (1997); Benmore et al., J. Phys.: Condens. Matter 11, 3091 (1999)]. Moreover, the reliability of the asymptotic form of the integral equation is assessed for the specific case of dispersion forces including the three-body contributions, by an analysis at low wave vector and low density. It is seen that the effects of the Axilrod-Teller triple-dipole potential cannot be ignored to describe the structure and the thermodynamic properties of fluid krypton even at low density.

Structure of fluid krypton using the integral-equation theory for three-body forces

The formalism of the hybridized mean spherical approximation integral equation is extended to calculate the pair correlation function for krypton, beyond the critical isotherm, by using the two- and three-body contributions to the interatomic potential. The calculations are intended to examine the change of the pair correlation function caused by the inclusion of the Axilrod-Teller triple-dipole potential. It is seen that the three-body interaction cannot be ignored and that their effects become more significant for intermediate densities. In addition, a good agreement is found with the recent small-angle neutron-scattering experiments of Formisano et al. [Phys. Rev. Lett. 79, 221 (1997)].

Transferable pair potentials for the description of liquid alkali metals

The structural and thermodynamic properties of liquid alkali metals near the melting point are presented. For this purpose, we use the thermodynamically self-consistent integral equation of the liquid state theory, called the hybridized mean-spherical approximation (HMSA). The effective interionic potential is derived via the second-order pseudopotential-perturbation method, in which the very recent pseudopotential of Fiolhais et al. [Phys. Rev. B 51, 14001 (1995)], designed for the solid state, is combined with our semianalytical local-field function [J. L. Bretonnet and M. Boulahbak, Phys. Rev. B 53, 6859 (1996)]. We show that this pseudopotential is transferable to the disordered environment characteristic of the liquid state and, if used with our local-field function, predicts the structural and thermodynamic properties of the liquid alkali metals with a reasonable accuracy.

Dynamical structure of undercooled liquid potassium

We perform a quite detailed theoretical investigation of the temperature dependence of the static and dynamical structure factors for undercooled potassium. The static structure factors are calculated from the hybridized mean-spherical approximation (HMSA) form of the integral approximation using pair potentials constructed from a non-local pseudopotential and the dynamical structure factors within the viscoelastic approximation. We show that the characteristic features of the static structure factors as obtained from molecular dynamics simulation are reproduced within the present framework and that, essentially, the general features of at the melting points are still preserved in the undercooled region.

A new pair potential for liquid argon

Recently, the well-known point molecular attractive pair term, r-6 only asymptotically correct, has been modified (Lu J. X. and Marlow W. Ç. (1995) Phys. Rev. Lett. 74. 1724) by taking into account the effect of a molecular size through a parameter a characteristic of the atom. Our interest is to test this specific feature on the properties of argon in the liquid state. A new pair potential has been generated by adding to the short-range repulsion, modelled by an r-12 term. the attractive term proposed by Lu and Marlow. Parameters have been fitted on the excess internal energy for argon over a wide range of densities and temperatures. In order to achieve this test, the hybridized-mean spherical approximation (HMSA) integral equation has been used. The HMSA has proven to be very accurate to reproduce the structure and the thermodynamics self-consistently. Structural and thermodynamic results with the new pair potential are in very good agreement with the experiments as well as simulation data.