Thermodynamics of pseudo-hard body mixtures

Condensed Matter Physics, 2013

Very recently the effect of equisized charged hard sphere solutes in a mixture with core-softened fluid model on the structural and thermodynamic anomalies of the system has been explored in detail by using Monte Carlo simulations and integral equations theory [J. Chem. Phys., 2012, 137, 244502]. Our objective of the present short work is to complement this study by considering univalent ions of unequal diameters in a mixture with the same soft-core fluid model. Specifically, we are interested in the analysis of changes of the temperature of maximum density (TMD) lines with ion concentration for three model salt solutes, namely sodium chloride, potassium chloride and rubidium chloride models. We resort to Monte Carlo simulations for this purpose. Our discussion also involves the dependences of the pair contribution to excess entropy and of constant volume heat capacity on the temperature of maximum density line. Some examples of the microscopic structure of mixtures in question in terms of pair distribution functions are given in addition.

Physical Review Letters, 1999

We study the phase behavior of additive binary hard-sphere mixtures by direct computer simulation, using a new technique which exploits an analog of the Gibbs adsorption equation. The resulting phase diagrams, for size ratios q 0.2, 0.1, and 0.05, are in remarkably good agreement with those obtained from an effective one-component Hamiltonian based on pairwise additive depletion potentials, even in regimes of high packing (solid phases) and for relatively large size ratios (q 0.2) where one might expect the approximation of pairwise additivity to fail. Our results show that the depletion potential description accounts for the key features of the phase equilibria for q # 0.2.

The Journal of Chemical Physics, 2012

The canonical Monte Carlo computer simulations and integral equation theory were applied to examine the structural and thermodynamic properties of a mixture of ions and a core-softened fluid molecules. The positive and negative ions forming a +1:−1 salt were modeled as charged hard spheres, immersed in the dielectric medium. It was shown previously that the core-softened fluid under study is characterized by a set of structural, thermodynamic, and dynamic anomalies. The principal objective of this work was to elucidate how the presence of ions alters this behavior. The structural properties of the mixtures are discussed in terms of the pair distribution functions; in addition, the pair contribution to the excess entropy was calculated. Thermodynamic properties are investigated by using the dependencies of energy and compressibility factor on density, composition of the mixture, and reduced temperature. The heat capacity was also evaluated. Our principal findings concern the description of structural anomalies in the mixture, the dependence of the temperature of maximum density on the ionic concentration, and establishing the regions delimiting the structural and thermodynamic anomalies of the model mixture.

Physical Chemistry Chemical Physics

In this paper we study excluded volume interactions, the free volume fraction available, and the phase behaviour, in mixtures of hard spheres (HS) and hard rods, modeled as spherocylinders. We...

In this work we study a set of soft-sphere systems characterised by a well-defined variation of their softness. These systems represent an extension of the repulsive Lennard-Jones potential widely used in statistical mechanics of fluids. This type of soft spheres is of interest because they represent quite accurately the effective intermolecular repulsion in fluid substances and also because they exhibit interesting properties. The thermodynamics of the soft-sphere fluids is obtained via an effective hard-sphere diameter approach that leads to a compact and accurate equation of state. The virial coefficients of soft spheres are shown to follow quite simple relationships that are incorporated into the equation of state. The approach followed exhibits the rescaling of the density that produces a unique equation for all systems and temperatures. The scaling is carried through to the level of the structure of the fluids.

The Journal of Chemical Physics, 2007

We consider binary mixtures of soft repulsive spherical particles and calculate the depletion interaction between two big spheres mediated by the fluid of small spheres, using different theoretical and simulation methods. The validity of the theoretical approach, a virial expansion in terms of the density of the small spheres, is checked against simulation results. Attention is given to the approach toward the hard-sphere limit, and to the effect of density and temperature on the strength of the depletion potential. Our results indicate, surprisingly, that even a modest degree of softness in the pair potential governing the direct interactions between the particles may lead to a significantly more attractive total effective potential for the big spheres than in the hard-sphere case. This might lead to significant differences in phase behavior, structure and dynamics of a binary mixture of soft repulsive spheres. In particular, a perturbative scheme is applied to predict the phase diagram of an effective system of big spheres interacting via depletion forces for a size ratio of small and big spheres of 0.2; this diagram includes the usual fluid-solid transition but, in the soft-sphere case, the metastable fluid-fluid transition, which is probably absent in hard-sphere mixtures, is close to being stable with respect to direct fluid-solid coexistence. From these results the interesting possibility arises that, for sufficiently soft repulsive particles, this phase transition could become stable. Possible implications for the phase behavior of real colloidal dispersions are discussed.

nt.ntnu.no

A simple volume-explicit equation of state (EOS) for hard sphere mixtures has been developed on the basis of the pressure form of the virial expansion. The resulting equation yields the dependence of the compressibility factor on the packing fraction and mole fraction for different size ratios within the error estimates of simulation data in most cases. The new equation also gives the exact second and third pressure virial coefficients. An advantage of such equations of state is the fact that they yield easily the Gibbs energies and consequently hard-sphere diagrams. The equations also predict with good accuracy the compressibility factor of non-additive hard sphere mixture with a small negative or positive value of nonadditivity parameter (∆).

2014

A simulation technique is described for quantifying the contribution of three-body interactions to the thermodynamical properties of coarse-grained representations of complex fluids. The method is based on comparing the third virial coefficient B3 for a complex fluid with that of an approximate coarse-grained model described by a pair potential. To obtain B3 we introduce a new technique which expresses its value in terms of the measured volume-dependent asymptote of a certain structural function. The strategy is applicable to both Molecular Dynamics and Monte Carlo simulation. Its utility is illustrated via measurements of three-body effects in models of star polymer and highly size-asymmetrical colloid-polymer mixtures. arXiv:1403.3368v2 [cond-mat.soft]

The Journal of Chemical Physics, 2021

Comprehensive calculations were performed to predict the phase behaviour of large spherical colloids mixed with small spherical colloids that act as depletant. To this end, the free volume theory (FVT) of Lekkerkerker et al. [Europhys. Lett. 20 (1992) 559] is used as a basis and is extended to explicitly include the hard-sphere character of colloidal depletants into the expression for the free volume fraction. Taking the excluded volume of the depletants into account in both the system and the reservoir provides a relation between the depletant concentration in the reservoir and in the system that accurately matches with computer simulation results of Dijkstra et al. [Phys. Rev. E 59 (1999) 5744]. Moreover, the phase diagrams for highly asymmetric mixtures with size ratios q 0.2 obtained by using this new approach corroborates simulation results significantly better than earlier FVT applications to binary hard-sphere mixtures. The phase diagram of a binary hard-sphere mixture with a size ratio of q = 0.4, where a binary interstitial solid solution is formed at high densities, is investigated using a numerical free volume approach. At this size ratio, the obtained phase diagram is qualitatively different from previous FVT approaches for hard-sphere and penetrable depletants, but again compares well with simulation predictions.

Lecture Notes in Physics, 2008

An overview of some analytical approaches to the computation of the structural and thermodynamic properties of single component and multicomponent hard-sphere fluids is provided. For the structural properties, they yield a thermodynamically consistent formulation, thus improving and extending the known analytical results of the Percus-Yevick theory. Approximate expressions for the contact values of the radial distribution functions and the corresponding analytical equations of state are also discussed. Extensions of this methodology to related systems, such as sticky hard spheres and squarewell fluids, as well as its use in connection with the perturbation theory of fluids are briefly addressed.

Physical Review E, 2002

Monte Carlo simulations on the structural properties of ternary fluid mixtures of additive hard spheres are reported. The results are compared with those obtained from a recent analytical approximation [S. B. Yuste, A. Santos, and M. López de Haro, J. Chem. Phys. 108, 3683 (1998)] to the radial distribution functions of hard-sphere mixtures and with the results derived from the solution of the Ornstein-Zernike integral equation with both the Martynov-Sarkisov and the Percus-Yevick closures. Very good agreement between the results of the first two approaches and simulation is observed, with a noticeable improvement over the Percus-Yevick predictions especially near contact.

Cornell University - arXiv, 2022

We present an equilibrium thermodynamic properties of binary hard-sphere mixtures from integral equation approach combined with the Percus-Yevick (PY) and the Martynov-Sarkisov (MS) approximations. We use the virial, the compressibility and the Boublík-Mansoori-Carnahan-Starling-Leland (BMCSL) equations of state in the PY approximation, while the virial equation of state is only employed in the MS approximation. We employ a closed-form expression for evaluating the excess chemical potential. The excess Helmholtz free energy is obtained using the Euler relation of thermodynamics. For a number of binary sets of the mixtures we compare our findings for thermodynamic properties with previously obtained results in the literature. Generally, the findings from the MS approximation show better agreement with the results than those from the PY approximation.

Proceedings of 7th Symposium on Thermophysical Properties , 1977

The Gibbs-Bogoliubov inequality is used to produce inequalities for the variational calculations of thermodynamic· properties of pure-fluid, pure-solid, and mixture of soft-spheres. For the pure-fluid and pure solid soft spheres it is shown that the results of the variational theory are in agreement with the Monte Carlo data for steep soft-sphere systems. Through Gibbs-Bogoliubov inequality it is shown that in addition to the variational theory of mixture, the Scott (lf) and Scott (2f) theories also give upper bounds to the Helmholtz; free· energy of soft-sphere mixture. It is also shown that vdW (1£) theory gives an approximation to an upper bound of the entropy of mixture while the case for vdW (2f) is not clear. Over all it is shown that vdW (lf) and the variational theories are superior to vdW (2f), Scott (lf), a d Scott (2f) theories in predicting the thermodynamic n properties of soft-sphere mixture.

Physical Review E, 2009

A method of numerical calculation of the fourth virial coefficients of the mixture of additive hard spheres is proposed. The results are compared with an exact analytical formula for the fourth partial virial coefficient B 4 ͓1͔ ͑i.e., three spheres of diameters 1 and one sphere of diameter 2 ͒ and a semiempirical expression for B 4 ͓2͔ ͑i.e., two spheres of each kind͒. It is shown that the first formula is nonanalytic and the implication to the equations of state for hard-sphere mixtures is discussed.

Journal of Chemical Physics, 1996

We have tested the capabilities of a new self-consistent integral equation, closely connected with Verlet's modified closure, for the study of fluid-fluid phase separation in symmetric non-additive hard-sphere mixtures. New expressions to evaluate the chemical potential of mixtures are presented and play a key role in the construction of the phase diagram. The new integral equation, which implements consistency between virial and fluctuation theorem routes to the isothermal compressibility, together with chemical potential and virial pressure consistency via the Gibbs-Duhem relation, yields a phase diagram which especially at high densities agrees remarkably well with the new semi-Grand Ensemble Monte Carlo simulation data also presented in this work. Deviations close to the critical point can be understood as a consequence of the inability to enforce virial-fluctuation consistency in the neighborhood of the spinodal decomposition curve.