Mean spherical approximation algorithm for multicomponent multi‐Yukawa fluid mixtures: Study of vapor–liquid, liquid–liquid, and fluid–glass transitions

Phase behavior of a symmetrical binary fluid mixture

We have investigated the phase behavior of a symmetrical binary fluid mixture for the situation where the chemical potentials mu(1) and mu(2) of the two species differ. Attention is focused on the set of interparticle interaction strengths for which, when mu(1)=mu(2), the phase diagram exhibits both a liquid-vapor critical point and a tricritical point. The corresponding phase behavior for the case mu(1) not equalmu(2) is investigated via integral-equation theory calculations within the mean spherical approximation and grand canonical Monte Carlo (GCMC) simulations. We find that two possible subtypes of phase behavior can occur, these being distinguished by the relationship between the triple lines in the full phase diagram in the space of temperature, density, and concentration. We present the detailed form of the phase diagram for both subtypes and compare with the results from GCMC simulations, finding good overall agreement. The scenario via which one subtype evolves into the other is also studied, revealing interesting features.

Thermodynamically self-consistent liquid state theories for systems with bounded potentials

The mean spherical approximation (MSA) can be solved semianalytically for the Gaussian core model (GCM) and yields exactly the same expressions for the energy and the virial equations. Taking advantage of this semianalytical framework, we apply the concept of the self-consistent Ornstein-Zernike approximation (SCOZA) to the GCM: a state-dependent function K is introduced in the MSA closure relation which is determined to enforce thermodynamic consistency between the compressibility route and either the energy or virial route. Utilizing standard thermodynamic relations this leads to two differential equations for the function K that have to be solved numerically. Generalizing our concept we propose an integrodifferential-equation-based formulation of the SCOZA which, although requiring a fully numerical solution, has the advantage that it is no longer restricted to the availability of an analytic solution for a particular system. Rather it can be used for an arbitrary potential and even in combination with other closure relations, such as a modification of the hypernetted chain approximation.

Type-IV phase behavior in fluids with an internal degree of freedom

We have identified a fourth archetype of phase diagram in binary symmetrical mixtures, which is encountered when the ratio of the interaction between the unlike and the like particles is sufficiently small. This type of phase diagram is characterized by the fact that the lambda line (i.e., the line of the second-order demixing transition) intersects the first-order liquid-vapor curve at densities smaller than the liquid-vapor critical density.

Cluster formation in two-Yukawa fluids

We present a different and efficient method for implementing the analytical solution of Ornstein-Zernike equation for two-Yukawa fluids in the mean spherical approximation. We investigate, in particular, the conditions for the formation of an extra low-Q peak in the structure factor, which we interpret as due to cluster formation in the two-Yukawa fluid when the interparticle potential is composed of a short-range attraction and a long-range repulsion. We then apply this model to interpret the small angle neutron scattering data for protein solutions at moderate concentrations and find out that the presence of a peak centered at Q=0 (zero-Q peak) besides the regular interaction peak due to charged proteins implies an existence of long-range attractive interactions besides the charge repulsion.

Phase diagram of a binary symmetric hard-core Yukawa mixture

We assess the accuracy of the self-consistent Ornstein-Zernike approximation for a binary symmetric hard-core Yukawa mixture by comparison with Monte Carlo simulations of the phase diagrams obtained for different choices of the ratio alpha of the unlike-to-like interactions. In particular, from the results obtained at alpha=0.75 we find evidence for a critical endpoint in contrast to recent studies based on integral equation and hierarchical reference theories. The variation of the phase diagrams with range of the Yukawa potential is investigated.

Self-consistent Ornstein–Zernike approximation for the Sogami–Ise fluid

We generalize the self-consistent Ornstein-Zernike approximation (SCOZA) to a fluid of particles with a pair potential consisting of a hard-core repulsion and a linear combination of Sogami-Ise tails, w(r)=-epsilonsigma summation operator (nu)(K(nu)/r+L(nu)z(nu))e(-z(nu)(r-sigma)). The formulation and implementation of the SCOZA takes advantage of the availability of semianalytic results for such systems within the mean-spherical approximation. The predictions for the thermodynamics, the phase behavior and the critical point are compared with optimized random phase approximation results; further, the effect of thermodynamic consistency is investigated.

Ising fluids in an external magnetic field: an integral equation approach

The phase behavior of Ising spin fluids is studied in the presence of an external magnetic field with the integral equation method. The calculations are performed on the basis of a soft mean spherical approximation using an efficient algorithm for solving the coupled set of the Ornstein-Zernike equations, the closure relations, and the external field constraint. The phase diagrams are obtained in the whole thermodynamic space including the magnetic field H for a wide class of Ising fluid models with various ratios R of the strengths of magnetic to nonmagnetic Yukawa-like interactions. The influence of varying the inverse screening lengths z(1) and z(2), corresponding to the magnetic and nonmagnetic Yukawa parts of the potential, is investigated too. It is shown that changes in R as well as in z(1) and z(2) can lead to different topologies of the phase diagrams. In particular, depending on the value of R, the critical temperature of the liquid-gas transition either decreases monotonically, behaves nonmonotonically, or increases monotonically with increasing H. The para-ferro magnetic transition is also affected by changes in R and the screening lengths. At H=0, the Ising fluid maps onto a simple model of a symmetric nonmagnetic binary mixture. For H--> infinity, it reduces to a pure nonmagnetic fluid. The results are compared with available simulations and the predictions of other theoretical methods. It is demonstrated that the mean spherical approximation appears to be more accurate compared with mean field theory, especially for systems with short ranged attraction potentials (when z(1) and z(2) are large). In the Kac limit z(1), z(2) -->+0, both approaches tend to nearly the same results.

Equation of state and liquid-vapor equilibria of one- and two-Yukawa hard-sphere chain fluids: Theory and simulation

The accuracy of several theories for the thermodynamic properties of the Yukawa hard-sphere chain fluid are studied. In particular, we consider the polymer mean spherical approximation (PMSA), the dimer version of thermodynamic perturbation theory (TPTD), and the statistical associating fluid theory for potentials of variable attractive range (SAFT-VR). Since the original version of SAFT-VR for Yukawa fluids is restricted to the case of one-Yukawa tail, we have extended SAFT-VR to treat chain fluids with two-Yukawa tails. The predictions of these theories are compared with Monte Carlo (MC) simulation data for the pressure and phase behavior of the chain fluid of different length with one- and two-Yukawa tails. We find that overall the PMSA and TPTD give more accurate predictions than SAFT-VR, and that the PMSA is slightly more accurate than TPTD.

Theoretical description of phase coexistence in model C60

We have investigated the phase diagram of a pair interaction model of C60 fullerene [L. A. Girifalco, J. Phys. Chem. 96, 858 (1992)], in the framework provided by two integral equation theories of the liquid state, namely, the modified hypernetted chain (MHNC) implemented under a global thermodynamic consistency constraint, and the self-consistent Ornstein-Zernike approximation (SCOZA), and by a perturbation theory (PT) with various degrees of refinement, for the free energy of the solid phase. We present an extended assessment of such theories as set against a recent Monte Carlo study of the same model [D. Costa, G. Pellicane, C. Caccamo, and M. C. Abramo, J. Chem. Phys. 118, 304 (2003)]. We have compared the theoretical predictions with the corresponding simulation results for several thermodynamic properties such as the free energy, the pressure, and the internal energy. Then we have determined the phase diagram of the model, by using either the SCOZA, the MHNC, or the PT predictions for one of the coexisting phases, and the simulation data for the other phase, in order to separately ascertain the accuracy of each theory. It turns out that the overall appearance of the phase portrait is reproduced fairly well by all theories, with remarkable accuracy as for the melting line and the solid-vapor equilibrium. All theories show a more or less pronounced discrepancy with the simulated fluid-solid coexistence pressure, above the triple point. The MHNC and SCOZA results for the liquid-vapor coexistence, as well as for the corresponding critical points, are quite accurate; the SCOZA tends to underestimate the density corresponding to the freezing line. All results are discussed in terms of the basic assumptions underlying each theory. We have then selected the MHNC for the fluid and the first-order PT for the solid phase, as the most accurate tools to investigate the phase behavior of the model in terms of purely theoretical approaches. It emerges that the use of different procedures to characterize the fluid and the solid phases provides a semiquantitative reproduction of the thermodynamic properties of the C60 model at issue. The overall results appear as a robust benchmark for further theoretical investigations on higher order C(n>60) fullerenes, as well as on other fullerene-related materials, whose description can be based on a modelization similar to that adopted in this work.

Pole topology of the structure functions of continuous systems

We develop a theory of the pole topology of the Laplace transform of the structure functions of continuous N component systems based on the Wiener-Hopf technique. We classify systems according to the spectrum of the NxN matrix Q(t), with elements Q(ij)(t)=delta(ij)-2pi square root [rho(i)rho(j)]integrale(-tr)q(ij)(r)dr, associated with their factor functions q(ij)(r). For the simplest nontrivial class of systems--namely, that with only two eigenvalues of Q(t) different from one--a full and explicit analysis of the pole topology is possible. We illustrate the theory with exactly solvable examples, such as the Percus-Yevick equation for arbitrary mixtures of hard spheres (HS) and polydisperse HS and the mean spherical model for binary mixtures of adhesive spheres.

Thermodynamic properties of a polydisperse system

We use the virial theorem to derive a closed analytic form of the Helmholtz free energy for a polydisperse system of sticky hard spheres (SHS) within the mean spherical model (MSM). To this end we calculate the free energy of the MSM for an N-component mixture of SHS via the virial route and apply to it-after imposing a Lorentz-Berthelot type rule on the interactions-the stochastic (i.e., polydisperse) limit. The resulting excess free energy of this polydisperse system is of the truncatable moment free energy format. We also discuss the compressibility and the energy routes.

Pair distribution functions of a binary Yukawa mixture and their asymptotic behavior

Based on an analytic solution of the mean spherical model for a binary hard sphere Yukawa mixture, we have examined the pair distribution functions g(ij)(r), focusing, in particular, on two aspects: (i) We present two complementary methods to compute the g(ij)(r) accurately and efficiently over the entire r range. (ii) The poles of the Laplace transforms of the pair distribution functions in the left half of the complex plane close to the origin determine the universal asymptotic behavior of the g(ij)(r). Although the meaning of the role of the subsequent poles-which typically are arranged in two branches-is not yet completely clear, there are strong indications that the distribution pattern of the poles is related to the thermodynamic state of the system.