Surface tension of the Widom-Rowlinson model

We consider the computation of the surface tension of the fluid-fluid interface for the Widom-Rowlinson [J. Chem. Phys. 52, 1670 (1970)] binary mixture from direct simulation of the inhomogeneous system. We make use of the standard mechanical route, in which the surface tension follows from the computation of the normal and tangential components of the pressure tensor of the system. In addition to the usual approach, which involves simulations of the inhomogeneous system in the canonical ensemble, we also consider the computation of the surface tension in an ensemble where the pressure perpendicular (normal) to the planar interface is kept fixed. Both approaches are seen to provide consistent values of the interfacial tension. The issue of the system-size dependence of the surface tension is addressed. In addition, simulations of the fluid-fluid coexistence properties of the mixture are performed in the semigrand canonical ensemble. Our results are compared with existing data of the Widom-Rowlinson mixture and are also examined in the light of the vapor-liquid equilibrium of the thermodynamically equivalent one-component penetrable sphere model.     

A perturbation method for the Ornstein-Zernike equation and the generic van der Waals equation of state for a square well potential model

We calculate the generic van der Waals parameters A and B for a square well model by means of a perturbation theory. To calculate the pair distribution function or the cavity function necessary for the calculation of A and B, we have used the Percus-Yevick integral equation, which is put into an equivalent form by means of the Wiener-Hopf method. This latter method produces a pair of integral equations, which are solved by a perturbation method treating the Mayer function or the well width or the functions in the square well region exterior to the hard core as the perturbation. In the end, the Mayer function times the well width is identified as the perturbation parameter in the present method. In this sense, the present perturbation method is distinct from the existing thermodynamic perturbation theory, which expands the Helmholtz free energy in a perturbation series with the inverse temperature treated as an expansion parameter. The generic van der Waals parameters are explicitly calculated in analytic form as functions of reduced temperature and density. The van der Waals parameters are recovered from them in the limits of vanishing density and high temperature. The equation of state thus obtained is tested against Monte Carlo simulation results and found reliable, provided that the temperature is in the supercritical regime. By scaling the packing fraction with a temperature-dependent hard core, it is suggested to construct an equation of state for fluids with a temperature-dependent hard core that mimicks a soft core repulsive force on the basis of the equation of state derived for the square well model.     

Thermodynamic properties of unsymmetrical sticky electrolytes with overlap between ions from Ornstein-Zernike equation

Ornstein-Zernike (OZ) integral equation is solved for unsymmetrical sticky electrolyte solutions with overlap at various distances between ions equal to or less than the collision diameter. Based on the mean-spherical approximation (MSA), all correlation functions and thermodynamic properties can be expressed explicitly in terms of the sticky parameters obtained through a self-consistent procedure. With the reference of an ideal-gas mixture, numerical results of excess internal energy, excess Helmholtz function, osmotic coefficient and activity coefficient for mixtures with stickiness between oppositely charged ions as well as between identically changed ions are presented.     

Scaling fields and pressure mixing in the Widom-Rowlinson model

We address the issues of scaling fields and of pressure mixing in the penetrable sphere model. This model has an exact symmetry locus from which analytical results may be derived. Based on exact results, we demonstrate that the scaling fields are analytic functions of temperature and chemical potential only. We conclude that there is no pressure mixing in this model. Our findings are in accord with numerical simulations for the same model.     

The Ornstein-Zernike equation, critical phenomena, and the equation of state for liquids and gases

It is shown that the Ornstein-Zernike (OZ) equation has two solutions: the standard one, which depends explicitly on the interaction potential, and a second universal one, resulting from the infinity point of the partition function. It is stressed that there are two pressure components: the standard one and a universal one that is valid over the whole of the phase plane. It is concluded that the universal solution parameters depend in general on definite integrals of functions dependent on the interaction potential. In the vicinity of the critical point, however, the dependence on the interaction potential vanishes; i.e., the solution becomes fully universal. It is shown that in this range of the phase diagram, all results of the theory of critical phenomena (scaling theory) follow from the OZ equation.     

Critical behavior of the Widom-Rowlinson mixture: coexistence diameter and order parameter

The critical behavior of the Widom-Rowlinson [J. Chem. Phys. 52, 1670 (1970)] is studied in d = 3 dimensions by means of grand canonical Monte Carlo simulations. The finite-size scaling approach of Kim et al. [Phys. Rev. Lett. 91, 065701 (2003)] is used to extract the order parameter and the coexistence diameter. It is demonstrated that the critical behavior of the diameter is dominated by a singular term proportional to t(1-alpha), with t the relative distance from the critical point, and alpha the critical exponent of the specific heat. No sign of a term proportional to t(2beta) could be detected, with beta the critical exponent of the order parameter, indicating that pressure mixing in this model is small. The critical density is measured to be rhosigma3 = 0.7486 +/- 0.0002, with sigma the particle diameter. The critical exponents alpha and beta, as well as the correlation length exponent nu, are also measured and shown to comply with d = 3 Ising criticality.     

Application of efficient algorithm for solving six-dimensional molecular Ornstein-Zernike equation

In this article, we propose an efficient algorithm for solving six-dimensional molecular Ornstein-Zernike (MOZ) equation. In this algorithm, the modified direct inversion in iterative subspace, which is known as the fast convergent method for solving the integral equation theory of liquids, is adopted. This method is found to be effective for the convergence of the MOZ equation with a simple initial guess. For the accurate averaging of the correlation functions over the molecular orientations, we use the Lebedev-Laikov quadrature. The appropriate number of grid points for the quadrature is decided by the analysis of the dielectric constant. We also analyze the excess chemical potential of aqueous ions and compare the results of the MOZ with those of the reference interaction site model.     

Two solutions for the Ornstein-Zernike equation and critical phenomena in liquids

It is shown that the Ornstein-Zernike equation, the equivalent of the Gibbs distribution, has two simultaneous solutions: analytical and nonanalytical. The analytical solution disappears at a critical point and only the nonanalytical solution remains (which, however, is not zero as we move away from the critical point). It is found that pressure and isothermal compressibility also have two components away from critical point: analytical and nonanalytical.     

Ornstein-Zernike equation for a two-yukawa c(r)

The Ornstein-Zernike equation is solved for a direct correlation function that is the sum of two Yukawa terms outside a core region. Application is made to ionic systems.     

Corridor of existence of thermodynamically consistent solution of the Ornstein-Zernike equation

We obtain the exact equation for a correction to the Ornstein-Zernike (OZ) equation based on the assumption of the uniqueness of thermodynamical functions. We show that this equation is reduced to a differential equation with one arbitrary parameter for the hard sphere model. The compressibility factor within narrow limits of this parameter variation can either coincide with one of the formulas obtained on the basis of analytical solutions of the OZ equation or assume all intermediate values lying in a corridor between these solutions. In particular, we find the value of this parameter when the thermodynamically consistent compressibility factor corresponds to the Carnahan-Stirling formula.     

Structure and phase behavior of archaeal lipid monolayers

We report X-ray reflectivity (XRR) and grazing incidence X-ray diffraction (GIXD) measurements of archaeal bipolar tetraether lipid monolayers at the air-water interface. Specifically, Langmuir films made of the polar lipid fraction E (PLFE) isolated from the thermoacidophilic archaeon Sulfolobus acidocaldarius grown at three different temperatures, i.e., 68, 76, and 81 °C, were examined. The dependence of the structure and packing properties of PLFE monolayers on surface pressure were analyzed in a temperature range between 10 and 50 °C at different pH values. Additionally, the interaction of PLFE monolayers (using lipids derived from cells grown at 76 °C) with the ion channel peptide gramicidin was investigated as a function of surface pressure. A total monolayer thickness of approximately 30 ? was found for all monolayers, hinting at a U-shaped conformation of the molecules with both head groups in contact with the interface. The monolayer thickness increased with rising film pressure and decreased with increasing temperature. At 10 and 20 °C, large, highly crystalline domains were observed by GIXD, whereas at higher temperatures no distinct crystallinity could be observed. For lipids derived from cells grown at higher temperatures, a slightly more rigid structure in the lipid dibiphytanyl chains was observed. A change in the pH of the subphase had an influence only on the structure of the lipid head groups. The addition of gramicidin to an PLFE monolayer led to a more disordered state as observed by XRR. In GIXD measurements, no major changes in lateral organization could be observed, except for a decrease of the size of crystalline domains, indicating that gramicidin resides mainly in the disordered areas of the monolayer and causes local membrane perturbation, only.     

Structure and phase behavior of polyelectrolyte star solutions

Using the recently developed effective interaction potentials between polyelectrolyte stars, we examine the structure and phase behavior of solutions of the same. The effective interaction is ultrasoft and density dependent, owing to the integration of the counterionic degrees of freedom. The latter contribute extensive volume terms that must be taken into account in drawing the phase diagram of the system. The structural behavior of the uniform fluid is characterized by anomalous structure factors, akin to those found previously for solutions of uncharged star polymers. The phase diagram of the system is very rich, featuring a fluid phase at low arm numbers of the stars, two reentrant melting regions, as well as a variety of crystal structures with unusual symmetry. The physical origin of these features can be traced back to the ultrasoft nature of the effective interaction potential.     

The interfacial tension and phase diagram of the Widom-Rowlinson mixture via Monte Carlo simulations

Results of Monte Carlo simulations are reported for the interfacial tension between two fluid phases in a binary mixture of penetrable spheres in which molecular pairs of like species do not interact, while those of unlike species interact as hard spheres. Semigrand canonical ensemble Monte Carlo simulations in a cubic cell with periodic boundary conditions are used to obtain histograms for various system sizes at various densities. At a given density, the interfacial tension and compositions of coexisting phases for an infinite system are evaluated via histogram analysis combined with finite-size scaling. The density dependence of the interfacial tension and phase diagram for an infinite system are thus obtained. The simulated behavior of the interfacial tension close to the critical density corroborates previous suggestions that the model belongs to the three-dimensional Ising universality class.     

Constructing a new closure theory based on the third-order Ornstein-Zernike equation and a study of the adsorption of simple fluids

The third-order Ornstein-Zernike equation (OZ3) is used in the construction of a bridge functional that improves over conventional liquid-theory closures (for example, the hypernetted chain or the Percus-Yevick equations). The OZ3 connects the triplet direct correlation C((3)) to the triplet total correlation h((3)). By invoking the convolution approximation of Jackson and Feenberg, we are able to express the third-order bridge function B(3) as a functional of the indirect correlation γ. The resulting expression is generalized to higher-order bridge terms. This new closure is tested on the adsorption of Lennard-Jones fluid on planar hard surfaces by calculating the density profiles and comparing with Monte Carlo simulations. Particular attention is paid to the cases where molecular depletion on the substrate is evident. The results prove to be highly accurate and improve over conventional closures.     

Structure and phase behavior of self-assembled DPPC-DNA-metal cation complexes

Multilamellar liposomes of dipalmitoylphosphatidylcholine (DPPC) in solution with DNA and bivalent metal cations (Ca2+, Mn2+, Mg2+) self-assemble into a ternary DPPC-DNA-Me2+ complex. The supramolecular structure of the complex consists of an ordered multilamellar assembly where hydrated DNA helices are sandwiched between the lipid bilayers and the metal cations bind the phosphate groups of DNA to the lipid polar heads. In the range of explored incubation times, the complex coexists with the uncomplexed DPPC over the whole temperature range investigated (20-55 degrees C). Accordingly, two distinct coexisting lamellar phases are observed, one corresponding to the ternary complex and the other to the uncomplexed lipid. The structure and thermotropic phase behavior of both of these have been investigated by means of synchrotron X-ray diffraction, and the relevant structural data are deduced from experimental electron density profiles. While the uncomplexed lipid exhibits the same phase behavior as pure DPPC, that is, L beta'-P beta'-L alpha, the thermotropic behavior of the bound lipid in the complex is partially altered. This is manifested as an increase in the main transition temperature and the disappearance of the ripple phase leading to the single -phase transition. The role of the different metal cations in promoting and stabilizing the DNA condensation into the ternary complex is also discussed.     

Ion current rectification behavior of a nanochannel having nonuniform cross-section

Due to its versatile applications in biotechnology, ion current rectification (ICR), which arises from the asymmetric nature of the ion transport in a nanochannel, has drawn much attention, recently. Here, the ICR behavior of a pH-regulated nanochannel comprising two series connected cylindrical nanochannels of different radii is examined theoretically, focusing on the influences of the radii ratio, the length ratio, the bulk concentration, and the solution pH. The results of numerical simulation reveal that the rectification factor exhibits a local maximum with respect to both the radii ratio and the length ratio. The values of the radii ratio and the length ratio at which the local maximum in the rectification factor occur depend upon the level of the bulk salt concentration. The rectification factor also shows a local maximum as the solution pH varies. Among the factors examined, the solution pH influences the ICR behavior of the nanochannel most significantly.     

Application of a maximum likelihood method using implicit constraints to determine equation of state parameters from binary phase behavior data

The maximum likelihood method has been modified to allow the use of implicit constraints in the determination of model parameters from experimental data and the associated experimental uncertainties. The use of the implicit constraints greatly facilitates phase behavior modeling since models typically are complex functions of pressure, temperature, volume, and composition. The new form of the maximum likelihood method is illustrated using recently obtained data for the binary systems m-cresol + quinoline, tetralin + quinoline, and m-cresol + tetralin. Parameters were obtained for six different mixing rules used in conduction with the Soave-Redlich-Kwong equation of state. The mixing rules ranged from a simple interaction parameter to more complex rules involving temperature and volume dependencies.     

Structure and phase behavior of a confined nanodroplet composed of the flexible chain molecules

A polymer density functional theory has been employed for investigating the structure and phase behaviors of the chain polymer, which is modelled as the tangentially connected sphere chain with an attractive interaction, inside the nanosized pores. The excess free energy of the chain polymer has been approximated as the modified fundamental measure-theory for the hard spheres, the Wertheim's first-order perturbation for the chain connectivity, and the mean-field approximation for the van der Waals contribution. For the value of the chemical potential corresponding to a stable liquid phase in the bulk system and a metastable vapor phase, the flexible chain molecules undergo the liquid-vapor transition as the pore size is reduced; the vapor is the stable phase at small volume, whereas the liquid is the stable phase at large volume. The wide liquid-vapor coexistence curve, which explains the wide range of metastable liquid-vapor states, is observed at low temperature. The increase of temperature and decrease of pore size result in a narrowing of liquid-vapor coexistence curves. The increase of chain length leads to a shift of the liquid-vapor coexistence curve towards lower values of chemical potential. The coexistence curves for the confined phase diagram are contained within the corresponding bulk liquid-vapor coexistence curve. The equilibrium capillary phase transition occurs at a higher chemical potential than in the bulk phase.     

Isothermal compressibility and correlation radius near the critical point: Numerical analysis of the Ornstein-Zernike equation

Solution of the Ornstein-Zernike equation is analyzed numerically in the Percus-Yevick and hyperchain approximations for a system of Lennard-Jones particles in a critical region. The temperature dependences of correlation functions, isothermal compressibility η, and correlation radius of density fluctuations ζ are investigated at a critical density; the corresponding critical indices are determined. It is shown that the Percus-Yevick approximation yields satisfactory results when the correlation functions are calculated within a range corresponding to approximately 50 atomic (molecular) diameters. In this case, with ≈5% deviations from the critical temperature, the calculated and experimental values of η and critical indices are in good agreement. Tver State University. Translated fromZhurnal Strukturnoi Khimii, Vol. 36, No. 5, pp. 799–807, September–October, 1995. Translated by I. Izvekova