Nonadditive Hard-sphere Mixtures Research Articles

Population Inversion of Confined Symmetric Nonadditive Hard-Sphere Mixtures

Population Inversion of Confined Symmetric Nonadditive Hard-Sphere Mixtures

Phase equilibria in polydisperse nonadditive hard-sphere systems

Colloidal particles naturally exhibit a size polydispersity that can greatly influence their phase behavior in solution. Nonadditive hard-sphere (NAHS) mixtures are simple and well-suited model systems to represent phase transitions in colloid systems. Here, we propose an analytical equation of state (EOS) for NAHS fluid mixtures, which can be straightforwardly applied to polydisperse systems. For positive values of the nonadditivity parameter Delta the model gives accurate predictions of the simulated fluid-fluid coexistence curves and compressibility factors. NPT Monte Carlo simulations of the mixing properties of the NAHS symmetric binary mixture with Delta>0 are reported. It is shown that the enthalpy of mixing is largely positive and overcomes the positive entropy of mixing when the pressure is increased, leading to a fluid-fluid phase transition with a lower critical solution pressure. Phase equilibria in polydisperse systems are predicted with the model by using the density moment formalism [P. Sollich, Adv. Chem. Phys. 116, 265 (2001)]. We present predictions of the cloud and shadow curves for polydisperse NAHS systems composed of monodisperse spheres and polydisperse colloid particles. A fixed nonadditivity parameter Delta > 0 is assumed between the monodisperse and polydisperse spheres, and a Schulz distribution is used to represent the size polydispersity. Polydispersity is found to increase the extent of the immiscibility region. The predicted cloud and shadow curves depend dramatically on the upper cutoff diameter sigmac of the Schulz distribution, and three-phase equilibria can occur for large values of sigmac.

On the Origin of Excess Thermodynamic Quantities in Liquid Mixtures

The nature of the interactions between components in liquid mixtures has been investigated by means of Brillouin light scattering. Several binary systems, able of mixing over the whole concentration range, have been studied. In each case, deviations of the adiabatic compressibility from ideal behaviour have been observed. This result has been interpreted within the framework of a well-established theoretical model, namely the nonadditive hard-sphere mixture. Despite similar findings were rationalized in terms of enhanced interactions between molecules, the analysis of excess thermodynamic functions indicates that they are mainly due to excluded volume effects and that the differences in the local intermolecular interaction act as higher order contributions: this can be a general consideration for liquid mixtures. A discussion is proposed on the revaluation of excess thermodynamic data and on their ability in providing direct information on intermolecular interactions.

Fundamental measure density functional theory for nonadditive hard-core mixtures: The one-dimensional case

We treat a one-dimensional binary mixture of hard-core particles that possess nonadditive diameters. For this model, a density functional theory is constructed following similar principles as an earlier extension of Rosenfeld's fundamental measure theory to three-dimensional nonadditive hard-sphere mixtures. The theory applies to arbitrary positive and moderate negative nonadditivity and reduces to Percus' exact functional in the additive case. Bulk direct correlation functions are obtained as functional derivatives of the excess free energy functional. Results for the partial pair correlation functions in bulk, as calculated via the Ornstein-Zernike route and using the direct correlation functions as input, show very good agreement with results from our Monte Carlo computer simulations of the mixture.

Excess Thermodynamic Properties in Mixtures of a Representative Room-Temperature Ionic Liquid and Acetonitrile

The nature of the interactions between a representative room-temperature ionic liquid, namely 1-butyl-3-methyl imidazolium tetrafluoroborate ([BMIM][BF(4)]) and a common organic solvent, acetonitrile (CH(3)CN) has been investigated by means of Brillouin light scattering, over the whole concentration range and in the temperature range from -20 to 45 degrees C. Negative deviations from the ideal behavior of both molar volumes and adiabatic compressibility have been observed. This result has been interpreted within the framework of a well-established theoretical model, namely a nonadditive hard-sphere mixture. Despite that similar findings were rationalized in terms of enhanced interactions between molecules, a more detailed analysis of excess thermodynamic functions indicates that they are mainly due to excluded volume effects and that the differences in local intermolecular interactions act as higher order contributions: we have found that this can be a general feature of liquid mixtures. On this basis we present a reconsideration for excess thermodynamic data and for their role in providing direct information on intermolecular interactions.

Virial Coefficients and Demixing of Athermal Nonadditive Mixtures

We compute the fourth virial coefficient of a binary nonadditive, hard-sphere mixture over a wide range of deviations from diameter additivity and size ratios. Hinging on this knowledge, we build up a y expansion (Barboy, B.; Gelbart, W. N. J. Chem. Phys. 1979, 71, 3053) in order to trace the fluid-fluid coexistence lines, which we then compare with the available Gibbs-ensemble Monte Carlo data and with the estimates obtained through two refined integral-equation theories of the fluid state. We find that in a regime of moderately negative nonadditivity and largely asymmetric diameters, relevant to the modeling of sterically and electrostatically stabilized colloidal mixtures, the fluid-fluid critical point is unstable with respect to crystallization.

Demixing can occur in binary hard-sphere mixtures with negative nonadditivity

A binary fluid mixture of nonadditive hard spheres characterized by a size ratio gamma = sigma(2)/sigma(1) < 1 and a nonadditivity parameter Delta = 2 sigma(12)/(sigma(1) + sigma(2)) - 1 is considered in infinitely many dimensions. From the equation of state in the second virial approximation (which is exact in the limit d--> infinity) a demixing transition with a critical consolute point at a packing fraction scaling as eta approximately d2(-d) is found, even for slightly negative nonadditivity, if Delta >-1/8 (ln gamma)(2). Arguments concerning the stability of the demixing with respect to freezing are provided.

Fluid–fluid and fluid–solid phase separation in nonadditive asymmetric binary hard-spheremixtures

Very asymmetric mixtures of hard spheres naturally arise in the modellization of colloidaldispersions. Effective potentials have emerged as a powerful tool for describing thesesystems and have often been employed to extract the phase diagram in both theadditive and nonadditive cases. However, most theoretical investigations havebeen carried out by means of mean-field-like approaches, so their quantitativeaccuracy remains to be assessed. Here we employ previously determined effectivepotentials for nonadditive hard-sphere mixtures to study the fluid–fluid phasetransition by the hierarchical reference theory (HRT), which is designed to takerealistically into account the effects of long-range fluctuations on phase separation.Fluid–solid equilibrium is addressed by supplementing HRT with thermodynamicperturbation theory for the solid phase. We apply this approach both to a potential withadjustable nonadditivity parameter (Louis et al 2000 Phys. Rev. E 61 R1028) and to theAsakura–Oosawa (AO) potential, which represents an extreme case of nonadditivity. Ourresults for the phase diagram, including modified hypernetted chain (MHNC)calculations, are compared to those of other liquid-state theories and are found toagree nicely with available simulation data. Unlike commonly adopted liquid-statetheories, HRT is capable both of getting arbitrarily close to the fluid–fluid criticalpoint, and of giving nontrivial critical exponents. In particular, the fluid–fluidcoexistence curve is much flatter than that obtained via perturbation theory, inagreement with a recent finite-size scaling Monte Carlo analysis of the AO model.

Equation of state of nonadditive d-dimensional hard-sphere mixtures

An equation of state for a multicomponent mixture of nonadditive hard spheres in d dimensions is proposed. It yields a rather simple density dependence and constitutes a natural extension of the equation of state for additive hard spheres proposed by us [A. Santos, S. B. Yuste, and M. Lopez de Haro, Mol. Phys. 96, 1 (1999)]. The proposal relies on the known exact second and third virial coefficients and requires as input the compressibility factor of the one-component system. A comparison is carried out both with another recent theoretical proposal based on a similar philosophy and with the available exact results and simulation data in d=1, 2, and 3. Good general agreement with the reported values of the virial coefficients and of the compressibility factor of binary mixtures is observed, especially for high asymmetries and/or positive nonadditivities.

Integral Equation Theory for Symmetric Nonadditive Hard Sphere Mixtures

An integral equation theory is presented for the pair correlation functions and phase behavior of symmetric nonadditive hard sphere mixtures with hard sphere diameters given by sigma(A)(A)() = sigma(BB) = lambdad and sigma(AB) = d. This mixture exhibits a fluid-fluid phase separation into an A-rich phase and a B-rich phase at high densities. The theory incorporates, into the closure approximation, all terms that can be calculated exactly in the density expansion of the direct correlation functions. We find that the closure approximation developed in this work is accurate for the structure and phase behavior over the entire range of lambda, when compared to computer simulations, and is significantly more accurate than the previous theories.

Nonadditive Binary Hard Sphere Mixture in Disordered Hard Sphere Matrices: Integral Equations and Computer Simulation

We have studied adsorption of nonadditive binary symmetric hard sphere mixtures in hard sphere matrices and in templated hard sphere matrices. Adsorption is described by using replica Ornstein−Zernike integral equations complemented by Martynov−Sarkisov closure relations. This theory permits straightforward calculation of the chemical potential of fluid species and to describe equilibrium between the bulk phase in a model adsorbent body. Theoretical results for adsorption isotherms agree well with Monte Carlo computer simulation data. On the other hand, we have captured the effect of matrix modification on adsorption via templating. Finally, we have described the coexistence curve (in terms of concentration vs density and in terms of concentration vs chemical potentials of fluid species) for the demixing transition by using theoretical procedure and by semigrand computer simulation in hard sphere matrices and in corresponding templated matrices. We have shown that the explanation of the phase behavior is ...

Replica Ornstein-Zernike self-consistent theory for mixtures in random pores.

We present a self-consistent integral equation theory for a binary liquid in equilibrium with a disordered medium, based on the formalism of the replica Ornstein-Zernike (ROZ) equations. Specifically, we derive direct formulas for the chemical potentials and the zero-separation theorems (the latter provide a connection between the chemical potentials and the fluid cavity distribution functions). Next we solve a modified-Verlet closure to ROZ equations, which has built-in parameters that can be adjusted to satisfy the zero-separation theorems. The degree of thermodynamic consistency of the theory is also kept under control. We model the binary fluid in random pores as a symmetrical binary mixture of nonadditive hard spheres in a disordered hard-sphere matrix and consider two different values of the nonadditivity parameter and of the quenched matrix packing fraction, at different mixture concentrations. We compare the theoretical structural properties as obtained through the present approach with Percus-Yevick and Martinov-Sarkisov integral equation theories, and assess both structural and thermodynamic properties by performing canonical standard and biased grand canonical Monte Carlo simulations. Our theory appears superior to the other integral equation schemes here examined and provides reliable estimates of the chemical potentials. This feature should be useful in studying the fluid phase behavior of model adsorbates in random pores in general.

Critical-point and coexistence curve properties of a symmetric mixture of nonadditive hard spheres: A finite size scaling study

The behavior of binary mixtures of nonadditive hard spheres with positive nonadditivity parameter is investigated. The coexistence curves are calculated with a high accuracy in Monte Carlo simulations. Finite size scaling analysis is used to determine precisely the location of the critical point. The calculations strongly support the hypothesis that mixtures of nonadditive hard spheres belong to the Ising universality class. The dependence of the critical packing fraction on the nonadditivity parameter is investigated.

Monte Carlo simulations for the phase behavior of symmetric nonadditive hard sphere mixtures

Computer simulation results are presented for the phase behavior of a symmetric binary mixture of nonadditive hard spheres. In this model, the hard sphere diameters are given by σAA=σBB=λd and σAB=d. At high densities and for small enough λ, this hard sphere mixture exhibits a fluid–fluid phase separation into an A-rich and a B-rich phase. Semigrand ensemble simulations are performed for the critical point and the phase behavior of this model for various values of λ. The results for the critical density are significantly different from previous simulation estimates. A comparison of our simulation results to existing theories shows that none of the theories are accurate for the location of the critical point, over the entire range of λ.

Stability and interfacial properties of confined nonadditive hard-sphere binary mixture

Monte-Carlo simulations are performed to investigate fluid–fluid phase equilibria and interfacial properties of nonadditive hard-sphere binary mixtures adsorbed in a slit pore. The behavior of critical density with wall separation and a nonadditive parameter is analyzed using mean field theory and simulations. The mixtures exhibit phase separation with the critical density ρ c larger than its bulk counterpart. It is found that ρ c decreases by increasing both the pore width H and the nonadditive parameter. The mean-field-like perturbation theory predicts ρ c − ρ bulk c ∼ H −1; for large H and small ρ c , good agreement with simulation is found. The phase diagram, density profile, and interfacial tension are also obtained using different simulation methods. Interfacial tension, γ, increases with the nonadditive parameter for a given total density and H. The effect of confining is to increase γ for a given nonadditive parameter. A coupling between pore size and nonadditivity is discussed in connection with a possible spatially anisotropic separation.

Entropy and Fluid−Fluid Separation in Nonadditive Hard-Sphere Mixtures: The Asymmetric Case

We report Monte Carlo simulation results for the thermodynamic and structural properties of binary nonadditive mixtures of hard spheres with not too dissimilar sizes. The simulations were carried out over a range of parameters where fluid-fluid separation is known to compete with freezing. We investigated the onset of structural ordering in a one-phase scheme as that provided by the residual multiparticle entropy, an integrated measure of the weight of spatial correlations involving more than two particles in the configurational entropy of the system. This approach has been already tested in the symmetric case [Saija, F.; Pastore, G.; Giaquinta, P. V. J. Phys. Chem. B 1998, 102, 10368]. The present study confirms the indication that a rather small amount of nonadditivity may significantly influence the phase behavior of the mixture also in a thermodynamic regime where osmotic depletion effects do not play a leading role.

Theory of asymmetric nonadditive binary hard-sphere mixtures.

It is shown that the formal procedure of integrating out the degrees of freedom of the small spheres in a binary hard-sphere mixture works equally well for nonadditive as it does for additive mixtures. For highly asymmetric mixtures (small size ratios) the resulting effective Hamiltonian of the one-component fluid of big spheres, which consists of an infinite number of many-body interactions, should be accurately approximated by truncating after the term describing the effective pair interaction. Using a density functional treatment developed originally for additive hard-sphere mixtures the zero, one, and two-body contribution to the effective Hamiltonian are determined. It is demonstrated that even small degrees of positive or negative nonadditivity have significant effect on the shape of the depletion potential. The second virial coefficient B2, corresponding to the effective pair interaction between two big spheres, is found to be a sensitive measure of the effects of nonadditivity. The variation of B2 with the density of the small spheres shows significantly different behavior for additive, slightly positive and slightly negative nonadditive mixtures. Possible repercussions of these results for the phase behavior of binary hard-sphere mixtures are discussed and it is suggested that measurements of B2 might provide a means of determining the degree of nonadditivity in real colloidal mixtures.

Effective potentials for polymers and colloids: beyond the van der Waals picture of fluids?

This contribution briefly reviews some recent work demonstrating the partial breakdown of the colloidal fluid <--> atomic fluid analogy. The success of liquid state theory for atomic fluids stems in part from the van der Waals picture, where steric interactions dominate the structure, and attractive interactions can be added as a perturbation. For complex fluids described by effective potentials, this picture may break down. In the first example discussed, depletion potentials in non-additive hard-sphere mixtures are shown to be surprisingly complex, leading to fluid structure and fluid-solid transitions dominated by properties of the attractive potentials instead of by the hard-cores. Many colloidal suspensions, and possibly globular proteins, fall into this {\em energetic fluid} category. In the second example, the coarse-graining of polymers leads to soft-core effective potentials and associated {\em mean field fluid} behaviour distinguished by a breakdown of the virial expansion, an equation of state that is nevertheless nearly linear in density, and correlation functions well described by the random phase approximation.

Fluid–fluid phase equilibria in disordered porous media. Nonadditive hard sphere mixture

We report a computer simulation and integral equation study of fluid–fluid phase equilibria of nonadditive hard sphere binary mixture adsorbed in disordered hard sphere matrix. The mixture exhibits phase separation with critical density ρ c f lower than its bulk counterpart. It is found that ρ c f decreases with increasing both porosity and nonadditivity parameter.

Crystallization and phase separation in nonadditive binary hard-sphere mixtures

We calculate for the first time the full phase diagram of an asymmetric nonadditivehard-sphere mixture. The nonadditivity strongly affects the crystallization and the fluid-fluid phase separation. The global topology of the phase diagram is controlled by an effective size ratio y(eff), while the fluid-solid coexistence scales with the depth of the effective potential well.