A general mixture theory. I. Mixtures of spherical molecules

Virial coefficients, equation of state, and demixing of binary asymmetric nonadditive hard-disk mixtures

Values of the fifth virial coefficient, compressibility factors, and fluid-fluid coexistence curves of binary asymmetric nonadditive mixtures of hard disks are reported. The former correspond to a wide range of size ratios and positive nonadditivities and have been obtained through a standard Monte Carlo method for the computation of the corresponding cluster integrals. The compressibility factors as functions of density, derived from canonical Monte Carlo simulations, have been obtained for two values of the size ratio (q = 0.4 and q = 0.5), a value of the nonadditivity parameter (Δ = 0.3), and five values of the mole fraction of the species with the biggest diameter (x₁ = 0.1, 0.3, 0.5, 0.7, and 0.9). Some points of the coexistence line relative to the fluid-fluid phase transition for the same values of the size ratios and nonadditivity parameter have been obtained from Gibbs ensemble Monte Carlo simulations. A comparison is made between the numerical results and those that follow from some theoretical equations of state.

Liquid-Liquid Phase Transitions in Tetrahedrally Coordinated Fluids via Wertheim Theory

Network interpenetration has been proposed as a mechanism for generating liquid-liquid phase transitions in one component systems. We introduce a model of four coordinated particles, which explicitly treats the system as a mixture of two interacting interpenetrating networks that can freely exchange particles. This model can be solved within Wertheim's theory for associating fluids and shows liquid-liquid phase separations (in addition to the gas-liquid) for a wide range of model parameters. We find that originating a liquid-liquid transition requires a small degree of interpenetrability and a preference for intranetwork bonding. Physically, these requirements can be seen as controlling the softness of the particle-particle interaction and the bond flexibility, in full agreement with recent findings [Smallenburg, F.; Filion, L.; Sciortino, F. Nat. Phys. 2014, 10, 653].

Virial coefficients, thermodynamic properties, and fluid-fluid transition of nonadditive hard-sphere mixtures

Different theoretical approaches for the thermodynamic properties and the equation of state for multicomponent mixtures of nonadditive hard spheres in d dimensions are presented in a unified way. These include the theory by Hamad, our previous formulation, the original MIX1 theory, a recently proposed modified MIX1 theory, as well as a nonlinear extension of the MIX1 theory proposed in this paper. Explicit expressions for the compressibility factor, Helmholtz free energy, and second, third, and fourth virial coefficients are provided. A comparison is carried out with recent Monte Carlo data for the virial coefficients of asymmetric mixtures and with available simulation data for the compressibility factor, the critical consolute point, and the liquid-liquid coexistence curves. The merits and limitations of each theory are pointed out.

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.

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.

Thermodynamic perturbation theory for fused sphere hard chain fluids using nonadditive interactions

A model is developed for the equation of state of fused chains based on Wertheim thermodynamic perturbation theory and nonadditive size interactions. The model also assumes that the structure (represented by the radial distribution function) of the fused chain fluid is the same as that of the touching hard sphere chain fluid. The model is completely based on spherical additive and nonadditive size interactions. The model has the advantage of offering good agreement with simulation data while at the same time being independent of fitted parameters. The model is most accurate for short chains, small values of Delta (slightly fused spheres) and at intermediate (liquidlike) densities.

Investigation of the microstructure of micelles formed by hard-sphere chains interacting via size nonadditivity by discontinuous molecular dynamics simulation

Micelle formation by short nonadditive hard surfactant chains was investigated at different size ratios, reduced densities, and nonadditivity parameters using molecular dynamics simulation. It was found that spherical, cylindrical, lamellar, and reverse micelles can form in systems with different head, tail, and solvent characteristics. Hard-core surfactant chains composed of a head segment and three tail segments were simulated in a solvent of hard spheres. The formation of micelles was found to be a strong function of the packing fraction and nonadditivity parameter. Micelles were more stable at higher densities and larger nonadditivity parameters. At lower densities, micelles tended to break into small, dynamic globules.