Fourth virial coefficients of asymmetric nonadditive hard-disk mixtures

The fourth virial coefficient of asymmetric nonadditive binary mixtures of hard disks is computed with a standard Monte Carlo method. Wide ranges of size ratio (0.05 ≤ q ≤ 0.95) and nonadditivity (-0.5 ≤ Δ ≤ 0.5) are covered. A comparison is made between the numerical results and those that follow from some theoretical developments. The possible use of these data in the derivation of new equations of state for these mixtures is illustrated by considering a rescaled virial expansion truncated to fourth order. The numerical results obtained using this equation of state are compared with Monte Carlo simulation data in the case of a size ratio q = 0.7 and two nonadditivities Δ = ±0.2.     

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.     

Phase behavior and interfacial properties of nonadditive mixtures of Onsager rods

Within a second virial theory, we study bulk phase diagrams as well as the free planar isotropic-nematic interface of binary mixtures of nonadditive thin and thick hard rods. For species of the same type, the excluded volume is determined only by the dimensions of the particles, whereas for dissimilar ones it is taken to be larger or smaller than that, giving rise to a nonadditivity that can be positive or negative. We argue that such a nonadditivity can result from modeling of soft interactions as effective hard-core interactions. The nonadditivity enhances or reduces the fractionation at isotropic-nematic (IN) coexistence and may induce or suppress a demixing of the high-density nematic phase into two nematic phases of different composition (N(1) and N(2)), depending on whether the nonadditivity is positive or negative. The interfacial tension between coexisting isotropic and nematic phases shows an increase with increasing fractionation at the IN interface, and complete wetting of the IN(2) interface by the N(1) phase upon approach of the triple-point coexistence. In all explored cases bulk and interfacial properties of the nonadditive mixtures exhibit a striking and quite unexpected similarity with the properties of additive mixtures of different diameter ratio.     

Simulation and model development for the equation of state of heteronuclear non‐additive copolymer chains

Molecular dynamics simulations of hard alternating copolymer chains composed of size asymmetric nonadditive segments were performed. Different degrees of polymerization, densities, size ratios and nonadditivities were used. The equation of state for these copolymers was investigated and models based on the first order thermodynamic perturbation theory (TPT1) and the polymeric analog of the Percus‐Yevick approximation (PPY) were developed to predict the compressibility factor of the copolymers. The models predicted the compressibilities of the mixtures accurately at small size ratios, low degrees of polymerization and higher densities. The TPT1 model was generally more accurate in predicting the compressibility factor than the PPY model.     

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.     

Thermodynamic stability of fluid-fluid phase separation in binary athermal mixtures: the role of nonadditivity

We studied the thermodynamic stability of fluid-fluid phase separation in binary nonadditive mixtures of hard-spheres for moderate size ratios. We are interested in elucidating the role played by small amounts of nonadditivity in determining the stability of fluid-fluid phase separation with respect to the fluid-solid phase transition. The demixing curves are built in the framework of the modified-hypernetted chain and of the Rogers-Young integral equation theories through the calculation of the Gibbs free energy. We also evaluated fluid-fluid phase equilibria within a first-order thermodynamic perturbation theory applied to an effective one-component potential obtained by integrating out the degrees of freedom of the small spheres. A qualitative agreement emerges between the two different approaches. We also addressed the determination of the freezing line by applying the first-order thermodynamic perturbation theory to the effective interaction between large spheres. Our results suggest that for intermediate size ratios a modest amount of nonadditivity, smaller than earlier thought, can be sufficient to drive the fluid-fluid critical point into the thermodinamically stable region of the phase diagram. These findings could be significant for rare-gas mixtures in extreme pressure and temperature conditions, where nonadditivity is expected to be rather small.     

The fourth virial coefficient of a nonadditive hard-disc mixture

The fourth virial coefficient of symmetric nonadditive hard-disc mixtures is calculated over a wide range of nonadditivity. The irreducible cluster integrals were evaluated numerically using a standard Monte Carlo method. The coexistence line relative to the fluid-fluid phase transition, calculated through two equations of state built using the new virial coefficients, is compared with some numerical simulation results.     

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.     

On the separation of nonadditive symmetric mixtures in nanoscopic slitlike pores: A simple model for racemic fluids

A grand canonical ensemble Monte Carlo simulation method is used to study the adsorption of nonadditive symmetric mixtures of Lennard-Jones spherical particles in nanoscopic slitlike pores. The walls of the pore are assumed to be formed by the parallel (100) planes of the model face centered cubic crystal of adjustable corrugation potential. It is demonstrated that depending on the nonadditivity effects in the mixture and the pore width the condensed phases formed inside the pore may have different structures. In particular, it is shown that the mixture may separate into layers containing only one component each and the stacking may depend on the pore width and properties of the mixture.     

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.     

Nonadditive nature of nucleobases interactions in model d(GpG) dinucleotide steps

High nonadditive character of intermolecular interaction energy (IIE) has been found for many d(GpG) dinucleotide steps in B‐DNA conformations. Although three‐ and four‐body terms posses opposite signs in all cases, positive nonadditivity is observed. On the other hand, the pairwise additive simplification may still be applied because there is linear correlation between magnitude of additive and nonadditive terms of IIE. The application of the linear regression leads to a higher accuracy with values of standard deviation about 0.5 kcal/mol. The heterogeneity of intermolecular interactions in two subsequent GC pairs was identified as the main source of nonadditivity. The higher the difference between hydrogen bonding and interstrand stacking, the higher the absolute values of three‐ and four‐body terms. This trend is of linear character and may be used for both parametric correction and measure of nonadditivity in d(GpG) steps without necessity of energy calculations for the whole tetramer. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Phase behavior of polymer mixtures with nonadditive hard-sphere potential

The phase behavior of a binary mixture of homopolymers in which macromolecules are composed of tangent hard spheres was studied. The interaction of unlike units is characterized by the contact distance (1/2)(σ_A + σ_B)(1 + Δ), where σ _i is the diameter of the ith sphere (unit) and Δ is the nonadditivity parameter. The effect of nonadditivity was taken into account by means of the perturbation theory relative to the additive system (Δ = 0) considered earlier (Polymer Science, 47, 2146 (2005)) in terms of the Percus-Yevick approximation. The theoretical consideration presented is completely analytical. It was found that a polymer mixture experiences phase separation with an increase in pressure; the two-phase region extends with an increase in both the size ratio between the units α = σ_A/σ_B and the length of the chain per se. Closed phase diagrams were first predicted for athermal mixtures; such diagrams appear at Δ < 0 and certain values of α. It was shown that the thermodynamics of an incompressible mixture of hard-chain molecules at α = 1 follows the Flory-Huggins theory with the temperature-independent interaction parameter. Phase separation in polymer solutions with the nonadditive hard-sphere potential was also analyzed.     

Molecular dynamics and theory for the contact values of the radial distribution functions of hard-disk fluid mixtures

We report molecular dynamics results for the contact values of the radial distribution functions of binary additive mixtures of hard disks. The simulation data are compared with theoretical predictions from expressions proposed by Jenkins and Mancini [J. Appl. Mech. 54, 27 (1987)] and Santos et al. [J. Chem. Phys. 117, 5785 (2002)]. Both theories agree quantitatively within a very small margin, which renders the former still a very useful and simple tool to work with. The latter (higher-order and self-consistent) theory provides a small qualitative correction for low densities and is superior especially in the high-density domain.     

Nanostructural organization and anion effects in the optical Kerr effect spectra of binary ionic liquid mixtures

This article reports a study of the effect of anions on the optical Kerr effect (OKE) spectra of binary ionic liquid mixtures with one mixture comprising the 3-methyl-1-pentylimidazolium ([C 5mim] (+)) cation and the anions PF 6 (-) and CF 3CO 2 (-) (TFA (-)), and another mixture comprising the [C 5mim] (+) cation and the anions Br (-) and bis(trifluomethanesulfonyl)imide (NTf 2 (-)). The spectra were obtained by the use of optical heterodyne-detected Raman-induced Kerr Effect Spectroscopy at 295 K. The OKE spectra of the mixtures are compared with the calculated mole-fraction weighted sum of the normalized OKE spectra of the neat liquids. The OKE spectra are nearly additive for [C 5mim]Br/[C 5mim][NTf 2] mixtures, but nonadditive for [C 5mim][PF 6]/[C 5mim][TFA] mixtures. In the case of the equimolar [C 5mim][PF 6]/[C 5mim][TFA] mixture, the nonadditivity is such that the experimental OKE spectrum is narrower than the calculated OKE spectrum. The additivity or nonadditivity of OKE spectra for IL mixtures can be explained by assuming ionic liquids are nanostructurally organized into nonpolar regions and ionic networks. The ionic networks in mixtures will be characterized by "random co-networks" for anions that are nearly the same in size (PF 6 (-) and TFA (-)) and by "block co-networks" for anions that differ greatly in size (Br (-) and NTf 2 (-)).     

Simulation and model development for the equation of state of self assembling non-additive hard chain–hard monomer mixture

Molecular dynamics simulations for a short hard chain composed of a head and three tail groups interacting with non-additive size interactions with a hard sphere solvent were performed. Different densities and non-additivities were used. The equation of state for this mixture was investigated and models based on the first-order thermodynamic perturbation theory (TPT1) and the polymeric analog of the Percus–Yevick approximation (PPY) were developed to predict the compressibility factor of the mixture. The models predicted the compressibilities of the mixtures accurately at zero and negative non-additivities. However, at positive non-additivities, the models overpredicted the compressibilities especially at high densities. The TPT1 model was generally more accurate in predicting the compressibility factor than the PPY model. Microphase separation was observed at high densities and positive non-additivities.     

Nonadditive interactions and the relative stability of neutral and anionic silver clusters

We discuss the physical nature of nonadditivity in many-particle systems and the methods of calculations of nonadditive contributions to the interaction energy. For neutral clusters, a closed recurrence formula which expresses the energy of m-body interactions through the energies of 2-, 3-, and (m – 1)-body ones is obtained. The general approach for calculation of the nonadditive contribution in the interaction energy of charged systems is developed. The comparative calculation of anionic and neutral silver clusters shows that the geometry of the most stable anionic clusters is established mainly by the additive forces. The stability of neutral silver clusters is determined by the competition of attractive additive forces and repulsive nonadditive ones. © 1995 John Wiley & Sons, Inc.     

Structure and phase behavior of Widom-Rowlinson model calculated from a nonuniform Ornstein-Zernike equation

The second-order integral-equation formalism of [Attard J. Chem. Phys. 91, 3072 (1989); 95, 4471 (1991)], applied previously to one-component hard spheres and Lennard-Jones fluids, as well as to their mixtures, is used to binary Widom-Rowlinson mixtures. Comparison with Monte Carlo simulations of the pair correlation functions and of the demixing phase diagram shows that this method is also quite accurate in the case of highly nonadditive mixtures. Moreover, the results of the second-order theory are compared with previous theoretical predictions. Our interest is also in the calculation of the bridge functions, i.e., parts of the radial distribution functions either not included or simply approximated in the usual theories.     

Fluid-phase diagrams of binary mixtures from constant pressure integral equations

A new algorithm for solving integral equations of the theory of liquids at fixed pressure is introduced. Combining this technique with the Lee's star function approximation for the chemical potentials, we obtain an efficient method to investigate fluid-phase diagrams of binary mixtures. We have tested the capabilities of such technique to study symmetric and asymmetric phase diagrams in nonadditive hard spheres and Lennard-Jones mixtures. We find that the integral equation theories, although approximate, can provide a flexible tool to determine the fluid-phase diagrams whose accuracy is critically dependent on the quality of the closure and of the resulting chemical potentials.     

Cluster algorithm for nonadditive hard-core mixtures

In this paper, we present a cluster algorithm for the numerical simulations of nonadditive hard-core mixtures. This algorithm allows one to simulate and equilibrate systems with a number of particles two orders of magnitude larger than previous simulations. The phase separation for symmetric binary mixtures is studied for different nonadditivities as well as for the Widom-Rowlinson model [B. Widom and J. S. Rowlinson, J. Chem. Phys. 52, 1670 (1970)] in two and three dimensions. The critical densities are determined from finite size scaling. The critical exponents for all the nonadditivities are consistent with the Ising universality class.     

Nonadditivity of the SCF interaction energy in the (LiH)3 complex

The role of nonadditivity of the interaction energy between three LiH molecules was investigated within the SCF ab initio framework. The nonadditive part of the interaction energy is more important in the case of a cyclic structure than in a linear trimer, and is stabilizing in both cases. The value of the ratio of three-body and two-body terms for different points on the energy hypersurface is discussed.