Hard-body Mixtures Research Articles

Entropy effects at dimerisation equilibrium in hard-sphere fluids with different diameters

Statistical-thermodynamic analysis for the calculation of chemical equilibrium in the case of dimerization of hard-sphere monomer species of different sizes into an asymmetric dumbbell was considered. The description of the dimerization was carried out within two models: a) the simplest yet analytical description of the van der Waals type in order to take into account excluded volume effects, and b) the approach of the Largo and Solana type for more accurate description of hard-body mixtures with the effective form factor. Deviations of dimerization equilibrium from ideality depending on the ratio of the reacting monomers' diameters and their overlapping in the dimer were analyzed. It was shown that the reduction in entropy of the resulting hard-body mixture is more noticeable with a larger difference in the diameters but with less fusion of spheres in the dimer.

Many-fluid Onsager density functional theories for orientational ordering in mixtures of anisotropic hard-body fluids

The extension of Onsager's second-virial theory [L. Onsager, Ann. N.Y. Acad. Sci. 51, 627 (1949)] for the orientational ordering of hard rods to mixtures of nonspherical hard bodies with finite length-to-breadth ratios is examined using the decoupling approximations of Parsons [Phys. Rev. A 19, 1225 (1979)] and Lee [J. Chem. Phys. 86, 6567 (1987); 89, 7036 (1988)]. Invariably the extension of the Parsons-Lee (PL) theory to mixtures has in the past involved a van der Waals one-fluid treatment in which the properties of the mixture are approximated by those of a reference one-component hard-sphere fluid with an effective diameter which depends on the composition of the mixture and the molecular parameters of the various components; commonly this is achieved by equating the molecular volumes of the effective hard sphere and of the components in the mixture and is referred to as the PL theory of mixtures. It is well known that a one-fluid treatment is not the most appropriate for the description of the thermodynamic properties of isotropic fluids, and inadequacies are often rectified with a many-fluid (MF) theory. Here, we examine MF theories which are developed from the virial theorem and the virial expansion of the Helmholtz free energy of anisotropic fluid mixtures. The use of the decoupling approximation of the pair distribution function at the level of a multicomponent hard-sphere reference system leads to our MF Parsons (MFP) theory of anisotropic mixtures. Alternatively the mapping of the virial coefficients of the hard-body mixtures onto those of equivalent hard-sphere systems leads to our MF Lee (MFL) theory. The description of the isotropic-nematic phase behavior of binary mixtures of hard Gaussian overlap particles is used to assess the adequacy of the four different theories, namely, the original second-virial theory of Onsager, the usual PL one-fluid theory, and the MF theories based on the Lee (MFL) and Parsons (MFP) approaches. A comparison with the simulation data for the mixtures studied by Zhou et al. [J. Chem. Phys. 120, 1832 (2004)] suggests that the Parsons MF description (MFP) provides the most accurate representation of the properties of the isotropic-nematic ordering transition and density (pressure) dependence of the order parameters.

Entropic segregation in smectic phases of hard-body mixtures

Using an extension of the Parsons–Lee density-functional theory, we have calculated the phasebehaviour of mixtures of hard bodies, focusing on the formation of smectic phases. The interactionsare represented by hard spherocylinders, and the mixtures have two components of lengthsL1,L2 andwidths D1,D2, respectively,with D1 = D2. The special case where one of the components is a hard sphere(L1 = 0,) is also studied. Particular emphasis is put on the interplay between smectic-phaseformation and smectic–smectic segregation. In general, smectic–smectic segregation is seento occur in a wide range of compositions and pressures, except when the length ratio is relatively close to unity, i.e. particles have similar lengths; in this casesegregation appears only at high pressure. Finally, in the case whereq is very different from unity and the composition is such that there is a small fraction oflong molecules, even when the mixture is macroscopically homogeneous, there appears amicrosegregated phase where the minority component is expelled to the interstitial regionsbetween the smectic layers.

Self-consistent equations of state for hard body mixtures

The self-consistency (S-C) constraints on the solute chemical potential and equation of state are stated and employed to find corrections to thermodynamic functions in the colloidal limit for the most often used equations of state. It is shown that the S-C approach and Henderson's expression for the contact radial distribution functions yield the same correction term in the case of the Boublik—Mansoori—Carnahan—Starling—Leland (BMCSL) equation of state for hard spheres. For hard sphere (and hard convex body) mixtures a new variant of the equation of state and Helmholtz energy is proposed that fulfils better the self-consistency constraints than the frequently used equations. It is shown that the correction term for Δμ 2 in hard convex body mixtures described by improved scaled particle theory differs from that for BMCSL only by the non-sphericity parameter. For the Kolafa—Boublik and modified scaled particle theory versions the correction terms are more complex.

Fourth virial coefficient of hard-body mixtures in two and three dimensions

We have computed the fourth virial coefficient of a binary mixture composed of different-sized hard discs and hard spheres with additive diameters. The irreducible cluster integrals were evaluated numerically using the Monte Carlo method.

ERRATUM Fourth virial coefficient of hard-body mixtures in two and three dimensions

ERRATUM Fourth virial coefficient of hard-body mixtures in two and three dimensions

Entropy driven demixing: why?

An exact solution is found for a model of N different, in general, hard convex bodies moving without rotation in independent cells of hard walls and fixed total volume. It is shown that the entropy of the system is maximal when the cell shapes are the same as the body shapes, and their volumes depend on the body sizes in a universal way. The obtained distribution of volume into cells indicates the mechanism of phase separation in mixtures of hard bodies of different sizes and/or shapes. A planar system of hard squares and equilateral triangles of equal sides is considered as an example. An argument is presented that these bodies do not mix near close packing.

Fourth virial coefficient of hard-body mixtures in two and three dimensions

We have computed the fourth virial coefficient of a binary mixture composed of different-sized hard discs and hard spheres with additive diameters. The irreducible cluster integrals were evaluated numerically using the Monte Carlo method.

Fourth virial coefficient of hard-body mixtures in two and three dimensions

Fourth virial coefficient of hard-body mixtures in two and three dimensions

Excess entropy of the systems of molecules differing in size and shape

The excess entropy of mixing of mixtures of hard spheres and spherocylinders is determined from an equation of state of hard convex bodies. The obtained dependence of excess entropy on composition was used to find the accuracy of determining ΔSE from relations employed for the correlation and prediction of vapour-liquid equilibrium. Simple rules were proposed for establishing the mean parameter of nonsphericity for mixtures of hard bodies of different shapes allowing to describe the P-V-T behaviour of solutions in terms of the equation of state fo pure substance. The determination of ΔSE by means of these rules is discussed.