Distribution functions of a heteronuclear hard dumbbell at a hard wall. Pure fluid and mixtures with hard spheres

Starting from well-known relations for the derivatives of the radial distribution functions of a mixture of fluids, and allowing the diameter of one particle to become exceedingly large, three sum rules for a fluid with density inhomogeneities are obtained. None of these sum rules are new. However, the relation between the Lovett–Mou–Buff–Wertheim and the Born–Green hierarchy of equations seems not well known. The accuracy of a recent parametrization of the pair correlation of hard spheres near a hard wall and of the solutions of the Percus–Yevick and hypernetted-chain equation for this same function are examined by determination of how well these functions satisfy these sum rules and the accuracy of their surface tension, calculated from the sum rule of Triezenberg and Zwanzig. Generally speaking, the Percus–Yevick theory gives the best results and the hypernetted-chain approximation gives the worst results with the parametrization being intermediate.

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Distribution functions of the hard heteronuclear dumbbells and of their mixtures with hard spheres near a hard wall

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc2009524 ◽

2010 ◽

Vol 75 (3) ◽

pp. 289-302 ◽

Cited By ~ 2

Author(s):

Tomáš Boublík

Keyword(s):

Distribution Function ◽

Hard Spheres ◽

Packing Fraction ◽

Distribution Functions ◽

Sphere Diameter ◽

Hard Wall ◽

Simple Method ◽

Body Distribution ◽

Planar Wall ◽

Different Diameters

The recently proposed method to determine the hard body distribution function on the basis of values of the residual chemical potentials of a pair of hard molecules and that of the corresponding combined body is applied to describe behavior of the inhomogeneous systems of pure heteronuclear hard dumbbells or a mixture of heteronuclear dumbbells with hard spheres near a hard wall. Two variants of the main orientation of the dumbbells – i.e. the perpendicular orientation with respect to the hard planar wall – are studied and several values of the packing fraction are considered. The used simple method yields a fair prediction of the slices of the distribution function or average correlation function for the heteronuclear dumbbell (composed of two hard spheres with rather different diameters (σ2/σ1 = 0.5) and site–site separation (l/σ1 = 0.625)) near a wall; in the case of mixtures of hard spheres and hard heteronuclear dumbbells the hard sphere diameter σhs = σ1.

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Radial Distribution Function in the Hard Sphere Mixtures

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc20080388 ◽

2008 ◽

Vol 73 (3) ◽

pp. 388-400 ◽

Cited By ~ 3

Author(s):

Tomáš Boublík

Keyword(s):

Aspect Ratio ◽

Hard Sphere ◽

Hard Spheres ◽

Heterogeneous Systems ◽

Distribution Functions ◽

Ternary Mixtures ◽

Hard Wall ◽

Density Profiles ◽

Equilibrium Structures

Equilibrium structures of both homogeneous and heterogeneous systems are, within statistical thermodynamics, characterized by distribution functions. Using the approach proposed recently - based on the determination of the cavity functions for the pair of hard spheres (HS) and the combined body - we studied the effect of different choices of the probe HS (which determines the shape of the combined hard body - enlarged dumbbell) on the prediction of the distribution functions in binary mixtures of HS with the aspect ratio 0.9, ternary mixtures with diameter ratios 1, 0.6 and 0.3, and density profiles of HS mixture with the aspect ratio 2 near a hard wall. It was found that the method, that uses the average geometric functionals determined for the probe HS with individual diameters multiplied by the respective mole fractions yields better results than the approaches based on average probe diameters.

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