Evaluation of thesscf andpy approximations for quadrupolar fluids

Two approximations, the single super chainf-expansion (sscf), and Percus-Yevick (py) approximation, are evaluated for a molecular fluid in which the molecules interact with a pair potential, that is the sum of Lennard-Jones and quadrupole-quadrupole parts at two values of reduced quadrupole moment. These results are compared with Monte-Carlo results. Except for the harmonic coefficienth (222;r), thesscf approximation seems to be quite accurate for the lower value of quadrupole moment but at higher valuespy approximation produces much better results except forh(220;r).     

A turbidity study of particle interaction in latex suspensions

A turbidimetric analysis of particle interaction in latex suspensions is given. The turbidity measured at different wavelengths can be rendered by the product of an integrated form factorQ(²) and a suitably defined integrated structure factorZ(²,c). This factorization rests on the expansion of the form factor of the particlesP(q) and the structure factorS(q) [q=(4/)sin(/2); : scattering angle] of the system in even powers ofq. The accuracy of this approximation has been shown by calculating the turbidity for a system of hard spheres in terms of the Percus-Yevick structure factor by numerical integration. Also, the effect of polydispersity has been taken into account within the frame of Percus-Yevick-Vrij theory for non-uniform hard spheres. It is shown that the influence of small polydispersity (standard deviation below 8%) is within experimental uncertainty. The method is applied to precise UV-spectra (400800 nm) obtained from a polystyrene latex with a diameter of 77.4 nm. The integrated structure factorZ(²,c) obtained experimentally can be interpreted in terms of an effective diameter of interaction giving a measure for the strength of electrostatic interaction.     

Estimation of the parameters in the Kirkwood-Buff theory of solution using Percus-Yevick fluid mixtures

Parameters G _ij in the Kirkwood-Buff theory of solution were calculated for binary fluid mixtures of Lennard-Jones (LJ) 6–12 molecules by using the Percus-Yevick theory. Calculations were carried out for various parameters in the LJ potential. Under the Lorentz-Berthelot rules, G ₁₁ and/or G ₂₂ -composition curves do not show a maximum for any parameters in the LJ potential. When the intermolecular interaction between different species becomes much weaker than that expected from the Berthelot rule, G ₁₁ and G ₂₂ show a maximum and G ₁₂ a minimum. The pressure effect on G _ij was examined and calculations at constant pressure were also carried out. G _ij is almost independent of the pressure when the ratio of the molecular volume of two components is in the range 1.0 to 2.5. Comparison was made between experimental and calculated G _ij for cyclohexane-2,3-dimethylbutane and acetonitrile-toluene systems. For the latter system, the quantitative agreement between the calculated and experimental could not be obtained but showed that the characteristics of G _ij -composition curves can be explained qualitatively by using the PY theory.Adjunct Associate Professor of Institute for Molecular Science (April 1982–March 1984)     

Sticky spheres and related systems

Some properties of a system of hard-core particles with attractive wells in the Baxter sticky-sphere limit and a related limit are considered, as is the approach to these limits. A demonstration of the result of Stell and Williams that sticky spheres of equal diameter in the Baxter limit are not thermodynamically stable is given, and the way in which size polydispersity can be expected to restore thermodynamic stability is discussed. The implications of these results for the PY sticky-sphere approximation and recent sticky-sphere computer simulations are then examined. It is concluded that the Baxter PY sticky-sphere approximation for a monodisperse system may well be a reasonable one for a slightly polydisperse system of sticky spheres and that existing simulation results may also be relevant to such a system. How polydisperse a system must be in quantitative terms in order for the PY approximation to be useful remains to be seen, however. The question of whether the PY sticky-sphere approximation may prove to be useful and appropriate in describing monodisperse systems with pair potentials for which the attractive wells arenot extremely narrow is also considered; it is noted that firm evidence concerning this question also appears to be lacking. Implications for systems near, but not in, the limit of zero attractive-well width are also considered, especially in terms of the relative size of the well width and the degree of size polydispersity in the repulsive cores. The possible pertinence of such considerations to colloidal systems is observed. The importance of taking into consideration the extremely long equilibration times that can be expected for systems with very narrow attractive wells is also pointed out, in connection both with real colloidal systems and in computer simulations. It is further observed that in the Baxter limit sticky spheres described quantum mechanically are indistinguishable from hard spheres so described; near the zero-well-width limit, the quantal behavior hinges on the number of bound states and thus the well depth as well as the relative size of the de Broglie thermal wavelength and the well width. Related results and investigations relevant to the issues described above are cited.     

Moments of the Percus-Yevick hard-sphere correlation function

A simple recursive relation is derived for the momentsM _n ,n=1, 2,..., of the Percus-Yevick correlation functionh(r) for identical hard spheres. TheM _n are rational functions of the volume fractionw occupied by the spheres; the first ten are given explicitly, and a single-term asymptotic form is obtained to suffice for the rest. Applications of theM _n(w) include testing different approximations forh by numerical integration ofh(r) r ⁿ . We compare exact moments with shell approximationsM _n [h ^s ] corresponding to integration fromr=0 tos+1 fors=3–8, and with hybrid approximationsM _n [h ^s +h ^a ] which supplement the shell approximations with integrals of an asymptotic tail froms+1 to . For a givens, the hybrid approximation is better forw increasing than the shell approximation, andM _n [h ³+h ^a ] is even better thanM _n [h ⁸]     

Analytical representation of the density derivative of the Percus–Yevick hard-sphere radial distribution function

ABSTRACT

Explicit analytical expressions are presented for the density derivative, ?g_HS(R; ρ)/?ρ, of the Percus–Yevick approximation to the hard-sphere radial distribution function for R ≤ 6σ, where σ is the hard-sphere diameter and ρ = (N/V)σ³ is the reduced density, where N is the number of particles and V is the volume. A FORTRAN program is provided for the implementation of these for R ≤ 6σ, which includes code for the calculation of g_HS(R; ρ) itself over this range. We also present and incorporate within the program code convenient analytical expressions for the numerical extrapolation of both quantities past R = 6σ. Our expressions are numerically tested against exact results.     

SSOZ-HNC and SSOZ-PY integral equation studies of the structure of three-site polar fluids

Structure factors and site-site distribution functions for models of liquid carbon disulphide (CS₂) and acetonitrile (CH₃CN) are obtained by using the site-site Ornstein-Zernike (SSOZ) integral equation with the Percus-Yevick (PY) and the hypernetted chain (HNC) closures. The calculated structure factors are found to be in good agreement with the neutron and X-ray diffraction data as well as with the simulation data. The site charges have a significant effect on the distribution functions but not on the structure factors of both the systems. There is very good qualitative agreement between the calculated distribution functions and the results from computer simulations. Distinctive shoulders found in the simulation results for the first peaks of the C-N and CH₃-CH₃ distribution functions are enhanced in the calculations using the integral equations.     

Perturbative solution to order βɛ of the Percus-Yevick equation for triangular well potential forn=2

The radial distribution function for a fluid in which the molecules interactvia a triangular well potential is considered. Expanding the radial distribution function in pwoers of βɛ, where ɛ is the depth of the potential andβ=1/k _BT the first-order terms are calculated analytically using the Percus-Yevick theory in the Baxter’s formulation. The first-order terms in the direct correlation functionc(r) are also calculated. The first- and second-order terms in the free energy obtained from the energy equation of state are calculated and compared with other calculations. An erratum to this article is available at .