On the triplet structure of binary liquids

185

364

We demonstrate the accuracy of the hypernetted chain closure and of the mean-field approximation for the calculation of the fluid-state properties of systems interacting by means of bounded and positive pair potentials with oscillating Fourier transforms. Subsequently, we prove the validity of a bilinear, random-phase density functional for arbitrary inhomogeneous phases of the same systems. On the basis of this functional, we calculate analytically the freezing parameters of the latter. We demonstrate explicitly that the stable crystals feature a lattice constant that is independent of density and whose value is dictated by the position of the negative minimum of the Fourier transform of the pair potential. This property is equivalent with the existence of clusters, whose population scales proportionally to the density. We establish that regardless of the form of the interaction potential and of the location on the freezing line, all cluster crystals have a universal Lindemann ratio Lf=0.189 at freezing. We further make an explicit link between the aforementioned density functional and the harmonic theory of crystals. This allows us to establish an equivalence between the emergence of clusters and the existence of negative Fourier components of the interaction potential. Finally, we make a connection between the class of models at hand and the system of infinite-dimensional hard spheres, when the limits of interaction steepness and space dimension are both taken to infinity in a particularly described fashion.

Section: Nonuniform Fluidsmentioning

confidence: 99%

Why do ultrasoft repulsive particles cluster and crystallize? Analytical results from density-functional theory

Likos

Mladek

Gottwald

et al. 2007

185

364

“…The method used to solve each coupled system of equations is the Generalized Minimal RESidual algorithm for nonlinear systems of equations 19 ͑GMRESNL͒ previously introduced by Fries and Cosnard 20 in the context of liquid state theory. It has also been used in complex problems with molecular liquids, 21 in the calculation of triplet correlations of hard-sphere mixtures within the BHP approach 4 and more recently to solve the HNC3 equation in pure simple liquids. 16 We refer the reader to Refs.…”

Section: B the Numerical Implementationmentioning

confidence: 99%

An inhomogeneous integral equation for the triplet structure of binary liquids

Jorge

Lomba

Abascal

2001

Self Cite

The inhomogeneous integral equation proposed by Attard for the study of triplet correlations ͓J. Chem. Phys. 91, 3072 ͑1989͔͒ has been generalized to multicomponent systems. Defining one of the particles of a triplet as the source of an external field, the three particle distribution functions for the mixture are calculated using the inhomogeneous Ornstein-Zernike equation, an approximate closure relation and the Triezenberg-Zwanzig relation. The proposed theory performs satisfactorily for asymmetric mixtures of Lennard-Jones fluids for which other approximations at the two particle level tend to be rather inaccurate.

“…Other sophisticated schemes of approximation to h (3) , as discussed earlier or found in literature, [46][47][48][49][50][51][52][53][54][55][56] can be developed along the same line and will be taken up at a later date.…”

Section: Resummation Of the Higher-order Bridge Termsmentioning

confidence: 99%

Constructing a new closure theory based on the third-order Ornstein-Zernike equation and a study of the adsorption of simple fluids

Lee

2011

The third-order Ornstein-Zernike equation (OZ3) is used in the construction of a bridge functional that improves over conventional liquid-theory closures (for example, the hypernetted chain or the Percus-Yevick equations). The OZ3 connects the triplet direct correlation C((3)) to the triplet total correlation h((3)). By invoking the convolution approximation of Jackson and Feenberg, we are able to express the third-order bridge function B(3) as a functional of the indirect correlation γ. The resulting expression is generalized to higher-order bridge terms. This new closure is tested on the adsorption of Lennard-Jones fluid on planar hard surfaces by calculating the density profiles and comparing with Monte Carlo simulations. Particular attention is paid to the cases where molecular depletion on the substrate is evident. The results prove to be highly accurate and improve over conventional closures.