Sticky spheres in adhesive pores

(2n,n) potential and sticky-sphere fluids

The authors investigate the behavior of a model fluid for which the interaction energy between molecules at a separation r is of the form 4epsilon[(sigma/r)2n-(sigma/r)n], where epsilon and sigma are constants and n is a large integer. The particular properties they study are the pressure p, the mean square force F2, the elastic shear modulus at infinite frequency Ginfinity, the bulk modulus at infinite frequency Kinfinity, and the potential energy per molecule u. They show that if n is sufficiently large it is possible to derive the properties of the system in terms of two parameters, the values of the cavity function and of its derivative at the position r=sigma. As an example they examine in detail the cases with n=144 and n=72 for three different temperatures and they test the theory by comparison with a computer simulation of the system. They use the simulated pressure and the average mean square force to determine the two parameters and use these values to evaluate other properties; it is found that the theory produces results which agree with computer simulation to within approximately 3%. It is also shown that the model, when the parameter n is large, is equivalent to Baxter's sticky-sphere model with the strength of the adhesion determined by the value of n and the temperature. They use Baxter's solution of the Percus-Yevick equations for the sticky-sphere model to determine the cavity function and from that the values of the same properties. In this second approach there are no free parameters to determine from simulation; all properties are completely determined by the theory. The results obtained agree with computer simulation only to within approximately 6%. This suggests that for this model one needs a better approximation to the cavity function than that provided by the Percus-Yevick solution. Nevertheless, the model looks promising for the study of (typically small) colloidal liquids where the range of attraction is short but finite when compared to its diameter, in contrast to Baxter's sticky-sphere limit where the attractive interaction range is taken to be infinitely narrow. The continuous function approach developed here enables important physical properties such as the infinite shear modulus to be computed, which are finite in experimental systems but are undefined in the sticky-sphere model.

Global and critical test of the perturbation density-functional theory based on extensive simulation of Lennard-Jones fluid near an interface and in confined systems

The structure of a Lennard-Jones (LJ) fluid subjected to diverse external fields maintaining the equilibrium with the bulk LJ fluid is studied on the basis of the third-order+second-order perturbation density-functional approximation (DFA). The chosen density and potential parameters for the bulk fluid correspond to the conditions situated at "dangerous" regions of the phase diagram, i.e., near the critical temperature or close to the gas-liquid coexistence curve. The accuracy of DFA predictions is tested against the results of a grand canonical ensemble Monte Carlo simulation. It is found that the DFA theory presented in this work performs successfully for the nonuniform LJ fluid only on the condition of high accuracy of the required bulk second-order direct correlation function. The present report further indicates that the proposed perturbation DFA is efficient and suitable for both supercritical and subcritical temperatures.