(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.