Fluids of Core-Softened Particles in Dimension Two: an Integral Equation Study
Résumé
An interaction model with core-softening, that produces clustered phases in dimension two, is studied by integral equation theories, and compared with corresponding simulation results. It is shown that the Hypernetted-chain (HNC) equation is suprizingly accurate and easier to solve numerically than the Percus-Yevick (PY) equation which appears unable to get to the cluster phase region. This is compared to the behaviour of the two theories in the absence of the core-softening: in the high temperature regime the Percus-Yevick theory is more accurate while in the low temperature regime it is the HNC theory that become more accurate. It is the inclusion of an infinite class of cluster diagrams allows the latter theory to better describe phases where local structures and small clusters play a predominant role in characterizing their macroscopic properties, and the opposite behaviour observed for continuous phases of hard and soft interactions must be due to fortuitous diagram compensations in the real system. The HNC theory gives a very accurate structural description of the various cluster phases, as shown by comparing the radial distribution functions and structure factors with those from simulations.
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