Phase Behaviour and Criticality in Simple Liquids and Their Mixtures

Liquid state theories establish a link between the microscopic properties of a liquid (in terms of its pair potential) and its structural and thermodynamic properties. Statistical Mechanics provides the versatile formalism to determine the relevant relations. In practice, however, these expressions cannot be applied directly, not even for the simplest non-ideal system, i.e., to hard spheres: the reason is that they become intractably complex and therefore require simplifying assumptions. These simplifications lead to approximate schemes that can be derived systematically (e.g., via graph-theoretical considerations) from the exact expressions for partition sums and related quantities. One thus arrives at so-called closure relations to the Ornstein-Zernike equation that relate the total and the direct correlation functions which describe the structural properties of the system. In early years of liquid state theory well-known conventional schemes, such as the mean spherical approximation (MSA), the Percus-Yevick (PY), or the hypernetted chain (HNC) approximations have been derived.

In recent time we have successfully extended the Self-Consistent Ornstein-Zernike Approximation (SCOZA) to a large variety of systems: for liquids with repulsive core (as they are, e.g., encountered in atomic systems) we are now able to consider potentials with arbitrary attractive tails. Comparison with computer simulations has shown that SCOZA does indeed remain accurate close to phase boundaries and in the critical region. Particular attention has recently been dedicated to soft systems, i.e., liquids where the potential of the particles remains finite at the origin or diverges only weakly for short distances; such interactions are typical for soft matter particles. Also here we could show that computer simulation data for the structural and thermodynamic properties could be reproduced with high accuracy.

Special emphasis has furthermore been put on closer investigations of the HRT scheme. It is in particular the implementation of HRT which represents a challenge (both from the conceptual as well as from the numerical point of view). In an effort to localize the phase boundaries and the critical point with high accuracy, states of diverging compressibility have to be identified which turned out to be a very delicate problem.