Clustering phenomena in adhesive hard sphere fluids. Theory of freezing

We develop a version of the physical cluster theory of the equation of state based on a definition of a “cluster” which depends both on particle positions and relative momenta, namely we choose to call a group of i molecules a physical cluster if their total energy (kinetic energy plus interactions) does not exceed the translation energy of the centre-of-mass of the whole group. This definition in addition with the “microcrystal” model of a cluster allows us to calculate the properties of individual clusters, to consider the clustering phenomena and to write down an equation of state for a dilute system as well as for a system at moderate and high densities. The interaction between molecular aggregates is taken into consideration by using the adhesive hard sphere model and the Percus-Yevick approximation. Based on the relations obtained we develop the theory of freezing and perform a numerical investigation of the equilibrium behavior of the system at various temperatures and densities. In particular, the theory enables us to describe the regular phase diagram which includes (in coordinates pressure-temperature) three branches intersecting at the triple point. It is interesting that the coexistence curve of the fluid-solid as well as liquid-gas phase transition has an end point.