Perturbation calculations Phase diagrams

The application of this approach to the hard-sphere system was presented by Ree and Hoover in a footnote to their paper on the hard-sphere phase diagram. They made a calculation where they used Eq. (2.27) for the solid phase and an accurate equation of state for the fluid phase to obtain results that are in very close agreement with their results from MC simulations. The LJD theory in combination with perturbation theory for the liquid state free energy has been applied to the calculation of solid-fluid equilibrium for the Lennard-Jones 12-6 potential by Henderson and Barker [138] and by Mansoori and Canfield [139]. Ross has applied a similar approch to the exp-6 potential. A similar approach was used for square well potentials by Young [140]. More recent applications have been made to nonspherical molecules [100,141] and mixtures [101,108,109,142]. 

A method based on thermodynamic perturbation theory is described which allows strong directional Intermolecular forces to be taken into account when calculating thermodynamic properties. This is applied to the prediction of phase equilibrium and critical loci for mixtures containing polar or quadrupolar constituents. Two applications of the theory are then considered. In the first, the relation between intermolecular forces and the type of phase behavior is explored for binary mixtures in which one component is either polar or quadrupolar. Such systems are shown to give rise to five of the six classes of binary phase diagrams found in nature. The second application Involves comr-parison of theory and experiment for binary and ternary mixtures. 

The perturbing action of the surface cannot be accounted for by comparison with the phase diagrams for filled and unfilled alloys. For comparison of the phase diagrams and data on AB, we have to use the unperturbed%ab values. The comparison of data calculated by two methods allows estimation of the contribution to the system stability both of the changes in the perturbed component interaction and in the decreasing stability of each component in the filled system. The calculation by the first method gives only changes in the interphase interaction between two polymers, whereas the second method represents the total effect of filler action on the thermodynamic stability of the system. 

The elaborated in [R. V. Chepulskii, Analytical method for calculation of the phase diagram of a two-component lattice gas, Solid State Commun. 115 497 (2000)] analytical method for calculation of the phase diagrams of alloys with pair atomic interactions is generalized to the case of many-body atomic interactions of arbitrary orders and effective radii of action. The method is developed within the ring approximation in the context of a modified thermodynamic perturbation theory with the use of the inverse effective number of atoms interacting with one fixed atom as a small parameter of expansion. By a comparison with the results of the Monte Carlo simulation, the high numerical accuracy of the generalized method is demonstrated in a wide concentration interval. 

---