| Summary: | The Mie ( λr, λa) intermolecular pair potential has been suggested as an alternative to the traditional (12,6) Lennard-Jones potential for modelling real system both via simulations and theory. Its implementation as a molecular-based equation of state for the fluid phase has led to accurate derivative thermophysical properties, which cannot be obtained when potentials of fixed exponents are considered. In this work, the effect the attractive and repulsive exponents have on the solid-liquid-vapour phase behaviour of this class of potentials is studied. A novel simulation technique, involving use of a direct interfacial methodology, is presented and is used to obtain the solid-fluid phase boundaries of monomer and chain systems of Mie potentials. The methodology is used in conjunction with simulation techniques for vapour-liquid and solid-vapour coexistence to determine the global phase behaviour of a number of potentials of this family. The application of the principle of corresponding states is discussed, with the focus of obtaining a unified view of the thermodynamic equilibrium properties of the Mie potential. A three parameter corresponding states model is presented, where a third parameter α, which corresponds to the mean-field integrated energy is proposed. A unique relationship between the stable fluid range and α is presented, which can be used to predict exponent parameters of the Mie models that can be used to treat real systems. An equation of state (EOS) for the solid phase of Mie spheres and chains is presented by extending Wertheim's thermodynamic perturbation theory (TPT1) to the solid phase. The SAFT-VR framework (on which TPT1 is based) is used in conjunction with the perturbation theory of Kang et al. for treatment of simple spherical solids to develop the SAFT-VR Mie solid EOS. This EOS is used with the recently presented SAFT-VR Mie fluid EOS of Lafitte et al., to solve for coexistence and determine the global phase behaviour of a host of Mie potentials of varying range of attraction. The accuracy of the theory is validated against the simulation results of this work and following this, the limiting behaviour of Mie chain systems is determined using the theory.
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