This work considers the extent to which the virial expansion can describe the structure and phase behaviour of several model fluids. These are the hard-sphere fluid, inverse-power potential fluids, the Lennard-Jones fluid and two kinds of 'square-shoulder' potential. The first novel contribution to knowledge that this work makes is in using virials to obtain the direct correlation function of a hard-core inverse-power potential fluid at densities close to freezing. Predicted radial distribution functions for the fluid at these densities are found that agree well with integral equation theory and simulation data. For softer-core potentials, a convergent direct correlation function is obtained at densities up to those at which a convergent virial expansion is known to exist. The study then extends to a Lennard-Jones fluid. At super-critical temperatures, a convergent direct correlation function is found as before. However, at sub-critical temperatures, the direct correlation function is found to diverge at all points for densities below criticality. Several recently-proposed re-summations of the pressure virial expansion are studied to improve its convergence at high densities. Some promise is shown in improving the accuracy of the virial expansion at high densities, but a re-summed virial expansion is found to be unable to fully capture the true behaviour of the system at densities close to criticality. A second novel contribution to knowledge is made by the reporting of virial coefficient data for several dissipative particle dynamics and penetrative square well potential forms. This is used to study the effect of re-summing the virial expansion for these systems in order to improve its convergence at high densities. The virial expansions of these potentials are found to perform increasingly poorly in the proximity of a vapour-liquid phase transition. This is in agreement with the results of investigating the Lennard-Jones fluid. Thirdly, this investigation considers the whether the virial expansion can describe the freezing of a hard sphere fluid and therefore predict the entire phase diagram for this system. This is investigated using a virial expansion to model the excess contribution to the Helmholtz energy functional. The virial expansion is not found to be able to accurately the point of phase transition, most likely due to questions remaining over the choice of a Gaussian basis set to describe lattice.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:727904 |
| Date | January 2016 |
| Creators | Bourne, Thomas |
| Contributors | Masters, Andrew |
| Publisher | University of Manchester |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | https://www.research.manchester.ac.uk/portal/en/theses/applications-of-the-virial-equation-of-state-to-determining-the-structure-and-phase-behaviour-of-fluids(809267a4-117a-49a2-9e36-44baa5f12860).html |
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