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Monte Carlo studies of phase transitions in open systems Daub, Christopher David

Abstract

This thesis consists of the investigation of two different problems involving phase transitions using grand canonical Monte Carlo simulations. The first problem sought to understand the nature of the condensation phase transition in simple ionic fluid models, and in particular the restricted primitive model. A specific focus of this investigation was the resolution of a discrepancy between calculations of the constant volume heat capacity near the condensation critical point in the canonical ensemble versus the grand canonical ensemble. By doing calculations on a fluid of hard spheres with attractive power law interactions, we have demonstrated that the near-critical heat capacity calculated in the grand canonical ensemble leads to results which are inconsistent with analytical results for the criticality of these fluids. Although the reasons for this discrepancy remain unclear, we believe that it stems from an incomplete consideration of the finite size effects which affect the grand canonical calculation. We then return to the original problem of the criticality of ionic fluids. We have simulated the critical region of a model of charged hard dumbbells, and we have done a mixed field finite size scaling analysis and calculated the canonical heat capacity. We find no qualitative differences between the criticality of the dumbbells and the ionic model, suggesting that the pairing of ions does not affect the critical behaviour. We surmise that the lack of a peak in the canonical heat capacity of ionic fluid models is a consequence of the very slow convergence of this calculation toward the correct results in the thermodynamic limit, and is not a signature of non-Ising criticality. The second problem we investigated is the adsorption of CO₂ on MgO crystals. This study was driven by experimental results indicating a phase transition between a low temperature, ordered monolayer and a high temperature, disordered monolayer. There is also experimental evidence that this disordered phase has a higher density than the ordered phase. We were able to simulate the formation of an unusual disordered high density phase, however, some discrepancies between the experimental results and our simulations remain to be resolved.

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