Computer simulations of core-softened attractive disks: phase behaviour and inverse melting

Almudallal, Ahmad Mustafa (2014) Computer simulations of core-softened attractive disks: phase behaviour and inverse melting. Doctoral (PhD) thesis, Memorial University of Newfoundland.

[English] PDF (Migrated (PDF/A Conversion) from original format: (application/pdf)) - Accepted Version Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission. Download (4MB) [English] PDF - Accepted Version Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission. (Original Version)

Abstract

We use several Monte Carlo computer (MC) simulation techniques to calculate the phase diagram of a system of hard disks interacting through a discrete square-shoulder square-well potential. The phase diagram shows the gas, liquid and five crystal phases, and we find that all the melting lines are first-order phase transitions, despite the system being two dimensional. The melting line of the square crystal exhibits a temperature maximum, meaning that above a certain pressure P the density of liquid becomes higher than that of a crystal. The same melting line also exhibits a pressure maximum that implies inverse melting, meaning that at constant pressure the liquid crystallizes by heating. To increase the range of pressure over which inverse melting occurs, we vary the potential parameters systematically and determine that the extent of the shoulder is the parameter that has the greatest impact. We calculate the new melting curve for the new potential parameter set, and we check the accuracy of the calculations by several methods including the calculation of the Gibbs free energy as a function of density at conditions of constant P and temperature T. The melting transition is first order and to a liquid rather than to a hexatic or to a quasicrystal. Finally, we perform MC simulations at constant P, T and number of particles N, to study the high pressure phase behaviour of a model with parameters that produce pronounced inverse melting. We detect three fascinating behaviours. First, the high pressure triple point present in the original model disappears, leaving behind a “liquid corridor” in the phase diagram for which the liquid appears to retain its position as the thermodynamically stable phase down to low temperature. However we find a new crystal that likely usurps the liquid as the stable phase. Second, we find a particular state point, which we name the “funny point”, at which the free energy barrier between the liquid and the high density triangular crystal vanishes along their coexistence line. Although the explanation of this funny point remains a mystery, it appears to be connected to the third discovery: a transition between low and high temperature forms of the high density triangular crystal. The potential studied in this thesis was previously developed to help understand anomalous behaviour in systems such as water and liquid metals. Moreover similar potentials have been used to model lipids interacting within bilayer membranes. Thus, it is possible that some of the phenomenology we observe for the model is relevant in these or related real systems.

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