Abstract

In 1952 Sir Charles Frank popularised the idea that the stability of supercooled liquids arises from a tendency of the particles to cluster together into small structures that are geometrically incommensurate with crystallisation. In this thesis the local structural arrangement of particles within a number of systems is considered. A method called the topological cluster classification (TCC) is used to detect local structures of particles that are equivalent to the potential energy minimum clusters of 13 or fewer particles in isolation. The dynamics of different local structural arrangements within a bulk are considered by developing an algorithm to quantify the lifetimes that the structures persist within the system.

The first system considered is a model colloid-polymer mixture, where the colloids self-assemble into small clusters. The structures of the clusters that form are mapped out as a function of attraction and repulsion strength of the colloidal interactions, and the density of the system. In the case of six-particle clusters, the entropic contribution to the free-energy must be accounted for in order to correctly predict the structures that prevail. As the strength of the colloidal attractions is increased, ergodicity is broken and the clusters become kinetically trapped. The structures formed under these conditions are determined by the aggregation sequence of the colloids from the random initial configuration. The effect of long-ranged electrostatic repulsions between clusters on the intra-cluster structure is considered. As the repulsion strength and density increase it is possible for the intra-cluster structure to be perturbed by the presence of neighbouring clusters, demonstrating that it may not always be appropriate to consider each cluster as if it were an isolated system.

The structure at liquid-gas interfaces is considered with the TCC algorithm by measuring the fraction of particles participating within clusters as a function of distance from the interface. The participation ratios monotonically decrease in the interfacial region between the liquid and the gas. For interfaces with a high surface tension, the orientations of two types of elongated cluster are found to align near to the free surface and to oscillate with respect to the density fluctuations of the interfacial layers that propagate into the bulk liquid.

The clustering of particles in two model supercooled liquids is considered. The temperature behaviour of the participation fractions of particles in clusters and the dynamical persistence of clusters at low temperatures are measured. The domains of long-lived clusters in the supercooled regime are characterised and an association with spatial heterogeneities in the dynamics is demonstrated. Correlation lengths for the static structure and the dynamic heterogeneities are found to grow on cooling, however the manners in which the lengths grow are different. An inverse power law reference potential for one of these systems shows clustering that is significantly different to the full system with attractions, even though the viscous slowdown of the two models is the same. We propose avenues for further research to clarify the relationship between local structure and the glass transition.

A. Malins
PhD, Faculty of Science, University of Bristol, July 2013
Supervisors: Dr Paddy Royall & Professor Jens Eggers

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