Matthew Dennison

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Colloidal particles

Colloids are particles with a diameter that lies in the range of tens of nanometers to a few micrometers, and which are suspended in a liquid. As well as having practical applications in areas as diverse as food, paint and cosmetic formulations, they are also useful as experimental model systems. Their dimensions are much larger than those of atoms and molecules, while their dynamics and the structures they form are still governed by thermal fluctuations.

My research uses computer simulations and theoretical models to study the phase behaviour of various colloidal particles, focusing on how particle shape can affect the phases a system will form. In addition, I am interested in elastic and structural properties of liquid, liquid crystalline, and crystalline phases.

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Colloidal crystals: mimicking atomic behaviour

The earliest computer simulations dealt with the simplest of shapes, such as hard-discs in 2d and hard-spheres in 3d. Even these basic particles can undergo phase transitions, forming a crystalline phase upon compression. Modern computers allow for increasingly more complex shapes to be studied. Even slight particle anisotropy is sufficient for a rich phase behaviour: hard-sphere dumbbells, for example, which consist of two rigidly fused hard spheres of equal size, can form liquid phases, plastic crystalline phases (where the particle centres of mass are aligned but they can rotate [relatively] freely), aperiodic crystals (where the constituent spheres of the dumbbells form a crystal, but the particle centres of mass do not) and, finally, periodic crystals (where both the constituent spheres and the centres of mass lie on lattice sites).

The phase behaviour becomes even richer if one considers anisotropic dumbbells: two hard spheres of uneven size, rigidly fused together. Using computer simulations, we have shown that such particles, often named snowmen-shaped particles, can form a wide range of stable crystalline phases depending on the ratio of the diameters of the constituent spheres. Here the constituent spheres form crystals with lattices that resemble such atomic crystals as NaCl (salt), CrB (chromium boride), αIrV and γCuTi. Another interesting feature is that the phase behaviour of systems of snowmen particles is richer than that of the corresponding binary mixture of hard spheres. Binary hard sphere mixtures will tend to only form the best packed crystalline structure, while for snowman particles, there are multiple ways of arranging the bonds connecting the two spheres, giving rise to a degeneracy entropy that can stabilize non-best packed structures.

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Onsager theory: thermal, elastic and structural properties

The Onsager theory of nematic liquid crystals describes the phase transition from a positionally and orientationally disordered isotropic phase to a positionally disordered but orientationally ordered nematic phase. In this theory, the transition is described by the competition between two different contributions to the free energy: an orientation entropy, where there is a free energy cost for aligning particles, and an interaction entropy, where alignment is favoured in order to reduce the number of interactions between particles. Onsager gave a virial expansion of the Helmholtz free energy which he truncated at second order, making the theory exact for infinitely long rods.

By including higher order virial terms, we have used Onsager theory to accurately predict the phase behaviour for various particle shapes, such as hard spheroids, cut-spheres, Saturn-shaped particles and cuboids. The theory can also be expanded to study other phases, such as the novel cubatic liquid crystalline phase, where discotic particles form a distinct phase in which they are positionally disordered but align along three orthogonal axes, as opposed to the single axis for nematic liquid crystals. Furthermore, it is possible to use the theory to calculate the three Frank elastic constants for nematic phases, which describe how a nematic phase resists twist, splay and bend deformations. These theoretical calculations have shown that the three coefficients can differ widely from one another depending on the particle shape. Another application is for the calculation of the pair correlation function for liquid and nematic phases

Colloidal rods: the effects of shape and flexibility

The fd-virus is a semi-flexible virus particles often used in experimental studies as a model colloidal rod. One reason is its dimensions, as its aspect ratio (the ratio of length to diameter) is very large (L/D ∼ 100), while its persistence length (the length over which a particle's orientation remains correlated) it a few times its length (LP ∼ 2.5L), meaning that it is still relatively stiff. Another is the fact that it is highly monodisperse, whereas synthesized colloidal rods tend to be much more polydisperse. These properties mean that their phase behaviour can be accurately predicted by a simple expansion of the Onsager theory to describe semi-flexible rods.

We have generalized the Onsager theory still further to describe binary mixtures of semi-flexible rods. This theory can be used to accurately predict both qualitatively and quantitatively the phase behaviour of thick-thin fd-virus mixtures, which have been shown in experimental studies to exhibit a very rich phase behaviour. The theoretical calculations can go beyond the experiments in terms of precision, locating the cross-overs between different types of phase behaviour. Another interesting application of this model is to study the alignment of guest particles immersed in a host nematic phase. The nematic field causes the guest particles to align, and experimental studies have shown that flexible and semi-flexible polymers will undergo a coil-rod transition, straightening out under the influence of the nematic field of the host. Our theory can account for and describe this behaviour for both long, flexible guest particles and short, rigid ones.

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