Current Research Interests

My work involves applying state-of-the-art Monte Carlo simulation methods to explore the fascinating physics that occurs in colloidal systems. A main focus is to develop novel simulation algorithms that allow phenomena to be revealed that are inaccessible to conventional simulation techniques. Below are a few recent examples of my work. If you are interested in pursuing PhD work in any of these areas, then please don't hesitate to contact me.

Polydisperse fluids

In a polydisperse fluids the particles are not all identical, but have a spread of sizes or interaction strengths. Polydispersity is common in colloids or polymers that form the basis of in many everyday materials such as paints, fuels, personal care products and foodstuffs. Understanding its effects is thus a matter of practical as well as fundamental interest.

Recently together with Peter Sollich, I have investigated the effects of size polydispersity on the crystalline phases of spherical particles in thermal equilibrium. In the absence of polydispersity we know from Kepler's conjecture, that such spheres can be packed to fill maximally just over 74% of space, in the face centred cubic (fcc) structure familiar from greengrocers' displays of oranges. But what is the thermodynamically optimal structure for dense spheres which have a spread of diameters?

Using specialized computer simulation methods and theoretical calculations we have shown that dense polydisperse spheres demix into coexisting fcc phases, with more phases appearing as the spread of diameters increases. We managed to track up to four coexisting phases in our simulations. Each of these is fractionated ie. it contains a narrower distribution of particle sizes than is present in the system overall.

[see P. Sollich and N.B. Wilding, Phys. Rev. Lett. 104, 118302 (2010) ]

Highly size asymmetrical fluid mixtures

In contrast to molecular or atomic matter, the effective interactions between colloidal particles in suspension can be controlled by adding a species of much smaller particles in the form of polymers or nanoparticles. The theoretical challenge is then to understand how the properties of the small particles influence the interactions between the large ones. Doing so potentially allows one to produce designer materials eg. ones that self assemble into useful structures or exhibit novel phase behaviour. Traditionally, however, the task of simulating such size asymmetrical fluid mixtures has been computationally very demanding. This is because the small particles tend to jam the larger particles, restricting their movement and making it prohibitively time consuming to explore configuration space. Together with Douglas Ashton and Erik Luijten I have been tackling this problem in the context of determining the phase behaviour of highly size asymmetrical fluid mixtures. The idea behind our approach is to swap groups of particles (large and small together) between two boxes which house the distinct equilibrium coexisting phases. The Monte Carlo moves used are highly efficient (rejection free) and allow us to determine the phase behaviour and how it depends on the number of small particle additives and the form of their interaction with the large particles. In related work we have developed a staged insertion scheme that allows grand canonical simulation of highly size asymmetrical fluids. There is a movie showing how our method works in two dimensions. [see D.J. Ashton, J. Liu, E. Luijten and N.B. Wilding, J. Chem. Phys. 133, 194102 (2010)] Fluids with competing interactions

The interactions between charged colloidal nano-particles in solution can be complex and varied. One particularly interesting case is when the particles attract one another at small separations, but repel at larger separatons. The short ranged attractions arises from van der Waals or polymer-induced depletion forces, while the long ranged repulsion arises from screen Coulomb forces. The competition of attraction and repulsion can give rise to exotic self-assembled structures such as clusters stripes, columns or void, as well as unusual crystal structures such as honeycomb lattices. Apart from the great fundamental interest of such structures, they may offer practical benefits as templates for advances functional materials, eg. for nano-electronics and photonics applications.

But before this glimpse into the materials physics of the future can become reality, we shall need a much deeper fundamental understanding of the precise relationship betweeen the interparticle interactions and the resulting self-assembled structures. One then can particular structures be targeted via the synthesis of the particles. In collaboration with Andrew Archer at Loughborough, we are applying state of the art Monte Carlo simulation techniques to study the range of structure that occur as the parameters of the interaction potential are varied.

(see A.J. Archer and N.B. Wilding, Phys. Rev. E 76, 031501 (2007)]

Lock and key colloids

As their name implies, these are colloidal particles that have complementary geometrical shapes that allow them to fit together. When immersed in a fluid of much smaller nanoparticles they spontaneously self assemble into ordered structures such as colloidal molecules or strings. The self assembly is driven by the so called depletion attraction, an entropic force that pushes the key into the lock. This mechanism can be finely tuned by changing the geometry of the colloids and the properties of the nanoparticles. Using cluster algorithm techniques and theoretical methods we are investigating self assembly in lock and key systems with a view to better understanding the fundamental principles that permit rapid and relaibly assembly into ordered products.

Core softened fluids

These are fluids in which the particles interact via a potential whose repulsive core exhibits a region of "softening" in the form of a shoulder or a ramp. Physical motivation for such models derives from the desire to encapsulate within a simple two-body isotropic potential, the complicated features of systems interacting via anisotropic potentials. Examples of the latter include liquid metals tetrahedrally bonded molecular liquids such as phosporous and, most notably, water. Performing such simplifications yield models that are analytically and computationally tractable but which, one hopes, nevertheless retain the qualitative physical features of the real systems they seek to describe.

It is well established, that core softened fluids have a much richer phase behaviour than their conventional single-component counterparts. As well as exhibiting interesting anomalous thermodynamic properties, such as becoming less dense when cooled, the most intriguing feature of core-softening is the existence of a demixing transition between two liquids of different densities, over and above the usual liquid-gas phase transition. In ongoing work, we are applying state-of-the-art MC simulation techniques to study the phase behaviour of a number of models of core-softened fluids in the hope of determining exactly which features of the potential give rise to a stable second critical point. Recent work [5] has shown that it is possible to find a core-softenced potential which captures important aspects of the phase behaviour of water.

(See H.M. Gibson and N.B. Wilding, Phys. Rev. E 73, 061507 (2006)]