Lock and key colloids: Controlling self assembly via depletion forces

It is a famous result from mathematics that the most efficient way to pack spherical particles is to stack them in layers, like oranges in a box. Another result, less well-known, is that microscopic plastic spheres (colloids) will form the same ordered structure spontaneously, on immersion in a simple mixture of chemicals. This is an example of self-assembly: no energy is used up and individual particles are not manipulated by hand, but an ordered product is assembled. Furthermore, these systems are simple enough that the forces between the particles can be calculated theoretically and the systems simulated in computers.

Self-assembly is also relevant in many other contexts, including biology. There, complicated biological molecules come together and form ordered structures that might might be essential for life (for example, microscopic filaments that give cells their shape) or might cause disease (for example, viruses). Inspired by these biological systems, proposals have been made to use self-assembly in nanotechnology, building novel solar cells or computers.

However, while these ideas are exciting, the problem in designing such self-assembled products is one of control. The biological systems can assemble into complex functional structures but the interactions between the particles are complicated and it is not easy to design and build similar systems for our own specific purposes. On the other hand, simple spherical colloids can be controlled accurately but can only be used to make stacked layers of spheres. Recently, an important step was made: by making colloids with different shapes, new ordered structures could self-assemble: not stacked layers but clusters and strings of particles. The new particles are called "locks" and "keys" because of the way they fit together as they assemble.

This proposal will use computer simulation to explore the self-assembly of these lock and key particles. As in the spherical case, the fundamental physics are understood, so we can use computer simulations to predict and explain the results of experiments. In particular, we will investigate the range of structures that might self-assemble, both with existing lock and key particles and with other similar particles that might be made in the future. In this way we aim to guide future experiments in this area, and look into possible technological applications of lock and key systems.

More generally, by starting from a relatively simple system of colloidal particles with different shapes, we aim to develop guiding principles that can be used more generally in designing and controlling self-assembly. If a system might form several different structures, how can we select one out of the many choices? Is it easier to assemble flexible structures or rigid ones, and how might this flexibility be controlled? Can we design structures that can still assemble even if their shapes are imperfect or slightly different from each other? Such questions occur in many different self-assembling systems: by investigating them in the relatively simple context of lock and key particles, we look for insight that might one day be used to mimic or disrupt biological assembly, or to build nano-scale products of machines.

Self-assembly processes are those in which simple components come together spontaneously to form ordered products. For examples, consider the assembly of viruses; the formation of two-dimensional ordered arrays of organic or inorganic molecules; and the production of crystalline nanoparticles with a variety of complex shapes. Yet despite this range of applications across science and engineering, methods for design and control of self-assembling systems are still in their infancy. The wide-ranging potential impact of such methods has been acknowledged by the recent EPSRC signpost `Control of self-assembly'.

The aim of this proposal is to explore a novel class of self-assembling systems where our understanding of the underlying physics offers an unusual opportunity for accurate design and control. These are lock-and-key colloids, whose interactions are controlled by depletion forces. In general terms, this project will be of interest and benefit to the world-wide community of scientists in academe and industry -- in fields ranging from physics and chemical engineering to chemistry and applied mathematics -- who require a basic science platform for understanding and predicting the nature of self assembly in all its various guises.

More specifically, the lessons that we will learn by the studies proposed here will guide predictions for production and processing lock-and key colloidal systems. We will explore what self-assembled structures are accessible and how the dynamical assembly process can be optimised to make it efficient and robust. In this way, we aim towards a road map for potential technological applications.

To achieve this, we work primarily by contacts with other academics, some of whom are closer to emerging technologies and industrial partners. We will also be proactive in fostering links with relevant people who could take the work forwards on the applied side. One possible route here is via Jack's strong connections with the
Molecular Foundry, Berkeley, US., where there is considerable interest in generating ordered nanostructures for applications. We anticipate that the physical insight and predictions arising from our work could inspire work there (and elsewhere) to test our predictions and to exploit lock and key colloids in nanotechnology.

Finally, the mathematical, computational and logical reasoning skills required in statistical mechanics are extremely valuable outside academia. For example, recent PhD students and postdocs in the Condensed Matter Theory group at Bath have gone on to work in climate modelling (Met Office), analysis of financial risk (Barclays and Barclays Capital), effectiveness of bibliometric analyses (Higher Education Funding Council for England), and statistical modelling of traffic and public transport networks (Transport Research Laboratory). These career paths all exploit the postgraduate and postdoctoral training and skills development that come from studies of theoretical physics. The postdoc supported by this grant will also further develop such skills, enhancing their potential to contribute both to future academic research and to non-academic employment.