Research paper: Spinodal fractionation in a polydisperse square well fluid

EDITED: August 2012

The paper has been published in final form by Physical Review E — the final arXiv update is available here.

Here my first publication co-authored with Mike Evans. As well as being published in Physical Review E, it’s available on arXiv, which is freely accessible and contains copies of most of the papers published in recent years in a variety of physics and other fields. In fact, the conditions of my PhD funding explicitly require that my work has to be freely available — isn’t science good?

Most substances in soft matter (colloids, polymers, biological stuff and so on) are ‘polydisperse’ which, as explained here, means that all the constituent particles of a big container of the stuff are different in terms of e.g. their size or charge. This is in contrast to simple molecular fluids like water, in which every molecule of H2O is identical. Statistical mechanics and thermodynamics were originally designed for these simple fluids, so while they have been applied in soft matter with some success, traditional theories fail to capture some important and interesting phenomena in polydisperse materials.

For example, during phase separation, particles with different properties can end up being partitioned, or fractionated, into the different phases. In a simple example, a crystal growing from an initially disordered fluid of size-polydisperse particles might end up incorporating predominantly larger than average particles. This might not matter too much, but if you’re trying to create a precisely-characterised photonic crystal with a certain lattice parameter, it could matter quite a lot. Or, you might want the particles to fractionate between the phases, in order to then scoop out some of one phase and end up with a purer substance than you had before. In any case, it’s important to know how fractionation happens in polydisperse systems.

In the paper, we’ve simulated gas-liquid phase separation in a polydisperse fluid, and observed fractionation of particles between the two phases on a surprisingly short timescale. Even while the system is very quickly changing and coarsening its spinodal texture, particles of different sizes end up finding their way preferentially into one or the other phase. There’s also a striking dependence on a very trivial-seeming detail of the particle interaction, which ends up completely altering the observed ‘direction’ of the fractionation.

Fractionation has been measured in experiments, but the early stages of phase separation are very difficult to access because of how quickly the system is evolving. So, our simulations give a nice insight into how the final states observed in experiments are actually enacted through the course of the phase separation, and as far as we know constitute the first such measurements on a truly polydisperse model colloidal fluid. There are some nice pictures too.

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