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Nucleation in binary hard spheres

Hard spheres are the simplest non-trivial model of atoms. Simply little billiard balls, there is no energy, they are simply not allowed to overlap. So if there is not energy, the system is driven entirely by entropy, and, thus one might expect that, up to random close-packing of around 0.64 that there would be a disordered fluid phase, promoting entropy. Not so!

Controversial results from computer simulation in the 1950s showed that in fact, freezing occurred at 0.494 and melting at 0.55. In other words, entropy was making the system freeze. Was it just an artefact of the computer simulation? Nobody knew for sure until the seminal experimenatal work of Pusey and van Megen, who, using poly methyl methacrylate colloids synthesized here in Bristol (the experiments were done at Malvern) found that the results of the earlier computer simulations were in fact correct.

 

Binary hard spheres

Mixing two sizes of particles together is a fundamental model for alloys. Furthermore, judicious control of the composition, size ratio, and density, can lead to crystal superlattices such as zincblende and AB13, while other compositions can inhibit crystallisation. The image above shows a majority species (green) whose nuclei expel the smaller, minority species (red). However, this leads to a concentration of red around the crystal nucleus, resulting in self-poisoning...(right).Meanwhile in computer simulations, with Stephen WIlliams and Gary Bryant, we have shown that classical nucleation theory cannot be applied even to such a simple sysytem as binary hard spheres: Phys Rev Lett 100 225502 (2008).

 

 

Taffs J, Williams SW, Tanaka H and Royall CP, “Structure and kinetics in the freezing of nearly hard spheres”, Soft Matter, 9, 297 - 305 (2013). PDF download.