Séminaire Paddy Royall (ESPCI Paris)

Higher-Order Structure in Self-Organisation: from Crystallisation of Hard Spheres to Active Matter

Crystallisation is among the most familiar physical phenomena of everyday life. One would quite reasonably imagine that it has been long understood. And yet in arguably the most basic non-trivial material, hard spheres, after decades of intense research, predicted and measured nucleation rates differ so much that this failure has been dubbed “the second worst discrepancy in physics” [1]. And hard spheres are by no means the only material that exhibit such a discrepancy [2].

Since the experimental work relevant to this discrepancy was carried out in the last millennium, we expect that technological developments, such as the development of particle-resolved studies of colloids should shed new light on this phenomenon [3]. Such experiments, like computer simulation, are amenable to analysis with higher—order structural measures. This allows us to directly test Sir Charles Frank’s conjecture that “five-fold symmetry is abhorrent to crystallisation” (Fig. 1 a,b). It is [4]. We then investigate whether fivefold symmetry might explain the hard sphere nucleation discrepancy. It doesn’t [5]. But with very careful matching of state pint between experiments and simulation, we do find agreement for the energy barriers to form pre-critical nuclei (Fig. 1c).

We have used our higher order structural analysis to deduce the mechanism of polymorph selection in hard spheres [6]. We apply our methods to other systems, such as dipolar colloids [7], a model system which forms a significant number of polymorphs. Finally we investigate the role of activity in the dipolar colloid system, developing a 3d active colloidal system (Fig. 1d) [8]. The coupling of activity and hydrodynamic interactions leads to new structures not seen in the passive analogue.

Fig. 1. Real space imaging and higher–order structure combine to understand crystal nucleation. (a) Birth of a colloidal crystal nucleus imaged with confocal microsocopy. (b) Coordinates determined from (a) showing a nucleus of hexagonal close–packed (hcp) crystal (grey particles) and “7A” pentagonal bipyramids (green particles) showing five–fold symmetry in the surrounding liquid. (c) measurements of energy barriers for pre–critical nuclei. Shading denotes error bounds from computer simulation. Colours are volume fractions φ indicated. (d) Rendering of 3d active colloids forming a body-centered tetragonal crystal. Shown are metal (orange) and dielectric (white) hemispheres of the Janus particles.