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DY: Fachverband Dynamik und Statistische Physik

DY 39: Pattern Formation and Reaction-Diffusion Systems

DY 39.4: Talk

Thursday, September 8, 2022, 10:45–11:00, H19

Phase Field Crystal model for particles with n-fold rotational symmetry in two dimensions — •Robert F. B. Weigel and Michael Schmiedeberg — Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany

We introduce a Phase Field Crystal (PFC) model for particles with n-fold rotational symmetry in two dimensions [1]. The n-fold symmetry of the particles corresponds to the one that can be realized for colloids with symmetrically arranged patches, with the patches being either attractive or repulsive.

Our approach is based on a free energy functional that depends on the reduced one-particle density, the strength of the orientation, and the direction of the orientation, where all these order parameters depend on the position. The functional is constructed such that for particles with axial symmetry (i. e. n=2) the PFC model for liquid crystals [2] is recovered. We explain how both, repulsive as well as attractive patches, are described in our model.

We discuss the stability of the functional and explore phases that occur for 1≤ n≤ 6. In addition to isotropic, nematic, stripe, and triangular order, we also observe cluster crystals with square, rhombic, honeycomb, and even quasicrystalline symmetry.

[1]  arXiv:2204.00051 [cond-mat.soft]
[2]  H. Löwen, J. Phys.: Condens. Matter 22, 364105 (2010)