Colloidal Crystals on Conical Surfaces

Abstract

The curvature of surfaces affects the organisation of condensed matter upon them. In biology, the curvature of cell membranes affects how proteins are arranged within them and the growth of virus capsids is affected by their curvature, for example. Curvature is also used to guide colloidal self-assembly in industrial nanoscale manufacturing processes, to produce, among other things, drug delivery systems, biosensors and photonic crystals.

An open question in the field concerns how two-dimensional crystalline systems deal with the closure constraint imposed by finite curved surfaces. A crystal on a conical surface is a good model for studying this as the curvature strain associated with surfaces of non-zero Gaussian curvature is eliminated and the closure constraint is variable, unlike on, for example, cylindrical surfaces.
In this work, putative global minimum energy structures of two-dimensional, model colloidal crystals confined on conical surfaces of a range of angles are generated using basin-hopping and visualised with Voronoi tessellation. The colloidal particles interact via an isotropic Morse potential. The defect patterns observed in these model, minimum energy crystals are discussed and analysed. The interparticle potential range and the cone angle affect whether any defects are seen in the minimum energy structures, and, if defects are produced, what they are. Both wedge-shaped defects reported in experiment and novel bulk-terminating helical defects are observed. At small cone angles, the type of defect is very sensitive to changes in angle, as different defects can alleviate different amounts of strain. A phase diagram of preferred defect type against cone angle and interparticle potential range is produced for near-cylindrical conical surfaces. Another interesting feature of the crystal is the vertical position on the cone that it prefers to occupy; a preliminary line energy model is constructed which explains this behaviour qualitatively.