Crystallography on Curved Surfaces (To be updated)

Recently there has been much experimental progress in realising two dimensional crystals with a given constant mean curvature. A particularly interesting setup is colloids embedded at the interface of a liquid droplet or a capillary bridge. The interactions between the colloids can be dominated by (repulsive) electrostatic interactions, (attractive) depletion interactions, or surface tension (capillarity).

We have analysed these problems using energy landscape techniques. Of particular interests are the defect motifs of the ground state configurations, the typical transition pathways between local minimum configurations, and the type of landscape the system displays (single/multiple funnels; structure-seeker/glassy).  As one can see below (repulsive colloids on catenoids), we typically observe multiple funnels, in some cases with different scales for the energy barriers. The larger barrier can usually be associated to concerted rotation of groups of colloids (see movie below).

Below is a movie showing a typical rearrangement pathway between local minimum configurations. A combination of local and global (concerted rotation of a row of colloids) rearrangements is required.

We are now complementing our energy landscape approach with finite temperature simulations.