Curvature-assisted self-assembly of Brownian squares on cylindrical surfaces

We hypothesize that curved surfaces, including cylindrical surfaces, which go beyond prior experiments using flat surfaces, can significantly influence and alter the phase behavior and self-assembly of dense two-dimensional systems of Brownian colloids.

Here, we report a first experimental study regarding the self-assembly of Brownian square platelets with an edge length L = 2.3 μm on cylindrical surfaces having different curvatures; these platelets are subjected to a depletion attraction in order to form a monolayer above the cylindrical surface, yet have nearly hard interactions within the monolayer. Simulations are also performed to confirm and explain the experimental observations.

Phase diagrams as a function of curvature are determined experimentally. Interestingly, hexagonal rotator crystal structures are observed for tubes having radii > 10.9L, but a tetratic phase is seen instead for the 10.9L tube at the corresponding platelet area fractions. We show that this transition is caused by the curvature-induced orientation-dependence of the depletion attraction between the squares and the underlying cylindrical surface. Brownian dynamics simulation results confirm the experimental observations and also illustrate helical structures formed by squares packing on cylinders. Our results demonstrate a way towards control over the self-assembly of anisotropic particles through curvature and depletion-attraction-induced orientational confinement.