Self-Assembly of Optimally Packed Cylindrical Clusters inside Spherical Shells

Abstract

Systems with short-range attraction and long-range repulsion can form ordered microphases in bulk and under confinement. Using grand canonical Monte Carlo simulations, we study a colloidal system with competing interactions under confinement in narrow spherical shells at thermodynamic conditions at which the hexagonal phase of cylindrical clusters is stable in bulk. We observe spontaneous formation of different ordered structures. The results of the simulations are in a very good agreement with the predictions of a simple mathematical model based on the geometry and optimal packing of colloidal clusters. The results of the simulations and the explanation provided by a relatively simple geometric model may be helpful in manufacturing copolymer nanocapsules and may indicate possible ways of coiling DNA strands on spherical objects.

Structural characterization of systems with competing interactions confined in narrow spherical shells

“…We will only consider the structural properties of the system under thermodynamic conditions at which the hexagonal phase is stable in bulk since it exhibits the most interesting behaviour as we showed in a previous work. 18…”

“…Both in bulk and under confinement, different SALR potentials such as Lennard-Jones + Yukawa 11,32,41 and Hard Spheres + Double Yukawa 1, 13,33 have shown the same qualitative results as those reported for the SWL. 12,15,18 A plot of the pair potential is presented in Fig. 1a.…”

“…We focus on conditions under which the hexagonal phase is stable in bulk since it shows the most interesting behaviour under spherical confinement, as was already shown in a previous work. 18…”

“…This method is inspired by the geometrical solutions to the problem of the longest rope on the surface of a sphere as we discussed in a previous work. 18 The original problem considered in ref. 35 looks for the longest closed curve (rope) with a constant thickness (diameter of the rope) on the surface of the unit sphere avoiding self-overlapping.…”

“…We focus on conditions under which the hexagonal phase is stable in bulk since it shows the most interesting behaviour under spherical confinement, as was already shown in a previous work. 18 Systems with competing interactions confined in spherical geometries have already been studied. For instance, the phase behaviour of a binary blend of diblock copolymer AB/homopolymer C has been explored using a simulated annealing technique.…”