Impact of interaction range and curvature on crystal growth of particles confined to spherical surfaces

Abstract

When colloidal particles form a crystal phase on a spherical template, their packing is governed by the effective interaction between them and the elastic strain of bending the growing crystal. For example, if growth commences under appropriate conditions, and the circular crystal that forms reaches a critical size, growth continues by incorporation of defects to alleviate elastic strain. Recently it was found experimentally that, if defect formation is somehow not possible, the crystal instead continues growing in ribbons that protrude from the original crystal. Here we report on computer simulations in which we observe both the formation of ribbons at short interaction ranges and packings that incorporate defects if the interaction is longer-ranged. The ribbons only form above some critical crystal size, below which the nucleus is roughly spherically shaped.We find that the scaling of the critical crystal size differs slightly from the one proposed by the Manoharan group, and reason this is because the actual process is a two-step heterogeneous nucleation of ribbons on top of roughly circular crystals.

Beyond icosahedral symmetry in packings of proteins in spherical shells

“…that are allowed to move on the surface of the sphere or change type, while interacting via a truncated LJ interaction of strength . The packing of particles on spherical surfaces have been used also as a model for colloidosomes [38][39][40][41][42][43]. For reference, we take our ideal [44] system as only composed of hexagonal (σ H = σ) and pentagonal (σ P = σ/(2 sin(π/5))) particles.…”

Phase transitions on non-uniformly curved surfaces: coupling between phase and location

“…This potential has an adjustable range parameter r, which is important because the behaviour of crystals of attractive particles on curved surfaces is known to depend on the softness of their interactions. 11,12 The pair potential energy is given by…”

“…For this work we have chosen to set r c /r 0 = 2.23, in line with comparable investigations. 11,25 The potential is plotted in Fig. 1.…”

“…Techniques include a rotating cuvette, 4 lithography, 5 suspending a liquid surface from a post, 6 and 3D printing. 7 These surfaces can play host to a variety of two-dimensional systems, including membrane proteins, 1 stress fibres, 8 active and passive liquid crystals, 9,10 capsid protein shells 2,11 and colloidal particles adsorbed onto a surface by depletion forces or tethered to one with DNA. 12,13 Additionally, it has been shown that the dimple patterns in buckled curved elastic bilayers form a crystal structure with similar properties to colloidal crystals on a curved surface.…”

“…Even in this simplest scenario, a wide range of phenomena are observed which are absent on flat surfaces, including the presence of defects and branching in the ground-state crystals, 12,15,16 and of modified nucleation pathways. 17,18 These studies have been successful in describing natural phenomena such as the structure and formation of virus capsids, 11 and the packing of particles on a Pickering emulsion droplet. 15 An even richer picture emerges for surfaces with varying curvature, where the symmetry of the surface is broken.…”