Directed self-assembly of spherical caps via confinement

TL;DR

This study uses Monte Carlo simulations to explore how spherical cap-shaped particles self-assemble under confinement, revealing various crystal phases influenced by particle shape and confinement height.

Contribution

It introduces a particle model based on spherical caps with varying heights and analyzes their phase behavior under confinement, connecting simulations with experimental observations.

Findings

Different particle shapes lead to distinct self-assembled crystal structures.

The phase diagram for three-quarter height caps closely matches experimental results.

Confinement height significantly influences the formation of ordered phases.

Abstract

In this work we use Monte Carlo simulations to study the phase behavior of spherical caps confined between two parallel hard walls separated by a distance H. The particle model consists of a hard sphere of diameter \sigma cut off by a plane at a height \chi, and it is loosely based on mushroom cap-shaped particles whose phase behavior was recently studied experimentally [E. K. Riley and C. M. Liddell, Langmuir, 26, 11648 (2010)]. The geometry of the particles is characterized by the reduced height \chi^* = \chi/\sigma, such that the model extrapolates between hard spheres for \chi^* \leftarrow 1 and infinitely thin hard platelets for \chi^* \letfarrow 0. Three different particle shapes are investigated: (a) three-quarter height spherical caps (\chi^* = 3/4), (b) one-half height spherical caps or hemispheres (\chi^* = 1/2), and (c) one-quarter height spherical caps (\chi^* = 1/4). These three models are used to rationalize the effect of particle shape, obtained by cutting off spheres at different heights, on the entropy-driven self-assembly of the particles under strong confinements; i.e., for 1 < H/\chi < 2.5. As H is varied, a sequence of crystal structures are observed, including some having similar symmetry as that of the structures observed in confined hard spheres on account of the remaining spherical surface in the particles, but with additional features on account of the particle shapes having intrinsic anisotropy and orientational degrees of freedom. The \chi^* = 3/4 system is found to exhibit a phase diagram that is most similar to the one obtained experimentally for the confined mushroom cap-shaped colloidal particles under. A qualitative global phase diagram is constructed that helps reveal the interrelations among different phases for all the particle shapes and confinements studied.