Theory of rotational columnar structures of soft spheres

TL;DR

This paper presents an analytical model and phase diagram for the self-assembly of soft spheres into cylindrical structures under rotation, supported by preliminary numerical simulations, advancing understanding of soft particle packing.

Contribution

It introduces a comprehensive analytic energy calculation method and phase diagram for soft sphere structures under rotation, extending prior experimental work.

Findings

Identification of phase diagram features including peritectoid points

Analytic energy calculations for soft sphere structures

Preliminary numerical simulations supporting the model

Abstract

There is a growing interest in cylindrical structures of hard and soft particles. A promising new method to assemble such structures has recently been introduced by Lee et al. [T. Lee, K. Gizynski, and B. Grzybowski, Adv. Mater. 29, 1704274 (2017)]. They used rapid rotation around a central axis to drive spheres of lower density than the surrounding fluid towards this axis. This resulted in different structures as the number of spheres is varied. Here we present comprehensive analytic energy calculations for such self-assembled structures, based on a generic soft sphere model, from which we obtain a phase diagram. It displays interesting features, including peritectoid points. These analytic calculations are complemented by preliminary numerical simulations for finite sample sizes with soft spheres. A similar analytic approach could be used to study packings of spheres inside cylinders of fixed dimensions, but with a variation in the number of spheres.