  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.
