Comment on “Self-assembly of magnetic balls: From chains to tubes”

The paper states that magnetic balls preferably assemble in a tube geometry if the number of particles exceeds $N\ge 14$. We find that for substantially higher particle counts, such as $N>1300$, a round cluster of densely packed magnetic balls with an fcc lattice can outmatch the described tube structure.

Figure 1

An upper bound of the reduced potential energy as a function of the cluster size. The circles indicate the value obtained by the numerical procedure, the gray connecting curves should guide the eye, the short dashed line indicates the energy for an infinitely long chain for comparison (Eq. (4) of Ref. [1]), and the long dashed line is the asymptotic value for a tube (Eq. (8) of Ref. [1]). The lower left inset shows the experimental realization of a cluster with $R=d=5\mathrm{mm}(N=13)$. The inset above is the corresponding computed dipole arrangement. The inset on the right hand side shows $N=767$ dipoles obtained for $R=5d$.