Phase separation of two-dimensional Coulombic crystals of mesoscale dipolar particles from mesoscale polarizable “solvent”

To avoid any dependence of $Φ$ on the density of spheres on the plate, we defined the “neighbors” of sphere $n$ as the six spheres closest to sphere $n$⁠, regardless of their actual distance from sphere $n$⁠. For all the calculations in this paper, we set $ntot=6$ (i.e., we considered only the six nearest neighbors of each sphere). Other values of $ntot$ did not yield qualitatively different results from those reported here.

Previous work showed that at this frequency and amplitude, $30s$ was long enough for the charge on each sphere to become constant.

We calculated $ΦmaxC-S$ for each density (Fig. S6),⁶ and divided the values of $Φ$ by $ΦmaxC-S$ to obtain $Φ*$⁠; this normalization allowed us to compare directly the values of $Φ$ for different densities of particles.

We agitated the particles at the combination of $A$ $(0.25mm)$ and $ω$ $(60Hz)$ for which $Φ(t)$ increased monotonically and most rapidly at $ρ=8.8spheres∕cm2$ (Fig. 2).