This letter describes the formation of two-dimensional (2D) crystals of dipolar particles (TN) made of electrostatically charged, joined, millimeter-scale Teflon (T) and nylon-6,6 (N) spheres, and the separation of these crystals, as a distinct phase, from a mixture of TN and similar, capacitively charged particles that were coated with gold . The extent of separation increased with increasing amplitude of agitation, and with decreasing density of particles. Above a threshold in the amplitude of agitation, the crystals broke apart and the particles remixed. This system is a 2D model of the nucleation of crystals of polar molecules in a polarizable liquid.
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To avoid any dependence of on the density of spheres on the plate, we defined the “neighbors” of sphere as the six spheres closest to sphere , regardless of their actual distance from sphere . For all the calculations in this paper, we set (i.e., we considered only the six nearest neighbors of each sphere). Other values of did not yield qualitatively different results from those reported here.
Previous work showed that at this frequency and amplitude, was long enough for the charge on each sphere to become constant.
We calculated for each density (Fig. S6),6 and divided the values of by to obtain ; this normalization allowed us to compare directly the values of for different densities of particles.
We agitated the particles at the combination of and for which increased monotonically and most rapidly at (Fig. 2).