Diffusion studies in a nonequilibrium system with repulsive interactions

The diffusion behavior of silver islands on charged silicone oil surfaces has been studied. Compact Ag islands with an average diameter of $1.2\hspace{0.5em}\mu \mathrm{m}$ form after thermal deposition of silver on a charged silicone oil surface. In contrast to the behavior of the uncharged oil surface, no aggregation of the Ag islands is observed. Instead the average distance of the islands increases as the islands diffuse toward the edge of the oil substrate. This process is driven by the repulsive Coulomb interaction. An exponential decay of the island density n with time t results everywhere on the oil surface, and the corresponding time constant $O_f$ ranges between $1.0\times {10}^{-4}$ and $2.0\times {10}^{-4}\hspace{0.5em}{\mathrm{s}}^{-1}.$ In the central area of the substrate, the relative speed V between two islands increases linearly with their distance L according to $V_{\mathrm{fit}}=HL,$ where $V_{\mathrm{fit}}$ is the linear fit speed of V. The slope H is of the order of $2.0\times {10}^{-4}–3.0\times {10}^{-4}\hspace{0.5em}{\mathrm{s}}^{-1}$ after the deposition, and decreases with time. Our theoretical analysis indicates that $O_f\approx H,$ in agreement with the experimental finding. The experiment also shows that this nonequilibrium expansive diffusion already starts at the early stage of deposition. During their motion, the islands must carry a small fraction of the electron charge on the oil surface. After the islands reach the sample edge, they form a band-shaped silver film along the border. This results in the accumulation of charge, which slows down the speed of the remaining islands, which diffuse toward the edge.