Percolation-induced conductor-insulator transition in a system of metal spheres in a dielectric fluid

We develop a model to investigate the insulator-conductor transition observed in a system of spherical metal particles suspended in a quasi-two-dimensional viscous liquid between planar electrodes when the voltage of the electrodes is increased. Our model captures the main ingredients of the process in experimental system, and reveals the insulator-conductor transition at a well-defined critical voltage. Based on the simulation data we demonstrate that characteristic quantities of the system show power-law scaling in the vicinity of the critical point. These scaling analysis show clearly that the transition between the insulating and conducting phases is analogous to second-order phase transitions.

Figure 1

Snapshots of the experimental system at high voltage values obtained in the experiments of Ref. [22]. The snapshot (a) shows clearly that the particles form chains which merge into a large cluster spanning between the electrodes. The model construction is illustrated by (b) and (c).

Figure 2

Simulation configuration of the equilibrium state for the system of size $L=400$ at the voltage $V=$ (a) 0, (b) 500, (c) 600, (d) 700, and (e) 2400, respectively. The figures in the right-hand column present magnified views of the areas indicated by the rectangles.

Figure 3

Conductivity $\sigma$ as a function of voltage $V$ for different system sizes $L$. The system size increases from up-left to the down-right as $L=200$, 300, 400, 500, 600, 700, 800, 900, 1000.

Figure 4

The saturation value of the conductivity ${\sigma }_0$ as a function of the system size $L$. Power law behavior is evidenced with a fractal section of the conducting backbone.

Figure 5

Critical voltage $V_c$ obtained by the fastest change of the conductivity (squares) and by the peak of the average cluster size (cross) as a function of the system size $L$. A high-quality power-law behavior is obtained with the exponent $1+\gamma$, where $\gamma =0.23\pm 0.02$ is for the data represented by squares.

Figure 6

Size of the clusters $S$ as a function of the radius of gyration $R_g$ obtained at different system sizes $L$. Each symbol represents an individual cluster. On a double logarithmic plot, the data can be well approximated by straight lines. The inset presents a magnified view of the cluster structure.

Figure 7

The size distribution of clusters $n_V(S)$ obtained at different voltages $V$ for the system size $L=900$. As the critical voltage is approached, $V_c\approx 1377\hspace{0.5em}\mathrm{V}$, the distribution becomes a power law. The slope of the straight line is $2.12$.

Figure 8

Average cluster size $S_{\mathit{av}}$ as a function of voltage rescaled with the system size $L$. With an appropriate choice of the exponent of $L$, the curves can be collapsed onto each other.