FIG. 8.
PNP solution of the resistance versus L at applied potential of 1 V and KCl concentrations 0.1 mol/L (top panel) and 1.0 mol/L (bottom panel) for cylindrical cells with hp = 1 nm, a = 1 nm, and aspect ratios (α =1.4, 1.1 and 0.8). The solid lines show the fit with f and R∞ as fitting parameters (shown in bold) and the dashed lines show the extrapolation. Since the applied field is large, the resistance at smaller L (< 100 nm) is highly nonlinear and cannot be scaled to extract R∞ with Eq. 12 as is done for the smaller applied voltages in Fig. 6. Hence, a larger L is necessary to employ the scaling form when the electric field is large and ion concentrations are small. Note that the resistance for the 0.1 mol/L solution is substantially smaller than at lower voltages. For 0.1 mol/L solution, the error of the fit for f and R∞ are about 3 % and 0.03 % respectively, whereas for 1.0 mol/L solution the respective errors are less than 1 % and 0.01 %.