FIG. 6.
PNP solution of the resistance versus L for cylindrical cells with hp = 1 nm, a = 1 nm, and various aspect ratios (α = 1.4, 1.1 and 0.8 from top to bottom). The labels at the top show the applied potential and the labels at the right show the concentration of KCl. The golden aspect ratio remains the same as in the homogeneous medium calculation for the smaller voltages (10 mV and 100 mV) and for both 1 mol/L and 0.1 mol/L concentrations. For 300 mV applied voltage, the golden aspect ratio seems to take on a lower value due to the increased concentration of ions near the membrane, which is more pronounced for low concentrations due to a diminished ability to screen and generate local fields. The legends show the fits to Eq. (12) with the fit parameters shown in bold. The error of the fits for f’s and R∞’s are about 0.5 % and 0.1 % respectively.