Electric conductance of highly selective nanochannels

We consider electric conductance through a narrow nanochannel in the thick-double-layer limit, where the space-charge Debye layers adjacent to the channel walls overlap. At moderate surface-charge densities the electrolyte solution filling the channel comprises mainly of counterions. This allows to derive an analytic closed-form approximation for the channel conductance, independent of the salt concentration in the channel reservoirs. The derived expression consists of two terms. The first, representing electromigratory transport, is independent of the channel depth. The second, representing convective transport, depends upon it weakly.

Figure 1

Nanochannel schematic. The shapes of the counterion-concentration distribution (red) and electrokinetic-flow profile (blue), respectively, correspond to expressions (13) and (17), evaluated for $\sigma =5$.

Figure 2

The dimensionless channel conductance, calculated using Eqs. (12) and (21), as a function of $\sigma ={\sigma }^{*}{h}^{*}/{\epsilon }^{*}{\phi }^{*}$, for $\alpha =0.5$.