Electrical Conductance of Charged Nanopores

A nanopore's response to an electrical potential drop is characterized by its electrical conductance, G∼. For the last two decades, it has been thought that at low electrolyte concentrations, c∼0, the conductance is concentration-independent such that G∼c∼00. It has been recently demonstrated that surface charge regulation changes the dependency to G∼∼c∼0α, whereby the slope typically takes the values α = 1/3 or 1/2. However, experiments have observed slopes of 2/3 and 1 suggesting that additional mechanisms, such as convection and slip-lengths, appear. Here, we elucidate the interplay between three mechanisms: surface charge regulation, convection, and slip lengths. We show that the inclusion of convection does not change the slope, and when the effects of hydrodynamic slip are included, the slope is doubled. We show that when all effects are accounted for, α can take any value between 0 and 1 where the exact value of the slope depends on the material properties. This result is of utmost importance in designing any electro-kinetically driven nanofluidic system characterized by its conductance.