Charge Selectivity of an Ionic Transistor

The charge selective properties of a long planar nanochannel with an embedded finite uniformly charged section in the middle are studied. The probability flux of a single test ion initially confined to the inlet reservoir is determined by integrating the Smoluchowski equation using a previously published series solution for the Debye-Hückel potential in this geometry. The charge selective properties are characterized by a dimensionless quantity that we call the "fractional blockage". We study how the fractional blockage depends on the dimensionless parameters that characterize the charge state and channel geometry. In the limit of strongly overlapped wall Debye layers, analytical expressions for the fractional blockage are presented that are found to be in good agreement with numerically computed values in the appropriate asymptotic regimes. These results may be helpful in the design of nanofluidic devices that have a variety of applications.