Formalizing Poisson-Boltzmann Theory for Field-Tunable Nanofluidic Devices

Nanofluidic devices support unconventional ion transport appealing to energy and information technologies, thanks to the susceptibility of confined electric double layers (EDLs) to various external physical fields. Although experimental studies advance rapidly, the rationalization of field-tunable nanofluidic transport has not reached a formalized and unified level. Here we reformulate the Poisson-Boltzmann theory and reveal distinct EDL regimes on the parameter space. Based on the regime classification, we establish a formal framework for the tunable nanofluidic transport and discuss the electrostatic modulation (ionic transistor) extensively. The framework reproduces the observed conductivity-concentration scaling behaviors, rationalizes the ionic transistors with reconfigurable polarities, and predicts one fundamental thermodynamic limit for electrostatic modulation (60 mV/dec). Being accurate, generalizable and extensible, this framework can account for a wide range of ion transport in confined spaces.