Equivalent circuits in nanopore-based electrochemical systems

Single-nanopore membranes constitute physical models for biological ion channels and are also central to electrochemical energy transducers, logical circuits in sensors and actuators, and converters in bioelectrical interfaces. The membrane potential, defined as the electrical potential difference established between two different ionic solutions separated by the membrane, is crucial for the electrical coupling of nanofluidic concentration cells to electronic components such as load capacitors and resistors. Here we analyze, theoretically and experimentally, the validity of basic principles governing electric circuit theory such as the Thévenin equivalent circuit, the additivity of voltages and resistances, and the Millman theorem in nanopore-based concentration cells. To this end, we consider a wide range of practical conditions with respect to salt concentrations, nanopore asymmetry, electrical capacitances, and series and parallel arrangements. Additionally, we investigate the scaling of the single pore results to the multipore case. The results obtained suggest that basic circuit models offer approximate tools to guide the analysis of the nanofluidic concentration cells.