Nanopore ionic memristive effects

In the past few years many significant innovations in the fabrication of solid-state nanopores have triggered a large number of new biophysics applications, due to the small dimension (5-20 nm) reached using a large scale of membrane materials. These significant improvements catalyzed a deeper understanding in the mechanism of charge diffusion inside nanopores (concerning the ionic flux). To correlate the physical phenomena (under dynamic excitation) inside the nanopore result highly important to easily predict and control the ionic transport throughout the nanopore. Here, we show an innovative study, based on Poisson-Nernst-Planck (PNP) equations, to derive a circuit model which is useful in designing nanopores with specific properties. We obtained analytical simulations which highlighted pinched hysteresis voltage-current loops (i.e. a memristor) related to the local ionic concentration response to AC external sources. Through finite difference space discretization, we are able to show how the memristor and the conductance parameters are derived. Finally, a space-varying transmission line with memristor defines the transport phenomena in the nanopore. We believe the combination of the electrical circuit presented here, correlated by the physics in the nanopores, can provide an effective tool to more accurately predict the diffusion in case of networks of nanopores in a membrane.