Beyond the Ohmic Limit: Co-Ion Control and Conductance Scaling Regimes in Rectifying Nanochannels

Abstract The power-law scaling of ionic conductance G ∼ cα serves as a fundamental probe of transport physics in confined geometries, where transport is traditionally restricted to sublinear regimes (α < 1) governed by majority counterions. While current rectification is widely exploited in nanofluidic diodes and iontronic circuits, its direct consequence on this scaling law remains unexplored. Here, we show that moving beyond the ohmic limit establishes a co-ion control paradigm that dictates transport in asymmetric nanoenvironments. By pairing an analytical electrodiffusion framework with experimental validation across a diverse spectrum of heterogeneous systems, including bipolar biological channels (OmpF, gramicidin A) and unipolar synthetic conical nanopores, we demonstrate a polarity-driven transition in ionic control. In the rectifying polarity, the formation of an electrostatic depletion zone transfers transport control from majority counterions to minority co-ions. Remarkably, this electrostatic reconfiguration yields supralinear scaling (α > 1) in bipolar configurations while driving unipolar ones toward linearity (α ∼ 1). By unifying biological and solid-state membranes under a single predictive model, these findings clarify how pore geometry, charge asymmetry, and voltage polarity cooperatively govern nanoscale ion transport.