Integrated circuits are present in all electronic devices, and enable signal amplification, modulation, and relay. Nature uses another type of circuits composed of channels in a cell membrane, which regulate and amplify transport of ions, not electrons and holes as is done in electronic systems. Here we show an abiotic ionic circuit that is inspired by concepts from electronics and biology. The circuit amplifies small ionic signals into ionic outputs, and its operation mimics the electronic Darlington amplifier composed of transistors. The individual transistors are pores equipped with three terminals including a gate that is able to enrich or deplete ions in the pore. The circuits we report function at gate voltages < 1 V, respond to sub-nA gate currents, and offer ion current amplification with a gain up to ~300. Ionic amplifiers are a logical step toward improving chemical and biochemical sensing, separations and amplification, among others.

Single pores in the resistive-pulse technique are used as an analytics tool to detect, size, and characterize physical as well as chemical properties of individual objects such as molecules and particles. Each object passing through a pore causes a transient change of the transmembrane current called a resistive pulse. In high salt concentrations when the pore diameter is significantly larger than the screening Debye length, it is assumed that the particle size and surface charge can be determined independently from the same experiment. In this article we challenge this assumption and show that highly charged hard spheres can cause a significant increase of the resistive-pulse amplitude compared to neutral particles of a similar diameter. As a result, resistive pulses overestimate the size of charged particles by even 20%. The observation is explained by the effect of concentration polarization created across particles in a pore, revealed by numerical modeling of ionic concentrations, ion current, and local electric fields. It is notable that in resistive-pulse experiments with cylindrical pores, concentration polarization was previously shown to influence ionic concentrations only at pore entrances; consequently, additional and transient modulation of resistive pulses was observed when a particle entered or left the pore. Here we postulate that concentration polarization can occur across transported particles at any particle position along the pore axis and affect the magnitude of the entire resistive pulse. Consequently, the recorded resistive pulses of highly charged particles reflect not only the particles' volume but also the size of the depletion zone created in front of the moving particle. Moreover, the modeling identified that the effective surface charge density of particles depended not only on the density of functional groups on the particle but also on the capacitance of the Stern layer. The findings are of crucial importance for sizing particles and characterizing their surface charge properties.