Fig. 1. Measurements of cross-membrane potential.
a Schematic of devices used in this work. b The electrical conductance of a monolayer graphene device, where the gate potential shifts the Fermi level of graphene with respect to the neutrality point (yellow). c Measurements of the output Ib (at Vb = 0) and d the Vb (at Ib = 0) under the applied input potential Vt. The Ib0 and the Vb0 are the saturated output currents and voltages, as defined by the black dashed lines in (c, d), respectively. In (c, d), the bottom insets show schematics of the gate potential (Φ) as a function of the distance from the graphene for different gate configurations (c, Vb = 0; d, Vb = Vb0). Note that the applied Vt or Vb is relative to the Fermi surface of graphene defined as Φ = 0 in the energy scale. The interfacial Φint experienced by electrolytes measures the difference between Vt (or Vb) relative to the neutrality point of graphene indicated by the dashed lines. The Vt and Vb shift the Fermi level of graphene with respect to the neutrality points (yellow). For simplicity, only positively charged ions (green sphere) are shown to indicate ion transport direction. Analogous analysis is applicable to anions. Hydration shell of ions is omitted for clarity. The dark gray balls represent carbon atoms. e Vb0 and Ib0 modulated by Vt in a representative monolayer graphene device. The black line indicates the relationship when Vb0 = Vt. f The relation between Ib0 and Vb0. The red solid line is the best linear fit. In all experiments, both the top and bottom reservoirs were filled with 0.01 M KCl of pH ≈ 6.5. The slight deviation from neutral can be attributed to dissolved CO2 from environment. Error bars in (e, f) are the uncertainties due to signal noise.