Coupling effects on access resistance of in-series nanopores

We present an analytical model for the electrical resistance of two nanopores in series, where the membrane thickness is considered negligible-a configuration relevant to nanopores in atomically thin 2D materials such as graphene, hexagonal boron nitride, or molybdenum disulfide. We consider an axisymmetric (cylindrical) geometry with a finite-size central compartment separating two non-permselective nanopores and adopt a radial inverse square root current density distribution in each nanopore of radius r_n, which we demonstrate is required for accurate quantitative description of the access resistances. Finite element simulations validate the analytical predictions for nanopore-to-central-compartment radius ratios r_n/r_c up to 0.5. Our results accurately describe the crossover from two uncoupled pores in series to a single nanopore as the central compartment length decreases from infinity to zero. We quantify inter-pore coupling via a characteristic coupling length , defined as the central compartment length at which the total access resistance decreases to 95% of the uncoupled value. We find that exhibits a nonlinear dependence on r_n/r_c: for small r_n/r_c (≲ 0.1), the coupling length can reach up to an order of magnitude greater than r_n, whereas for larger r_n/r_c (approaching 0.5), approaches r_n. We additionally find that nanopore coupling is accompanied by a focusing of the current density towards the nanopore center. Our work provides criteria that allow for the better-informed design of nanopores in series devices for use in single biomolecule sensing experiments.