Coupling Effects on Access Resistance of In-Series Nanopores

Abstract

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 (j(r) ∝ 1/√(1-r²/r_n²)) 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 l'_c,95, defined as the central compartment length at which the total access resistance decreases to 95 % of the uncoupled value. We find that l'_c,95 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), l'_c,95 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.