Nanopores have been explored for various biochemical and nanoparticle analyses, primarily via characterizing the ionic current through the pores. At present, however, size determination for solid-state nanopores is experimentally tedious and theoretically unaccountable. Here, we establish a physical model by introducing an effective transport length, Leff, that measures, for a symmetric nanopore, twice the distance from the center of the nanopore where the electric field is the highest to the point along the nanopore axis where the electric field falls to e-1 of this maximum. By [Formula: see text], a simple expression S0 = f (G, σ, h, β) is derived to algebraically correlate minimum nanopore cross-section area S0 to nanopore conductance G, electrolyte conductivity σ, and membrane thickness h with β to denote pore shape that is determined by the pore fabrication technique. The model agrees excellently with experimental results for nanopores in graphene, single-layer MoS2, and ultrathin SiNx films. The generality of the model is verified by applying it to micrometer-size pores.
Keywords: algebraic solution; conductance measurement in electrolyte; effective transport length; nanopores; physical model.