Access Resistance in Atomically Thin Nanopores

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Access resistance indicates how well current carriers from the bulk medium can converge to a pore or opening, and it sets the upper limit of the current that can flow into ion channels. In classical electrical conduction, Maxwell - and later Hall for ionic conduction - predicted this access or convergence resistance to be independent of the bulk dimensions and inversely dependent on the pore radius for a perfectly circular pore when the bulk dimensions are balanced and infinite. These conditions are often not valid in simulations of transport properties due to the computational cost of large simulation cells, and can even break down in micro- and nano-scale systems due to strong confinement. More generally, though, this resistance is contextual, it depends on the presence of functional groups/charges and fluctuations, as well as the effective constriction geometry/dimensions. Addressing the context generally requires all-atom simulations, but this demands enormous resources due to the algebraically decaying nature of convergence. We develop a finite-size scaling analysis - reminiscent of the treatment of critical phenomenon - that makes the convergence resistance accessible in such simulations. This analysis suggests that there is a “golden aspect ratio” for the simulations cell that yields the infinite system result with a finite system. We employ this approach to resolve the experimental and theoretical discrepancies in the radius-dependence of graphene nanopore resistance.