Maxwell-Hall access resistance in graphene nanopores

The resistance due to the current paths converging from bulk to a constriction – e.g., a nanopore – is a mainstay of transport phenomena. In classical electrical conduction, Maxwell, and later Hall for ionic conduction, predicted this access/convergence resistance to be independent of the bulk dimensions and inversely dependent on the pore radius. 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 generically requires all-atom simulations, but this demands enormous resources due to the algebraically decaying nature of convergence with respect to the bulk size. We develop a finite-size scaling analysis – reminiscent of the treatment of critical phenomena – that makes the access resistance accessible in such simulations. This analysis suggests that there is a “golden aspect ratio'' for the simulation 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.