Maxwell-Hall access resistance in graphene nanopores
Subin Sahu, Michael P. Zwolak
The resistance due to the convergence 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 or convergence resistance to be independent of the bulk dimensions and inversely dependent on pore radius, a, for a perfectly circular pore. 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. We develop a finite-size scaling analysis -- reminiscent of the treatment of critical phenomena -- that makes the convergence resistance accessible in such simulations. This analysis suggests that there is an ``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.