Maxwell-Hall access resistance in graphene nanopores

TL;DR

This paper develops a finite-size scaling method to accurately determine access resistance in graphene nanopores, resolving discrepancies between experimental and theoretical results by identifying a 'golden aspect ratio' for simulations.

Contribution

The paper introduces a finite-size scaling analysis that enables precise calculation of access resistance in nanopores, accounting for complex factors like charges and geometry.

Findings

Identifies a 'golden aspect ratio' for simulation cells.

Resolves previous discrepancies in nanopore resistance measurements.

Provides a scalable method for all-atom simulations of transport phenomena.

Abstract

The resistance due to the convergence from bulk to a constriction, for example, 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 the 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 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.