Issue 7, 2018

Maxwell-Hall access resistance in graphene nanopores

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.

Graphical abstract: Maxwell-Hall access resistance in graphene nanopores

Supplementary files

Article information

Article type
Communication
Submitted
24 Nov 2017
Accepted
23 Jan 2018
First published
24 Jan 2018

Phys. Chem. Chem. Phys., 2018,20, 4646-4651

Maxwell-Hall access resistance in graphene nanopores

S. Sahu and M. Zwolak, Phys. Chem. Chem. Phys., 2018, 20, 4646 DOI: 10.1039/C7CP07924A

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