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.Ion transport through pores and channels plays an important role in physiological functions [1][2][3] and in nanotechnology, with applications such as DNA sequencing [4][5][6], imaging living cells [7][8][9], filtration [10], and desalination [11], among others. These pores localize the flow of ions and molecules across a membrane, where sensors, for example, nanoscale electrodes for DNA sequencing [12][13][14][15][16][17][18] , can interrogate the flowing species as they pass through and where functional elements can selectivity regulate the movement of different species (for example, ion types).In particular, from DNA sequencing [19][20][21][22] to filtration [23][24][25][26][27], graphene nanopores and porous membranes are one of the most promising materials for applications. Novel fabrication strategies and designs are under development to create large-scale, controllable porous membranes [25,26,28] and graphene laminate devices [23,24]. Moreover, their single atom thickness makes these systems ideal for interrogating ion dehydration [29,30], which both sheds light on recent experiments on ion selectivity in porous graphene [25,26,28] and will help analyze the behavior of biological pores [29,30]. Dehydration has been predicted to give rise to ion selectivity and quantized conductance in long, narrow pores [31][32][33][34][35] but the energy barriers are typically so large that the currents are minuscule, which is rectified by the use of membranes with single-atom thickness [29,30].Despite the intense and broad interest in ion transport, one of its most fundamental aspects, the convergence of the bulk to the pore, is essentially not computable with all-atom molecular dynamics (MD) [36], yet is very important for understanding in vivo operation and characteristics of ion channels [37]. Experiments on mono-or bi-layer graphene, show a dominant 1/a access ...

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“…8). Because the membrane was so thin and the electric field distribution about the waist so narrow and the diameter so small, it was conjectured that a sub-nanopore acted essentially like an electrolytic point contact 39,40 . Since the conductance through an ideal point contact associated with a circular hole of diameter d through a vanishingly thin membrane, immersed in electrolyte of conductivity σ , scaled linearly with the diameter according to g = σ ⋅ d , a linear extrapolation to zero conductance was used as a measure of the size of the metal ions.…”

Electrical conductivity and tortuosity of solid foam: Effect of pore connections

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“…Before moving to the next section, we briey discuss the golden aspect ratio introduced by Sahu and Zwolak [23,24]. For this special aspect ratio (H/D b ) * , nite size eects should be eliminated in numerical simulations (i.e.…”

Prehistory probability distribution of ion transition through graphene nanopore

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