The transport of fluids at the nanoscale is fundamental to manifold biological and industrial processes, ranging from neurotransmission to ultrafiltration. Yet, it is only recently that well-controlled channels with cross sections as small as a few molecular diameters became an experimental reality. When aqueous electrolytes are confined within such channels, the Coulomb interactions between the dissolved ions are reinforced due to dielectric contrast at the channel walls: We dub this effect “interaction confinement.” Yet, no systematic way of computing these confined interactions has been proposed beyond the limiting cases of perfectly metallic or perfectly insulating channel walls. Here, we introduce a new formalism, based on the so-called surface response functions, that expresses the effective Coulomb interactions within a two-dimensional channel in terms of the wall’s electronic structure, described to any desired level of precision. We use it to demonstrate that in few-nanometer-wide channels, the ionic interactions can be tuned by the wall material’s screening length. We illustrate this approach by implementing these interactions in Brownian dynamics simulations of a strongly confined electrolyte and show that the resulting ionic conduction can be adjusted between Ohm’s law and a Wien effect behavior. Our results provide a quantitative approach to tuning nanoscale ion transport through the electronic properties of the channel wall material.
REFERENCES
1.
N.
Kavokine
, R. R.
Netz
, and L.
Bocquet
, “Fluids at the nanoscale: From continuum to subcontinuum transport
,” Annu. Rev. Fluid Mech.
53
, 377
–410
(2021
).2.
J.
Feng
, M.
Graf
, K.
Liu
, D.
Ovchinnikov
, D.
Dumcenco
, M.
Heiranian
, V.
Nandigana
, N. R.
Aluru
, A.
Kis
, and A.
Radenovic
, “Single-layer MoS2 nanopores as nanopower generators
,” Nature
536
, 197
–200
(2016
).3.
R. H.
Tunuguntla
, R. Y.
Henley
, Y.-C.
Yao
, T. A.
Pham
, M.
Wanunu
, and A.
Noy
, “Enhanced water permeability and tunable ion selectivity in subnanometer carbon nanotube porins
,” Science
357
, 792
–796
(2017
).4.
B.
Radha
, A.
Esfandiar
, F. C.
Wang
, A. P.
Rooney
, K.
Gopinadhan
, A.
Keerthi
, A.
Mishchenko
, A.
Janardanan
, P.
Blake
, L.
Fumagalli
, M.
Lozada-Hidalgo
, S.
Garaj
, S. J.
Haigh
, I. V.
Grigorieva
, H. A.
Wu
, and A. K.
Geim
, “Molecular transport through capillaries made with atomic-scale precision
,” Nature
538
, 222
–225
(2016
).5.
S.
Faucher
, N.
Aluru
, M. Z.
Bazant
, D.
Blankschtein
, A. H.
Brozena
, J.
Cumings
, J.
Pedro de Souza
, M.
Elimelech
, R.
Epsztein
, J. T.
Fourkas
, A. G.
Rajan
, H. J.
Kulik
, A.
Levy
, A.
Majumdar
, C.
Martin
, M.
McEldrew
, R. P.
Misra
, A.
Noy
, T. A.
Pham
, M.
Reed
, E.
Schwegler
, Z.
Siwy
, Y.
Wang
, and M.
Strano
, “Critical knowledge gaps in mass transport through single-digit nanopores: A review and perspective
,” J. Phys. Chem. C
123
, 21309
–21326
(2019
).6.
A.
Parsegian
, “Energy of an ion crossing a low dielectric membrane: Solutions to four relevant electrostatic problems
,” Nature
221
, 844
–846
(1969
).7.
M. H.
Cheng
and R. D.
Coalson
, “An accurate and efficient empirical approach for calculating the dielectric self-energy and ion-ion pair potential in continuum models of biological ion channels
,” J. Phys. Chem. B
109
, 488
–498
(2005
).8.
A.
Kamenev
, J.
Zhang
, A. I.
Larkin
, and B. I.
Shklovskii
, “Transport in one-dimensional Coulomb gases: From ion channels to nanopores
,” Physica A
359
, 129
–161
(2006
).9.
J.
Zhang
, A.
Kamenev
, and B. I.
Shklovskii
, “Ion exchange phase transitions in water-filled channels with charged walls
,” Phys. Rev. E
73
, 051205
(2006
).10.
J.
Zhang
, A.
Kamenev
, and B. I.
Shklovskii
, “Conductance of ion channels and nanopores with charged walls: A toy model
,” Phys. Rev. Lett.
95
, 148101
(2005
).11.
I. K.
Kaufman
, P. V. E.
McClintock
, and R. S.
Eisenberg
, “Coulomb blockade model of permeation and selectivity in biological ion channels
,” New J. Phys.
17
, 083021
(2015
).12.
D.
Nicholson
and N.
Quirke
, “Ion pairing in confined electrolytes
,” Mol. Simul.
29
, 287
–290
(2003
).13.
N.
Kavokine
, S.
Marbach
, A.
Siria
, and L.
Bocquet
, “Ionic Coulomb blockade as a fractional Wien effect
,” Nat. Nanotechnol.
14
, 573
–578
(2019
).14.
P.
Robin
, N.
Kavokine
, and L.
Bocquet
, “Modeling of emergent memory and voltage spiking in ionic transport through angstrom-scale slits
,” Science
373
, 687
–691
(2021
).15.
W.
Zhao
, Y.
Sun
, W.
Zhu
, J.
Jiang
, X.
Zhao
, D.
Lin
, W.
Xu
, X.
Duan
, J. S.
Francisco
, and X. C.
Zeng
, “Two-dimensional monolayer salt nanostructures can spontaneously aggregate rather than dissolve in dilute aqueous solutions
,” Nat. Commun.
12
, 5602
(2021
).16.
P.
Robin
, T.
Emmerich
, A.
Ismail
, A.
Niguès
, Y.
You
, G.-H.
Nam
, A.
Keerthi
, A.
Siria
, A.
Geim
, B.
Radha
, and L.
Bocquet
, “Long-term memory and synapse-like dynamics of ionic carriers in two-dimensional nanofluidic channels
,” arXiv:2205.07653 (2022
).17.
R. P.
Misra
and D.
Blankschtein
, “Insights on the role of many-body polarization effects in the wetting of graphitic surfaces by water
,” J. Phys. Chem. C
121
, 28166
–28179
(2017
).18.
R. P.
Misra
and D.
Blankschtein
, “Uncovering a universal molecular mechanism of salt ion adsorption at solid/water interfaces
,” Langmuir
37
, 722
–733
(2021
).19.
S.
Kondrat
and A.
Kornyshev
, “Superionic state in double-layer capacitors with nanoporous electrodes
,” J. Phys.: Condens. Matter
23
, 022201
(2011
).20.
A. A.
Lee
, S.
Kondrat
, and A. A.
Kornyshev
, “Single-file charge storage in conducting nanopores
,” Phys. Rev. Lett.
113
, 048701
(2014
).21.
C.
Merlet
, B.
Rotenberg
, P. A.
Madden
, P.-L.
Taberna
, P.
Simon
, Y.
Gogotsi
, and M.
Salanne
, “On the molecular origin of supercapacitance in nanoporous carbon electrodes
,” Nat. Mater.
11
, 306
–310
(2012
).22.
G.
Mahan
, Many-Particle Physics
(Dover
, 1990
), Chap. V, pp. 442
–443
.23.
M.
Vorotyntsev
and A.
Kornyshev
, “Electrostatic interaction on a metal/insulator interface
,” Zh. Eksp. Teor. Fiz.
78
, 1008
–1019
(1980
).24.
A. A.
Kornyshev
and M. A.
Vorotyntsev
, “Nonlocal electrostatic approach to the double layer and adsorption at the electrode-electrolyte interface
,” Surf. Sci.
101
, 23
–48
(1980
).25.
A. A.
Kornyshev
, W.
Schmickler
, and M. A.
Vorotyntsev
, “Nonlocal electrostatic approach to the problem of a double layer at a metal-electrolyte interface
,” Phys. Rev. B
25
, 5244
–5256
(1982
).26.
J.
Comtet
, A.
Niguès
, V.
Kaiser
, B.
Coasne
, L.
Bocquet
, and A.
Siria
, “Nanoscale capillary freezing of ionic liquids confined between metallic interfaces and the role of electronic screening
,” Nat. Mater.
16
, 634
–639
(2017
).27.
V.
Kaiser
, J.
Comtet
, A.
Niguès
, A.
Siria
, B.
Coasne
, and L.
Bocquet
, “Electrostatic interactions between ions near Thomas-Fermi substrates and the surface energy of ionic crystals at imperfect metals
,” Faraday Discuss.
199
, 129
–158
(2017
).28.
L.
Scalfi
, T.
Dufils
, K. G.
Reeves
, B.
Rotenberg
, and M.
Salanne
, “A semiclassical Thomas–Fermi model to tune the metallicity of electrodes in molecular simulations
,” J. Chem. Phys.
153
, 174704
(2020
).29.
A.
Schlaich
, D.
Jin
, L.
Bocquet
, and B.
Coasne
, “Electronic screening using a virtual Thomas–Fermi fluid for predicting wetting and phase transitions of ionic liquids at metal surfaces
,” Nat. Mater.
21
, 237
–245
(2022
).30.
A.
Liebsch
, Electronic Excitations at Metal surfaces
(Springer
, 1995
), Chap. III, pp. 49
–105
.31.
J. M.
Pitarke
, V. M.
Silkin
, E. V.
Chulkov
, and P. M.
Echenique
, “Theory of surface plasmons and surface-plasmon polaritons
,” Rep. Prog. Phys.
70
, 1
–87
(2007
).32.
33.
J.
Rammer
, Quantum Field Theory of Non-Equilibrium States
(Cambridge University Press
, Cambridge
, 2007
), Chap. VI.34.
A.
Griffin
and J.
Harris
, “Sum rules for a bounded electron gas
,” Can. J. Phys.
54
, 1396
–1408
(1976
).35.
R. H.
Ritchie
and A. L.
Marusak
, “The surface plasmon dispersion relation for an electron gas
,” Surf. Sci.
4
, 234
–240
(1966
).36.
A.
Schlaich
, E. W.
Knapp
, and R. R.
Netz
, “Water dielectric effects in planar confinement
,” Phys. Rev. Lett.
117
, 048001
(2016
).37.
L.
Fumagalli
, A.
Esfandiar
, R.
Fabregas
, S.
Hu
, P.
Ares
, A.
Janardanan
, Q.
Yang
, B.
Radha
, T.
Taniguchi
, K.
Watanabe
, G.
Gomila
, K. S.
Novoselov
, and A. K.
Geim
, “Anomalously low dielectric constant of confined water
,” Science
360
, 1339
–1342
(2018
).38.
D. J.
Bonthuis
, S.
Gekle
, and R. R.
Netz
, “Dielectric profile of interfacial water and its effect on double-layer capacitance
,” Phys. Rev. Lett.
107
, 166102
(2011
).39.
S.
Teber
, “Translocation energy of ions in nano-channels of cell membranes
,” J. Stat. Mech.: Theory Exp.
2005
, P07001
.40.
Y.
Levin
, “Electrostatics of ions inside the nanopores and trans-membrane channels
,” Europhys. Lett.
76
, 163
–169
(2006
).41.
P.
Loche
, C.
Ayaz
, A.
Schlaich
, Y.
Uematsu
, and R. R.
Netz
, “Giant axial dielectric response in water-filled nanotubes an effective electrostatic ion-ion interactions from a tensorial dielectric model
,” J. Phys. Chem. B
123
, 10850
–10857
(2019
).42.
E.
Weber
, “The electrostatic field produced by a point charge in the axis of a cylinder
,” J. Appl. Phys.
10
, 663
–666
(1939
).43.
S.
Plimpton
, “Fast parallel algorithms for short-range molecular dynamics
,” J. Comput. Phys.
117
, 1
–19
(1995
).44.
A. P.
Thompson
, H. M.
Aktulga
, R.
Berger
, D. S.
Bolintineanu
, W. M.
Brown
, P. S.
Crozier
, P. J.
in't Veld
, A.
Kohlmeyer
, S. G.
Moore
, T. D.
Nguyen
, R.
Shan
, M. J.
Stevens
, J.
Tranchida
, C.
Trott
, and S. J.
Plimpton
, “Lammps—A flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales
,” Comput. Phys. Commun.
271
, 108171
(2022
).45.
H.
Miyazaki
, S.
Odaka
, T.
Sato
, S.
Tanaka
, H.
Goto
, A.
Kanda
, K.
Tsukagoshi
, Y.
Ootuka
, and Y.
Aoyagi
, “Inter-layer screening length to electric field in thin graphite film
,” Appl. Phys. Express
1
, 034007
(2008
).46.
E. H.
Hwang
and S.
Das Sarma
, “Dielectric function, screening, and plasmons in two-dimensional graphene
,” Phys. Rev. B
75
, 205418
(2007
).47.
R.
Geick
, C. H.
Perry
, and G.
Rupprecht
, “Normal modes in hexagonal boron nitride
,” Phys. Rev.
146
, 543
–547
(1966
).48.
A.
Robert
, H.
Bethoumieux
, and M.-L.
Bocquet
, “Coupled interactions at the ionic graphene/water interface
,” arXiv:2204.08779.49.
N.
Kavokine
, M.-L.
Bocquet
, and L.
Bocquet
, “Fluctuation-induced quantum friction in nanoscale water flows
,” Nature
602
, 84
–90
(2022
).© 2022 Author(s). Published under an exclusive license by AIP Publishing.
2022
Author(s)
You do not currently have access to this content.
