It has recently been suggested that a breakdown of electroneutrality occurs in highly confined nanopores that are encompassed by a dielectric material. This work elucidates the conditions for this breakdown. We show that the breakdown within the pore results from the response of the electric field within the dielectric. Namely, we show that this response is highly sensitive to the boundary condition at the dielectric edge. The standard Neumann boundary condition of no-flux predicts that the breakdown does not occur. However, a Dirichlet boundary condition for a zero-potential predicts a breakdown. Within this latter scenario, the breakdown exhibits a dependence on the thickness of the dielectric material. Specifically, infinite thickness dielectrics do not exhibit a breakdown, while dielectrics of finite thickness do exhibit a breakdown. Numerical simulations confirm theoretical predictions. The breakdown outcomes are discussed with regard to single pore systems and multiple pore systems.

1.
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
,
J. Phys. Chem. C
123
,
21309
(
2019
).
2.
N.
Kavokine
,
R. R.
Netz
, and
L.
Bocquet
,
Annu. Rev. Fluid Mech.
53
,
377
(
2020
).
3.
J. P.
Thiruraman
,
P.
Masih Das
, and
M.
Drndić
,
ACS Nano
14
,
3736
(
2020
).
5.
A.
Siria
,
M.-L.
Bocquet
, and
L.
Bocquet
,
Nat. Rev. Chem.
1
,
0091
(
2017
).
6.
J. K.
Holt
,
H. G.
Park
,
Y.
Wang
,
M.
Stadermann
,
A. B.
Artyukhin
,
C. P.
Grigoropoulos
,
A.
Noy
, and
O.
Bakajin
,
Science
312
,
1034
(
2006
).
7.
R. H.
Tunuguntla
,
R. Y.
Henley
,
Y.-C.
Yao
,
T. A.
Pham
,
M.
Wanunu
, and
A.
Noy
,
Science
357
,
792
(
2017
).
8.
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
,
Science
360
,
1339
(
2018
).
9.
Y.
Noh
and
N. R.
Aluru
,
ACS Nano
14
,
10518
(
2020
).
10.
A.
Levy
,
J. P.
de Souza
, and
M. Z.
Bazant
,
J. Colloid Interface Sci.
579
,
162
(
2020
).
11.
J. P.
de Souza
,
A.
Levy
, and
M. Z.
Bazant
,
Phys. Rev. E
104
,
044803
(
2021
).
12.
A.
Bakhshandeh
,
M.
Segala
, and
T.
Colla
,
Soft Matter
16
,
10488
(
2020
).
13.
S.
Schlumpberger
,
R. B.
Smith
,
H.
Tian
,
A.
Mani
, and
M. Z.
Bazant
, arXiv:2011.02605 [physics] (
2021
).
14.
O.
Maxian
,
R. P.
Peláez
,
L.
Greengard
, and
A.
Donev
, arXiv:2101.07088 [cs, math] (
2021
).
15.
I. G.
Wenten
,
K.
Khoiruddin
,
M. A.
Alkhadra
,
H.
Tian
, and
M. Z.
Bazant
,
Adv. Colloid Interface Sci.
284
,
102269
(
2020
).
16.
M.
Matse
,
P.
Berg
, and
M.
Eikerling
,
J. Chem. Phys.
152
,
084103
(
2020
).
17.
M.
Matse
, “
Mathematical modelling of electrokinetic phenomena in soft nanopores
,” Ph.D. thesis,
Science: Department of Physics
,
2020
.
18.
H.
Tian
,
M. A.
Alkhadra
, and
M. Z.
Bazant
,
J. Colloid Interface Sci.
589
,
605
(
2021
).
19.
K. D.
Fong
,
H. K.
Bergstrom
,
B. D.
McCloskey
, and
K. K.
Mandadapu
,
AIChE J.
66
,
e17091
(
2020
).
20.
Z.
Sarkadi
,
D.
Fertig
,
Z.
Ható
,
M.
Valiskó
, and
D.
Boda
,
J. Chem. Phys.
154
,
154704
(
2021
).
21.
M. S.
Miranda
,
R.
Lyttleton
,
P. H.
Siu
,
S.
Diez
,
H.
Linke
, and
A. P.
Micolich
,
New J. Phys.
23
,
065003
(
2021
).
22.
T.
Hennequin
,
M.
Manghi
, and
J.
Palmeri
, arXiv:2104.14824 [cond-mat] (
2021
).
23.
R.
Dolatabadi
,
Z.
Gharehnazifam
,
F.
Moraffah
,
A.
Mohammadi
, and
M.
Baghani
,
Transp. Porous Media
(published online,
2021
).
24.
O.
Maxian
,
R. P.
Peláez
,
L.
Greengard
, and
A.
Donev
,
J. Chem. Phys.
154
,
204107
(
2021
).
25.
D.
Fertig
,
Z.
Sarkadi
,
M.
Valiskó
, and
D.
Boda
,
Mol. Simul.
2021
,
1
.
26.
P.
Berg
and
P.
Nadon
,
Soft Matter
17
,
5907
(
2021
).
27.
Y.
Green
,
J. Chem. Phys.
154
,
084705
(
2021
).
28.
P. M.
Biesheuvel
,
J. Colloid Interface Sci.
238
,
362
(
2001
).
29.
P. M.
Biesheuvel
and
M. Z.
Bazant
,
Phys. Rev. E
94
,
050601
(
2016
).
30.
P. B.
Peters
,
R.
van Roij
,
M. Z.
Bazant
, and
P. M.
Biesheuvel
,
Phys. Rev. E
93
,
053108
(
2016
).
31.
J. D.
Jackson
,
Classical Electrodynamics
, 3rd ed. (
Wiley
,
New York
,
1998
).
32.
T.
Kailath
,
Linear Systems
(
Prentice-Hall
,
Englewood Cliffs, NJ
,
1980
).
33.
M.
Mao
,
J. D.
Sherwood
, and
S.
Ghosal
,
J. Fluid Mech.
749
,
167
(
2014
).
34.
B. J.
Kirby
,
Micro- and Nanoscale Fluid Mechanics: Transport in Microfluidic Devices
(
Cambridge University Press
,
2010
).
35.
R. F.
Probstein
,
Physicochemical Hydrodynamics: An Introduction
, 2nd ed. (
Wiley-Interscience
,
Hoboken, NJ
,
2003
).
36.
Y.
Green
,
R.
Abu-Rjal
, and
R.
Eshel
,
Phys. Rev. Appl.
14
,
014075
(
2020
).
37.
O.
Schnitzer
and
E.
Yariv
,
Phys. Rev. E
87
,
054301
(
2013
).
38.
Y.
Uematsu
,
R. R.
Netz
,
L.
Bocquet
, and
D. J.
Bonthuis
,
J. Phys. Chem. B
122
,
2992
(
2018
).
39.
E.
Secchi
,
A.
Niguès
,
L.
Jubin
,
A.
Siria
, and
L.
Bocquet
,
Phys. Rev. Lett.
116
,
154501
(
2016
).
40.
Y.
Green
and
G.
Yossifon
,
Phys. Rev. E
89
,
013024
(
2014
).
41.
Y.
Green
,
S.
Shloush
, and
G.
Yossifon
,
Phys. Rev. E
89
,
043015
(
2014
).
42.
Y.
Green
,
S.
Park
, and
G.
Yossifon
,
Phys. Rev. E
91
,
011002(R)
(
2015
).
43.
Y.
Green
,
R.
Eshel
,
S.
Park
, and
G.
Yossifon
,
Nano Lett.
16
,
2744
(
2016
).
44.
R. A.
Lucas
and
Z. S.
Siwy
,
ACS Appl. Mater. Interfaces
12
,
56622
(
2020
).
45.
J. P.
Kleinubing Abal
and
M. C.
Barbosa
,
J. Chem. Phys.
154
,
134506
(
2021
).
46.
Y.-C.
Chou
,
J.
Chen
,
C.-Y.
Lin
, and
M.
Drndić
,
J. Chem. Phys.
154
,
105102
(
2021
).
47.
M.
Valiskó
,
B.
Matejczyk
,
Z.
Ható
,
T.
Kristóf
,
E.
Mádai
,
D.
Fertig
,
D.
Gillespie
, and
D.
Boda
,
J. Chem. Phys.
150
,
144703
(
2019
).
48.
D.
Fertig
,
B.
Matejczyk
,
M.
Valiskó
,
D.
Gillespie
, and
D.
Boda
,
J. Phys. Chem. C
123
,
28985
(
2019
).
49.
M. F.
Döpke
and
R.
Hartkamp
,
J. Chem. Phys.
154
,
094701
(
2021
).
50.
H.
Gao
,
J.
Wang
,
Y.
Liu
,
Y.
Xie
,
P.
Král
, and
R.
Lu
,
J. Chem. Phys.
154
,
104707
(
2021
).
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