We present the coupling of two frameworks—the pseudo-open boundary simulation method known as constant potential molecular dynamics simulations (CμMD), combined with quantum mechanics/molecular dynamics (QMMD) calculations—to describe the properties of graphene electrodes in contact with electrolytes. The resulting CμQMMD model was then applied to three ionic solutions (LiCl, NaCl, and KCl in water) at bulk solution concentrations ranging from 0.5 M to 6 M in contact with a charged graphene electrode. The new approach we are describing here provides a simulation protocol to control the concentration of electrolyte solutions while including the effects of a fully polarizable electrode surface. Thanks to this coupling, we are able to accurately model both the electrode and solution side of the double layer and provide a thorough analysis of the properties of electrolytes at charged interfaces, such as the screening ability of the electrolyte and the electrostatic potential profile. We also report the calculation of the integral electrochemical double layer capacitance in the whole range of concentrations analyzed for each ionic species, while the quantum mechanical simulations provide access to the differential and integral quantum capacitance. We highlight how subtle features, such as the adsorption of potassium graphene or the tendency of the ions to form clusters contribute to the ability of graphene to store charge, and suggest implications for desalination.

1.
D.
Cohen-Tanugi
and
J. C.
Grossman
, “
Water desalination across nanoporous graphene
,”
Nano Lett.
12
(
7
),
3602
3608
(
2012
).
2.
M.
Heiranian
,
Y.
Noh
, and
N. R.
Aluru
, “
Dynamic and weak electric double layers in ultrathin nanopores
,”
J. Chem. Phys.
154
(
13
),
134703
(
2021
).
3.
S. P.
Surwade
,
S. N.
Smirnov
,
I. V.
Vlassiouk
,
R. R.
Unocic
,
G. M.
Veith
,
S.
Dai
, and
S. M.
Mahurin
, “
Water desalination using nanoporous single-layer graphene
,”
Nat. Nanotechnol.
10
(
5
),
459
464
(
2015
).
4.
P.
Simon
and
Y.
Gogotsi
, “
Materials for electrochemical capacitors
,” in
Nanoscience and Technology: A Collection of Reviews from Nature Journals
(
World Scientific
,
2008
), pp.
320
329
.
5.
Y.
Wang
,
L.
Zhang
,
H.
Hou
,
W.
Xu
,
G.
Duan
,
S.
He
,
K.
Liu
, and
S.
Jiang
, “
Recent progress in carbon-based materials for supercapacitor electrodes: A review
,”
J. Mater. Sci.
56
(
1
),
173
200
(
2021
).
6.
J. D.
Elliott
,
A. A.
Papaderakis
,
R. A. W.
Dryfe
, and
P.
Carbone
, “
The electrochemical double layer at the graphene/aqueous electrolyte interface: What we can learn from simulations, experiments, and theory
,”
J. Mater. Chem. C
10
,
15225
15262
(2022).
7.
Y.
Wang
,
Z.
Shi
,
Y.
Huang
,
Y.
Ma
,
C.
Wang
,
M.
Chen
, and
Y.
Chen
, “
Supercapacitor devices based on graphene materials
,”
J. Phys. Chem. C
113
(
30
),
13103
13107
(
2009
).
8.
C.
Liu
,
Z.
Yu
,
D.
Neff
,
A.
Zhamu
, and
B. Z.
Jang
, “
Graphene-based supercapacitor with an ultrahigh energy density
,”
Nano Lett.
10
(
12
),
4863
4868
(
2010
).
9.
A.
Yu
,
I.
Roes
,
A.
Davies
, and
Z.
Chen
, “
Ultrathin, transparent, and flexible graphene films for supercapacitor application
,”
Appl. Phys. Lett.
96
(
25
),
253105
(
2010
).
10.
L. L.
Zhang
,
R.
Zhou
, and
X. S.
Zhao
, “
Graphene-based materials as supercapacitor electrodes
,”
J. Mater. Chem.
20
(
29
),
5983
5992
(
2010
).
11.
Y.
Zhu
,
S.
Murali
,
M. D.
Stoller
,
K. J.
Ganesh
,
W.
Cai
,
P. J.
Ferreira
,
A.
Pirkle
,
R. M.
Wallace
,
K. A.
Cychosz
,
M.
Thommes
,
D.
Su
,
E. A.
Stach
, and
R. S.
Ruoff
, “
Carbon-based supercapacitors produced by activation of graphene
,”
Science
332
(
6037
),
1537
1541
(
2011
).
12.
K. H.
An
,
W. S.
Kim
,
Y. S.
Park
,
Y. C.
Choi
,
S. M.
Lee
,
D. C.
Chung
,
D. J.
Bae
,
S. C.
Lim
, and
Y. H.
Lee
, “
Supercapacitors using single-walled carbon nanotube electrodes
,”
Adv. Mater.
13
(
7
),
497
500
(
2001
).
13.
Z.
Yang
,
J.
Tian
,
Z.
Yin
,
C.
Cui
,
W.
Qian
, and
F.
Wei
, “
Carbon nanotube- and graphene-based nanomaterials and applications in high-voltage supercapacitor: A review
,”
Carbon
141
,
467
480
(
2019
).
14.
C.
Merlet
,
B.
Rotenberg
,
P. A.
Madden
, and
M.
Salanne
, “
Computer simulations of ionic liquids at electrochemical interfaces
,”
Phys. Chem. Chem. Phys.
15
(
38
),
15781
15792
(
2013
).
15.
P.
Iamprasertkun
,
W.
Hirunpinyopas
,
A.
Keerthi
,
B.
Wang
,
B.
Radha
,
M. A.
Bissett
, and
R. A. W.
Dryfe
, “
Capacitance of basal plane and edge-oriented highly ordered pyrolytic graphite: Specific ion effects
,”
J. Phys. Chem. Lett.
10
(
3
),
617
623
(
2019
).
16.
H.
Yang
,
J.
Yang
,
Z.
Bo
,
X.
Chen
,
X.
Shuai
,
J.
Kong
,
J.
Yan
, and
K.
Cen
, “
Kinetic-dominated charging mechanism within representative aqueous electrolyte-based electric double-layer capacitors
,”
J. Phys. Chem. Lett.
8
(
15
),
3703
3710
(
2017
).
17.
Q. T.
Qu
,
B.
Wang
,
L. C.
Yang
,
Y.
Shi
,
S.
Tian
, and
Y. P.
Wu
, “
Study on electrochemical performance of activated carbon in aqueous Li2SO4, Na2SO4 and K2SO4 electrolytes
,”
Electrochem. Commun.
10
(
10
),
1652
1655
(
2008
).
18.
J. D.
Elliott
,
A.
Troisi
, and
P.
Carbone
, “
A QM/MD coupling method to model the ion-induced polarization of graphene
,”
J. Chem. Theory Comput.
16
(
8
),
5253
5263
(
2020
).
19.
X.
Wang
,
S. M.
Tabakman
, and
H.
Dai
, “
Atomic layer deposition of metal oxides on pristine and functionalized graphene
,”
J. Am. Chem. Soc.
130
(
26
),
8152
8153
(
2008
).
20.
M.
Gouy
, “
Sur la constitution de la charge électrique à la surface d’un électrolyte
,”
J. Phys. Theor. Appl.
9
(
1
),
457
468
(
1910
).
21.
D. L.
Chapman
, “
LI. A contribution to the theory of electrocapillarity
,”
London, Edinburgh Dublin Philos. Mag. J. Sci.
25
(
148
),
475
481
(
1913
).
22.
S.
Otto
, “
Zur theorie der elektrolytischen doppelschicht
,”
Z. Elektrochem. Angew. Phys. Chem.
30
(
21–22
),
508
516
(
1924
).
23.
M.
Popović
and
A.
Šiber
, “
Lattice-gas Poisson-Boltzmann approach for sterically asymmetric electrolytes
,”
Phys. Rev. E
88
(
2
),
022302
(
2013
).
24.
I.
Borukhov
,
D.
Andelman
, and
H.
Orland
, “
Steric effects in electrolytes: A modified Poisson-Boltzmann equation
,”
Phys. Rev. Lett.
79
(
3
),
435
(
1997
).
25.
M. V.
Fedorov
and
A. A.
Kornyshev
, “
Ionic liquid near a charged wall: Structure and capacitance of electrical double layer
,”
J. Phys. Chem. B
112
(
38
),
11868
11872
(
2008
).
26.
J. J.
Howard
,
J. S.
Perkyns
, and
B. M.
Pettitt
, “
The behavior of ions near a charged wall - Dependence on ion size, concentration, and surface charge
,”
J. Phys. Chem. B
114
(
18
),
6074
6083
(
2010
).
27.
R. P.
Misra
and
D.
Blankschtein
, “
Ion adsorption at solid/water interfaces: Establishing the coupled nature of ion–solid and water–solid interactions
,”
J. Phys. Chem. C
125
(
4
),
2666
2679
(
2021
).
28.
C.
Perego
,
M.
Salvalaglio
, and
M.
Parrinello
, “
Molecular dynamics simulations of solutions at constant chemical potential
,”
J. Chem. Phys.
142
(
14
),
144113
(
2015
).
29.
A. R.
Finney
,
I. J.
McPherson
,
P. R.
Unwin
, and
M.
Salvalaglio
, “
Electrochemistry, ion adsorption and dynamics in the double layer: A study of NaCl(aq) on graphite
,”
Chem. Sci.
12
(
33
),
11166
11180
(
2021
).
30.
K.
Doblhoff-Dier
and
M. T. M.
Koper
, “
Modeling the Gouy–Chapman diffuse capacitance with attractive ion–surface interaction
,”
J. Phys. Chem. C
125
(
30
),
16664
16673
(
2021
).
31.
A.
France-Lanord
and
J. C.
Grossman
, “
Correlations from ion pairing and the Nernst-Einstein equation
,”
Phys. Rev. Lett.
122
(
13
),
136001
(
2019
).
32.
R. P.
Misra
and
D.
Blankschtein
, “
Uncovering a universal molecular mechanism of salt ion adsorption at solid/water interfaces
,”
Langmuir
37
(
2
),
722
733
(
2021
).
33.
C. D.
Williams
,
J.
Dix
,
A.
Troisi
, and
P.
Carbone
, “
Effective polarization in pairwise potentials at the graphene–electrolyte interface
,”
J. Phys. Chem. Lett.
8
(
3
),
703
(
2017
).
34.
J. I.
Siepmann
and
M.
Sprik
, “
Influence of surface topology and electrostatic potential on water/electrode systems
,”
J. Chem. Phys.
102
(
1
),
511
(
1995
).
35.
A.
Coretti
,
C.
Bacon
,
R.
Berthin
,
A.
Serva
,
L.
Scalfi
,
I.
Chubak
,
K.
Goloviznina
,
M.
Haefele
,
A.
Marin-Laflèche
,
B.
Rotenberg
,
S.
Bonella
, and
M.
Salanne
, “
MetalWalls: Simulating electrochemical interfaces between polarizable electrolytes and metallic electrodes
,”
J. Chem. Phys.
157
(
18
),
184801
(
2022
).
36.
C.
Merlet
,
C.
Péan
,
B.
Rotenberg
,
P. A.
Madden
,
B.
Daffos
,
P.-L.
Taberna
,
P.
Simon
, and
M.
Salanne
, “
Highly confined ions store charge more efficiently in supercapacitors
,”
Nat. Commun.
4
(
1
),
2701
(
2013
).
37.
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
(
4
),
306
310
(
2012
).
38.
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
(
17
),
174704
(
2020
).
39.
A.
Landi
,
M.
Reisjalali
,
J. D.
Elliott
,
M.
Matta
,
P.
Carbone
, and
A.
Troisi
, “
Simulation of polymeric mixed ionic and electronic conductors with a combined classical and quantum mechanical model
,”
J. Mater. Chem. C
(published online) (2023).
40.
N.
Di Pasquale
,
J. D.
Elliott
,
P.
Hadjidoukas
, and
P.
Carbone
, “
Dynamically polarizable force fields for surface simulations via multi-output classification neural networks
,”
J. Chem. Theory Comput.
17
(
7
),
4477
4485
(
2021
).
41.
M. J.
Abraham
,
T.
Murtola
,
R.
Schulz
,
S.
Páll
,
J. C.
Smith
,
B.
Hess
, and
E.
Lindahl
, “
GROMACS: High performance molecular simulations through multi-level parallelism from laptops to supercomputers
,”
SoftwareX
1-2
,
19
25
(
2015
).
42.
G. A.
Tribello
,
M.
Bonomi
,
D.
Branduardi
,
C.
Camilloni
, and
G.
Bussi
, “
Plumed 2: New feathers for an old bird
,”
Comput. Phys. Commun.
185
(
2
),
604
613
(
2014
).
43.
B.
Hourahine
,
B.
Aradi
,
V.
Blum
,
F.
Bonafé
,
A.
Buccheri
,
C.
Camacho
,
C.
Cevallos
,
M. Y.
Deshaye
,
T.
Dumitrică
,
A.
Dominguez
,
S.
Ehlert
,
M.
Elstner
,
T.
van der Heide
,
J.
Hermann
,
S.
Irle
,
J. J.
Kranz
,
C.
Köhler
,
T.
Kowalczyk
,
T.
Kubař
,
I. S.
Lee
,
V.
Lutsker
,
R. J.
Maurer
,
S. K.
Min
,
I.
Mitchell
,
C.
Negre
,
T. A.
Niehaus
,
A. M. N.
Niklasson
,
A. J.
Page
,
A.
Pecchia
,
G.
Penazzi
,
M. P.
Persson
,
J.
Řezáč
,
C. G.
Sánchez
,
M.
Sternberg
,
M.
Stöhr
,
F.
Stuckenberg
,
A.
Tkatchenko
,
V. W.-z.
Yu
, and
T.
Frauenheim
, “
DFTB+, a software package for efficient approximate density functional theory based atomistic simulations
,”
J. Chem. Phys.
152
(
12
),
124101
(
2020
).
44.
J. D.
Elliott
,
M.
Chiricotto
,
A.
Troisi
, and
P.
Carbone
, “
Do specific ion effects influence the physical chemistry of aqueous graphene-based supercapacitors? Perspectives from multiscale QMMD simulations
,”
Carbon
207
,
292
304
(2023).
45.
M.
Elstner
,
D.
Porezag
,
G.
Jungnickel
,
J.
Elsner
,
M.
Haugk
,
T.
Frauenheim
,
S.
Suhai
, and
G.
Seifert
, “
Self-consistent-charge density-functional tight-binding method for simulations of complex materials properties
,”
Phys. Rev. B
58
(
11
),
7260
(
1998
).
46.
W. M.
Haynes
,
D. R.
Lide
, and
T. J.
Bruno
,
CRC Handbook of Chemistry and Physics
(
CRC Press
,
2016
).
47.
I. M.
Zeron
,
J. L. F.
Abascal
, and
C.
Vega
.
A force field of Li+, Na+, K+, Mg2+, Ca2+, Cl, and SO42 in aqueous solution based on the TIP4P/2005 water model and scaled charges for the ions
.
J. Chem. Phys.
,
151
(
13
):
134504
,
2019
.
48.
T. A.
Ho
and
A.
Striolo
, “
Capacitance enhancement via electrode patterning
,”
J. Chem. Phys.
139
(
20
),
204708
(
2013
).
49.
K.
Xu
,
H.
Shao
,
Z.
Lin
,
C.
Merlet
,
G.
Feng
,
J.
Zhu
, and
P.
Simon
, “
Computational insights into charge storage mechanisms of supercapacitors
,”
Energy Environ. Mater.
3
(
3
),
235
246
(
2020
).
50.
R. S.
Mulliken
, “
Electronic population analysis on LCAO–MO molecular wave functions. I
,”
J. Chem. Phys.
23
(
10
),
1833
1840
(
1955
).
51.
H. J. C.
Berendsen
,
D.
van der Spoel
, and
R.
van Drunen
, “
Gromacs: A message-passing parallel molecular dynamics implementation
,”
Comput. Phys. Commun.
91
(
1–3
),
43
56
(
1995
).
52.
D.
van der Spoel
,
E.
Lindahl
,
B.
Hess
,
G.
Groenhof
,
A. E.
Mark
, and
H. J. C.
Berendsen
, “
Gromacs: Fast, flexible and free
,”
J. Comput. Chem.
26
(
16
),
1701
1718
(
2005
).
53.
H. J. C.
Berendsen
,
J. R.
Grigera
, and
T. P.
Straatsma
, “
The missing term in effective pair potentials
,”
J. Phys. Chem.
91
(
24
),
6269
6271
(
1987
).
54.
S.
Miyamoto
and
P. A.
Kollman
, “
Settle: An analytical version of the SHAKE and RATTLE algorithm for rigid water model
,”
J. Comput. Chem.
13
,
952
962
(
1992
).
55.
Y.
Huang
,
J.
Liang
, and
Y.
Chen
, “
An overview of the applications of graphene-based materials in supercapacitors
,”
Small
8
(
12
),
1805
1834
(
2012
).
56.
I. S.
Joung
and
T. E.
Cheatham
III
, “
Determination of alkali and halide monovalent ion parameters for use in explicitly solvated biomolecular simulations
,”
J. Phys. Chem. B
112
(
30
),
9020
9041
(
2008
).
57.
A.
Hagberg
,
P.
Swart
, and
D. S.
Chult
, in
Exploring Network Structure, Dynamics, and Function Using Networkx
(
Los Alamos National Lab.(LANL)
,
Los Alamos, NM
,
2008
), Technical report.
58.
M. F.
Döpke
,
O. A.
Moultos
, and
R.
Hartkamp
, “
On the transferability of ion parameters to the TIP4P/2005 water model using molecular dynamics simulations
,”
J. Chem. Phys.
152
(
2
),
024501
(
2020
).
59.
J.
Dočkal
,
M.
Lísal
, and
F.
Moučka
, “
Molecular dynamics of the interfacial solution structure of alkali-halide electrolytes at graphene electrodes
,”
J. Mol. Liq.
353
,
118776
(
2022
).
60.
J.
Dockal
,
F.
Moučka
, and
M.
Lísal
, “
Molecular dynamics of graphene–electrolyte interface: Interfacial solution structure and molecular diffusion
,”
J
. Phys. Chem. C
123
(
43
),
26379
(
2019
).
61.
A. A.
Kornyshev
, “
Double-layer in ionic liquids: Paradigm change?
,”
J. Phys. Chem. B
111
(
20
),
5545
5557
(
2007
).
62.
I.
Snook
and
W.
van Megen
, “
Finite ion size effects in the electrical double layer—A Monte Carlo study
,”
J. Chem. Phys.
75
(
8
),
4104
4106
(
1981
).
63.
H.
Hwang
,
Y. C.
Cho
,
S.
Lee
,
Y.-H.
Lee
,
S.
Kim
,
Y.
Kim
,
W.
Jo
,
P.
Duchstein
,
D.
Zahn
, and
G. W.
Lee
, “
Hydration breaking and chemical ordering in a levitated NaCl solution droplet beyond the metastable zone width limit: Evidence for the early stage of two-step nucleation
,”
Chem. Sci.
12
(
1
),
179
187
(
2021
).
64.
A. R.
Finney
and
M.
Salvalaglio
, “
Multiple pathways in NaCl homogeneous crystal nucleation
,”
Faraday Discuss.
235
,
56
80
(
2022
).
65.
A. R.
Finney
and
M.
Salvalaglio
, “
Bridging the gap between mesoscopic and molecular models of solid/liquid interfaces out-of-equilibrium
,”
Chem. Eng. Res. Design
180
,
285
295
(2022).
66.
I.-C.
Yeh
and
G.
Hummer
, “
System-size dependence of diffusion coefficients and viscosities from molecular dynamics simulations with periodic boundary conditions
,”
J. Phys. Chem. B
108
(
40
),
15873
15879
(
2004
).
67.
C. S.
Widodo
,
H.
Sela
, and
D. R.
Santosa
, “
The effect of NaCl concentration on the ionic NaCl solutions electrical impedance value using electrochemical impedance spectroscopy methods
,”
AIP Conf. Proc.
2021
,
050003
(2018).

Supplementary Material

You do not currently have access to this content.