Redox-active binary eutectics: Preparation and their electrochemical properties

Article abstract of DOI:10.1016/j.elecom.2021.107028

Eutectics are emerging as promising candidate for electrochemical energy storage. However, the eutectics usually show high viscosity that usually arises from strong intermolecular interactions greatly limits their application. In this communication, we design and prepare two redox-active molecules that both are able to form binary eutectics with TBMA-TFSI. Combined experimental and computational studies indicate the intermolecular interaction is weakened after eutectic formation, resulting in decreased viscosity and enhanced ionization ratio of TBMA-TFSI without affecting the redox behaviors of the individual molecules. Further, the redox-active binary eutectic is used as solvent-free electrolyte for battery application.

Full text of DOI:10.1016/j.elecom.2021.107028

Electrochemistry Communications 126 (2021) 107028
Contents lists available at ScienceDirect
Electrochemistry Communications
journal homepage: www.elsevier.com/locate/elecom
Short Communication
Redox-active binary eutectics: Preparation and their
electrochemical properties
a
b
a,c,*
Hui Chen , Zhihui Niu , Yu Zhao
a
Institute of Functional Nano and Soft Materials (FUNSOM), Jiangsu Key Laboratory for Carbon-Based Functional Materials and Devices, Soochow University, Suzhou,
Jiangsu 215123, China
b
School of Physics and Optoelectronic Engineering, Shandong University of Technology, Zibo, Shandong 250049, China
c
College of Materials, Chemistry and Chemical Engineering, Hangzhou Normal University, Hangzhou, Zhejiang 311121, China
A R T I C L E I N F O
A B S T R A C T
Keywords:
Eutectics are emerging as promising candidate for electrochemical energy storage. However, the eutectics usually
show high viscosity that usually arises from strong intermolecular interactions greatly limits their application. In
this communication, we design and prepare two redox-active molecules that both are able to form binary eu-
tectics with TBMA-TFSI. Combined experimental and computational studies indicate the intermolecular inter-
action is weakened after eutectic formation, resulting in decreased viscosity and enhanced ionization ratio of
TBMA-TFSI without affecting the redox behaviors of the individual molecules. Further, the redox-active bi-
nary eutectic is used as solvent-free electrolyte for battery application.
Eutectics
Intermolecular interactions
Ionization
Electrical energy storage
1
. Introduction
A eutectic, also known as the deep eutectic solvent, is a homogeneous
cations [15–17]. Electrochemical energy storage in those eutectics pre-
pared by mixing a redox-active metal chloride and an organic salt are of
particular interest as they avoid the use of large amount of electro-
chemically inactive species such as the solvent [18,19]. However, owing
to their relatively high viscosity, most eutectics exhibit low ionization
ratio, which would lead to the raise of internal resistance and insuffi-
cient mass transport inside the device. As a consequence, the demon-
strated examples of eutectics need dilution or the coexistence of
additional additives, which bring in uncertainties regarding the
decreased electrochemical window and the side reactions among the
active material, solvent molecules and additives.
mixture composed of Lewis or Brønsted acids and bases containing a
collection of anionic and/or cationic species that are capable of self-
association, often through hydrogen bond interactions [1–3]. Different
from traditional ionic liquids that composed of solely ionized species,
eutectics usually are nonvolatile, nonflammable and biodegradable
while being much cheaper and more environmentally friendly, thus
grasping growing interest in the fields of catalysis, organic synthesis,
electrochemical energy storage and material science [4–9]. Most of
eutectics exhibit relatively high viscosities owing to the presence of an
extensive hydrogen bond network between each component, the elec-
trostatic or van der Waals interactions, and the free volume. To further
expand practical implementation, the development of eutectics with low
viscosities and high ionization ratio is highly desirable, because ioni-
zation ratio can be monotonically increased via the decrease of viscosity
In this study, we report a binary eutectic composed of 2-pentyl-1H-
′
isoindole-1,3(2H)-dione (PHD), 1,1 -diacetylferrocene (DDF) and trib-
utylmethylammomium bis(trifluoromethanesulfonyl)imide (TBMA-
TFSI) as the electrolyte for electrochemical energy storage. Experi-
mental and theoretical investigations suggest that the decreased vis-
cosity and enhanced ionization ratio of TBMA-TFSI should result from
the decreased intermolecular interactions. The as-prepared eutectic
shows good electrochemical reversibility and maintains the redox
characteristics of pristine PHD and DDF. As a proof-of-concept study,
their ability to store the electrical energy is also investigated. Such a
redox-active eutectic voids the use of solvent and other additives, and
thus can be regarded as the simplest form of electrolyte for battery
[
10–13].
To date, several strategies have been proposed to decrease the vis-
cosity. For instance, the use of small cations or fluorinated hydrogen-
bond donors can lead to eutectic formation with low viscosity [14],
and the use of hydrogen bond acceptors as such as urea and acetamide
can effectively decrease the viscosity of the eutectic containing metal
*
Corresponding author.
E-mail address: yuzhao@suda.edu.cn (Y. Zhao).
https://doi.org/10.1016/j.elecom.2021.107028
Received 5 March 2021; Received in revised form 29 March 2021; Accepted 30 March 2021
Available online 3 April 2021
1
388-2481/© 2021 The Author(s).
Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license
(
http://creativecommons.org/licenses/by-nc-nd/4.0/).

H. Chen et al.
Electrochemistry Communications 126 (2021) 107028
electrolyte.
for PHD and ꢀ 0.2 – 0.7 V (vs. AgCl/Ag) for PHD with various sweeping
◦
rates at 60 C. The cell was assembled in a glove box (H
2
O and O
2
2
. Experimental section
concentration <1 ppm), and the active material and cell components
were housed within two 2032-coin cell halves. Each half was placed a
stainless-steel spacer (15.5 mm in diameter, MTI) and a piece of graphite
felt. A Daramic 175 porous separator sandwiched between two Celgard
2500 membranes was used as the separator. The cell was charged at a
2
.1. Synthesis of 2-pentyl-1H-isoindole-1,3(2H)-dione (PHD)
Phthalimide (20.4 mmol) was dissolved in ethanol (60 mL), and 2 M
KOH in ethanol (30 mL) was added dropwise to the phthalimide ethanol
constant voltage of 2.1 V and discharged at a constant current of 30
μ
A
◦
ꢀ 2
solution. The mixture was agitated for 24 h at 60 C and filtered to
cm in the potential range of 1.1–2.1 V. The as-prepared PHD/DDF and
TBMA-TFSI were stored in an Ar-filled glove box (water content <1
collect the white solid phthalimide potassium salt (91%). Then, to a
solution of 1-chloropentane (30 mmol) in N,N-dimethylformamide (50
mL) was added potassium phthalimide (27 mmol). The reaction mixture
◦
ppm) and dried in vacuum at 80 C for 6 h before use.
◦
was stirred for 6 h at 130 C. After addition of water (50 mL) and
3. Results & discussion
dichloromethane (150 mL), the aqueous phase was extracted with
dichloromethane (3 × 50 mL) and the organic phase was dried over
The synthetic routes for PHD and DDF are summarized in Fig. 1a,
which displays both compounds with long alkyl chain can be prepared
by two step reaction with high yield. The resultant PHD and DDF were
2 4
Na SO . After filtration and removal of the solvent, the residue was
further purified by flash chromatography to afford compound PHD
◦
◦
ꢀ 1
◦
(
5.86 g, 97%, m.p. 16 C), which was further dried at 80 C under
oil-like liquid with viscosity of 23.1 and 4.4 mPa s at 30 C and
1
ꢀ 1
◦
vacuum for 3 days, and stored under N
2
atmosphere. H NMR (400 MHz,
) δ 7.81 – 7.72 (m, 2H), 7.66 – 7.58 (m, 2H), 3.63 – 3.58 (m, 2H),
.60 (dd, J = 14.5, 7.1 Hz, 2H), 1.31 – 1.22 (m, 4H), 0.82 (t, J = 6.9 Hz,
gradually decreased to 1.9 and 1.3 mPa s at 120 C, respectively
CDCl
3
(Fig. 1b). After forming eutectic, the melting point decreased to ꢀ 17 and
◦
1
3
7
ꢀ 44 C for PHD/TBMA-TFSI and DDF/TBMA-TFSI eutectic, respec-
1
3
H); C NMR (400 MHz, CDCl
3
): δ 168.50, 133.84, 132.20, 123.15,
tively, and the viscosity of both eutectics increased compared with
pristine PHD and DDF but remained lower than that of TBMA-TFSI.
Infrared spectra of the eutectics (Fig. 1c and d) revealed that the char-
acteristic vibrational bands of carbonyl in PHD and ethyl-
cyclopentadienyl in DDF located at wavenumbers of 3467/1773 and
7.35, 77.03, 76.71, 38.06, 28.98, 28.30, 13.94 ppm; HRMS (m/z):
Calcd for C13
H
15NO
2
: 218.11. Found: 218.04.
′
2
.2. Synthesis of 1,1 -diacetylferrocene (DDF)
ꢀ 1
3
089 cm , respectively [26–28]. These bands together with others
′
1
,1 -Diacetylferrocene (DAF) was prepared according to a previous
belonging to the alkyl chains showed little shift after forming eutectics
with TBMA-TFSI. It’s thus plausible to deduce that the intermolecular
hydrogen bonding and Van der Waals interactions in the as-prepared
eutectics were weak. Such weak intercalation was beneficial to main-
tain the pristine electrochemical characteristics such as the redox po-
tential and redox kinetics of PHD and DDF.
report [20]. A solution of distilled DAF (10.81 g, 40 mmol) in dry
tetrahydrofuran (50 mL) was placed in a dropping funnel and was added
to the stirred ice-cooled suspension of the reductant dropwise. The re-
◦
action mixture was heated to 35 C for 5 h, and then was dripped into
ice-cooled water (150 mL) to quench this reaction. The aqueous phase
was extracted with ethyl acetate (3 × 200 mL) and the organic phase was
The intermolecular interaction was also studied by the analysis of
spatial geometry of TBMA-TFSI with the existence of PHD or DDF.
Fig. 2a and b shows the optimized geometry of PHD/TBMA-TFSI and
DDF/TBMA-TFSI eutectics with PHD/DDF in its pristine and oxidized/
reduced states. In all cases, forming eutectics benefitted to enhance the
intercalation between PHD/DDF and TBMA-TFSI. For PHD/TBMA-TFSI
2 4
dried over Na SO . After concentrated under the reduced pressure, the
resultant dark-red syrup was purified by column chromatography to
◦
afford compound DDF (7.2 g, 83%, m.p. ꢀ 34 C), which was further
◦
dried at 60 C under vacuum for 12 h, and stored under N
2
atmosphere.
1
H NMR (400 MHz, CDCl
3
) δ 4.06 (s, 8H), 2.40–2.25 (q, J = 7.5 Hz, 4H),
13
ꢀ 1
1
6
2
.17 (t, J = 7.5 Hz, 3H); C NMR (400 MHz, CDCl
3
): δ 91.49, 68.28,
18Fe: 242.08. Found:
eutectic, the binding energy decreased from ꢀ 18.01 kJ mol of TBMA-
ꢀ
1
7.91, 22.12, 14.85. HRMS (m/z): Calcd for C14
H
TFSI to –23.34 kJ mol
of PHD/TBMA-TFSI eutectics, and further
ꢀ 1
42.07.
decreased to ꢀ 49.44 kJ mol when PHD transforms from its original
state to reduced state. While for DDF/TBMA-TFSI eutectic, the binding
ꢀ 1
2
.3. Computational method
energy also decreased to ꢀ 20.20 and ꢀ 36.15 kJ mol
when DDF
transforms from its original state to the oxidized state, respectively.
These results can be explained by the weakened intramolecular inter-
action of TBMA-TFSI. When mixing with pristine PHD or DDF, the
Molecular dynamics (MD) simulations were performed using Gro-
macs program [21], with Amber99sb-ildn force field coupled with TIP3P
water model to describe the interactions between atoms [22]. A cubic
+
ꢀ
average distance between the TBMA and TFSI was elongated,
resulting in weakened electrostatic interaction. When PHD and DDF
transform into anionic and cationic species, they took part in balancing
3
box of 5 × 5 × 5 nm was set to simulate the experiment environment of
PHD/TBMA-TFSI or DDF/TBMA-TFSI eutectic. All simulations were
performed in the NPT ensemble with a coupling constant of 2 fs at
ꢀ
+
the charge of TFSI and TBMA , respectively, further weakening the
electrostatic interaction of TBMA-TFSI, resulting in increased ionization
ratio.
2
98.15 K. A 12 Å cut-off radius was used for van der Waals forces and
Coulomb interactions. The structure optimization and interaction en-
ergy were carried out with the Gaussian16 software. The B3LYP func-
tional [23], 6-311+G(d) (for Non-metal atoms) [24] and SDD (for Fe
atom) [25] basis sets were adopted in geometry optimization. The
interaction energy was also calculated considering the dispersion
correction using the D3BJ method of Grimme.
FPMD simulation was further used to reveal the enhanced ionization
of TBMA-TFSI by forming eutectics. Fig. 2c and d shows a segment of the
spatial distribution of the PHD/TBMA-TFSI and DDF/TBMA-TFSI
eutectic with a molar ratio of PHD/DDF: TBMA-TFSI 1:4. Through the
+
ꢀ
radial distribution function shown in Fig. 2e, TBMA and TFSI in PHD/
TBMA-TFSI eutectic were mainly distributed at a distance around 10 Å
+
2
.4. Electrochemical test
from the PHD molecules, and the probability of occurrence for TBMA
ꢀ
ꢀ
was higher than that of TFSI . Because PHD can be regarded as a
+
Cyclic voltammogram (CV) tests were carried out using an electro-
nucleophile that preferably interact with the positively charged TBMA
chemical cell with three-electrode configuration. The graphite felt (SGL
Group, G334-01), a Pt plate and an AgCl/Ag electrode were used as the
working, the counter and the reference electrode, respectively. The tests
were carried out in the potential range of ꢀ 1.3 – ꢀ 1.8 V (vs. AgCl/Ag)
through electrostatic interaction. For DDF/TBMA-TFSI eutectic, the
+
ꢀ
distribution of TBMA and TFSI was similar, with a distance around 8
ꢀ
Å from the DDF molecules, but the probability of occurrence for TFSI is
+
higher than that of TBMA . The FPMD simulation suggests that the
2

H. Chen et al.
Electrochemistry Communications 126 (2021) 107028
Fig. 1. Synthesis and characterization of the binary eutectic. (a) Synthetic routes for PHD and DDF. (b) Temperature-dependent viscosity of PHD, DDF and their
corresponding PHD/TBMA-TFSI (1:4) and DDF/TBMA-TFSI (1:4) eutectics. The viscosity was measured with a rheometer (AR-2000EX, TA instrument) attached with
2
5 mm parallel upper plate and a peltier bottom plate. (c and d) IR spectra of PHD/TBMA-TFSI and DDF/TBMA-TFSI eutectics. IR curves from top to down represents
the PHD or DDF mole ratio between 1 and 0 with an interval of 10%.
Fig. 2. Theoretical investigation of the as-prepared eutectics. (a) Intermolecular interactions of PHD/TBMA-TFSI eutectic with PHD in its pristine and oxidized states.
(
b) The molecular interactions of DDF/TBMA-TFSI eutectic with PHD in its pristine and reduced states. Simulated structure of (c) PHD/TBMA-TFSI and (d) DDF/
TBMA-TFSI eutectics showing the distribution of TBMA and TFSI in a 50 × 50 × 50 Å matrix, respectively. (e) Radial distribution function of TBMA+ and
+
ꢀ
ꢀ
TFSI around PHD or DDF. The distance refers to the molecular distance between their center of gravity.
+
ꢀ
ꢀ
+
spatial distribution of TBMA and TFSI changed from an even distri-
bution in TBMA-TFSI to an uneven distribution by forming eutectics,
constant were similar to those of PHD/PHD and DDF/DDF reported in
the literature [31–33], suggesting that PHD and DDF maintained their
pristine electrochemical characteristics after forming eutectics. Such
phenomenon should arise from the aforementioned weak intermolec-
ular interactions that are not strong enough to distort the electronic
structure of the molecules.
+
ꢀ
and TBMA-TFSI was forced to split into TBMA and TFSI when interact
with PHD or DDF, which is responsible for the enhanced ionic
conductivity.
ꢀ
CV profiles shown in Fig. 3a revealed that both PHD/PHD and DDF/
+
DDF redox couples were electrochemically reversible, and the ratio of
Given the fact the existence of PHD or DDF promotes the ionization
ratio of TBMA-TFSI, a static redox cell was used to testify the possibility
by using such eutectics as the electrolyte. As a demonstration, the
charge-discharge profiles of the cell using PHD/TBMA-TFSI and DDF/
TBMA-TFSI serving as the cathode and anode is shown in Fig. 3e. The
cell exhibited an average discharge voltage of 1.3 V, close to the peak-to-
peak separation of 1.5 V in the CV profiles. One should note that because
of the relatively high viscosity, the diffusion coefficient of PHD or DDF
was about 2 orders of magnitude lower than conventional electrolytes.
It’s therefore necessary to design more appropriate molecule structure to
tune the intermolecular interactions as well as to further tailor the
peak cathodic and anodic current was close to 1.0 at different sweeping
rates. The peak current showed good linear response with the square
root of the sweeping rate, through which the diffusion coefficient of
ꢀ
+
ꢀ 8
2
PHD/PHD and DDF/DDF was determined to be 1.9/4.4 × 10 cm
ꢀ
1
ꢀ 8
2
ꢀ 1
s
s
and 5.7/8.7 × 10 cm
, respectively. Based on Nicholson’s
ꢀ
analysis [29,30], the electron transfer rate constant of PHD/PHD and
+
ꢀ 3
ꢀ 3
DDF/DDF redox couple was estimated as 6.4 × 10 and 6.5 × 10
ꢀ 1
cm s , respectively. Note that the iR-compensation was relatively low,
the uncompensated resistance would not seriously affect the electron
transfer rate constant by this method. Both redox potential and rate
3

H. Chen et al.
Electrochemistry Communications 126 (2021) 107028
Fig. 3. Electrochemical characterization of PHD/TBMA-TFSI and DDF/TBMA-TFSI eutectics. (a) CV profiles of the eutectics at variable scan rate. The concentration
1
/2
of PHD and DDF is 0.2 mmol. (b) Peak current (i
p
) during the cathodic/anodic scans as a function of the square root of sweeping rate (
υ
) derived from the CV
ꢀ 1/2
profiles. Plot of (c) Ψ values versus the peak-to-peak separation (ΔE ) and (d) Ψ versus υ
to 15th cycle.
p
in the CV profiles. (e) Voltage profile over time of the 1st to 5th and 11th
composition of the eutectic.
Acknowledgement
4
. Conclusions
The authors acknowledge the support from the National Natural
Science Foundation of China (Grant No. 51772199), the National Nat-
ural Science Foundation of Shandong Province (Grant No.
ZR2020QB126), and the Collaborative Innovation Center of Suzhou
Nano Science & Technology.
In conclusion, we report the design, preparation and electrochemical
properties of binary eutectics composed of redox-active PHD/DDF and
ꢀ
TBMA TFSI. FPMD simulations reveal that TBMA-TFSI is forced to split
+
ꢀ
into TBMA and TFSI when interact with PHD or DDF, resulting in an
enhanced ionization of TBMA-TFSI. Owing to the enhanced ionic con-
ductivity, the eutectics are electrochemically reversible and show fast
electron transfer rate that is comparable to most redox couples applied
in redox-flow batteries. To our knowledge, this is the first successful
demonstration of eutectics without additional solvents and additives as
the electrolyte for redox-flow batteries, though optimization such as
decreasing the viscosity and accelerating the mass diffusion is necessary
to further enhance the electrochemical performance. Nevertheless, such
binary eutectics may be of contribution to overcome the issues of con-
ventional electrolytes for redox-flow batteries, such as the dominated
mole ratio of electrochemically inactive solvent, side reactions among
the constituents, and solvent evaporation and decomposition.
References
[
[
1] M.H. Chakrabarti, F.S. Mjalli, I.M. AlNashef, M.A. Hashim, M.A. Hussain,
L. Bahadori, C.T.J. Low, Renew. Sustain. Energy Rev. 30 (2014) 254–270.
2] N.S. Sinclair, D. Poe, R.F. Savinell, E.J. Maginn, J.S. Wainright, J. Electrochem.
Soc. 168 (2021), 020527.
[
[
[
3] E.L. Smith, A.P. Abbott, K.S. Ryder, Chem. Rev. 114 (2014) 11060–11082.
4] G. Desimoni, G. Faita, K.A. Jorgensen, Chem. Rev. 111 (2011) PR284–PR437.
5] H. Kim, D.A. Boysen, J.M. Newhouse, B.L. Spatocco, B. Chung, P.J. Burke, D.
J. Bradwell, K. Jiang, A.A. Tomaszowska, K. Wang, W. Wei, L.A. Ortiz, S.A. Barriga,
S.M. Poizeau, D.R. Sadoway, Chem. Rev. 113 (2013) 2075–2099.
[
6] X. Wei, L. Cosimbescu, W. Xu, J.Z. Hu, M. Vijayakumar, J. Feng, M.Y. Hu, X. Deng,
J. Xiao, J. Liu, V. Sprenkle, W. Wang, Adv. Energy Mater. 5 (2015) 1400678.
[7] L. Wylie, T. Blesch, R. Freeman, K. Hatakeyama-Sato, K. Oyaizu, M. Yoshizawa-
Fujita, E.I. Izgorodina, ACS Sustain. Chem. Eng. 8 (2020) 17988–17996.
[
[
8] C. Zhang, L. Zhang, Y. Ding, S. Peng, X. Guo, Y. Zhao, G. He, G. Yu, Energy Storage
Mater. 15 (2018) 324–350.
CRediT authorship contribution statement
9] Q. Zhang, K. De Oliveira Vigier, S. Royer, F. Jerome, Chem. Soc. Rev. 41 (2012)
7
108–7146.
[
[
[
[
10] O. Colombani, M. Ruppel, F. Schubert, H. Zettl, D.V. Pergushov, H. Axel,
Macromolecules 40 (2007) 4338–4350.
Hui Chen: Investigation, Methodology, Formal analysis, Visualiza-
tion, Writing - original draft. Zhihui Niu: Investigation Formal analysis,
Writing - original draft. Yu Zhao: Conceptualization, Supervision,
Writing - review & editing, Project administration, Funding acquisition.
11] S. Thiyagarajan, A. Sonthalia, V. Edwin Geo, B. Ashok, K. Nanthagopal,
V. Karthickeyan, B. Dhinesh, J. Therm. Anal. Calorim. 138 (2019) 633–644.
12] Q. Xu, Y. Ji, L. Qin, P. Leung, A. Shah, Y. Li, H. Su, H. Li, Chem. Phys. Lett. 708
(
2018) 48–53.
13] H. Wang, Y. Jing, X. Wang, Y. Yao, Y. Jia, J. Mol. Liq. 163 (2011) 77–82.
Declaration of Competing Interest
[14] Y. Wang, Z. Niu, Q. Zheng, C. Zhang, J. Ye, G. Dai, Y. Zhao, X. Zhang, Sci. Rep. 8
2018) 5740.
(
[
[
15] A.P. Abbott, G. Capper, S. Gray, ChemPhysChem 7 (2006) 803–880.
16] Y. Wang, H. Zhou, Energy Environ. Sci. 9 (2016) 2267–2272.
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence
the work reported in this paper.
[17] C. Zhang, Y. Ding, L. Zhang, X. Wang, Y. Zhao, X. Zhang, G. Yu, Angew. Chem. Int.
Ed. 56 (2017) 7454–7459.
[
18] A. Shimizu, K. Takenaka, N. Handa, T. Nokami, T. Itoh, J.I. Yoshida, Adv. Mater.
2
9 (2017) 1606592.
4

H. Chen et al.
Electrochemistry Communications 126 (2021) 107028
[
[
19] C. Zhang, Z. Niu, Y. Ding, L. Zhang, Y. Zhou, X. Guo, X. Zhang, Y. Zhao, G. Yu,
Chem 4 (2018) 2814–2825.
[26] F. Ji, J. Li, X. Li, W. Guo, W. Wu, H. Jiang, J. Org. Chem. 83 (2018) 104–112.
[27] T. Kaicharla, M. Thangaraj, A.T. Biju, Org. Lett. 16 (2014) 1728–1731.
[28] N. Mohammadi, A. Ganesan, C.T. Chantler, F. Wang, J. Organomet. Chem. 713
(2012) 51–59.
20] M.A. Carroll, A.J.P. White, D.A. Widdowson, D.J. Williams, J. Chem. Soc. 1 (2000)
1
551–1557.
[
[
21] E. Lindahl, B. Hess, D. van der Spoel, J. Mol. Model. 7 (2001) 306–317.
22] M.J. Abraham, T. Murtola, R. Schulz, S. P ´a ll, J.C. Smith, B. Hess, E. Lindahl,
Software X 1 (2015) 19–25.
[29] J. Luo, A. Sam, B. Hu, C. DeBruler, X. Wei, W. Wang, T.L. Liu, Nano Energy 42
(2017) 215–221.
[30] R. Nicholson, Anal. Chem. 37 (1965) 1351–1355.
[
[
[
23] K. Burke, J. Chem. Phys. 136 (2012) 150901.
[31] G. Cong, Y. Zhou, Z. Li, Y.-C. Lu, ACS Energy Lett. 2 (2017) 869–875.
[32] S. Hwang, H.-S. Kim, J.H. Ryu, S.M. Oh, J. Power Sources 395 (2018) 60–65.
[33] A.M. Kosswattaarachchi, T.R. Cook, Electrochim. Acta 261 (2018) 296–306.
24] W.J. Hehre, R. Ditchfield, J.A. Pople, J. Chem. Phys. 56 (1972) 2257–2261.
25] M. Dolg, U. Wedig, H. Stoll, H. Preuss, J. Chem. Phys. 86 (1987) 866–872.
5