Journal of Power Sources 325 (2016) 91e97
Contents lists available at ScienceDirect
Journal of Power Sources
journal homepage: www.elsevier.com/locate/jpowsour
Computational insights into the effect of carbon structures at the
atomic level for non-aqueous sodium-oxygen batteries
H.R. Jiang, M.C. Wu, X.L. Zhou, X.H. Yan, T.S. Zhao*
Department of Mechanical and Aerospace Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China
h i g h l i g h t s
The effect of atomic carbon structures is investigated for NaeO2 batteries.
SV defect has the largest adsorption energy for NaO2 among samples studied.
The dangling atoms and the O-attachment are the origin of large adsorption energy.
Increasing the number of SV defect leads to large capacity and good cyclability.
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 22 March 2016
Received in revised form
21 May 2016
Accepted 30 May 2016
Carbon materials have been widely used to form air cathodes for non-aqueous sodium-oxygen (NaeO2)
batteries due to their large specific surface area, high conductivity and low cost. However, the effect of
carbon structures at the atomic level remains poorly understood. In this work, a first-principles study is
conducted to investigate how representative carbon structures, including graphite (0001) surface, point
defects and fractured edge, influence the discharge and charge processes of non-aqueous NaeO2 batteries. It is found that the single vacancy (SV) defect has the largest adsorption energy (5.81 eV) to NaO2
molecule among the structures studied, even larger than that of the NaO2 molecule on NaO2 crystal
(2.81 eV). Such high adsorption energy is attributed to two factors: the dangling atoms in SV defects
decrease the distance from NaO2 molecules, and the attachment through oxygen atoms increases the
electrons transfer. The findings suggest that SV defects can act as the nucleation sites for NaO2 in the
discharge process, and increasing the number of SV defects can facilitate the uniform formation of smallsized particles. The uniformly distributed discharge products lower the possibility for pore clogging,
leading to an increased discharge capacity and improved cyclability for non-aqueous NaeO2 batteries.
© 2016 Elsevier B.V. All rights reserved.
Keywords:
First-principles study
Non-aqueous sodium-oxygen batteries
Atomic carbon structures
Adsorption energy
Solution mechanism
1. Introduction
Rechargeable metal-oxygen batteries are considered to be the
potential energy storage systems for future electric vehicles (EVs)
due to their high theoretical energy densities, which are achieved
by the facts that the anode materials are metals and the cathode
reactant O2 is retrieved from ambient air without occupying the
cathode volume [1]. Especially, non-aqueous lithium-oxygen
(LieO2) batteries have been widely investigated in the past few
years [2e6], but varieties of critical issues (e.g., poor electrolyte
stability, low energy efficiency, short cycle life and poor power
capacity [7,8]) limit their further commercial exploitation, most of
* Corresponding author.
E-mail address: [email protected] (T.S. Zhao).
http://dx.doi.org/10.1016/j.jpowsour.2016.05.132
0378-7753/© 2016 Elsevier B.V. All rights reserved.
which are related to the high charge overpotential during oxygen
evolution reaction (OER) process. One widely applied strategy to
decrease the high charge overpotential is developing catalysts, such
as carbon-based materials [9e11], noble metals [12,13], metal oxides [14,15] and metal alloys [16,17]. However, some investigated
electrocatalysts undesirably promote the decomposition of electrolytes [18,19]. Even worse, the discharge product Li2O2 itself in
non-aqueous LieO2 batteries was supposed to be the origin of high
charge overpotential [20e22].
By contrast, non-aqueous sodium-oxygen (NaeO2) batteries
exhibit a much lower charge overpotential (<300 mV) than nonaqueous LieO2 batteries (typically >1V) do, thus attracting great
attention recently [23e26]. In 2010, the rechargeable NaeO2 batteries were firstly investigated and demonstrated to run for several
cycles at 105 C by Peled et al. [27]. After that, Sun et al. reported the
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H.R. Jiang et al. / Journal of Power Sources 325 (2016) 91e97
first room temperature NaeO2 batteries and exhibited up to 20
cycles [28]. Unlike the instability of LiO2 at room temperature
[29,30], NaO2 is a stable superoxide and found to be the main
discharge product in non-aqueous NaeO2 batteries by both
experimental [31,32] and theoretical [22,33] investigations.
Therefore, the electrochemical reaction of non-aqueous NaeO2
batteries can be described as Naþ þ e þ O2 4 NaO2, which is
kinetically favored as only one electron transfers for a formula unit.
More importantly, sodium is the 6th most abundant element in the
earth’s crust and its amount is more than 1000 times larger than
that of lithium [34], suggesting its much lower cost and greater
suitability than lithium to be the power source for future EVs.
However, an issue with non-aqueous NaeO2 batteries is that the
discharge product NaO2 is insoluble to the electrolyte and would
deposit in the cathode, leading to the pores clogging and oxygen
transports blocking, which significantly limits the discharge capacity and cyclability. Therefore, the design over the porous
geometrical structures and surface properties for the cathode material is of great importance to non-aqueous NaeO2 batteries. In
this regard, porous carbon is widely adopted as the air cathode due
to its large variety, high specific surface area, good conductivity and
low cost. For example, Liu et al. investigated graphene nanosheets
(GNS) as the air cathode and obtained a high discharge capacity of
8268 mA h g1 at a current density of 200 mA g1 [35]. Jian et al.
used a carbon nanotube paper as a binder-free air cathode. Results
showed a discharge capacity of 7530 mA h g1 at current density of
500 mA g1 and a charge overpotential less than 200 mV [36]. Zhao
et al. founded that the non-aqueous NaeO2 batteries could be
cycled for up to 100 cycles at a limited capacity of 750 mA h g1 by
pre-depositing a thin NaO2 layer on vertically aligned carbon
nanotubes (VACNTs) network [37]. Although great progress has
been made, experiments have so far yielded little mechanistic
understanding on the effect of carbon structures at the atomic level
in the discharge and charge processes.
In this work, a density functional theory (DFT) based firstprinciples study is used to investigate the effect of carbon structures at the atomic level on the discharge and charge processes for
non-aqueous NaeO2 batteries. Seven carbon structures, including
graphite (0001) surface, SV defect, DV5-8-5 defect, DV555-777
defect, DV5555-6-7777 defect, S-W defect and fractured edge, are
considered. Firstly, the adsorption energies of NaO2 molecules on
these carbon structures are calculated. By doing Bader charge
analysis, we then build the relationship between electrons transfer
and adsorption energies through electrostatic interaction. Thirdly,
the investigation of the most favorable carbon structure is presented by comparing several adsorption sites and charge difference
plots. Finally, based on the solution mechanism [38,39], the influence of carbon structures at the atomic level on the growing and
decomposition processes of product is proposed, and suggestions
for the development of high capacity air cathode in non-aqueous
NaeO2 are obtained accordingly.
In this work, all the slab models were presented based on a
monolayer graphite (0001) surface. The feasibility of the computational domain has been proved by many previous investigations
[44e47]. To make a further validation, we calculated the adsorption
of NaO2 molecule on a triple-layers graphite (0001) surface and that
with SV defects, the structures of the built model and optimized
structures were shown in Figures S1 and S2. It was found that the
energy differences for the monolayer and triple layers were less
than 2%. A 4 4 1 supercell was prepared for graphite (0001)
surface and defective graphite surfaces, and the Brillouin zone was
sampled using a 4 4 1 k-point Monkhorst-Pack grids. A
5 5 1 supercell was also built to test the convergence, and a less
than 0.05 eV difference of adsorption energy for NaO2 molecule was
gotten, confirming the rationality of our model. To represent the
fractured edge of graphite, the ideal model in the graphite (0001)
surface and the selected model in real calculations, including
adsorption sites, were presented in Figure S3. In our work, a 9 C
atom-wide graphene nanoribbon (GNR) (44 atoms) with armchair
edge was used [48]. One edge of GNR was decorated by hydrogen
atoms, which were fixed after structure optimization, and the other
edge was exposed. The distance between two neighboring nanoribbon was set to be 13.7 Å to ensure the isolation of the edge sites
and the k-point mesh for the GNR was set to be 1 4 1.
The adsorption energy of NaO2 molecule on the model carbon
structures was presented by:
Ead ¼ Ecarbon þ ENaO2 ENaO2 =carbon
(1)
where Ead is the adsorption energy, Ecarbon , ENaO2 and ENaO2 =carbon
are the DFT total energies of carbon structures, NaO2 molecule and
NaO2-carbon adsorption system, respectively. The Bader charge
analysis was implemented by the AIM program [49] in the ABINIT
code.
3. Results and discussion
NaO2 is reported to show a crystal structure of Pa3 space group
between 196 and 223 K, and the OeO bonds arrange disordered
above 223 K [50,51]. The optimized structures of pyrite phase and
molecular NaO2 are shown in Fig. 1. The lattice constants of crystal
NaO2 are a ¼ b ¼ c ¼ 5.54 Å, consistently with previous theoretical
(a ¼ b ¼ c ¼ 5.509 Å) [52] and experimental (a ¼ b ¼ c ¼ 5.460 Å)
[50] investigations. In NaO2 molecule, the bond lengths of NaeO
and OeO are 2.153 and 1.361 Å. The optimized structures of
graphite (0001) surface, SV defect, DV5-8-5 (two pentagons and
one octagon) defect, DV555-777 (three pentagons and three heptagons) defect, DV5555-6-7777 (four pentagons, one hexagon and
2. Computational methods
All of the calculations were performed using ABINIT [40,41]
code. The exchange correlation interaction was implemented
within the generalized gradient approximation (GGA) of PerdewBurke-Ernzerhof (PBE) type [42], and the core electrons were
described by projector augmented wave (PAW) method [43]. The
energy cutoff for the plane wave basis expansion was set to be 22
Ha to ensure a good convergence. Periodic boundary condition was
used and the vacuum between slabs in z-direction was 15 Å. The
force tolerances for self-consistent-field (SCF) cycles and structural
optimization were set to be 4.0 105 Ha/Bohr and 6 104 Ha/
Bohr, respectively.
Fig. 1. Optimized structures of (a) Pa3 NaO2 bulk and (b) NaO2 molecule. The yellow
and red balls represent sodium and oxygen atoms, respectively. (For interpretation of
the references to colour in this figure legend, the reader is referred to the web version
of this article.)
H.R. Jiang et al. / Journal of Power Sources 325 (2016) 91e97
93
Fig. 2. Optimized structures of (a) graphite (0001), (b) SV defect, (c) DV5-8-5 defect, (d) DV555-777 defect, (e) DV5555-6-7777 defect, (f) S-W defect and (g) GNR. The brown and
white balls represent carbon and hydrogen atoms, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this
article.)
Fig. 3. The most stable structures of NaO2 molecule adsorbed on (a) graphite (0001), (b) SV defect, (c) DV5-8-5 defect, (d) DV555-777 defect, (e) DV5555-6-7777 defect, (f) S-W
defect and (g) GNR.
four heptagons) defect, S-W defect and GNR used in this work are
presented in Fig. 2aeg, respectively. For the defective structures,
the SV defect is formed by removing one carbon atom from the
graphite (0001) surface, and the DV5-8-5 defect removes another
adjacent carbon atom from optimized SV defect. By rotating CeC
bonds in DV5-8-5 defect, the structure of DV555-777 and DV55556-7777 defects can be obtained. The S-W defect is generated by
rotating a CeC bond in graphite (0001) for 90 and shows a
“sinelike” structure from the side view.
The most stable structures of NaO2 molecule adsorbed on carbon structures are displayed in Fig. 3. And the corresponding
adsorption energies are presented in Table 1. Results show that the
adsorption energies of NaO2 molecule decrease in the sequence of
SV defect > DV555-777 defect > DV5-8-5 defect > DV5555-6-7777
defect > GNR > S-W defect > graphite (0001). Especially, SV defect
has the largest structural deformation and presents a much larger
adsorption energy than other structures. In addition, all the
graphite defects and fractured edge show larger adsorption
Table 1
The adsorption energies (Ead ) of NaO2 molecule on carbon structures at the atomic level.
Ead (eV)
Graphite (0001)
SV defect
DV5-8-5 defect
DV555-777 defect
DV5555-6-7777 defect
S-W defect
GNR
0.520
5.813
0.889
0.940
0.819
0.600
0.680
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H.R. Jiang et al. / Journal of Power Sources 325 (2016) 91e97
Fig. 4. The adsorption energy of NaO2 molecule as a function of electrostatic
interaction.
energies than that of clean graphite (0001) surface, indicating a
larger ability to attract NaO2 molecules. In Fig. 3a, the most stable
structure of NaO2 molecule adsorbed on the graphite (0001) surface is by sodium-attachment with sodium atom locating at the
center of hexagonal ring, similarly with the adsorption states of
LiO2 molecule on graphite in non-aqueous LieO2 batteries [53].
Moreover, the NaO2 molecule prefers to locate at the largest rings in
DV5-8-5 (octagon), DV555-777 (heptagon) and SeW (heptagon)
defects, but it tends to adsorb on the pentagon of DV5555-6-7777
defect. In GNR, the most stable site for NaO2 molecule adsorption
is the edge with hydrogen atoms decorated instead of in-plane
rings, suggesting the fractured edge is more active than in-plane
rings. To better understand the origin of adsorption energies on
carbon surfaces for the NaO2 molecule, we do the Bader charge
analysis to quantitatively analyze. It is known that the electrostatic
interaction between molecules and the substrates is critical in
determining the adsorption energies when the molecules are
adsorbed [17]. In Fig. 4, the influence of electrostatic interactions
(QdefectQNaO2/H) on adsorption energies is built, SV defect is not
included in this part as its adsorption energy is much larger than
those of others’. Results show a linear relationship between electrostatic interaction and adsorption energy with a correlation coefficient (R2) of 0.93, suggesting a potential way to evaluate the
adsorption energies from electrons transfer.
More importantly, the ultra-large adsorption energy of NaO2
molecule on SV defect presents an imperative need to clarify its
origin and summarize some principles for molecular adsorption. In
this regard, several potential adsorption sites on SV defect with
initial and final structures as well as the charge difference plots of
the final state are shown in Fig. 5. The adsorption energies of site
1e4 are 5.813 eV, 1.087 eV, 1.071 eV and 1.079 eV, respectively, all of
which are larger than those on other carbon structures and site 1 is
the most favorable one for NaO2 molecule adsorption. From the
Fig. 5. Initial and final structures as well as the charge difference plots of the final states of NaO2 molecule adsorbed on SV defect: (a) site 1, (b) site 2, (c) site 3 and (d) site 4. The
yellow and blue area represent electron gains and lose. The charge difference plot is calculated by r ¼ rtotal rSV rNaO2 , where rtotal ,rSV and rNaO2 are the total charge of the final
structure, substrates and NaO2 molecule, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 6. Schematic representations comparing the growing mechanism of NaO2 on carbon surface (a) without defect and (b) with SV defects.
H.R. Jiang et al. / Journal of Power Sources 325 (2016) 91e97
95
Fig. 7. The optimized structures of DME molecule adsorbed on (a) graphite (0001), (b) SV defect, (c) DV5-8-5 defect, (d) DV555-777 defect, (e) DV5555-6-7777 defect, (f) S-W defect
and (g) GNR.
final structures with different initial sites, it is seen that all the NaO2
molecules tend to locate at the center of the vacancy after optimization. In addition, protuberant carbon atoms are found in the
optimized structures, leading to the decreased distance between SV
defect and NaO2 molecule as well as the increased deformation of
vacancies. Therefore, the existence of dangling carbon atoms in SV
defect may be the origin of its larger adsorption energy than other
structures. And it is suggested an effective structure for molecular
adsorption would better have some dangling atoms. Meanwhile,
although all the NaO2 molecules locate at the center of the vacancies, the adsorption energy on site 1 is much larger than that of
other sites. Interestingly, this tendency is in consistent with NaO2
molecule anchored on SV defect through oxygen atoms in site 1 and
anchored through sodium atoms in site 2e4. From the charge difference plot, it is found that a large number of electrons accumulate
around oxygen atoms while the sodium atom loses electrons due to
the decreased electronegative of O (3.44) > C (2.55) > Na (0.93). In
site 1, when NaO2 molecule adsorbs on the SV defect through oxygen atoms, two oxygen atoms can simultaneously attract electrons
from carbon atoms. However, in site 2e4 when NaO2 molecule
adsorbs on the SV defect through sodium atom, only one sodium
atom involves in the electrons transfer. Meanwhile, the substrate
and oxygen atoms jointly attract electrons from sodium atom,
resulting in less electrons transfer between NaO2 molecule and SV
defect. Thus, the large adsorption energy of NaO2 molecule adsorbed on SV defect is attributed to two factors, one is the existence of
dangling carbon atoms in the vacancy decreases the distance between molecule and substrate, the other is the attachment through
oxygen atoms increases the electrons transfer.
In the cathode of non-aqueous NaeO2 batteries, porous carbons
with various pore sizes and pore volumes are widely used for the
deposition of solid state discharge product NaO2 to increase the
discharge capacity. Unfortunately, most of the pores are not fully
used due to the fact that the deposition of discharged product
unavoidably clogs pores and blocks the pathways for oxygen
transport, resulting in the loss of three-phase interface and a waste
of pore volume, like what happens in non-aqueous LieO2 batteries
with solid state Li2O2 as the discharge product [54e56]. Since the
deposition process strongly depends on the carbon surface properties, it is of great significance to evaluate the effect of carbon
structures at the atomic level on real non-aqueous NaeO2 batteries
systems. Hence, the adsorption energy of NaO2 molecule on the
most stable (100) surface [57] of crystal Pa3 NaO2 is also calculated
for comparison. The corresponding adsorption energy is 2.78 eV,
which is smaller than that on SV defect but larger than those on
other model carbon structures. Therefore, the existence of SV carbon defect in the cathode materials of non-aqueous NaeO2 batteries may greatly affect the growing mechanism in the discharge
process, and further influence the charge process.
Based on the solution mechanism, the validity of which has
been demonstrated in non-aqueous NaeO2 batteries by recent
works [25,26,58], we compare the growing mechanism of
discharge product on carbon surfaces without defect and with SV
defects, as shown in Fig. 6. The DOS of pristine graphite (0001)
surface and SV defect are presented in Figure S4. It is found that the
SV defect displays a metallic behavior and would benefit the electronic conductivity. In the discharge process, O2 molecules dissolve
in the electrolyte, diffuse to the pores and react with sodium ions
on the carbon surface. Then, the obtained molecular NaO2 dissolves
into the electrolyte, leading to the coexistence of NaO2 and O2
molecules in the electrolyte, as shown in the initial states of Fig. 6a
and b. The adsorption energies of NaO2, Naþ and O
2 are compared
on a model with two sufficiently separated SV defects, as presented
in Figure S5. Results show that the adsorption of NaO2 is energetically favorable than that of Naþ and O
2 , suggesting the deposition
of discharge products tends to be in the form of NaO2 instead of Naþ
and O
2 . The same tendency is also available for the pristine
graphite (0001) surface. In Fig. 6a with no defect existing in the
pore, all adsorption sites are equal for NaO2 molecules, so the
molecules can locate at anywhere randomly. Then, due to the
adsorption energy of NaO2 molecule on crystal NaO2 is larger than
that on graphite (0001) surface, this site becomes a nucleation site
for further growing process. When more and more NaO2 molecules
get together on this “seed”, the solid state discharge product grows
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H.R. Jiang et al. / Journal of Power Sources 325 (2016) 91e97
and finally clogs the pores. At this time, although the growth of
discharge products stops, large volumes inside the pore are still
unused. To make full use of the space in pores and increase the
discharge capacity, it is proposed that some SV defects should be
created on the carbon surface, as shown in Fig. 6b. In this case,
when the NaO2 molecules deposit, they tend to adsorb on the SV
defects first due to the much larger adsorption energy here than
that on NaO2 crystals. After all the SV defects are covered by NaO2
molecules, they all become NaO2 nucleation sites for the further
growth. In the final state, compared with carbon surface without
defect, the discharge products prefer to form small-sized particles
in large numbers. The distribution of discharge products become
much more uniform and the possibility for pore clogging deceases,
increasing the discharge capacity in non-aqueous NaeO2 batteries.
Meanwhile, for a fixed discharge capacity, the thickness of
discharge products in the second case is greatly reduced. Therefore,
the decomposition of solid state discharge products becomes much
easier in the charge process, leading to the lower charge overpotential and better cyclability. Even if the NaO2 molecules do not
all adsorb on the SV defects with the most stable structure, the
adsorption energies are still larger than those on other carbon
structures at the atomic level, also contributing to the uniform
distribution of discharge products. Based on our calculation and
proposed mechanism, it is suggested that a promising carbon
cathode in non-aqueous NaeO2 batteries would better have lots of
SV defects to increase its discharge capacity and cyclability.
In real non-aqueous NaeO2 batteries systems, the carbon
cathode is exposed to the aprotic electrolyte. To further validate the
proposed mechanism, we investigate the adsorption of electrolyte
molecules on representative carbon surfaces and compare the
adsorption energies with that of NaO2. Here, methyl ether (DME) is
chosen as the sample solvent due to the fact that it is widely
adopted in previous experimental investigations [58e60]. The
optimized structures of DME molecule on graphite (0001) surface,
SV defect, DV5-8-5 defect, DV555-777 defect, DV5555-6-7777
defect, SW defect and GNR are shown in Fig. 7. It is found that
DME molecule is not decomposed on all the representative carbon
structures, suggesting its stability on carbon cathode. In addition,
the adsorption energies of DME on graphite (0001) surface, SV
defect, DV5-8-5 defect, DV555-777 defect, DV5555-6-7777 defect,
SW defect and GNR are 0.035 eV, 0.003 eV, 0.018 eV, 0.023 eV,
0.022 eV, 0.041 eV and 0.092 eV, respectively, which is much
smaller than that of NaO2, indicating SV defect would not be
covered by electrolyte and our proposed mechanism is also available when carbon cathode is exposed to electrolyte in real nonaqueous NaeO2 batteries.
4. Conclusion
In this work, a DFT based first-principles study is used to
investigate the effect of carbon structures at the atomic level for
non-aqueous NaeO2 batteries. Seven representative carbon structures are presented, including graphite (0001) surface, SV defect,
DV5-8-5 defect, DV555-777 defect, DV5555-6-7777 defect, SeW
defect and fractured edge. It is found that the SV defect has the
largest adsorption energy to NaO2 molecules among the samples
studied. From Bader charge analysis, it is also found that the
adsorption energy of NaO2 molecule has a linear relationship with
electrostatic interaction with a correlation coefficient of 0.93. To
clarify the large adsorption energy of NaO2 on SV defect, several
initial and final sites as well as the charge difference plots are
shown. Results indicate that the large adsorption energy is attributed to two factors, one is the dangling atoms in SV defect decrease
the distance between molecule and substrate, the other is the NaO2
molecule anchored on SV defect through oxygen atom increases
electrons transfer. Based on the solution mechanism, SV defects can
act as the nucleation sites for NaO2 in the discharge process, and
increasing the number of SV defects leads to the uniform formation
of small-sized particles, which lowers the possibility for pore
clogging and thus leads to an increased discharge capacity and
improved cyclability for non-aqueous NaeO2 batteries. Therefore, it
is recommended that a porous carbon with lots of SV defects would
better be used as the air cathode in experiments to increase the
battery performance. Our investigation increases the mechanistic
understanding of non-aqueous NaeO2 batteries, helping the future
cathode design and in principle other types of metal-oxygen batteries as well.
Acknowledgements
The work described in this paper was fully supported by a grant
from the Research Grants Council of the Hong Kong Special
Administrative Region, China (Project No. 16213414).
Appendix A. Supplementary data
Supplementary data related to this article can be found at http://
dx.doi.org/10.1016/j.jpowsour.2016.05.132.
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