Amorphous structural models for graphene oxides
Lizhao Liua,b, Lu Wanga,b, Junfeng Gaoa,b, Jijun Zhaoa,b,*, Xingfa Gaoc,
aCollege of Advanced Science and Technology, Dalian University of Technology, Dalian 116024, China
bKey Laboratory of Materials Modification by Laser, Ion and Electron Beams, Dalian University of Technology, Ministry of Education,
Dalian 116024, China
cKey Laboratory for Biomedical Effects of Nanomaterials and Nanosafety, Institute of High Energy Physics,
Chinese Academy of Sciences, Beijing 100049, China
dDepartment of Chemistry, Institute for Functional Nanomaterials, University of Puerto Rico, San Juan, Puerto Rico 00931, USA
A R T I C L E I N F O
Received 11 October 2011
Accepted 1 December 2011
Available online 8 December 2011
A B S T R A C T
Based on the experimental observations, amorphous structural models of graphene oxides
(GOs) were constructed and investigated by first-principles computations. Geometric struc-
tures, thermodynamic stabilities, and electron density of states of these amorphous GO
models were examined and compared with the previously proposed ordered GO structures.
The thermodynamically most favorable amorphous GO models always contain some
locally ordered structures in the short range, due to a compromise of the formation of
hydrogen bonds, the existence of dangling bonds, and the retention of the p bonds. Com-
pared to the ordered counterparts, these amorphous GO structures possess good stability at
low oxygen coverage. Varying the oxygen coverage and the ratio of epoxy and hydroxyl
groups provides an efficient way to tune the electronic properties of the GO-based
? 2011 Elsevier Ltd. All rights reserved.
Since the synthesis in 2004 , graphene has demonstrated
promise for a variety of applications [2–7]. In the family of
graphene-based materials, graphene oxide (GO), a single
layer of graphite oxide (first produced by treating graphite
with strong aqueous oxidizing agents ), is also a focus of
intensive studies partially because it is an important material
to massively produce graphene [9–13]. More importantly, GO
itself has manifested many unique properties that may lead
electronic devices [14–17], chemical sensors [18,19], optical
devices [20–24], energy storage [7,13,25,26], and composite
Determining the atomic structure of GO is essential for a
better understanding of its fundamental properties and for
realization of the future technological applications. Over the
Among numerous experimental techniques, the most rel-
evant one is the nuclear magnetic resonance (NMR) measure-
ment [28–32]. The solid-state13C NMR and1H CPMAS NMR
reveal the evidence of epoxy (C–O–C), hydroxyl (OH), carbox-
ylic (COOH), and a small amount of other groups in GOs. How-
ever, it is extremely challenging to determine the detailed
atomic structure of GO due to the following factors: (1) GO
is a nonstoichiometric compound with a variety of composi-
tions depending on its synthesis condition; (2) GO is strongly
hydrophilic and hygroscopic; (3) GO is thermally unstable and
slowly decomposes above 60–80 ?C [31,33–35].
0008-6223/$ - see front matter ? 2011 Elsevier Ltd. All rights reserved.
* Corresponding author at: College of Advanced Science and Technology, Dalian University of Technology, Dalian 116024, China. Fax: +86
E-mail address: firstname.lastname@example.org (J. Zhao).
C A R B O N 5 0 (2 0 12 ) 1 69 0 –1 6 98
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In addition to NMR, various microscopic means were em-
ployed to characterize the atomic structures of GOs, including
transmission electron microscopy (TEM) [34,36–40], scanning
electron microscopy (SEM) [35,36], atomic force microscopy
(AFM) [37,38,41–44], scanning tunneling microscopy (STM)
. Besides, measurements using optical analysis tech-
niques [34–37,41–46], such as X-ray diffraction (XRD), X-ray
photoelectron spectroscopy (XPS), Fourier transform infrared
spectroscopy (FT-IR) and Raman spectroscopy, demonstrated
that GO contains carbon atoms with different types of bond-
ing states, for example, graphitic C, C–O–C, C–O, C@O, O–C@O,
and so on.
Now it is generally accepted that GO bears hydroxyl and
epoxy groups mostly on its basal plane [37,46]. The ratio of
each bonding type of carbon can be tailored by the synthesis
conditions, which enhances the complexity of atomic struc-
ture of GO. All these experimental observations suggest that
the atomic structure of GO is nearly amorphous in large
Theoretically, many GO structural models have been pro-
posed. Decades ago, four structural models respectively pro-
posed by Hofmann and Holst , Ruess , Scholz and
Boehm , Nakajima et al. [50,51], and Lerf and co-workers
[30–32], were generally accepted, depending on the character-
ization technique prevalent at that time. Among them, the
modelproposedby Lerfandco-workers, in which the hydroxyl
and epoxy groups distribute on the basal layer in a nearly dis-
ordered manner, explains the aforementioned experimental
results very well. Recently, based on Cai’s NMR experiment
, Yan et al. [52,53] and our group [25,54] have identified the
energetically favorable atomic configuration of GO, which con-
tains epoxy and hydroxyl groups in close proximity with each
other, and found that these functional groups prefer to aggre-
gate. In addition to hydroxyl and epoxy, groups of epoxy pair
and epoxy-hydroxyl pair in GO were also proposed by Zhang
et al. . Employing genetic algorithm and first-principles ap-
oxidized graphene by considering various epoxy groups (nor-
mal epoxy, unzipped epoxy and epoxy pair), and found that
phase separation between bare graphene and fully oxidized
graphene is thermodynamically favorable in partially oxidized
found the long hydroxyl chains are not expected to be widely
present in the real GO samples owing to their high chemical
shifts according to the simulated NMR spectra.
Note that although the disordered GO models proposed by
Hofmann and Holst , Ruess , Scholz and Boehm ,
namically most favorable, they can meet with the experimen-
tal observations to some extent; while the thermodynamically
more favorable ordered GO models proposed recently are
between the experiments and theories: the structures of GOs
are amorphous from experimental observations; but the
ordered GO models are thermodynamically preferred from
theoretical point of view.
To address this controversial issue and gain a deeper
insight into the structural characteristics of GOs, here we
considered the possibility of amorphous structural models
for GOs and compared them with the ordered structures. It
is interesting that the energetically preferred structures of
our constructed amorphous GO models always exhibit some
locally ordered structural motifs in the short range. Moreover,
the energetically preferred amorphous GOs are nearly as sta-
ble as the ordered ones at low oxygen coverage. Our computa-
tions reveal an overall trend for the amorphous GO structures,
which exhibit a locally ordered configuration but are disor-
dered in the long range. These results not only are in line with
the experimental observations of amorphous GOs, but also
help understand the previous theoretical ordered models
with lower energies.
2.1. Amorphous GO models
Our amorphous GO models start from a rectangular supercell
of graphene consisting of 80 carbon atoms (17.21 A˚· 12.45 A˚
in dimension). Based on the structural characteristics of the
stable GO structures proposed by previous computations
[25,52–56], we summarize the following rules to construct
the amorphous structural models: (1) two functional groups
cannot locate at the same carbon atom; (2) paired hydroxyl
groups are added to two adjacent carbon atoms, one above
and another below the graphene layer; (3) the numbers of
the functional groups on each side of graphene sheet should
be nearly equal to reduce the tension energy; (4) on one six-
membered ring, more than four carbon atoms bonded with
hydroxyl or five carbon atoms bonded with epoxy for each
side of graphene basal is not allowed due to steric effect.
For a given stoichiometry, certain numbers of epoxy and hy-
droxyl groups are randomly placed on the basal graphene
layer according to the above rules.
By varying the numbers of epoxy and hydroxyl groups
within the simulation supercell, amorphous GOs with differ-
ent oxidation extents can be obtained. Here we define an oxy-
gen coverage rate (R) as:
R ¼ number of sp3C ðbonded with O or OHÞ=
total number of C atoms ? 100%:
modelswithR = 10%(C80O6H4),20%(C80O12H8),30%(C80O18H12),
40% (C80O24H16), 50% (C80O30H20), 60% (C80O36H24), and 70%
(C80O42H28), respectively. Note that for the amorphous GOs
with different R, we assumed an OH:O ratio of 2.00, falling in
the range of 1.06–3.25 in the experimental observations .
As a representative, one structural model of amorphous GO
(R = 50%) is shown in Fig. 1a (top view) and Fig. 1b (side view).
To be well considered, the amorphous GOs with the same cov-
erage rate but different OH:O ratios are also investigated.
Choosing a representativecoverage of R = 50%, we constructed
a series of models with OH:O = 0.22 (C80O22H4), 0.50 (C80O24H8),
0.86 (C80O26H12),1.33 (C80O28H16),
(C80O32H24), 4.67 (C80O34H28), 8.00 (C80O36H32), respectively.
For the ordered GOs, our previous work [25,54] showed that
the epoxy and hydroxyl groups tend to locate and aggregate
along the armchair direction from the energetic point of view.
To compare with the amorphous GOs, we also assumed an
C A R B O N 5 0 ( 20 1 2 ) 1 6 9 0–16 9 8
OH:O ratio of 2.00 in the ordered GOs. Hence, chain configura-
tion composed of h2eI
the ordered GO structure (top view in Fig. 1c and side view in
Fig. 1d). In order to compare with their amorphous counter-
parts, ordered GO structural models with corresponding cov-
erage of R = 10% (C80O6H4), 20% (C40O6H4), 33% (C24O6H4), 40%
(C20O6H4), 50% (C16O6H4), and 67% (C12O6H4) were constructed
by expanding the width of supercell with inclusion of only
one h2e2Ichain, and keeping pristine graphene as the rest part
of the supercell.
2motif in  was adopted to represent
2.2. Computational methods
Periodic first-principles computations were performed with
the plane-wave pseudopotential technique implemented in
the CASTEP program based on the density functional theory
(DFT) [59,60]. The Perdew–Burke–Ernzerhof (PBE) functional
in the generalized gradient approximation (GGA) was em-
ployed to describe the exchange–correlation energy . The
norm-conserving pseudopotentials  were adopted for
describing the ion–electron interactions. A kinetic energy
cut-off value of 600 eV was used. During the geometry optimi-
zation, the k space for amorphous GO was sampled by the U
point, and the Monkhorst–Pack grids  with separation of
0.03 A˚?1were chosen for the ordered GO supercell structures
with different sizes. The supercell dimension perpendicular
to the GO plane is chosen as 12 A˚to avoid the interaction be-
tween the GO layer and its periodic images.
and the atomic coordinates of the initial configurations were
fully relaxed. During optimization, dissociation of epoxy, for-
on the basal plane, and other structural damages were ob-
served in some of the random GO configurations, especially
for those with relatively high coverage rates (R P 30%). At the
beginning, we have considered a large number of initial
random structures (totally ?500) forcoarse optimizationswith
lower SCF tolerance of total energyof 1.0 · 10?5eV/atom. After
that, for each coverage rate and OH:O ratio, we picked out
optimizations with higher SCF tolerance of total energy of
2.0 · 10?6eV/atom. Note that these ten energetically favorable
configurations are all locally stable without the above men-
tioned damages. Finally, the lowest-energy structure among
the ten refined configurations was selected as the representa-
tive for discussions of structural and electronic properties.
3.Results and discussion
3.1.Structural and electronic properties
In this part, we have considered the amorphous GOs with
OH:O = 2.00 but different coverage rates. As an example,
Fig. 2a displays the further optimized amorphous GO struc-
ture with R = 70%. Clearly the whole system is amorphous,
but some ordered motifs exist in the short range, which are
highlighted and shown individually on the top of the graph.
After relaxation, the epoxy and hydroxyl groups in the high-
lighted parts are arranged in an ordered manner, i.e., aggre-
gating along either armchair or zigzag directions. The
armchair chain is similar to the h2eI
structure, taking the ordered GO with R = 40% as a representa-
tive in Fig. 2b. Moreover, these ordered fragments may aggre-
gate. Such locally ordered motifs are also observed in the
amorphous GOs with other coverage rates (R = 10–60%) in
our structural models, which seem to be a universal feature.
This observation can be explained by a compromise of the
formation of hydrogen bonds, the existence of dangling
bonds, and the retention of the p bonds. When the functional
groups aggregate, more hydrogen bonds will be formed to
OH:O = 2.00 with R = 10–70%
2motif in ordered GO
Fig. 1 – Representatively atomic structural models of GOs with R = 50% under optimization are presented, where (a) is top view
and (b) is side view for the amorphous structure; (c) is top view and (d) is side view for the ordered structure, respectively. The
red atom is O, the gray atom is C, and the light blue atom is H. (For interpretation of the references to colour in this figure
legend, the reader is referred to the web version of this article.)
C A R B O N 5 0 (2 0 1 2) 1 6 90 –1 6 98
lower the energy and stabilize the structure. Fig. 3 shows the
hydrogen bonds in the structural model of Fig. 2a. Obviously,
hydrogen bonding network is amassed in the vicinities of
those three ordered parts (highlighted in Fig. 2a). Meanwhile,
there are some dangling bonds (or unsaturated electrons) on
the GO sheet, which are energetically unfavorable. Aggrega-
tion of epoxy and hydroxyl groups in an ordered way can effi-
ciently eliminate these dangling bonds (or unsaturated
electrons) by self-termination and thus to stabilize the GO
structure. Reportedly, when the functional groups in the GO
are assembled, large area of sp2carbon network will be
separated from the sp3domain. This local phase separation
will reduce the number of p bonds to be destroyed and is
thermodynamically favorable as far as enthalpy is considered,
as mentioned in [54,56].
Typically, GO is an insulator with a band gap of ?3 eV
[38,53,64–66]. Its electronic properties can be effectively tuned
by varying ratio of sp2/sp3carbon bonds (concentration and
relative ratio of the functional groups) on the basal plane
. By changing the oxidation level and the location of the
oxidized region of GOs, Yan et al. [52,53] obtained variable
band gaps from 0.2 to 4.2 eV using LDA calculations. More-
over, electrical conductivity of GOs is also tunable depending
on the level of oxidation, and the magnitude of variation can
be as high as >106times . In this work, we calculated the
electron density of states (DOS) for both ordered and amor-
phous GO structures, aiming to reveal the correlation be-
theoretical DOS of ordered and amorphous GOs with
R = 20%, 40%, and 50% are given in Fig. 4. As expected, the or-
dered GO structures always present a clean band gap. The
band gaps of ordered GOs with R = 20%, 40%, and 50% are
1.22, 1.92 and 2.06 eV, respectively. For the ordered GOs, as
the coverage rate increases, the band gap is widened due to
increasing ratio of sp3carbon, which destroys the p-conju-
gated bonds on sp2graphene basal plane. On the contrary,
as shown in Fig. 4 (right), DOS of the amorphous GOs usually
exhibit some defective peaks around the Fermi level, which
indicates existence of certain amount of dangling bonds in
these disordered structures.
Here we define the minimum of conduction band contrib-
uted by sp3carbon as conduction-band minimum (CBM) and
the maximum of valence band contributed by sp3carbon as
valence-band maximum (VBM), respectively. There are some
defect-induced states between CBM and VBM, which may
originate from the unsaturated dangling bonds, structural
distortion, and locally residual sp2and sp2–sp3bonds. These
defect-induced states are almost localized and may trap the
Fig. 3 – Hydrogen bonds in the amorphous GO with R = 70%
are shown. The hydrogen bonds are highlighted by green
dish lines. (For interpretation of the references to colour in
this figure legend, the reader is referred to the web version
of this article.)
Fig. 2 – Optimized structures of GOs, (a) amorphous structure with R = 70% and (b) ordered structure with R = 40%, are
presented. The highlighted parts in the amorphous GO (shown in the upper plot of graph (a)) are the locally ordered motifs.
C A R B O N 5 0 ( 20 1 2 ) 1 6 9 0–16 9 8
electrons so as to barely (or not) affect the electrical conduc-
tivity in real material applications . If we ignore these mid-
states and only consider the band gap between the CMB and
VBM, the band gaps of amorphous GOs with R = 20%, 40%, and
50% are about 0.53, 0.80 and 1.77 eV, respectively. Hence, the
trend of band gap for the amorphous GO structures with dif-
ferent coverage rate is also consistent with that for the or-
defective states and trend of band gap versus coverage rate
have been reported in previously experimental measure-
this trappingeffect of
To further confirm our results, the amorphous GOs with
R = 50% but different OH:O ratios are investigated. Two of
the optimized GO structures are presented in Fig. 5 as repre-
sentatives: one with abundant epoxy groups (OH:O = 0.22,
upper plot), and the other with numerous hydroxyl groups
with (OH:O = 8.00, lower plot). As highlighted in Fig. 5, the
epoxy groups nearly form a chain in the epoxy-dominant
upper structure (OH:O = 0.22), while there are also several lo-
cally ordered motifs in the lower one (OH:O = 8.00) with many
hydroxyl groups. In other words, amorphous GO structures
with different OH:O ratios also contain the locally ordered
structures to enhance the thermodynamic stability. Thus,
the stable amorphous structures of GOs from our random
construction and first-principles relaxations exhibit disor-
dered features in the long range but contain ordered struc-
tural motifs in the short range.
The DOS of amorphous GOs with different OH:O ratios of
0.50, 2.00, and 8.00 are displayed in Fig. 6. As the OH:O ratio
increases, more electrons would transfer into the valence
states. Again, the band gap between the CBM and VBM (ignor-
ing the mid-states within the gap region) becomes larger as
the OH:O ratio increases. The band gaps of amorphous GOs
R = 50% with OH:O ratio from 0.22 to 8.00
with OH:O ratio = 0.50, 2.00, and 8.00 are about 1.46, 1.76
and 2.45 eV, respectively.
The increased band gap between the CBM and VBM with
increasing OH:O ratio may be partially attributed to the
hybridization of carbon atoms. Intuitionally, the carbon atom
Fig. 5 – Amorphous GO structures with R = 50% but different
OH:O ratios, (upper) OH:O = 0.22 and (lower) OH:O = 8.00, are
presented. The locally ordered structures are highlighted by
balls and sticks for the guide of eyes.
R = 20%
Density of States (arb. unit)
R = 40%
R = 50%
Density of States (arb. unit)
Fig. 4 – DOS of the ordered (left) and amorphous (right) GOs with different coverage rates R = 20%, 40%, 50% are plotted.
C A R B O N 5 0 (2 0 1 2) 1 6 90 –1 6 98
bonded with a hydroxyl group has a larger bond angle (?105?)
than that bonded with an epoxide group (?55?); thus the for-
mer is very close to that of ideal sp3hybridization state
(109.47?). Therefore, carbon atoms in the GO structures with
high OH:O ratio might be dominated by sp3hybridization,
which would lead to a large band gap [52,71].
The thermodynamic stability of these amorphous and or-
dered GOs is discussed in terms of their formation energies.
Here we define the heat of formation (Hf) from the total ener-
gies for all relevant systems using the following equation :
Hf¼ ECxOyHzðGOÞ ? xECðgrapheneÞ ? y=2EOðO2Þ ? z=2EHðH2Þ;
where ECxOyHzis the total energy of GO with the chemical for-
mula of CxOyHz, and EC is the energy per carbon atom in
graphene. EOand EHare the total energies of gaseous O2mol-
ecule and H2molecule, respectively.
The computed Hf for both amorphous and ordered GO
structures are plotted as function of coverage rate R in
Fig. 7. First, all Hfare negative, indicating that formation of
GO through oxidation of graphene is an exothermic process,
as found before [52–54,56]. Note that the heat of formation
for those ordered GO structures varies linearly with R, which
is a natural consequence of the chain-based supercell model
used here. On the other hand, the Hfof amorphous GOs is not
a straight line of oxidation rate R and it is higher than the Hf
for the ordered ones by up to 0.19 eV per C atom. The energy
difference between the amorphous and ordered GO structures
reduces as the oxidation rate decreases. Extrapolation to low
coverage limit shows that the amorphous GOs could be as
stable as the ordered GOs when coverage rate reaches below
5%. This result coincides with our previous theoretical work
of kinetic analysis for GO formation (see Fig. 4 in ) that
the homogenous GO phase is favored at low coverage,
whereas inhomogeneous GO phase or phase separation is
more likely to occur at relatively higher coverage.
The heats of formation for the amorphous GO structures
with fixed R = 50% but different OH:O ratios are presented in
Fig. 8. As the OH:O ratio increases, the heat of formation
becomes lower and thus the GO system becomes thermody-
namically more favorable. This result indicates that function-
alization of hydroxyl groups on the GO sheet energetically
prevails over epoxy groups, which is consistent with the
previous theoretical results [52,53].
From the above discussions, we find that random configu-
rations of GOs usually contain some locally ordered structural
motifs and the previously proposed ordered structural models
[25,52–55] are lower in energy than the disorder configura-
tions. But why it is hard to observe large-scale ordered struc-
tures of GOs in experiment? Several possible effects such as
kinetic factors during growth process and configuration
Heats of formation (eV per C atom)
intersect at 5%
Fig. 7 – Heats of formation for the amorphous and ordered
GO structures as function of coverage rate R are plotted.
Heats of formation (eV per C atom)
OH : O
R = 50%
Fig. 8 – Heats of formation of the amorphous GOs with
R = 50% but different OH:O ratios are plotted.
Density of States (arb. unit)
OH : O = 0.50
OH : O = 2.00
OH : O = 8.00VBM
Fig. 6 – DOS of the amorphous GOs with different OH:O
ratios (OH:O = 0.50, OH:O = 2.00, and OH:O = 8.00) are plotted.
C A R B O N 5 0 ( 20 1 2 ) 1 6 9 0–16 9 8
entropy must be taken into account. Since formation of GO
through oxidation of graphene is an exothermic process, the
functional groups can be easily added onto the graphene
sheet. In the initial stage of growth, functional groups prefer
to aggregate along the direction with lower growth barrier
that is determined by the chemical environment of the exist-
ing groups on the GO layer. While considering the kinetic fac-
tors during growth, there are high diffusion energy barriers
(up to 2.89 eV) between local minima to prevent growing large
ordered structures . In other words, the ordered structural
models predicted by the theoretical simulations are only the
consequence of thermodynamic factors but are prevented
by the kinetic factors during realistic synthesis condition. Be-
sides, the effect of configuration entropy , which prefers
the disordered structures with high probability and becomes
more significant at higher temperature, may also contribute
to the experimentally observed amorphous GO structures. Re-
cently, GO samples with ordered wrinkles have been synthe-
sized, which confirmed the ordered arrangement of epoxide
groups . With improvement of experimental technology,
we anticipate that the large-scale ordered GO with different
oxygen functional groups will be fabricated in the future.
A series of amorphous GO structures with different coverage
rates and OH:O ratios were constructed by randomly adding
epoxy and hydroxyl groups onto a perfect graphene supercell
with 80 carbon atoms following some structural rules. Or-
dered GO structures with epoxy and hydroxyl chains along
the armchair direction were considered for comparison. The
main conclusions from our first-principles computations are
itemized as follows.
First, the thermodynamically stable amorphous GO is usu-
ally disordered in long range but exhibit some short-range or-
dered motif to stabilize the structures. The ordered structural
models proposed by the previous theoretical calculations are
more energetically favorable than the present amorphous
ones. Since dealing with periodic supercells without edges
and hole defects, here we only considered epoxide and hydro-
xyl, which are the dominant groups on graphene basal plane.
However, in the realistic GO samples, there may exist some
other groups, such as carboxyl and ketone; and these groups
will most likely locate at the edges and hole defects. In addi-
tion, our present results are limited by the finite size effect of
simulation supercell and zero-temperature in DFT optimiza-
tion. In reality, at finite temperatures, migration and transfor-
mation of different functional groups may occur and the
effects of kinetic factor and configuration entropy must be ta-
ken into account. This may answer the inconsistency be-
tween the experiments and theoretical predictions about
the atomic structures of GOs.
Second, the amorphous GO structures exhibit reasonable
thermodynamic stability and can be as stable as the ordered
ones as the coverage rate is below 5%, which may correspond
to the cases of reduced GO.
Third, the electronic properties of GOs can be effectively
tailored by varying the concentration and/or relative ratio of
epoxy and hydroxyl groups. The electrical conductivity of
GOs will be enhanced by either lowering the coverage rate
or increasing the relative ratio of epoxy groups.
The present theoretical results shed some lights on the
atomic structures of GOs and suggest some possible ways of
controlling the electronic properties of GO materials.
This work is supported in China by the Fundamental Re-
search Funds for the Central Universities of China (No.
DUT10ZD211) and the National Natural Science Foundation
of China (No. 11134005), and in USA by NSF Grant EPS-
1010094 and the Environmental Protection Agency (EPA Grant
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