# Novel First-Principles Insights into Graphene Fluorination

Tahereh Malakoutikhah<EMAIL_ADDRESS>S. Javad Hashemifar
<EMAIL_ADDRESS>Mojtaba Alaei  Department of Physics, Isfahan University
of Technology, Isfahan 84156-83111, Iran

###### Abstract

Comprehensive first-principles calculations are performed on diverse
arrangements of relevant chemical defects in fluorographene to provide
accurate microscopic insights into the process of graphene fluorination. The
minimum energy paths for the half- and full-fluorination processes are
calculated for a better understanding of these phenomena. While experimental
observations indicate a much slower rate of the full-fluorination process,
compared with the half-fluorination one, the obtained energy profiles
demonstrate much enhanced fluorine adsorption after the half-fluorination
stage. This ambiguity is explained in terms of significant chemical activation
of the graphene sheet after half-fluorination, which remarkably facilitates
the formation of chemical contaminants in the system and thus substantially
slows down the full-fluorination procedure. After considering the binding
energy and durability of the relevant chemical species, including hydrogen,
oxygen, and nitrogen molecules and xenon atom, it is argued that oxygen-
fluorine ligands are the most likely chemical contaminants opposing the full-
fluorination of a graphene sheet. We propose an oxygen desorption mechanism
for the atomic description of the full-fluorination procedure in realistic
situations. It is argued that the proposed mechanism explains well much
enhanced rate of the full-fluorination procedure at elevated temperatures.

##  I Introduction

Fluorographene (FG) is a distinguished member of graphene (Gr) derivatives,
which is formed by covering both sides of a Gr sheet with a fluorine
monolayer, leading to the FC2F chemical formula. The applicable properties of
FG added to its extraordinary features inherited from pristine graphene, have
attracted great interest over the last decade. The stoichiometric FG has an
ordered structure that is thermally stable up to 400$\rm{}^{\,o}C$.Nair et al.
(2010) The experimental Young modulus of this 2D material is 100 N/m which
shows its high mechanical stability. Finally, what makes FG prominent among
others is having the widest measured band gap of about 3 eV among all of the
Gr derivatives.Nair et al. (2010) Recent studies confirm its potential
applications in batteries and supercapacitors, electrochemical sensors, solar
cells, organic field-effect transistors, electrocatalytic oxygen and hydrogen
reactions, spintronic devices, anti-corrosion and self-cleaning coatings, oil-
water separation, biomedicine, optoelectronic, and photonic. Chronopoulos et
al. (2017)

Fluorination of graphene sheets with a proper chemical agent is a systematic
method for the synthesis of stoichiometric FG samples. Xenon difluoride (XeF2)
is a popular fluorinating agent that is utilized for the fluorination of
graphene at various temperatures. Nair and colleagues observed that complete
fluorination may take more than two weeks at 70$\rm{}^{\,o}C$, while at
200$\rm{}^{\,o}C$ about 10 hours is enough to obtain full-fluorinated
samples.Nair et al. (2010) Creutzburg et al. performed the same procedure at
120$\rm{}^{\,o}C$ and found that after about 48 hours the Gr samples are fully
fluorinated.Creutzburg et al. (2021) Kashtiban and others employed accurate
electron microscopies to distinguish two stages in the fluorination procedure.
They argue that in the first stage, one side of the Gr sheet is rapidly
fluorinated (half-fluorination stage) and then the fluorination of the
opposite side will be started (full-fluorination stage).Kashtiban et al.
(2014) These experimental results suggest the presence of some nontrivial and
temperature-dependent mechanism against the adsorption of fluorine atoms on
the graphene sheet, in the second fluorination stage. A theoretical molecular
dynamics (MD) simulation further complicates the situation, as it shows that
adsorption of a fluorine atom on a Gr sheet encourages adsorption of a second
fluorine atom at the opposite side of the sheet.Paupitz et al. (2012) Another
discrepancy is the theoretical band gap of FG which is much higher than the
measured one. While the experimental band gap of FG is expected to be in the
range of 3-3.8 eV,Nair et al. (2010); Jeon et al. (2011) the most accurate
first-principles techniques predict a band gap of 5.1-7.49 eV for this 2D
system. Şahin et al. (2011); Leenaerts et al. (2010); Wei and Jacob (2013);
Yuan et al. (2015) Considering some kinds of defects may somewhat reduce the
theoretical band gap of FG toward the experimental value. Yuan et al. (2015);
Huang et al. (2017)

The nontrivial ambiguities observed in fluorographene suggest possible
misunderstanding in the graphene fluorination process. Hence, in this work, we
employ accurate first-principles calculations to provide new microscopic
insights for a more precise understanding of the graphene fluorination
procedure.

##  II Method

Our electronic structure calculations and structural relaxations were
performed in the framework of density functional theory by using the full
potential numeric atom-center orbital (NAO) technique implemented in the FHI-
aims package.Blum et al. (2009) The NAO basis functions:

$\varphi_{i}(r)=\frac{u_{i}(r)}{r}Y_{lm}(\omega)$ (1)

are composed of radial solutions $u_{i}(r)$ of a Schrödinger-like equation and
spherical harmonics $Y_{lm}$. The numerically tabulated functions, $u_{i}(r)$,
are proven to be very efficient for accurate simulation of non-periodic and
periodic systems.

For simulating the 2D sheets, we use a slab supercell containing a vacuum
thickness of about 15 Å, to prevent artificial interactions between adjacent
layers. Among possible atomic configurations for FG, we adopt the chair
structure, sketched in Fig. 2, which is argued to be the lowest energy
configuration of this 2D material. A mesh of $8\times 8\times 1$ k-points was
used for our Brillouin zone integrations and the PBEsol exchange-correlation
functional was employed for our structural optimizations.Perdew et al. (2008)
The scalar relativistic atomic-ZORA approximation (zero-order regular
approximation) was implemented to involve the relativistic effects,van Lenthe
et al. (1994) while the full relativistic spin-orbit effect was only
considered for the adsorption of the heavy Xe element. Moreover, the van der
Waals correction based on the Hirshfeld partitioning of the electron density
and spin polarization was considered in the calculations.Tkatchenko et al.
(2012)

##  III Results and Discussions

As it was mentioned in the Introduction, a major experimental observation in
the FG synthesis is that fluorination of the second side of the system takes
weeks to be completed Kashtiban et al. (2014) and it is significantly
accelerated by increasing temperature from 70 to 200$\rm{}^{\,o}C$.Nair et al.
(2010) This observation may be attributed to the appearance of an energy
barrier for the adsorption of fluorine atoms on the opposite side of a half-
fluorinated graphene (hFG) sheet. Hence, in the first step, we calculated and
compared the adsorption energy path of a fluorine atom on a pristine and a
half-fluorinated Gr sheet. In this regard, the energy of the system was
minimized at several F atom-sheet distances by constrained relaxation of the
atomic positions and unit cell parameters, in a $2\times 2$ slab supercell.
The obtained energy path diagrams, presented in Fig. 1, indicate no energy
barrier for the adsorption of the fluorine atom on either the pristine or the
half-fluorinated Gr sheet. Moreover, the adsorption energy of the fluorine
atom on hFG is remarkably enhanced with respect to the pristine sheet, in
agreement with a recent MD simulation.Paupitz et al. (2012) These observations
sound inconsistent with the very low experimentally observed rate of the full-
fluorination process of graphene.Nair et al. (2010) Therefore, we propose a
different scenario to explain this discrepancy.

Figure 1:  Top and side views of the chair structure of a fluorographene
monolayer (FC2F) and the calculated adsorption energy path of a fluorine atom
on a pristine graphene sheet and a half-fluorinated one.

The much higher binding energy of a fluorine atom on hFG, compared with the
pristine Gr, indicates that the adsorption of a fluorine layer on a graphene
sheet significantly activates the opposite facet of the sheet for adsorbing
chemical species. Therefore, the opposite facet of the hFG sheet is expected
to be suddenly contaminated with available chemical species in the
environment. In other words, on the opposite side of hFG, close competition is
expected between the fluorine atoms and other available chemical species to
occupy the free adsorption sites of the sheet. This competition is anticipated
to be the main mechanism for slowing the rate of the full-fluorination of a Gr
sheet. Moreover, the presence and persistence of unwanted chemical species in
the adsorption sites of FG may explain the large difference between the
theoretical and experimental band gap of the system.

Figure 2:  Top and side views of the relaxed structures of the hFG sheet, after adsorption of different chemical species.  Table 1:  Obtained equilibrium parameters of the pristine (C8) and the half-fluorinated (F4/C8) graphene sheet after adsorption of various chemical species, including F and Xe atoms and N2, O2, and H2 molecules; $E_{b}$ (eV): binding energy, $2a$ (Å): equilibrium lattice parameter of the supercell, $d$ (Å): equilibrium molecule-sheet vertical distance. In two more important cases, a larger $4\times 4$ supercell ($\rm F_{16}/C_{32}/F_{14}O_{2}$) is also considered. In these cases, the equilibrium lattice parameter is divided by two, to be comparable with the other results. It should be clarified that the binding energy and vertical distance have been calculated for the last chemical species written in the first column.  system | $E_{b}$ | $2a$ | $d$
---|---|---|---
C8 | — | 4.915 | —
C8/F | $-2.06$ | 4.927 | 1.492
C8/Xe | $-0.16$ | 4.914 | 3.920
C8/N2 | $-0.12$ | 4.923 | 2.953
C8/O2 | $-0.09$ | 4.914 | 2.650
C8/H2 | $-0.05$ | 4.917 | 2.808
F4/C8/F | $-5.46$ | 5.079 | 1.420
F4/C8/Xe | $-0.18$ | 5.070 | 3.764
F4/C8/N2 | $-0.34$ | 5.085 | 1.395
F4/C8/H2 | $-4.67$ | 5.095 | 1.106
F4/C8/O2 | $-3.97$ | 5.071 | 1.334
F4/C8/F1N2 | $-0.29$ | 5.097 | 1.402
F4/C8/F2N2 | $+0.00$ | 5.118 | 1.409
F4/C8/F3N2 | $-0.12$ | 5.167 | 3.568
F4/C8/F1O2 | $-3.49$ | 5.124 | 1.324
F4/C8/F2O2 | $-3.27$ | 5.174 | 1.332
$\rm F_{16}/C_{32}/F_{14}O_{2}$ | $-2.38$ | 5.158 | 1.307
F4/C8/F2(OH)2 | $-4.44$ | 5.180 | 1.399
F4/C8/F2(OF)2 | $-2.29$ | 5.212 | 1.333
$\rm F_{16}/C_{32}/F_{14}(OF)_{2}$ | $-3.08$ | 5.179 | 0.961

To verify this scenario, we considered the adsorption of four inert chemical
species (Xe atom and H2, N2, and O2 molecules) on the pristine and the half-
fluorinated graphene sheet. These natural molecules are available in the dry
atmosphere of a glove box used for the traditional fluorination of Gr samples.
The adsorption of these species was studied in a 2$\times$2 lateral supercell
(Fig. 2) to reduce the effects of the adjacent replicas. The obtained relaxed
geometries are sketched in Fig. 2 and the computed physical parameters are
presented in table 1. We observe the physical adsorption of these inert
species on the pristine sheet (C8), the corresponding absolute adsorption
energies are below 0.2 eV, whereas the bond lengths are above 2.6 Å. In the
case of the heavy Xe atom, we considered the spin-orbit correction and found a
negligible relativistic effect in the corresponding binding energy. These
observed low binding energies may be well compensated by the room temperature
vibrational energy of the adsorbate atoms as well as by the kinetic energy of
the incident F atoms during the fluorination process. To speculate the
vibrational energy of the adsorbates, we calculated the gamma point
vibrational modes of the xenon atom, adsorbed on the pristine (C8) sheet. The
results indicate three soft modes at about 6, 10, and 31 cm-1, all below 4
meV. These soft modes are well saturated at room temperature and hence the
corresponding vibrational energy would be $3k_{B}T$, which equals about 0.08
eV at room temperature. Similarly, a diatomic molecule physically adsorbed on
graphene, is expected to have five soft vibrational modes and hence the
corresponding room temperature vibrational energy should be roughly about 0.13
eV. Adapting a Maxwell-Boltzmann distribution for the incident F atoms (Fig.
3), we observe that at the temperature of 70$\rm{}^{\,o}C$ about 8% of the F
atoms have a kinetic energy higher than 0.1 eV. Therefore, we conclude that
the thermal vibrational energies and the kinetic energy of the incident F
atoms at 70$\rm{}^{\,o}C$ are sufficient to clean up the surface of the
pristine graphene from the weakly bounded chemical contaminants (table 1) and
consequently give rise to a fast half-fluorination process for the pristine
graphene at 70$\rm{}^{\,o}C$.

Figure 3:  Maxwell-Boltzmann distribution D(k) as a function of the particle
kinetic energy k at 70$\rm{}^{\,o}C$ (D1) and 200$\rm{}^{\,o}C$ (D2), and the
resulting fraction of particles f(k) with a kinetic energy above k
($f(k)=\int_{k}^{\infty}D(k^{\prime})dk^{\prime}$). The inset shows the
enlarged tail of the f(k) functions.

The obtained binding energies on hFG (F4/C8) exhibit a clear enhancement with
respect to the corresponding values on the pristine graphene. This observation
confirms the proposed scenario about the chemical activation of the second
facet of graphene after half-fluorination. The largest activation is seen for
the O2 and H2 molecules where experience a tight chemical bonding to the half-
fluorinated graphene. As it is seen in Fig. 2, both molecules prefer a
parallel configuration to the sheet. In the case of H2 molecule, the hydrogen
atoms are almost decoupled on the sheet, and each one binds to its underlying
carbon atom. On the other hand, oxygen atoms keep their bonding on the
graphene sheet and thus slightly deviate from the carbon top sites. Although
N2 exhibits much weaker binding to F4/C8, compared with O2 and H2, it is still
significantly enhanced with respect to the N2 binding on the pristine graphene
(C8). Moreover, this molecule prefers a vertical alignment on the sheet (Fig.
2). The Xe atom shows the lowest binding enhancement, after half-fluorination
of graphene. The stable position of this noble element on F4/C8 is the carbon
top site, while on C8 it prefers the hollow sites of the sheet. Comparing the
binding energy of F and other investigated species on F4/C8 (table 1)
clarifies the anticipated competition between these species to occupy the
adsorption sites of the second facet of the hFG. In our proposed scenario,
this competition is the main reason behind the very slow rate of the full-
fluorination process of graphene. It should be stressed that the main
competition likely happens between oxygen molecules and F atoms, because of
the close binding energy of these entities. Although H2 has closer binding
energy to the fluorine atom, the very low amount of hydrogen in the
environment rules out its significant impact on the fluorination process.
However, our data suggest the presence of rare hydrogen defects in the
fluorographene samples which may have nontrivial influences on the electronic
structure of the system. It may also be noted that N2 and H2 exhibit a second
stationary position on F4/C8 which involves much weaker bonding relative to
the first one discussed above. In the case of N2, this weaker bonding happens
about 3.5Å above the sheet with a binding energy of $-0.11$ eV, while, H2
displays a second stationary position around 2.73 Å above the sheet with a
similar binding energy of $-0.11$ eV.

Now, we can explain some important observations about graphene fluorination in
the dry atmosphere of a glove box.Nair et al. (2010) It should be noted that
the graphene sheets were assembled on a gold grid to make both sides of the
sheet exposable to F atoms. However, one side of the sheet is practically more
accessible to the available adsorbates. Hence, in the first stage, one side of
graphene is rapidly fluorinated, because available chemical species are not
able to compete with the fluorine atoms for occupying the adsorption site of
the sheet. The half-fluorination process significantly increases the chemical
activity of the opposite facet of the sheet and hence in addition to the
fluorine atoms, mainly the oxygen molecules and to a lower extent, the
nitrogen molecules also occupy the adsorption sites of the hFG sheet and thus
remarkably slow down the full-fluorination process. Our scenario predicts very
fast full-fluorination of graphene in an oxygen-free ambient, confirmed by a
very recent experiment. Li and others observed very a high rate of
fluorographene synthesis at a vacuum condition of 10-6 mbar.Li et al. (2020)
Moreover, the observation of the high chemical activity hfG rules out the
stability and feasibility of the individual half-fluorinated graphene samples.

In the next step, we investigate the durability of N2 and then O2 impurities
in the fluorographene samples. The gamma point vibrational frequencies of an
N2 molecule adsorbed on C8 and F4/C8 were estimated to be (12,18,57,94,96) and
(10,20,36,49,50) cm-1, respectively, which in both cases give rise to a
thermal energy of about 0.15 and 0.20 eV at 70 and 200$\rm{}^{\,o}C$,
respectively. These thermal energies are not sufficient to compensate for the
binding energy of an individual N2 molecule ($-0.34$ eV) on hFG (table 1). In
order to provide more information, we investigated the accumulation of F atoms
and other chemical species in the neighborhood of an adsorbed N2 molecule on
the hFG. In the first step, we found that N2 molecule does not permit
adsorption of a further N2 in the adjacent sites. Then, we studied the
adsorption of F atoms in the neighborhood of an N2 molecule (table 1). This
procedure was seen to weaken the binding of N2 molecule to the hFG. Adsorption
of one F atom (F4/C8/F1N2) increases the binding energy of N2 molecule to
$-0.29$ eV while adsorption of two F atoms (F4/C8/F2N2) almost decouple the N2
molecule from the sheet. Adsorption of the third F atom shifts the molecule to
its second stationary position which is about 3.56 Å far above the sheet and
thus may be easily removed by thermal effects. It should also be noted that an
N2 adsorbate on F4/C8 has a slight influence on the binding of F atoms in the
adjacent sites. The binding energy of the first, the second, and the third F
atom in the vicinity of N2 is $-5.41$, $-5.20$, and $-5.45$ eV which are
pretty close to the binding energy ($-5.46$ eV) of an individual F atom on the
clean facet of the hFG (table 1). These results show that while individual N2
adsorbates on hFG are rather stable, the prior accumulation of F atoms in
their vicinity detaches these molecules from the surface, even at low
temperatures of about 70$\rm{}^{\,o}C$.

The same scheme was applied around an O2 adsorbate on the hFG. First, we found
that this adsorbate significantly increases the binding energy of a further
oxygen molecule in the adjacent sites to a value of about $-1.05$ eV. Then,
adsorption of F atoms was considered around the O2 molecule. Because of the
parallel configuration of O2 on the hFG, only two F atoms may be adsorbed in
the vicinity of O2 in a $2\times 2$ supercell. The first and the second F
atoms increase the binding energy of oxygen to $-3.49$ and $-3.27$ eV,
respectively (table 1). Despite these weakening effects, the O2 molecule is
still tightly attached to the sheet and thermal effects are far lower to
compensate for the remained binding energy. In order to reduce the effects of
adjacent O2 molecules, we repeated the last calculation in a larger $4\times
4$ supercell and found a high binding energy of about $-2.38$ eV for the O2
molecule fully surrounded by F atoms ($\rm F_{16}/C_{32}/F_{14}O_{2}$). These
findings argue that the complete elimination of the oxygen defects from the
fluorographene samples is an elaborating task. This observation may explain
the observed rare difference between the experimental (3.1-3.8 eV)Jeon et al.
(2011) and the theoretical excitonic band gap of this system (5.1 eV).Yuan et
al. (2015) The obtained spin polarized band structure of $\rm
F_{16}/C_{32}/F_{14}O_{2}$ is compared with that of an ideal FG sample in Fig.
4. It is seen that O2 impurities may significantly decrease the theoretical
band gap of FG, obtained within the single-particle Kohn-Sham framework.not
Moreover, some minority spin states occupy the band gap and cross the Fermi
level of the oxygen defected FG, indicating the chemical activity of the
oxygen defect in this system.

Figure 4:  Obtained band structures for F/C2/F (fluorographene), $\rm
F_{16}/C_{32}/F_{14}O_{2}$, and $\rm F_{16}/C_{32}/F_{14}(OF)_{2}$. $\rm
F_{16}/C_{32}/F_{14}O_{2}$ exhibits an spin polarized band structure, blue and
red colors show spin majority and spin minority states, respectively. The
shaded areas show the band gap region and the band gap values are written in
the figures.

After confirming the very probable presence of O2 defects in the FG samples,
we considered their chemical activity by adsorbing a further H2 and F2
molecule on top of these defects. The obtained results, presented in table 1,
exhibit the rather high chemical activity of this point defect. The binding
energy of H2 on O2 is about $-4.44$ eV and we observed that this strong
binding almost decouples the two H atoms from each other. The binding of F2 on
O2 is also predicted to be rather strong, each F atom attaches to one of the O
atoms with a binding energy of about $-1.13$ eV/atom. Because of the much
higher abundance of F atoms in the FG synthesis environment, compared with the
H2 molecules, the anticipated O2 defects in FG are likely covered by further F
atoms, leading to the pairs of OF ligands. In order to approach the more
realistic situations, we optimized the atomic configuration of these ligands
in a larger $4\times 4$ supercell (Fig. 5) and observed a cross geometry in
the neighboring OF ligands. The electronic band structure of this system is
also calculated and presented in Fig. 4. Compared with the system with a bare
oxygen defect ($\rm F_{16}/C_{32}/F_{14}O_{2}$), we observe that the
semiconducting feature of FG is well recovered with a band gap of about 2.78
eV, that it is still about 7% lower than the ideal FG.

——————————————————————————–  ——————————————————————————–
——————————————————————————– ABCD

Figure 5:  A: predicted atomic configuration of an oxygen defected FG in a
$4\times 4$ supercell ($\rm F_{16}/C_{32}/F_{14}(OF)_{2}$). The red, green,
and gray balls stand for the oxygen, fluorine, and carbon atoms, respectively.
B, C, D: initial, transition state, and final configurations of the $\rm
F_{16}/C_{32}/F_{14}(OF)_{2}+F$ complex in the proposed oxygen desorption
reaction. bottom: optimized energy path of the oxygen desorption reaction as a
function of the reaction coordinate.

In the last part of the paper, we provide some first-principles arguments
about the significant enhancement of the full-fluorination procedure of
graphene in the glove box, after increasing the temperature from
70$\rm{}^{\,o}C$ to 120$\rm{}^{\,o}C$ and 200$\rm{}^{\,o}C$.Nair et al.
(2010); Creutzburg et al. (2021) According to the above discussions,
neighboring OF ligands are the most likely defects in the FG samples, hence
the full-fluorination process requires an effective mechanism for removing the
adsorbed oxygen atoms. We focus on the optimized model of an oxygen defected
FG sample in a $4\times 4$ supercell (Fig. 5) and propose the following oxygen
desorption reaction:

$\rm F_{16}/C_{32}/F_{14}(OF)_{2}+F~{}\longrightarrow~{}\rm
F_{16}/C_{32}/F_{14}(OF)+F_{2}O$

An incident F atom picks up one of the OF ligands from the sample and forms a
free F2O molecule. In order to calculate the energy barrier of this reaction,
we selected the vertical distance between the oxygen atom of the target ligand
and its underlying carbon atom (C-O distance) as the reaction coordinate and
then optimized the energy of the system at different values of this
coordinate. The obtained reaction energy path is presented in Fig. 5. Four
configurations are labeled in the energy path and sketched in the figure for a
better understanding of the oxygen desorption reaction. As it was mentioned,
the configuration A represents the predicted structure of the oxygen defected
FG in a $4\times 4$ supercell. The minimized energy of this system plus the
energy of a free F atom has been selected as the reference of energy in the
reaction energy path. The configuration B shows an equilibrium position of the
incident F atom above the ligand, however, the kinetic energy of the atom
prevents it from stopping at this position. Hence, the incident F atom may
approach and then attach to the target OF ligand to form an F2O molecule on
the surface. If the incident F atom has enough kinetic energy, the formed
molecule at the surface may climb the energy barrier to reach the transition
configuration C, where the oxygen atom of the V-shape F2O molecule is about 2
Å above the central graphene layer (Fig. 5). On the other hand, in the final
configuration D, the desorbed F2O molecule exhibits an inverted V-shape
geometry. Our results indicate an energy barrier of about 0.43 eV for the
proposed oxygen desorption reaction. It should be noted that the activation
barrier should be calculated from A, not B that is an intermediate
configuration of the reaction.

In our proposed oxygen desorption reaction, the incident F atom should have a
kinetic energy of at least 0.43 eV, to overcome the activation barrier of the
reaction. According to the Maxwell-Boltzmann distribution (Fig. 3), at
70$\rm{}^{\,o}C$ only about $2.5\times 10^{-3}$ % of the particles have a
kinetic energy above 0.43 eV, which may explain the very low rate of the full-
fluorination of graphene at this temperature. Nair and others found that
complete fluorination of a graphene sheet at 70$\rm{}^{\,o}C$ takes more than
two weeks, while at 200$\rm{}^{\,o}C$ about 10 hours is enough for the full-
fluorination procedure.Nair et al. (2010) At 200$\rm{}^{\,o}C$, the number of
particles with enough kinetic energy increases by a factor of about 4 (Fig.
3), which qualitatively confirms the mentioned rate enhancement. However, a
more accurate comparison of the reaction rate ($k(T)$) at different
temperatures requires the Arrhenius scheme:

$k(T)=Ae^{-E_{a}/k_{B}T}$

$A$, $E_{a}$, $k_{B}$, and $T$ are frequency factor, activation energy, the
Boltzmann constant, and the Kelvin temperature, respectively. Inserting the
obtained activation energy (0.43 eV) and neglecting the temperature dependence
of the frequency factor, the above equation predicts that the reaction rate at
200$\rm{}^{\,o}C$ is about 55 times higher, compared with 70$\rm{}^{\,o}C$.
Hence the more than two weeks (336 hours) full-fluorination procedure of
graphene at 70$\rm{}^{\,o}C$, is expected to reduce to more than 6 hours at
200$\rm{}^{\,o}C$, in close agreement with the observation of Nair and
colleagues ($\sim$10 hours).Nair et al. (2010) In the same way, the full-
fluorination time at 120$\rm{}^{\,o}C$ is predicted to be more than 39 hours,
well consistent with the very recent record of Creutzburg et al. (48
hours).Creutzburg et al. (2021) Therefore, our proposed oxygen defected FG and
oxygen desorption mechanism explain well the observed features in the graphene
fluorination procedure.

##  IV Conclusions

In this work, we performed extensive full-potential DFT calculations on
various arrangements of the relevant atomic and molecular defects in
fluorographene (FG) to understand the experimentally observed two stages
fluorination procedure of Gr. In a glove box, at 70$\rm{}^{\,o}C$ the half-
fluorination of a pristine graphene sheet was found to happen quickly while
the full-fluorination procedure takes more than two weeks. In the first step,
the adsorption energy profile of a fluorine atom on the pristine and half-
fluorinated graphene (hFG) sheet was calculated and compared to identify a
significant enhancement in the chemical activity of graphene after the half-
fluorination stage. This observation rules out the feasibility of individual
half-fluorinated graphene samples. Afterward, adsorption of the relevant
chemical species, including Xe atom and N2, O2, and H2 molecules were
considered on the pristine and half-fluorinated graphene to confirm the
predicted chemical activation. After considering various arrangements of the
adsorbed N2 molecule on FG, it was argued that this point defect is not
durable and typical thermal energies at 70$\rm{}^{\,o}C$ are enough to clean
up the FG samples from this defect. On the other hand, the O2 molecule
exhibits a different behavior and may form thermally stable defects in FG. We
calculated diverse configurations of this molecule and concluded that pairs of
OF ligands with a cross geometry are likely the most abundant impurities in
the realistic FG samples, opposing the full-fluorination procedure. We
proposed an oxygen desorption reaction for removing the OF ligands from the
sample and thus enhancing the complete fluorination of graphene. In this
mechanism, an incident F atom with enough kinetic energy attaches to an OF
ligand to form an F2O molecule on the sheet. This molecule then should
overcome an energy barrier of about 0.43 eV to leave the sample. These results
explain very well the substantially increased rate of the full-fluorination
procedure at 120 and 200$\rm{}^{\,o}C$.

##  V ACKNOWLEDGMENTS

The authors appreciate the useful comments of Dr. Mehdi Abdi from Isfahan
University of Technology (IUT). This work was supported by the IUT Vice-
Chancellor in Research Affairs.

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  * (17) Unfortunately, we were not able to verify this trend in the excitonic or quasiparticle band gaps, beacuse our computational resources are not powerfull enough to apply first principles GW or excitonic calculations to our rather large supercells.