Proceedings of ITC/ISHW2007

Hydrogen Adsorption of Back Side of Graphene
Atsushi ITO1) , Arimichi TAKAYAMA2) and Hiroaki NAKAMURA2)
1)

Department of Physics, Graduate School of Science, Nagoya University, Furo–cho, Chikusa–ku, Nagoya 464–8602,
Japan.
2)
National Institute for Fusion Science, Oroshi–cho 322–6, Toki 509–5292, Japan.
(Received 15 October 2007 / Accepted ** ** 2007)
We studied the interaction between a single hydrogen atom and a single graphene using classical molecular
dynamics simulation with modified Brenner REBO potential. Three interactions, which are adsorption, reflection,
penetration, were observed. Overhang structure appears and creates an adsorption site on the backside of thegraphene. It is considered that backside adsorption occurs under the two conditions that an incident hydrogen
atom should have incident energy which is larger than the potential barrier of a hexagonal hole of the grapheneand that after the hydrogen atom passes through the graphene, it does not keep its kinetic energy to be trappedby the adsorption site. The conditions explained that as the incident energy increased, the incident point of thebackside adsorption shifted to the periphery of a hexagonal hole of the graphene in the simulation. Moreover,when a hexagonal hole of the graphene was expanded by the hydrogen atom incidence to the periphery of thehexagonal hole, its potential barrier was reduced.
Keywords: Chemical sputtering, Hydrogen, Graphene, Graphite, Adsorption
DOI: ****/pfr.****

1 Introduction
In the context of research into nuclear fusion, the plasma
surface interaction (PSI) problem has been studied [1–5].
A portion of the plasma confined in an experimental device
falls onto a divertor wall, which is shielded by graphite
or carbon fiber composite tiles. The incident hydrogen plasma erodes these carbon tiles in a process calledchemical sputtering. The erosion produces hydrocarbon
molecules, such as CHx and C2 Hx , which affect the plasma
confinement.
To solve the PSI problem, the mechanism of thegraphite erosion has been researched using molecular dynamics (MD) simulation [6–9]. Previously, we investigated the PSI of graphite surface which consists of 8graphene sheets using the modified Brenner reactive empirical bond order (REBO) potential [10]. Subsequently,
the isotope dependence of incident hydrogen atoms is investigated [11]. These simulations achieve steady stateof the graphite erosion, the incident energy linear dependence of total carbon yield accords with experimental results [12, 13].
The MD simulation of graphite surface showed that
if incident energy was 5 eV, almost of all incident hydrogen atoms were adsorbed by the graphite surface, while
if the incident energy was 15 eV, most incident hydrogen atoms were reflected. This adsorption and reflection
can be explained by the MD simulation of the elemental
processes which is the chemical reaction between a sinauthor’s e-mail: ito.atsushi@nifs.ac.jp, nakamura.hiroaki@nifs.ac.jp,
takayama@nifs.ac.jp

gle hydrogen atom and a single graphene [14–16]. ThisMD simulation indicates also that in a certain incident energy, the hydrogen atom can be adsorbed to the backsideof the graphene. On the other hand, the other MD simulation for graphene erosion due to hydrogen atom gas implied that para–overhang configuration which has hydrogen atoms onto both side of the graphene is created and its
C–C bond is easy broken [17]. Therefore, we consider that
if the incident energy which brings about the backside adsorption is selected, the MD simulation of graphite surface
shows a different dynamics.
Here, we attach weight to not only the macroscopic
simulation of graphite surface but also understanding a elemental mechanism and dynamics. We, therefore, investigate the backside adsorption of the interaction between asingle hydrogen atom and a single graphene in the present
paper. We describe the simulation model and method in§2. In §3, we present and discuss the simulation results.
This paper concludes with a §4.

2 Simulation Method
A graphene [18] consists of 160 carbon atoms measuring
2.13 nm × 1.97 nm, and is placed at the center of simulation box parallel to x–y plane. The simulation box in thex– and y–directions measures 2.13 nm × 1.97 nm with periodic boundary condition. In the z–direction, we do notprepare the boundary of the simulation box and the initialcoordinate of the center of mass of the graphene is z = 0 Å.
The initial graphene temperature is set to 0 K. The carbon
atoms of the graphene are relaxed initially and compose

Proceedings of ITC/ISHW2007
Adsorption
Reflection
Penetration

1

Adsorption rates

0.8

1.0
Rate of reactions

frontbackside

0.8
0.6

0.6
0.4
0.2

0.4
0
0

0.2
0.0
0.1

1
10
Incident energy EI [eV]100Fig. 1 The incident energy dependence of the rates of adsorption, reflection and penetration where the graphene temperature is 0 K. Dash–dotted line with open circle, long–
dashed line with filled triangle, and short–dashed linewith square denote the rates of adsorption, reflection andpenetration, respectively.

completely flat graphene structure. A hydrogen atom is
injected from z = 4 Å parallel to the x–y plane, that is, normal incidence to the graphene surface. Incident position in
the x– and y– directions are determined under a uniformed
distribution function. The incident energy EI decides aninitial momentum vector (0, 0, p0 ) as follows:pp0 = 2mEI ,(1)
where and m is the mass of the hydrogen atom.
We performed our MD simulation under NVE conditions, where the number of atoms, volume, and total energy
are conserved. The simulation time was developed using
second order symplectic integration [19]. The chemical interaction was represented by the modified Brenner REBO
potential [15, 20]:


X 


R
B
DH
A

U≡
V[i j] (ri j ) − b̄i j ({r}, {θ }, {θ })V[i j] (ri j ), (2)i, j>iwhere ri j is the distance between the i–th and j–th atoms.
The functions V[iRj] and V[iAj] represent repulsion and attraction, respectively. The function b̄i j generates multi–bodyforce. To conserve the accuracy of the calculation, the time
step was 5 × 10−18 s.
We note the condition to judge the type of reaction,
which corresponds to the condition to finish the simulation. While the incident hydrogen atom interacts with one
carbon atom, we count a trapped time. When the hydrogen
atom leaves the carbon atom or starts interaction with theother carbon atom, the trapped time is cleared. When thetrapped time reaches 0.1 ps (20000 time steps), the simulation is finished and this reaction is regarded as adsorption.

5

10 15 20 25 30 35 40 45 50
Incident energy EI [eV]Fig. 2 The incident energy dependence of the rates of the front
and backside adsorption where the graphene temperature
is 0 K.

Moreover, if the relative position from the nearest carbon
atom to the hydrogen atom in the z–coordinate is positive,
the reaction is front adsorption, while if the relative position in the z–coordinate is negative, the reaction is backsideadsorption. When the hydrogen atom leaves the nearest
carbon atom, we begin counting a escaping time. If thehydrogen atom interacts a carbon atom again, we clear theescaping time and restart counting the trapped time. Whenthe escaping time reaches 0.05 ps (10000 time steps), thesimulation is finished. And, if the escaping hydrogen atom
has positive momentum in the z–coordinate, this reaction
is reflection, while it has negative momentum, the reaction
is penetration.
We repeated the above simulation 200 times for each
incident energy, where the incident position in the x– andy– directions are every time changed randomly under theuniformed distribution function. Since we counted thetypes of the reactions, we obtained the rates of the reactions. Of course, the sum of the rates of the adsorption,reflection and penetration is always 1.

3 Results and Discussion
The simulations were executed for incident energy of 0.1
eV to 200 eV. The three interactions, which are adsorption,reflection, penetration, were observed. Figure 1 shows thatthe rates of the three interactions depend on the incident
energy. Especially, the rate of adsorption has two peaks.
Next, Fig. 2 shows the rates of the front and backsideadsorption. Although the front adsorption occurs aroundthe both adsorption peaks, the backside adsorption occurs
around the high incident energy adsorption peak only. In
the process of front adsorption, the nearest carbon atomwhich is connected to the incident hydrogen atom by a covalent bond is pulled out from flat surface of the graphene.
This is called a overhang structure and creates an adsorption site for a hydrogen atom [14, 15]. In the backside ad-Proceedings of ITC/ISHW2007(a) 20 eV
ads. : ref. : pen. = 25 : 175 : 0(0 back abs.)ads. : ref. : pen. = 61 : 136 : 3(35 back abs.)

potential
[eV]
45

1.0
y-coordinate [A](b) 25 eV

0.5

35
25

0.0

15
(c) 27 eV-0.5

ads. : ref. : pen. = 59 : 119 : 22
(37 back abs.)(d) 30 eV
ads. : ref. : pen. = 31 : 103 : 66
(19 back abs.)

-1.0

-1

-0.5
0
0.5
x-coordinate [A]1Fig. 3 The potential barrier of a hexagonal hole of the graphene.
The mapped value is potential energy when the hydrogen
atom is located in the plane of z = 0 Å.

sorption also, the overhang structure appears. That is, anadsorption site is created in the backside of graphene after
the incident hydrogen atom goes through the graphene.
The incident energy dependence of the rates of interactions Fig. 1 is understood using energetics, which relates
π–electron on the graphene surface, structure transformation to the overhang structure and the potential barrier ofa hexagonal hole of the graphene [15]. In the present paper, we discuss the backside adsorption. We consider thatthe backside adsorption needs the following two conditions. One is that to go through the graphene, the incident
hydrogen atom should have the incident energy which islarger than the potential barrier of a hexagonal hole of thegraphene. The other is that after the hydrogen atom passes
through the graphene, it is trapped by the adsorption site
due to the overhang structure. Namely, to occur the backside adsorption, the kinetic energy of the hydrogen atom
is diffused to carbon atoms of the graphene and must notremain. Concerning the first condition, the potential barrier of a hexagonal hole of the graphene, where the hydrogen atom is located at z = 0 Å, is shown by Fig. 3. The
center of this figure corresponds to the center of a hexagonal hole of the graphene. The six white regions indicate
higher potential barrier of more than 50 eV because carbon atoms exist there. The point of minimum potential
barrier is not the center of a hexagonal hole of graphene
and appears between the locations of carbon atoms andthe center of a hexagonal hole of the graphene. Figure 4
shows incident points and the types of their interactions. It
is understood and consistent with the potential barrier ofFig. 4 Incident points v.s. the types of its interactions. Circles
indicate incident points which bring about hydrogen atom
adsorption where the opaque circles correspond to backside adsorption. Triangles and squares are reflection andpenetration, respectively. Big six circles and six line represent six carbon atoms and six covalent bonds composing a hexagonal hole of the graphene.

a hexagonal hole of the graphene Fig. 3 that the backsideadsorption occurs around the points of minimum potential
barrier and does not occur around the center of a hexagonal hole of the graphene. As the incident energy increases,
the incident points for the backside adsorption shift fromthe points of minimum potential barrier to the peripheryof a hexagonal hole of the graphene which is over the covalent bonds between carbon atoms. This phenomenon is
explained as follows. In the incident energy of 20 eV, because all incidences become the front adsorption or reflection, the hydrogen atom does not have enough incident energy to go over the potential barrier of a hexagonal hole of
the graphene. In the incident energy of 25 eV, because theincident energy is higher than but close to the minimum potential barrier, only the hydrogen atoms which are injectedaround the points of the minimum potential barrier gothrough the hexagonal hole of the graphene and are trappedby adsorption site of the backside of the graphene. Whenthe incident energy increases (27 and 30 eV), the regionin which the potential barrier of a hexagonal hole of thegraphene is lower than the incident energy extends. Therefore, the backside adsorption occurs in the periphery of ahexagonal hole of the graphene. However, the backside ad-Proceedings of ITC/ISHW2007
sorption around the potential minimum point changes into
penetration because the hydrogen atom leaves the kinetic
energy enough to escape out of the adsorption site after itpassed through a hexagonal hole of the graphene. More
important thing is that while the backside adsorption happens in the periphery of a hexagonal hole of the graphene,
it does not happen in the center of a hole of the graphenein spite of same potential barrier. It is demonstrated by the
trajectory of atoms in the MD simulation that when the hydrogen atom is injected into the periphery of a hexagonalhole of the graphene, near two carbon atoms move and thehexagonal hole of the graphene is expanded. The expansion of the hexagonal hole of the graphene seems to reduce
the potential barrier of the hexagonal hole of the graphene
because the distance between hydrogen atom and the nearcarbon atoms become larger. On the other hand, if the hydrogen atom is injected to the center of a hexagonal hole of
the graphene, it must push six carbon atoms to expand thehexagonal hole of the graphene. It is considered that at theincident energy of 30 eV, even if the hydrogen atom canmove two carbon atoms, it cannot move six carbon atoms
because of their larger mass. Consequently, the backsideadsorption and penetration hardly occur in the center of ahexagonal hole of the graphene.

4 Summary
We study the interaction between a single hydrogen atom
and a single graphene using classical molecular dynamics
simulation with modified Brenner REBO potential. The
three interactions, which are adsorption, reflection, penetration, were observed. Especially, in the present paper,
we discuss the backside adsorption. As well as the front
adsorption, the overhang structure appears in the backsideof the graphene and creates the adsorption site. It is considered that the backside adsorption occurs under the two conditions that the incident hydrogen atoms should have theincident energy which is larger than the potential barrier ofa hexagonal hole of the graphene and that after the hydrogen atom passes through the graphene, it does not keep its
kinetic energy to be trapped by the adsorption site. The hydrogen atom in the incident energy of 25 eV brings about
the backside adsorption only around the points of the minimum potential barrier, which is not the center of a hexagonal hole of the graphene and is the region between the center of a hexagonal hole and the locations of carbon atoms.
When the incident energy increases, the incident points forthe backside adsorption shift to the periphery of a hexagonal hole of the graphene. In addition, the backside adsorption around the potential minimum point change into penetration because the hydrogen atom leaves enough kinetic
energy to escape from the adsorption site after it passed
through a hexagonal hole of the graphene. Moreover, whena hexagonal hole of the graphene is expanded by the hydrogen atom incidence to the periphery of the hexagonal hole,its potential barrier is reduced. However, even if the hydrogen atom can move two carbon atoms in the incidence
to the periphery of the hexagonal hole, it cannot move six
carbon atoms in the incidence to the center of the hexagonal hole. Therefore, the backside adsorption and penetration hardly occur in the center of a hexagonal hole of thegraphene.

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