Self-organizing Behavior of Y-junctions of Graphene Nanoribbons

Dávid Fülep.et.al. Int. Journal of Engineering Research and Application www.ijera.com
ISSN : 2248-9622, Vol. 7, Issue 5, ( Part -3) May 2017, pp.34-47
www.ijera.com DOI: 10.9790/9622-0705033447 34 | P a g e
Self-organizing Behavior of Y-junctions of Graphene
Nanoribbons
Dávid Fülep*
, Ibolya Zsoldos**
, István László***
* Faculty of Technology Sciences, Széchenyi István University, Hungary
** Department of Mathematics and Computational Sciences, Széchenyi István University, Hungary
*** Department of Theoretical Physics, Budapest University of Technology and Economics, Hungary
ABSTRACT
With the help of our molecular dynamics simulation we want to motivate emerging and development of
technological methods for building of carbon nanostructure networks. We shall study self-organizing behaviors
of graphene nanoribbons in Y-junctions. We determine the conditions for perfect formation of nanotube Y-
junctions from parallel nanoribbons. The role of graphene nanolithography in nanoribbon network and nanotube
network production is studied. Our simulations show the possibility of nanotube network realization as well.
Keywords: molecular dynamics, graphene, nanoribbon, nanotube, network, simulation.
I. INTRODUCTION
The graphene as one graphite sheet is a
zero-band gap semiconductor, which hinders its
application as a semiconductor devise. The band
structure turns to be more favorable if we cut out
graphene ribbons from the sheet [1-3]. Depending on
the orientation of the ribbon on the sheet, the band
gap will be different of zero. The width of the band
gap of armchair nanoribbons depends on the number
of the carbon atoms modulo 3 in the cross direction.
If the remainder is 0 or 1 the ribbon is
semiconductor and 2 belongs to the zero-band gap in
tight-binding calculation [4]. According to the
theoretical calculations the zigzag ribbons are
semiconductors due to the small band gap.
According to the experiences the graphene ribbons
are semiconductors [5]. After clarifying the
electronic behaviors, it was proved that the graphene
based structures can be building boxes of the nano
size electronic devises in the future. The appropriate
technological conditions are however missing. The
electronic properties of the nanoribbons are very
interesting but the experimental realizations are still
not without problem. The present methods are based
mostly on chemical and physical procedures. With
the help of chemical methods Yang et al. constructed
graphene nanoribbons of length 12 nm from 1,4-
diiodo-2,3,5,6-tetraphenylbenzene and 4-bro-
mophenylboronic acid molecules [6]. They were
using various catalysts. Cai et al. connected to chains
the precursor molecules with the help of active
surfaces and after cyclic dehydrogenization they
obtained nanoribbons of various widths [7].
According to the experiences these methods can not
control the length, the width and the edges of the
ribbons.
The physical methods are more promising
concerning the accuracy [8]. Kosynkin et al.
produced 100 % perfect nanoribbons by cutting
nanotubes with oxidative methods [9]. Jiao et al.
were using plasma for cutting up multi wall carbon
nanotubes [10]. The tailoring methods of the
graphene sheets are named lithographic methods.
The simplest lithographic method applies an STM
needle to move or brake the graphene sheet [11]. In
the other methods a voltage is applied between the
AFM needle and the graphene sheet. By changing
the voltage and by moving the needle the graphene
can be oxidized and various patterns can be cut out
from the graphene [12-14].
In other lithographic methods etching is
used with nanoparticles in diffusion processes in
gases. The present most precise lithographic method
is the carbothermic etching (CTE) [18], where in the
first step artificial defects are produced on a
graphene/SiO2 support system. In this method not
only ribbons but predefined patterns, as Y-junction
ribbons can be produced. With this method even a
ribbon of 2.5 nm can be produced. In our days this is
the most precise lithographic method for producing
nanoribbons.
As there is missing only an order of
magnitude for obtaining atomic precise
nanopatterns, theoretical calculations were
motivated to simulate the formation of 3D
nanostructures from graphene patterns. It was
proved in molecular dynamics calculations that C60
and C70 fullerene molecules can be formed from
one graphene pattern in molecular dynamics
simulations [19-21]. It was proved also that zigzag
and armchair nanotubes can be obtained from
graphene patterns in molecular dynamics
simulations. As the driving force was generated with
RESEARCH ARTICLE OPEN ACCESS

the help of a half fullerene the final tube was closed
with a half fullerene at one end [21].
The production of nanotubes of two
nanoribbons is important because in this way open
ended nanotubes can be produced [21]. The
production of nanotubes from two parallel
nanoribbons is not a trivial task. First the possibility
was published [22-23], and after that the topological
and energetic conditions for obtaining perfect tubes
were published [24]. It is well known that the
nanotubes have very interesting electronic and
mechanical properties. They are more stable than the
ribbons and they are also suitable for interesting
electronic nanodevices. As the nanotubes do not
have such kind of dangling bonds as the ribbons,
they do not have the instability at edges. From
nanotubes more stable structures can be built as from
the ribbons. The production of nanotubes with given
properties is not yet solved. As the graphene
tailoring with atomic precision will be possible, the
graphene lithography of nanotube production from
parallel graphene ribbons can make possible at the
same time the production of networks for nanotubes
and nanoribbons as well. In nanotube networks the
Y-junctions play the principal role beside the
straight tubes [25]. Thus, the study of Y-junctions
has basic important beside that of the straight tubes.
In this paper we study the formation of nanotube Y-
junctions from graphene ribbons. We examine
whether the topological and energetic conditions
obtained for the nanotube formation are sufficient or
not in the case of more complicated structures, like
Y-junctions.
II. THE METHOD
We have studied the formation of Y-
junctions in molecular dynamics (MD) [26-27]
calculations where the initial structure was made of
two Y-shaped graphene patterns cut out from the
graphene sheet. The initial distance between the two
patterns was 0.35 nm. The carbon-carbon interaction
was calculated with the help of Density Functional
Theory adjusted Tight Binding method (DFT-TB)
[28]. The time step was ∆t=0.7 fs and Verlet
algorithm [29] was used in the calculation of the
velocities of the carbon atoms. The environmental
temperature was controlled with the help of Nosé-
Hoover thermostat [27-28, 30-31]. The application
of the Nosé-Hoover thermostat made it possible that
we could start our simulation with randomly
determined initial velocities of the carbon atoms.
The corresponding Tinit atomic temperature was
different of the environmental temperature of the
simulation. This initial temperature was taken from
the range [1000,1100] Kelvin. According to our
experiences the final structure was not depending
strongly by increasing or decreasing the
temperatures with scaling. In contrast, it was found
that the final results were influenced much more
strongly when randomly changing the initial
velocities.
In our previous publication [24, 32] we
have studied the self-organized formation of
nanotubes from graphene ribbons in molecular
dynamics simulation. The distance between the two
initial ribbons was 0.35 nm. There we defined the
Ec = Etube – Egraphene curvature energy of nanotubes,
where Etube and Egraphene are the formation energies of
nanotube and graphene. We have found further a
linear function between reciprocal square of the tube
radius R and the curvature energy: Ec = a/R2
+ b.
Here Ec is in eV, the radius R is in Å and
a = 2.4005 eVÅ2
and b = -0.0227 eV. Using this
function for the curvature energy and applying
several test calculations we defined critical ribbon
widths under which there is a very small probability
of nanotube formation from ribbons. These critical
ribbon widths are in order 9.23 Å and 15.99 Å for
the straight armchair and zigzag nanotubes.
We have found further that the application
of support increases significantly the efficiency of
nanotube formation. Beside this advantage the
support has an another one as well. Namely it makes
possible precise positioning of the patterns one over
the other in a practical realization. Between the
ribbon and the support, we supposed van der Waals
interaction [32]. In a recent publication nanoribbon
rings role up in a self-organizing way on metal wires
[33]. Similar rolling up process was studied on
nanotubes due to van der Waals interactions [34].
Self-assembly of fullerenes and graphene flakes
were studied in molecular dynamics calculations
[35]. Artificial defects on graphene ribbons [36] or
tailoring of graphene flakes [37] also induced self-
scrolling by the van der Waals interaction. Important
role was played by van der Waals force in
interaction of nano spheres [38] as well.
III. BUILDING UP OF THE Y-JUNCTION
IN A SELF-ORGANIZING MANNER
FROM ONLY ONE GRAPHENE
FORMATION
In case of carbon nanotube Y-junctions, in
accordance with the topological conditions, the
possibility of designing from a single graphene
formation also emerges. As to, a junction consisting
of closed-end tubes, can be designed topologically
from a single formation [21]. The graphene
formation that can be seen in Fig. 1.c, designed for a
closed-end Y-junction, is shown in Fig. 1.a.

a b c
Fig. 1: Constructability of a closed end carbon
nanotube Y-junction from a sole graphene formation
[21]. a: The model of a graphene formation for the
construction of a carbon nanotube Y-junction. b: A
nanotube Y-junction model made by the up-folding
of the formation shown in Fig. a. c: The entire model
of the derived nanotube Y-branch (pentagons and
heptagons highlighted by different colors). The
ellipses indicate the location of the formation of
some pentagons, see below.
The formation is made up of hexagons clearly, and
the number of vertices (carbon atoms) on both
models are identical. If we wind up the graphene
formation seen in Fig. 1.a, then according to Fig. 1.b
we get the designed structure.
It is therefore legitimate to wonder whether the
carbon nanotube Y-junctions can build up in a self-
organizing way, from a single graphene formation?
We expect that by the abandonment of the graphene
formation, that can be seen in Fig. 1.a, bonds get
established in the framed areas (the figure was not
encumbered with the indication of all the
occurrences), with the new bonds pentagons get into
the structure, due to the pentagons the structure
winds up and the proposed Y-junction could
coalesce. For the examination of the question, on the
graphene formation that can be seen in Fig. 1.a, we
performed a molecular dynamics simulation. We
have met several problems, due to which we could
not build the planned Y-junction from only one
graphene formation.
a b c
Fig. 2: Input model and molecural dynamics
simulation results for the build-up of a carbon
nanotube Y-juction from a single graphene
formation. a: Another input model constructed
similarly to Figure 1.a. b: The result of the MD
simulation for the model of Fig. 1.a. c: The result of
MD simulation for the model of Fig. 2.a.
The first problem is that the pentagons,
created because the new chemical bonds, wind up
the structure into different, unexpected directions,
therefore the build-up of the Y-junction is
impossible, as shown in Fig 2.b. Similarly to the
graphene formation shown in Fig. 1.a, several other
formations can be designed for the build-up of the
same carbon nanotube Y-junction, we can see
another example in Fig. 2.a. The other problem can
be seen on the MD simulation run result of this new
formation (Fig. 2. c): though, the formation started
to wind up into the planned directions, in this case,
near the centre, the structure went wrong due to
unwanted coalescences. We have found that by
varying the formations, after further experiments
ending with similar results, for the flawless
adhesion, taking place in a self-organizing manner,
the building process must be carried out from an
over-complicated graphene formation, there are too
many possibilities for bending into different
directions and for the coalescences in unexpected
places.
IV. THE SELF-ORGANIZING BUILD-UP
OF A Y-JUNCTION FROM PARALLEL
GRAPHENE RIBBONS
Because of the complexity of the structure of
the only graphene formation, moreover, it is also
justified to evolve open-end tubes, that we build the
carbon nanotube Y-junctions by coalescence of
parallel graphene ribbons. We studied the following
topological cases:
● the models of the Y-junctions consisting of
armchair nanotubes,
● the models of the Y-junctions consisting of
zigzag nanotubes,
● heterogeneous Y-junction models, where, in the
structure, there are armchair and zigzag nanotube
branches as well.
In every case, we started from a model
consisting of two parallel graphene ribbons [24]. The
distance of the ribbons was equal to the equilibrium
distance between the layers of the graphite crystals:
3.35 Å (in case of the zigzag models, containing the
substrates as well, we deviated from this, this will be
indicated in the right place). We examined by
molecular dynamics simulation that after the
abandonment of the structure whether there are any
new bonds forming between the ribbon edges,
whether these two parallel graphene ribbons
coalesce into a nanotube Y-junction.
The dimensions have been chosen in order
to conform to the earlier research results obtained for
the straight carbon nanotubes [24]: Critical ribbon
width, derived from curvature energy, distinguishes
cases of low and high probability of perfect

coalescence. This critical width is 9.23 Å for
armchair and 15.47 Å for zigzag straight
nanoribbons, as it was mentioned in the
Introduction.
In case of the models of the Y-junctions we
examined the critical ribbon width range. For the
molecular dynamics simulation experiments we used
models of three different widths from the range
around critical width.
The topological cases of Y-junctions are
examined in detail in the following chapters.
4.1. Armchair-type Y-junctions, case without
substrates
In Fig. 3. input models can be seen that
were prepared for the molecular dynamics
simulation for the construction of Y-junctions
composed of armchair type nanotubes.
With molecular dynamics simulations,
starting from ribbons that are narrower than the
critical ribbon width, we did not get an immaculate
structure. We have experienced that even if certain
parts begin to build up faultlessly, the smoothing
force form a graphene sheet spoils the structure in
the other places.
In Fig. 4. the results of two independent runs are
presented. The structure goes wrong in Fig. 4.a at
two branches, and in Fig. 4.b at one branch so that
the coalescence starts on one side only, after that the
branch osculates into a graphene sheet instead of
winding up and forming a tube. We performed both
experiments on the model presented in Fig. 4.a.
Starting from ribbons of critical ribbon width or
from ribbons the width of which is wider that the
critical one, from the parallelly superposed graphene
ribbons a perfect carbon nanotube Y-junction was
built. We present the results of the molecular
dynamics simulation belonging to this in Figs. 5.a
and 5.b.
Regarding the case of the armchair-type Y-junctions,
based on the above experiments, it can be said that
the tendency for straight carbon nanotubes prevails,
that is to say, that after the abandonment in an
equilibrium distance, the graphene ribbons of critical
and of wider than critical width can coalesce into a
flawless carbon nanotube Y-junction in a self-
organizing manner.
Fig. 3: Graphene nanoribbon models planned for the construction of armchair carbon nanotube Y-junctions. a:
the width of the ribbons is less than the critical ribbon-width: 7.1 Å, b: the width of the ribbons is equal to the
critical ribbon width: 9.23 Å, c: the width of the ribbons is more than the critical ribbon-width 11.36 Å.
Fig. 4: The simulation results run on the model of Fig. 3.a for the construction of carbon nanotube Y-junctions.

Fig 5. a: Simulation result ran on the model of Figure 4.b for the construction of a carbon nanotube Y-junction.
b: Simulation result ran on the model of Figure 4.c for the construction of a carbon nanotube Y-junction.
4.2. Heterogeneous and zigzag type Y-junctions,
the case without substrates
As heterogeneous carbon nanotube Y-
junctions, those structures are defined, between the
branches of which both armchair-type and zigzag-
type straight tubes are located. When we design an
electronic network from Y-junctions, in all
likelihood, the heterogeneous junctions will be the
most interesting ones, because, due to the different
electrical behavior dependent on the crystal-
orientation, this is where there is a big chance for the
construction of various electronic devices.
If we insert a zigzag branch into the structure,
instead of one of the branches of the armchair
graphene Y-junction presented in Fig. 6., we get a
heterogeneous junction. On the example in Fig. 6.
we present how the zigzag branch can be constructed
between the armchair branches.
In Fig. 6. it can be seen that the atoms located at the
edges of the zigzag branch are in a less favorable
position in terms of adhesion than the atoms of the
armchair branches:
● The atoms of the armchair ribbons are situated
one above the other in an exact cover along the
ribbon edges as well.
● This favorable position at the edges of the zigzag
branch is topologically not allowed. One of the
ribbons should be slightly wider so that at the
coalescence the expected hexagon pattern can
develop.
In Fig. 6., in the enlarged details of the
edges, we labeled the distances between the atoms
located on the edges with d1 and d2. We expected
that there
would be a bond established between the labeled-
positioned atoms that are d1, or d2 distance away
from each other and thereby the two parallel ribbons
coalesce. In case of an equilibrium ribbon distance
(3.35 Å) d1 = 3.63 Å, d2 = 3.35 Å. Since d1 > d2, as a
consequence, the zigzag branch has less chance to
coalesce than the armchair branches.
Fig. 6: Heterogeneous Y-junctions of parallel
graphene ribbons in top view (the ribbons cover each
other), as well as the enlarged detail of the meeting
of two different branches of crystal-orientation. In
the zigzag branch the upper ribbon along the
circumference is smaller with one atom row than the
lower ribbon, while the ribbons below each other at
the armchair branches are of the same width.
From the molecular dynamics simulations,
it has been found that the Y-junctions of graphene
ribbons, containing zigzag branches, abandoned in
an equilibrium distance did not coalesce into a
perfect carbon nanotube Y-junction in any of the
tested ribbon- width cases. This result has also come
out regarding the junctions comprising of purely
zigzag junctions.
In Figs. 7. and 8. we show the examined graphene
models: the heterogeneous junction models can be

seen in Fig. 7. the models containing zigzag
branches exclusively in Fig. 8. The ribbon widths, in
case of all models, were chosen in a range close to
the critical ribbon width.
Fig. 7: Heterogeneous Y-junction models. a: small-width (7.1 Å, 7.1 Å, 8.61 Å), b: medium-width (11.36 Å,
11.36 Å and 11.07 Å), c: large-width (13.0 Å, 13.0 Å and 15.99 Å) models. At the armchair branches the
ribbons that are located below each other have the same width and they are in exact cover, at the zigzag branch
the top ribbon along the circumference is smaller with one atomic row than the lower ribbon.
Fig. 8: Zigzag Y-junction models. The top ribbon along the circumference is one atomic row smaller than in
case of the lower ribbon. a: small-width (7.38 Å and 9.84 Å), b: medium-width (12.3 Å and 14.76 Å), c: large-
width (14.76 Å and 17.22 Å) models.
In Table 1 we summarized the MD
simulation results of the graphene ribbon Y-
junctions abandoned at an equilibrium distance.
Overall it can be stated that for the armchair
junctions, the tendency of flawless coalescence in
the case of straight nanotubes has remained,
however, as soon as only one zigzag branch gets into
the structure it is unfavorable from the viewpoint of
flawless coalescence: the possibility of a flawless
self-organizing formation could not be justified with
a successful run.
WITHOUT
SUBSTRATE
Self-organizing behavior of carbon nano-tube Y-junctions with
models without substrates
Size Armchair Heterogeneous Zigzag
small
(model of Fig. 3.a) (model of Fig. 7.a) (model of Fig. 8.a)
medium
(model of Fig.3.b) (model of Fig. 7.b) (model of Fig. 8.b)
large
(model of Fig.3.c) (model of Fig. 7.c) (model of Fig. 8.c)
Table 1: Running experiences of different sized and oriented carbon nanotube Y-junctions without substrate
means: unsuccessful coalescence, means: perfect (flawless) coalescence.

The unsuccessful coalescence of the heterogeneous
Y-junctions could clearly be explained with the
unfavorable position of the edges of the zigzag
branches. In Fig. 9. some typical heterogeneous
cases of the unsuccessful attempts are shown.
In Fig. 9.a the coalescence of one of the armchair
branches has taken place properly, but only one side
of the other armchair branch and zigzag branch has
coalesced, the opposite side has remained open, and
due to the opening up into a graphene sheet there
was no chance to perform a perfect coalescence. In
Fig. 7.b such runtime results are shown where the
armchair branches have coalesced properly, but in
the zigzag branch the coalescence has not even
begun. Finally, the lesson to be learnt from the
simulation results of Fig. 7.c is that the osculation of
the zigzag branch into a graphene sheet did not
allow the neighboring armchair branch to grow
together either.
a
b c
Fig. 9: Typical cases of unsuccessful coalescence of (heterogeneous) graphene ribbon Y-junctions, containing
zigzag branches. a: model consisting of 7.1 Å, 7.1 Å wide armchair and 8.61 Å wide zigzag ribbons run on the
model of Figure 7.a. b: model consisting of 11.36 Å, 11.36 Å wide armchair and 11.07 Å wide zigzag ribbons
run on the model of Figure 7.b, c: zigzag model consisting of 13.0 Å, 13.0 Å wide armchair and 15.99 Å wide
ribbons, run on the model of figure 7.c.
a b
c
Fig 10:. Broken, zigzag Y-junctions without substrates. a: a model prepared based on Fig. 8.a, b: a model the
size of which is identical to the size of Fig. 8.b, c: a model the size of which is identical to the size of Fig. 8.c.
In Fig. 10. the running results of the full zigzag-
branch cases are presented. In case of the models of
small and medium ribbon width, the coalescence has
taken place on one or two sides, but the structure has
opened up, see Fig. 10.a-b.
In case of the model of wider ribbons, after
the slight displacement that took place due to the
unfavorable speed directions, the structure has
started to coalesce, however, instead of the sides, it
happened at the ends of the ribbons, Fig. 10.c.

4.3 Coalescence of substrate-containing parallel
graphene Y-junction models
From the edifications of the unsuccessful
runs illustrated in Fig. 9. and 10, we have found
likely, that we can get significantly better results if
the simulations are carried out with substrates. On
models of straight carbon nanotubes, we have
already succeeded in showing the beneficial effect of
the substrates from the viewpoint of coalescence
[32]. We thought that the substrate, as a physical
constraint, will not allow, in case of the junctions
either, the turning out of the half-coadunate sections
abiding to the evolution of coercion into graphene
sheet, moreover, it will not allow the graphene
ribbons positioned one above the other to slip aside
either.
In this case, as a substrate, similarly to the
case of the straight ribbons [32], we have chosen a
multi-layer graphene sheet, too. At the simulation
input we placed the two parallel graphene ribbons
between the substrates in accordance with the
equilibrium distance characteristic to the crystal
planes of the graphite crystal (see in Fig. 11), here
we launched the runs also with the conditions of dA
= dB = dn = 3.35 Å.
For the modeling of the van der Waals interaction
between the substrates and the graphene
nanoribbons, in the present case, we applied the
Lennard-Jones potential as well, with the parameters
used in case of straight tubes [32].
During the simulations, in case of models
that also contain substrates, the structure was
abandoned only after the bonds between the carbon
atoms placed at the edges of the two graphene
ribbons had already been established, that is, the
structure was already coalesced.
In case of the models presented in Figs. 3.,
7. and 8. we executed MD simulation runs. We have
summarized the results obtained by resource to the
substrate in Table 2. The content of Table 2 is worth
to be compared with the data of Table 1. We have
presented, where and under what conditions the
successful self-organizing build-up of 3D junctions
seems possible. The problem regarding the zigzag
branches, the role of the substrates and the necessity
of compressing the substrates at the zigzag junctions
can be seen clearly.
Fig. 11. Placement of nanoribbons between substrates (side view)
The results prove the important role of the
substrates:
● In case of the armchair Y-junctions, even in
the case of a ribbon width below the critical
width, a perfect coalescence has been achieved.
● In case of the heterogeneous junctions, the
simulation experiments also resulted in a perfect
coalescence.
● As for the zigzag junctions, the first attempts
have ended unsuccessfully in case of all sizes
and we found defective coalescences even in the
presence of substrates. When we started the
simulation from the equilibrium distance
between the parallel ribbons (dn = 3.35 Å) the
structures have not coalesced perfectly due to the
unfavorable positions of the edges of the zigzag
branches, even in the presence of substrates.
With additional runnings we have managed to
show that if in case of the input model the
equilibrium distance between the parallel ribbons
is reduced to dn = 3 Å (namely the substrates, and
thereby the ribbons of the input model are
compressed) then, even in case of the zigzag
junctions, a flawless coalescence is obtained
during the MD simulations.
WITH
SUBSTRATE
Self-organizing behavior of carbon nano-tube Y-junctions with
models containing substrates

Size ™Armchair Heterogeneous Zigzag
small
dn= 3.35 Å
(model of Fig. 3.a)
dn= 3.35 Å
(model of Fig. 7.a)
dn= 3.35 Å
dn= 3,00 Å
(model of Fig. 8.a)
medium
dn= 3.35 Å
(model of Fig.3.b)
dn= 3.35 Å
(model of Fig. 7.b)
dn= 3.35 Å
dn= 3,00 Å
(model of Fig. 8.b)
large
dn= 3.35 Å
(model of Fig.3.c)
dn= 3.35 Å
(model of Fig. 7.c)
dn= 3.35 Å
dn= 3,00 Å
(model of Fig. 8.c)
Table 2: Experiences about the running of Y-junctions of different sizes and orientation, containing substrates.
means: unsuccessful coalescence, means: perfect coalescence.
In Fig. 12 the runtime results of the
armchair, while in Fig. 13 the runtime results of the
heterogeneous junctions are shown. In case of both
orientation models, in case of all three dimensions,
perfectly coalesced nanotube Y-junctions were
obtained, therefore the self-organizing formation is
possible.
In Fig. 14. we present the results of the MD
simulations launched on the models of the ribbons
containing only zigzag branches, with the help of
substrates from an equilibrium (dn = 3.35 Å)
distance. Beside the positive effect of the substrates,
uncertainties still have remained in the system: the
slight sliding of the ribbons, one above the other,
have made the models predisposed to initiate the
coalescence at the end of the ribbons instead of at
the edges. Basically, this was the reason why all the
models have gone wrong.
In Fig. 15. the results of the MD
simulations launched on the models of only zigzag
ribbons can be seen, with the help of substrates from
a distance less (dn = 3.00 Å) than the equilibrium (dn
= 3.35 Å) distance. From the ribbons compressed
between the substrates, in case of all three
dimensions, flawlessly coalesced nanotube Y-
junction was obtained.
V. CONCLUSION
According to our molecular dynamics
simulations the topological and energetic conditions
of successful nanotube formation from nanoribbons
are not completely valid in Y-junction cases. At the
equilibrium distance of 3.35 Å they are valid only in
the case of armchair cases. Only one zigzag
nanotube in any branch of the junction can destroy
the perfect coalescence of the Y patterns. With the
help of the support the number of favorable junction
formations increases significantly even in the case of
zigzag tubes in any branch. We obtained perfect
coalescence in the case of only zigzag nanotubes in
each branch by decreasing the initial equilibrium
distance between the patterns from 3.35Å to 3Å.

a
b
c
Fig. 12: Models of successful armchair Y-junctions grown with substrates a: the result of the MD simulation
run on the model of Fig. 3.a, b: the result of the MD simulation run on the model of Fig. 3.b, c: the result of the
MD simulation run on the model of Fig. 3.c.
a

b
c
Fig. 13: Models of successful heterogeneous Y-junctions grown with substrates. a: the result of the MD
simulation run on the model of Fig. 7.a, b: the result of the MD simulation run on the model of Fig. 7.b,
c: the result of the MD simulation run on the model of Fig. 7.c
a
b
c

Fig. 14: The models of unsuccessful zigzag Y-junctions with substrates, after the running of an MD simulation
from an equilibrium (dn = 3.35 Å) distance. a: the result of the MD simulation run on the model of Fig. 8.a,
b: the result of the MD simulation run on the model of Fig. 8.b, c: the result of the MD simulation run on the
model of Fig. 8.c.
a
b
c
Fig. 15: The models of successful zigzag Y-junctions with substrates, after the running of an MD simulation
from a distance less than equilibrium (dn = 3.00 Å). a: the result of the MD simulation run on the model in
figure 8.a, b: result of the MD simulation run on the model Fig. 8.b , c: result of the MD simulation run on the
model of Fig. 8.c.
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