Vibrational Properties of Defected Graphene Nanoribbon

This study aims to investigate the vibrational properties of defected graphene nanoribbon. It includes research on various defects of graphene, investigating the features of graphene, evaluating the effects of defects on properties of graphene, and evaluating the feature of defected graphene.

PROJECT 1
[Author Name(s), First M. Last, Omit Titles and Degrees]
[Institutional Affiliation(s)]

Introduction
Graphene which a novel two dimensional material structured in the shape of a honeycomb is
normally formed by one layer of sp2 hybrid orbital atoms of carbon. It has a thickness of about
0.335 nm which corresponds to the thickness of a single atom of carbon. Graphene is able to
form one dimensional nanotubes, a three dimensional graphite as well as a zero dimensional
fullerene through stacking, wrapping among others. As a result of the unique features, graphene
has been established to be of excellent chemical as well as physical features among them thermal
conductivity, superior stiffness as well as strength, ultrahigh specific surface area, high mobility
of electrons among others [1]. Besides, it has unique quantum tunneling impacts as well as semi-
integer Hall effect. Such features make graphene one of the most popular if not the only popular
low dimensional functional material of carbon followed by carbon nanotubes and fullerene
In as much as graphene demonstrates excelling features it is unable to be applied in
semiconductor IC technology of fabrication due to the zero bandgap features. Different
techniques have been deployed in tuning a definite bandgap in the structure of graphene. It is
commonly understood that confinement of the function of electronic wave in a quasi-ID system
may were to open the bandgap that is within graphene. In cases where graphene has been
patterned into a width that is finite, the effect of quantum confinement results in the opening of
the bandgap. Hence, graphene nanoribbon may be used for the purpose of fabrication of various
nonelectric devices.
Owing to the numerous unique features of the substance as with regard the electrical and
chemical features, graphene has been found to be applicable in numerous fields including
thermal applications, micro-nano devices as well as reinforcing substances. Still, graphene may

as well be used in bio sensing for example deoxyribonucleic acid sequencing devices, detection
of glucose as well as fanon resonances [2]. Besides, it is of very high potential in the research
areas for new energy including super capacitors, solar cells as well as lithium-ion batteries.
Hence, there is need of a precise conception on the different (types of) defected graphene and
among them the grain boundary (which is one of the defected graphene) will be used as an
example to show the vibrational properties of defected graphene [3].
Research Problem
The study aims to investigate the vibrational properties of defected graphene nanoribbon
The objective includes:
 Conducting research on the various defects of graphene
 Investigating the features of graphene
 Evaluating the effects of defects on properties of graphene
 Evaluate the feature of defected graphene
Graphene is one of the materials that are widely used in various industrial processes owing to the
unique and excellent physical and chemical properties. Nevertheless, the presence of defects has
significantly impacted on the properties both on the negative and positive ways. An
understanding of the effects on defects on vibration properties of graphene is integral in
enhancing an understanding of such defects as well as coming up with strategies aimed at
improving the performance if not eliminating the defects. A study into this topic would see
enhanced industrial processes that required graphene as well as offer alternatives to the challenge
of the defects.

LITERATURE REVIEW
Defect types in Graphene
Some of the earlier studies have analyzed the structural defects in carbon as well as carbon
nanotubes hence an imagination that graphene should as well be defective at the level of an atom
should not pose as a challenge. The kinds of structural defects that are present in graphene
cannot be easily accurately and quantitatively identified. Nevertheless, the ability to resolve each
atom that is found in the graphene lattice has been achieved through the use of high resolution
new transmission electron microscope and can do so even in the case of suspended single layer
graphene. Besides, atomic free microscope as well as the scanning electron microscope is
extensively used as experimental devices that used in the characterization of the nano materials.
Hence, direct imaging of the theoretical prediction configurations is highly possible [4].
The defects in graphene may be generally grouped into two: intrinsic defects that include carbon
atoms in non-sp2 orbital hybrid in graphene. Such defects are often as a result of the presence of
non-hexagonal rings enclosed by hexagonal rings. Extrinsic defects form the second group of
graphene defects. In these defects, the crystalline order is altered with the atoms of non-carbon
that are present in the graphene.
Besides, there is enough reason to assume that the defects may not often be stationary and
random following the previous studies that have been conducted on the bulk crystal defects
migrations, specifically the study of carbon nanotubes remodelling under disturbance of external
energy, moving with a specific mobility controlled by the temperature as well as activation
barrier.

Intrinsic defects in Graphene
There are possible five categories of intrinsic defects:
 Single vacancy defects
 Stone-wales defects
 Line defects
 Carbon adotoms
 Multiple vacancy defects
Stone-wales defects
These defects are a creation of the rotation of one pair of atoms of carbon hence leading to the
adjacent heptanol and pentagonal rings. Thus, in this defect, the formation of the defects does not
lead to the introduction or even elimination of atoms of carbon or dangling bonds. The energy of
formation that is needed for this defect may be around 5eV. Intentional mechanisms including
electron radiation on quick cooling environments of high temperature may be used for the
introduction of stone-wales defects [5]. A TEM image of stone-wales defects as well as the
estimated atomic structure is shown in the figure below. Electron impact may be attributed to be
the reason for the formation of such defects.

Figure 1: Single vacancy defect on graphene
Line Defects
Graphene starts growing are various positions on the surface of the metal during the process in
which graphene is prepared through chemical vapors deposition. Chemical vapor deposition
technique renders polycrystallinity of graphene almost impossible to avoid. Various orientations
in the crystallography result from the randomness that I experienced in the growth in various
regions. Cross fusion starts when graphene grows to some size [6]. The line defect of graphene is
as shown in the figure below and as shown in the figure, stitching together of two crystals occurs
by a chain of hexagons, pentagons as well as heptagons predominantly. The boundaries of the
grain are not straight neither are the defects along the same boundaries periodic. The same line
defects in graphene have as well be noted in numerous cases in other researches.

Figure: Aberration-corrected dark-field scanning transmission electron microscopy
Multiple vacancy defects
In case of a loss of another atom of carbon in a single vacancy defect, then a double vacancy
defect occurs. The TEM image as well as the arrangement of the atom structure diagram of the
three various noted multiple vacancies are as shown in the figure below. As illustrated in the
figure, there is a single octagon alongside two pentagons that have no dangling as opposed to
four hexagons [7]. The results of simulation indicate that the energy of formation of such a
double vacancy defect may be around 8 eV with the theoretical estimations indicating that the
figure in (a) may be changed into the figure in (b) under some conditions. Still, the latter figure
has high chances of being created due to its lower energy of formation that is approximately 7
eV.

Figure 3: Multiple vacancy defects on graphene
Out-of-plane carbon atoms
The missing carbon atoms which are produced from single as well as multipole vacancy defects
may not be divorced completely from the plane of graphene. Instead, such carbon atoms move
on the graphene surface upon separating from the initial carbon hexagon ring. A new bond tends
to be formed in case carbon atom relocates to another new in-plane position [8].
New defects may result in the interaction of atoms of carbon with a perfect layer of graphene and
these defects may lead to the destruction of the initial planar structure as well as lead to the
formation of a three-dimensional structure. A typical illustration of out-of-plane carbon adotoms
is shown in the figure below and as illustrated, a bridge configuration is formed by a graphene
and carbon adatom layer. Figures (b & e) demonstrate them metastable dumbbell configuration
as a result of the migration of carbon atom via the lattice. The inverse of stone-wales defect is
shown in figure (c & f) which is formed as a result of the relocating adotoms of carbon.

Figure 5: Introducing defects to the carbon atom outside surface in graphene
Defects introduction on Graphene
There are two classifications of the defects introduced in graphite: substitution and foreign
adotoms implies as described below:
Foreign adotoms
For the case of methods of strong vapors oxidation or Chemical vapors deposition, there is
introduction of the metal atoms or functional groups that contain oxygen to the graphene surface
in the course of the process. Such adotoms are often bonded with movement bonds or even weak
Van der Waals forces with the adjacent atoms of carbon. Such defect types are described as
foreign adotoms. Studies that have recently been carried have demonstrated that metal adotoms
may result in significant relocation on graphene surface [9]. Numerous theoretical studies are in
place following experimental analyses on the defects of foreign adotoms on graphene with some
of the studies concentrating on the surface motion as well as absorption and others on an
investigation into the relationship between the magnetic features, electrical properties and the
defects.
Generally, such foreign adotoms are either atoms of oxygen or functional groups that contain
oxygen for example carboxyl groups or hydroxyl groups. The defect is as a result of a type of

preparation method for graphene known as the Hummer method. The method is extracted from
the research on the Hummers for oxidized graphite preparation. Even though most of the
researchers have enhanced the method for graphene, the skeleton process is intact and the same.
The process uses very string oxidants all through including concentrated potassium
permanganate, nitric acid as well as sulfuric acid among others.
Substitutional impurities
Some atoms including boron and nitrogen among others may form three chemical bonds and
hence substitute the atoms of carbon in graphene. Such heteroatoms make up Substitutional
impurity defects of graphene. A model of the graphene molecular structure bearing such a defect
is as shown in the table below. Nitrogen and boron may independently exist in graphene besides
being able to exist simultaneously through control method.
Figure 6: Graphene in-plane heteroatom substitution defect model
The introduction of boron and nitrogen through the control method into the graphene is often
deliberate and is normally done since boron-doped and nitrogen-doped graphene has been found
to be bear excellent features with regard to conductivity as well as catalytic activity. Its
conductivity among other features is as well excellent [10]. The electron cloud around the
graphene is often changed with the introduction of boron and nitrogen alongside making such

regions more active. Nitrogen and boron are as well associated with their own features that are
unique to each other that would have an impact on the features of graphene.
Defects of Double Graphene Structure
Graphene forms structure that resembles graphite when built in a manner that is layered.
Chemically bonded atoms of carbon would not be available between the layers in case the
graphene used if free from defects. Nevertheless, there will be formation of new chemical bonds
with the neighbouring atoms of carbon with defective graphene sheet layers as there are intrinsic
defects within the graphene [11].
The complexity of the structural effects will increase within an increase in the number of
graphene layers that are used in the stacking process. Such sophisticated defects are therefore
likely to finally influence the building material microstructure. Besides, it will have an effect on
the chemical as well as physical features of the material. Graphene in various stack locations
have to include the concurrent domain processes during graphite structure construction as the
graphene nanosheets as well as the monolithic graphene are never infinitely big in terms of space
scale. In case the domain process is not good enough, a long-range order may be created in the
material which may in turn result in material defects.
Graphene Preparation and Production of Defects
The formation of defects on graphene is closely linked with the method used in its preparation.
In general terms, the process of preparation is not able to eliminate or avoid introduction of
defect in graphene as a result of the environment, method of preparation as well as temperature
among others. Among the main defects include chemical doped as well as morphological defects
and the most commonly used preparation methods may be grouped into two groups: graphene

exfoliation and chemical vapors deposition [11]. Various defects are introduced by various
methods of preparation with topological defects often being introduced by chemical vapors
depositions since the dissolution method is not sufficiently mature.
Graphite exfoliation is yet another method usable in the preparation of graphene. The method
results in defects even though in comparison with chemical vapors deposition, the defects are
mainly as a result of reduction process and oxidation. Various oxidizing agents as well as
temperature have effects on graphene and still as a result of uneven reaction; the final product is
not an all single structural oxide of graphene but as well containing traces of graphite oxide or
oxides of multi-structural graphene. The oxides are normally bonded using various functional
groups including aldehyde and alcohol groups and be it a thermal or chemical process, changing
extents of chemical defects are introduced. The oxidation method has the potential of opening
the carbon nanotubes in such a way that the three dimensions are reduced to two even though the
final product is normally composed of uneven layers that lead to structural defects [12].
Vibrational Properties of Defected Graphene Nanoribbon
The investigation of the present work is performed on the AGNR with opportunity and stone
ridges imperfection as shown in the diagram utilizing sub-atomic unique reproduction with
streamlined Tersoff and Brenner observational potential. As indicated by the sub-atomic
powerful reenactment the nearby vibrational desnisty of state (LVDOS) on a nuclear site I for a
frequency Ȧ is given by:

where, the summation is performed over every one of the modes Ȟ and the space bearings Į, Ȧȟ
and ui,ȟ(į) are the recurrence and the (i,į) segment of the Ȟth phonon eigenvector, separately.
These parameters are determined by utilizing the cross section elements conditions as
where, ȕ implies the bearing along the Cartesian facilitate and D speak to the dynamical lattice
communicated by
where, M indicates the majority of ith and jth molecules and ijφ is the power consistent tensor
speaking to the full data of the cooperations between these particles of the structure. The phonon
thickness of states is accordingly determined by the summation of LVDOS realized that ijφare
the prevailing amounts to be acquired so as to figure the LVDOS [10]. These power consistent
tensors have been determined with the assistance of enhanced Tersoff and Brenner exact
potential. The complete vitality for AGNR can be communicated as
where, fc(rij) is known as the cut-off-remove work between the particles and VR(r) is ghastly
and VA(r) is appealing pieces of the potential. The bij is a coefficient dictated by the points
between the bond I and j and every single other bond produced using the I and j locales. The
parameters of the exact potential rely upon the nearby coordination number. A great deal of
figurings speak to the legitimacy of this potential while tending to basic properties of carbon

based frameworks, for example, fullerenes, nanotubes and graphene [10]. The upgraded Tersoff
and Brenner experimental potential is utilized to improve the power consistent tensor. In
streamlining geometry the Limited memory Broyden Fletcher Goldfarb Shanno (LBFGS)
enhancer strategy is utilized, where the power resilience is 0.01 eV/Ang. furthermore, stress
resistance is 0.0001 eV/Ang.3 and most extreme number of steps is 200. In the dynamical grid
we have utilized focal limited contrast technique with a nuclear dislodging of 0.01 Ang. In the
PDOS figuring, the C-C bond length is 1.42086 Ang. what's more, the Brillouin zone is tested by
Monkhorst pack-lattice with 51×1×1 k-point matrix though for transmission range it is 60×1×1
k-point framework. The phonon transmission range has been determined by a recursive strategy
where the normal Fermi level is 1×10-6 eV.
Effects of Defects on Graphene Properties
Due to its unique as well as perfect hexagonal single layer carbon atom flake structure, graphene
has been known to bear numerous chemical and physical features making it very easy to imagine
of negative impacts when discussing lattice defects. For instance the real conductivity of
manufactured graphene is often lower than the one obtained through theoretical values of
calculation. This can be translated to mean that the presence of defects in the layer results in
destruction of the perfection as well as the geometric symmetry [12]. Lattice defects results in
the destruction of the symmetry as well as the integrity of graphene crystals and consequently
affects the transmission of electrons and on another hand the formed gap as a results of the defect
open the path for ion transport. Still, it improves the rate of interaction between the graphene and
atoms and thereby contributing to graphene based composite applications.

I. Magnetic Properties
Despite graphene not being a magnetic material, graphene with defects has demonstrated
reaction towards the magnetic field thereby drawing significant attention. The hysteresis curve of
the oxide of graphene alongside graphene materials was studied by Wang Yan et al. when
prepared through high temperature reduction. From the study, it was established that oxidized
graphene lowered from at 400⁰C as well as 600⁰C portrayed ferromagnetism at room
temperature as opposed to graphene oxide [12]. It is strongly believed that the ferromagnetism is
as a result of the intrinsic defect that results from the elimination of the functional groups that
contain oxygen from the oxidized graphene at very high temperatures. Studies have been carried
out on the new intrinsic defect in the reaction of graphene reduction and the availability of
defects results in ferromagnetisms within the graphene.
II. Electrical properties
The defects in graphene have the effect of changing the length of the bond of interatomic valence
bond as well as changing the kind of hybrid trajectories of the atom of partial carbon. The
alterations on the length of the bond as well as the orbital result in changes in the domain of the
electrical features of the graphene defect. Graphene point defect as well as single vacancy
defects form a center of electron scattering on graphene surface as well as have an effect on the
transfer of electron and thereby leading to a reduction in the graphene conductivity. The methods
that are currently used in the preparation of graphene make it very hard to avoid introducing
point as well as single vacancy defects which offer the basis of the explanation of the real
conductivity of graphene as different from the one of the ideal state. Still, it shows the direction

for the proceeding study which revolves around the reduction of intrinsic graphene defects with
the aim of enhancing the conductivity [13].
In comparison with the intrinsic defects, the impacts of the defects of foreign atoms on the
electrical features of graphene tend to be more sophisticated and of particular interest. Research
has revealed that graphene oxide does not conduct electricity and the square resistance may get
to beyond 1012Ω. It is alleged that the conductivity of graphene reduced due to the presence of
oxygen atoms and functional groups containing oxygen. Nevertheless, other theoretical
researchers have indicated that the defects of oxygen atoms on graphene including C-O-C defect
have the potential of making the support metal of graphene conductive should the position be
reasonable.
III. Mechanical properties
The Young’s modulus may rise to the tune of 0.7-1 TPa for graphene in theoretical terms even
though various defect would have an impact on the modulus. The impacts of single vacancy and
point defects were investigated by Hao Feng et al., on the mechanical strength of graphene. It
was established that graphene’s Young’s modulus decreased with an increase in the density of
the defects. There is a linear relationship between the change in the Young’s modulus of
graphene with defects and single vacancy defects’ density. Nevertheless, the density of point
defect and the Young’s modulus of graphene are nonlinear. Still, with the increase in the density,
the rate of change in the Young’s modulus is gradual representing a platform meaning that
Young’s modulus is not sensitive to the density of point defect. the mechanical feature of
graphene when subjected to sp3 hybrid carbon atoms as well as vacancy defects were studied by
Zandiatashbar et al., who found out that graphene elastic modulus was not sensitive to the

density of the defect with sp3 hybrid atoms of carbon. On the contrary, vacancy defects tend to
present relatively the reverse as they would generate significant reduction in graphene elastic
modulus.
Methodology and Plan
To achieve the project aims and objectives, the research will bring on board both qualitative as
well as qualities methods of analysis. Some of the different types of defected graphene will be
shown in this research and this will attained through literature review including use the grain
boundary (which is one of the defected graphene) as an example to show the vibrational
properties of defected graphene. Various softwares will be used in showing the effects of grain
boundary including:
 For Modelling: MATLAB
 For visualization: VMD
 For atomic simulation: LAMMPS
 For analysis: VMD
Among the tasks that will be carried out in this research including:
Conducting literature review-This would be helpful in offering insights into the various graphene
defects, their properties and their effects on the various features. This will serve as the basis of
background information and idea on the topic
Conducting experiment: Samples of the defected graphene will be collected and used in
performing the various experiments using the different software mentioned. Each of the
softwares will be testing different properties

Analysis of the results: This will involve making sense of the findings of the experiment and
relating the results will the theoretical or background Knwoledge, making the necessary
comparisons.
Proposal Submission
Proposal Acceptance
Background Study and Literature Review
Data Gathering
Results Analysis and Presentation
Results Collation
Project Writeup
19-Jul
7-Sep
27-Oct
16-Dec
4-Feb
26-Mar
15-May
References

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