This document provides a final report on a research project simulating projectile impacts on graphene nanosheets using molecular dynamics modelling. The report includes an executive summary, literature review on graphene and relevant modelling potentials, methodology outlining the molecular dynamics simulation setup, results and discussion of simulations of pristine graphene compared to graphene with defects and nanopores, proposed future work, and conclusions. Simulation results showed defects and nanopores caused a small decrease in impact resistance of graphene for most impact velocities simulated, with some variability observed. The effects were determined to be acceptable for the proposed applications of desalination membranes and ballistic armor.
MANUFACTURING PROCESS-II UNIT-1 THEORY OF METAL CUTTING
Β
Molecular dynamics modelling of projectile impacts on 2D graphene nanosheets
1. EGH408 β RESEARCH PROJECT
Final Report
Molecular dynamics modelling of projectile impacts
on graphene nanosheets
Supervisors
Dr Yuantong Gu
Edmund Pickering
Christian Douglas
N5928966
2. ii
Dedication
This honours dissertation is dedicated to my Mum, Christine and to my Partner, Jess.
The women who lit the fire in my mind and heart.
βAll my family are here.β
3. iii
Executive Summary
This report provides project documentation on the simulation and analysis of
projectile impacts on graphene nanosheets for applications in water desalination and
next-generation ballistic armour. This project was completed under the EGH408 β
Research Project unit at the Queensland University of Technology over Semester 2,
2017.
A review of academic literature relevant to projectile impacts on graphene nanosheets
identified current research gaps pertaining to the presence of defects and nanopores
within graphene experiencing projectile impact. Subsequently, research questions and
project aims and objective were developed to close this research gap.
Molecular dynamics techniques were employed using LAMMPS, Virtual Nanolab
and Ovito visualisation software to successfully produce a realistic, functioning
molecular dynamics simulation of a diamond projectile impacting pristine, defective
and nanoporous graphene sheets. Impact velocities of 1 km/s to 5 km/s, at 1 km/s
intervals were simulated with the Tersoff, AIREBO and Morse potentials utilised to
model the diamond projectile, graphene sheet and projectile/graphene interaction,
respectively.
Simulation results displayed a small decrease in impact resistance for both the
defective and nanoporous sheet, with the uniform exception of 2 km/s which indicated
adverse effects on impact resistance for both the defective and nanoporous graphene
sheets within this velocity range. However, the observed effects defects and
nanopores had on the impact resistance of graphene were ultimately determined
acceptable within the context of the proposed applications.
Future work on the project was proposed, encompassing validation of results,
improvements to the model and the completion of an unfinished dual sheet
simulation.
βComputational (and/or data visualisation) resources and services used in this work
were provided by the HPC and Research Support Group, Queensland University of
Technology, Brisbane, Australiaβ
4. iv
Table of Contents
Executive Summary ................................................................................................ ii
List of Figures ......................................................................................................... v
List of Tables .......................................................................................................... v
1. Introduction .................................................................................................... 1
2. Project Definition ............................................................................................ 2
2.1 Research Questions ............................................................................................................................ 2
2.2 Aims & Objectives ............................................................................................................................... 2
3. Literature Review ........................................................................................... 3
3.1 Graphene ................................................................................................................................................ 3
3.2 Graphene Defects ................................................................................................................................ 4
3.2.1 Stone-Wales Defects ......................................................................................................................... 5
3.2.2 Graphene Nanopores ........................................................................................................................ 6
3.3 Potentials ................................................................................................................................................ 7
3.3.1 Lennard-Jones Potential ................................................................................................................. 7
3.3.2 Tersoff Potential ................................................................................................................................. 8
3.3.3 AIREBO Potential ............................................................................................................................... 8
3.3.4 Morse Potential ................................................................................................................................... 9
4. Methodology ................................................................................................ 11
4.1 Model Requirements and Initial Framework ...................................................................... 11
4.2 Model Geometries ............................................................................................................................ 11
4.2.1 Projectile Geometry ....................................................................................................................... 11
4.2.2 Graphene Sheet Geometry ........................................................................................................... 12
4.2.3 Graphene Defects and Nanopores ........................................................................................... 12
4.3 Model Potentials ............................................................................................................................... 13
4.3.1 Projectile Potential ........................................................................................................................ 13
4.3.2 Graphene Sheet Potential ............................................................................................................ 13
4.3.3 Impact Interaction Potential ..................................................................................................... 14
4.4 Final Model Configurations ......................................................................................................... 14
4.5 Model Outputs ................................................................................................................................... 15
5. Results and Discussion .................................................................................. 16
5.1 Stone-Wales Defects Results ....................................................................................................... 16
5.2 Nanoporous Sheet Results ........................................................................................................... 18
5.3 Results Summary ............................................................................................................................. 19
6. Future Work ................................................................................................. 20
7. Conclusion .................................................................................................... 21
8. References .................................................................................................... 22
9. Appendix ...................................................................................................... 27
9.1 Appendix A β LAMMPS Input Script ........................................................................................ 27
9.2 Appendix B β Virtual Nanolab Pristine Graphene Sheet Geometry ........................... 30
9.3 Appendix C - Virtual Nanolab Defective Graphene Sheet Geometries ...................... 31
9.5 Appendix D β LAMMPS Compatible Tersoff File ................................................................ 32
5. v
List of Figures
Figure 1 β Graphene water filter medium. ........................................................................................................................ 1
Figure 2 β Graphene sheets held together with Van der Waalβs forces ............................................................... 3
Figure 3 β Graphene hexagonal lattice image produced by ADF-STEM imaging .......................................... 4
Figure 4 β Stone-Wales defects in a graphene sheet ................................................................................................... 5
Figure 5 β Ideal graphene structure vs Stone-Wales defect structure comparison. ..................................... 5
Figure 6 β An induced nanopore within a graphene sheet. ...................................................................................... 6
Figure 7 β Graphical representation of the Lennard-Jones potential .................................................................. 7
Figure 8 β Representation of Lennard-Jones potential term ................................................................................... 7
Figure 9 β Morse potential plot ......................................................................................................................................... 10
Figure 10 β Projectile geometry created in LAMMPS .............................................................................................. 12
Figure 11 β Graphene sheet with partitioned edges ................................................................................................ 12
Figure 12 β Stone-Wales defect generated in VNL .................................................................................................... 13
Figure 13 β Graphene nanopore generated in VNL .................................................................................................. 13
Figure 14 β Initial simulation model with projectile and graphene sheet ..................................................... 14
Figure 15 β Successful impact simulation ..................................................................................................................... 15
Figure 16 β Pristine and Stone-Wales graphene comparison .............................................................................. 16
Figure 17 β Kinetic energy vs simulation steps (pristine and Stone-Wales comparison) (2km/s) ..... 17
Figure 18 β Pristine and Nanoporous Graphene Comparison ............................................................................. 18
Figure 19 - Kinetic energy vs simulation steps (3 sheet comparison - 2km/s) ............................................. 19
Figure 20 β Unfinished dual graphene sheet simulation ........................................................................................ 20
List of Tables
Table 1 - Pristine and defective graphene percentage difference in kinetic energy .................................. 17
Table 2 - Pristine and nanoporous graphene percentage difference in kinetic energy ............................ 18
6. 1
1. Introduction
Access to uncontaminated, fresh water is a fundamental daily requirement for human health
and development. However, recent estimates indicate that up to 40% of the global population
is affected by fresh water scarcity (United Nations, 2017). Australiaβs growing population has
been identified as a key component in a possible fresh water crisis (CSIRO, 2017). Whereby,
fresh water scarcity would adversely affect Australia, regardless of its status of as a first
world nation.
Collaterally, modern ballistics armour has seen a steadily expanding scope of requirements.
Traditionally, ballistics armour in military applications consistently demands greater
protection against projectile impact, at lower weight and increased flexibility (Yang & Chen,
2017). However, growing areas of specialist applications, including shielding/armour for
undersea cables, flight control systems (Madej-KieΕbik et al, 2015) and orbiting satellites
(NASA Orbital Debris Program Office, 2017), are expanding these requirements to include
incredibly high-strength properties and resistance to extreme environments.
Graphene, a two-dimensional nanostructure comprising of a single layer of carbon atoms has
displayed incredible material properties since its successful isolation (Novoselov & Geim,
2004). Two characterised graphene properties of direct significance to ballistics armour and
desalination applications are grapheneβs extreme strength (Xia et al, 2016) and grapheneβs
impermeability to gases coupled with the ability to synthesize nanopores (Berry, 2013),
where impurities will impact the sheet as it acts as a filter medium (Cohen-Tanugi &
Grossman, 2012). Figure 1 displays a representation of a graphene desalination membrane.
Figure 1 β Graphene water filter medium (Wang, 2012).
Under this context, this project has conducted molecular dynamics simulations and analysis
to understand the effects of projectile impacts on graphene nanosheets for applications in
water desalination and next-generation ballistic armour. Specifically, this report will outline
the project aims and objectives, review relevant academic literature highlighting current
research gaps and to provide thorough documentation of project, with discussion of results
and their effects on the intended applications.
7. 2
2. Project Definition
Over the course of the project, the following research questions have been developed in order
to guide the purpose of the project and to formulate relevant aims and objectives, in the
context of understanding the effects of projectile impacts on graphene nanosheets for
desalination and ballistic armour applications.
The research questions, as well as, the aims and objectives of the project have also been
influenced by gaps in current research surrounding the effect of defects and nanopores within
an otherwise pristine graphene sheet. These current research gaps have had an important
effect on the project scope and will be highlighted, and expanded upon in the literature
review section.
2.1 Research Questions
The fundamental research questions driving the project are:
β’ How do defects and nanopores within the graphene sheet affect grapheneβs resistance
to impact?
β’ How do the impact resistant properties of graphene make it a strong candidate for
applications as a desalination membrane and ballistics armour?
β’ What influence do defects and nanopores have the in the desalination membrane and
ballistics armour applications?
2.2 Aims & Objectives
In order to address the defined research questions, the following aims and objectives have
been proposed:
β’ Utilizing LAMMPS software, generate functioning geometries to reflect a realistic
impact simulation on a graphene sheet
β’ Integrate more complex morphologies, with particular focus on defects and nanopores
to the simulated graphene sheet
β’ Investigate the effects on the impact resistance of defective graphene
β’ Integrate hybrid structures and compare impact resistance properties
To address both the research questions and the aims and objective of the project, a review of
the relevant academic literature has been conducted, with current research gaps highlighted
and discussed.
8. 3
3. Literature Review
To support the research questions, as well as the aims and objects of the project, a literature
review of topics relevant to the project is presented. This review will first present a summary
of current research on the characterisation and applications-based research on graphene with
current gaps in research highlighted.
Following the graphene literature review, relevant literature on graphene defects and
nanopores will be presented, with particular focus on the theoretical implications of defects
and nanopores on the impact resistance of graphene. Finally, a review of the mechanics of
modelling potentials used in the LAMMPS simulation will be conducted.
3.1 Graphene
Graphene is a two-dimensional (2D) crystalline allotrope of carbon, where the carbon atoms
form an indefinitely repeating hexagonal sheet (Sharon & Sharon, 2015). Previous to its
successful isolation in 2004 (Novoselov & Geim, 2004), graphene had been inadvertently
produced in applications requiring its three-dimensional (3D) equivalent, graphite (Niyogi et
al, 2006).
When in its 3D graphite form, the 2D hexagonal graphene sheets are held together by weaker
Van der Waalβs forces, where the 2D graphene sheets will separate by breaking the Van der
Waalβs forces when under applied shear forces (Chan, 2009). Figure 2 illustrates the 2D
graphene sheets held together by the weaker Van der Waalβs forces, constituting 3D graphite.
Figure 2 β Graphene sheets held together with Van der Waalβs forces (Skoda et al, 2014)
When isolated, the carbon atoms that constitute the 2D graphene sheet are chemically bonded
together by covalent bonds (Niyogi et al, 2011). These covalent bonds between the carbon
atoms are the source of grapheneβs strength, where it is reported that graphene has a Youngβs
modulus value of 1 TPa and an intrinsic strength ~130 GPa, confirming graphene as the
strongest material ever tested (Warner et al, 2013).
9. 4
The strong covalent bonds and tightly packed hexagonal structure of graphene denies any
other atom to pass between the sheet atoms. This effect means graphene is impermeable to all
gases, as the atoms of the gas are too large to fit between each gap in the sheet (Brunetto &
Galvao, 2014). The hexagonal structure of graphene has been empirically observed by
annular dark-field scanning transmission electron microscopy (ADF-STEM), as displayed in
Figure 3.
Figure 3 β Graphene hexagonal lattice image produced by ADF-STEM imaging (Huang et al, 2011)
Studies devoted to understanding grapheneβs failure strength under impact have mainly
focussed on slower indentation type simulations (Sha et al, 2014) or increasing central
loading (Wang et al, 2014), with few studies focusing on projectile impacts (Zhang, Li &
Gao, 2015).
Select studies that have focussed on projectile impact, have focussed on hypervelocity
impacts (Xia et al, 2016) and metal nanoparticle collision (Sadeghzadeh, 2016). These
studies have displayed promising results, however, these studies have been conducted on
pristine sheets of graphene, where the presence of any defects is not considered.
Conducting research only on pristine sheets of graphene creates an important research gap in
the understanding the impact behaviour of graphene, where the production of totally pristine
graphene sheets may not always be guaranteed (Kim et al, 2014).
3.2 Graphene Defects
Despite the perfect hexagonal lattice being a defining feature of graphene aside from
deliberately induced nanopores, from a first principalβs basis, defects are omnipresent in
crystalline structures (Ziman, 1979) and are expected, as a function of proposed graphene
production techniques (Gravagnuolo et al, 2015)
For more realistic applications based research, any effect defects may have on the fracture
strength of graphene demands consideration. Especially when considering any effect defects
may have on the fracture behaviour of graphene can be distinct in such as low-dimension
material (Shirodkar & Waghmare, 2012). The creation of defects and their possible removal,
depend upon factors such as: thermal processes, ion bombardment or irradiation-induced
processes (Skowron, 2015). However, the generation or removal of defects is not within the
scope of this study.
10. 5
3.2.1 Stone-Wales Defects
A notable defect within graphene is the Stone-Wales defect (Stone & Wales, 1986). The
Stone-Wales defect is a commonly occurring defect within graphene and other low-
dimension, carbon bonded materials (Ma, Alfe, Michaelides & Wang, 2009) and has been
empirically observed within graphene using scanning transmission electron microscopy
(Figure 5).
Figure 4 β Stone-Wales defects in a graphene sheet (Rao & Sood, 2013)
A Stone-Wales defect is produced by a 90-degree rotation of one of the Carbon-Carbon (C-
C) bonds, generating a pair of pentagons and a pair of larger heptagons, in place of the ideal
hexagonal arrangement (Podlivaev & Openov, 2015), as displayed in Figure 5.
Figure 5 β Ideal graphene structure vs Stone-Wales defect structure comparison (Podlivaev & Openov, 2015).
The studied effects of Stone-Wales defects on graphene has predominantly centred around
changes in electronic behaviour (Zhoa et al, 2015). The studies focusing on projectile impacts
on graphene nanosheets featuring Stone-Wales defects are mainly focussed on the removal of
Stone-Wales defects through impact-induced stresses (Sun et al, 2012).
As Stone-Wales defects do not involve the adsorption of foreign atoms (Carlsson &
Scheffler, 2006), it can be postulated that Stone-Wales defects would have an effect on the
mechanical properties of graphene by possibly placing additional stresses on the covalent
bonds affected by the defect. Therefore, the effect Stone-Wales defects may have on the
behaviour of graphene under impact is an important research gap to close. Especially in
consideration to the intended ballistics-armour applications where reliability is a critical
factor.
11. 6
3.2.2 Graphene Nanopores
To effectively exploit the impermeable properties of graphene discussed in Section 3.1,
nanopores within graphene have been successfully induced and stabilised, as shown in
Figure 6. The methods used to create the nanopores include: diblock copolymer templating,
helium-ion beam drilling, and chemical etching methods, where each method is effectively
removing select carbon atoms from the sheet (Lee et al, 2014).
Figure 6 β An induced nanopore within a graphene sheet (Russo & Golovchenko, 2012).
The methods used to induce the nanopores within graphene have been demonstrated to be
extremely precise (Bell et al, 2009). These accurate processes allow for pores of a
predetermined size to be induced in the sheet to deny unwanted particles, while allowing the
desired particles passage, promoting the proposed utilisation of graphene as a filter
membrane (Kim et al, 2016).
Studies on the effect of graphene nanopores have predominantly focused on electronic effects
produced by the nanopore, where the intended applications have mainly centred around DNA
sequencing or electronics applications, where the nanopore is considered beneficial (Garaj,
Liu, Golovchenko & Branton, 2013).
Studies with the focus of desalination as the intended application have studied impact against
the graphene membrane. However, the studies more focussed on collisions of ion particles
(Inui et al, 2010), as opposed to metallic or covalently bonded materials as the projectile,
with the intention of generating a form of ion selectivity within the graphene membrane
(Rollings, Kuan & Golovchenko, 2016).
Similar to the research gaps concerning Stone-Wales defects, the lack of understanding on
possible effects nanopores may have on the impact resistant properties of graphene is an
important research gap to close. This is especially the case when considering the lack of
understanding surrounding the combination of covalently bonded projectiles impacting a
nanoporous graphene sheet.
12. 7
3.3 Potentials
In order to produce a realistic simulation, correctly describing the interactions between atoms
by selecting the correct atomic potentials is of critical importance (Kubicki, 2016). The
following section provides a literature review on four potentials utilised within the
simulation, where the mathematical methods used to describe the interactions are defined
alongside their respective utilisation within the model.
3.3.1 Lennard-Jones Potential
The Lennard-Jones potential is considered a basic method to approximate atomic
interactions. It describes atomic interaction through basic attraction and repulsion energy
terms (Jensen, 2010), where a cut-off distance is employed to reduce the non-bonded
interaction potential values to zero at a predetermined distance in order to decrease
computational requirements (Hinchliffe, 2005).
While not directly featured in the simulation model, the Lennard-Jones potential is an in-built
feature within the other, more advanced potentials used in the model and is explained to
provide the proper context. The Lennard-Jones Potential is expressed as:
πΈ"# = π
π
π
()
β
π
π
+
π€βπππ,
π = πππ‘πππ‘πππ π€πππ ππππ‘β π π‘πππππ‘β ππ ππ‘π‘ππππ‘πππ
π = πππ πππ πππππ πππππ’π
π = ππππ‘ππππ π ππππππ‘πππ πππ π‘ππππ
The
@
A
()
term describes the increase in the non-bonded energy as atoms are experiencing
Pauli repulsion in the short-range distances. The negative
@
A
+
term is describing the
attraction at longer-ranges (Nguyen & Wei, 2017). Figure 7 and Figure 8 display a graphical
representation and the terms of the Lennard-Jones potential, respectively.
Figure 7 β Graphical representation of the
Lennard-Jones potential (Lewars, 2016)
Figure 8 β Representation of Lennard-Jones
potential term (Lewars, 2016)
13. 8
3.3.2 Tersoff Potential
Unlike the more generalised Lennard-Jones potential, the Tersoff potential has been
repeated demonstrated to effectively describe particle interaction driven by covalent
bonding. The Tersoff potential achieves this through effectively describing the
creation and separation of covalent bonds, by not limiting attachment of individual
atoms to their respective neighbours (Stuart, Tutein & Harrison, 2000).
The Tersoff potential is expressed as:
πΈBCADEFF =
1
2
πI πJK [πM πJK + πJK πP πJK ]
J
JRK
π€βπππ,
πJK = πππ π‘ππππ πππ‘π€πππ ππ‘πππ π πππ (π)
πP = ππ‘π‘ππππ‘ππ£π ππ’πππ‘πππ
πM = ππππ’ππ ππ£π ππ’πππ‘πππ
πI = π ππππ‘β ππ’π‘πππ ππ’πππ‘πππ
πJK = ππ‘ππππ ππππ π π‘πππππ‘β πππ ππ ππ πππ£ππππππππ‘ πππ #ππππβπππ’ππ
The Tersoff potential can therefore more accurately describe covalent bonding in
nonelectrostatic materials such as carbon. In describing carbon atomic interaction, the
Tersoff potential has been demonstrated to accurately describe carbon over a range of
configurations, where the elastic properties, energies, defects and mechanics of
diamond and graphite have been particularly successful (Tersoff, 1988).
However, the Tersoff potential does have some limitations. Historically, the Tersoff
potential has presented difficulties in computing larger atomic structures, a problem
which has eased with advances in available computational power (Monteverde,
Migliorato & Powell, 2012). However, computational power aside, the Tersoff
potential can have limitations in accurately predicting simultaneous vibration and
elastic properties in crystalline structures (Porter, Justo & Yip, 1997).
3.3.3 AIREBO Potential
Generated from the Reactive Empirical Bond Order (REBO) potential, the Adaptive
Intermolecular Reactive Empirical Bond Order (AIREBO) potential was generated by
increasing requirements to model physical processes and not solely chemical
reactions (Ariza, Ventura & Ortiz, 2011).
The (AIREBO) potential utilises first-principles methods to model dynamic processes
in covalent bonds, specifically carbon and hydrocarbon allotropes (Stuart, Tutein &
Harrison, 2000). In order to achieve this, the AIREBO potential adds the non-bonded
atomic interactions of the carbon and hydrocarbon allotropes to the covalent REBO
potential, and a carbon and hydrocarbon specific Lennard-Jones potential.
14. 9
The AIREBO potential is expressed as:
πΈPYMZ[ =
(
)
(πΈJK
MZ[
+ πΈJK
"#
+ πΈ]JK^
BEADJE_J
^RJ,JK,]
J
]RJ,K
J
KRJ
J
J )
π€βπππ,
πΈJK
MZ[
= π πΈπ΅π πππ‘πππ‘πππ ππππ
πΈJK
"#
= πΏππππππ β π½ππππ πππ‘πππ‘πππ ππππ
πΈ]JK^
BEADJE_
= ππππ πππππ πΈπππππ¦ ππππ
The (πΈJK
MZ[
) term, utilises the REBO potential to compute the total potential energy
of the system as a summation of the distance dependent neighbouring atomic
interactions. The REBO term computes this similar to the Tersoff potential, discussed
in Section 3.2.2, but with the addition of a bond order function describing pair bond
interactions (Brenner, 1990).
The addition of the Lennard-Jones potential term (πΈJK
"#
) allows the AIREBO potential
the ability to model the Van der Waalβs interaction of carbon atoms, which the REBO
potential could not compute. As a consequence, covalent dependent elastic
interactions are notably stiffer when utilising the AIREBO potential over the REBO
potential (Stuart, Tutein & Harrison, 2000).
While being able to model carbon and hydrocarbon systems effectively, the AIREBO
potential has limitations when modelling systems extending beyond ambient
temperature and ambient pressure, due to difficulty parameterizing complex systems
(O'Connor, Andzelm & Robbins, 2015).
This has been encountered when studying shocks in hydrocarbon systems (Mattsson
et al, 2010), whereby the AIREBO potential sacrifices the ability to accurately
describe the full range responses, for the ability to model large system sizes
3.3.4 Morse Potential
To accurately describe full system behaviour, it is a requirement to be able to
accurately and realistically describe dislocation of atomic bonds. While the Lennard-
Jones, Tersoff and AIREBO potentials are able to effectively model dynamic system
behaviour, they do not describe dislocations explicitly.
The Morse potential is able to explicitly describe the dislocation of atomic bonds, as
well as atomic collisions, by effectively describing the energy increase of a system as
the atoms increasingly vibrate to the point of inducing an eventual dislocation (Costa
Filho et al, 2013). As a result, the Morse potential has been repeatedly used to model
harmonic or vibrational interactions such as atom absorption by other solids and
deformation of metallic solids (Znojil, 2016).
15. 10
The Morse potential is expressed as:
πhEADC π = βπ·C 1 β 1 β πjk AjAl
)
π€βπππ,
π = πππ π‘ππππ πππ‘π€πππ ππ‘πππ
πm = πππ’πππππππ’π πππ π‘ππππ πππ‘π€πππ ππ‘πππ , π πππ π
π·C = πππ π πππππ‘πππ ππππππ¦
πΌ = πππ‘πππ‘πππ π€πππ π€πππ‘β ππ’πππ‘πππ
The Morse potential is displayed graphically in Figure 9, where the (π·C) and (πC)
terms can be seen to describe the respective magnitude and location of the minimum
energy values for bond dislocation. While, the (πΌ) termβs influence can be observed
modifying the system curve at the minimum bond dislocation values (O'Connor,
Andzelm & Robbins, 2015).
Figure 9 β Morse potential plot. Retrieved November 1st
, 2017, from tdqms.uchicago.edu
The limitations of the Morse potential centre around its description of atomic
attraction and repulsion. While providing an effective description of atomic bond
dislocations, the Morse potential providing a small under-estimation of repulsive
atomic energy while simultaneously providing a small over-estimation of attractive
energy, resulting in a slight increase in bond hardness (Lim, 2007). Additionally, the
Morse potential is limited to two-body interactions only (Silvestre, 2016), possibly
restricting the use of the potential depending on simulation objectives.
17. 12
A spherical diamond projectile was created containing 98 type 1 atoms. The diamond
projectile was positioned at 40 Angstroms above the center of the graphene sheet.
Figure 10 displays the diamond projectile visualized by Ozito.
Figure 10 β Projectile geometry created in LAMMPS
4.2.2 Graphene Sheet Geometry
For ease of replication and defect addition, the geometry for the pristine graphene
sheet geometry was created in VNL and imported into the LAMMPS simulation using
the LAMMPS read_data command. Subsequently, a 100 Angstrom by 100 Angstrom
pristine graphene sheet was generated (Appendix B).
Upon import into LAMMPS, the graphene sheet geometry was created containing
3772 type 2 atoms and was positioned at the zero-point of the z-axis. The graphene
sheet geometry was then partitioned to create regulated, fixed edges with a width of 2
Angstroms for future simulation. Figure 11 displays the imported graphene sheet with
partitioned edges.
Figure 11 β Graphene sheet with partitioned edges
4.2.3 Graphene Defects and Nanopores
In order to rapidly generate realistic Stone-Wales defects and nanopores, VNL was
again utilized to generate a graphene sheet of the same dimensions (100 x 100
Angstroms). Stone-Wales defects and nanopores were added to the respective sheets
(Appendix C) and then imported into LAMMPS with no additional changes to the
LAMMPS input script.
18. 13
With respect to the Stone-Wales literature review conducted in Section 3.3.1, the
Stone-Wales defects were generated in VNL by manually selecting two carbon atoms
and rotating them 90 degrees while maintaining the atomic bonds, forming the
distinctive pair of heptagons and pentagons (Figure 12). The nanopore was simply
created by manually selecting carbon atoms and deleting them to form a nanopore
(Figure 13).
Figure 12 β Stone-Wales defect generated in VNL Figure 13 β Graphene nanopore generated in VNL
4.3 Model Potentials
With the creation of the model geometries, the correct potentials could be assigned to
ensure a realistic simulation. With respect to the reviewed literature discussed in
Section 3.3.2 through 3.3.4, the following potentials were selected for each model
component.
4.3.1 Projectile Potential
To realistically model the diamond projectile, the Tersoff potential was selected due
to its ability to accurately describe covalent bonding in carbon and its historically
successful modelling of the elastic properties, energies and mechanics of diamond
materials. To compute the Tersoff potential in LAMMPS, a Tersoff potential input
file was used with the appropriate diamond parameters defined (Appendix D).
The simulation size and inaccurate vibration limitations of the Tersoff potential
(Section 3.3.2) were deemed acceptable due to the small size of the diamond
projectile. Additionally, any inaccurate vibrations imposed by the Tersoff potential
could considered negligible as they could be supplemented by including an additional
potential to describe vibration.
4.3.2 Graphene Sheet Potential
The potential selected to model the graphene sheet was the AIREBO potential.
AIREBO was selected due to its successful utilization of first-principles methods to
model covalent bonds and that it specifically models carbon-carbon interactions. With
respect to these two factors, the AIREBO potential was considered the appropriate
selection for the graphene sheet.
The ambient temperature and pressure restrictions inherent to the AIREBO potential
(Section 3.3.3) were negated by setting the simulation to 300 Kelvin (ambient
temperature) at ambient temperature. Additionally, the small scale of the simulation
and lack of complexity were considered well within AIREBOβs parameterization
bounds.
19. 14
4.3.3 Impact Interaction Potential
Finally, to accurately model the interaction between the diamond projectile and
graphene sheet upon impact, the Morse potential was selected. The deciding factor in
the Morse potential selection was its ability to explicitly describe bond dislocations
and vibrations, which was a critical factor in accurately assessing the fracture strength
of graphene.
Any respective under-estimation or over-estimation of repulsive and attractive atomic
energies generated by the inclusion of the Morse potential were considered negligible
in the context of a high-velocity impact. Additionally, any small increases in bond
hardness the Morse potential would generate were also considered negligible, as it
was deemed that the Tersoff and AIREBO potentials would have overriding influence
on the respective hardness of the bonds.
4.4 Final Model Configurations
Before applying dynamic behaviour settings, the model was iteratively output into
Ovito to check that the model framework, model geometries and applied potentials
were functioning correctly. Figure 14 displays the simulation model prior to final
configuration, with the projectile and graphene sheet geometries correctly generated,
and in the correct locations.
Figure 14 β Initial simulation model with projectile and graphene sheet
To finalize the model for simulation, parameters controlling the dynamic behaviour of
the model were implemented. These parameters include fixed model behaviour,
applied velocities, simulation time-step and run-time.
Fixed model behaviour included fixing the partitioned edges of the graphene sheet,
effectively setting the edge forces to zero to hold the center section of the graphene
sheet in place. All atoms within the diamond projectile were fixed as a rigid body in
order to displace all atoms uniformly.
Velocity values were applied to the projectile in the negative z-axis, to displace the
projectile at the graphene sheet for impact. The simulation was given the time-step
value of 0.00099 and the large run-time value of 2000 in order to effectively observe
the maximum amount of atomic interactions.
20. 15
Velocities of 1 km/s through 5 km/s, at integrals of 1 km/s, were selected to
progressively reflect hypervelocity in earth orbit (NASA Orbital Debris Program
Office, 2017). The 1 km/s to 5 km/s range of velocities was tested uniformly on the
pristine graphene sheet, defective graphene sheet and nanoporous graphene sheet.
Each individual simulation took a total computation time of ~3 minutes for each
simulation.
4.5 Model Outputs
The selection and implementation of the simulation framework, model geometries,
applied potentials and dynamic behaviour of the final model configurations
culminated in the diamond projectile successfully making impact with the graphene
sheet, displayed in Figure 15.
Figure 15 β Successful impact simulation
As displayed in Figure 15, a noticeable ripple was observed as the diamond projectile
made impact with the graphene sheet. Bonds in both the projectile and sheet were also
observed to dislocate more as the velocities were increased. This behaviour in the
model validated the selection of potentials and simulation parameters.
To produce quantifiable data for analysis of the system, LAMMPS compute
commands were implemented to output values for the total kinetic energy and total
potential energy of the system. The thermo_style command was also utilized to
concatenate the total kinetic and potential energy values for each time-step into a
compatible format for analysis in Microsoft Excel.
21. 16
5. Results and Discussion
To effectively understand the effects of defects on grapheneβs resistance to impact
and to perform a proper appraisal of grapheneβs proposed applications in desalination
and ballistics-armour, a comparison of the pristine and defective/nanoporous
graphene simulation results is conducted.
In order to successfully compare the results and describe the difference in impact
resistance, the relationship between the velocity of the projectile and the kinetic
energy of the system was explored. Therefore, it is proposed that the differences in
kinetic energy between pristine graphene and defective/nanoporous graphene will
reveal the extent defects and nanopores have on the impact resistance of graphene.
As discussed, the pristine, defective and nanoporous graphene sheets were each
uniformly tested against a range of projectile velocities of 1 km/s through 5 km/s, at
integrals of 1 km/s. The kinetic energy values were recorded for each of the 2000
steps, where the difference in kinetic energy was computed as:
ΞπΎπΈ = πΎπΈDrCs ( β πΎπΈDrCs )mmm
The difference in kinetic energy was computed for all three sheets over the range of
velocities. The pristine sheet values were then compared against the defective sheet
and nanoporous sheet values, respectively.
5.1 Stone-Wales Defects Results
To effectively illustrate the comparison of kinetic energies for the pristine and defect
graphene sheets, Figure 16 displays a comparison at each impact velocity with the
kinetic energy represented in units of electron-Volts (eV).
Figure 16 β Pristine and Stone-Wales graphene comparison
22. 17
The results of the Stone-Wales sheet comparison show minor differences in kinetic
energy between pristine graphene and graphene featuring Stone-Wales defects.
Table 1 displays the differences in kinetic energy between the pristine graphene and
graphene featuring Stone-Wales defects as a percentage, respective for each velocity.
Table 1 - Pristine and defective graphene percentage difference in kinetic energy
Stone-Wales Sheet Comparison
1 km/s 2 km/s 3 km/s 4 km/s 5 km/s
4% -13% 1% -3% -5%
The percentage differences displayed in Table 1 further illustrate the minor magnitude
of differences in kinetic energy. The differences in kinetic energy are within the Β±5%
range with the exception of the 2 km/s velocity which displays a decrease in kinetic
energy of -13%.
However, when plotting the kinetic energy against simulation steps for the 2 km/s
velocity (Figure 17), the graphene sheet featuring Stone-Wales defects exhibits a
similar curve to the pristine graphene sheet, and therefore is exhibiting similar
behaviour.
Figure 17 β Kinetic energy vs simulation steps (pristine and Stone-Wales comparison) (2km/s)
At the 2 km/s velocity, the bonds of the sheet are observed to only partially break,
while still managing to successfully deflect the projectile, instead of remaining intact
at 1 km/s or completely breaking at 3 km/s onwards. It is proposed then, that the
Stone-Wales defects do have a small influence on the impact resistance of graphene at
the 2 km/s velocity.
23. 18
5.2 Nanoporous Sheet Results
Similar to the Stone-Wales sheet comparison, Figure 18 displays a comparison of
kinetic energies (eV) for the pristine and nanoporous graphene sheets at each impact
velocity.
Figure 18 β Pristine and Nanoporous Graphene Comparison
Similar to the results of the Stone-Wales sheet comparison, the nanoporous sheet
comparison shows minor differences in kinetic energy between pristine graphene and
nanoporous graphene. Table 2 displays the differences in kinetic energy between the
pristine graphene and the nanoporous graphene as a percentage, respective for each
velocity.
Table 2 - Pristine and nanoporous graphene percentage difference in kinetic energy
Nanoporous Sheet Comparison
1 km/s 2 km/s 3 km/s 4 km/s 5 km/s
0% -13% 6% -3% -2%
The percentage differences displayed in Table 2 show minor magnitudes in kinetic
energy differences and in the case of the 1 km/s velocity, no change is observed at all.
Most notably, the percentage differences for the nanoporous graphene sheet (Table 2)
display remarkably similar to the Stone-Wales defect comparison values displayed in
Table 1.
Interestingly, the nanoporous graphene sheet displays a -13% decrease in kinetic
energy at the 2 km/s velocity, identical to the Stone-Wales graphene sheet. When
comparing the Stone-Wales and nanoporous results for the other velocities, the results
are shown to be within the Β±5% of each other.
24. 19
When plotting the kinetic energy against simulation steps for the 2 km/s velocity for
all three sheets (Figure 19), the nanoporous graphene sheet features a similar curve to
both the Stone-Wales defect sheet and the pristine graphene sheet. Therefore, the
nanoporous graphene sheet is exhibiting similar behaviour to the pristine sheet and
Stone-Wales defect sheet, providing insights into the similarity of results.
Figure 19 - Kinetic energy vs simulation steps (3 sheet comparison - 2km/s)
Identical to the Stone-Wales sheet, at the 2 km/s velocity the bonds of the nanoporous
sheet are observed to only partially break, while again managing to deflect the
projectile. It is proposed then, that the nanopores do have a small influence on the
impact resistance of graphene at the 2 km/s velocity.
5.3 Results Summary
The presence of Stone-Wales defects or nanopores within the graphene sheet only
exert a small influence on the impact resistance of graphene, with the uniform
exception of the 2 km/s impact velocity. However, interpreting the presented results
with respect to the proposed desalination and ballistics-armour applications, the
results become significant.
When considering the Stone-Wales defects in a ballistics-armour application, the
reasonably small 13% decrease in impact resistance shown at 2 km/s is deemed
manageable. Additionally, the 4% increase in impact resistance at 1 km/s is an
encouraging result for applications requiring protection from projectiles with velocity
under 1 km/s and the small variation in results above 3 km/s is also encouraging as it
indicates that the presence of Stone-Wales defects do not greatly decrease protection
against hypervelocity projectiles, such as orbiting debris.
Similarly encouraging, the minor differences in kinetic energy of the nanoporous
graphene sheet, specifically the 0% change in impact resistance for the 1 km/s
velocity, indicates that the presence of nanopores will not affect the impact resistance
of graphene utilised in desalination applications with particle velocities dramatically
less than 1 km/s.
In summary, grapheneβs ability to maintain high strength, even in the presence of
Stone-Wales defects and nanopores, make it an ideal candidate for desalination and
ballistics-armour applications.
25. 20
6. Future Work
To continue this project, several recommendations for avenues of improvement and
further research have been identified. The identified avenues of improvement centre
around the validity of presented results and making further improvements to the
simulation model, in order to make the model as realistic as possible.
Possible improvements to the model are as follows:
β’ Removing the fixed edges around the graphene sheet as they would not
be considered 100% realistic from a Newtonian perspective.
β’ Tuning the Morse potential to more accurately describe bond dislocations
β’ A reduction in the large run time value of 2000 to save on computational
costs and time
β’ Simulating a larger projectile at a greater range of velocities
Additionally, proposed future work of the project would be to include a second, or
third, graphene sheet in simulations and provide a comparison of results. Attempts
were made at generating a dual sheet simulation (Figure 20), where the projectile was
able to successfully impact the dual sheet arrangement. However, due to time
constraints of completing the project in one semester, the dual sheet model was not
able to be completed to function realistically.
Figure 20 β Unfinished dual graphene sheet simulation
26. 21
7. Conclusion
In conclusion, the following project has conducted successful molecular dynamics
simulations of projectile impacts on pristine, Stone-Wales defect and nanoporous
graphene nanosheets. Subsequent analysis of simulation results has satisfied the
defined research questions and have successfully fulfilled the aims and objectives of
the project.
Effective analysis of both graphene featuring Stone-Wales defects and nanoporous
graphene sheets, have shown that the presence of either Stone-Wales defects or
nanopores do not significantly affect grapheneβs resistance in projectile impacts when
compared against pristine graphene sheets. Subsequently, it is determined that
graphene featuring Stone-Wales defects or nanopores do not substantially affect
graphene in desalination and ballistics armour applications.
It is the hope of this study that these findings can provide a contribution of knowledge
to the understanding of the impact resistance of graphene and to further the
understanding of the effects of defects and nanopores within these mechanical
processes.
Additionally, it is the hope of this study that a contribution to the understanding of
defect behaviour in graphene may indirectly influence the validity and development
of graphene production techniques. Where, driven by an application-based
understanding of defect behaviour, the production of graphene with acceptable defects
is accelerated. Creating a prosperous future of unrestricted access to uncontaminated
fresh water and protection for all.
27. 22
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9. Appendix
9.1 Appendix A β LAMMPS Input Script
#-----3D diamond sphere simulation-----
dimension 3
units metal
boundary s s s
atom_style atomic
neighbor 1.5 nsq
neigh_modify delay 5
#-----geometry-----
region box block 0 110.0 0 110.0 0 80 units box
create_box 2 box
mass 1 12.0
mass 2 12.0
lattice diamond 3.57
region diamond sphere 50 50 40 5 units box
create_atoms 1 region diamond units box
region 1 block 0 100.0 0 100.0 0 1 units box
group sheet region 1
read_data Thesis_Graphene.data add append group sheet
#nanopore sheet input file: graphene_np5.data
#Stone-Wales defect sheet input file: graphene_sw10.data
#-----potentials-----
pair_style hybrid airebo 2.5 tersoff morse 2.5
pair_coeff * * tersoff C.tersoff C C
pair_coeff * * airebo CH.airebo NULL C
pair_coeff 1 2 morse 6.0585 5.11 2.522 2.5
#-----groups------
#projectile
group projectile region diamond
#edges of graphene sheet
region AAA block 0 2 3 95 0 5 units box
group leftsheet region AAA
region BBB block 96 100 3 95 0 5 units box
group rightsheet region BBB
region CCC block 0 100 0 3 0 5 units box
group bottomsheet region CCC
region DDD block 0 100 95 100 0 5 units box
group topsheet region DDD
33. 28
group edge union leftsheet topsheet rightsheet bottomsheet
#centre of graphene sheet
region EEE block 2 96 3 95 0 5 units box
group centre region EEE
#atom types
set group projectile type 1
set group edge type 2
set group centre type 2
#-----initial velocities-----
compute mobile projectile temp
velocity projectile create 300 260888 temp mobile
#-----fixes-----
fix 1 all nve
fix 2 edge setforce 0.0 0.0 0.0
fix 3 projectile rigid single
#-----impact-----
velocity projectile set 0.0 0.0 -10
#-----timestep-----
timestep 0.00099
thermo 1 #print every 1 timesteps
thermo_modify temp mobile
#-----computes-----
compute pecentre all pe
compute kecentre all ke
#compute peprojectile projectile pe
#compute keprojectile projectile ke
thermo_style custom step temp c_pecentre c_kecentre
#thermo_style custom step temp c_peprojectile c_keprojectile
compute sigma all stress/atom NULL
variable sigma_VM atom (0.5*((c_sigma[1]-c_sigma[2])+(c_sigma[1]
c_sigma[3])+(c_sigma[2]-
c_sigma[3])+6*((c_sigma[4])^2+(c_sigma[5])^2+(c_sigma[6])^2)))^0.5
#-----run-----
dump 1 all custom 1 dump.sheet_test.dat id type x y z fx fy fz v_sigma_VM
#dump 2 centre custom 2000 pesheet.lammpstrj
#dump 3 centre custom 2000 kesheet.lammpstrj
run 2000
#-----hold-----
34. 29
#dump 2 all image 250 image.*.jpg type type &
# zoom 1.6 adiam 1.5
#dump_modify 2 pad 4
#dump 3 all movie 250 movie.mpg type type &
# zoom 1.6 adiam 1.5
#dump_modify 3 pad 4
37. 32
9.5 Appendix D β LAMMPS Compatible Tersoff File
# Tersoff parameters for various elements and mixtures
# multiple entries can be added to this file, LAMMPS reads the ones it needs
# these entries are in LAMMPS "metal" units:
# A,B = eV; lambda1,lambda2,lambda3 = 1/Angstroms; R,D = Angstroms
# other quantities are unitless
# This is the Si parameterization from a particular Tersoff paper:
# J. Tersoff, PRB, 37, 6991 (1988)
# See the SiCGe.tersoff file for different Si variants.
# format of a single entry (one or more lines):
# element 1, element 2, element 3,
# m, gamma, lambda3, c, d, costheta0, n, beta, lambda2, B, R, D, lambda1, A
C C C 3.0 1.0 0.0 38049 4.3484 -0.930 0.72751
0.00000015724 2.2119 430.0 1.95 0.15 3.4879 1393.6
