Roy Downs University of Arkansas

Faculty Mentor: Dr. Joseph J. RencisGraduate Student Mentor: Sachin Terdalkar

Nano-indentation of Graphene Sheet using

Molecular Dynamic Simulation

Monolayer Structure of Carbon Atoms

Hexagonal Shape Lattice

Characteristics Very Strong Highly Conductive High Opacity

Graphene Sheet

http://en.wikipedia.org/wiki/File:Graphene_xyz.jpg

• Nano-scale Electronics

• Ultracapacitors

• Pressure Sensors

• Nano Resonators

Potential Applications

[Freitag, M., Nature Nanotechnology 2008]

Graphene Transistor

Experimental Measurement of Mechanical Properties

Mechanical Properties: Project Focuso Young’s Modulus (measured average E=1.0

TPa)o Intrinsic Strength (measured sint=130 GPa)

Indentation Experiment of Graphene on Silicon

Substratehttp://www.sciencemag.org/

Silicon Substrat

eGraphe

ne Sheet AFM Measured E varies

from 0.9 to 1.2 TPa

Atomic Force Microscope

Tip

F - applied force - pretension in graphene sheet - diameter of graphene sheet - indentation depth - Young’s modulus - dimensionless constant

v – Poisson’s ratio varied values of and to fit

the curve in experimental data

Analytical Solution

3322

0

aaqE

aaF DD

D20

DE 2

q

a

216.015.005.1/1 vvq

DE 2 D20

Atoms are assumed lumped point masses

Interaction through Inter-atomic Potential

Atomic position from numerical integration of equations of motion

Molecular Dynamics Simulation

F = ma

http://en.wikipedia.org/wiki/File:Argon_dimer_potential_and_Lennard-

Jones.png

Inte

racti

on e

nerg

y (e

V)

Using MD SimulationsGenerate Load-indentation CurveDetermine Young’s Modulus

Goals

http://www.physorg.com/news135959004.html

Graphene Sheet

Indenter

Monolayer of Graphene SheetLAMMPS - http://lammps.sandia.gov.52873 AtomsRed Atoms Fixed – Outer Diameter Thickness

15 Å Green Atoms Free - Coupled to the External

BathIndenter - 150Å Diameter AIREBO Potential for C-C Interaction

MD Simulation Model

Rigid Indenter

Mobile AtomsFixed Atoms

Stretched with Very Small Velocity to Produce an Infinitesimal Longitudinal and Lateral Strain

Experiment Poisson’s Ratio – 0.165MD Simulation Poisson’s Ratio – 0.166

Calculation of Poisson’s Ratio

y1 = 175.7Å y2

x1=186.3Åx2

Initial Position(t=0; vx = 0)Final Position(t>0)

(vx =0.5 Å/ps)

x

y

x

y

StrainalLongitudin

StrainLateralv

Indentation

100Å Indenter Diameter 130Å Indenter Diameter

E=1.07 TPa E=1.13 TPa

Varying Diameter of Indenter

3

3220

aaqE

aaF DD AFM Experimentally

Measured E varies from 0.9 to 1.2 TPa

nm.

EE

D

335

2

150Å Indenter Diameter 200Å Indenter Diameter

E=1.18 TPa E=1.28 TPa

Varying Diameter of Indenter

3

3220

aaqE

aaF DD AFM Experimentally

Measured E varies from 0.9 to 1.2 TPanm335.

EE

2D

150Å Indenter Diameter 150Å Indenter Diameter

5Å Eccentricity E=1.17 TPa 10Å Eccentricity E=1.16TPa

Eccentric Indenter

AFM Experimentally Measured

E varies from 0.9 to 1.2 TPanm335.

EE

2D

3

3220

aaqE

aaF DD

MD simulation Compared to Analytical Solution

Indenter SizeIncrease Indenter Diameter -> Increased

Young’s ModulusIndenter Contact Area Affects Measured Value

of Young’s ModulusEccentric Indenter

Does not affect measured value of Young’s modulus

Conclusion

Determine Interaction Between Silicon Substrate and Graphene Sheet

Use MD Simulations

Stone-Wales Defect in Graphene Sheet

Future Work

Silicon Substrat

eGraphene

Sheet

NSF REU Program

Acknowledgements

Questions ?