Nano-indentation of Graphene Sheet using Molecular Dynamic Simulation

1. Nano-indentation of Graphene Sheet using Molecular Dynamic Simulation Roy Downs University of Arkansas Faculty Mentor: Dr. Joseph J. Rencis Graduate Student Mentor: Sachin Terdalkar

2. Graphene Sheet • Monolayer Structure of Carbon Atoms • Hexagonal Shape Lattice • Characteristics • Very Strong • Highly Conductive • High Opacity http://en.wikipedia.org/wiki/File:Graphene_xyz.jpg

3. Potential Applications • Nano-scale Electronics • Ultracapacitors • Pressure Sensors • Nano Resonators Graphene Transistor [Freitag, M., Nature Nanotechnology 2008]

4. Experimental Measurement of Mechanical Properties • Mechanical Properties: Project Focus • Young’s Modulus (measured average E=1.0 TPa) • Intrinsic Strength (measured sint=130 GPa) Atomic Force Microscope Tip Silicon Substrate Graphene Sheet Indentation Experiment of Graphene on Silicon Substrate AFM Measured E varies from 0.9 to 1.2 TPa http://www.sciencemag.org/

5. Analytical Solution • 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

6. Molecular Dynamics Simulation • Atoms are assumed lumped point masses • Interaction through Inter-atomic Potential • Atomic position from numerical integration of equations of motion Interaction energy (eV) http://en.wikipedia.org/wiki/File:Argon_dimer_potential_and_Lennard-Jones.png F = ma

7. Goals • Using MD Simulations • Generate Load-indentation Curve • Determine Young’s Modulus http://www.physorg.com/news135959004.html Graphene Sheet Indenter

8. MD Simulation Model • Monolayer of Graphene Sheet • LAMMPS - http://lammps.sandia.gov. • 52873 Atoms • Red Atoms Fixed – Outer Diameter Thickness 15 Å • Green Atoms Free - Coupled to the External Bath • Indenter - 150Å Diameter • AIREBO Potential for C-C Interaction Rigid Indenter Mobile Atoms Fixed Atoms

9. Initial Position (t=0; vx = 0) Final Position (t>0) Calculation of Poisson’s Ratio • Stretched with Very Small Velocity to Produce an Infinitesimal Longitudinal and Lateral Strain • Experiment Poisson’s Ratio – 0.165 • MD Simulation Poisson’s Ratio – 0.166 y y2 y1= 175.7Å (vx =0.5 Å/ps) x x1=186.3Å x2

10. Indentation

11. Varying Diameter of Indenter • 100Å Indenter Diameter 130Å Indenter Diameter E=1.07 TPa E=1.13 TPa AFM Experimentally Measured E varies from 0.9 to 1.2 TPa

12. Varying Diameter of Indenter • 150Å Indenter Diameter 200Å Indenter Diameter E=1.18 TPa E=1.28 TPa AFM Experimentally Measured E varies from 0.9 to 1.2 TPa

13. Eccentric Indenter • 150Å Indenter Diameter 150Å Indenter Diameter 5Å Eccentricity E=1.17 TPa 10Å Eccentricity E=1.16TPa AFM Experimentally Measured E varies from 0.9 to 1.2 TPa

14. Conclusion • MD simulation compared to analytical solution • Indenter Size • Increase indenter diameter -> increased Young’s modulus • Indenter contact area affects measured value of Young’s modulus • Eccentric Indenter • Does not affect measured value of Young’s modulus

15. Future Work • Determine Interaction Between Silicon Substrate and Graphene Sheet • Use MD Simulations • Stone-Wales Defect in Graphene Sheet Silicon Substrate Graphene Sheet

16. Acknowledgements • NSF REU Program

17. Questions ?