1. Roy Downs University of Arkansas Faculty Mentor: Dr. Joseph J. Rencis Graduate Student Mentor: Sachin Terdalkar

2. 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. Nano-scale Electronics Ultracapacitors Pressure Sensors Nano Resonators [Freitag, M., Nature Nanotechnology 2008] Graphene Transistor

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

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

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

8. 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. 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 1 = 175.7 Å y2y2 x 1 =186.3 Å x2x2 Initial Position (t=0; v x = 0) Final Position (t>0) (v x =0.5 Å/ps) x y

11. 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. 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. 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. 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. Determine Interaction Between Silicon Substrate and Graphene Sheet Use MD Simulations Stone-Wales Defect in Graphene Sheet Silicon Substrate Graphene Sheet

16. NSF REU Program