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Shear Properties and Wrinkling Behaviors of Finite Sized Graphene

Shear Properties and Wrinkling Behaviors of Finite Sized Graphene. PHYS466 Project Kyoungmin Min, Namjung Kim and Ravi Bhadauria. Contents. INTRODUCTION CURRENT RESEARCH OBJECTIVES SIMULATION SETUP RESULT AND DISCUSSION CONCLUSION REFERENCES. Graphene: Introduction. Graphene.

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Shear Properties and Wrinkling Behaviors of Finite Sized Graphene

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  1. Shear Properties and Wrinkling Behaviors of Finite Sized Graphene PHYS466 Project Kyoungmin Min, Namjung Kim and Ravi Bhadauria

  2. Contents • INTRODUCTION • CURRENT RESEARCH • OBJECTIVES • SIMULATION SETUP • RESULT AND DISCUSSION • CONCLUSION • REFERENCES

  3. Graphene: Introduction Graphene • A single layer of sp2 hybridized carbon atoms in a honeycomb lattice • Multiple use in areas of Electronics, Material Science and Mechanical Engineering • Extraordinary mechanical properties (fracture strength is 200 times greater than steel) [2]

  4. Current research Young’s modulus Shear modulus Poisson’s ratio Wrinkling behavior

  5. Objectives •  Investigate the shear properties of finite sized graphene under various shear loading conditions. • Chirality effects and size dependence • Investigate the wrinkling behavior under shear conditions.

  6. Simulation Setup LAMMPS[12] •  Large-scale Atomic/Molecular Massively Parallel Simulator(LAMMPS) is used as molecular dynamics engine. POTENTIAL FUNCTION • Adaptive Intermolecular Reactive Empirical Bond Order(AIREBO)[11] extends the interaction range by changing cutoff function based on REBO potential [13]. • AIREBO potential allows for covalent bond breaking and creation with associated changes in atomic hybridization within classical potential.

  7. Simulation Setup BOUNDARY CONDITIONS Apply velocity on top Move and Fix top and bottom Fix top and bottom after simple shear 1) Apply strain directly 2) Displace and relax top atoms 3) Apply velocity BC • Similar to 2), takes more time • Time Step: 0.1 fs • Relaxed 10000 steps • before simulation • Displaced 0.05 Å and • relaxed 100000 steps • Easily unstable

  8. Results and Discussion RELAXATION • After 400 steps, temperature, pressure and potential energy reached at the stable state. Temperature Pressure Potential E Relaxation point

  9. Results and Discussion UNDER SHEAR LOAD • Temperature, pressure and potential energy show discontinuity to corroborate the fracture. Temperature Pressure Potential E Fracture

  10. Armchair Armchair Shear 1 (Armchair) Shear 2 (Armchair) Zigzag Zigzag Shear 1 (Zigzag) Shear 2 (Zigzag)

  11. Results and Discussion SHEAR STRESS-STRAIN RELATIONSHIP • As the size of structure increases, more shear stress and strain can be hold. • For small atoms case, chirality affects more on shear modulus comparing to large atoms case. • Shear modulus increases as the size of structure increases.

  12. Results and Discussion SHEAR PROPERTIES • As the size is increased, shear properties are converged to bulk value(shear modulus = 480GPa(zigzag) and 450GPa(armchair), shear strength=60GPa) • The edge effect from different chiralities influences the behavior of the structure, especially in small size. Shear Modulus Shear modulus in bulk case = 480Gpa(zigzag) and 450GPa(armchair) Shear Strength Shear strength in bulk case = 60 GPa Fracture shear strain

  13. Results and Discussion THEORETICAL RESULTS WRINKLING BEHAVIOR • The ratio of amplitude and half wave length relationship [10] MD result, 836 atoms AC A / λ ZZ Wrinkle view γ

  14. Conclusion • Optimized boundary condition for shear stress was explored. • The shear properties and wrinkling behavior of finite size graphene have been studied in this work. • Chirality effect and size dependency of shear modulus, shear strength and fracture shear strain are observed. • Wrinkles were observed and needed further investigation.

  15. References [1] F. Schendin et al., Nature Materials, Vol. 6, pp. 652-655 (2007) [2] C. Lee et al., Science, Vol. 321, No. 5887, pp. 385-388 (2008) [3] I. W. Frank et al., Journal of Vacuum Science and Technology B, Vol. 25, No. 6, pp. 2558-2561 (2007) [4] J. Meyer et al., Nature, Vol.446, pp. 60-63 (2007) [5] A. Sakhaee-Pour, Solid State Communications, Vol. 149, No. 1-2, pp. 91-95 (2009) [6] C. Li and T. W. Chou, International Journal of Solid and Structures, Vol. 40, No. 10, pp. 2487-2499 (2003) [7] R. Faccio et al., Journal of Physics: Condensed Matter, Vol. 21, No. 28, pp. 5304-5310 (2009) [8] H. Bu et al., Physics Letters A, Vol. 373, No. 37, pp. 3359-3362 (2009) [9] H. Zhao et al., Nano Letters, Vol. 9, No. 8, pp. 3012-3015 (2009) [10] Y. W. Wong and S. Pellegrino, Journal of Mechanics of Materials and Structures, Vol. 1, No. 1, pp. 27-61 (2006) [11]S. Stuart et al., Journal of Chemical Physics, Vol. 112, No. 14, pp. 6472-6486 (2000) [12]S. J. Plimpton, Journal of Computational Physics, Vol. 117, pp. 1-19 (1995) [13] D. W. Crenner et al., journal of Physics: Condensed Matter, Vol. 14, No. 4, pp. 783-802 (2002) [14] K. Min and N. R. Aluru, In preparation (2010)

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