Can graphene allotropes surpass the high thermal conductivity of graphene?

1. 6 6 6 6 5 7 7 5 Can graphene allotropes surpass the high thermal conductivity of graphene? Zacharias G. Fthenakis, Zhen Zhu and David Tománek Michigan State University T8-4 (Fthenakis, Zhu, Tomanek)

2. Why studying the thermal conductivity? On-chip power density the last two decades (Moore’s Law) Laptop on fire Heat is a problem in nano-electronics Pop et al, Proc. IEEE 94, 1587 (2006) T8-4 (Fthenakis, Zhu, Tomanek)

3. Why studying the thermal conductivity of carbon nanostructures? 4000 3500 3000 2500 2000 1500 1000 500 0 Thermal Conductivity λ (W/m K) 0 100 200 300 400 500 600 700 Temperature K cV = specific heat per volume vs = speed of sound Ī = phonon mean free path Experimental thermal conductivity of graphene (A. A. Balandin, Nature Materials10, 569 (2011)) How do defects affect thermal conductivity? Thermal conductivity for a (10,10) nanotube (S. Berber, Y.-K. Kwong and D. Tomanek, Phs. Rev. Lett. 84, 4613 (2000)) T8-4 (Fthenakis, Zhu, Tomanek)

4. 200000 150000 100000 50000 0 Thermal conductivity of defective graphene Graphene with 13C isotopic impurities 13Cx12C1-x x=0.00 x=0.05 vacancies 1% Narrow ribbon (11Å width) with 13C impurities and vacancies Z. G. Fthenakis and D. Tománek, Phys. Rev. B 86, 125418 (2012) T8-4 (Fthenakis, Zhu, Tomanek)

5. What about Stone-Wales defects? • Graphene allotropes = Periodically arranged Stone-Wales defects • Infinite number of different structures. We focus on pentaheptites (5-7) • QUESTION: How do periodically arranged Stone-Wales defects affect thermal conductivity? T8-4 (Fthenakis, Zhu, Tomanek)

6. Methods to study thermal conductivity λ L • Direct Molecular Dynamics (usually L < mean free path) • Equilibrium Molecular Dynamics(Green-Kubo formula) (convergence is very slow) • Non Equilibrium Molecular Dynamics ΗΟΤ COLD Heat Flux J Fe T8-4 (Fthenakis, Zhu, Tomanek)

7. Heat bath Non Equilibrium Molecular Dynamics Tersoff Potential Nose – Hoover Thermostat Non equilibrium driving forces . i Thermal Conductivity Heat Flux T8-4 (Fthenakis, Zhu, Tomanek)

8. Details of Molecular Dynamics • Solving the equations of motion for various Fe using periodic boundary conditions • About 30-50 different Fe values for each T • Extrapolation • N = 100 – 400 atoms • Simulation time t = 0.2 – 2 nsec (Δt = 0.2 fsec, maximum 107 time steps) • Structures: Pentaheptite (5-7) and pentaheptite lines T8-4 (Fthenakis, Zhu, Tomanek)

9. y x RESULTS A. Pentaheptites (5-7) A B T8-4 (Fthenakis, Zhu, Tomanek)

10. graphene ribbon 1% vacancies y x RESULTS A. Pentaheptites (5-7) A B Same anisotropy for A and B T8-4 (Fthenakis, Zhu, Tomanek)

11. graphene nanoribbon (11Å width) graphene with 1% vacancies B. A single line of 5-7 Stone-Wales defects (GRAIN BOUNDARIES) initially T=300K N=160 N=32 + L T8-4 (Fthenakis, Zhu, Tomanek)

12. Conclusions • 5-7 haeckelites exhibit much smaller thermal conductivity (λ) than graphene • λ values for 5-7 haeckelites are similar to those found for 1% vacancies and narrow nanoribbons • Anisotropy (different thermal conductivity for different directions) • Stone-Wales grain boundaries affects significantly the thermal conductivity of graphene Thank you T8-4 (Fthenakis, Zhu, Tomanek)