MATERIALS LS SCIENCE AND ENGINEERING Tailoring thermal conductivity of graphene via defect-and-molecular engineering Stefan Bringuier Contributing authors: Krishna Muralidharan, Pierre Deymier, Jean-Francois Robillard Collaborators: Nick Swinteck, Keith Runge University of Arizona Department of Materials Science and Engineering 11/14/2014 1 S. Bringuier
MATERIALS LS SCIENCE AND ENGINEERING Carbon Hybrid Nanostructures What do we know about the thermal properties of such hybrid structures?? Are they tunable?? 11/14/2014 2 S. Bringuier
MATERIALS LS SCIENCE AND ENGINEERING Carbon Hybrid Nanostructures Let us examine the simplest representation of such hybrid structures: An equivalent heavy atom periodic structure We will investigate its structure-thermal conductivity relations using MD 11/14/2014 3 S. Bringuier
MATERIALS LS SCIENCE AND ENGINEERING Molecular Dynamics Simulation LAMMPS MD package* AIREBO interatomic potential by 109.1 nm Brenner/Stuart † . Good for functionalizing SLG with hydrocarbons Lower end of thermal conductivity 1. Equilibrate using NVT 300K 94.5 nm 2. Run NVE * Stuart, Steven J., Alan B. Tutein, and Judith A. Harrison. "A reactive potential for hydrocarbons with intermolecular interactions." The J of Chem Phys 112.14 (2000): 6472-6486. Potential reproduces bandstructure † S. Plimpton, Fast Parallel Algorithms for Short-Range Molecular Dynamics, J Comp Phys, 117, 1-19 (1995). 11/14/2014 4 S. Bringuier
MATERIALS LS SCIENCE AND ENGINEERING Calculation of Thermal Conductivity Heat current – Linear response due to time dependence of equilibrium fluctuations 𝑓 𝑗 𝒘 𝑗 + 1 𝑲 = 2 𝒔 𝑗𝑘 𝒈 𝑗𝑘 ⋅ 𝒘 𝑗 + 𝒘 𝑘 𝑗 𝑗<𝑘 Convective term Conduction term Green-Kubo method for calculating thermal conductivity from heat current autocorrelation function (HCACF) ∞ 1 𝝀 = 𝑙 𝑐 𝑈 2 𝑊 𝑲 𝑢 ⋅ 𝑲(0) 𝑒𝑢 0 Ensemble average 100 ps correlation length averaged over 2 ns (6 such data sets) 11/14/2014 5 S. Bringuier
MATERIALS LS SCIENCE AND ENGINEERING Analytical Fit To HCACF As suggested by A.J.H McGaughey and M. Kaviany * the HCACF can be expressed as the sum of two decaying exponentials: 𝑗=𝑦,𝑧,𝑨 = 𝐵 𝑝 exp − 𝑢 + 𝐵 𝑏 exp − 𝑢 𝐾 𝑗 𝑢 ⋅ 𝐾 𝑗 0 𝜐 𝑝 𝜐 𝑏 Lifetime of optical modes Lifetime of acoustic modes The thermal conductivity can be obtained from: 1 𝜆 𝑗 = 𝑙 𝑐 𝑈 2 𝑊 (𝐵 𝑝 𝜐 𝑝 + 𝐵 𝑏 𝜐 𝑏 ) *A.J.H. McGaughey, M. Kaviany, Int. J. Heat Mass Transfer 47 (2004) 1799. 11/14/2014 6 S. Bringuier
MATERIALS LS SCIENCE AND ENGINEERING Pristine SLG In-plane thermal conductivity 562 W/mK consistent with values reported for AIREBO* * Qiu, B.; Ruan, X. Molecular Dynamics Simulations of Thermal Conductivity and Spectral Phonon Relaxation Time in Suspended and Supported Graphene. arXiv:1111.4613 [cond- mat] 2011. 11/14/2014 7 S. Bringuier
MATERIALS LS SCIENCE AND ENGINEERING Thermal conductivity trends with the periodic heavy atom a 6 nm: thermal conductivity reduction due to scattering What about the sweet spot at 23 nm ??. 11/14/2014 8 S. Bringuier
MATERIALS LS SCIENCE AND ENGINEERING In-Plane HCACF a 6nm system: long time oscillatory behavior. Oscillatory behavior disappears as period increases . 11/14/2014 9 S. Bringuier
MATERIALS LS SCIENCE AND ENGINEERING Out-of-Plane HCACF 6nm: “saw tooth” oscillatory behavior 11/14/2014 10 S. Bringuier
MATERIALS LS SCIENCE AND ENGINEERING Fourier analysis: Out-of-plane vs In-plane 11/14/2014 13 S. Bringuier
MATERIALS LS SCIENCE AND ENGINEERING Fourier analysis: Out-of-plane vs In-plane • Distinct non over-lapping (in-plane and out-of- plane) standing wave modes for 6 nm • Maximum overlap for the 23 nm system: Resonant energy transfer leads to the observed maximum in conductivity 11/14/2014 14 S. Bringuier
MATERIALS LS SCIENCE AND ENGINEERING Concluding Remarks and Future Directions Characterized the interplay between scatterers (heavy atom) and the resonant energy transfer between in-plane and out-of-plane modes induced by the scatterers!! The 23nm periodicity represents a “sweet” spot as a result of this interplay. More statistics and functionalized graphene systems Special Thanks To: Coauthors Collaborators 11/14/2014 15 S. Bringuier
MATERIALS LS SCIENCE AND ENGINEERING Questions? Thank you! Further question please contact: Stefan Bringuier Email: stefanb@email.arizona.edu Website: www.u.arizona.edu/~stefanb 11/14/2014 16 S. Bringuier
MATERIALS LS SCIENCE AND ENGINEERING Intentionally Blank 11/14/2014 17 S. Bringuier
MATERIALS LS SCIENCE AND ENGINEERING Talking Points 1. Objectives 2. MD 3. HCACF 4. SLG 5. Trends 6. HCACF In-plane / Out-of-plane 7. FFT significant overlap between in-plane and out-of-plane suggest coupling 11/14/2014 18 S. Bringuier
MATERIALS LS SCIENCE AND ENGINEERING Pristine SLG In-plane thermal conductivity 562 W/mK consistent with values reported for AIREBO* Optical lifetime: 0.3182 ps Acoustic lifetime: 1.783 ps * Qiu, B.; Ruan, X. Molecular Dynamics Simulations of Thermal Conductivity and Spectral Phonon Relaxation Time in Suspended and Supported Graphene. arXiv:1111.4613 [cond- mat] 2011. 11/14/2014 19 S. Bringuier
MATERIALS LS SCIENCE AND ENGINEERING Fourier analysis of In-Plane HCACF 6nm shows in-plane standing wave modes 11/14/2014 20 S. Bringuier
MATERIALS LS SCIENCE AND ENGINEERING Continued: FFT of Out-Of-Plane HCACF HIDDEN SLIDE 6nm has very distinct characteristic standing wave modes. These modes disappear or broaden with increase period length 11/14/2014 21 S. Bringuier
MATERIALS LS SCIENCE AND ENGINEERING Thermal Conductivity of Heavy Mass (C60) 6nm thermal conductivity obtain by integration of HCACF Lifetime of phonons contributing to thermal conductivity 11/14/2014 22 S. Bringuier
MATERIALS LS SCIENCE AND ENGINEERING Single Vacancy SLG lx = 94.5 nm ly = 109.1 nm lx/2 ly/2 No significant change in thermal conductivity FFT of HCACF Some increase in lifetimes: Optical lifetime: 0.504 ps Acoustic lifetime: 4.9305 11/14/2014 23 S. Bringuier
MATERIALS LS SCIENCE AND ENGINEERING Periodic Vacancies in SLG No significant change in thermal conductivity Large drop in lifetime at period of 6 nm due to defect scattering. Data suggest no significant Bragg scattering (no phononic effect) 11/14/2014 24 S. Bringuier
MATERIALS LS SCIENCE AND ENGINEERING Single C60 Chemisorbed on SLG lx = 94.5 nm ly = 109.1 nm lx/2 ly/2 Similar behavior as single vacancy Periodically placed C60 does not stay absorbed to SLG using AIREBO 11/14/2014 25 S. Bringuier
MATERIALS LS SCIENCE AND ENGINEERING Related Study (Nick Swinteck*) Graphene strip with “1D nanobutton ” a Vary mass and to examine effect of resaonence modes Distinctive plateau as increase in mass? Norm. HCACF 3 ⋅ 𝑛 𝑑𝑏𝑠𝑐𝑝𝑜 Related Talk: 𝑛 𝑑𝑏𝑠𝑐𝑝𝑜 “Coherent thermal phonons in Si-Ge nanoscale phononic crystals” by N. Swinteck et al. given May 27 th . 4 ⋅ 𝑛 𝑑𝑏𝑠𝑐𝑝𝑜 2 ⋅ 𝑛 𝑑𝑏𝑠𝑐𝑝𝑜 Number of timstep *Nick Swinteck is a Postdoctoral Research Associate at the University of Arizona in the Department Materials Science and Engineering 11/14/2014 26 S. Bringuier
MATERIALS LS SCIENCE AND ENGINEERING Continued: FFT of HCACF Resonant shift Intensity (a.u.) Frequency Low frequency shifts as mass increases Possible coupling between propagating phonons and resonance. Tailor bandstructure – Hybridization of bands 11/14/2014 27 S. Bringuier
MATERIALS LS SCIENCE AND ENGINEERING Continued: Power Spectrum Fourier transform of velocity autocorrelation gives the accessed phonon modes, i.e. PDOS No spatial component (i.e. wave vector dependence) 𝑓 𝑗𝜕𝑢 𝑒𝑢 𝜕 = 𝑤 𝑢 ⋅ 𝑤 0 11/14/2014 28 S. Bringuier
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