Tailoring thermal conductivity of graphene via defect-and-molecular - PowerPoint PPT Presentation

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