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

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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

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Carbon Hybrid Nanostructures

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What do we know about the thermal properties of such hybrid structures?? Are they tunable??

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Carbon Hybrid Nanostructures

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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

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Molecular Dynamics Simulation

• LAMMPS MD package*
• AIREBO interatomic

potential by Brenner/Stuart†.

• Good for functionalizing

SLG with hydrocarbons

• Lower end of thermal

conductivity

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94.5 nm

109.1 nm

* 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. † S. Plimpton, Fast Parallel Algorithms for Short-Range Molecular Dynamics, J Comp Phys, 117, 1-19 (1995).

Potential reproduces bandstructure

• 1. Equilibrate using

NVT 300K

• 2. Run NVE

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Calculation of Thermal Conductivity

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• Heat current – Linear response due to time dependence of

equilibrium fluctuations

• Green-Kubo method for calculating thermal conductivity from heat

current autocorrelation function (HCACF)

𝑲 =

𝑗

𝑓𝑗𝒘𝑗 + 1 2

𝑗<𝑘

𝒔𝑗𝑘 𝒈𝑗𝑘 ⋅ 𝒘𝑗 + 𝒘𝑘

Convective term Conduction term

𝝀 = 1 𝑙𝑐𝑈2𝑊

∞

𝑲 𝑢 ⋅ 𝑲(0) 𝑒𝑢

Ensemble average

• 100 ps correlation length averaged over 2 ns (6 such data sets)

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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:

• The thermal conductivity can be obtained from:

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𝐾𝑗 𝑢 ⋅ 𝐾𝑗 0

𝑗=𝑦,𝑧,𝑨 = 𝐵𝑝 exp − 𝑢

𝜐𝑝 + 𝐵𝑏 exp − 𝑢 𝜐𝑏 𝜆𝑗 = 1 𝑙𝑐𝑈2𝑊 (𝐵𝑝𝜐𝑝 + 𝐵𝑏𝜐𝑏)

Lifetime of optical modes Lifetime of acoustic modes

*A.J.H. McGaughey, M. Kaviany, Int. J. Heat Mass Transfer 47 (2004) 1799.

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• In-plane thermal conductivity 562 W/mK

consistent with values reported for AIREBO*

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Pristine SLG

* 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.

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• 6 nm: thermal conductivity reduction due to scattering
• What about the sweet spot at 23 nm ??.

a

Thermal conductivity trends with the periodic heavy atom

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In-Plane HCACF

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• 6nm system: long time oscillatory behavior.
• Oscillatory behavior disappears as period increases.

a

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Out-of-Plane HCACF

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• 6nm: “saw tooth” oscillatory behavior

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Fourier analysis: Out-of-plane vs In-plane

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Fourier analysis: Out-of-plane vs In-plane

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• 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
• bserved maximum in conductivity

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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

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Special Thanks To:

• Coauthors
• Collaborators

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Further question please contact: Stefan Bringuier Email: stefanb@email.arizona.edu Website: www.u.arizona.edu/~stefanb

Questions? Thank you!

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Intentionally Blank

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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

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• In-plane thermal conductivity 562 W/mK

consistent with values reported for AIREBO*

• Optical lifetime: 0.3182 ps
• Acoustic lifetime: 1.783 ps

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Pristine SLG

* 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.

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Fourier analysis of In-Plane HCACF

• 6nm shows in-plane standing wave modes

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Continued: FFT of Out-Of-Plane HCACF

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• 6nm has very distinct characteristic standing wave modes.
• These modes disappear or broaden with increase period

length

HIDDEN SLIDE

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• 6nm thermal conductivity obtain

by integration of HCACF

• Lifetime of phonons contributing

to thermal conductivity

Thermal Conductivity of Heavy Mass (C60)

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Single Vacancy SLG

• No significant change in thermal conductivity
• Some increase in lifetimes:
• Optical lifetime: 0.504 ps
• Acoustic lifetime: 4.9305

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lx = 94.5 nm ly = 109.1 nm

lx/2 ly/2 FFT of HCACF

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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)

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Single C60 Chemisorbed on SLG

• Similar behavior as single vacancy
• Periodically placed C60 does not stay absorbed to SLG using

AIREBO

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lx = 94.5 nm ly = 109.1 nm

lx/2 ly/2

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Related Study (Nick Swinteck*)

• Graphene strip with “1D

nanobutton”

• Vary mass and to examine

effect of resaonence modes

• Distinctive plateau as

increase in mass?

• Related Talk:

“Coherent thermal phonons in Si-Ge nanoscale phononic crystals” by N. Swinteck et al. given May 27th.

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a

2 ⋅ 𝑛𝑑𝑏𝑠𝑐𝑝𝑜 3 ⋅ 𝑛𝑑𝑏𝑠𝑐𝑝𝑜 𝑛𝑑𝑏𝑠𝑐𝑝𝑜 4 ⋅ 𝑛𝑑𝑏𝑠𝑐𝑝𝑜

• Norm. HCACF

Number of timstep

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Continued: FFT of HCACF

• Low frequency shifts as mass increases
• Possible coupling between propagating phonons and resonance.
• Tailor bandstructure – Hybridization of bands

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Resonant shift

Intensity (a.u.) Frequency

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Continued: Power Spectrum

• Fourier transform of velocity autocorrelation gives the accessed

phonon modes, i.e. PDOS

• No spatial component (i.e. wave vector dependence)

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𝑕 𝜕 = 𝑤 𝑢 ⋅ 𝑤 0 𝑓𝑗𝜕𝑢 𝑒𝑢