NanoEngineering Group

Extraordinary Heat Transfer at Nanoscale

Gang Chen

Department of Mechanical EngineeringMassachusetts Institute of Technology

Cambridge, MA 02139

Email: gchen2@mit.eduhttp://web.mit.edu/nanoengineering

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Thermal Conductivity of Matter

10-110-2 100 101 102 103

W/m.K

Electrical Conductivity : 10-14 ~ 108 S/m

Thermal Conductivity : 10-2 ~ 103 W/m.K

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Low Thermal Conductivity of Nanostructures

Superlattices Nanowires Nanocomposites

Poudel et al., Science, 320, 634, 2008

Necessary Conditions for Strong Phonon Size Effects:

Λ (bulk) > d

Phonon Mean Free Path

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Results from First Principle Calculations

Esfarjani et al., Phys. Rev. B 84, 085204, 2011. Shiomi et al., Phys. Rev. B84, 104302, 2011.Tian et al., Appl. Phys. Lett.. 99, 053122, 2011.Zebarjadi et al., Energy & Env. Sci, 2012.

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First Principle (DFT)calculations

Anharmonic Interatomic force constants

Molecular dynamics simulations

e-band, e-DOS

ph-band, ph-DOS

Thermal conductivity + mean free path (mode-dependent)

∑∑∑∑ Χ+Ψ+Φ+Π+=ijkl

lkjiijklijk

kjiijkij

jiiji

ii uuuuuuuuuuVV!4

1!3

1!2

10

ψ∂∂ψ Ht

i =h

Vdtdm i

i −∇=2

2r

Scattering calculation

Alloy effects

kk’

k’’ k’

ρπ 22 iVfW fih

=→

k’’k

First Principle Simulation

•Density functional perturbation theory•Real space approach

Seebeck,e-conductivity

D. Brodio et al., PRB, 80 (2009)

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Pump-probe System for Thermal Conductivity Measurement

Schmidt et al. Review of Scientific Instruments, 79, 114902, 2008.

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Experimental Results on Si

D=55μm

D=15μm

D=30μm

102101

102

103

Temperature (K)

Ther

mal

con

duct

ivity

(W/m

K)

LiteratureTTR, D=55 μmTTR, D=30 μmTTR, D=15 μm

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Effect of Quasi-ballistic Transport

BallisticPhonon radiation

DiffusiveFourier’s Law

DD

~B

D

q Dq

ω

ω ωΛBallistic heat flux is less than Fourier law prediction

Chen, J. Heat Transf., 1996

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Comparison with Experiments

Contribution by phonons with MFP > 55 μm

Contribution by MFP > 15 μm

D=55μm

D=15μm

D=30μm

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Thermal Conductivity Spectroscopy

Minnich et al., PRL, 2011

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Improving Thermal Conductivity of Polymers

• Thermal conductivity of polymers ~ 0.2 W/mK• Various fillers and composites are being developed

to improve polymer thermal conductivity• Carbon nanotubes + polymer nanocomposites

Choi, JAP, 2003Kim et al., PRL, 2001

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Polymer Structure

Natural

What is the thermal conductivity of an individual polymer chain?

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Theoretical Foundation

• Even in strongly nonlinear one-dimensional system, equipartition theorem is not valid, initial states reappearing.

Fermi, Pasta, and Ulam, Studies of Nonlinear Problems. I,  (1955).

Remarkable Little Discovery!

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Divergent Thermal Conductivity

Henry and Chen, Physical Review Letters, 101, 235502 , 2008.

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Ultra-Drawn Polyethylene Nanofiber

• Shen et al, Nature Nanotechnology, 2010.

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Thermal Conductivity Measurement

nanofiber

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Thermal Conductivity

Thermal Conductivity

K= 105 W/m.K

Shen et al, Nature Nanotechnology, 2010.

Nature 464, 328 (18 March 2009)

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NanofluidsNanofluids

Lee and Choi (1998)

影响半导体异质结构光催化效率的因素：Putnam et al.(2006)

Eapen et al (2007)

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Potential MechanismsPotential Mechanisms

• Brownian motion• Clustering• Atomic layering• Ballistic transport

……E

nhan

cem

ent (

%)

Freezing Experiment

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Potential MechanismsPotential Mechanisms

J. Gao et al. Nano Letters, 4128, 2009.

• Brownian motion• Clustering• Atomic layering• Ballistic transport

……

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MicrostructuresMicrostructures

Hexandecane

Hog Fat

Before Freezing After Freezing

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Synthesis of Graphite Suspensions

Sulfuric acidintercalation

Microwaveexpansion

Ultrasonicdispersion

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Amphiphilic Graphite SuspensionsWater Water

PAO PAO

Before

Before

After

After

Graphite in PAO

Graphite in Ethylene Glycol

Graphite in Water

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High Thermal ConductivityHigh Thermal Conductivity

0.2 0.4 0.6 0.8 1.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Ther

aml c

ondu

ctiv

ity (W

/m.K

)

% Volume Fraction

PAO Ethylene glycol DI water

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Kink in Thermal ConductivityDependence on Volume Fraction

0 0.1 0.2 0.3 0.40

10

20

30

40

50

60

Volume fraction %

Enh

ance

men

t %

c

25 minutes sonication

30 minutes sonication

Different sonication time

The kink behavior occurs at 0.07%

R.T. Zheng et al., Nano Letters, 2012.

Electrical Percolation at 0.07%

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Microstructures

0.03% volume fraction 0.1% volume fraction

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AC Impedance Spectroscopy

R1

C1

R2

C2

circuit model

0 0.5 1 1.5 2 2.5x 106

0

4

8

12 x 105

Z'

-Z"

a

0.1%0.15%

0.07%

0.05%

Intra-cluster transport

Inter-clustertransport

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Transport Picture

0 0.1 0.2 0.3 0.4 0.5 0.610-7

10-6

10-5

10-4

10-3

10-2

Inte

r-clu

ster

con

duct

ance

(S)

Volume fraction %

0 0.1 0.2 0.3 0.4 0.5 0.60

0.5

1

1.5

2

2.5

3

3.5

4

4.5x 10-8

Inte

r-cl

uste

r cap

acita

nce

(F)

c

0 0.1 0.2 0.3 0.4 0.5 0.610-5

10-4

10-3

Intra

-clu

ster

con

duct

ance

(S)

Volume fraction %0 0.1 0.2 0.3 0.4 0.5 0.6

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2x 10-9

Intra

-clu

ster

cap

acita

nce

(F)

bIntra‐cluster response

Inter‐cluster response

R.T. Zheng et al., Nano Letters, 2012.J.J. Wang et al., Nanotoday, in press

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Blackbody radiation is the maximum of thermal radiation?

Planck’s Blackbody Radiation Law“Throughout the following … the linear dimensions of all parts of space considered, as well as radii of curvature of all surfaces … are large compared with the wavelengths of the rays considered

– M. Planck, “The theory of heat radiation” (1906)

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Tunneling of Evanescent Waves at Near Field

θcrincidentreflected

transmitted

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Contributions from Surface Waves

ε1 ε2= 1

Surface wave

Polar material

+_

+_

+_

+_

+_

+_

+_

Energy density in the vicinity of

a half-plane of BN.

ωFree Space

k

Surface Modes

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Radiation Heat Transfer between Two Parallel Glass Plates

10-2 10-1 100 101 102100

101

102

103

104

105

Gap Size (μm)

Hea

t Tra

nsfe

r Coe

ffici

ent (

W/m

2 K)

Near-field

Blackbody limit

Th = 323 KTC = 297 K

10 20 30 400

10

20

30

40

50

60

70

Wavelength (μm)

Spec

tral

Flu

x (W

/m2 μ

m)

Near-field (gap = 1 μm)Far-fieldBlackbody

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Bi-material AFM Cantilevers

150 160 170 180 190 200 210-7

-6

-5

-4

-3

-2

-1

Absorbed Power (μW)

Cant

ileve

r Def

lect

ion

Sig

nal (

V)

experimental datay= -0.0928x+12.474

29.5 30 30.5 31 31.5 320.5

1

1.5

2

2.5

3

Temperature (oC)

Cant

ileve

r Def

lect

ion

Sign

al (V

)

experimental datay=-0.8388x+27.5179

~ 10-100 pWSensitivity

10-5 K Sensitivity

(Barnes et al., Nature, 1994)

(Gimzewski et al., CPL, 1994)

IR detector : (Datskos et al., APL, 1996)

(Varesi et al., APL, 1997)

SThM : (Nakabeppu et al., APL, 1995)

S. Shen et al., APL, 92, 063509, 2008.

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PSD

AFM-based Experiment

PSD

SiN/Au cantilever

Silica sphere

SiN/Au cantilever

Silica sphere

100 μm

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Approximating spheres by flat platesR

Near-field radiation between a sphere and a plate(Proximity Force Theorem)

( ) ( )

22

2

dBπRd

dsshπRdGds

≅

≅ ∫∞

=

Effective areaHeat transfer

coefficient for plate-plate

d

Proximity Force Theorem

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Nanoscale Thermal Radiation beyond Planck’s Law

• Shen et al, Nano Letters, 2009. Nature 460, 934 (20 August 2009)

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Application Examples

Kraemer et al., Nature Materials, 2011

10-2

10-1

100

101 G

10521

Freezing RemeltingEl

ectr

ical

Con

duct

ivity

(S/c

m)

Recycle Times

Zheng, et al., Nature Communication, 2011

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ACKNOWLEDGMENTS• Current Members • Collaborators (Partial List)

C.M. Ho, M.S. Dresselhaus, K. NelsonZ.F. Ren, X. Zhang

• Past Members (Partial List)Z. ChenM. ChiesaC. Dames D. Borca-TasciucT. Borca-TasciucH.P. FengA. GuzmanF. HashemiC. HinC.T. HarrisQ. HaoA. HenryL. HuH. LeeA. JacquotM.S. JengR. Kumar

Sponsors: DOE (BES, ARPA-E, EERE, EFRC), AFOSR, NSF, Industry

ThermoelectricsS.Y. Lee, K. McEnaney, B. Liao, J. MondozaG. Ni, L. Weinstein, Dr. M. Zarbajardi

Photon Management and PVM. Branham, V. Chiloyan, W.-C. Hsu, D. Kramer, P. Sambegoro, J. Tong, Dr. S. Boriskina, Dr. B. Burg, Dr. S.E. Han, Dr. A. Mavrokefalos, Dr. S. Yerci

Soft MaterialsA. Bajpayee, S.H. Kim, Z.C. Liu, L. Ma, J. Wang, J. Wang, Dr. T.F. Zeng

Phonon TransportK. Collins, M. Luckyanova, L.P. Zeng, Z.T. Tian, Dr. K. Esfarjani, Dr. J. Garg, Dr. K. Ihara, Dr. Y.J. Hu

A. MinnichA. MutoW.L. Liu T.F. LuoA.NarayanaswamyA. SchmidtJ. ShiomiD. SongS. ShenD. Vashaee S.G. Volz B. YangR.G. YaoD.-J.Yao