NanoEngineering Group
Extraordinary Heat Transfer at Nanoscale
Gang Chen
Department of Mechanical EngineeringMassachusetts Institute of Technology
Cambridge, MA 02139
Email: [email protected]://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
