Is there a ‘Nano’ Revolution in Thermal Management and Energy Conversion?
Advances in Nanostructure basedThermal Interface and Thermoelectric Materials
Sebastian Volz
Laboratoire EM2C UPR CNRS 288, Ecole Centrale ParisThermal Nanosciences Group - [email protected]
EUROTHERM 2012 – Poitiers, France – September 5th 2012
« Nano » wire dConduction
Heat Transfer Laws at Small Scales Deviate from Classical Ones
Ballistic conduction in airKn>>1
L
NEAR FIELD
Radiation When L < the Predominant Photon Wavelength,coupling of Evanescent Surface Waves increases heat flux.
Transition from a regime of propagative waves emitted by charges motions to a direct electrostatic interaction.
STEFAN-BOLTZMANN
European CNRS Network on Thermal Nanosciences and NanoEngineering
ConvectionIf Nu<1, heat conduction in air predominates.If Kn>>1 heat conduction becomes ballistic.
Diffusive to Ballistic transition is well-knownin gases and radiation.
Heat carries in solids are SOUND PARTICLES or PHONONs,the quanta of lattice vibrational energy
i-1 i i+1
a
un=u.expi(kna-wt)
Fij = K.(uj- ui)
Periodic Boundary Conditions:
k = n . 2/L Density of states
E
kst( ) =hωks. nks t( ) +
12
⎛
⎝⎜⎞
⎠⎟
€
∂ω∂k
=aK
mcos
ka
2
⎛
⎝ ⎜
⎞
⎠ ⎟
€
ω =2K
amsin
ka
2
⎛
⎝ ⎜
⎞
⎠ ⎟
k
w
m&&un =−K 2un −un−1 −un+1( )
∂ω∂k
=aK
m
Acoustics: Coherent Phonons
Continuous limit k=>0
k
w
ϕ = Cωvω .Λω dω0
ωmax
∫
Heat Flux: the Phonon Gas
ρ&&u = K '
∂2u
∂x2
Phonons form a GAS of particles to propagate heat !
Knudsen Transport Applies
Phonon Wien’s Wavelength: 3nm (300K) Mean free path: 1-1000nm
p(, , pol, )=1/3 C v
Kn>1: Boundary scattering predominates over diffusive scattering
L
Confinement: Cavity modes appear if L< Wavelength
Periodicity: e ik(L+x)=e ikx
un ~ expi(kna-wt)+ expi(-kna-wt) ~ cos(kna)e-iwt
e ikL=e ika=0
a STEADY WAVE has ZERO group velocity=1/3 C v
The number of phonon modes depends on Dimensionnality
Dimension: Number of States /dk:
=1/3 C v
k-space
1D (wire) D(k) ~ 1
2D (film/SR) D(k ) ~ k
3D (bulk) D(k) ~ k2
At nanoscales, thermal resistance arises from boundaries
At nanoscales, thermal resistance arises from boundaries
The KEY is to understand phonon transfer at the surface and between two
systems
Thermal Resistance is an Ambiguous Concept Relating Equilibrium and Non-Equilibrium Quantities
R= (T1-T2)/Q
N1 N2
Q
Heat Bath T1
HeatBath T2
‘Cheating’Seems
Unavoidable
Atomic Simulations involve dubious Non-Equilibrium Conditions
-Thermostats Parameters
-Equilibrium Temperatures:coupling with heat bath?
NEMD - TRANSIENT
-Thermostat Parameters (weaker)
-’Short time’ non-equilibrium
-Equilibrium Temperatures at each time step?
NEMD - STEADY
Equilibrium Temperature Correlation defines Thermal Resistance
τau
FLUCTUATIONAL THERMODYNAMICS
INTERNAL SCATTERING ACF NEGLECTED (?)
JAP, 108, 094324, 2010
A Flux based Thermal Conductance can be equivalently derived
Q t( ) =
ddt
HL =−1ih
HL ,Hsys⎡⎣
⎤⎦
Q t( ) =12
&ui (t) fij (t) − f ji (t)&uj (t)( )i∈Lj∈D
∑
kB
G ω( )=
1N1
+1N2
⎛
⎝⎜⎞
⎠⎟ΔT ω( )
2
ΔT 2 0( )ΔT ω( ) =
Q ω( )
G ω( )
-Interfacial Thermal Resistance only depends on Interactions between Atoms of both Sub-Systems
-Temperatures involved in the definition of resistance are the Temperatures of the Interacting Atoms
Nanostructures have exceptional thermal conductivities
Carbon Nanotubes2400-3000 W/mK@RT
Silicon Nanowires1-3 W/mK@RT
Nanostructures can be used to taylor thermal conductivity
Thermal Interface Materials: Increase
Thermoelectricity: Decrease
ZT =S2σλ
T
Can Carbon Nanotubes be used as Thermal Interface Materials?
Use Carbon Nanotube Pellets
J
€
σ
€
κ3D =σ
72π
ρ
ρ Sgr
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
2
L2
D
D
L
Isotropy
Isotropic Pellet Thermal Conductivity is promising but….
€
κ3D =σ
144π
ρ
ρ Sgr
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
2
L2
R
Chalopin, Volz, Mingo, Journal of Applied Physics, 105, 084301, (2009) €
κ3D =σ
72π
ρ
ρ Sgr
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
2
L2
D
…Measured Thermal Conductivity is more than disappointing
€
κ3D =σ
144π
ρ
ρ Sgr
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
2
L2
R
Prasher, Hu, Chalopin, Mingo, Lofgreen, Volz, Cleri, Keblinski, Phys. Rev. Lett.,102, 105901, 2009
CNT Orientation is drastically affecting thermal conductivity
Volkov and Zhigilei Phys. Rev. Lett. 104, 215902 (2010)
Use of Hybrid Charges Imposes Isotropy
Bozlar, He, Bai, Chalopin, Mingo and Volz, Advanced Materials, 21, 1, (2009)
Vertically aligned CNTs appears as the optimized option
CNT-Superstrate contact resistance cancels performances
Applying pressure?
Thermal Conductance is increased when applying Pressure
Chalopin, Srivastava, Mingo, Volz, submitted to APL
Transmission shows the opening of inelastic channels when increasing pressure
Harmonic Green Functions
Fluctuations
Anharmonic Green Functions
G =kB T ω( )dω0
ωmax
∫
Introducing a polymer layer at contact reduces thermal resistance
2.5mm2K/W
Introducing Covalent Bonds Should Increase Conductance
HLK5
CNT-HLK5 resistance is three times lower than CNT-PEMA one
RMDPEMA
RMDHLK 5
=RP1 / NP
RH1 / NH
=3→ 6
Ni, LeKhahn, Bai, Divay, Chalopin, Lebarny,, Volz Appl. Phys. Lett. 100, 193118 (2012)
CONCLUSION on Thermal Interface Materials
Ni, LeKhahn, Bai, Divay, Chalopin, Lebarny,, Volz Appl. Phys. Lett. 100, 193118 (2012)
2007
2010
THANK YOUFOR YOUR ATTENTION
Collaborators:
Team: Y. Chalopin (CNRS)T. Antoni (Ass. Prof.)T. Dumitrica (Inv. Prof.)Pdocs:J. OrdonezO. PokropivnyPhDs: Y. Ni, S. Xiong, L. TranchantW. Kassem, J. JaramilloA. Ramière, H. HanB. Latour, J. Soussi
AbroadG. Chen (MIT)H. Ban (Utah U.)C.W. Chang (National Taiwan Uniiversity)B. Kim (U Tokyo)H. Fujita (U Tokyo)H. Kawakatsu (U. Tokyo)Y. Kosevich (Semenov Inst. Moscow)M. Kazan (U Américaine de Beyrouth)B. Rajabpour (U Teheran)Y. Ciumakov (Moldova)
France:N. Mingo (CEA-LITEN)E. Ollier (CEA-LITEN)A. Ziaei (Thales R&T)L. Divay (Thales R&T)P. Cortona (SPMS, Ecole Centrale Paris)H. Dammak (SPMS, Ecole Centrale Paris)J. Bai (SPMS, Ecole Centrale Paris)L. Aigouy (LPM, ESPCI)B. Palpant (LPQM, ENS Cachan)S. Merabia (LPMNC, U Lyon)P. Chantrenne (MATTEIS, U Lyon)D. Lacroix (LEMTA, U Nancy)J. Amrit (LIMSI, U Orsay)B. LePioufle (SATIE, ENS Cachan)D. Fourmy (Centre de Génétique Mol., Gif)K. Termentzidis (LEMTA, Nancy France)
European CNRS NetworkThermal Nanosciences and NanoEngineering
Quantitative Micro and Nano Thermal Imaging and Analysis
10-12 July 2013
Reims, France
GRESPI
Université de Reims-Champagne-Ardenne
http://qmntia2013.univ-reims.fr/
QMNTIA 2013