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Thermal Multiscale Modeling of Nanoparticle
based Materials
Sebastian Volz1, Jean-Jacques Greffet1 Denis
Rochais2, Gilberto Domingues2 and Karl Joulain3
1Laboratoire dEnergétique Moléculaire et
Macroscopique, Combustion, CNRS - Ecole Centrale
Paris - France 2Laboratoire Microstructrures et
Comportements CEA/Le Ripault, Monts,
France 3Laboratoire dEtudes Thermiques Ecole
Nationale Supérieure de Mécaniques et
dAérotechniques Poitiers
Nanoscale Energy and Information Processing
Device - Workshop
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Content
1 Intro
2 Thermal Conductance Between Two Nanoparticles
3- Near field and Clustering
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Clustering
DECREASE THERMAL CONDUCTIVITY Aerogels SiO2
amorphous particle 10nm in diameter Porosity
90, open paths 100nm-1micron 15 mW/mK in
ambient and 5 mW/mK at primary vacuum
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Near Field
INCREASE THERMAL CONDUCTIVITY
Colloidal solution
Uniformely dispersed Nanoparticles
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2-Thermal Conductance between two Particles
d
T1
T2
L wvlength
L
Interaction between 2 Bodies o Classical
Radiation Far Field L,d gtgtL o Near-Field
Radiation LltdltL GNFgt106 W.m-2.K-1 Not done
yet for NPs o Conduction GCDl/d1010
W.m-2.K-1
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Modeling
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Near-Field
1 NP 1 DIPOLE 1 polarisation, 1 Local Field EL
Sphere
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Physical Mechanism
d-6 dipole-dipole interaction - aV gt G R6
p
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Molecular Dynamics
ATOM MASS POINT
fij in SILICA BKS POTENTIAL U(rij)qiqje2/r
ij Aij exp(-Bij.rij) - Cij/rij6
COULOMB SHORT RANGE VdW and REPULSIVE
60nm 1nm
POSITIONS Beta-cristobalite lattice cell
1800K
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MD Experiment
? COMPUTE THE NET POWER BETWEEN NP1 and NP2 AT
EQUILIBRIUM
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MD Output
FLUX- FORCE
DISSIPATION
W.K-2
FD THEOREM
Puech 1986, Barrat 2003
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Results
Atom Heat Capacity / Atomic Period x Number of
Atoms 3kB x f x N 3 x 1.38.10-23 x 3.1013 x
3000 4 10-6 W/K
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Near FieldgtThermal Conductivity Increase
Unifomely dispersed NPs
q2i
q4i
i
q1i
3D
q3i
PROBLEM Gji 10-20 to 10-3 W/K gt ITERATIONS
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Convergence
1 Week Calculation on 1 CPU 1000 NPs
T
Lx
LY
Lx
LZ
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Volume Fraction
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Aerogels Thermal Modeling
Heat Conduction
Near-Field Radiation neglected
10Volume Fraction lt Percolation Thermal Pathes
ltgt Structure
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Aerogel Skeleton
Aggregates with realistic fractal dimension
1.8 Kolb-Botet-Jullien Model (PRL, 51, 1123,
1983) Particles with inital random
positions Particles move one by one Make a
cluster with neighbours The clusters move as
particle (no rotation)
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Results
2D structure Df1.4 3D structure Df1.77
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Scattering of Contact Resistance
50 MD experiments with different NPs contact gt
50 R values Random choice of R
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Effective Thermal Conductivitiy
Hot Plate experiment
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Results
25000 particles, 2D
50 MD experiments with different NPs contact gt
50 R values Random choice of R
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Conclusion
Clusters in Air
Experiments
Numerical
Near-Field
Clusters in Vacuum
Air
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Conclusion

• o Modeling/Experiments agree in Aerogels (no NF
  paths)
• o Uniform NPs Dist. early NF percolation gt
  many percolation paths
• Application Heat Sink/Dirty Material
• Coupling clustering and Near-Field
• Fractal dimension and Thermal Conductivity

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THANK YOU !