1. Thermal Multiscale Modeling of Nanoparticle based Materials Sebastian Volz 1, Jean-Jacques Greffet 1 Denis Rochais 2, Gilberto Domingues 2 and Karl Joulain 3 1 Laboratoire d’Energétique Moléculaire et Macroscopique, Combustion, CNRS - Ecole Centrale Paris - France 2 Laboratoire Microstructrures et Comportements CEA/Le Ripault, Monts, France 3 Laboratoire d’Etudes Thermiques Ecole Nationale Supérieure de Mécaniques et d’Aérotechniques Poitiers Nanoscale Energy and Information Processing Device - Workshop

2. 1 – Intro 3- Near field and Clustering 2 – Thermal Conductance Between Two Nanoparticles Content

3. 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

4. Near Field Al 2 O 3 /Water Q.Z. Xue, Physics Letters, 307, 313, 2003 Colloidal solution Uniformely dispersed Nanoparticles INCREASE THERMAL CONDUCTIVITY

5. T1T1 T2T2 L d  wvlength Interaction between 2 Bodies: o Classical Radiation – Far Field L,d >>  o Near-Field Radiation L 10 6 W.m -2.K -1 Not done yet for NPs o Conduction: G CD = /d~10 10 W.m -2.K -1 2-Thermal Conductance between two Particles

6. NP1 NP2 vjvj f ij i j STATISTICAL MECHANICS: WORK done by NP1 on NP2 NP1 NP2 j i j ELECTROMAGNETICS: POWER dissipated in NP2 E inc E loc Modeling

7. 1 NP = 1 DIPOLE – 1 polarisation, 1 Local Field E L Sphere: j j E inc ELEL r2r2 0 p Near-Field

8.  ’’ - Glass Optical Phonon Eigen-frequencies d -6 : dipole-dipole interaction -  ~V => G ~ R 6 -++- Oscillating Dipoles => Field Emission Phonon – Polariton p Physical Mechanism

9. ATOM = MASS POINT 1800K POSITIONS: Beta-cristobalite lattice cell f ij in SILICA : ‘BKS’ POTENTIAL U(r ij )=q i q j  2 /r ij + A ij exp(-B ij.r ij ) - C ij /r ij 6 COULOMBSHORT RANGE VdW and REPULSIVE 60nm1nm Molecular Dynamics

10.  COMPUTE THE NET POWER BETWEEN NP1 and NP2 AT EQUILIBRIUM NP1 NP2 v f ij i j MD Experiment

11. W.K -2 FD THEOREM DISSIPATION FLUX- FORCE MD Output Puech 1986, Barrat 2003

12. Results 1 microW/K NF FF Atom Heat Capacity / Atomic Period x Number of Atoms 3k B x f x N = 3 x 1.38.10 -23 x 3.10 13 x 3000 = 4 10 -6 W/K Near-Field Cluster

13.  pp -E0 Lx Lx+E T1T1 T2T2 pp q 1i q 2i q 3i q 4i i SOLVE T i PROBLEM: G ji 10 -20 to 10 -3 W/K => ITERATIONS 3D Near Field=>Thermal Conductivity Increase Unifomely dispersed NPs

14. Convergence Lx T LYLY LZLZ 1 Week Calculation on 1 CPU 1000 NPs

15. Volume Fraction

16. Aerogels Thermal Modeling Heat ConductionNear-Field Radiation: neglected 10%Volume Fraction < Percolation Thermal Pathes Structure

17. 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)

18. Results 2D structure Df=1.43D structure Df=1.77

19. Scattering of Contact Resistance 50 MD experiments with different NPs contact => 50 R values Random choice of R

20. Effective Thermal Conductivitiy ‘Hot Plate’ experiment

21. Results TemperaturesTemperature Gradients 25000 particles, 2D 50 MD experiments with different NPs contact => 50 R values Random choice of R

22. Conclusion Clusters in Air Air Experiments NumericalNear-Field Clusters in Vacuum

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

24. THANK YOU !