Defining interfacial thermal resistance between carbon nanotube and polymer with molecular dynamics method

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1 Defining interfacial thermal resistance between carbon nanotube and polymer with molecular dynamics method Yuxiang i, Yann Chalopin, Hung Le Kanh 2, Pierre Lebarny 2, Laurent Divay 2, Sebastian Volz : Laboratoire d Energétique Moléculaire et Macroscopique, Combustion, UP CS 288,Ecole Centrale Paris, Grande Voie des Vignes, Chatenay Malabry, France 2: Thales esearch and Technology,, Avenue Augustin Fresnel F-9767 Palaiseau Cedex, France Eurotherm seminar 9 Microscale heat transfer III Poitiers, France August 29-3, 20

2 Optimizing heat path between surfaces with thermal interface materials (TIMs) Used to lower the thermal resistance between contact areas AI TIM To fill the small air voids between the device being cooled and the heat sink Thermal conductivity of an isolated CT is up to ~3000 W/mK, and hundreds of W/mK were measured on aligned CTs samples. [,2] VACTs are considered as effective TIMs. [] Kim, P.; Shi, L.; Majumdar, A.; McEuen, P. L.Phys. ev.lett. ; 200, 87, [2] Hone, J.et al. J. Appl. Phys. Lett., 2000, 77(5), 666 vertically aligned carbon nanotbues (VACTs)

3 Thermal contact resistance decreased with PEMA bonding Si Cu Dry thermal contact resistance: 40 to 70 mm 2 K/W Cu Cu PEMA Si Si H. Le Khanh et al. THEMIIC 200 Thermal contact resistance with PEMA bonding: 2.5 to 2 mm 2 K/W The CT length dependent measurements allow the extraction of contact resistance

4 esistance between CT and polymer is the predominant factor to the total contact resistance Cu Polymer Si The tail group of PEMA, -CH 3, is an inert group, it could not have strong interaction with CT PEMA HLK5 introducing CT- Polymer covalent bond Tg=60 Tg=8

5 Defining interfacial thermal resistance with equilibrium molecular dynamics simulation. The thermal conductance G between two materials with temperature T and T2 is related to the net heat flux Q and the temperature difference ΔT= T-T2: Q= GΔT () 2. The substraction between the energy conservation equations of both bodies : T t = K B GΔT T t = K 2 B 2 GΔT (2) 3. Yields the equation of the temperature difference ΔT: ΔT t = K B ( + 2 ) GΔT (3) 4. According to linear response theory, the heat flux is a convolution integration product time between the conductance and the temperature difference : ΔT t K B = K 5. If this expression is multiplied by T(0) 0 2 and averaged in the phase ensemble, ΔT 0 the thermal resistance appears as : A. ajabpour, S. Volz. Journal of Applied Physics, 08, (200) B + 2 t 0 ( t' ) ΔT ( t' ) dt' G t ( 0) ΔT ( t) ( ) dt + = ΔT 2 (4) (5)

6 Defining interfacial thermal resistance with equilibrium molecular dynamics simulation: Simulation parameters Equilibrium molecular dynamics (EMD) simulations are conducted using the LAMMPS software package. Potentials: C-C and C-H : Adaptive intermolecular reactive empirical bond order (AIEBO) C-, C-O and C=O: dreiding potential Periodic boundary conditions in x, y and z directions. polymer VE ensemble at 300 K, time step: 0.5 fs z y million time steps of system relaxation, another million time steps were considered to compute the temperatures in both subsystems. x CT (5,5), length 4.87 nm

7 MD Visualization CT-PEMA CT-HLK5

8 Defining interfacial thermal resistance with equilibrium molecular dynamics simulation ormalized ACF of the temperature difference ΔT(t) and the integral of the ACF vs the simulation time decreased by a factor of 3 CT PEMA CT HLK5 Thermal esistance (GK/W) Thermal Conductance (nw/k)

9 Discussion: what is the link between cnt-one polymer chain and total cnt-polymer? CT/PEMA P =2 CT/HLK5 H =4 Thermal interface resistance between CT and one unit polymer chain umber of CT-Polymer contact: H P 2 Total thermal interface resistance P P P between CT and Polymer ( P, H ): = = 3 6 H H H P = = / / H 3

10 Experimental data match the range of MD prediction MD prediction P H = 3 6 Experimental data mesured by thermal impedancementer Experimental data: P H = = 4.36 Interface contact resistance further decreased from.5 to 0.34 mm 2 K/W

11 Conclusions Interface thermal resistance between polymer and CT could be calculated from EMD by equilibrium fluctuations of temperature difference. It is a simple and effective way which can yield key rules to control the exchanged heat flux. The EMD prediction for the resistance decrease of CT-Polymer matches the experimental data. The thermal resistance between the loose end of CTs and polymer is the main contribution to the total contact resistance. Designing polymers with covalent bond to CT is an effective way to lower the contact resistance.

12 Thank you for your attention! Yuxiang i, Yann Chalopin, Hung Le Kanh, Pierre Lebarny, Laurent Divay, Sebastian Volz Eurotherm seminar 9 Microscale heat transfer III Poitiers, France on August 29-3, 20