Research Papers: Micro/Nanoscale Heat Transfer

Combined Microstructure and Heat Transfer Modeling of Carbon Nanotube Thermal Interface Materials1

[+] Author and Article Information
Sridhar Sadasivam, Stephen L. Hodson

Department of Mechanical Engineering
and Birck Nanotechnology Center,
Purdue University,
West Lafayette, IN 47907

Matthew R. Maschmann

Department of Mechanical and Aerospace Engineering,
University of Missouri,
Columbia, MO 65211

Timothy S. Fisher

Department of Mechanical Engineering
and Birck Nanotechnology Center,
Purdue University,
West Lafayette, IN 47907
e-mail: tsfisher@purdue.edu

2Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received April 22, 2015; final manuscript received August 24, 2015; published online January 12, 2016. Assoc. Editor: Alan McGaughey.

J. Heat Transfer 138(4), 042402 (Jan 12, 2016) (12 pages) Paper No: HT-15-1292; doi: 10.1115/1.4032174 History: Received April 22, 2015; Revised August 24, 2015

A microstructure-sensitive thermomechanical simulation framework is developed to predict the mechanical and heat transfer properties of vertically aligned CNT (VACNT) arrays used as thermal interface materials (TIMs). The model addresses the gap between atomistic thermal transport simulations of individual CNTs (carbon nanotubes) and experimental measurements of thermal resistance of CNT arrays at mesoscopic length scales. Energy minimization is performed using a bead–spring coarse-grain model to obtain the microstructure of the CNT array as a function of the applied load. The microstructures obtained from the coarse-grain simulations are used as inputs to a finite volume solver that solves one-dimensional and three-dimensional Fourier heat conduction in the CNTs and filler matrix, respectively. Predictions from the finite volume solver are fitted to experimental data on the total thermal resistance of CNT arrays to obtain an individual CNT thermal conductivity of 12 W m−1 K−1 and CNT–substrate contact conductance of 7 × 107 W m−2 K−1. The results also indicate that the thermal resistance of the CNT array shows a weak dependence on the CNT–CNT contact resistance. Embedding the CNT array in wax is found to reduce the total thermal resistance of the array by almost 50%, and the pressure dependence of thermal resistance nearly vanishes when a matrix material is introduced. Detailed microstructural information such as the topology of CNT–substrate contacts and the pressure dependence of CNT–opposing substrate contact area are also reported.

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Fig. 1

Schematic representation of the modeling approach used to develop a microstructure-dependent heat transfer model of VACNT TIMs

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Fig. 2

Schematic representation of the coarse-grain model

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Fig. 3

Schematic of CNTs embedded in a filler matrix. One-dimensional discretization is performed along the length of the CNTs and three-dimensional rectangular cells are used in the discretization of the filler matrix.

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Fig. 4

(a) Experimental load–displacement curve obtained from nanoindentation of a 10 μm tall CNT array. (b) Simulated stress–strain curves obtained from coarse-grain mechanics simulations.

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Fig. 5

(a) Experimental load–displacement curve of a 10 μm tall array with unloading at indentation depths of 2 and 3 μm. (b) Unloading stress–strain curve obtained from coarse-grain simulations of 10 μm tall arrays (results averaged over four random realizations).

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Fig. 6

Energy-relaxed configurations of a 5 μm tall CNT array containing 400 CNTs in the simulation box. (a) No load (point A in Fig. 4(b)), (b) strain = 0.014, load = 75 kPa (point B in Fig. 4(b)), (c) strain = 0.045, load = 160 kPa (point C in Fig. 4(b)), (d) strain = 0.11, load = 122 kPa (point D in Fig. 4(b)), and (e) strain = 0.14, load = 119 kPa (point E in Fig. 4(b)).

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Fig. 7

Cumulative distribution of the number of consecutive bead–bead contacts among CNT pairs having at least one van der Waals contact

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Fig. 8

(a) Total thermal resistance of 3, 5, and 10 μm tall CNT arrays compared with experimental measurements. (b) Diffusive thermal resistance of 3, 5, and 10 μm tall CNT arrays.

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Fig. 9

(a) Dependence of total thermal resistance of a 5 μm tall CNT array on the CNT–CNT contact conductance. (b) Sensitivity of total thermal interface resistance to CNT–CNT contact conductance (Gcc), CNT thermal conductivity (kc), and CNT–substrate contact conductance (Gcs).

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Fig. 10

(a) Variation of mean CNT tip inclination with applied load. (b) Fraction of CNTs in contact with the substrate as function of applied load. (c) Variation of CNT–substrate contact area with applied load. All the results in this figure are averaged over four random initial realizations of the CNT array.

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Fig. 11

Effect of paraffin wax on the total thermal resistance of a 10 μm tall CNT array

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Fig. 12

Convergence of mechanics and thermal results of a 3 μm tall array with respect to simulation parameters ro and N. (a) Stress–strain curves. (b) Pressure dependence of total thermal resistance.

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Fig. 13

Convergence of mechanics and thermal results of a 5 μm tall array with respect to simulation parameters ro and N. (a) Stress–strain curves. (b) Pressure dependence of total thermal resistance.



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