The Effect of Polydispersivity on the Thermal Conductivity of Particulate Thermal Interface Materials

A critical need in developing thermal interface materials (TIMs) is an understanding of the effect of particle/matrix conductivities, volume loading of the particles, the size distribution, and the random arrangement of the particles in the matrix on the homogenized thermal conductivity. Commonly, TIM systems contain random spatial distributions of particles of a polydisperse (usually bimodal) nature. A detailed analysis of the microstructural characteristics that influence the effective thermal conductivity of TIMs is the goal of this paper. Random microstructural arrangements consisting of lognormal size-distributions of alumina particles in silicone matrix were generated using a drop-fall-shake algorithm. The generated microstructures were statistically characterized using the matrix-exclusion probability function. The filler particle volume loading was varied over a range of 40-55 %. For a given filler volume loading, the effect of polydispersivity in the microstructures was captured by varying the standard deviation(s) of the filler particle size distribution function. For each particle arrangement, the effective thermal conductivity of the microstructures was evaluated through numerical simulations using a network model previously developed by the authors. Counter to expectation, increased polydispersivity was observed to increase the effective conductivity up to a volume loading of 50%. However, at a volume loading of 55%, beyond a limiting standard deviation of 0.9, the effective thermal conductivity decreased with increased standard deviation suggesting that the observed effects are a trade-off between resistance to transport through the particles versus transport through the inter-particle matrix gap in a percolation chain

Simulations of near -percolation thermal transport in particulate composites

The effective thermal transport in particulate composites depend, in addition to particle/matrix conductivities and volume loading of the particles, on particle distribution and particle size, and the interfacial thermal resistance between the particles and the matrix. However, the relative contributions of these effects have not been identified in the literature with sufficient clarity owing to a lack of realistic simulations of these systems. In this thesis, a meshless computational procedure based on hierarchical partition of unity field compositions (HPFC) is used to simulate heat transport in three-dimensional microstructures. Applying the HPFC procedure random microstructures of Alumina (kp = 25 W/mK) as well as Aluminum (k p = 250 W/mK) particles in Silicone (k m = 0.2 W/mK) were simulated at 58% filler volume loading. Identically constituted (in % volume loading) particle systems were also characterized using laser-flash technique. The microstructures were statistically characterized using void nearest surface exclusion probability functions. A comparison was made between the experimental measurements, numerical simulations and classical effective medium approximations (CEMA). It is shown that beyond approximately 30% volume loading, the CEMA are inaccurate. The numerical simulation results using the HPFC procedure was very accurate and ranged within 10% of the fifteen experimentally measured values. The HPFC procedure, though accurate, is computationally expensive. A random network model (RNM) that is more efficient is developed in this thesis. The RNM captures the physics of inter-particle interactions in near percolation and allows for random size distributions. Twenty random microstructural arrangements each of Alumina and Silver particles in Silicone and Epoxy matrices were generated and evaluated through both full-field simulations and RNM. In all cases, it is shown that the RNM results are accurate to within 5% of the full-field simulations. The RNM simulations were efficient since they required two orders of magnitude smaller computation time in comparison to the full-field simulation. Furthermore, realistic microstructural RVE\u27s based on the experimental particle size distribution data were generated and simulated using the RNM. The mean thermal conductivities of the RNM simulations matched to within ∼15% of the experiments. Finally, the affect of polydispersivity on the effective thermal transport in particulate composites is elucidated