Comparative Evaluation of Algorithms for Achieving Ultrapacked Thermal Greases: Microstructural Models and Effective Behavior

Abstract

In this work, we develop and evaluate algorithms for generating ultrapacked microstructures of particles. Simulated microstructures reported in the literature rarely contain particle volume fractions greater than 60%. However, commercially available thermal greases appear to achieve volume fractions in the range of 60–80%. Therefore, to analyze the effectiveness of commercially available particle-filled thermal interface materials (TIM), there is a need to develop algorithms capable of generating ultrapacked microstructures. The particle packing problem is initially posed as a nonlinear programming problem, and formal optimization algorithms are applied to generate microstructures that are maximally packed. The packing efficiency in the simulated microstructure is dependent on the number of particles in the simulation cell; however, as the number of particles increases, the packing simulation is computationally expensive. Here, the computational time to generate microstructures with large number of particles is systematically evaluated first using optimization algorithms. The algorithms include the penalty function methods, best-in-class sequential quadratic programming method, matrix-less conjugate gradient method as well as the augmented Lagrangian method. Heuristic algorithms are next evaluated to achieve computationally efficient packing. The evaluated heuristic algorithms are mainly based on the drop-fall-shake (DFS) method, but modified to more effectively simulate the mixing process in commercial planetary mixers. With the developed procedures, representative volume elements (RVE) with volume fraction as high as 74% are demonstrated. The simulated microstructures are analyzed using our previously developed random network model to estimate the effective thermal and mechanical behavior given a particle arrangement.