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Description
Polymeric composite materials are among the most researched in the industry because of their excellent performance in several applications that combine the properties of metals or ceramics with the lightness and flexibility of polymers. Percolation theory is relevant in research on these materials because it allows the estimation of the percolation threshold $f_c$, which is the critical volumetric fraction at which phase transition occurs, where certain properties of the filler material begin to dominate those of the polymeric matrix. In this work is proposed an efficient computational model for the estimation of the electrical percolation threshold for spherical conductive particles in 3D composites using the continuum percolation approach, where the particles are dispersed freely in space. The particle distribution method is based on a simple reflex agent that distributes particles by following conditional rules to avoid an overlap between them. Percolation evaluation is performed by pathfinding conduction through the material, considering both the contact and quantum tunnelling conduction mechanisms. The $A$* heuristic algorithm was used owing to its efficiency and capacity to find the shortest paths. Experiments were performed with different particle sizes ranging from 15 to 500 nm, considering a constant maximum tunnelling distance of 10 nm. The obtained results show percolation threshold values of $f_c=0.06$ for the smallest particles and values of $f_c=0.29$ for larger particles, indicating the effect of particle size on the percolation threshold. Similar results have also been reported in other studies
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| Keywords | Percolation threshold, polymeric composites, continuum percolation |
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