Percolation thresholds of 3D all-sided percolation clusters in non-cubic domains

Abstract

Abstract. The critical 3D all-sided percolation clusters in aL×L×L and aL×aL×L threedimensional domains with a side length L and an aspect ratio a obtained from continuous percolation problem were analysed in this paper. The simulations of continuous percolation were performed in parallelepiped domains starting from a = 1 and ending at a = 10 using the Monte Carlo algorithm. The resulting percolation thresholds for the simulated domains and percolation clusters as well as variability of number of cells in a domain and in a percolation cluster with variation of a were analysed. The obtained results are useful for evaluation of a content of electrically conducting particles in the dielectric matrix of a composite developed for aircraft lightning strike protection purposes.

Chemiresistive and Chemicapacitive Devices Formed via Morphology Control of Electroconductive Bio‐nanocomposites

“…The transition at 30 wt% PAn‐Cl in Figure C is consistent with four‐point probe resistivity measurements (Figure B) that show a similar transition. This data agrees with the literature, as Monte Carlo simulations have indicated that the percolation threshold of polyaniline is > 10 wt% . These transitions are not evident in DI water within which there is a gradual decline in membrane resistance with increasing PAn‐Cl content.…”

Numerical analysis of electrically conductive fillers of composites for aircraft lightning strike protection

“…aspect ratio), material and spatial orientation. To ensure existence of a percolation cluster within the modelled RVEs, it was assumed that for CNT-epoxy composite the content of CNT is of 10%, while for PANI-epoxy composite the content of PANI is of 30% based on previous numerical and experimental results (Katunin, 2016; Katunin et al , 2017a). In both cases, the random distribution of inclusions was simulated.…”

“…In contrast to CNT, the simulations performed for spherical particles of ICPs using the Monte Carlo method returned the values ca. 30–35% (Katunin and Krukiewicz, 2015; Katunin, 2016). Numerous experimental studies focused on validation of these values of ICPs filler content, polyaniline in this case, reveal good coincidence between obtained theoretical and experimental results (Katunin et al , 2017a; Katunin et al , 2017 b).…”

Lightning Strike Protection of Aircraft Composite Structures: Analysis and Comparative Study

“…(see [11,12] for details). The content of PANI was assumed based on numerical simulations using the percolation theory [13] as well as conducted during the manufacturing of specimens [12]. In order to obtain the required mechanical strength and stiffness a carbon fibre reinforcement was impregnated into the obtained polymeric mixture.…”