Effects of uniaxial and biaxial orientation on fiber percolation in conductive polymer composites

Abstract

A Monte Carlo simulation was built to estimate the percolation threshold of fibers in a system under different fiber orientations. A 3-D model was built. The orientation effect was modeled by introducing a degree of alignment in the randomly generated fibers via appropriate mathematical relationships and various degrees of uniaxial strain were applied. The critical volume fraction was then analyzed in both normal direction (through-plane) and parallel direction (in-plane) to that of the cross-section plane. The effect of uniaxial orientation was modeled by measuring the through-plane percolation threshold under tensile strain. The effect of biaxial orientation was modeled by measuring the in-plane percolation threshold under compressive strain. The results indicated that the introduction of fiber alignment changed both through-plane and in-plane threshold values, albeit with different trends. With the introduction of slight uniaxial orientation, the through-plane percolation threshold reached a minimum value and further uniaxial orientation gave it a rise, while the in-plane threshold continuously increased with an increase in uniaxial orientation. On the other hand, under compression, an increase in biaxial orientation resulted in a monotonic increase in the through-plane threshold, whereas the in-plane threshold showed a minimal behavior before its rise. The results of this study indicate that the percolation threshold is minimized when fibers are slightly oriented (both uniaxial and biaxial) rather than being completely isotropic, and therefore, generation of conductive paths in a particular direction of interest can be induced via a proper choice of applied orientation with a lower critical concentration, thereby potentially reducing the filler loading. One particular implication of this work is modeling the percolation threshold in cellular polymer composites where local stresses are applied on the fillers around the cell walls during bubble growth.