A three-dimensional Monte Carlo model for electrically conductive polymer matrix composites filled with curved fibers

Electrical Conductivity of Melt Compounded Functionalized Graphene Sheets Filled Polyethyleneterephthalate Composites

“…5 shows the double-logarithmic plot of electrical conductivity of PET/graphene nanocomposites versus (φ-φc), and an "anomalous" critical exponent (4.22) was obtained from the slope of linear fit curve, much larger than the theoretically predicted value (~ 2) for three-dimensional system (Balberg, 1987). To predict the electrical percolation threshold in theory, filler shape must be first considered in view of its strong influence on the electrical properties of composites (Ma & Gao, 2008). However, the electrical percolation threshold cannot be directly related to filler morphology, fortunately, geometrical percolation threshold (pc) provides some insight into the former although cannot be simply identified as it.…”

Monte Carlo simulation for investigating influence of junction and nanofiber properties on electrical conductivity of segregated-network nanocomposites

“…x i , y i , z i , a i 1 , a i 2 , and h i 1 were randomly generated. Note that h i 2 is a dependent variable [24]. Thus, the fiber is defined by six random numbers for a given diameter D and length L. In order to generate random numbers, a multiplicative congruential (MC) random number generator was adopted [26].…”

“…The effect of aspect ratio and critical volume fraction for straight and tortuous fibers of zero width was demonstrated. Ma and Gao in 2008 developed a simple model which took into account both fiber thickness and flexibility [24].…”

Investigation of the Effective Reinforcement Modulus of Carbon Nanotubes in an Epoxy Matrix

“…An exhaustive discussion on the calculation of excluded volume for curved rods is beyond the scope of this work. Remarkable efforts have been reported by Behran and Sastry, 2007, Li and Chou, 2007, Ma and Gao, 2008, nevertheless, these studies are limited by the main assumption of rod shapes. As stated previously, contacts between nanotubes imply a reduction of the stress transfer efficiency of the reinforcement, afterwards the rule of mixtures could be modified by reducing the stress transfer coefficient by the average number of contacts…”