Abstract
The electrical conductivity of extrinsically conducting polymer composite systems passes through a transition state known as percolation threshold. A discussion has been made on how different Sigmoidal models (S-models), such as Sigmoidal–Boltzmann (SB), Sigmoidal–Dose Response (SD), Sigmoidal–Hill (SH), Sigmoidal–Logistic (SL), and Sigmoidal–Logistic-1 (SL-1), can be applied to predict the percolation threshold of electrical conductivity for ethylene vinyl acetate copolymer (EVA) and acrylonitrile butadiene copolymer (NBR) conducting composite systems filled with different carbon fillers. An interesting finding that comes from these observations is that the percolation threshold for electrical conductivity determined by SB and SD models are similar, whereas, the other models give different result when estimated for a particular composite system. This similarity and discrepancy in the results of percolation threshold have been discussed by considering the strength, weakness, and limitation of the models. The percolation threshold value for the composites has also been determined using the classical percolation theory and compared with the sigmoidal models. Moreover, to check the universal applicability, these Sigmoidal models have also been tested on results from some published literature. Finally, it is revealed that, except SL-1 model, the remaining models can successfully be used to determine the percolation threshold of electrical conductivity for extrinsically conductive polymer composites.
Highlights
Most of the polymers are inherently insulating in nature
We have investigated the percolation threshold of electrical conductivity by applying different Sigmoidal models such as Sigmoidal–Boltzmann (SB), Sigmoidal–Dose response (SD), Sigmoidal–Hill (SH), Sigmoidal–Logistic (SL), and Sigmoidal–Logistic-1 (SL-1)
The physical characteristics of conductex and printex carbon blacks are reported in Table S1, whereas short carbon fiber has been reported in Table S2 and some discussion of their physical characteristics are made in the Curing agent, Dicumile peroxide (DCP), MP = 80 ◦ C and a purity of 98%, was supplied by Aldrich chemical company, St
Summary
Most of the polymers are inherently insulating in nature. these insulating polymers can be made semi-conducting/conducting by the inclusion of a certain amount of conducting fillers. A percolation model has been developed by Janzen based on the concept of mean number of contacts between the filler particles [12] Other than these models, many approaches have been made to explain the percolation behavior of conducting polymer composite systems [13,14,15,16,17,18]. Many approaches have been made to explain the percolation behavior of conducting polymer composite systems [13,14,15,16,17,18] No such model alone predicts the percolation threshold of electrical conductivity when one considers all of the experimental results of conductivity. Their applicability to determine the percolation threshold value has been tested with the conductivity data of some published literature
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