Abstract
The electrical percolation of polymer-matrix composites (PMCs) containing hybrid fillers of carbon nanotubes (CNTs) and carbon black (CB) is estimated by studying the connection possibility of the fillers using Monte Carlo simulation. The 3D simulation model of CB-CNT hybrid filler is established, in which CNTs are modeled by slender capped cylinders and CB groups are modeled by hypothetical spheres with interspaces because CB particles are always agglomerated. The observation on the effects of CB and CNT volume fractions and dimensions on the electrical percolation threshold of hybrid filled composites is then carried out. It is found that the composite electrical percolation threshold can be reduced by increasing CNT aspect ratio, as well as increasing the diameter ratio of CB groups to CNTs. And adding CB into CNT composites can decrease the CNT volume needed to convert the composite conductivity, especially when the CNT volume fraction is close to the threshold of PMCs with only CNT filler. Different from previous linear assumption, the nonlinear relation between CB and CNT volume fractions at composite percolation threshold is revealed, which is consistent with the synergistic effect observed in experiments. Based on the nonlinear relation, the estimating equation for the electrical percolation threshold of the PMCs containing CB-CNT hybrid fillers is established.
Highlights
Polymers have been widely used in industrial manufactures, military equipment, and daily life due to their excellent plasticity, lightweight, and low cost
This paper aims to better understand the synergistic effect and systematically study the effecting factors on electrical percolation threshold of Carbon black (CB)-Carbon nanotubes (CNTs) hybrid filler, including CB and CNT volume fractions, aspect ratio of CNTs, and diameter ratio of CB groups to CNTs
The electrical percolation threshold of polymer-matrix composites (PMCs) with hybrid filler system of CNT and CB is studied by Monte Carlo simulation on the connection possibility of the fillers
Summary
Polymers have been widely used in industrial manufactures, military equipment, and daily life due to their excellent plasticity, lightweight, and low cost. Carbon nanotubes (CNTs) have been considered as an ideal reinforcement phase in composites due to their excellent mechanical and physical properties [3,4,5,6] Their high aspect ratio (over 1000) and high conductivity (up to 104 S/cm) enable them to greatly improve the conductivity of polymer-matrix composites (PMCs) with a very low volume fraction [7,8,9]. Carbon black (CB) is one of the most widely used conductive nanoparticles in industrial applications so far and considered as a suitable candidate because of its low cost, good dispersion a dCNT A. ability, and especially synergistic effect with CNTs which can further improve conductivity and other properties of PMCs. Experimental studies have shown the advantages of the synergistic effect of CB. A 3D simulation model for the CB-CNT hybrid filler is set up and a nonlinear law to estimate the percolation threshold is obtained, in which the synergistic effect between CB and CNT volume fractions as well as the effects of geometric dimensions of CB groups and CNTs is taken into account
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