Estimation of contact area among carbon black nanoparticles in composites by tunneling properties, interphase depth and contact number

The contact area (S) among the carbon black (CB) nanoparticles directly and significantly manipulates the conductivity of composites, but it is an unknown and inexact factor. In this article, two conductivity models for polymer CB nanocomposite (PCB) are suggested and verified by at least five conductivity points per composite system at the filler fraction range from 0 to 20 vol.% and 5% quantitative error bound in the calculations. Besides, these novel models are joined to express an applicable equation for the S by tunneling properties, CB size, interphase depth (t), network fraction, contact number (m), interfacial tension (γ_pf), and percolation onset ([Formula: see text]). The impacts of all factors on the S are plotted and validated. Bigger interphase and more m expand the S. t = 20 nm and m = 100 grow the S to 16*10⁵ nm², while the shortest interphase (t < 10 nm) produces S = 0. Also, higher tunneling diameter (d) with shorter tunnels raise the S. d = 40 nm and tunneling distance (λ) of 1 nm expand the S to 19*10⁵ nm², but d < 13 nm or λ = 10 nm cannot produce the contact area (S = 0). This novel equation is applicable to expand the contact area, which reduces the tunneling resistance and optimizes the charge transfer in PCBs.