Abstract
Despite the numerous experimented works on the conductivity of carbon black (CB) polymer nanocomposites (PCBs), the modeling methods remain imperfect and require further investigation. Herein, a simple and applicable model for estimating the PCB electrical conductivity is proposed by measurable and meaningful features of CB nanoparticles, interphase, network and tunnelling zone among nearby CBs. Our model also incorporates the significant terms such as the percolation onset, polymer – CB interfacial tension, the percentage of CB and interphase contributing to the network and interphase conductivity (σi). Many experimented conductivities of real PCBs and parametric checkups are used to verify the suggested model. The thickest interphase (t = 20 nm) with the highest conductivity (σi = 400 S/m) yields the conductivity of 7 S/m, while the composite is insulated by the thinnest interphase with the poorest conductivity (t = 3 nm and σi < 250 S/m). Also, the slimmest tunnels (λ = 1 nm) and their poorest polymer resistivity (p = 30 Ω.m) raise the conductivity to 2.2 S/m. However, bigger tunnels (λ > 5.5 nm) highly weaken the conductivity to 0.1 S/m. Accordingly, the characteristics of interphase and tunnels largely handle the conductivity of PCBs.
Data availability
The data that support the findings of this study are available on request from corresponding authors.
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Y.Z. and N.G. wrote the main manuscript text. J-H.C. and K.Y.R. revised the paper.
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Zare, Y., Gharib, N., Choi, JH. et al. Modeling of conductivity for carbon black nanocomposites incorporating network concentration, interphase conductivity and tunneling dimensions. Sci Rep (2026). https://doi.org/10.1038/s41598-026-38008-6
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DOI: https://doi.org/10.1038/s41598-026-38008-6
