Two-Step Simulating of Conductivity for Carbon Black Polymer Nanocomposites by Tunneling Distance and Interphase Aspects Publisher



Abdollahi F ; Mohammadi M ; Naqvi M ; Arefian M ; Zare Y
Source: Materials and Design Published:2026

Abstract

This study proposes a two-step modeling framework to predict the conductivity of composites filled with carbon black nanoparticles (PCB). In the first step, carbon black (CB) nanoparticles together with their surrounding interphase are conceptualized as a core–shell structure, and its effective conductivity is estimated. In the second step, this core–shell structure is treated as a dispersed phase within the polymer matrix, enabling the prediction of nanocomposite conductivity. The model explicitly incorporates interfacial tension, interphase conductivity ( σi ), percolation threshold ( ϕp ) and tunneling distance ( d ). Validation against experimental data and parametric studies confirm the predictive accuracy of the present approach. At a CB particle radius of 10 nm combined with an interphase thickness of 20 nm, the composite conductivity reaches 1.9 S/m, but when the CB radius exceeds 20 nm and the interphase depth is reduced below 5 nm, the sample is insulated. At CB volume portion ( ϕf ) of 0.12 and σi = 1000 S/m, the predicted conductivity is 0.12 S/m, while as ϕf drops below 0.08, the nanocomposite exhibits insulating behavior. Also, at ϕp = 0.001 and d = 1 nm, the estimated conductivity approaches 0.16 S/m, but when d surpasses 2 nm, the sample is insulated. © 2026 The Author(s).