Numerical modeling of the effects of the shape and aspect ratio of 3D curved fiber on the percolation threshold and electrical conductivity of conductive polymer composites

Abstract

For designing conductive polymer composites (CPCs), understanding how the fiber curvature affects the percolation behavior of curved conductive fibers is essential for determining the effective electrical conductivity σ_eff of the CPCs. In this work, CPCs were considered as a polymer matrix filled with the random packing of overlapped curved spherocylinders. The geometries of the curved spherocylinders were defined, and inter-curved spherocylinder contact-detecting and system-spanning fiber cluster searching algorithms were developed. The finite-size-scaling method was used to explore how the aspect ratio α and bending central angle θ of a curved spherocylinder affect the percolation threshold ϕ_c of an overlapped curved spherocylinder system in 3D space. The findings suggest that ϕ_c decreases as α increases and increases initially before declining as θ increases. An empirical approximation formula was proposed to quantify the effect of the curved spherocylinder's morphology, characterized by the dimensionless excluded volume V_dex of the curved spherocylinder, on ϕ_c. The new rigorous bound for ϕ_c of the soft-curved spherocylinder system was further proposed. A random resistor network model was constructed, and the reliability of this model was validated by comparing the simulations and published data. Finally, a fitting formula was developed to assess the impacts of the normalized reduced density (η − η_c)/η_c and V_dex on the σ_eff of CPCs. A distinct linear correlation between σ_eff and (η − η_c)/η_c was constructed, denoted as σ_eff ∼ [(η − η_c)/η_c]^t(α,θ). An empirical approximation model was proposed to establish the relationship between the fiber shape and conductivity exponent t. Our study may provide a theoretical hint for the design of CPCs.