Conductive Network Formation and Electrical Transport in Carbon-Nanotube-Filled Diblock Copolymers

Abstract

We study the combined effects of microphase-selective localization and aggregation of carbon nanotubes (CNTs) on conductive network formation and electrical conductivity in CNT-filled, microphase-separated diblock copolymers (DBCs) with a lamellar morphology. Using a phase-field description of the DBC, we compute equilibrium order-parameter profiles and derive the immersion energies of CNTs whose interaction with the DBC is characterized by an adhesion parameter $\gamma$. These immersion energies are incorporated into Monte Carlo simulations of CNTs in the DBC system, in which steric repulsion is combined with an effective Hamaker-type attraction of strength $A$ to model CNT bundling. Aggregation of CNTs is quantified via the bundle-size distribution $f\left(s\right)$, defined as the fraction of CNTs contained in bundles of size $s$. Each simulated configuration is mapped onto a random resistor-network model to compute the composite conductivity. We find that increasing $\gamma$ drives CNTs into the selective microphase, lowering the percolation threshold and enhancing conductivity at fixed CNT load. In contrast, attractive CNT–CNT interactions ($A>0$) promote bundling, which suppresses conductivity at small filler concentrations. Overall, the results reveal a competition between localization-controlled connectivity and interaction-driven aggregation in determining electrical transport and suggest strategies to optimize conductivity by tuning the CNT–DBC adhesion and CNT–CNT cohesion.