The Influence of Curvature of Multi-walled Carbon Nanotubes in the Matrix on the Thermal Conductivity of Multi-walled Carbon Nanotube/Natural Rubber Composites

The bending of one‑dimensional (1D) fibrous fillers, such as multi‑walled carbon nanotubes (MWCNTs), within a composite matrix often results in an overestimation of the thermal conductivity (TC) enhancement—an effect commonly overlooked in conventional modeling. In this work, a uniformly dispersed 4.2 phr MWCNTs/natural rubber (NR) composite prepared by solution blending served as the model system, exhibiting a 125% increase in TC. A simple image‑derived parameter \(\gamma\) was introduced to quantify the fiber curvature based on transmission electron microscopy (TEM). Finite‑element models of MWCNTs constructed with random Bézier curves yielded an average \(\gamma=\) 1.203, closely matching the TEM‑statistical value of 1.194 (< 1% error), and a range of 0.867 versus 0.909 from TEM (< 5% error). Modeling comparisons showed that a parallel‑equivalent solid cylinder model based on effective‑medium theory deviates by only 0.2% from a hollow‑tube model while substantially reducing computational cost. From the simulation data, an effective aspect ratio ( \(kₑ\) ) was derived and incorporated into the Mori–Tanaka model, correcting its underestimation of bending effects and lowering the prediction error to 6.8% relative to experimental data. The presented TEM‑based curvature characterization is broadly applicable to other 1D‑nanomaterial‑reinforced composites, and the refined Mori–Tanaka model provides improved accuracy for theoretical predictions.