Machine Learning Model for Electrical and Thermal Conductivities of Copper – Carbon Nanotubes Composites

The miniaturization in electronics and the demands for high-power transmission cables call for conductors that can carry greater current density than copper. There have been extensive studies on carbon nanotubes (CNTs), since single-walled CNTs have been theoretically shown to offer extremely large ampacities with a theoretical limit up to ~10⁹ A/cm² attributing to their electrical and thermal conductivities. For example, several studies reported that single-walled CNTs exhibited electrical conductivity of ~5× 10⁵S/cm and thermal conductivity of ~7000 W/mK at room temperature. However, due to the scalability in synthesis, it is still not practical to replace the copper with CNTs in real-scale electronics and power cables. To utilize the excellent CNTs properties for large-scale applications, there has been great interest in creating scalable Cu-CNT composites by using copper as a matrix material. In a previous experimental study, Cu-CNT composite with a CNT volume fraction of 45% presented 100 times greater ampacity, 26% greater electrical conductivity, and similar thermal conductivity compared to pure copper at room temperature. On the other hand, in several recent experimental studies, the inclusion of CNTs did not effectively improve the conductivities of copper matrix possibly due to the imperfect adhesions between CNTs and copper and nonuniform distribution of CNTs in the matrix. As an effort to understand the electrical and thermal properties in bulk-scale Cu-CNT composites, theoretical models have been presented based on Maxwell-Garnett effective medium approach or numerical simulations. However, the previous models require the following assumptions: (1) the CNTs are uniformly distributed in the matrix; (2) the volume fraction of CNTs is below percolation threshold (~0.1%); (3) and CNT-CNT interface resistance is less prominent than Cu-CNT interface resistance. The modeling of three-dimensional structures of CNT-based composites necessitated extensive computational resources since extremely fine mesh was necessary for modeling CNTs. Therefore, when modelling for Cu-CNT composites with a large volume fraction (> 50%) and random distributions of CNTs, the existing model approaches are still limited despite they are useful for understanding a variety of CNT based composites. Herein, our study first presents a machine learning ( ML) model that rapidly predicts the electrical and thermal properties of Cu-CNT composites. We aim to develop a ML model that approximates the electrical and thermal conductivities of the Cu-CNT composites when the layouts of CNTs in a Cu matrix are provided in two-dimensional (2D) image format. This model considers the interface resistances both at CNT-CNT and Cu-CNT contacts, random distributions of CNTs, and CNT fraction factor up to 80%. To prepare the training dataset for the ML model, we develop a 2D simulation model for Cu-CNT composites that employ the CNT layout, CNT fraction factor, and interfacial contact resistances as parameters. The ML model is trained by the pairs of CNT layouts and simulated property values, and the ML model hyperparameters are tuned to enhance the accuracy. Then, the nonlinear interpolation capability of the ML model is tested using various unseen Cu-CNT composite designs. Our work demonstrates the potential of ML approach to enable rapid and computationally efficient modelling of complex Cu-CNT composites.