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Understanding and controlling the self-assembly of vertically oriented carbon nanotube (CNT) forests is essential for realizing their potential in myriad applications. The governing process–structure–property mechanisms are poorly understood, and the processing parameter space is far too vast to exhaustively explore experimentally. We overcome these limitations by using a physics-based simulation as a high-throughput virtual laboratory and image-based machine learning to relate CNT forest synthesis attributes to their mechanical performance. Using CNTNet, our image-based deep learning classifier module trained with synthetic imagery, combinations of CNT diameter, density, and population growth rate classes were labeled with an accuracy of >91%. The CNTNet regression module predicted CNT forest stiffness and buckling load properties with a lower root-mean-square error than that of a regression predictor based on CNT physical parameters. These results demonstrate that image-based machine learning trained using only simulated imagery can distinguish subtle CNT forest morphological features to predict physical material properties with high accuracy. CNTNet paves the way to incorporate scanning electron microscope imagery for high-throughput material discovery.

 

The parameter space of CNT forest synthesis is vast and multidimensional, making experimental and/or numerical exploration of the synthesis prohibitive. We propose a more practical approach to explore the synthesis-process relationships of CNT forests using machine learning (ML) algorithms to infer the underlying complex physical processes. Currently, no such ML model linking CNT forest morphology to synthesis parameters has been demonstrated. In the current work, we use a physics-based numerical model to generate CNT forest morphology images with known synthesis parameters to train such a ML algorithm. The CNT forest synthesis variables of CNT diameter and CNT number densities are varied to generate a total of 12 distinct CNT forest classes. Images of the resultant CNT forests at different time steps during the growth and self-assembly process are then used as the training dataset. Based on the CNT forest structural morphology, multiple single and combined histogram-based texture descriptors are used as features to build a random forest (RF) classifier to predict class labels based on correlation of CNT forest physical attributes with the growth parameters. The machine learning model achieved an accuracy of up to 83.5% on predicting the synthesis conditions of CNT number density and diameter. These results are the first step towards rapidly characterizing CNT forest attributes using machine learning. Identifying the relevant process-structure interactions for the CNT forests using physics-based simulations and machine learning could rapidly advance the design, development, and adoption of CNT forest applications with varied morphologies and properties 

A time-resolved two-dimensional finite element simulation is developed to model the forces generated during the self-assembly of actively growing CNT populations with distributed properties and growth characteristics. CNTs are simulated as interconnected frame elements that undergo the base growth mechanism. Mechanical equilibrium at each computational node is determined at each time step using the Updated Lagrangian method. Emphasis is placed on the transmission of force to the growth substrate, where catalyst particles reside. The simulated CNT forest structural morphology is similar to that of physical CNT forests, and results indicate that stresses on the order of GPa are transmitted to catalyst particles. The force transmitted to a given catalyst particle is correlated to the rate at which the CNT grows relative to the population averaged growth rate. The effect of diameter-dependent CNT growth rates and the persistence of vdW bonds are also examined relative to the forces generated during forest self-assembly. Results from this study may be applied to the study of CNT forest self-assembly, resultant ensemble forest properties, and force-modulated CNT growth kinetics.