Progress in computational methods and mechanistic insights on the growth of carbon nanotubes

Carbon nanotubes (CNTs), as a promising nanomaterial with broad applications across various fields, are continuously attracting significant research attention. Despite substantial progress in understanding their growth mechanisms, synthesis methods, and post-processing techniques, two major goals remain challenging: achieving property-targeted growth and efficient mass production. Recent advancements in computational methods driven by increased computational resources, the development of platforms, and the refinement of theoretical models, have significantly deepened our understanding of the mechanisms underlying CNT growth. This review aims to comprehensively examine the latest computational techniques that shed light on various aspects of CNT synthesis. The first part of this review focuses on progress in computational methods. Beginning with atomistic simulation approaches, we introduce the fundamentals and advancements in density functional theory (DFT), molecular dynamics (MD) simulations, and kinetic Monte Carlo (kMC) simulations. We discuss the applicability and limitations of each method in studying mechanisms of CNT growth. Then, the focus shifts to multiscale modeling approaches, where we demonstrate the coupling of atomic-scale simulations with reactor-scale multiphase flow models. Given that CNT growth inherently spans multiple temporal and spatial scales, the development and application of multiscale modeling techniques are poised to become a central focus of future computational research in this field. Furthermore, this review emphasizes the growing role played by machine learning in CNT growth research. Compared with traditional physics-based simulation methods, data-driven machine learning approaches have rapidly emerged in recent years, revolutionizing research paradigms from molecular simulation to experimental design. In the second part of this review, we highlight the latest advancements in CNT growth mechanisms and synthesis methods achieved through computational techniques. These include novel findings across fundamental growth stages, i.e., from nucleation to elongation and ultimately termination. We also examine the dynamic behaviors of catalyst nanoparticles and chirality-controlled growth processes, emphasizing how these insights contribute to advancing the field. Finally, in the concluding section, we propose future directions for advancements of computational approaches toward deeper understanding of CNT growth mechanisms and better support of CNT manufacturing.