Multiscale modeling of carbon nanotube (CNT) growth via chemical vapor deposition (CVD) integrates quantum mechanical, molecular dynamics, and continuum-scale simulations to unravel the complex interplay of atomic-scale nucleation, nanoscale tube elongation, and macroscale reactor conditions. This hierarchical approach bridges length and time scales, enabling predictive insights into chirality control, growth kinetics, and defect formation.

At the quantum mechanical level, density functional theory (DFT) calculations elucidate the catalytic nucleation process on transition metal surfaces such as Fe, Ni, or Co. The binding energy of carbon adatoms to the catalyst, typically ranging from 1.5 to 3.5 eV depending on the metal and crystallographic facet, determines the nucleation rate. Simulations reveal that step edges and defects on the catalyst surface serve as preferential sites for cap formation, with pentagon-heptagon defects influencing the initial chirality. For instance, DFT predicts that Ni(111) surfaces favor armchair (n,n) nucleation due to lower energy barriers for carbon incorporation at specific edge sites compared to zigzag (n,0) configurations.

Molecular dynamics (MD) simulations extend these insights to the nanoscale dynamics of tube elongation. Reactive force fields like ReaxFF capture the interplay between carbon feedstock dissociation, diffusion on the catalyst, and incorporation into the growing nanotube edge. Simulations at temperatures between 900 and 1200 K show that the carbon diffusion coefficient on Fe nanoparticles varies from 10^-14 to 10^-12 m²/s, directly affecting growth rates. Chirality control emerges from the dynamic equilibrium between cap stability and edge kinetics; armchair edges exhibit lower energy barriers for carbon addition (0.3-0.5 eV) compared to zigzag edges (0.6-0.8 eV), explaining the predominance of near-armchair tubes in experimental yields. MD also captures defect formation, such as Stone-Wales transformations, which occur at rates of 10^10 to 10^11 s^-1 under typical CVD conditions.

Continuum models integrate these atomic-scale phenomena into reactor-scale optimization. Computational fluid dynamics (CFD) simulations solve mass, momentum, and energy transport equations to predict temperature gradients and gas-phase species concentrations. For a horizontal CVD reactor operating at 1000°C, temperature variations of ±20°C across the substrate can lead to a 30% difference in CNT density due to changes in precursor decomposition rates. Gas flow rates between 100 and 500 sccm determine the boundary layer thickness, which modulates the carbon supply to the catalyst. Coupling CFD with kinetic Monte Carlo (kMC) methods enables prediction of CNT forest morphology, with growth rates varying from 1 to 10 µm/s depending on local C2H2 partial pressure.

Successful multiscale predictions include the correlation between catalyst particle size and CNT diameter. Simulations show that Fe nanoparticles below 3 nm favor single-walled CNTs, while larger particles produce multi-walled structures, matching experimental observations. Another validated prediction is the effect of H2 co-flow, which simulations identify as critical for etching amorphous carbon and maintaining catalyst activity. Optimal H2:C2H4 ratios of 4:1 suppress parasitic carbon deposition, aligning with experimental growth yields.

Challenges persist in defect modeling, particularly for chiral angle deviations during growth. While MD captures single-point defects, the cumulative impact of these defects on chirality purity remains difficult to predict over micrometer-length scales. Additionally, the role of subsurface carbon diffusion in catalyst deactivation is not fully resolved, with simulations suggesting that saturation occurs after 10-15 layers of carbon accumulation.

Multiscale coupling strategies vary in complexity. Sequential coupling passes parameters like activation energies from DFT to MD and then to continuum models, but neglects real-time feedback between scales. Concurrent coupling, such as adaptive resolution schemes, dynamically adjusts the simulation method based on local requirements but demands significant computational resources. Hybrid approaches, like embedded quantum mechanics/molecular mechanics (QM/MM), balance accuracy and efficiency by treating the catalyst-carbon interface with DFT while modeling the surrounding environment with classical potentials.

Future advancements require tighter integration of machine learning for parameterization and accelerated sampling. Neural network potentials trained on DFT data can reduce MD computational costs by two orders of magnitude while preserving quantum-level accuracy. Additionally, high-throughput screening of catalyst alloys using combinatorial DFT-MD workflows could identify novel compositions for chirality-specific growth.

In summary, multiscale modeling of CVD-grown CNTs provides a mechanistic framework linking atomic-scale chemistry to macroscopic reactor performance. By elucidating the roles of temperature, gas flow, and catalyst composition, these simulations guide experimental optimization while highlighting unresolved questions in defect dynamics and chirality control. Continued refinement of coupling strategies and computational methods will further enhance predictive capabilities for tailored nanotube synthesis.