We are going to present the limits of carbon nanotubes (CNT) growth: (i) The limit of CNTs growth rate: In this study,a previously overlooked step of carbon nanotube (CNT) growth,incorporating C atoms into the CNT wall through the CNT-catalyst interface,is studied by density functional theory calculations.A significant barrier for incorporating C atoms into the CNT wall (～2eVfor most used catalysts,Fe,Co,and Ni) is revealed and the incorporation can be the threshold step of CNT growth in most experiments.In addition,the temperature dependent CNT growth rate is calculated and our calculation demonstrates that growing 0.1–1 m long CNTs in 1 h is theoretically possible.