Abstract

The Schulz–Flory distribution is a mathematical function that describes the relative ratios of polymers of different length after a polymerization process, based on their relative probabilities of occurrence. Carbon nanotubes (CNTs) are big carbon molecules which have a very high length-to-diameter ratio, somewhat similar to polymer molecules. Large amounts of ultralong CNTs have not been obtained although they are highly desired. Here, we report that the Schulz–Flory distribution can be applied to describe the relative ratios of CNTs of different lengths produced with a floating chemical vapor deposition process, based on catalyst activity/deactivation probability. With the optimized processing parameters, we successfully synthesized 550-mm-long CNTs, for which the catalyst deactivation probability of a single growth step was ultralow. Our finding bridges the Schulz–Flory distribution and the synthesis of one-dimensional nanomaterials for the first time, and sheds new light on the rational design of process toward controlled production of nanotubes/nanowires.