Growth of half-meter long carbon nanotubes based on Schulz-Flory distribution

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.