摘要

A quantitative thermodynamic model has been presented to investigate the effects of the size of carbon nanotubes and graphene on endocytosis, which provides a simple method to evaluate the optimal size with the fast endocytosis speed. It is found that the optimal radius of a close-ended nanotube increases from 12 nm to 25 nm by reducing its length to zero. However, an open-ended carbon nanotube has a larger optimal size than that of a close-ended nanotube. Furthermore, theoretical results show that a disk-shaped graphene has an optimal radius of about 25-100 nm when its thickness decreases from 20 nm to 5 nm. The agreement between theoretical results and experimental observations implies that the developed model could be applicable to understand the basic physical mechanism of endocytosis of carbon nanotubes and graphene.