▎ 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. Copyright (C) EPLA, 2012