“…To understand the dynamic transporting process in-depth, another key parameter, the average speed during the process of CDs transmembrane transporting was calculated (displacement divided by duration). Figure displays that the displacement ( D ) of CD transporting includes the bending distance of the AFM tip cantilever ( d ) and the stretching length of the PEG linker ( Q ), as expressed by the following equation. According to the relationship between PEG stretching behavior and the force, the value of Q could be obtained by the extended worm-like chain (WLC) model: Where L p is the persistence length, k B stands for the Boltzmann constant, T refers to the absolute temperature, the extension of the PEG linker is Q , L 0 is the contour length, and k 0 presents the enthalpic correction. Referring to the literature, , the persistence L p is 3.8 ± 0.02 Å, and k 0 is 1561 ± 33 pN.…”