(Georgia Institute of Technology, 2004-04-12)
Wang, Tong
Carbon nanotubes, and particularly single wall carbon nanotubes (SWNTs) have attracted much attention for their unique structure, as well as for their excellent mechanical, electrical and thermal properties. Most properties of carbon nanotubs are closely related with its anisotropic structure and geometry factor. Characterization of carbon nanotube length is critical for understanding their behavior in solutions as well as in polymer composites. Microscopy, particularly atomic force microscopy, has been used for their length measurement. Microscopy, though straightforward, is quite laborious, particularly for statistically meaningful sampling.
Light scattering can be used to measure particle dimensions. In this study, light scattering has been used to study polyvinyl pyrrolidone (PVP) wrapped SWNTs surfactant assisted aqueous dispersion and SWNT dispersion in oleum. To determine the length of SWNTs, Stokes - Mueller formalism was used, which is a universal model for particles with any size and shape. The Mueller matrix for an ensemble of long, thin cylinders proposed by McClain et al. was used in this study. This Mueller matrix includes the information of size (length and radius) and optical constants (refractive index and extinction coefficient) of cylinders. In this matrix, extinction coefficient, radius and length of SWNTs are unknown. By normalizing scattering intensity I(theta) (theta from 30 to 155 degree) to that at 30degree , the effects of radius and extinction coefficient were cancelled out. Thus, the effect of SWNT length on scattering intensity could be studied independently. A series of curves of normalized scattering intensity of SWNTs (I(theta) /I(30degree)) with varied length as a function of wave vector were predicted. A curve of normalized scattering intensity of SWNT as a function of wave vector was also obtained experimentally. By comparing experimental and predicted curves, average SWNT length in the dispersion has been determined.
Scattering intensity at a given angle initially increases with concentration, and then reaches a critical concentration(C*), above which the scattering intensity decreases. This phenomenon has been attributed to the competition between scattering and absorption of light by the presence of SWNT. By using Beer-Lambert law, this phenomenon has been used to determine the molar absorption coefficient of SWNTs.