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Simplified tube form factor for analysis of small‐angle scattering data from carbon nanotube filled systems
Author(s) -
Justice Ryan S.,
Wang David H.,
Tan LoonSeng,
Schaefer Dale W.
Publication year - 2007
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s0021889807004153
Subject(s) - tube (container) , form factor (electronics) , scattering , maxima and minima , shape factor , materials science , cylinder , structure factor , carbon nanotube , fractal , core (optical fiber) , small angle scattering , filling factor , work (physics) , nanotube , scanning electron microscope , optics , geometry , composite material , physics , crystallography , chemistry , mathematics , mathematical analysis , thermodynamics , quantum mechanics
This work presents an analysis method for small‐angle scattering data utilizing a simplified tube (hollow cylinder) form factor. The simplified form factor captures the rod‐like character of a tube at long length scales (one‐dimensional), the sheet‐like character of the tube wall at intermediate length scales (two‐dimensional), and the surface characteristics of a tube at small length scales while suppressing the deep minima seen in the exact form factor. Ultra‐small‐angle X‐ray scattering data from composites made with multi‐walled carbon nanotubes and a bismaleimide resin are analyzed using the simplified form factor and compared with scanning electron micrographs. Although a hollow core is not evident via microscopy, a solid rod form factor does not fit the data. However, a tube form factor does fit the data and generates reasonable geometric parameters. At higher concentrations, evidence for aggregation is seen in the data. Aggregation is accommodated by including a fractal structure factor within the simplified approach, allowing facile analysis of data from aggregated (poorly dispersed) fillers.