Pair Diffraction Function Analysis of Conversion of a Fermat Scroll to an Archimedean Scroll in Multiwalled Carbon Nanotubes

The paper represents results from synchrotron high-energy X-ray diffraction (HEXRD) studies of multiwall carbon nanotubes (MWCNTs) heated and cooled in the temperature range of 298–450 K. Structural features of MWCNT powders have been studied by the real–space atomic pair distribution function (PDF) technique. XRD thermal study established that the MWCNTs are mainly of scroll type. The PDF structures on different length scales were used to study the interlayer spacing distribution in the carbon nanotube scrolls (CNSs). The method discovers that the pristine CNSs are described as left- or right-handed Fermat spiral (r =  ±aθ1/2) with uneven interlayer distances, rather than the XRD crystallography equidistance Archimedean spiral (r = aθ). The increased interlayer spacings of the innermost layers are caused primarily by the high curvature and thus the high strains are caused by π–π coulombic repulsion between the curved layers. At larger diameters, the CNS layers are less deformed and extensively interact through the van der Waals force affecting interlayer spacing shrinkage. The irregular interlayer spacing of the pristine CNS converses to a uniform spacing between layers at heating-cooling cycles within 298–450 K. The spatial changes in CNSs demonstrate the transformation of Fermat-type stroll in pristine nanotubes to more stable Archimedean spiral at heating-cooling processes.