Determination of Distortions and Sizes of Cellulose Nanocrystallites

The wide angle X-ray scattering (WAXS) is widely used method to evaluate sizes of cellulose nanocrystallites by means of the Scherrer’s equation. However, the Scherrer’s methodology has a limitation, since a width of X-ray diffraction peaks depends not only on the size of crystallites but also on other factors, such as instrumental effect, second-order distortion degree of crystalline lattice, δ, and factor Δ=4δtg. Since these factors are ignored this leads to understated sizes of nanocrystallites. In this research a simple procedure was proposed to determine δ and Δ factors, as well as actual sizes of CIβ nanocrystallites. Values of δ were calculated using average deviation of interplanar spacing in the distorted lattice from its value in undistorted crystalline lattice. It was also shown that δ and Δ factors are linear functions of interplanar spacings (d) of crystalline lattice. After finding the δ and Δ factors, the correction for broadening of diffraction peaks was calculated, which allows determining the actual width (Da) and actual length (La) of nanocrystallites. Study of various samples of CIβ showed that tunicate cellulose has the largest crystallites: Da=13 nm and La = 400 nm. Actual sizes of nanocrystallites in isolated celluloses of other origin (herbaceous plants, wood, bast fibers, cotton fibers, etc.) were smaller: Da was in the range of 4.2 to 10 nm, whereas La in the range of 48 to 116 nm.

Keywords: WAXS, Peaks broadening, Instrumental factor, Lattice distortions, Cellulose, Nanocrystallites, Approximate sizes, Actual sizes.