Summary: The average lateral dimensions of cellulose microfibrils in paper sheets can be determined from the width of X-ray Bragg peaks at half the maximum height. The method assumes it is the finite size of the crystallite which is the main contributor to peak broadening in the directions orthogonal to the long axis of the crystallite. This assumption is examined in the context of samples from different botanical sources, of varying crystallinity and cellulose content and the various instrumental sources of broadening X-ray powder patterns. Excellent fits to the data from paper samples can be obtained by using five Voigt functions to the powder diffraction patterns, for the 101, , 021, 002 and 040 reflections. Of these reflections, the 020 is the clearest, and the best able to determine the lateral dimension of the crystallite. Results indicate that the size of microfibrils is dependent on the botanical source of the fibres.

On the Interpretation of X-Ray Diffraction Powder Patterns in Terms of the Nanostructure of Cellulose I Fibres

It has now been established that paracrystals are the 'building blocks' of many materials including polymers, biological materials, colloids, molten metals and alloys, and catalysts. The concept of paracrystallinity and the main equations which are needed for the practical application of the theory to X-ray, neutron and electron diffraction are presented in a simplified style which can be easily grasped by scientists from all disciplines. Examples of the application and usefulness of the theory which support the fact that paracrystals are the building blocks of condensed matter are presented. X-ray diffraction, neutron diffraction, electron diffraction, scanning electron microscopy and transmission electron microscopy are among the techniques which have been used for the assessment of the paracrystalline nature of the materials given in the examples.

https://iopscience.iop.org/article/10.1088/0022-3719/21/23/004/pdf

Paracrystals representing the physical state of matter

The experience of microparacrystals, in intermediate stages between “perfect crystalline” and “amorphous structures,” and as “building bricks” in condensed matter, has become accepted as a basic physical concept. Their existence was proven by optical and x-ray diffraction studies. A review and summary of the following aspects is presented mainly for the benefit of scientists working in the field of polymers: (1) basic features of the paracrystal; (2) types of paracrystalline distortions and their effects on the reflection profiles of the x-ray diffraction pattern; (3) the physical basis of the theory of paracrystallinity; (4) experimental determination of the paracrystalline distortion parameter g, the crystallite size Lhkt , and the α∗ value; (5) x-ray diffraction evidence of the existence of microparacrystals; and (6) examples of electron microscope observations of paracrystals in polymers as well as in other materials.

Structure of crystalline and paracrystalline condensed matter

8 Other Long Vegetable Fibers*: Abaca, Banana, Sisal, Henequen, Flax, Ramie, Hemp, Sunn, and Coir

The paracrystallinity of cellulose samples was studied with a complex of investigation methods including X-ray, NMR, sorption, calorimetry, and some others It was found that the paracrystalline fraction of cellulose is located on the surface of crystallites as thin monomolecular layers having an average thickness of 04 nm The paracrystalline surface layers have distorted and loose packing that is characterized by a high distortion parameter δp = 018, increased specific volume Vp=0664 cm3/g, and decreased specific gravity ρp= 151 g/cm3 The paracrystalline fraction of the crystallite can be quantified by the parameter (α), which has an expressed influence on some properties of cellulose Increasing of the α-value causes expansion of inter-plane distances in the C1 unit cell, as well as promotes mercerization and dissolution of cellulose

https://ojs.cnr.ncsu.edu/index.php/BioRes/article/download/BioRes_05_3_1393_1407_Ioelovich_LF_Cellulose_Paracrystallinity/646

P.S. Mukherjee

Papers

X-ray diffraction study of fibrous polymers. I. Degree of paracrystallinity—a new parameter for characterizing fibrous polymers

Anisotropy of X-ray structural parameters of the three phase model in cellulose I