Origin of the twist of cellulosic materials.

Molecular Mechanics, Hartree-Fock, and semi-empirical geometry optimizations were carried out on cellulose oligomers and crystallites with and without water solvation. The intramolecular bonding is visualized with the Delocalized Molecular Orbitals (DLMOs). Internal coordinates were relaxed and the structures were gradient optimized for cellulose oligomers composed of 4, 10, 12, 14, 19, and 65 glucose units. The cellulose conformation of minimum energy deviates from the flat ribbon conformation giving rise to half-twist repeating units of about 3-4nm and 60nm along the chain axis. An optimized cellulose chain which is ten glucose units long is 9.57kcal/mol more stable than the flat ribbon model. The DLMOs show the twisted model retains the same hydrogen bonding scheme as the flat model while minimizing steric interactions between H1 and H4'. In cellulose crystallites the twist, which can be left- or right-handed, calls into question the assumption of twofold symmetry in the current flat unit cell. Additionally the hydrogen bonded sheets reorient themselves, suggesting the crystallites are in fact crystalloids. The overall length of the crystal twist is dependent on the cross-section of the crystal. Powder X-ray diffraction patterns of the optimized crystallites were simulated.