Twofold screw axis symmetry cellulose

It is often said that cellulose has a cellobiose repeating unit. In the minds of some workers, that statement conveys the shape that results from twofold screw-axis symmetry. In this work, we propose that the ideal shape for cellulose does not have a twofold structure and that a range of shapes should occur. To the extent that the cellulose molecule can take various shapes, it is unjustifiably limiting to define cellulose in terms of a particular shape. 

In addition to selection of the structure of the monomer as the basis for defining the internal coordinates of the repeat unit, the possible structures are usually further constrained by taking advantage of any symmetry possessed by the unit cell. The symmetry is derived from the systematic absence of reflections which are forbidden by the selection rules for a particular space group. In the case of cellulose, the simplification usually introduced is the application of the symmetry of space group P2, which includes a twofold screw axis parallel to the direction of the chains. The validity of this simplification remains the subject of controversy, however, because the reflections which are disallowed under the selection rules of the space group are in fact frequently observed. 

The 1 kcal/mol contours in Figures 15-14 and 15-15 are to the right of the twofold screw-axis line, as are most crystal structures. Thus, based on both experiment and theory, it is reasonable to expect that most cellulose structures that are deviate from twofold symmetry will be left-handed helices. 

Cellulose is a poly-/3-D-l,4-glucoside. The /3-D-glucose units exist in chan-conformations with hydroxyl groups at the equatorial position. Chiral recognition ability of native cellulose is attributed to the crystalline array of parallel chains with a twofold screw axis of symmetry along the chain axes. 

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