Theoretical evaluation of three-dimensional elastic constants of native and regenerated celluloses: role of hydrogen bonds

Abstract

Three-dimensional elastic constants were calculated for cellulose crystalline forms I and II (native and regenerated celluloses, respectively). The calculated Young's modulus E l along the chain axis is 167.5 GPa for form I and 162.1 GPa for form II. The E l of form II has only a slightly lower value than that for form I. This is consistent with the X-ray data ( c. 120–140 GPa for form I and c. 110 GPa for form II) although the absolute values are large. The E l was found not to be affected by intermolecular interactions but by intramolecular hydrogen bonds along the chain axis, especially the bond between the hydroxyl side group and the ether oxygen atom of the glucose ring (type a). A calculation neglecting this hydrogen bond gives the largely reduced E l of c. 70 GPa. Anisotropy of the Young's modulus and linear compressibility in the planes perpendicular to the molecular chain axis were also calculated. In the form I crystal, where the hydrogen-bonded sheet planes are stacked together by non-bonded van der Waals interactions, the modulus is large within the sheet plane and small in the direction perpendicular to the sheet: the anisotropy is similar to that reported for the nylon 6 α and γ forms. In form II the modulus is large but the anisotropy is not so remarkable, which is similar to atactic poly(vinyl alcohol) and poly( m-phenylene isophthalamide). The same tendency is seen also for the linear compressibility. In parallel with the calculation of the elastic constants, the lattice vibrational frequencies were calculated for forms I and II and compared with the observed infra-red and Raman spectral data so as to confirm whether the force fields used were reasonable.