Anisotropy of the elastic properties of crystalline cellulose Iβ from first principles density functional theory with Van der Waals interactions
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In spite of the significant potential of cellulose nanocrystals as functional nanoparticles for numerous applications, a fundamental understanding of the mechanical properties of defect-free, crystalline cellulose is still lacking. In this paper, the elasticity matrix for cellulose Iβ with hydrogen bonding network A was calculated using ab initio density functional theory with a semi-empirical correction for van der Waals interactions. The computed Young’s modulus is found to be 206 GPa along  (c-axis), 98 GPa along  (b-axis), and 19 GPa along  (a-axis). Full compliance matrices are reported for 1.0, 1.5 and 2.0 % applied strains Color contour surfaces that show variations of the Young’s modulus and average Poisson’s ratio with crystallographic direction revealed the extreme anisotropies of these important mechanical properties. The sensitivity of the elastic parameters to misalignments in the crystal were examined with 2D polar plots within selected planes containing specific bonding characteristics; these are used to explain the substantial variability in the reported experimental Young’s moduli values. Results for the lattice directions ,  and  are within the range of reported experimental and other numerical values.
KeywordsCrystalline cellulose Cellulose Iβ Density functional theory Young’s modulus
The authors wish to acknowledge the staff of the High Performance Computing Center at General Motors. Additional computational resources, networking, and support were provided by GM Information Systems and Services. R.J.M. and P.D.Z. are also grateful to financial support by the Forest Products Laboratory under USDA Grants: 11-JV-11111129-086, 07-CR-11111120-093, the Purdue Research Foundation and National Science Foundation through Grant No. CMMI-1131596.
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