Anisotropy and temperature dependence of structural, thermodynamic, and elastic properties of crystalline cellulose I_β: a first-principles investigation

Anisotropy and temperature dependence of structural, thermodynamic and elastic properties of crystalline cellulose I_β were computed with first-principles density functional theory (DFT) and a semi-empirical correction for van der Waals interactions. Specifically, we report the computed temperature variation (up to 500 K) of the monoclinic cellulose I_β lattice parameters, constant pressure heat capacity, C_p, entropy, S, enthalpy, H, the linear thermal expansion components, ξ_i, and components of the isentropic and isothermal (single crystal) elastic stiffness matrices, C_ij^S(T) and C_ij^T(T), respectively. Thermodynamic quantities from phonon calculations computed with DFT and the supercell method provided necessary inputs to compute the temperature dependence of cellulose I_β properties via the quasi-harmonic approach. The notable exceptions were the thermal conductivity components, λ_i (the prediction of which has proven to be problematic for insulators using DFT) for which the reverse, non-equilibrium molecular dynamics approach with a force field was applied. The extent to which anisotropy of Young's modulus and Poisson's ratio is temperature-dependent was explored in terms of the variations of each with respect to crystallographic directions and preferred planes containing specific bonding characteristics (as revealed quantitatively from phonon force constants for each atomic pair, and qualitatively from charge density difference contours). Comparisons of the predicted quantities with available experimental data revealed reasonable agreement up to 500 K. Computed properties were interpreted in terms of the cellulose I_β structure and bonding interactions. (paper)