Ab Initio Elasticity of Poly(lactic acid) Crystals

We investigate the elastic properties of poly(lactic acid) crystals using a first-principles pseudopotential plane wave method within the generalized gradient approximation of the density functional theory. Stiffness and compliance matrices of poly(l-lactic acid) (PLLA) alpha- and beta-forms, and the stereocomplex (sc) between PLLA and poly(D-lactic acid) (PDLA) (50:50) sc-form are calculated using the finite strain technique. The results indicate that crystalline poly(lactic acid) is highly mechanical anisotropic. Contributions from the crystalline phase to the anisotropy of the elastic modulus in an uniaxially oriented poly(lactic acid) fiber are estimated on the basis of a cylindrically symmetric polycrystalline aggregate model. Both symmetry and orientation distribution of the crystals have been taken into account. Voigt and Reuss bounds of Young's moduli and shear moduli and Poisson's ratio are calculated from single crystal elastic properties.