Theoretical and Experimental Evaluation of Crystallite Moduli of Various Crystalline Forms of Poly(L-lactic acid)

The crystallite modulus or ultimate Young's modulus along the chain axis in the crystal lattice was estimated theoretically and experimentally for poly(L-lactic acid) (PLLA) alpha and delta (disordered alpha) forms and the mesophase (isolated chain model) on the basis of the refined crystal structures reported in previous papers (Macromolecules 2011, 44, 6441, 9650; Polymer, 2011, 52, 6097). The calculated modulus was 14.7 (alpha form), 12.9 (delta form), and 6.7 GPa (mesophase), which are in good agreement with the values obtained by the X-ray diffraction method, 13.76 +/- 0.17, 12.58 +/- 0.15, and 7.47 +/- 0.20 GPa, respectively. (The experimental data were obtained under the assumption of homogeneous stress distribution, and so the experimentally obtained crystallite modulus should be assumed as the apparent crystallite modulus. But the observed tendency might be kept even if the true crystallite modulus is clarified in future.) The difference in Young's modulus among the three phases has been discussed in terms of the chain conformational regularity. The anisotropy in Young's modulus and linear compressibility in the ab plane perpendicular to the chain axis has been also calculated and compared with those of polyoxymethylene (POM), isotactic polypropylene, orthorhombic polyethylene, and poly(vinyl alcohol) crystals. They show more or less different anisotropy and magnitude of modulus (and compressibility) depending on the difference in chain conformation, chain packing mode and intermolecular interactions between the neighboring chains with and without bulk side groups. The difference in crystallite modulus may reflect on Young's modulus of the bulk sample. In fact, dynamic Young's modulus was measured for the three kinds of oriented PLLA samples of the alpha form, the delta form, and the mesophase in the heating process. In the temperature regions corresponding to the phase transitions from the mesophase to the delta form and to the alpha form, Young's modulus was found to change by reflecting the difference in the crystallite modulus of each phase.