Constitutive relation of an orthorhombic polycrystal with the shape coefficients

An orthorhombic polycrystal is an orthorhombic aggregate of tiny crystallites. In this paper, we study the effect of the crystalline mean shape on the constitutive relation of the orthorhombic polycrystal. The crystalline mean shape and the crystalline orientation arrangement are described by the crystalline shape function （CSF） and the orientation distribution function （ODF）, respectively. The CSF and the ODF are expanded as an infinite series in terms of the Wigner D-functions. The expanded coefficients of the CSF and the ODF are called the shape coefficients s^lm0 and the texture coefficients c^lmn respectively. Assuming that Ceff in the constitutive relation depends on the shape coefficients s^lm0 and the texture coefficients c^lmn by the principle of material frame-indifference we derive an analytical expression for C^eff up to terms linear in s^lmo and c^lmn and the expression would be applicable to the polycrystal whose texture is weak and whose crystalline mean shape has weak anisotropy. C^cff contains six unspecified material constants （λ, μ, c, s1, s2, s3）, five shape coefficients （s^2 00, s^2 20, s^4 00, s^4 20, s^4 40）, and three texture coefficients （c^4 99,c^4 20, c^4 40）, The results based on the perturbation approach are used to determine the five material constants approximately. We also find that the shape coefficients 2 and a s^2mo and s^4m0 are all zero if the crystalline mean shape is a cuboid. Some examples are given to compare our computational results.

Effect of Star-shaped Chain Architectures on the Polylactide Stereocomplex Crystallization Behaviors

Linear and star-shaped polylactides（PLA） with similar molecular weights of each arm are synthesized via ringopening polymerization of LA with 3-butyn-1-ol and pentaerythritol as initiators,respectively.By solution blending of equivalent mass of poly（L-lactic acid）s（PLLAs） and poly（D-lactic acid）s（PDLAs）,perfect PLA stereocomplexes（sc PLAs） are prepared and confirmed by WAXD and FTIR analysis.Effect of chain architectures on stereocomplex crystallization is investigated by studying the non-isothermal and isothermal crystallization of linear and star-shaped polylactide stereocomplexes.In dynamic DSC and POM test,star-shaped PLLA（4s PLLA）/PDLA and PLLA/star-shaped PDLA（4s PDLA） stereocomplexes reach rapid crystallization and higher crystallinity due to larger spherulite density of star-shaped chain and excellent chain mobility of linear chain.In isothermal crystallization test,much faster crystallization and less crystallization half-time is obtained with the increase of star-shaped chain.Meanwhile,4s PLLA/PDLA and PLLA/4s PDLA are found to have the highest crystallinity,suggesting limitation of too much star-shaped chain for 4s PLLA/4s PDLA and restriction of linear chain in nucleation capacity for PLLA/PDLA.The results reveal that star-shaped chain has an important influence on the crystallization of sc PLAs.