Effect of self-generated mechanical field on spatiotemporal growth of polymer single crystals, hedrites, and spherulites during isothermal crystallization

The spatio-temporal growth of single crystals in a crystalline polymer has been investigated theoretically based on a non-conserved time dependent Ginzburg-Landau equation (known as TDGL model A). In the description of the total free energy, an asymmetric double-well local free energy density signifying metastability of crystal ordering and latent heat of crystallization is combined with a non-local free energy term representing an interface gradient. The resulting nonlinear reaction diffusion equation after renormalization possesses a solitary wave property. Two-dimensional numerical calculations were performed to elucidate the faceted single crystal growth including square, rectangular, diamond-shaped, and curved single crystals. A three-dimensional simulation was also undertaken for the emergence of diamond-shaped single crystals in polyethylene. Of particular importance is that the model field parameters can be linked directly to the material parameters of polyethylene single crystals. Simulation with various elements of the interface gradient coefficient tensor captures various topologies of polymer single crystals.; Furthermore, theoretical elucidation of the possible effect of mechanical deformation on spatio-temporal emergence of unusual polymer morphology subjected to quiescent isothermal crystallization conditions has been made. The phase field model consisting of the non-conserved TDGL equation for the crystal order parameter is coupled with curvature elasticity and strain recovery potentials. Under quiescent crystallization conditions, the curvature elasticity term is needed to discern the emergence of sectorized single crystals. Upon coupling with the strain recovery potential, the numerical calculation captures ripple formation running across the long lamellar growth front, which may be attributed to lamellar buckling caused by the volume shrinkage. Of particular interest is that these simulated topologies of the single crystals are in good accord with the growth character of single crystals of isotactic polypropylene, syndiotactic polypropylene, and hedrites of isotactic polystyrene, observed experimentally during isothermal crystallization from the melt.; Finally, the spatio-temporal growth of spherulites in blends of isotactic and atactic polypropylene isomers has been investigated theoretically based on TDGL model C, which includes the non-conserved crystal order parameter and a conserved compositional order parameter. In the description of the total free energy, the local free energy density of crystallization is combined with the Flory-Huggins free energy for mixing between iPP and aPP isomers. The rejection of aPP from the growing spherulitic front has been modeled to compare with the reported experimental observation.