Crystal growth 25 symmetry elements

The rac-isomers have a twofold axis and therefore C2 symmetry. The meso-iso-mer has a mirror plane as the symmetry element and therefore Cs-symmetry. The racemic mixture can be used for polymerization reactions since the two chains produced by the two enantiomers are identical, if begin and end groups are not considered. The asymmetry possibly introduced initially in the crystal during crystal growth from a chiral catalyst will be removed by melting and crystallization. Note when catalysts of this type are to be used for asymmetric synthesis, e.g. as Lewis acids in Diels-Alder reactions, separation of the enantiomers is a prerequisite. 

The regularity of the polymer backbone is the key factor isotactic polypropylene crystallizes forming a rigid stable solid, whereas atactic polypropylene does not and forms a rubbery elastic solid. For flexible polymers, the structure of the solid is dictated by the symmetry of the polymer backbone. For the formation of a semi-crystalline solid it is necessary for there to be either an element of symmetry in the repeat unit chemical structure or strong interactions to aid the packing of the molecule and initiate the alignment that is required for the crystal growth process. 

Monoclinic and triclinic crystals have the lowest number of symmetry elements, and the smectic C phase also has a monoclinic symmetry. Therefore, the symmetry of alignment layers with monoclinic and triclinic crystal structures resembles the symmetry of the smectic C phase. It is plausible to think that the epitaxial growth of a smectic C liquid crystal proceeds most smoothly on alignment layers which resemble their crystallographic structures [12,13]. 

Epitaxy and Twinning in Polymer Single Crystals. Epitaxy and twinning are frequently observed in polymer single crystals. In most cases, they are always associated with traditional crystal defects. Epitaxy is generally applied to oriented growth of one crystalline substance on a substrate of a different substance. However, it is also common that epitaxy may occur within one crystalline substance at different hkl) crystalline planes. By contrast, the twin contains an added element of symmetry over and above that which either component possesses. In other words, epitaxy only needs lattice match whereas twinning introduces an additional symmetry axis. 

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