Chiral crystallization of helical polymers

Crystallization of achiral or racemic helical polymers in chiral crystals is quite frequent and while in some cases it may relate to the thermodynamic stability of the chiral polymorph, in others it must be associated with kinetic factors. Analysis of the available literature data suggests that in the second instance a key role must be played by the nucleation step, i.e. specifically by the formation of precrystalline entities. Furthermore a survey of the chiral crystal structures for helical polymers evidences that they are frequently characterized by a quasihexagonal packing. The hexagonality index H, defined as the ratio of the largest to the smallest distance between the axis of the reference helix and its six nearest neighbors, appears to be a reliable indicator of the presence of helices of a single handedness or, respectively, of both in a given crystal structure. A detailed analysis of the general energetic and entropic factors favouring chiral crystallization of helical polymers is carried out. It is shown that a hexagonal or pseudohexagonal arrangement (i.e. the six-fold coordination) in either the crystalline or in a precrystalline state, promotes chiral crystallization and is in its own turn favoured by clustering of isochiral helices.