Crystal structures of the α and β forms of isotactic polypropylene: a Monte Carlo simulation

Isotactic polypropylene has various crystalline modifications (α, β, γ, smectic). Molecular conformations in these modifications are common 3/1 helix of (TG)₃ or (TG^∗)₃. However crystal structures of the modifications, that is the modes of chain packing, are quite different and are subjects of intensive investigations nowadays. We study here, the detailed modes of chain packing in the α and β forms by Monte Carlo simulation. We assume that the molecular conformation is a rigid 3/1 helix, and that the chain axes are placed either in a monoclinic lattice (α form) or in a hexagonal lattice (β form). Most stable modes of chain packing are investigated, with respect to chain chirality (right or left handedness), chain rotation and translation, and the methyl-group direction (up or down positioning). We find that an initial random state in the monoclinic lattice converges to the α₁ or to the α₂ form, both with alternating rows of right-handed and left-handed helices; we also investigate a molecular process of growth of the α₂ crystal in the matrix α₁ crystal. On the other hand, the arrangement of the molecular axes in the hexagonal lattice is found to give rise to the β form structure, in which the chains form chiral domains surrounded by boundaries parallel to the (110) and (100) planes. It is also shown that detailed chain rotations (setting angles) have a unique superstructure, which conforms to the incommensurate packing recently proposed by Lotz and Meille.