Isotactic Block Length Distribution in Polypropylene: Bernoullian vs Hemiisotactic

Abstract

Derivation of the isotactic block length distribution is made for polypropylenes having Bernoullian (chain-end control) or hemiisotactic microstructures. For each of these tacticities, the isotactic block length distribution depends on a single stereochemical parameter and Mn, the number-average molecular weight. For polypropylene with Bernoullian statistics, the number of isotactic blocks of length n is given by Nn = (1 − σ)2(σ)(n-1)(Mn/42.08). For hemiisotactic polypropylene, the number of isotactic blocks of length one is given by N1 = [(0.5)(1 − α)2 + (0.5)(1 − α)](Mn/42.08) and the number of isotactic blocks of length n (where n is an odd integer greater than one) is given by Nn = (0.5)(1 − α)2(α)(n-1)/2(Mn/42.08). The distributions are compared and contrasted for hypothetical polypropylenes and real polypropylenes for which σ, α (13C NMR) and Mn (GPC) have been determined. For polypropylene with Mn = 100 000 an elastomeric morphology is calculated to exist for σ = 0.752−0.827 (Bernoullian) and for α...