Isotactic Block Length Distribution in Polypropylene:  Bernoullian vs Hemiisotactic

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 M_n, the number-average molecular weight. For polypropylene with Bernoullian statistics, the number of isotactic blocks of length n is given by N_n = (1 − σ)²(σ)^(n-1)(M_n/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)](M_n/42.08) and the number of isotactic blocks of length n (where n is an odd integer greater than one) is given by N_n = (0.5)(1 − α)²(α)^(n-1)/2(M_n/42.08). The distributions are compared and contrasted for hypothetical polypropylenes and real polypropylenes for which σ, α (¹³C NMR) and M_n (GPC) have been determined. For polypropylene with M_n = 100 000 an elastomeric morphology is calculated to exist for σ = 0.752−0.827 (Bernoullian) and for α = 0.575−0.693 (hemiisotactic). The lower limit defines the presence of at least two crystallizable isotactic segments (n ≥ 21) per chain; the upper limit defines the point at which the calculated percent crystallinity exceeds 10%, and the properties are dominated by the crystalline phase at the expense of the amorphous phase. The elastomeric properties observed in hemiisotactic polypropylenes with α ≈ 0.6 are readily explained by the statistical presence of crystallizable isotactic blocks in the presence of an otherwise amorphous medium. In contrast, the calculations suggest that most elastomeric Bernoullian polymers (i.e., atactic with σ near 0.5) rely on chain entanglements rather than crystallization phenomena for their elastomeric properties since the calculated distributions do not render a sufficient number and arrangement of crystallizable isotactic blocks.