# Moments of the End-to-End Vectors for p-Phenylene Polyamides and Polyesters

## Abstract

Moments of rank 1-4 formed from the components x, y, and z of the chain vector r and expressed in the coordinate system affixed to the first unit have been calculated as functions of chain length n for p-phenylene polyamides of type I., (-NHC6H4CO-)n, of type II, (-NHC6H4NH-COC6H4CO-)n/2, and of the corresponding polyesters. Structural data on model compounds furnished the required geometric parameters. Configurational averaging was performed on the basis of the torsional potentials presented in the preceding paper. The persistence vector a s = (r) is dominated by its x component (x) along the phenylene axis; the transverse component (y) in the plane of this axis and the amide or ester group is negligible owing to the (approximate) mutual independence of torsions about a given phenylene axis; symmetry dictates that (z) = 0 perpendicular to this plane. The magnitude of the persistence vector depends sensitively on the difference & between the skeletal bond angles at CO and at N or O. For the respective polyamides, with = 10°, (x∞) = 410 and 435Å; for the polyesters, with = 7.4°, (x∞) = 740 and 785Å. As n increases, the combined effects of departures of successive phenylene axes from parallelity and the random torsions introduce departures from the quasi-rod-like character manifested at comparatively small n. The chains become random coils at very large n (>2000 units for the polyamides). The course of the convergence of the distribution function W(r) to its Gaussian limit, depicted by the higher moments, establishes the scaling factor m relating the number of units to the number of bonds in the corresponding freely jointed model chain. In the limit 1/n → 0, m = 240 units (1560Å) for the p-phenylene polyamides and 450 units (2900Å) for the polyesters compared with m = 20 (31Å) for polyethylene. © 1980, American Chemical Society. All rights reserved.