Variability in the Persistence Length of an Atactic Polymer Due to Quenched Randomness, As Illustrated by Atactic Polystyrene
The persistence lengths of atactic polystyrene (PS) have a broad distribution due to the quenched randomness of the stereochemical sequences. The breadth of this distribution, and the implications for dynamic properties, is deduced from explicit calculations of the averaged end-to-end vector, ?r?, for all 2x stereochemical sequences of methyl-terminated oligomers with x up to 15, where x denotes the number of phenyl side chains in the methyl-terminated oligomer. There is a large variation in the values of ?r? for long subchains of atactic PS, depending on the stereochemical sequence within the given subchain. Average results, and the fluctuations in these results, are obtained for PS over the entire range of the probability of a meso diad, pm, with the assumption of Bernoullian statistics for the stereochemical sequences. These fluctuations are large at the intermediate values of pm characteristic of conventional atactic PS. The results imply that beads representing Kuhn monomers in a given atactic PS chain have an extremely broad distribution for τ0/?, where τ0 is the Kuhn monomer relaxation time and ? is the friction coefficient. This broad distribution, which is an inherent property of atactic chains, may be a contributing factor in earlier experimental observations of discrepancies in segment sizes deduced from static and dynamics measurements.