The Role of Quenched Randomness in the Stereochemical Sequences of Atactic Vinyl Polymers ~

The influence of quenched randomness on the mean square unperturbed end-to-end distance, $\langle r^{2}\rangle _{0}$, is assessed in polystyrene, using a rotational isomeric state (RIS) model based on virtual bonds between the centers of mass of the C$_{6}$ rings. This coarse-grained model is derived from a conventional RIS model expressed in terms of the C-C bonds in the main chain and contains bond lengths, angles, and torsions determined by the stereochemistry and conformations of the underlying tetrad. The zeroth approximation virtual bond model, which retains only the most probable conformation(s) of the six stereochemically unique tetrads, correctly finds $\langle r^{2}\rangle _{0}\sim n $in the limit as $n\to \infty $ if the probability for a \textit{meso }diad, $p_{m}$, is 0$