An Assessment of the Role of Quenched Randomness in the Stereochemical Sequences of Atactic Vinyl Polymers

Abstract

The influence of the quenched randomness in the stereochemical sequences of atactic chains on the mean-square unperturbed end-to-end distance, 〈r2〉0, is assessed. The method uses a rotational isomeric state (RIS) model based on virtual bonds between the centers of mass of the C6 rings in polystyrene. This virtual bond model is derived from a conventional RIS model expressed in terms of the C−C bonds in the main chain. The zeroth-approximation virtual bond model, which retains only the most probable conformations of each tetrad, correctly finds 〈r2〉0 ∼ n in the limit as n → ∞ if the probability for a meso diad, pm, is 0 < pm < 1, although the same zeroth-approximation model yields 〈r2〉0 ∼ n2 if pm is either 0 or 1. The values of 〈r2〉0 at intermediate pm are surprisingly close to the ones deduced from a full, C−C bond based RIS model. This achievement of the zeroth-approximation model demonstrates the important role of the quenched randomness of the stereochemical sequences in determining the unperturbed dimensions of atactic chains. Excellent agreement with the 〈r2〉0 from the full RIS model based on C−C bonds over the entire range of stereochemical composition, 0 ≤ pm ≤ 1, can be achieved in a first-approximation virtual bond model, which includes the next most probable conformations at each tetrad and refines slightly some of the conformations by minor adjustments in soft degrees of freedom.