A hierarchy of models for the dynamics of polymer chains in dilute solution

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Abstract
The dynamics of a hierarchy of sophisticated polymer models described by an interbond potential of quadratic form is derived in the optimized Rouse–Zimm (ORZ) approximation introduced by Bixon and Zwanzig. The resulting quadratic ORZ configurational potential for a generalized rotational isomeric states (RIS) model preserves the maximum of local details and of degree of stiffness compatible with a universal description of polymer dynamics. The present matrix-based RIS–ORZ description has analogies with Allegra’s scalar Fourier approach in terms of the generalized characteristic ratio for chains with periodic boundary conditions. The hierarchy of models amenable to quantitative calculations includes the more popular models used in polymer statistics as the freely jointed and freely rotating chain as well as the more sophisticated models with interdependent rotational states. Comparisons are made in the latter case between the present results and those obtained analytically with the simplifying assumption of a conformationally periodic chain. The relaxation spectra are explicitly calculated for polyethylene, isotactic polystyrene, isotactic polypropylene, and polydimethylsiloxane, which display large differences in stiffness among random coil polymers.