Polymer dynamics including side group motion: Free draining limit

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Abstract
We present an exactly soluble model of polymer chain dynamics in which the effects of side group interactions are explicitly treated. Calculations for the relaxation spectrum, intrinsic viscosity, [η (ω)], and dielectric dispersion for both longitudinal and perpendicular dipole moments are presented in the free draining limit. Perpendicular dipoles are described by attaching a dipole moment to each side group. The relaxation spectrum displays two branches corresponding to local and global chain motions, the latter being highly depressed. The low frequency behavior of [η (ω)] and of longitudinal dipoles is shown to be well represented by an effective Rouse model, whereas [η (ω)] displays a plateau, [η]∞, at higher frequencies which is (i) not associated with the gap in the relaxation spectrum, (ii) independent of molecular weight for long enough chains, and (iii) correlated to the degree of side group motional freedom in accordance with experiment. For short chains the plateau region [η]∞ vanishes, and the model displays a molecular weight dependence. The relaxation of perperdicular dipoles is demonstrated to be independent of molecular weight for long enough chains. For shorter chains, however, global chain motions (e.g., overall rotation) significantly affect the behavior of the dielectric loss. Our model is shown to reproduce the phenomenological model of Dubois–Violette et al. and of Stockmayer et al. which has been used to rationalize the perpendicular dipole dielectric data. Furthermore, we show how our model and generalizations thereof can be derived from a true molecular model with realistic bonding and nonbonding interactions using the Zwanzig–Mori projection operatior formalism.

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