Relaxation of the aspherical shapes of random-coil polymer chains

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Abstract
The conformations of random‐coil polymer chains are known to be appreciably more aspherical than might have been expected intuitively. However, this instantaneous asphericity will only affect the measured physical properties of flexible chains in solution if the relaxation of the asphericity requires a time longer than the inherent sampling time of the experiment. It is therefore important, in the analysis of phenomena which depend upon chain shape, to know the time scale over which deviations from spherical symmetry persist. In this paper we extend our previous work on the relaxation of asphericity in chains without excluded volume interactions and present corresponding results for chains with excluded volume. Autocorrelation functions for the radius of gyration squared, its principal components, and the moments of inertia are determined using a dynamical model for linear polymer chains which simulates excluded volume effects. The results suggest that the asphericity of a random‐flight chain is increased by the introduction of excluded volume interactions, and that the segment distribution will appear spherically symmetric only when it is averaged over a time comparable with or longer than the longest times in the relaxation‐time spectrum of the chain.