Segmental Motions of cis-Polyisoprene in the Bulk State: Interpretation of Dielectric Relaxation Data

Dipolar correlation functions are calculated for cis-polyisoprene in the bulk state. The time decay of the correlation functions results from the orientational motion of dipole moments accompanying the configurational transitions of the chain backbone. Examination of the intramolecular conformational energetics of the chain reveals that the transitions between rotational isomeric states takes place through coupled motion of triplets of neighboring bonds in the repeat units. The intermolecular effect on local chain dynamics is included in two stages: First, the relaxation in a homogeneous environment is treated through adoption of a local effective frictional resistance, increasing with the size of the kinetic segment. Second, two dynamically distinct environmental states representative of the free volume or density fluctuations of the medium are considered. The frequency distribution of relaxational modes is found to broaden with increasing number of bonds cooperatively participating in the segmental mode process. Calculations are performed for different sizes of kinetic segments which are defined as a sequences of bonds cooperatively participating in local relaxation. Predictions of the theory are compared with recent dielectric measurements (Boese, D.; Kremer, F. Macromolecules 1990, 23, 829) of bulk cis-polyisoprene. Calculations indicate that the experimentally observed Kohlrausch-Williams-Watts (KWW) exponent of 0.39 is reproduced when a kinetic segment of three repeat units cooperatively relaxing in the presence of free volume fluctuations of the environment is considered.