Extrapolation to Single-Relaxation-Time Behavior in Solutions of Poly(n-butylisocyanate)

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Abstract
The dielectric relaxation time of rodlike poly(n‐butylisocyanate) (PBIC), (–CO–NR–) n , where R = C 4 H 9 , has been observed for dilute solutions as a function of the polydispersity in the PBIC molecular weight. The mode of relaxation is rotation about the minor axis of the rodlike molecule (end‐over‐end rotation). The dielectric relaxation time for this mode is a sensitive function of molecular weight, and a distribution of relaxation times Φ(τ) is observed whenever a distribution of molecular weights ψ(M) is present. A one‐to‐one correspondence between Φ(τ) and ψ(M) is established by observing the half‐width W / 2 of the dielectric dispersion on a log frequency plot as a function of the ratio M w / M n , where M n and M w are the number and weight averages of ψ(M) . Extrapolation of the W / 2 vs M w / M n data to the monodispersed case (M w / M n = 1.0) is carried out in order to determine whether or not a monodispersed sample has a single relaxation time. The accuracy of the extrapolated half‐width suffers because the estimated uncertainty of the measured ratio M w / M n is ± 10%. The data do, however, satisfy a necessary condition for the presence of a single relaxation time. In the region M w / M n = 1.0 to 1.6 , the experimentally observed M w / M n is in good agreement with M w / M n calculated from the observed Φ(τ) . For these calculations it is assumed that each molecular species has a single relaxation time and that the molecular dipole moment is proportional to the molecular weight. A distribution ψ(M) may be obtained from the observed Φ(τ) if it can be assumed that all molecules have the same conformation.