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

Abstract

The dielectric relaxation time of rodlike poly(n-butylisocyanate) (PBIC), (–CO–NR–)n, where R = C4H9, 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 Mw / Mn, where Mn and Mw are the number and weight averages of ψ(M). Extrapolation of the W / 2 vs Mw / Mn data to the monodispersed case (Mw / Mn = 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 Mw / Mn is ± 10%. The data do, however, satisfy a necessary condition for the presence of a single relaxation time. In the region Mw / Mn = 1.0 to 1.6, the experimentally observed Mw / Mn is in good agreement with Mw / Mn 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.