  Polymer melts show a characteristic molecular weight dependent relaxation
time that can be related to the unentangled and entangled regime. At high
molecular weights, influence of contour length fluctuations and con-straint
release cease and pure reptation prevails. With the broad frequency range
dielectric spectroscopy can fol-low polymer dynamics over a very broad
temperature range, with the additional advantage of recording the spec-tral
shape which contains information on reptation. Here we investigate the apparent
discrepancy in the molecular weight for the onset of pure reptation from the
molecular weight dependence and the spectral shape. We examined the popular
derivative method and compared it with a version that includes higher order
terms. Higher order terms lead to a more accurate peak shape and position than
those determined with the simpler version. This becomes important if
experimental spectra contain conductivity and polarization contributions.
Higher order terms require the introduction of an interpolating function to
analyze experimental spectra, which lets the Havriliak-Negami function appear
to be a more robust, yet reliable tool to determine the peak shapes. We reach
the conclusion that molecular weight dependence and spectral shape can be both
strongly affected by conductivity and polarization contributions. While this
leaves uncertainties on the accurate value of the transition molecular weight,
the peak shape points to the existence of reptation and contour length
fluctuations in polyisoprene with a molecular weight greater than 1000 kg/mol,
which would imply a ten times greater threshold molecular weight than expected
from previous estimates using the molecular weight dependence.
