Journal of Physical Chemistry, Vol.98, No.31, 7674-7684, 1994
Determination of Molecular-Weight Distribution of Entangled Cis-Polyisoprene Melts by Inversion of Normal-Mode Dielectric Loss Spectra
We consider inversion of experimental normal-mode dielectric loss spectra of entangled cis-polyisoprene melts to obtain the samples’ molecular weight distributions. Extrapolation and data completion procedures are proposed to compensate for incomplete data sets and enable separation of the normal-mode spectrum from relaxations unrelated to the normal-mode process. Two inversion methods are considered, namely, Tikhonov regularization and a regula-falsi iterative algorithm patterned after a scheme proposed by Imanishi and co-workers. Inversions by both methods of loss spectra simulated by a linear mixing rule and the autocorrelation function of reptation produce molecular weight distributions that are in close agreement with each other, indicating that results’ accuracy is primarily limited by the noise. Inversions of experimental loss spectra of three cis-polyisoprene melts above entanglement are in good agreement with the molecular weight distributions from size exclusion chromatography. We also discuss the use of the regula-falsi algorithm to invert spectra described by nonlinear mixing rules, to which Tikhonov regularization is not directly applicable. Inversions of loss spectra simulated by the Tsenoglou/des Cloizeaux theory correctly reproduce the main features of the original molecular weight distributions, indicating that the method may be useful to invert viscoelastic data. Noise and a lower sensitivity of the mixing rule to composition (relative to the linear mixing case) are believed to be the chief factors limiting resolution in this case.