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The relaxation of linear flexible polymers: Correlation between molar mass distribution and rheological data of polymer melts
Abstract
The focus of this work is on the relaxation behavior of linear flexible polymers in their melt state. Points of interest are the determination of the relaxation time spectrum, scaling relations in the spectrum of model systems and the correspondence between rheological properties and structural parameters such as the molar mass distribution. A powerful but easy to use technique is proposed for processing and analysis of dynamic mechanical data. The experimentally determined dynamic moduli, G$\sp\prime(\omega)$ and G$\sp{\prime\prime}(\omega),$ are converted into a discrete relaxation spectrum. A non-linear regression simultaneously adjusts the parameters g$\sb{\rm i},$ $\lambda\sb{\rm i},$ i = 1 ... N, of the discrete spectrum to obtain the best fit of G$\sp\prime,$ G$\sp{\prime\prime}.$ Ill-posedness is avoided by allowing the algorithm to reduce the total number of relaxation modes. The spectrum, which is denoted as the parsimonious spectrum, contains the minimum number of modes which describe the experimental data within the scatter. A relation has been derived between the continuous and the discrete form of linear viscoelastic relaxation time spectra. Both forms can be interconverted, and they are equivalent in their ability to reproduce G$\sp\prime(\omega),$ G$\sp{\prime\prime}(\omega),$ or G(t) data. The linear superposition of a few Maxwell-modes is already able to mimic the continuous form. Typical experimental spectra of broadly distributed and of monodisperse polymers provide the means for testing the proposed relations. The analysis of linear viscoelastic data indicates that linear flexible polymer chains of uniform length follow a scaling relation during their relaxation, having a linear viscoelastic spectrum of the form $\rm H(\lambda)=n\sb{e}\ G\sbsp{N}{0}(\lambda/\lambda\sb{max})\sp{n\sb{e}}$ for $\lambda<\lambda\sb{\rm max},$ the Baumgaertel-Schausberger-Winter-spectrum (BSW-spectrum). Data are well represented with a scaling exponent n$\sb{\rm e}$ = 0.23 for polystyrene, polybutadiene and polyethylene, while a scaling exponent n$\sb{\rm e}$ = 0.17 is found for polyisoprene. The BSW-spectrum is used in conjunction with a blending rule for polydisperse linear flexible polymers. In the blending rule, the broadly distributed polymer (blend) is viewed as a mixture of monodisperse fractions and the relaxation of the blend is assumed to be a linear superposition of the relaxation spectra of these monodisperse fractions which now are known as BSW-spectra. The blending rule predicts the molar mass distribution of a linear polymer from the spectrum and vice versa with a high degree of accuracy. The physical interaction between the molecules of the various fractions is accounted for by horizontal and vertical shifts of the BSW-spectra before adding them up.
Subject Area
Chemical engineering
Recommended Citation
Baumgaertel, Michael, "The relaxation of linear flexible polymers: Correlation between molar mass distribution and rheological data of polymer melts" (1992). Doctoral Dissertations Available from Proquest. AAI9219402.
https://scholarworks.umass.edu/dissertations/AAI9219402