A powerful but still easy to use technique is proposed for the processing and analysis of dynamic mechanical data. The experimentally determined dynamic moduli, G'(co) and G"(co), are converted into a discrete relaxation modulus G (t) and a discrete creep compliance J(t). The discrete spectra are valid in a time window which corresponds to the frequency window of the input data.A nonlinear regression simultaneously adjust the parameters gi, 2i, i= 1,2,•.. N, of the discrete spectrum to obtain a best fit of G', G", and it was found to be essential that both gi and 2i are freely adjustable. The number of relaxa-
Abstract." The analysis of dynamic mechanical data indicates that linear flexible polymer chains of uniform length follow a scaling relation during their relaxation, having a linear viscoelastic relaxation spectrum of the form H(2) = n I G ° × (2/~.max) nl for 2.---).max. Data are well represented with a scaling exponent of about 0.22 for polystyrene and 0.42 for polybutadiene. The plateau modulus G ° is a material-specific constant and the longest relaxation time depends on the molecular weight in the expected way. At high frequencies, the scaling behavior is masked by the transition to the glassy response. Surprisingly, this transition seems to follow a Chambon-Winter spectrum H(2) = Cit-% which was previously adopted for describing other liquid/solid transitions. The analysis shows that the Rouse spectrum is most suitable for low molecular-weight polymers M~-M C, and that the de Gennes-Doi-Edwards spectrum clearly predicts terminal relaxation, but deviates from the observed behavior in the plateau region.
A radiation crosslinked model linear low-density polyethylene (LLDPE) exhibits power-law relaxation, G ( t ) = S t -n at its gel point (GP). The relaxation exponent has a value of about 0.46. The relaxation behavior is dominated by power laws, not only directly at GP, but in a very broad vicinity of GP and in a frequency window, which narrows with distance from the gel point. The power law exponent decreases with increasing radiation dose (increasing extent of crosslinking). Independent measurements of the gel fraction and the molecular-weight distribution of the radiated samples' soluble fraction support the rheological observations.
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