Journal of Rheology, Vol.44, No.4, 831-841, 2000
Don't cry for me Charlie Brown, or with compliance comes comprehension
The different linear viscoelastic functions are, in theory, equivalent to each other, although the information that they emphasize is different. However, since viscoelastic measurements are never available over the entire time or frequency scale, and the results are not known with infinite precision, it is worthwhile to look at various of the otherwise equivalent viscoelastic functions. We present experimental data which show what appears to be an entanglement network plateau in the modulus, in nonentangled samples of selenium and a low molecular weight polystyrene with a narrow distribution of molecular weights. We show how the confusion can be easily avoided by inspecting the compliances and the retardation spectrum. We also present data on the molecular weight dependence of the length of the plateau as determined from the dynamic storage modulus and from the retardation spectrum. We find that the retardation spectrum identifies the presence of an entanglement network of polymer chains, whereas at low molecular weights the storage modulus does not. The origin of the false entanglement plateaus is shown to arise from the reciprocal of steady-state recoverable creep compliance J(s), which is convoluted in the modulus functions but is additive in the compliances.