Rheol Acta DOI 10.1007/s00397-008-0280-5 ORIGINAL CONTRIBUTION Relaxation patterns of long, linear, flexible, monodisperse polymers: BSW spectrum revisited

Abstract Theoretical predictions for the dynamic mod-uli of long, linear, flexible, monodisperse polymers are summarized and compared with experimental obser-vations. Surprisingly, the predicted 1/2 power scaling of the long-time modes of the relaxation spectrum is not found in the experiments. Instead, scaling with a power of about 1/4 extends all the way up to the longest relaxation times near τ /τmax = 1. This is expressed in the empirical relaxation time spectrum of Baumgaertel-Schausberger-Winter, denoted as “BSW spectrum,” and justifies a closer look at the properties of the BSW spectrum. Working with the BSW spectrum, however, is made difficult by the fact that hypergeometric func-tions occur naturally in BSW-based rheological mate-rial functions. BSW provides no explicit solutions for the dynamic moduli, G′(ω), G′′(ω), or the relaxation modulus G(t). To overcome this problem, close ap-proximations of simple analytical form are shown for these moduli. With these approximations, analysis of linear viscoelastic data allows the direct determination of BSW parameters