Self-Similarity and Power-Law Spectra of Polymer Melts and Solutions

Both the Rouse and Doi-Edwards models can be expressed by the relaxation spectra, in the form of power-law functions. The concept of self-similarity has offered a simple solution to many problems in polymer physics. Since the solutions derived from self-similarity are power-law functions, it is essential to check whether the relaxation spectrum of polymeric fluids can be derived by self-similarity. In this study, the power-law spectrum of an unentangled polymer solution is derived by using the self-similarity approach, which does not work for entangled polymeric fluids. Although Baumgaertel et al. (Rheol. Acta 29, 400–408 (1990)) showed that the power-law spectrum can quantitatively describe the linear viscoelasticity of monodisperse polymer melts, regardless of molecular weight, they did not find the universality of the exponent of the spectrum because they found different exponents for different polymers. Under the consideration existing the universality of linear viscoelasticity of polymer melts, this paper deals with the universality of the exponent by employing a new regression algorithm and confirms that the exponent is independent of the type of polymer.