Implications of Spectral Self‐Similarity for Polymer Melts and Solutions

Abstract

Abstract

ABSTRACT The linear viscoelasticity of monodisperse, linear, flexible, entangled polymer chains is inherently self‐similar. As is well known, in both melts and solutions their relaxation‐time spectrum H ( τ ) adopts a common structure independently of molecular detail or solvent content. Remarkably, the same self‐similar spectrum reappears in other (non‐polymeric) monodisperse disordered materials, including dense colloidal suspensions, interfacial colloids, and low‐molecular‐weight glass formers. Despite profound differences in chemistry, architecture, and length scale, these systems converge onto a common spectral organization, implying that molecular or particular details primarily influence spectral parameter values, whereas the overall form is governed by a more universal self‐similar dynamical framework. The self‐similar framework involves linearly superimposed branches: the fast branch, , associated with Rouse‐type local segmental motion, and the slow branch, , reflecting cooperative dynamics under topological constraints (self‐caging). The slow branch terminates at the longest relaxation time . Then H ( τ ) crosses over to terminal Maxwell flow. Molecular details, while having no influence on the universal shape of the spectrum, determine the values of its five parameters: the plateau modulus , the characteristic times and , and the exponents and . The purpose of this perspective is to articulate this universality and to examine its implications for polymer rheology.