Singular behavior of Rouse-like spectra

In this study an extended Rouse formalism is used to obtain results belonging to (i) linear chains (K beads; K−1 Hookean springs), (ii) K×K cubic networks, or (iii) K×K×K cubes immersed in a Newtonian fluid. These three systems are subjected to small-amplitude oscillatory shear flow of frequency ω and the resulting dynamic moduli G′(ω) and G″(ω) show significant differences. For large K, the corresponding relaxation spectra H(λ) appear to be smooth functions of time λ, in which some obvious discontinuities are observed, i.e., the so-called Van Hove singularities (well known in solid-state physics). Actually, for these three systems a relation is obtained between H(λ) and the frequency spectra g(ω) used in solid-state physics.