Multifractal spectra and the relaxation of model polymer networks

Abstract

The mechanical and dielectric relaxation of polymer networks depends (especially in simple Gaussian-type approaches which extend the Rouse model) on the eigenvalues of the corresponding connectivity matrices. We use this to evaluate explicitly experimentally accessible relaxation forms for finite Sierpinski-type networks, whose eigenvalue spectra are multifractal. It turns out that the observable quantities are by far less singular than the eigenvalue spectra, since the underlying spectral structures get smoothed out. Our results establish unequivocally the spectral dimension as fundamental relaxation parameter; to see this, however, the finite fractal networks have to be sufficiently large.