INTERRELATION BETWEEN CONTINUOUS AND DISCRETE RELAXATION-TIME SPECTRA

A relation has been derived between the continuous and the discrete forms of linear viscoelastic relaxation-time spectra. Both forms can be interconverted, and they are equivalent in their ability to reproduce G'(omega), G"(omega), or G(t) data. The linear superposition of even only a few Maxwell-modes is able to mimic the continuous form. This rapid conversion leads to the 'parsimonious' spectrum which models the linear viscoelastic relaxation with the smallest possible number of modes. Typical experimental spectra of broadly distributed and of monodisperse polymers provide the means for testing the proposed relations. Effects of noise and data density were studied for G', G"-data sets.