Relaxation time spectra from short frequency range small-angle dynamic rheometry

In this work, the influence of the experimental frequency range over the relaxation time spectrum is studied. The relaxation time spectra were calculated from dynamic moduli, a well-known ill-posed problem, using a regularization method. The method solves the ill-posed problem by simultaneous minimization of the regularized standard deviation and a restriction function. The solution was validated using a simulated spectrum. Truncated moduli data generated from simulated spectra were used to evaluate the method for smaller frequency range data. Finally, experimental data of a wormlike micellar system mixed in aqueous solution with a zwitterionic copolymer were used to validate the method. It was possible to obtain relaxation time spectra from short frequency range data if the relaxation time range is allowed to be higher than the inverse of the highest and lowest experimental frequencies. These spectra can be used qualitatively to describe complex systems when no time-temperature superposition experiments are feasible.