Abstract
The application of the Marquardt‐Levenberg procedure for the determination of discrete relaxation spectra from dynamic mechanical experiments on molten polymers is reviewed. It allows the calculation of a minimum number of relaxation modes, relaxation times and contribution of each time to the modulus in the terminal zone. All parameters are kept freely adjustable. The Marquardt‐Levenberg procedure enables the minimisation of the χ^2^ function between the measured values, G′(ω) and G″(ω), and those obtained by the simulated spectrum. The number of relaxation modes is smoothly increased until no improvement on the minimum value of χ^2^ is observed. The criterium to stop the iterative procedure can be the appearance of physically improper values (negative values), but it is shown that it is better to stop the increase of the number of modes before the problem becomes ill‐posed. This can be done by a comparison between the uncertainties on the calculated parameters and the values of these parameters. The uncertainties can be calculated by the Marquardt‐Levenberg algorithm at each step of the calculation. The method has been tested on its ability to recover a given spectrum from model data and on a set of real experimental measurements on a monodisperse polystyrene. The calculated spectra enable calculation of the various rheological parameters. The agreement between the calculated values of G′ and G″ obtained from the recovered spectra, and the experimental ones is very good and the relative errors are very low (less than 4%). Furthermore, the calculated rheological parameters are found to be very close to those that can be evaluated from the experimental curves.