A new method for obtaining distributions of relaxation times from frequency relaxation spectra

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Abstract
Starting from the well‐known C O N T I N algorithm/program [S. W. Provencher, Comput. Phys. Commun. 27, 213 (1982)] for the calculation of inverse Laplace transformations, we have developed a new method for obtaining distributions of relaxation times out of frequency relaxation spectra. The method has been tested under several different restrictive conditions, many of them harder than those of actual real experiments and has proved to be successful. Moreover, to our knowledge, it gives the best power resolution ever referenced and its ability to undergo the problem of noise seems to be better than those of other algorithms used to treat the kind of ill‐conditioned problems presented here. Our program can be directly applied on the data without the need of performing any interpolation nor extrapolation, which could somehow bias the results, especially in the extrapolation case. Some practical applications of the method are shown for the analysis of the dielectric relaxation spectra of both, a bulk homopolymer polyvinyl chloride and a liquid crystalline polymer. The method is also generalized to deal with different problems where the physical mechanisms involved or the technical procedure suggest to use distributions of non‐Debye processes.