Determination of Relaxation Spectra from Damping Measurements

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Abstract
A method is shown for the determination of the relaxation spectrum from the data furnished by dynamical experiments, and in particular from the damping (imaginary part of the complex modulus) as a function of frequency. The circular functions are eigenfunctions of the relevant integral equation, which can therefore be solved numerically by expansion. The spectrum is obtained by first making a Fourier analysis, multiplying every coefficient by the associated eigenvalue, and then synthesizing the new Fourier series. An estimate is given of the resolving power of the method, which is limited only by the error in the experimental data. As an illustration, the spectrum of polyisobutylene in the frequency domain corresponding to the rubber-glass transition is found from published data.