Analysis of two-dimensional energy and relaxation-time distributions from temperature-dependent broadband dielectric spectroscopy

We present a method to determine the two-dimensional 2D distribution G(W,ln tau(o)) of the relaxation time tau=tau(o)exp(W/k(B)T) using an inversion of temperature-dependent broadband dielectric data. In contrast to the usual evaluation of 1D distributions g(tau), the 2D analysis reveals whether the broadening of a relaxation peak has its physical origins in a variation of the activation energy W, or the preexponential factor tau(o), or both. A study of the beta relaxation of a polymer blend demonstrates the validity of the analysis. We compare the distribution obtained from dielectric ac data (5 Hz-300 MHz, 100 K-300 K) with the results of a thermally stimulated depolarization currents sampling technique. The contour line of G(W,ln tau(o)) is shown to follow the compensation law. [S0163-1829(98)05815-9].