Maximum entropy deconvolution of dielectric and impedance data

Abstract

Dielectric relaxation and impedance measurements are often made on systems which possess a distribution of relaxation times. The data can be interpreted as a convolution of the distribution of relaxation times with a single Debye relaxation. In this case, it is desirable to determine the distribution. Most methods of deconvolution rely upon Fourier inversion, which is not ideal. In this paper we describe how the maximum entropy (MaxEnt) method can be used to deconvolute dielectric and impedance data. The MaxEnt result was sensitive to the amount of noise in the data and to the parameters of the program (noise tolerance and baseline). In general, as a result of the entropy term, the magnitudes of the deconvoluted relaxations were lower than the theoretical values. The MaxEnt method was quite resistant to the introduction of artificial peaks. However, when the data contained a large noise component, the noise could be interpreted as spurious additional relaxations when the noise tolerance was poorly chosen. For very broad relaxations, there was no advantage to be gained from deconvolution. The resolution of adjacent or overlapping peaks was not very good. The MaxEnt method would have serious difficulty in deconvoluting the real component of immittance data because of its sigmoidal shape. Most dielectric and impedance data contain a small number of relaxations, unlike other spectroscopic techniques where there may be hundreds. Thus, for most applications, complex non-linear least-squares regression would be preferable. The only promising use of MaxEnt in dielectric and impedance work would be for the extrapolation or interpolation of missing or unmeasured data.