Immittance-Diffusion Model

Bulk diffusion of electrolytes in solution results in an impedance that is inversely proportional to the square root of the angular frequency. In this case the real and imaginary components are the same. Complex-plane impedance plots of diffusion-limited conductance results in straight lines with unit positive slopes.

To determine the effect of diffusion on the expectation-maximization (EM) fit of the imaginary immittance to a superposition of Debye dielectrics, a model diffusion-limited process was formulated and run through the model-fitting EM algorithm.

Shown below are the results of this test. The imaginary immittance is plotted in dark blue and the expectation, or fit to the synthetic data, is plotted in pink. The equation used to synthesize the input data is displayed above the plot field, as is the model. In a word, the expectation fit faithfully follows the input data.

The affects of diffusion on the relaxation time spectrum can be seen below. Plotted below are the amplitudes of Lorentzian functions, or a(t), as a function of the relaxation time, t. The relaxation times are logarithmically distributed in the EM algorithm. Apparent is the fact that the relaxation time spectrum exhibits a long-time-constant plateau that declines for times shorter than lowest inverse angular frequency in the synthetic data.

Last Updated on Tuesday, August 03, 2004
By Stephen Bialkowski