A Non-Stationary Model for Analysis of Impedance Spectra of Biological Samples

Electric impedance spectrum (EIS) is attracting attention in many areas of science, ranging from electrochemistry and material science to medical diagnosis. Interestingly, theoretical description often stops at material constants and specific physical mechanisms are represented by equivalent circuit elements, which is also motivated by the common use of various bridge methods. This specifically applies to biological samples, which exhibit a rich variety of responses to the electric field. Here, we present a step further from the description that utilizes equivalent circuit elements. We demonstrate how alteration of the mesoscopic structure affects the EIS in a biological sample: a cucumber under thermal treatment that comprises a cooling and warming phase. As the freezing temperature of water is exceeded during the cycle, the cucumber becomes frosted, which leads to unrecoverable changes in the internal structure, with no change of chemical composition. The experimental evidence is complemented by theoretical analysis, based on a novel approach to modeling non-stationary problems, derived from the stationary Poisson-Boltzmann equation. We demonstrate a qualitative agreement between the theoretical and the experimental results, and discuss the procedure for tuning the model. We also demonstrate that, of the temperature variations of the position of the beta dispersion, the one related to the mesoscopic structure, can be used to assess the ionic strength of the material, determine the microscopic diffusion constant, or reflect the changes in mesoscopic structure, depending on experimental protocol.