Anomalous diffusion and memory effects on the impedance spectroscopy for finite-length situations

Immittance Data Validation using Fast Fourier Transformation (FFT) Computation - Synthetic and Experimental Examples

Exact data of an electric circuit (EC) model of RLC (resistor, inductor, capacitor) elements representing rational immittance of LTI (linear, time invariant) systems are numerically Fourier transformed to demonstrate within error bounds applicability of the Hilbert integral tranform (HT) and Kramers-Kronig (KK) integral tranform (KKT) method. Immittance spectroscopy (IS) data are validated for their HT (KKT) compliance using non-equispaced fast Fourier transformation (NFFT) computations. Failing of HT (KKT) testing may not only stem from non-compliance with causality, stability and linearity which are readily distinguished using anti HT (KKT) relations. It could also indicate violation of uniform boundedness to be overcome either by using singly or multiply subtracted KK transform (SSKK or MSKK) or by seeking KKT of the same set of data at a complementary immit- tance level. Experimental IS data of a fuel cell (FC) are also numerically HT (KKT) validated by NFFT assessing whether LTI principles are met. Figures of merit are suggested to measure success in numerical validation of IS data.

Evaluating the Impact of the Covariance of the Friction and Potential Gradient on Describing the Infiltration Process

During infiltration of water in soil, menisci form at the interface of water, grains, and air in the pores, inducing suction due to surface tension. Due to the random distribution of interconnected pores of different sizes, characteristic of porous media, differences in suction and friction inside pores give a diffusing infiltration front. The process of infiltration is often simulated by solving Richards' equation in which the water flux is calculated with Darcy's law. Underlying Darcy's law is the assumption that the gradients in flow potential and the flow resistance due to viscous forces are independent from each other. This paper shows that these parameters are dependent and negatively correlated. A new method for calculating flows in unsaturated porous media has been developed to evaluate the impact of the covariance on infiltration predictions. The results show that the impact is significant and leads to a reduction in infiltration rate and mean friction experienced during infiltration. The method thereby provides a physical explanation for the subdiffusion observed during water infiltration in soil and is consequently expected to provide more insights into the processes of infiltration.

The Kramers-Kronig relations for usual and anomalous Poisson-Nernst-Planck models

The consistency of the frequency response predicted by a class of electrochemical impedance expressions is analytically checked by invoking the Kramers-Kronig (KK) relations. These expressions are obtained in the context of Poisson-Nernst-Planck usual or anomalous diffusional models that satisfy Poisson's equation in a finite length situation. The theoretical results, besides being successful in interpreting experimental data, are also shown to obey the KK relations when these relations are modified accordingly.

Three to six ambiguities in immittance spectroscopy data fitting

Several important ambiguities in immittance spectroscopy (IS) model data-fitting results are identified and illustrated by means of complex-nonlinear-least-squares (CNLS) fits of experimental and synthetic frequency response data. A well-known intrinsic ambiguity, following from Maxwell's electromagnetic equations, arises from the indistinguishability in external measurements of conduction and displacement currents. Usual fit models for either dielectric or conductive-system situations, such as the Davidson-Cole one, only involve a strength parameter, a dielectric constant, a characteristic relaxation time, and a fractional exponent and lead to no additional ambiguities. But the situation is different for more powerful and useful general models, such as ordinary or anomalous diffusion Poisson-Nernst-Planck ones: PNP and PNPA, used here, whose historical background, current status, and applicability are described and discussed herein. They apply to two different kinds of experimental IS situations and involve several additional, potentially free fit parameters, such as the mobilities of positive and negative charge carriers, and generation-recombination parameters that determine the partial or complete dissociation of a neutral entity of concentration N(0) into positive and negative charge carriers of equal concentration, c(0). Then, several additional ambiguities appear that may require information about the material system involved for their adequate resolution.

Effects of transducer size on impedance spectroscopy measurements

The response to an electric field of electrolytic solutions, gels, liquid crystals, and other soft materials is described by the drift-diffusion and Poisson equations. Existing models, used for the interpretation of experimental data, usually consider the system as one dimensional (1D), which is valid only for an infinite electrode size. Here we solve numerically the model equations in 2D, considering a circular electrode with a finite radius, and discuss the limit of validity of the 1D approximation.