Anomalous-diffusion approach applied to the electrical response of water

Detection of Salt Content in Canned Tuna by Impedance Spectroscopy: A Feasibility Study for Distinguishing Salt Levels

The electrical impedance of dilute aqueous solutions containing extracts from five brands of canned tuna is analyzed using impedance spectroscopy in order to analyze their salt content and detect the potential presence of other salts beyond the well-stated NaCl. A complex electrical impedance is modeled with an equivalent electrical circuit, demonstrating good agreement with experimental data. This circuit accounts for the contribution of ions in the bulk solution, as well as those contributing to electrode polarization. The parameters describing the equivalent circuits, obtained through fitting data to the electrical impedance, are discussed in terms of the various ion contributions to both the electrical double layer at the electrode interface and the electrical conductivity of each solution. The ionic contribution to the electrical impedance is compared with that of a pure NaCl solution at the same concentration range. This comparison, when extended to real samples, allows for the development of a model to estimate the electrical conductivity of canned tuna samples, thereby determining the salt concentration in tuna. The model enables differentiation among the various samples of tuna studied. Subsequently, the potential presence of other ions besides Na+ and Cl- and their contribution to the electrical properties of each canned tuna extract is considered, especially for samples with a higher ratio of the sum of K+ and phosphates to Na+ concentration. This analysis shows the potential of impedance spectroscopy for on-site and rapid analysis of salt content and/or detection of additives in canned tuna fish.

Extensions and solutions for nonlinear diffusion equations and random walks

We investigate a connection between random walks and nonlinear diffusion equations within the framework proposed by Einstein to explain the Brownian motion. We show here how to properly modify that framework in order to handle different physical scenarios. We obtain solutions for nonlinear diffusion equations that emerge from the random walk approach and analyse possible connections with a generalized thermostatistics formalism. Finally, we conclude that fractal and fractional derivatives may emerge in the context of nonlinear diffusion equations, depending on the choice of distribution functions related to the spreading of systems.

Ion Motion in Electrolytic Cells: Anomalous Diffusion Evidences

In this study, we argue that ion motion in electrolytic cells containing Milli-Q water, weak electrolytes, or liquid crystals may exhibit unusual diffusive regimes that deviate from the expected behavior, leading the system to present an anomalous diffusion. Our arguments lie on the investigation of the electrical conductivity and its relationship with the mean square displacement, which may be used to characterize the ionic motion. In our analysis, the Poisson-Nernst-Planck diffusional model is used with extended boundary conditions to simulate the charge transfer, accumulation, and/or adsorption-desorption at the electrode surfaces.

Warburg's impedance revisited

The derivation of Warburg's impedance presented in several books and scientific papers is reconsidered. In the past it was obtained by assuming that the total electric current across the sample is just due to the diffusion, and that the external potential applied to the electrode is responsible for an increase of the bulk density of charge described by Nernst's model. We show that these assumptions are not correct, and hence the proposed derivations are questionable. When the electrochemical impedance of a cell of an insulating material where external charges are injected of a given sign is correctly determined, in the high frequency region the real and imaginary parts do not follow the trends predicted by Warburg's impedance. The analysis presented in this paper is relevant to a symmetric cell, in the Nernstian approximation. It can be easily generalized to the case of an asymmetric cell, assuming boundary conditions where the conduction current across the electrodes is proportional to the surface electric field.

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.

Different diffusive regimes, generalized Langevin and diffusion equations

We investigate a generalized Langevin equation (GLE) in the presence of an additive noise characterized by the mixture of the usual white noise and an arbitrary one. This scenario lead us to a wide class of diffusive processes, in particular the ones whose noise correlation functions are governed by power laws, exponentials, and Mittag-Leffler functions. The results show the presence of different diffusive regimes related to the spreading of the system. In addition, we obtain a fractional diffusionlike equation from the GLE, confirming the results for long time.