-
-
We analyse the problem of impedance for a diffusion controlled charge transfer process across an irregular interface. These interfacial irregularities are characterized as two class of random fractals: (i) a statistically isotropic self-affine fractals and (ii) a statistically corrugated self-affine fractals. The information about the realistic fractal surface roughness has been introduced through the bandlimited power-law power spectrum over limited wave numbers. The details of power spectrum of such roughness can be characterized in term of four fractal morphological parameters, viz. fractal dimension ($D_H$), lower ($\ell$), and upper (𝐿) cut-off length scales of fractality, and the proportionality factor (𝜇) of power spectrum. Theoretical results are analysed for the impedance of such rough electrode as well as the effect of statistical symmetries of roughness. Impedance response for irregular interface is simplified through expansion over intermediate frequencies. This intermediate frequency expansion with sufficient number of terms offers a good approximation over all frequency regimes. The Nyquist plots of impedance show the strong dependency mainly on three surface morphological parameters i.e. $D_H$, $\ell$ and 𝜇. We can say that our theoretical results also provide an alternative explanation for the exponent in intermediate frequency power-law form.
-
Randles-Ershler admittance model is extensively used in the modeling of batteries, fuel cells, sensors etc. It is also used in understanding response of the fundamental systems with coupled processes like charge transfer, diffusion, electric double layer charging and uncompensated solution resistance. We generalize phenomenological theory for the Randles-Ershler admittance at the electrode with double layer capacitance and charge transfer heterogeneity, viz., non-uniform double layer capacitance and charge transfer resistance (c/d and R/CT ). Electrode heterogeneity is modeled through distribution functions of R/CT and c/d , viz., log-normal distribution function. High frequency region captures influence of electric double layer while intermediate frequency region captures influence from the charge transfer resistance of heterogeneous electrode. A heterogeneous electrode with mean charge transfer resistance RCT shows faster charge transfer kinetics over a electrode with uniform charge transfer resistance (R/CT ). It is also observed that a heterogeneous electrode having high mean with large variance in the RCT and cd can behave same as an electrode having low mean with small variance in the R/ CT and c/d. The origin of coupling of uncompensated solution resistance (between working and reference electrode) with the charge transfer kinetics is explained. Finally, our model provides a simple route to understand the effect of spatial heterogeneity
-
Theory is developed for the electrochemical impedance spectroscopy (EIS) of the diffusion limited adsorption process coupled with reversible charge transfer at rough electrodes under the influence of ubiquitous uncompensated solution resistance. This study quantitatively relates the impedance response ofrough electrode to its phenomenological components, viz., diffusion limited adsorption, reversible charge transfer and uncompensated solution resistance. The random roughness of electrode is expressed by thesurface statistical property, i.e., power spectrum of roughness. The fractal nature of roughness is characterizedin terms of fractal dimension, lower cut-off length and topothesy length. The high-frequency regime iscontrolled by the uncompensated solution resistance whereas the low-frequency regime is governed by theadsorption process. The magnitude of impedance as well as phase decreases with rise in adsorption isotherm(length) parameter. The intermediate frequency regime is controlled by the coupling of adsorption and uncompensated solution resistance with the diffusion process. The fractal roughness parameters has quantitative influence on the magnitude of impedance over whole frequency regime while the phase plot shows qualitative difference in the intermediate frequency regime. The governing length scales which controls the characteristic crossover frequencies are: diffusion length, adsorption-ohmic coupling length and topothesy length (or width of interface). The three emergent crossover frequencies are: (i) ohmic reduced innercrossover frequency (ii) adsorption roughness topothesy dependent pseudo-quasireversibility characteristic frequency (iii) outer crossover frequency.
Synopsis: This study quantitatively relates the impedance response of rough electrode to its phenomenological components, viz., diffusion limited adsorption, reversible charge transfer and uncompensated solution resistance. The random roughness of electrode is expressed by the surface statistical property, i.e., power spectrum of roughness.
-
The impedance method is developed for the
in-situ determination of electroactive RMS roughness of the electrode for different electrochemical systems. Three electrochemical systems are analyzed to showthe wider applicability of this method,viz ., (i) rough gold electrode in RTIL medium containing ferrocene, (ii)rough platinum electrode in a mixture of glycerol and water containing potassium ferro/ferricyanide, (iii) dropcasted rGO/glassy carbon electrode in aqueous sodium nitrate containing potassium ferro/ferricyanide. The electrochemical impedance spectroscopy (EIS) under reversible electron transfer condition on a rough electrode has an intermediate frequency domain with an anomalous Warburg response. When the diffusion length (√D/ω) becomes equal to the RMS roughness at a characteristic frequency (ωM) which is manifested in experimental EIS data as a maximum point in phase angle, where D is the diffusion coefficient of an electroactive species. The frequency range: (ωM/50≤ω≤5ωM) represents the anomalously enhanced diffusionwhich is caused by the trapping of diffusing electroactive molecules in rugged landscape. Additional advantage of this method is explored for determination of unknown diffusion coefficient through equation:√D1/ωM1=√D2/ωM2, using same electrode in two different media with diffusion coefficient D1 and D2.Finally, experimental results shows the resilience of this novel in-situ EIS method for the determination of h and D in different media.
-
-
Journal of Chemical Sciences
Volume 135, 2023
All articles
Continuous Article Publishing mode