Frequency Transition from Diffusion to Capacitive Response in the Blocked-Diffusion Warburg Impedance for EIS Analysis in Modern Batteries

Abstract

The use of the Blocked-diffusion Warburg (BDW) impedance within electrochemical impedance spectroscopy (EIS) measurements can unveil diffusion properties of the electroactive material of modern batteries at different states-of-charge. The impedance response of the BDW comprises a diffusion response of charge carriers through a shortdiffusion distance (e.g. the solid-phase in electroactive material of battery electrodes) and a capacitive response due to accumulation of charge carriers in a blocked-interface (e.g. impermeable current collector of a thin film electrode). This study has developed a mathematical expression based on the Newton-Raphson iteration method to calculate the frequency and time constant during the transition from diffusion to capacitive response in the BDW impedance. The mathematical procedure to calculate the frequency during the diffusioncapacitive transition response in the BDW has been written in a script in Matlab® software and is applied to BDW impedance responses reported in previous studies and extracted from EIS measurements in Li-ion and NiMH batteries. This study demonstrates that the time constant during the transition from diffusion to capacitive response in the BDW differs from the characteristic time constant commonly represented in the BDW mathematical expression. The characteristic time constant represented in the BDW mathematical expression is related to the rate of accumulation of charge carriers in the blocked-interface of the electrode. On the other hand, the time constant during the transition from diffusion to capacitance responses in the BDW impedance can be related to diffusion properties in solid-phase particles with heterogeneous size distribution in the electroactive material of modern battery electrodes.

Salt Concentration-Regulated Desalination Mechanism Evolution in Battery Deionization for Freshwater

“…Figure d shows that the resistance of the solution increases with the decrease of NaCl concentrations, and the resistivity of 0.01 M NaCl is 851 Ω cm. To elucidate the origin of the resistance increase, the detailed underlying relationships of resistances and ion concentrations are given in eqs – − where Z is the resistance of the electrode system; R m is the resistance of the active material; l is the distance between the working and counter electrodes; A is the area of an electrode; e 0 is the elementary charge; c ± and z ± are the concentration and charge of cations or anions, respectively; u + and u – are the ionic mobility of cations and anions, respectively; k i 0 is the rate constant; n is the number of moles of electrons involved in the electrochemical reaction; c i 0 presents the concentration of charged species in the electrolyte; and D is the diffusion coefficient of the ion. Furthermore, eq defines the relationship between the potential and resistance of the electrode where i is the current density.…”

Locating the Frequency of Turnover in Thin-Film Diffusion Impedance

“…Over the years, different criteria for the frequency of turnover have been suggested. ,,,, Armstrong proposed ω g = 5.12 ω d and Cabanel et al used ω g = 3.88 ω d . These criteria were developed from the geometrical properties of the impedance Z (ω), e.g., by taking a specific value of the derivative of the Z -line in the complex plane.…”

“…16,17 In particular, the identification of the frequency that marks the transition between diffusion in infinite space and capacitive charging of a film is an important problem that has been treated for decades. 6,13,15,18,19 Here, we provide a physical criterion to establish the frequency of transition in relation to the thin-film parameters.…”

“…Likewise, the impedance of diffusion-recombination, often determined by transmission line models, is widely used to understand the charging in semiconductor devices, solar cells, − and porous electrodes. The identification of characteristic frequencies of the impedance of electrochemical systems using both responses in the frequency and time domains has been treated extensively. , In particular, the identification of the frequency that marks the transition between diffusion in infinite space and capacitive charging of a film is an important problem that has been treated for decades. ,,,, Here, we provide a physical criterion to establish the frequency of transition in relation to the thin-film parameters.…”

Electrochemical Characterisations to Elucidate the Pseudocapacitance Mechanisms of a CdS/WOx Nanocomposite Photoanode in Acidic Aqueous Electrolytes

“…7 [52][53][54][55]; for instance, the extrapolated resistance in the limit of infinite f corresponds to the total series resistance of the electrode and electrolyte combination, Rin, whilst the electric double-layer capacitance, Cdl, and the effective resistance of charge-transfer processes, Rct, are commonly estimable from the diameter and peak position of the semi-circular relationship between imaginary and real impedance at intermediate frequencies. As one approaches the direct-current mode of operation, the EIS behaviour is predominantly dictated by pseudocapacitance mechanisms; this contribution can often be described by a finite-space Warburg impedance, ZW, given by [53][54][55][56][57][58][59][60][61]…”