Contribution of Surface Distributions to Constant-Phase-Element (CPE) Behavior: 3. Adsorbed Intermediates

doi:10.1016/j.electacta.2017.08.081

Electrochimica Acta

Volume 251, 10 October 2017, Pages 99-108

https://doi.org/10.1016/j.electacta.2017.08.081 Get rights and content

Highlights

•
Impedance simulations for reactions coupled by adsorbed intermediates.
•
Corresponding faradaic impedance shows dispersion at low frequencies.
•
Low-frequency dispersion caused by potential dependence of the faradaic impedance.
•
Low-frequency dispersion caused by surface distributions of rate constants.
•
Contribution of frequency dispersion reduced by use of small electrodes.

Abstract

The influence of surface distributions on rates of heterogeneous reactions coupled by adsorbed intermediates was studied to determine whether this form of surface heterogeneity can provide a physical explanation for constant-phase-element behavior. Results obtained from finite-element simulations on disk and recessed disk electrodes show that there are two components that give rise to frequency dispersion. Frequency dispersion occurs due to geometry-induced nonuniform current distributions which leads to a complex ohmic impedance. The effects of geometry-induced frequency dispersion may be mitigated by use of small electrodes. Frequency dispersion also occurs due to the potential dependence of the faradaic impedance. The characteristic frequency associated with this form of frequency dispersion is not dependent on disk radius, but the contribution of frequency dispersion associated with reactions coupled by adsorbed intermediates may be reduced with the use of small electrodes.

Introduction

Frequency dispersion is almost always observed in impedance measurements over a broad range of frequencies and is assumed to be caused by a distribution of time constants. Constant-phase elements (CPE) are often used to fit impedance measurements exhibiting frequency dispersion, but the extracted parameters do not necessarily have a clear physical significance. Therefore, there is a need to form an understanding of the factors that contribute to frequency dispersion in impedance measurements and to uncover the physical origin of the constant-phase element.

Jorcin et al.[1] used local impedance spectroscopy to show that frequency dispersion can arise from surface or normal distributions of time constants. The frequency dispersion associated with a distribution of time constants normal to the electrode surface is well established; whereas, the frequency dispersion associated with a surface distribution is not well understood. Hirschorn et al. [2], [3] showed that a power-law distribution of resistivity through a film yields CPE behavior. The power-law-model approach has been used successfully to extract a film capacitance and associated parameters for a variety of systems, including oxides on steel, [4] human skin, [4], [5] and polymer coatings.[6], [7]

Brug et al. [8] developed an expression for the capacitance extracted from a CPE caused by a surface distribution of capacitance. Córdoba-Torres et al. [9] showed that the Brug model accounted for the correlation observed between CPE parameters α and Q for two experimental conditions: the corrosion of polycrystalline iron and the deposition of CaCO₃ scale on gold electrodes. The results were attributed to a distribution of time constants associated with surface heterogeneity. The exact nature of the surface heterogeneity was not identified. In subsequent work, Córdoba-Torres et al. [10] suggested that the CPE behavior results from energetic distributions rather than geometric heterogeneity or roughness.

Alexander et al. [11] showed that a capacitance distribution gave rise to frequency dispersion, but the effect was seen at frequencies higher than that associated with the disk geometry. The characteristic length for a periodic radial distribution was the period of the distribution and, as the period decreased, the frequency dispersion occurred at higher frequencies. A surface distribution of reactivity for a single-step reaction mechanism did not produce frequency dispersion.[12] However, Wu et al. [13] showed that the geometry of a disk electrode embedded within an insulating plane with reactions involving adsorbed intermediates causes frequency dispersion at low frequencies. Their conclusions were supported by comparison to experimental results obtained for an iron disk in a 0.5 M H₂SO₄ solution.[14]

In many cases, for example the work of Córdoba-Torres et al. [9], the model presented by Brug et al., [8] based on a distribution of properties along the electrode surface, provides a convincing correlation of CPE parameters extracted from impedance data. The present work is part of an effort to understand what distribution of surface properties may give rise to CPE behavior in the experimentally observed frequency range. For disk electrodes, the frequency dispersion may be attributed to the influence of nonuniform current and potential distributions. For recessed electrodes, frequency dispersion may be caused by a surface distribution of reaction rates for reactions coupled by an adsorbed intermediate. Finite-element models were used to simulate the impedance of disk and recessed disk electrodes with and without surface heterogeneity of reactions coupled by an adsorbed intermediate.

Section snippets

Mathematical Development

The system under consideration involves two reactions coupled by an adsorbed ion. In the first step, $M \to {X_{ads}}^{+} + e^{-}$ where the metal reacts to form an adsorbed ion on the surface and an electron is released. In the second step, ${X_{ads}}^{+} \to P^{2 +} + e^{-}$ where the adsorbed ion desorbs and another electron is released. The total faradaic current may be expressed as the sum of the currents associated with reactions (1) and (2) $i_{F} = i_{M} + i_{X} .$ Armstrong et al. [15] described similar general mechanisms for the impedance response

Finite-Element Model

The impedance was simulated by solving Laplace's equation for the potential distribution in the electrolyte domain, expressed as $\nabla^{2} Φ = 0 .$ Following equation (7), the potential may be expressed as $Φ = \bar{Φ} + Re {\tilde{Φ} exp (j ω t)} .$ The electrolyte domain comprised a 2-D axisymmetric quarter of a circle domain, shown in Figure 3.

The counterelectrode was set as the curved boundary with the condition that $\bar{Φ} = 0$ for the steady-state solution and $\tilde{Φ} = 0$ for the oscillating condition. The working electrode was centered at r =

Results

Finite-element simulations were used to simulate the impedance of disk and recessed disk electrodes with reactions coupled by an adsorbed intermediate. The disk geometry produces a radial potential dependence which influences the impedance response. The recessed electrode was used to analyze the effect of heterogenous reaction rates on the impedance response without the confounding effect of the disk geometry. Steady-state results are presented to show the variation of surface properties on the

Discussion

The frequency dispersion observed in the present work arises from the influence of Laplaces equation for potential on the electrochemical reactions coupled by an adsorbed intermediate. For the disk electrode with uniform rate constants, the calculated impedance response for the system shows the influence of geometry-induced current and potential distributions at both high and low frequencies. The resulting frequency dispersion may be described as being caused by the complex frequency-dependent

Conclusions

On a recessed disk electrode, a distribution of rate constants for reactions coupled by an adsorbed intermediate can give rise to frequency dispersion at both high and low frequencies. For a disk geometry, the geometry-induced nonuniform current and potential distributions make an additional contribution to the complex ohmic impedance. Such frequency dispersions may take the form of a CPE given the right distribution of rate constants, but this CPE behavior would appear over relatively narrow

Acknowledgements

M. E. Orazem expresses appreciation for financial support associated with the ExxonMobil Chemical Engineering Alumni and University of Florida Research Foundation term professorships.

References (24)

J.-B. Jorcin et al.
Comparison of local electrochemical impedance measurements derived from bi-electrode and microcapillary techniques
Electrochimica Acta
(2009)
M. Musiani et al.
Determination of resistivity profiles in anti-corrosion coatings from constant-phase-element parameters
Progress in Organic Coatings
(2014)
A.S. Nguyen et al.
Impedance analysis of the distributed resistivity of coatings in dry and wet conditions
Electrochimica Acta
(2015)
G.J. Brug et al.
The analysis of electrode impedances complicated by the presence of a constant phase element
Journal of Electroanalytical Chemistry
(1984)
P. Córdoba-Torres et al.
On the intrinsic coupling between constant-phase element parameters α and q in electrochemical impedance spectroscopy
Electrochimica Acta
(2012)
C.L. Alexander et al.
Contribution of surface distributions to constant-phase-element (CPE) behavior: 2. capacitance
Electrochimica Acta
(2016)
C.L. Alexander et al.
Influence of micrometric-scale electrode heterogeneity on electrochemical impedance spectroscopy
Electrochimica Acta
(2016)
L. Péter et al.
Impedance of a reaction involving two adsorbed intermediates: Aluminum dissolution in non-aqueous lithium imide solutions
Journal of Electroanalytical Chemistry
(2000)
C.L. Alexander et al.
Contribution of surface distributions to constant-phase-element (CPE) behavior: 1. influence of roughness
Electrochimica Acta
(2015)
B. Hirschorn et al.
Constant-phase-element behavior caused by resistivity distributions in films: 1. Theory
Journal of the Electrochemical Society
(2010)

B. Hirschorn et al.

Constant-phase-element behavior caused by resistivity distributions in films: 2. Applications

Journal of the Electrochemical Society

(2010)

M.E. Orazem et al.

Dielectric properties of materials showing constant-phase-element (CPE) impedance response

Journal of the Electrochemical Society

(2013)

Cited by (31)

A mechanistic study on localized corrosion of sandwich multi-layered aluminium sheet in 3.5 wt.% NaCl solution
2024, Electrochimica Acta
Multi-layered aluminium sheets are quickly gaining wide applications in several industries. However, a complete understanding of how the macro- and microstructures of composite influence the corrosion behavior is still far from being achieved. In this work, the electrochemical behavior of a 4343/3003/7072 aluminum alloy (AA) composite in 3.5 wt.% NaCl solution was investigated using electrochemical impedance spectroscopy (EIS), potentiodynamic polarization and scanning electron microscopy (SEM). The evolution of corrosion morphologies was analyzed from cross-sectional and plane directions, and the localized corrosion mechanism was discussed. Due to the galvanic effect existed in the cross-section, the corrosion resistance of the cross-section was higher than that of the plane surface. From the cross-section, the AA3003 was protected as the cathode and the adjacent AA4343 and AA7072 acted as anodes. Localized corrosion mainly initiated around Al-Si-Mn-Fe and Si-rich phases.
Hybrid impedance spectroscopy and transients testing methodology
2023, Journal of Energy Storage
A comparison between transient measurements and Electrochemical Impedance Spectroscopy (EIS) has been developed using correct choice of Equivalent Electrical Circuit (EEC). This choice is based on the type of boundary conditions in low (ω = 0) and high (ω = ∞) frequency ranges. Numerous EEC can be classified on four families both in time and frequency domains. Different EEC and factorized models are equivalent. Cauer series or ladder models have an advantage due to simplicity of simulation algorithm calculation costs and a single solution. All steps of the loop methodology have been realized using EIS and transient measurements provided with studied Ferri-Ferrocyanide/Pt interface. The developed loop methodology allows to combine the advantages of both experimental approaches and can be useful for different practical applications. And the time saved is greater than a contribution of 30 in favor of the analysis of transients compared to the EIS.
Graphene intermediated synthesis of thin-packing stacking-free MnO<inf>2</inf> nanoflakes for high power output at high mass loading
2023, Electrochimica Acta
Numerous advanced pseudocapacitive MnO₂ with much-improved power output have been reported in recent years. However, most of their performance is verified in thin film form, with a mass density of less than 3 mg cm⁻², which falls short of the commercial electrode demand of 10 mg cm⁻². This high mass loading will inevitably diminish its power output, the crucial superiority of capacitive materials, to a considerable extent. To address this issue, their kinetic analysis for seeking out the rate-determining step (RDS) is a prerequisite. Herein, a comprehensive kinetic analysis protocol has been developed combining the interpretation of capacitance fitting and impedance spectroscopy. The results have demonstrated the RDS is dependent on the mass loading status, and it switches to resistance-controlled under high mass loading due to the high resistance from both thick-packing and laminar-stacking of MnO₂ flakes. To break such restriction, 3-D graphene foam intermediated MnO₂ hybrid structures have been synthesized via a strategy of high-voltage graphite exfoliation paired with simultaneous Mn²⁺oxidation. More than constructing an efficient electron migration network, the underlying graphene skeleton also tunes the MnO₂ nanostructure on its surface, leading to a thin-packing and stacking-free structure configuration. As a result, the optimized sample achieves an energy density of 8 mWh cm⁻² at a power density of 3,012 mW cm⁻² in a symmetrical capacitor, which is much higher than 0.1 mWh cm⁻² at 1,700 mW cm⁻² for the control sample. In summary, this study highlights the "mass effect" of energy storage kinetics for pseudocapacitive MnO₂ and proposes a graphene-intermediated protocol to improve its power output at high mass loading, which could be valuable in guiding its commercialization.
In operando detection of Lithium plating via electrochemical impedance spectroscopy for automotive batteries
2023, Journal of Power Sources
Reducing the charging time is one of the main goals towards increasing the acceptance of electric vehicles. One of the limits of fast charging lithium-ion batteries with graphite-based anodes is lithium plating, a process which occurs mainly at high charging rates, low temperatures and high state of charge. Detecting the onset of lithium plating during a charging procedure is essential in order to optimize fast-charging profiles. This paper introduces a new method that allows the detection of the onset of lithium plating in automotive lithium-ion batteries using on-line electrochemical impedance spectroscopy. Compared to similar approaches, the measurement itself does not result in a significant increase in the charging time. The detection is based on observing the real part of the impedance across the state of charge during the charging procedure. The onset of lithium plating can be detected by a deviation from the nominal behavior in the form of a drop towards lower impedance. The behavior is both explained theoretically using electrochemical equivalent circuits and shown experimentally. The impedance measurements are carried out using an integrated small-scale device to allow on-line impedance analysis in an automotive environment and an integration into future battery management systems.
Microstructure, wear and corrosion properties of B–C composite layers on pure titanium
2023, Journal of Materials Research and Technology
In this work, TA2 pure titanium was treated by borocarburizing (BC), boriding first and then carburizing (B + C), and carburizing first and then boriding (C + B), and morphology and wear and corrosion properties of these layers were investigated. The results show that the BC layer and B + C layer are composed of TiB, TiB₂, and TiC phases, while the C + B layer consists of TiC and TiB₂ phases. The wear type of these treated samples is abrasive wear, and wear resistance is in the sequence of B + C layer > BC layer > C + B layer. In 3.5 wt.% NaCl solution, corrosion resistance is in the order of B + C layer > C + B layer > BC layer > TA2. In 5.0 vol.% H₂SO₄ solution, corrosion resistance is in the order of C + B layer > B + C layer > BC layer > TA2. The B + C treatment can form a layer with gentle hardness gradient, excellent wear properties, and good corrosion resistance, which is most conducive to the bonding between layer and matrix.
Electrochemical impedance spectroscopy for studying the SO<inf>2</inf> electrocatalytic oxidation on Pt electrodes
2023, Electrochimica Acta
The generation of green hydrogen for a more environmentally friendly and energetic environment is in the spotlight of electrocatalysis for a while. One emerging strategy is assisted water electrolysis, in which the oxidative reaction, the limiting one, can be substituted and the SO₂ oxidation reaction (SO₂OR) is an interesting candidate since it will consume a lethal atmospheric pollutant, at lower potentials. To better comprehend the electrochemical kinetics of this process, in the present work, we applied electrochemical impedance spectroscopy (EIS) as a tool to understand the electrolyte composition's influence on the activity. In this way, we have shown that, despite the three tested electrolytes, 0.5 mol L⁻¹ H₂SO₄, HClO_4, and 1:1 mixture of these two, presented the same DC response, EIS has shown that the adsorption kinetic is different for them all, presenting the different potential of zero charge values, double layer capacitance vs applied potential profiles and very different charge transfer resistance Tafel plots.

View all citing articles on Scopus

View full text

Contribution of Surface Distributions to Constant-Phase-Element (CPE) Behavior: 3. Adsorbed Intermediates

Highlights

Abstract

Introduction

Section snippets

Mathematical Development

Finite-Element Model

Results

Discussion

Conclusions

Acknowledgements

Electrochimica Acta

Progress in Organic Coatings

Electrochimica Acta

Journal of Electroanalytical Chemistry

Electrochimica Acta

Electrochimica Acta

Electrochimica Acta

Journal of Electroanalytical Chemistry

Electrochimica Acta

Constant-phase-element behavior caused by resistivity distributions in films: 1. Theory

Journal of the Electrochemical Society

Constant-phase-element behavior caused by resistivity distributions in films: 2. Applications

Journal of the Electrochemical Society

Dielectric properties of materials showing constant-phase-element (CPE) impedance response

Journal of the Electrochemical Society