• Voltammetry of a thin Au film in 0.1 M NaF with and without Cl-
• Formation and removal of oxide layers on Ta in alkaline KIO3
• Electrodeposition of copper on gold
  
• Chemical roles of high-pH peroxide-based polishing slurries in chemical mechanical polishing (CMP) of Ta
• Redox reaction of [Fe(CN)₆ ]^3/4- on thin film Au in the presence of weakly adsorbing ClO₄^-
• Redox reaction of [Fe(CN)₆ ]^3/4- on thin film Au in the presence of specifically adsorbing Cl^-
• Electro-oxidation of methanol on a thin film Au electrode in alkaline solutions
• Voltammetry of Cu in 0.1 mM KI + 0.1 M KOH (pH = 12.0)
• Voltammetry of Cu in 0.1 mM KI + 0.1 M HClO4 (pH = 1.1)
  

Time Resolved Fourier Transform Electrochemical Impedance Spectroscopy (FT-EIS)

Introduction

Electrochemical impedance spectroscopy (EIS) is a powerful probe of electrochemical reactions. Application of traditional frequency domain EIS, however, generally is limited to certain experimental systems where the applied D.C. voltage must be kept fixed during the time (at least several minutes in most cases) when an impedance spectrum (Nyquist or Bode plot) is recorded. This makes it difficult to study transient systems. Apart from this limitation, it is also difficult in traditional EIS to distinguish between adsorption and desorption (or anodic and cathodic) processes. The time resolved technique of FT-EIS expands the capabilities of EIS beyond these constraints [1]. FT-EIS can provide detailed kinetic information about surface reactions at solid-liquid interfaces and thus, can considerably help to understand the mechanisms of multi-step reactions in multi-component solutions [2-15].

Main (unique) advantages of FT-EIS

1) FT-EIS can measure kinetic parameters for surface reactions during the occurrence of these reactions under D.C. potentiodynamic conditions. This provides the necessary framework for properly comparing and combining potentiodynamic (D.C) electrochemical data (voltammograms, Tafel plots) with kinetic parameters (rate constants, adsorption resistances and capacitances, Warburg elements) measured by (A.C.) EIS.

2) FT-EIS is sensitive to surface conditions that depend not only on the value of the applied D.C. voltage, but also on the direction in which this voltage is varied during a potentiodynamic (cyclic voltammetry) experiment. Thus, FT-EIS can distinguish between adsorption and desorption, as well as between anodic and cathodic processes.

3) A problem often encountered in frequency domain EIS is the difficulty of determining the "uniqueness" of the circuit-model obtained from experimental data. The circuit-fit is statistically more reliable if a large number of spectra for a given voltage range is used for fitting the same circuit. This option is available in the framework of FT-EIS. Unlike frequency domain EIS, FT-EIS records a large number (typically 300-400) of impedance spectra while D.C. voltage controlled surface reactions are allowed to occur. For example, in a typical cyclic voltammetry experiment exploring a D.C. voltage segment of 1.5 V at a scan rate of 10 mV/s, our FT-EIS method can record a full Nyquist (or Bode) spectrum (100-40,000 Hz) at every 0.01 V interval during the scan, providing a total of 300 full impedance spectra in the entire CV cycle. Each of these spectra is then analyzed using a complex nonlinear least square (CNLS) method to obtain the circuit model of the reactive interface. The criteria we use to determine the uniqueness of a circuit are as follows: (i) the uncertainty in the fitted value of each circuit element for a given spectrum must be <10% (a commonly accepted error margin); (ii) the uncertainty in the fitted value of a given circuit element must be <10% throughout the full set of all (300 in the above example) impedance spectra that contain this particular element. Simultaneous incorporation of these two requirements largely eliminates any possible ambiguities in the selection of circuits for modeling surface reactions.

4) Usually the circuit elements obtained by CNLS-fitting of A.C. impedance data depend on the applied D.C. voltage. Theoretical formulas describing such voltage dependencies of most commonly encountered EIS parameters are available in the literature. Fitting these formulas to experimentally measured voltage dependent circuit elements provides another quantitative test for confirming the uniqueness of circuit models. Such fitting procedures can also provide useful information about adsorption isotherms of reactant intermediates. These specific features of data analysis for trasnsient systems are only available in FT-EIS, and not in traditional frequency domain measurements.

5) Electrochemical interfaces are often associated with more than one simultaneously occurring parallel reactions -- some or all of which may occur in multiple sequential steps). In conventional EIS, usually it is difficult to identify the different reaction steps associated with the different circuit elements. This task is considerably simplified in FT-EIS where D.C. voltage dependencies of the individual circuit elements serve as signature features of different reaction steps. For instance, the capacitance and resistance of a given reaction step would generally vary in mutually opposite directions, while those representing two parallel reactions would not typically exhibit this correlation [3,7]. Often these observations serve as useful tools for identifying coupled and uncoupled reaction steps in multi-component solutions.

6) Voltage dependent FT-EIS spectra collected in real time during potentiodynamic scans have yet another advantage; most frequently, they can readily distinguish between kinetically controlled and diffusion controlled reactions even without requiring any detailed CNLS analysis of the data [6].

Applications of FT-EIS

FT-EIS is particularly useful for studying kinetically controlled time dependent electrochemical systems. These include:

- oxidation of organic molecules (for fuel cell studies)
- electrocatalysis
- double layer characterization
- electrodeposition studies
- characterization of bio-electrochemical reactions
- metal dissolution reactions (relevant for chemical mechanical and electrochemical mechanical planarization)
- electrochemistry of ionic liquids
- real time monitoring of corrosion reactions

Sinusoidal multi-frequency A.C. voltammetry (ACV) in the framework of FT-EIS

ACV typically involves measuring D.C. voltage dependent A.C. perturbation currents at fixed frequencies. The recent FT-based ACV experiments utilize multifrequency signals [see for example, Bond et al., Anal. Chem. 77 (2005)186A]. These latter experiments are very similar to FT-EIS meaasurements. In fact, the raw data collected in FT-EIS (A.C. current and phase as functions of A.C. frequency and D.C. voltage in cyclic voltammetry) correspond essentially to the same data-format considered in ACV. An illustrative example is shown here where D.C. voltage dependent FT-EIS data are presented in the format of ACV data. The same data can be analyzed in the framework of FT-EIS or using the formalism of multifrequency ACV.

ã D. Roy

Working principle and experimental setup

This subject is discussed in detail in Ref. [1], and is summarized in the following block diagrams:

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