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

Electrochemical impedance spectroscopy (EIS) is a powerful probe of electrochemical reactions. Time resolved FT-EIS can provide detailed kinetic information about surface reactions at solid-liquid interfaces and thus, can help to understand the mechanisms of multi-step reactions in multi-component solutions.

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. Moreover, FT-EIS can often distinguish between adsorption and desorption, as well as between anodic and cathodic processes.

In EIS measurements sometimes it becomes difficult to determine 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, where a large number (typically 300-400) of impedance spectra can be recorded 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, a typical FT-EIS run 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.

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.

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 such cases, often 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. 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.

FT-EIS is particularly useful for studying kinetically controlled time dependent electrochemical systems. These include: oxidation of organic molecules; 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

The experimental setup currently used for FT-EIS measurements in our laboratory has been discussed in Reference [1] listed below.

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 measurements. 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

Further Reading