## Electrochemical Impedance Spectroscopy Experiment

#### Goals

- To learn the effect of placing capacitors and resistors in series and parallel
- To model electrochemical impedance spectroscopy data

#### Experimental Apparatus

- Gamry Instruments Interface 1000T potentiostat
- Gamry Instruments Framework™ software package installed on a host computer
- Gamry Instruments AC Dummy Cell (Gamry part number 990-00419)
- Two 2.7 V, 3 F capacitors
- 20 Ω, ¼ W (or higher power-rating) resistor
- 100 Ω, ¼ W (or higher power-rating) resistor

#### Background

**Electrochemical impedance spectroscopy** (EIS) is a popular method for studying an electrochemical interface. EIS is a “two-part” technique, that is:

- First, the electrical response of the electrochemical interface is recorded when a small alternating current (AC) potential is applied, and
- Second, the data are fitted to a theoretical electronic circuit that is designed to be “equivalent” to the actual system.

In the first part (applying AC to the sample), the system is immersed in electrolyte, and an AC potential is applied, with the AC frequency carefully stepped from a high frequency (1 MHz or more) down to a low frequency (~1 Hz or less), usually in a logarithmic sequence. While perfect resistors respond without delay or loss in amplitude to AC input, all real electrical components (including surfaces undergoing corrosion) respond to such AC with a loss in amplitude, and a slight delay in time (phase-shift). How the electrochemical system responds to the AC input reveals much about the internal physical and chemical structure of the system. Therefore we cannot use the ideal Ohm’s Law equation to describe our electrochemical surface,

*R* =

where *R* is the resistance of the system, *E* is the potential applied to the system, and *I* is the current applied to the system. Instead, we must consider the actual phase-shifted response of the system to the applied potential. Now we can describe the AC excitation potential applied to the system as a sine wave:

*E*=*E*_{0} sin

where *E* is the applied potential as before, *E*_{0} is the AC amplitude, *t* is time, and *ω* is radial frequency (and *ω = 2πf*). The electrochemical system’s response (Figure 10.1), then, is

*I*=*I*_{0}sin

where the phase-shift away from the applied AC is ϕ. The amplitude of the excitation signal is kept small so that the cell’s response is pseudo-linear. In a pseudo- linear system the cell’s frequency response is the same frequency as the excitation signal.

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