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TUTORIAL ON ELECTROCHEMICAL IMPEDANCE SPECTROSCOPY

David C. Silverman


Table of Contents

Overview of Tutorial
Overview of EIS
Analysis Using Simple Circuits
Constant Phase Element
Corrosion Rate Estimation
         Two Capacitive Relaxation Time Constants
Critical Criteria for Proper Spectra
Diffusion Impedance
Pseudoinductance

Critical Criteria for Proper Spectra

The definition of the electrochemical impedance as presented in ASTM G-15 "Standard Terminology Relating to Corrosion and Corrosion Testing" is as follows:

Electrochemical impedance is the frequency dependent, complex valued proportionality factor, ΔE/ΔI, between the applied potential (or current) and the response current (or) potential in an electrochemical cell. This factor becomes the impedance when the perturbation and response are related linearly (the factor value is independent of the perturbation magnitude) and the response is caused only by the perturbation. The value may be related to the corrosion rate when the measurement is made at the corrosion potential.

Understanding this definition is important because several of the constraints mentioned are overlooked routinely by users of this technology. The transfer function between the perturbation and the response to the perturbation can only become the impedance when the following criteria are fulfilled:
  1. Linearity - the relationship between perturbation (voltage) and response (current) is independent of magnitude of perturbation. That is, the spectrum is independent of the amplitude of the perturbation.
  2. Causality - the response is a result of only the applied perturbation. That is, the spectrum is only a result of the relationship between the voltage and the current and not some additional phenomena or artifacts.
  3. Stability - the system returns to its starting point after the perturbation is removed. That is, the system returns to the same steady state value after each cycle of the perturbing wave and the system is in the same state before and after the spectrum is generated.
  4. Finite valued - the transfer function (impedance) is finite as the frequency approaches 0 and 8 and is finite at all intermediate frequencies. That is, no infinite values of the impedance modulus occur at any frequency, not just the measured frequencies.

    These criteria should be treated as the four commandments of electrochemical impedance spectroscopy. ASTM G-106 "Verification of Algorithm and Equipment for Electrochemical Impedance Measurements" also contains procedures for checking both the equipment and algorithm for generating electrochemical impedance spectra. At one point use of the Kramers-Kronig transformation was thought to be a way to help ensure that these criteria are fulfilled. But these tranformations require that the recorded spectrum contains all modulus and phase information as a function of frequency. The issue is that often the spectrum cannot be generated to low enough frequencies to use the transformations.



Next Page: Diffusion Impedance

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David C. Silverman, Ph.D. - Primary Consultant
E-Mail:     dcsilverman@argentumsolutions.com
Phone:     314-576-3586
Fax:         314-754-9825
Address:   The Argentum House
                14314 Strawbridge Ct.
                Chesterfield, MO 63017