7.1 Fundamentals of Impedance Spectroscopy

Impedance spectroscopy measures how electrochemical systems resist alternating current flow. It combines resistance and reactance, allowing us to separate and study different processes happening in the system based on their timing.

Interpreting impedance data involves analyzing Nyquist and Bode plots, which show how the system behaves at different frequencies. We can then model the system using equivalent circuits, helping us understand the physical processes occurring.

Fundamentals of Impedance Spectroscopy

Impedance in electrochemical systems

Top images from around the web for Impedance in electrochemical systems

• 

  The electrical modulus and other dielectric properties by the impedance spectroscopy of LaCrO 3 ... View original

  Is this image relevant?

• 

  Frontiers | Capacity Increase Investigation of Cu2Se Electrode by Using Electrochemical ... View original

  Is this image relevant?

• 

  Fundamentals and Applications of Electrochemical Impedance Spectroscopy - A Didactic Perspective View original

  Is this image relevant?

• 

  The electrical modulus and other dielectric properties by the impedance spectroscopy of LaCrO 3 ... View original

  Is this image relevant?

• 

  Frontiers | Capacity Increase Investigation of Cu2Se Electrode by Using Electrochemical ... View original

  Is this image relevant?

1 of 3

Top images from around the web for Impedance in electrochemical systems

• 

  The electrical modulus and other dielectric properties by the impedance spectroscopy of LaCrO 3 ... View original

  Is this image relevant?

• 

  Frontiers | Capacity Increase Investigation of Cu2Se Electrode by Using Electrochemical ... View original

  Is this image relevant?

• 

  Fundamentals and Applications of Electrochemical Impedance Spectroscopy - A Didactic Perspective View original

  Is this image relevant?

• 

  The electrical modulus and other dielectric properties by the impedance spectroscopy of LaCrO 3 ... View original

  Is this image relevant?

• 

  Frontiers | Capacity Increase Investigation of Cu2Se Electrode by Using Electrochemical ... View original

  Is this image relevant?

1 of 3

• Impedance measures the opposition to alternating current (AC) flow in an electrical circuit
• Complex quantity consisting of resistance and reactance represented as a vector sum: $Z = R + jX$, where $Z$ is impedance, $R$ is resistance, and $X$ is reactance
• Resistance opposes current flow in an ideal resistor, dissipating energy as heat and is frequency-independent
• Capacitance stores electrical charge, with capacitors storing energy in an electric field
• Capacitive reactance is frequency-dependent: $X_C = \frac{1}{2\pi fC}$, where $X_C$ is capacitive reactance, $f$ is frequency, and $C$ is capacitance

Principles of impedance spectroscopy

• Powerful technique for studying complex electrical properties of electrochemical systems
• Applies small amplitude AC signal over a range of frequencies to an electrochemical cell and measures current response to applied voltage
• Separates different electrochemical processes based on their time constants, such as charge transfer reactions, diffusion processes, and adsorption phenomena
• Data represented in Nyquist plots (imaginary vs. real impedance) or Bode plots (log impedance magnitude and phase angle vs. log frequency)

Interpretation of EIS plots

• Nyquist plots: each point represents impedance at a specific frequency
  • High-frequency region (left side) corresponds to charge transfer processes
  • Low-frequency region (right side) corresponds to mass transfer processes
  • Semicircle diameter related to charge transfer resistance
• Bode plots:
  • Impedance magnitude plot: plateaus represent frequency-independent processes (solution resistance), slopes of -1 indicate capacitive behavior
  • Phase angle plot: peaks indicate presence of time constants, frequency at peak maximum related to characteristic frequency of the process

Equivalent circuits for EIS

• Equivalent circuit models interpret EIS data and relate it to physical processes
• Common equivalent circuit elements:
  • Resistors (R): represent ohmic resistances (solution resistance, charge transfer resistance)
  • Capacitors (C): represent double-layer or coating capacitance, ideal capacitors have -90° phase angle
  • Constant Phase Elements (CPE): model non-ideal capacitive behavior due to surface roughness or inhomogeneity, impedance: $Z_{CPE} = \frac{1}{Q(j\omega)^n}$, where $Q$ is CPE coefficient and $n$ is CPE exponent (0 ≤ n ≤ 1)
  • Warburg elements (W): represent semi-infinite linear diffusion, impedance: $Z_W = \frac{\sigma}{\sqrt{\omega}} - j\frac{\sigma}{\sqrt{\omega}}$, where $\sigma$ is Warburg coefficient
• Equivalent circuits constructed by combining elements in series or parallel to model the electrochemical system