1. Impedance Spectroscopy Study of an SOFC Unit Cell

2. Model Definition

3. Model Definition
Material balances for all species using Maxwell-Stefan
Fluid flow in the open channels and in the porous electrodes:
Navier-Stokes equations
Brinkmann equations
Current balances and charge balances
Defined in the electrodes, pore electrolyte, and the electrolyte that separates the anode and cathode
Electrode kinetics using Butler-Volmer including concentration overpotential

4. Model Definition
Parametric sweeps in the study are done by applying a constant average current density of 1400 [A/m2] at the steady polarization, except for the last case where the current is varied:
A floating potential condition is applied so that an unknown constant potential is set at the current collector, but an additional equation is added that sets the integral of the current density at the current collector to a fixed value.

5. Specifying a Harmonic Perturbation
Add a Harmonic Perturbation feature to the Electric Potential boundary condition
Make the perturbation small (mV range) in order to obtain a linear approximation of the nonlinear system of equations
Laplace transform allows for solution in the frequency domain, which is done automatically by COMSOL

6. A Note on Post Processing
In the Nyquist plot the complex impedance Z is plotted, which is evaluated using integral operators at the current collector boundary
Z = ( Pertubation Voltage ) / ( Pertubation Current )
For a more accurate evaluation of the integral of the current density at the current collector boundary, the reacf() operator is used in combination with an integration operator using summation over the node points (See the Comsol Multiphysics Reference Manual for a general description of the reacf() operator)
The ”Compute Differential” check box should be disabled in the Nyquist plot in this case when plotting only the resulting harmonic pertubations

7. Study Settings AC Impedance Stationary Study used
Default solver sequenced modified to use a Fully Coupled solver
AC Impedance
Stationary Study
Selected in the Model Wizard
Add a Fully Coupled Solver and disable Segregated

8. Influence of Cathodic Exchange Current Density
The anodic and cathodic circles become more separated as the difference between the two exchange current densities increases:
- Turquoise curve i0_a = i0_c
Increasing frequency
Anodic exchange current density = 0.1 [A/m2]
Electrolyte conductivity = 5 [S/m]
Reference diffusivity = 3.8·10-8 [m2/s]

9. Influence of Anodic Exchange Current Density
The anodic and cathodic circles become more separated as the difference between the two exchange current densities increases:
- Blue curve i0_a = i0_c
Cathodic exchange current density = 0.01 [A/m2]
Electrolyte conductivity = 5 [S/m]
Reference diffusivity = 3.8·10-8 [m2/s]

10. Influence of Electrolyte Conductivity
Anodic exchange current density = 0.1 [A/m2]
Cathodic exchange current density = 0.01 [A/m2]
Reference diffusivity = 3.8·10-8 [m2/s]

11. Influence of Diffusivity
Anodic exchange current density = 0.1 [A/m2]
Cathodic exchange current density = 0.01 [A/m2]
Electrolyte conductivity = 5 [S/m]

12. Influence of Current Density
Anodic exchange current density = 0.1 [A/m2]
Cathodic exchange current density = 0.01 [A/m2]
Electrolyte conductivity = 5 [S/m]
Reference diffusivity = 3.8·10-8 [m2/s]
factor = 1 corresponds to 1400 [A/m2]
Anodic exchange current density = 0.1 [A/m2]
Cathodic exchange current density = 0.01 [A/m2]
Electrolyte conductivity = 5 [S/m]

13. Concluding Remarks
The model is small in order to run a parametric sweep and a frequency sweep in every parameter value in less than five minutes
Longer channels and larger number of channels can also be simulated
Heat transfer analysis can also be added
There are a lot of conclusions that can be drawn from these model studies, this only presents a scratch on the surface