Jochen Kieninger
Electrochemical Methods for the Micro- and Nanoscale
www.electrochemical-methods.org

Task 7.3 (Electrochemical impedance spectroscopy - simulation)¶

Simulating different basic equivalent circuits and changing the parameter helps to get a sound understanding of EIS models. Here, we use the library impedance.py (https://doi.org/10.21105/joss.02349), primarily designed to analysis experimental data.

In [1]:
from impedance.models.circuits import CustomCircuit
import numpy as np
import warnings
warnings.filterwarnings('ignore')
  • Frequency range: 10 mHz to 10 kHz
In [2]:
frequencies = np.logspace(-2, 4, 100)
  • Simple RC parallel circuit representing the charge transfer resistance (100 Ω) and double layer capacity (100 µF)
In [3]:
circuit = CustomCircuit(initial_guess=[100, 100e-6], circuit='p(R1,C1)')
Z_sim = circuit.predict(frequencies)
In [4]:
circuit.plot(f_data=frequencies, Z_data=Z_sim)
Out[4]:
  • Enhanced model with a CPE (exponent 0.8) instead of the capacitor and another element for the uncompensated resistance (10 Ω)
In [5]:
circuit = CustomCircuit(initial_guess=[10, 100, 100e-6, 0.8], circuit='R0-p(R1,CPE1)')
Z_sim = circuit.predict(frequencies)
In [6]:
circuit.plot(f_data=frequencies, Z_data=Z_sim)
Out[6]:
  • Enhanced model with a Warburg element (20 Ω s0.5) to consider mass transport limitation (semiinfinite diffusion)
In [7]:
circuit = CustomCircuit(initial_guess=[10, 100, 20, 100e-6, 0.9], circuit='R0-p(R1-W1,CPE1)')
Z_sim = circuit.predict(frequencies)
In [8]:
circuit.plot(f_data=frequencies, Z_data=Z_sim)
Out[8]: