## 2 Materials and Methods
### Basic Electrochemical Electrical Equivalent Circuit (EEC) Models  
Physicochemical reactions involve charge transport through the interface and the chemical phases. The kinetics are controlled by charge, mass transfer, or both and depend on the rate at which coupled chemical reactions take place at the electrode-solution interface. In general, a frequency-dependent model can be obtained to fit the impedance data and thus can be correlated with localized physicochemical processes. One of the most common cell models used to correlate basic electrochemical processes to Electrical Impedance Spectroscopy data is the simplified Randles model (also referred to as modified Kelvin-Voigt model) (Figure 2A) which comprises three processes: the solution bulk resistance (i.e., a single resistor, R\({}_{\text{B}}\)), a polarization resistance, R\({}_{\text{P}}\), and a capacitor (C\({}_{\text{D}}\)) that represents the double layer effect [20]. \begin{table}
\begin{tabular}{p{56.9 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline
**Measurement Method** & **Advantages** & **Disadvantages** & **Applicable Frequency Range** & **Applications** \\ \hline \multirow{8}{*}{Bridge} & High accuracy (0.1\% typically) & \multirow{4}{*}{Needs to be manually balanced coverage by using different types of bridges Low Cost} & \multirow{4}{*}{DC to 300 MHz instrument} & \multirow{4}{*}{Standard Lab} \\  & High frequency range & & & \\  & coverage by using different types of bridges Low Cost & & & \\ \hline \multirow{4}{*}{Resonant method} & Good Q accuracy up to high Q & Needs to be tuned to resonance Low impedance measurement accuracy & 10 kHz to 70 MHz measurement & High-Q device measurement \\ \hline \multirow{4}{*}{Current-voltage (I–V)} & Grounded device measurement & Operating frequency range is limited by transformer used in probe & 10 kHz to 100 MHz measurement & Grounded device measurement \\ \hline \multirow{4}{*}{RF I–V} & High accuracy (1\% typ.) and wide impedance range at high frequencies & Operating frequency range is limited by transformer used in test head & 1 MHz to 3 GHz measurement & RF component measurement \\ \hline \multirow{4}{*}{Network analysis} & Wide frequency coverage from LF to RF Good accuracy when the unknown impedance is close to characteristic impedance & \multirow{4}{*}{5 Hz and above measurement range} & \multirow{4}{*}{RF component measurement} \\  & Wide frequency coverage from LF to RF Good accuracy when the unknown frequency is changed frequency is changed & & & \\  & impedance is close to characteristic impedance & Narrow impedance measurement range & & \\ \hline \multirow{4}{*}{Auto-balancing bridge} & Wide frequency coverage from LF to HF & \multirow{4}{*}{20 Hz to 120 MHz measurement frequencyHowever, modelling electrochemical dynamic processes often require several additional parameters to be accounted for. For instance, modelling microbial fuel cells involve several processes such as \"electrolyte resistance, adsorption of electroactive species, charge transfer at the electrode surface and mass transfer from the bulk solution to the electrode surface\" [21]. Thus, a common approach is to combine series and/or parallel arrays of passive components (resistor and capacitors), constant phase elements (CPE) and/or Warburg elements to correlate the measured data with the electrochemical processes involved, including the charge transfer resistance, R\({}_{\text{CT}}\) (Figure 2B) as the interfacial charge transport, mass transfer or both behaviours can explain the interfacial charge transport process and the role of contacts quantitatively by using the electrical equivalent circuit (EEC) [22]. Although the suitability of a measurement model for extracting parameters from EIS experimental data depends on the nature of the electrochemical process, [PERSON] et al. [23] argue that a CPE may not represent distributed-time constant behaviours and therefore the use of a measurement model offers advantages for obtaining low- and high-frequency ohmic resistances. [PERSON] et al.