*2.2. Bode Plot*

Even though the Nyquist plot can give significant information on the resistance of the material used, it has one major shortcoming where it is unable to show the frequency used at the focal data point needed. Each point corresponds to a given frequency which is *ω s*−<sup>1</sup> or *f*(*Hz*), where *ω* = 2*π f* . Therefore, as an alternative, the data can be represented in a Bode plot by using Equation (3). Generally, the Bode plot provides a more comprehensible description of the electric systems' frequency-dependent behavior than the Nyquist plot, in which frequency values are not clear. In the Bode plot, the data are plotted with log of frequency on the *x*-axis and both the log of absolute value of the impedance (|*Z*|) and phase-shift (*θ*) on the *y*-axis (Figure 4) [34].

**Figure 4.** Bode plots of the frequency response (dotted line) and phase angle (solid line) for an electrochemical system.

A typical Bode plot is the same system as shown in Figure 2A. It is simpler to understand as there is only one semicircle that appears on the Nyquist plot. The log |*Z*| versus log *ω* curve can be used to determine the values of *R*<sup>p</sup> and *R*Ω. At very high and very low frequencies, |*Z*| becomes independent of frequency. At the highest frequencies, the ohmic resistance controls the impedance and log (*R*Ω) can be read from the high frequency horizontal level. On the other hand, at the lowest frequencies, log (*R*<sup>p</sup> + *R*Ω) can be read from the low frequency horizontal portion [35].

Besides that, the Bode plot can also prove the number of semicircles present in the corresponding Nyquist plot. It can be seen from the shapes of the phase angle plots. For example, from the Nyquist plot, a smaller semicircle appears at higher frequencies, followed by second larger semicircle at medium frequencies and a Warburg diffusion effect in low frequencies (Figure 5a). Therefore, to confirm the presence of these two semicircles, the shape from the phase angle graph in the Bode plot will be used (Figure 5b). It can then be seen that the slope is somewhat broadened. Therefore, it proves that there is more than one semicircle present in the Nyquist plot.

**Figure 5.** Nyquist plot with two semicircles (**a**) and Bode plot (**b**).

Lee et al. has researched a nicotine electrochemical sensor where a copper hexacyanoferratepolypyrrole (CuHCF–PPy) nanocomposite was deposited directly onto reduced graphene oxide (rGO) by a direct self-assembly technique. From the impedance results, they obtained two semicircles in their Nyquist plot. This was expected and is due to the presence of two layers' of materials comprising of rGO and the metal layer (CuHCF) or metalpolymer layer (CuHCF-PPy) on the electrodes. Therefore, from the Bode plot, two phase angles were observed. The phase angle in the high (*f* 1) frequency regions was attributed to the *R*ct which happens across the electrode-electrolyte interface (CuHCF or CuHCF-PPy/solution). Meanwhile, the second phase angle (*f* 2) was due to the CuHCF or CuHCF-PPy/rGO interface [36]. In research from a different perspective, Ratautaite et al. used Bode plots to evaluate the best frequency for further evaluation of capacity changes as a result of theophylline addition. They found that most sensitive impedance changes were in the frequency range from 10 Hz to 100 Hz. Therefore, in that frequency range, the capacitance changes at certain frequencies were further evaluated [37]. On the other hand, Al-Mokaram et al. used a Bode plot to study the frequency region of *R*ct of modified electrode nanocomposite films consisting of polypyrrole-chitosan-titanium dioxide (Ppy-CS-TiO2) in the development of a non-enzymatic glucose biosensor. It was found to collect in the frequency range of 0.01–10,000 Hz. The shifting of peaks toward the low frequency region of 1–0.01 Hz for composite and nanocomposite electrodes indicates the fast electrontransfer behavior of the nanocomposites (Figure 6). A perfect linear portion was observed at lower frequencies for the nanocomposite electrode compared to other electrodes. The results indicated that the Ppy-CS-TiO2 nanocomposite was successfully designed and it facilitated a diffusion-limited process at the electrode-solution interface [38].

**Figure 6.** Bode phase plot for 1 mM K3(Fe(CN)6) in 0.1 M KCl at a scan rate of 50 mV s−<sup>1</sup> vs. (Ag/AgCl) [38].
