*2.1. Nyquist Plot*

The Nyquist plot is a plot where the imaginary impedance *Z*"(*ω*) is plotted against real impedance *Z'*(*ω*). Generally, the resistance value can directly obtain from Ohm's law as shown in Equation (1), where the resistance is the ratio between voltage, *E*, and current, *I*.

$$R = \frac{E}{I} \tag{1}$$

It assumes an ideal resistor. An ideal resistor occurs when it follows the Ohm's law at all voltage and current levels, where the resistance value is independent of frequency and when AC voltage and current signals are in phase with each other while going through the resistor. However, this does not always happen because in reality, circuit behavior is far more complicated. Therefore, in this concept, the impedance element is much more suitable for use rather than simple resistance to explain the changes measured in the circuit. Impedance is a frequency-dependent measurement of the opposition to current flow in an electric circuit. Impedance measurement is performed by applying an AC excitation voltage to an unknown system while measuring the current. The ratio of the excitation voltage to the current gives the complex impedance of the system.

The first step after impedance measurement is done is the graphical representation from the experimental data. The data from the impedance measurement will consist of three main components which are the real and imaginary impedance, and the frequency. These data will then be represented in Cartesian coordinates as shown in Equation (2):

$$\mathbf{Z}(\mathbf{i}\omega\_{\mathbf{i}}) = \mathbf{Z}\_{\mathbf{i}}^{\prime} + \mathbf{i}\mathbf{Z}\_{\mathbf{i}}^{\prime\prime} \tag{2}$$

Or in polar coordinates as shown in Equation (3):

$$Z(i\omega\_i) = |Z\_i|e^{i\varphi\_i} \tag{3}$$

where |*Zi*| = - *Z*<sup>2</sup> *<sup>i</sup>* <sup>+</sup> *<sup>Z</sup>*<sup>2</sup> *i* 1/2 is the modulus and *ϕ<sup>i</sup>* = *tan*−<sup>1</sup> *Z <sup>i</sup>* /*Z i* is the phase, which corresponds to a given frequency.

The most common plot for impedance representation is based on Equation (2) which is a Nyquist plot with only one semicircle (Figure 3a). It shows the results from an electrical

equivalent circuit that is depicted in Figure 3b, which consists of a resistor and a capacitor in parallel. The direction of the frequency scanning is from high to low frequencies. At higher frequencies, the capacitor's impedance will be very low and a major part of the current will flow through the capacitor. With a decrease in the frequency, the capacitor's impedance increases and a bigger fraction of the current will then flow through the resistor. When most of the current flows through the resistor, the total imaginary resistance *Z*" will drop as the real part *Z*' increases. Sometimes, the plot may consist of several semicircles or only a portion of a semicircle (Figure 3c,e). The different semicircles represent different electrical equivalent circuits and are shown in Figure 3d,f.

**Figure 3.** *Cont*.

**Figure 3.** Nyquist plot with one semircircle and its equivalent circuit (**a**,**b**); two semicircles and its equivalent circuit (**c**,**d**); one semircircle with spike (45◦) and its equivalent circuit (**e**,**f**); only spike (45◦) and its electrical equivalent circuit (**g**,**h**) [28].

The equivalent circuit derived from the plot could then be used to analyze changes or the effects on the electrochemical sensor system that was added or modified. Besides that, the charge transfer resistivity, *R*ct, also can be obtained from the Nyquist plot. For example, Ramanavicius et al. described an immunosensing system model based on the bovine leukemia virus (BLV) protein (gp51) entrapped within electrochemically synthesized polypyrrole (PPy/gp51). They reported that another element was present in the blood serum sample after it was treated as detected in the fitted equivalent circuit. This was due to the slightly increased measurement of the real part of the impedance spectrum (resistivity increased). It was explained that an additional layer occurred outside the polypyrrole film and proved that the treatment was successful [29]. Devi et al. reported that *R*ct value was increased with the addition of xanthine oxidase (XOD) in a ZnO-NPs/PPy/Pt electrode, which is due to the immobilization of XOD onto the ZnO-NPs/PPy/Pt surface. It proved that the use of nanocomposites and PPy electrodeposited on the Pt surface electrode as a support for the immobilization of XOD resulted in an improvement of the xanthine biosensor performance with a detection limit of 0.8 μM [30]. Meanwhile, Chen et al. used impedance analysis to evaluate the charge separation efficiency of a PPy based photoelectrochemical sensor. There were two semicircles obtained from the impedance curve when Cu2O was added on top of the ITO electrode. The semicircles known as Rct were then reduced to one and became smaller when fabricated with and without Microcystin-LR and LiClO4 as template molecules during the electropolymerization process. As *R*ct become smaller, the charge transfer efficiency become higher [31]. Furthermore, Bao et al. electrodeposited gold nanoparticles/polypyrrole-reduced graphene oxide nanocomposites (Au/PPy-rGO) on top of a bare glass carbon electrode (GCE) in order to produce excellent sensing performance for mRNA-16. The *R*ct from a small semicircle (bare GCE) was decreased to almost a straight line (after electrodepositing) in the impedance curve results. When it is being further assembled using catalyzed hairpin assembly (CHA), and hybridization chain reaction (HCR), the *R*ct semicircle was greatly increased, demonstrating the successful CHA and HCR processes and the fact that more negatively charged DNA polymers were linked on the modified electrode [32]. Akshaya and co-workers researched a Palladium–Gold (PdAu) based electrochemical sensor which was developed by electrodepositing PdAu nanoparticles onto a Polypyrrole (PPy) modified carbon fiber paper (CFP) electrode. They found that with the modification of CFP using the PPy conducting polymer, the *R*ct decreased, indicating the conducting nature of PPy. Then, with further electrodeposition of PdAu nanoparticles onto the PPy/CFP, the value of *R*ct become significantly decreased. This confirmed the formation of a highly conducting electronic pathway at the electrode–electrolyte interface where Pd and Au nanoparticles facilitated electron transfer between the analyte and the electrode [33].
