Frequency Response of Electrode Materials in EIS Measurement

Furthermore, complementary information about the frequency response of electrode materials is provided by EIS measurements and one can estimate the capacitance changes with the operating frequency.^64-65 It is well know that the complex form of capacitance is dependent on frequency, which is defined as follow:^66-67

(6)

where C'(ω) is the real part of the complex capacitance and C"(ω) is the imaginary part of the complex capacitance C(ω) and they are expressed as formulas (7) and (8):^66-67

(7)

(8)

where Z'(ω) and Z"(ω) are the respective real and imaginary part of the complex impedance Z(ω). ω is the angular frequency and it is given by ω =2πf. At low frequency, C'(ω) corresponds to the capacitance of the electrode material and C"(ω) is ascribed to the energy dissipation by an irreversible process that leads to a hysteresis.^66-67 Fig. 15 shows the real and imaginary part capacitance as a function of frequency for Li-POAP/ERG/GC, POAP/ERG/GC and ERG/GC electrodes. It can be clearly observed that C'(ω) gradually decrease with the increase of scan rates for each electrode as shown in Fig. 12F, however, the Li-POAP/ERG/GC electrode exhibits slow deterioration of capacitance due to fast ion diffusion and transport (Fig. 15A). In addition, the C'(ω) of the Li-POAP/ERG/GC electrode approaches saturation at a frequency below ~ 0.01 Hz whereas the C'(ω) of POAP/ERG/GC electrode does not show any sign of saturation as low as 0.01 Hz, indicating slow diffusion of electrolyte ions (Figs. 15A and B). Importantly, the relaxation time constant (τ₀), which is also known as the dielectric relaxation time of the supercapacitor,^{66, 68} is a figure of merit of a supercapacitor. This parameter represents one of its discharge characteristics. It has been studied for each electrode based on the analysis of complex capacitance. The relaxation time constant, τ₀ (=1/2πf₀) can be calculated from the plots of C'(ω) and C"(ω) vs. frequency. From the frequency corresponding to the half of the maximum value of C'(ω), the relaxation time constant (τ₀) can be determined. The change in the imaginary part of the complex capacitance C"(ω) with frequency goes through a maximum at a frequency, f₀, from which the value of τ₀ can be calculated. From Figs. 15A and B, it can be noted that the Li-POAP/ERG/GC electrode shows a clear peak formation while the POAP/ERG/GC electrode has not reached the maximum even at the lowest frequency used in this study. The f₀ value of Li-POAP/ERG nanocomposite is 3.98×10^-2 Hz, corresponding to the characteristic relaxation time constant τ₀ = 3998 ms, which is much lower than that of POAP/ERG nanocomposite, revealing fast accessibility of the electrolyte ions for the former nanocomposite. The smaller τ₀ of the nanocomposite correlates with the better capacitance retention at high scan rates in the CV measurements. Therefore, lithium intercalated POAP/ERG nanocomposite is a potential promising electrode material for delivering high power and energy. In addition, investigation of the complex capacitance form of the ERG/GC electrode reveals that the C'(ω) of this electrode approaches saturation at a frequency below 15.8 Hz, which means that equilibrium ion adsorption can be achieved in 63.3 ms, suggesting most of the electrolyte ions reach the adsorption sites (Fig. 15C). In comparison to Li-POAP/ERG/GC electrode, the smaller value of relaxation time constant (τ₀ = 2.5 ms) correlates with very ultra-fast accessibility of the electrolyte ions for the ERG/GC electrode and the better capacitance retention at high scan rates in the CV measurements which is in good agreement with results obtained from cyclic voltammetric measurements (Fig. 12F, green line).

In order to investigate the effects of different types of anions on the specific capacitance of POAP/ERG nanocomposite, the modification of the ERG/GC electrodes has been carried out in different acidic solutions containing HNO₃, HClO₄ and HCl and corresponding lithium salts as supporting electrolyte and subsequently, have been evaluated in the corresponding monomer free solutions. The cyclic voltammograms of the modified electrodes in presence of different anions are shown in Fig. 16A. Qualitative analysis of total charges associated with the voltammograms recorded in the presence of different anions reveals that the specific capacitance for anions decreases in the direction of <<. The values of specific capacitance derived from the cyclic voltammetric (Fig. 15A) and impedance spectroscopic measurements (Figs. 16B and C) do indeed coincide as tabulated in Table 3. The greater specific capacitance obtained in presence of results from its smaller size and subsequent facile diffusion to/from the composite. Similarly, an experiment has been carried out to assess whether the same result is obtained in the same order for the POAP/ERC/GC electrode modified in the presence of different anions in the aforementioned acidic solutions but without supporting electrolyte. The related CVs and impedance spectra for POAP/ERG/GC electrode in the presence of different anions (Figs. S3A, B, C, and Table 3) reveal a complete overlap of their obtained results with each other and with those obtained in the presence of supporting electrolyte. That is, the existence of cations e.g. supporting electrolyte has no impact on the role of different anions, which influence the electrochemical behavior of POAP/ERG nanocomposite.

Along the lines of what described for different anions, the effect of different types of cations such as Li⁺, Na⁺ and K⁺ can also be investigated. In this case, the modification of ERG/GC electrodes has been carried out in 1 M HNO3 solution containing nitrate salts of the corresponding cations. Fig. 16D shows the typical cyclic voltammograms, and Figs. 16E and F show the Nyquist plots presenting the influence of the incorporated cations. From Fig. 16D and the obtained results tabulated in Table 3, it can be noted the specific capacitance for different cations decreases in order of Na⁺ > Li⁺ > K⁺. In addition, the values of specific capacitance derived from the cyclic voltammetric (Fig. 16D) and impedance spectroscopic measurements (Figs. 16E and F) do indeed coincide as tabulated in Table 3. Although one can expect the smaller size of Li⁺ ion to provide facile insertion/expulsion to/from the electroactive film, the greater specific capacitance has been obtained in the presence of Na⁺. As for studied anions, it has been noted that the trends in direction of ionic mobility and ionic radius are going the same way.^69-70 Possessing the greatest mobility and the smallest radius have led to estimation of the greater specific capacitance would be obtained as a consequence of more being intercalated into the POAP/ERG nanocomposite, which is in good agreement with experimental results. On the contrary, the trends in ionic mobility ⁶⁹ and ionic radius ⁷¹ contrast with those in hydration enthalpy ⁷⁰ and hydration number ⁷¹ for the studied cations. These inconsistencies have hindered prediction of which cation would be incorporated into the POAP/ERG nanocomposite easily. The obtained specific capacitance values (Table 3) decrease in the order of Na⁺ > Li⁺ > K⁺ which confirms the facile incorporation of Na⁺ into the POAP/ERG is more than likely.

Along the lines of evaluating of effects of different types of cations and anions on the POAP/ERG nanocomposite, we have examined the extent to which the incorporation of different cations and anions has affected each of components of the POAP/ERG nanocomposite. In this case, ERG/GC electrodes have been investigated in different solutions containing different cations and anions. The capacitive behavior of ERG/GC electrodes in the presence of different cations and anions have been evaluated at 50 mV s^-1 as shown in Figs. 17A and B, respectively. The electrodes have presented negligible difference in their current response while have shown typical rectangular shape indicating an excellent capacitive behavior. Therefore, it can be concluded that graphene sheets in the POAP/ERG nanocomposite act as numerous ion-buffering reservoirs and provide for ions shortened diffusion path into the composite which results in the superior electrochemical performance of the nanocomposite.