## 3 Results
### Electrochemical Measurements
The higher rate capability of the electrode based on the untreated (initial) composite can be interpreted by the higher concentration of the Mn(IV) oxide, which was established on the basis of the XPS analysis. It should be noted that the conductivity of the Mn(IV) oxide exceeds the conductivity of the Mn(III) oxide by several orders of magnitude [30]. The CV curves of Mn-580 + Re and Mn-700 + Re composites (Figure 7a) have a pair of peaks at potential values of 0.55 and 0.48 V on the cathode and anode branches of the curve, respectively. These peaks are associated with a redox reaction on the surface of the electrodes, apparently associated with changes in the degree of the oxidation of  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Sample**} & \multicolumn{6}{c}{**Potential Scan Rate, mV/s**} \\ \cline{2-7}  & **5** & **10** & **20** & **40** & **80** & **R * \\ \hline MWCNTs & 21.1 & 19.4 & 17.4 & 14.7 & 11.0 & 52\% \\ \hline Mn-0 & 49.2 & 43.3 & 36.8 & 25.4 & 14.4 & 29\% \\ \hline Mn-580 & 61.7 & 48.5 & 34.9 & 20.5 & 11.7 & 19\% \\ \hline Mn-700 & 41.2 & 31.3 & 24.2 & 15.6 & 10.1 & 24\% \\ \hline Mn-580 + Re & 67.  
rhenium, since these maxima are not observed on the CV curves of composites that do not contain rhenium oxide. The intensity of these peaks, as well as the area of the CV curve, is noticeably greater in the case of the Mn-580 + Re composite. This composite has a maximum specific capacitance at both high and low potential scan rates (Table 4). The good electrochemical behavior and the shape of the CV curves for composites with rhenium oxide (Figure 7b,c) suggest a higher availability of the surface of these composites for electrolyte ions, as well as the possible occurrence of redox reactions, even at high potential scan rates. In addition, the reason for the increase in rate capacitance may also be an increase in the electrical conductivity of the oxide component of composites due to an increase in the content of Mn(IV) oxide in them (see XPS data). To assess the contribution of capacitive and pseudocapacitance (e.g., Faraday) processes in the total capacitance of materials, a method is used based on the analysis of the capacitance characteristics of electrodes depending on the potential scan rate, taking into account Equations (4) and (5) [59, 60]:  
\[C=C_{v=\infty}+\alpha\cdot v^{-1/2} \tag{4}\]  
\[C^{-1}=C_{v=0}^{-1}+b\cdot v^{\frac{1}{2}} \tag{5}\]  
where \(C\) is the total specific capacitance, \(C_{v=\infty}\) is a specific capacitance of EDL (\(C_{\text{EDL}}\)), \(C_{v=0}\) is a maximal specific capacitance (\(C_{\text{max}}\)), and \(a\) and \(b\) are the constants. The dependences of \(C\) on \(v^{0.5}\) and \(C^{-1}\) on \(v^{-0.5}\) for the Mn-580 + Re composites are shown in Figure 7d,e. For electrodes based on other composites under study, these  
Figure 7: (a) CV curves of electrodes based on Mn-580 + Re and Mn-700 + Re, measured at a potential scan rate of 5 mV/\(s\); CV curves measured at different potential scan rates for electrodes based on (b) Mn-580 + Re and (c) Mn-700 + Re; (d) the dependence of the reciprocal of the total capacitance (\(C^{-1}\), (F/g)\({}^{-1}\)) on the square root of the scan rate (\(v^{0.5}\), mV\({}^{0.5}\).s\({}^{-0.5}\)) and (e) the total capacitance (C, F/g) on the reciprocal of the square root of the scan rate (\(v^{-0.5}\), mV\({}^{-0.5}\).s\({}^{0.5}\)) for the Mn-580 + Re electrode; (f) the ratios of the electric double layer capacitance (\(C_{\text{EDL}}\)) and the experimental capacitance (\(C_{\text{real}}\)) to the total theoretical capacitance (\(C_{\text{max}}\)) for electrodes based on MWCNTs and composites. dependencies are presented in Figure S5.