## 3 Results
### FT Alternating Current Voltammetry  
Before attempting to extract the \(k^{0}\), FTacV was performed on a Co-f-MWCNTs modified GC electrode with and without \(M\)tLPMO9H. The cathodic 5 th harmonic in acetate buffer 500 mM, pH 6 for \(A_{0}=0.2\) V and \(f=5\) is presented in Figure 3. In the case of the immobilised enzyme (black curve) a set of intense peaks around the principle peak at 0.25 V. On the other hand, in the absence of the \(M\)tLPMO9H, a faint peak of small amplitude appears at 0.2 V (red curve), leading to the conclusion that the high amplitude harmonic is indeed due to the enzyme and not the immobilization matrix. Then, FTacV was performed so as to apply the methodology introduced [17] for the extraction of the \(k^{0}\). At this point, the methodology is summarized:  
1. A harmonic \(h\) is chosen, being free of capacitance currents. This harmonic is recorded at a fixed amplitude and decreasing frequencies;
2. The limiting value of the normalized peak height, \(I_{\rm p,\,\,h}^{\rm(rev)}/f\), of the principal peak is determined. For this frequency, \(f\), the reaction is at the reversible region; \begin{table}
\begin{tabular}{c c} \hline \(k^{0}\)/s\({}^{-1}\) & \(\Delta E\)/V \\ \hline
100 & 0.000 \\
20 & 0.008 \\
10 & 0.014 \\
5 & 0.026 \\
2 & 0.059 \\
1 & 0.098 \\ \hline \end{tabular}
\end{table} 
Table 1: Peak separation values for an immobilised species assuming \(v=0.1\) V s\({}^{-1}\) and ideal capacitance. Figure 2: Computational results: Cyclic voltammetry for different \(k^{0}\) values. Parameter values: \(\Gamma^{0}=5.1\times 10^{-6}\) mol m\({}^{-2}\), \(C_{\rm dl}=1\) F m\({}^{-2}\), \(E^{0\prime}=0\) V, \(v=0.1\) V s\({}^{-1}\) and \(k^{0}=100\) (black), 20 (red), 10 (blue), 5 (green), 2 (orange) and 1 s\({}^{-1}\) (orange). If the transfer coefficient is to be determined, the shift in the potential of the principal peak is plotted as a function of the logarithm of the inverse frequency, \(1/f\). Linear regression is performed in the region of high frequencies and the transfer coefficient is determined;
4. The principal peak height \(I_{\text{p},h}\) of a quasi-reversible harmonic is determined and the value \(I_{\text{p},h}/I_{\text{p},h}^{\text{(rev)}}\) is calculated;
5. The kinetic constant is determined from the graph representing the dependance of \(I_{\text{p},h}/I_{\text{p},h}^{\text{(rev)}}\) on \(\log(k^{0}/f)\). Therefore, as a first step, FTacV was performed for two amplitudes, 0.2 and 0.25 V, at frequencies of 5, 3, 1, 0.5, 0.2 and 0.1 Hz. The scan rate was adjusted at each case accordingly in order to fullfill the slow scan rate approximation and render the experiment independent of this factor [16; 19]. The cathodic scan of the 4 th and the 5 th harmonics are presented in Figures 4 and 5, respectively, for \(A_{0}=0.2\) and 0.25 V. Looking at both the amplitudes employed, there is no intense deformation in the harmonics that would suggest a transfer coefficient that would deviate beyond the range of 0.4-0.6; thus, regarding the dominant peak [17], no significant errors would be inserted in the preliminary analysis in case an \(a=0.5\) is assumed. Moreover, both 4 th and 5 th harmonic seem free of capacitance contribution. As a second step, the trend of the main observable, i.e., the peak height of the principle peaks, is to be observed. In both cases, typical 4 th and 5 th harmonics for quasi-reversible reactions of immobilised species are presented for the higher applied frequencies (Figures 4a,c and 5a,c). Apparently, as the frequency is decreased, the amplitude of the harmonics decreases, as predicted theoretically. The trend of the normalized peak height of the principle peaks, \(I_{\text{p},h}/f\), on frequency is presented in Figures 4b,d and 5b,d. By observing these figures, it is evident that a saturation in the peak height of the dominant peak is observed for a frequency of 0.1 Hz. This indicates that reversibility is reached by that point, and the height of the dominant peak of the reversible harmonic, \(I_{\text{p},h}^{\text{(rev)}}\) has been determined.