## 3 Results
### FT Alternating Current Voltammetry
As a next step, a quasi-reversible harmonic is chosen and the ratio \(I_{\text{p},h}/I_{\text{p},h}^{\text{(rev)}}\) is calculated, where \(I_{\text{p},h}\) is the normalised peak current for a quasi-reversible harmonic and \(I_{\text{p},h}^{\text{(rev)}}\) the normalised peak current for the reversible harmonic at a certain \(A_{0}\) and \(a\). For all the combinations of amplitudes and harmonics, the chosen frequency for the quasi-reversible harmonic is that of 5 Hz, while for the peak of the reversible harmonic, it is 0.1 Hz. Let us now use the example of \(I_{\text{p},A}/I_{\text{p},A}^{\text{(rev)}}\) and \(I_{\text{p},5}/I_{\text{p},5}^{\text{(rev)}}\) for 0.25 V. The respective estimated values are 0.57 and 0.6, respectively. Figure 3: Experimental results: 5 th harmonics of \(M\)_t_LPMO9 Himmobilised on a Co-f-MWCNTs modified GC electrode (black) and Co-f-MWCNTs modified GC electrode without the enzyme (red) at 25 \({}^{\circ}\)C. Experimental conditions: acetate buffer 500 mM, pH 6, \(A_{0}=0.20\) V and \(f=5\). As a final step, these values shall be used for the estimation of the \(k^{0}\) from the nomograms of \(I_{\text{p,}h}/I_{\text{p,}h}^{\text{(rev)}}\) against the \(\log(k^{0}f^{-1})\). These nomograms are calculated for \(a=0.5\) (Figure 6a for the 4 th harmonic and Figure 6b for the 5 th). The same procedure is done for the amplitude of \(A_{0}=0.2\) V. By taking an average of the extracted values, the \(k^{0}\) is estimated at \(4.6\pm 2.6\) s\({}^{-1}\). Figure 4: Experimental results: (**a**) 4 th harmonics, (**b**) normalised peak height of the 4 th harmonic, (**c**) 5 th harmonics and (**d**) normalised peak height of the 5 th harmonic, of _Mt_LPMO9H immobilised on a Co-f-MWCNTs modified GC electrode at 25 \({}^{\circ}\)C. Experimental conditions: acetate buffer 500 mM, pH 6, \(A_{0}=0.2\) V, and \(f=5\) (black), 3 (red), 1 (blue), 0.5 (green), 0.2 (orange) and 0.1 (magenta) Hz. Figure 5: Experimental results: (**a**) 4 th harmonics, (**b**) normalised peak height of the 4 th harmonic, (**c**) 5 th harmonics and (**d**) normalised peak height of the 5 th harmonic, of _Mt_LPMO9H immobilised on a Co-f-MWCNTs modified GC electrode at 25 \({}^{\circ}\)C. Experimental conditions: acetate buffer 500 mM, pH 6, \(A_{0}=0.25\) V, and \(f=5\) (black), 3 (red), 1 (blue), 0.5 (green), 0.2 (orange) and 0.1 (magenta) Hz. In order to validate the value of \(k^{0}\), found experimentally, FTacV experiments were simulated numerically for \(k^{0}\) equal to 4.6 s\({}^{-1}\) and \(a\) equal to 0.57. In order to do so, Equation (5) was solved numerically where the potential ramp is perturbed by a sinusoidal of amplitude \(A_{0}\) and frequency \(f\),  
\[E=E_{\rm I}-vt_{\rm R}+v|t-t_{\rm R}|+A_{0}\sin 2\pi ft \tag{9}\]  
and the harmonics where calculated from the current obtained by multiplying the current density, Equation (4) with the electrode surface \(S\). Apparently, both the surface area \(S\) and the surface concentration of the oxidized form of the enzyme \(\Gamma^{0}\) are unknown and are expected to vary between different immobilisation experiments. Therefore, the factor \(\Gamma^{0}S\) was chosen by trial-and-error. The simulation results (red curves) together with the corresponding experimental plots (black curves) for \(A_{0}=0.2\), \(\Gamma^{0}S=3\times 10^{-13}\) mol and \(A_{0}=0.25\) V, \(\Gamma^{0}S=1.2\times 10^{-12}\) mol and \(f=1\) Hz, are presented in Figure 7a,b, respectively. A rather good agreement is observed, implying a satisfactory estimation of \(k^{0}\). Figure 6: Computational results: Dependence of the normalised principal peak height for the (**a**) 4 th and (**b**) 5 th harmonic of an immobilised species. Parameters: \(a=0.5\) and \(A_{0}=0.2\) (black) and 0.25 V (red).