## 4 Electrochemical Analysis
### Impedance  
To further evaluate the electrochemical performance of the three composite electrodes, electrochemical impedance spectroscopy (EIS) was performed before and after cycling. The Nyquist plots both prior to and post cycling are shown in Figure 13A,B. A typical impedance spectrum (Nyquist plot) of an anode material with the equivalent electrical circuit is shown in Figure 13C,D. The Nyquist plot of the circuit model shows a semicircle in the high and medium frequency regions and a straight line with a constant slope in the low frequency range. The initial intercept value of the semi-circle in the high to medium frequency region represents the impedance (R\({}_{\rm s}\)) associated with the resistance of the SEI layer formed on the electrode surface. The semicircle in the middle frequency range can be ascribed to the charge-transfer resistance (R\({}_{\rm ct}\)) at the electrode/electrolyte interface [57]. The straight line in the low frequency region represents the diffusion properties of Li\({}^{+}\) within the electrode; the slope of which gives the Warburg impedance. Figure 13 shows the characteristic impedance at both low and high frequencies of the Fe\({}_{2}\)O\({}_{3}\)/C, TiO\({}_{2}\)/C and \(\alpha\)-Fe\({}_{2}\)O\({}_{3}\)/TiO\({}_{2}\)/C to be an inclined line and semicircle, respectively. The semicircle comprises the combination of the contact resistance between the active material and current collector, the intrinsic resistance of the active materials, and the ionic resistance of the electrolyte, while the inclined line reflects the solid-state diffusion of Li within the electrode. The diameter of the intermediate-frequency semicircle indicates the electrode-electrolyte interfacial resistance R\({}_{\rm CT}\).  
Figure 13: Nyquist plots comparing fresh (**A**) and aged (**B**) electrochemical impedance between the metal oxide/carbon composite electrodes after 100 cycles, (**C**) schematic of equivalent impedance circuit model and (**D**) the corresponding Nyquist plot of the circuit model with all the parameters shown on the plot.  
It can be seen in Figure 13 that the electrode (fresh cell) with the highest charge transfer resistance (R\({}_{\text{CT}}\)) was that composed of the \(\alpha\)-Fe\({}_{2}\)O\({}_{3}\)/C fibers, as it showed an impedance of 26. The TiO\({}_{2}\)/C and \(\alpha\)-Fe\({}_{2}\)O\({}_{3}\)/TiO\({}_{2}\)/C composite electrodes showed much lower impedance values of 11 and 13, respectively. A post-cycling impedance analysis was evaluated (aged cells) to compare the results. Again, the \(\alpha\)-Fe\({}_{2}\)O\({}_{3}\)/C showed greater impedance compared to the other two electrodes where the charge transfer resistance (R\({}_{\text{CT}}\)) of the \(\alpha\)-Fe\({}_{2}\)O\({}_{3}\)/C composite-fiber electrodes was 171. This can be attributed to the poor ion intercalation kinetics of this composite electrode, as well as to the formation of a thick SEI layer. On the contrary, the \(\alpha\)-Fe\({}_{2}\)O\({}_{3}\)/TiO\({}_{2}\)/C electrode showed much lower charge transfer resistance (R\({}_{\text{CT}}\) = 56) than that for the TiO\({}_{2}\)/C (R\({}_{\text{CT}}\) = 69). and \(\alpha\)-Fe\({}_{2}\)O\({}_{3}\)/C after cycling (R\({}_{\text{CT}}\) = 168). This demonstrates how the stable structure of the TiO\({}_{2}\) nanoparticles improved the ionic transport in the composite-fiber electrode, hence leading to the improved performance. The effect of SEI layer formation on the electrochemical reversibility of graphite anode has been widely studied [58; 59]. Our future work will be focused on investigating the effect of surface area of fibers on the first charge capacity of composite-fiber anodes. The effect of the SEI formation at the first discharge cycle on the electrochemical performance of the electrode will be systematically investigated