## 2 Impedance Spectroscopy
### EleIS Modelling of Electrodeposited Ti-W Undoped and Vanadium Doped Humidity Sensor
Figures 14-16 display Nyquist plots for TiW, TiW-V5 and TiW-V7, confirming the adequacy of the chosen model; in them are plotted sets of obtained experimental and respective fitted data. As can be seen, the fits for all three electrospun films display a high level of superposition between the experimental and fitted data. Figure 13: Equivalent circuit adopted for modelling vanadium undoped and doped electrodeposited Ti-W films. In Tables 2-4, the values of the parameters for the known contributions, all of which are represented in the proposed electrical equivalent circuit, are displayed. In it, using a parallel association strategy of terms, the authors used the following matching criteria: a parallel association R1//C1, representing grains and grain agglomerates contribution; a constant-phase element CPEel, representing ion diffusion along the interface between the surface of the material and the measurement electrodes; a constant phase element, CPEpo, that stands for diffusion of charges along the voids filled by water molecules; a capacitor, Cgeo, representing the geometric effect of the location of the measurement electrodes (positioned on the upper face but at opposite ends of the material); a resistor in parallel with a capacitor, R2//C2, that accounts for the contribution of conduction along the boundaries between grains or between clusters of  
Figure 16: _Cont._  
Figure 15: TiW-V5 1 layer—Experimental and fitted data using the proposed model circuit for different RH concentrations: (a) 10%, (b) 40%, (c) 70%, (d) 100%. vanadium). For the pair R\({}_{1}\)//C\({}_{1}\), attributed to grain boundaries contribution, the overall impedance decreases with the introduction and subsequent increase of vanadium content, as expected. With doping, titanium or tungsten atoms are replaced by vanadium ones, which possess more valence electrons. Thus, additional free electrons are introduced into the system without establishing connections with the existing surrounding atoms of the initial matrix. Besides, the same pair of parameters also support the electronic nature of the p- to n-type transition; for all cases (undoped and doped), while the capacitive component slightly varies, the resistive contribution shows a tendency to increase to around 40-50% RH concentration, followed by a decrease. This behavior aligns with the established form regarding free electron transportation in ceramics as RH increases. Indeed, ion hopping mechanisms are weak for low RH concentrations, so charge transportation occurs through grain/grain agglomerates; however, it is conditioned by grain boundaries that are more negatively charged (higher number of free electrons) and originates in the higher potential energy barriers. Thus, impedance increases. However, as soon as water molecules start to get physiosorbed and condensate inside the voids and along the ceramic surface, ion hopping starts to dominate, and the grain contribution diminishes once the potential energy barriers in the grain boundaries no longer influence the dominant charge carriers' transportation paths, which change. That is also visible in the way the overall grain/grain agglomerates contribution varies with the amount of added dopant and with RH increase; with RH increase, for all compositions, the impedance of that pair of parameters, R\({}_{2}\)//C\({}_{2}\), shows a decreasing tendency, and with the addition of increasing amounts of dopant, the impedance of that pair of parameters also decreases. Consideration (ii). C\({}_{\text{goo}}\) shows a slight variation between samples and along the RH tested range, as expected, once electrode placement cannot be reproduced with complete exactitude. Even though the minor variations found for each sample with changing RH are slight, the overall differences are less than one half-order of magnitude, even for TiW-V5, where more significant adjustments are observed. Consideration (iii).