## 2 Impedance Spectroscopy
### EleIS Modelling of Electrodeposited Ti-W Undoped and Vanadium Doped Humidity Sensor  
In this section, the authors present their latest efforts in modelling Mixed Metal Oxide (MMO) nanostructures again using the parallel approach. Sample preparation and their structural, morphological, and electrical response with relative humidity (RH), characterized using EleIS, have already been reported in the literature [133]. A summary is given here to provide contextualization. TiO\({}_{2}\)/WO\({}_{3}\) (obtained by mixing powders in a molar ratio of 1:1) and doped TiO\({}_{2}\)/WO\({}_{3}\) with V\({}_{2}\)O\({}_{5}\) were incorporated into electrospun fibers (a weight ratio of 94:6 of both copolymers and oxide mixtures, all in wt.%, was used for all samples). The obtained composites were thermally treated to remove the polymeric matrix. Then, 0.7 g of each mixture was immersed in 3 mL of a polymeric alcohol solution and stirred. The resulting material was put into a conventional syringe and maintained under constant pressure. Using a 15-kV direct current voltage source connected to the dip of the syringe, an electrical field was established between the syringe and the grounded target. The deposition procedure was carried out for 5 min, and the fibers were collected on aluminum foil targets, where a pair of gold interdigital-shaped electrodes were previously deposited (this procedure was repeated to deposit successive layers on the electrode surface, providing one- and three-layer samples). Figure 12: Some data concerning the characterization of TiO\({}_{2}\):WO\({}_{3}\) compounds doped with Nb\({}_{2}\)O\({}_{5}\): (**a**) equivalent model developed; (**b–d**) experimental and simulated Nyquist diagrams using the model for a sample with 4% of niobium oxide, at 20 \({}^{\circ}\)C for 20, 50 and 70% RH, respectively; (**e–g**) experimental and simulated Nyquist diagrams using the model for sample with 6% niobium oxide, at 20 \({}^{\circ}\)C for 20, 50 and 70% RH, respectively [132]. Then, the samples were sintered in an oven for 1 h at 500 \({}^{\circ}\)C, with heating and cooling rates of 20 \({}^{\circ}\)C/min; the final doped samples that displayed the best moisture sensitivity were obtained for 5 and 7 wt.% addition of V\({}_{2}\)O\({}_{5}\) powder to the initial mixture (named Tiw) and were designated as TiW-V5 and TiW-V7, respectively. The humidity-dependent electrical properties of the thick films were evaluated by EleIS in the 10-100% RH interval at ambient temperature, employing frequency sweeps in the interval 400 Hz-40 MHz, with an alternating voltage potential possessing an amplitude of 0.5 V.  
The electrospun doped films showed increased sensitivity compared to the undoped ones; besides, a p- to n-type transition was observable for the doped sensors. Authors discussed and showed that the conduction-type transition was of an electronic nature since it took place at around 30% RH (the region that is usually typified as the frontier between low and high humidity ranges, when the first complete water layer, the chemisorbed one, covers the sensor surface entirely). Diverse transport mechanisms were found to contribute to the sensors' electrical response to RH variations: conduction along grains and grain agglomerates, conduction along the boundaries between grains or between clusters, diffusion along the interface between the surface of the material and the measurement electrodes, and diffusion of charges along the pores filled by water molecules; a capacitive contribution due to the geometric effect of the location of the measurement electrodes; charge transport along the surface of the samples covered along the material surface covered by layers of water vapor due to the effect of \"electron tunnelling\". With these contributions, the authors developed the electrical equivalent circuit shown in Figure 13, which accounts for all the identified contributions.