## 4 Discussion
Higher amounts of binder (20 wt.%) seemed to block the ion carrier transport at temperatures lower than 100 \({}^{\circ}\)C. In turn, at higher temperatures, water molecules (oxonium ions) were retained in the PAA structure, thus eliminating sharp drops in grain conductivity. It is known that impedance spectra illuminate the different electrical and polarization phenomena that occur in the materials. In general, for a given dataset, more than one equivalent circuit exists which gives a reasonable fitting. The choice between these circuits must be based both on simplicity and consistently with the known physical and chemical processes which take place in the system [48]. The proposed equivalent circuit modelfor evaluation/representation of the electrical response of the samples can be seen in Figure 12.  
The initial values of the components in the proposed model were obtained using EIS spectra analyzer software, followed by manual fine tuning. In Figure 13, some of the fits performed using the proposed model are shown, whereas in Table 2, the fitted parameters for both samples in the temperature range between 25 and 200 \({}^{\circ}\)C are summarized. From the plotted fittings, the adequation of the studied and developed equivalent model can be confirmed: indeed, both the Nyquist and Bode fits showed an agreement with the obtained experimental data. In detail, the proposed model is composed of: (1) a Warburg-type element, Warburg-Sofficient, allowing for representation of the strong ionic contribution present (the chosen Warburg element was a classic semi-infinite linear type). This contribution is mainly due to the transportation of charges along the binder surface and open pores. In addition, in the literature, other authors [27; 33] have already reported the high ionic conductivity of polyantimonic-acid-based membranes, which concurs with the obtained experimental data, giving support to the addition of this contribution to the electrical equivalent circuit; (2) two constant phase elements, CPE1 and CPE2, with respective pairs of components are present, with charge diffusion contributions arising from the interface between electrodes and the material, and along sample surfaces due to water retention on the material surface and mesoporousity (for both referred diffusion mechanisms, the interfacial character of their impedance makes it partly capacitive as well resistive in nature): regarding the second diffusion contribution, in the literature are references not only to water retention occurring in the membrane structures, but also to the role this has on the ionic conductivity of the materials [16; 50; 51; 52]. Following from the pore size distribution (Figure 3), diffusion contributions can also originate from significant mesoporousity, and diffusion can also occur along the pore surface and along the pores filled with water [53]; (3) one element is composed of a resistor in parallel with a capacitor, R//C (representing the bulky granular and grain boundaries contribution all together); (4) a geometric capacitance, CGEO, represents the geometric effect contributions of the electrode locations, which are placed on the extremities of the upper faces of the samples, and consequently, the measuring configuration exhibits a shape that has similarities to that of a capacitor with parallel plates, with the tested material in-between plates. In addition, the developed and presented equivalent circuit model  
\begin{table}
\begin{tabular}{l c c c c c c c c} \hline  & **R** & **C** & **C\({}_{\text{CEO}}\)** & **Q\({  
also fits well with the observed effects of relative humidity on the electrical response of the samples. From close inspection of the parameters shown in Table 2, we can conclude that: (1) For both samples, the dominant conduction mechanisms are ionic in nature, due to the presence of structural and adsorbed water.