## 4 Discussion  
As follows from the STA, thermo-XRD and porosimetry results obtained for the 80 PAA and 90 PAA membranes, their structures are rather similar. The addition of the fluoroplastic binder mostly affected the size of the pores. Their mean size decreased from \(\sim\)70 to 50 nm with the increase in binder content from 10 to 20 wt.%. According to the STA results, a 10 wt.% binder addition caused a shift in the maximum of the first endothermic effect from 57.1 to 100.5 \({}^{\circ}\)C, indicating the retention of 0.1 mol of non-specific adsorbed water in the PAA after synthesis, in agreement with the schematic reactions presented in Equations (4) and (5). Indeed, the presence of adsorbed water molecules contributed to the Raman signal (see Figure 8), where the individual water molecules had a number of overlapping O-H vibration bands at 3200-3600 cm\({}^{-1}\), with the most intense at 3400 cm\({}^{-1}\)[49]. At the same time, in the structure of Sb\({}_{2}\)O\({}_{5}\cdot\)nH\({}_{2}\)O, water molecules could be found in cavities in the [SbO\({}_{6/3}\)]\({}^{-}\) octahedron network. The vibration of \(\
u\)(OH) with different lattice phonons originated from the interaction of the PAA protons with water molecules, located in the cavities, and the formation of H\({}_{3}\)O\({}^{+}\) ions. The latter causes a shift in the band's maximum, to lower wave numbers. This assumption is in agreement with data previously reported in the literature [42], where H\({}_{2}\)O\({}_{5}\)\({}^{+}\) ions were shown to form in the structure of tetragonal PAA. This ion has more degrees of freedom; hence, its band maximum is present in the Raman spectra near typical values of 3400 cm\({}^{-1}\). In accordance with the Raman analysis, the structure of polyantimonic acid differed from that observed for individual antimony oxides: in fact, Sb-O polymeric chains vibrations are dominant. In the highly symmetric pyrochlore structure of PAA, water molecules and protons are mainly present in the form of H\({}_{3}\)O\({}^{+}\) ions, acting as ion carriers for proton transport in PAA membranes. Indeed, the water molecules accommodated in the anionic skeleton are responsible for high values of grain conductivity component (\(\sim\)5 \(\times\) 10\({}^{-2}\) S/cm). Relative humidity increases result in grain boundary conductivity increases at room temperature due to increases in the ion carrier's concentration. The temperature increase induces non-linear changes in the grain boundary resistance, areas under the Nyquist plots and grain-boundary-specific conductivity values of the studied 90 PAA and 80 PAA samples. The grain conductivity remained almost unchanged with temperature. Temperature increases caused slight unit cell shrinkage and the length of Sb-O bonds decreased, accordingly with thermo-XRD and Raman spectroscopy data (see Figures 6-8); thus, the PAA phase structure was almost unchanged. The differences in conductivity values of the 90 PAA and 80 PAA samples observed at 25 \({}^{\circ}\)C due to binder content increases are probably due to the lower mesoporosity and slightly more homogeneous microstructure of the 80 PAA membrane after compaction. The step-by-step water removal is in accordance with the boundary conductivity changes displayed by the membranes with temperature. The grain boundary conductivity of the 90 PAA sample increased in the range 25-100 \({}^{\circ}\)C due to charge carrier mobility increases (oxonium ions, see Figures 10 and 11). Above 100 \({}^{\circ}\)C, temperature increases resulted in an overall conductivity decrease, caused by stepwise water removal from the structure, following the reactions presented in Equations (4) and (5), and with the expectable decrease in the number of charge carriers at high temperature. In turn, for the 80 PAA membrane, an almost-linear decrease in the specific conductivity in the entire investigated temperature range was observed.