# Assessing the Efficacy of Seawater Batteries Using NASICON Solid Electrolyte
## 3 Results
### Investigating the Electrical Conductivity of the NASICON Ceramic Membrane
It is possible to express the total dielectric constant (\(\varepsilon_{\mathrm{r}}\)) as a function of the capacitance of a capacitor (Equation (1)) or as a multi-component parameter consisting of a real and imaginary component (\(\varepsilon^{\prime}{}_{\mathrm{r}}\) and \(\varepsilon^{\prime\prime}{}_{\mathrm{r}}\)) (Equations (2a) and (2b)):  
\[\varepsilon_{r}(\omega)=\frac{C_{p}}{C_{0}}=\frac{C_{p}d}{\varepsilon_{0}A} \tag{1}\]  
\[\varepsilon_{r}(\omega)=|\varepsilon_{r}(\omega)|\mathrm{cos}\;\delta=| \varepsilon_{r}(\omega)|\mathrm{sin}\;\theta \tag{2a}\]  
\[\varepsilon^{\prime\prime}{}_{r}(\omega)=|\varepsilon_{r}(\omega)|\mathrm{sin} \;\delta=|\varepsilon_{r}(\omega)|\mathrm{cos}\;\theta \tag{2b}\]  
\(C_{\mathrm{p}}\) is the capacitance taken on the parallel faces, and \(C_{0}\) is the capacitance of the vacuum, where \(C_{0}=\varepsilon_{0}A/d\), and where \(\varepsilon_{0}\) is the vacuum's permeability, the capacitor's transverse surface area is defined by \(A\) between the plates where the dielectric material is located, thickness of the dielectric layer can be measured by \(d\); \(\omega=2\pi f\) is the angular frequency of the applied field, and \(\delta=90-\theta\), where \(\theta\) is the phase angle. In Figures 6 and 7, it can be seen how the dielectric constant (DC) changes with the frequency for samples analyzed at room temperature. It has been noted that the dielectric constant values decrease with an increase in frequency. Imperfections, such as vacancies or concentrated electronic fields, can lead to dielectric relaxation in materials. The increase in dielectric constants in low frequencies can be explained by the mechanisms responsible for spatial load polarization. Load carriers follow the applied field at low frequencies according to this model, which leads to increased polarization and, therefore, high permittivity values. On the other hand, at high frequencies, load carriers cannot track the applied field because the period is too short, and the field changes direction before the tasks align with the direction of the field. Thus, the electrical constant decreases, as does the net trend. Figure 5: Nyquist diagrams for NAS-6% ceramic membranes prepared at different sintering temperatures (1150, 1175 and 1200 °C), analyzed at room temperature (RT). The DC ion conductivities (\(\sigma\)) of the analyzed samples were calculated at room temperature after analyzing the data from wideband dielectric spectroscopy (Figures 8 and 9). The conductivity values measured are compared with the ones obtained for commercial NASICON in a magnitude-wise comparison. Figure 6: Evolution of the dielectric constant of NASICON 2% samples with frequency at room temperature (RT). Figure 7: Evolution of the dielectric constant of NASICON 6% samples with frequency at room temperature (RT). The measured NASICON samples reached ionic conductivities ranging from 8.5 \(\times\) 10\({}^{-5}\) (1150 \({}^{\circ}\)C) to 4.0 \(\times\) 10\({}^{-4}\) S cm\({}^{-1}\) (1175 \({}^{\circ}\)C) for NAS-2% samples and values ranging from 7.3 \(\times\) 10\({}^{-5}\) (1150 \({}^{\circ}\)C) to 6.19 \(\times\) 10\({}^{-4}\) S cm\({}^{-1}\) (1200 \({}^{\circ}\)C) for NAS 6%. For comparison, a commercial NASICON membrane with an ionic conductivity of 3.62 \(\times\) 10\({}^{-4}\) S cm\({}^{-1}\). Experimental data analysis revealed that NASICON samples sintered at 1175 \({}^{\circ}\)C and 1200 \({}^{\circ}\)C  
Figure 8: Variation in conductivity of NASICON samples by 2% excess sodium and NAS Ref. at room temperature (RT). Figure 9: Variation in conductivity of NASICON samples by 6% excess sodium at room temperature (RT). had higher ion conductivity values than commercial ones. It should be noted that the higher the sintering temperature, the greater the ionic conductivity of the membranes.