## 3 Results and Discussion  
Although Ag has excellent solubility in MSA, the electrochemical efficiency of MSA is not expected to be good, owing to its high viscosity, because the Ag ions have lower mobility in a high-viscosity electrolyte [18], which is also related to diffusion [19; 20]. Therefore, CV was performed to confirm the diffusion coefficient according to the amount of water added to MSA and the CV curves are shown in Figure 1. The oxidation and reduction peaks tend to increase with increasing scanning speed in all the CV curves. In addition, as the concentration of the added water increased, the switching point rose to the upper side of the graph. In other words, the larger the concentration of the added water, the greater is the electrochemical behavior of the reversible electrode reaction. This means that the oxidation-reduction reaction of the material is fast enough to maintain the concentrations of the reactants and products on the electrode surface in equilibrium with the changes in voltage. When the concentration of the added water is small, the switching point drops to the bottom of the graph because the rate of diffusion of the material to the electrode surface is slow, and does not follow the rate of the oxidation-reduction reaction. To confirm the relationship between the concentration of the added water and the diffusion rate, the Randles-Sevcik equation was used to calculate the diffusion coefficient of the electrolyte according to the concentration of the added water. In general, the peak current of a diffusion-controlled reversible or quasi-reversible electrochemical reaction follows the Randles-Sevcik equation [21]:  
\[i_{p}=0.4463 nF\sqrt{\frac{nFD}{RT}}A\mathcal{C}\sqrt{\
u}, \tag{1}\]  
where \(i_{p}\) is the peak current, \(n\) is the number of electrons, \(F\) is the Faraday constant, \(T\) is the temperature in Kelvin, \(R\) is the gas constant, \(A\) is the surface area of the working electrode, \(D\) is the diffusion coefficient of the electroactive species, \(C\) is the bulk concentration of the electroactive species, and \(\
u\) is the scan rate employed in the CV measurements. Thus, the diffusion coefficients for the MSA solution at 298 K are calculated from the slope of the plot of \(i_{p}\) versus \(\sqrt{\
u}\), and the diffusion coefficients of Ag ions, as shown in Figure 2. As shown, the diffusion coefficient of the electrolyte solution increases with the addition of water. That is, the addition of water to the MSA electrolyte solution increases the degree of diffusion, which implies that the viscosity is controlled by the addition of water. The Stokes-Einstein equation can be given by the following generalized expression [22]:  
\[D=kT/6\pi\,\eta r, \tag{2}\]  
where \(D\) is the diffusion coefficient, \(\eta\) is the viscosity of solvent, and \(r\) is the radius of the diffusing particle. It can be seen from this equation that the diffusion coefficient and viscosity are inversely proportional. As shown in Figure 2, therefore, the diffusion coefficient increases with a decrease in the viscosity of the MSA solution. Even if the viscosity is controlled by adding water to the MSA solution, the solubility of the metal in the MSA solution is very high [23]; thus, the ion diffusion in the electrolyte can be controlled by adding water to the MSA solution. The viscosity of the MSA electrolyte was then measured to determine the actual viscosity according to the concentration of the added water, and the results are shown in Figure 3. In most cases, the viscosity was measured to be approximately 15 mPa-s, regardless of the experimental conditions. However, the measured viscosity tended to decrease sharply when the concentration of the added water was 20.8 M. This result is partially consistent with the diffusion coefficient calculated from the CV curve when the concentration of the added water was 20.8 M. Since the viscosity of MSA is too high, it is expected that the addition of 9.3 M of water will not have a significant effect on the measured viscosity.