Modeling
Pseudo kinetic model, which was first introduced by Lagergren17 and widely used in various studies18-22, was employed to express the deactivation of Ag as a function of aging time. The oxidation of Ag can be considered as a reversible reaction with an equilibrium in this study. The aging experiments in this study were conducted under a continuous flow system such that the concentrations of gas streams were constant during the aging processes. The pseudo reversible reaction model with a reaction equation (Eqn. 1) was applied to describe the kinetics of aging processes on Ag0Z. \(C_{\text{Ag}}\) is the normalized concentration of silver which indicates the amount of I2loaded on the aged Ag0Z, \(A\) is a gas component used in this study, \(C_{A}\) is the concentration of oxygen in dry air,\(C_{\text{Ag}^{+}}\) is the concentration of silver oxidized by oxygen in dry air, \(n\) is the reaction order, \(k_{1}\) is the forward reaction rate constant, and \(k_{-1}\) is the reverse reaction rate constant. Here \(k_{1}\) and \(C_{A}\) are lumped into \({k_{1}}^{*}\)because the gas concentration is constant all the time during aging experiment. The correlation coefficient (R2) was also employed to determine the applicability of each model using Eqn. 2.\(x\) is sample data from experimental results,\(\ \overset{\overline{}}{x}\) is the average of the sample data set from experimental results, \(y\) is sample data from model results, and \(\overset{\overline{}}{y}\) is the average of the sample data set from model results. In general, as the correlation cofficient is close to 1, it indicates strong correlation between experimental data and model results.
\begin{equation} {\text{Ag}{\text{Ag}_{s}}^{+}\backslash n}{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ v=\frac{\text{dC}_{\text{Ag}}}{\text{dt}}={-k}_{1}C_{A}{C_{\text{Ag}}}^{n}+k_{-1}{C_{\text{Ag}^{+}}}^{n}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (1)}\nonumber \\ \end{equation}\begin{equation} {k_{1}}^{*}=k_{1}C_{A}\nonumber \\ \end{equation}\begin{equation} v=\frac{\text{dC}_{\text{Ag}}}{\text{dt}}={{-k}_{1}}^{*}C_{\text{Ag}}+{k_{-1}C}_{\text{Ag}^{+}}\nonumber \\ \end{equation}\begin{equation} \text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Correlation\ coefficient\ }\left(R^{2}\right)=\frac{\sum{(x-\overset{\overline{}}{x}})(y-\overset{\overline{}}{y})}{\sqrt{{(x-\overset{\overline{}}{x})}^{2}{(y-\overset{\overline{}}{y})}^{2}}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (2)\backslash n\nonumber \\ \end{equation}