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}