Modeling
As mentioned through the kinetic data and chemical analysis above, aging
processes in dry air and humid air are controlled by the oxidation
reaction. The aging experiments were conducted under a continuous flow
system such that the concentrations of gas streams were constant during
the aging processes. Accordingly, the pseudo reversible reaction model
was applied to describe the kinetics of aging processes on
Ag0Z. For the modeling work, the correlation
coefficient (R2) was used to evaluate the goodness of
fit between experimental data and model results. According to the
modeling results, pseudo 1st order reversible reaction
models for aged Ag0Z in dry air and humid air at
different aging temperatures (100 oC, 150oC, and 200 oC) and different water
vapor concentrations (d.p. -40 oC, -15oC, and +15 oC) for up to 2 weeks
are placed in Figure 8 which are incorporated with the kinetic data
shown in Figure 7.
Modeling results on the aged Ag0Z in dry air at
different temperatures for different aging time are shown in Figure 8
(A). Eqn. (13) represents a reaction equation for a kinetic model on the
aged Ag0Z in dry air shown in Figure 8 (A).\(C_{\text{Ag}}\) is the normalized concentration of silver which
indicates the amount of I2 loaded on the aged
Ag0Z, \(C_{O_{2}}\) 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, and \(k_{1}\) is the
forward reaction rate constant, and \(k_{-1}\) is the reverse reaction
rate constant. Here, \(k_{1}\) and \(C_{O_{2}}\) are lumped into\({k_{1}}^{*}\) because the gas concentration was constant all the time
during the aging experiment. \(C_{\text{Ag}^{+}}\) can be calculated by
substracting the amount of I2 loaded on the aged
Ag0Z from the amount of I2 loaded on
the unaged Ag0Z. The model parameters of all reaction
models and correlation coefficients (R2) between
experimental data and model results are shown in Table 1. These results
indicate a model is fitted to experimental data well when \(n\geq 1\)with strong correlation coefficient (for example, R2 =
0.988 at 150 oC) using Eqn. 2, which means the Pseudo
1st reversible reaction model fits experimental data
(Figure 8 (A)). These results are consistent with experimental data
(Figure 7) that the aging effects of gas streams on
Ag0Z increase with increasing aging time and
temperatures.
\begin{equation}
{\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Ag}{\text{Ag}_{s}}^{+}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (13)\backslash n}{v=\frac{\text{dC}_{\text{Ag}}}{\text{dt}}={-k}_{1}C_{O_{2}}{C_{\text{Ag}}}^{n}+k_{-1}{C_{\text{Ag}^{+}}}^{n}}\nonumber \\
\end{equation}\begin{equation}
{k_{1}}^{*}=k_{1}C_{O_{2}}\nonumber \\
\end{equation}\begin{equation}
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ v=\frac{\text{dC}_{\text{Ag}}}{\text{dt}}={{-k}_{1}}^{*}C_{\text{Ag}}+{k_{-1}C}_{\text{Ag}^{+}}\ \ \ \ (for\ n=1)\nonumber \\
\end{equation}Modeling results on the aged Ag0Z in humid air with
different temperatures, aging time, and water vapor concentrations are
placed in Figure 8 (B) and (C). A reaction equation for the model is
provided in Eqn. (14). Considering the results of correlation
coefficient to each order model with the model results, when\(n\geq 1\), model results show good fitting to experimental data.\(C_{H_{2}O}\) and \(C_{O_{2}}\) are the concentrations of water vapor
and oxygen in humid air, \(k_{1}\) is the reaction rate constant,\(k_{-1}\) is the reverse reaction rate constant, and \(n\) is the
reaction order. Here, \(k_{1}\), \(C_{H_{2}O}\), and \(C_{O_{2}}\) are
lumped into \({k_{1}}^{*}\), and m is the power of the water vapor
concentration determined by a exponential curve expressed by\({k_{1}}^{*}\) versus \(C_{H_{2}O}\) as shown in Figure 9 (m = 0.20).
These modeling results indicate that the pseudo 1streversible reaction model fits experimental data (For example,
R2 = 0.985 at 150 oC) with similar
approach to the model result of dry air aged Ag0Z.
\begin{equation}
\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Ag}{\text{Ag}_{s}}^{+}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (14)\nonumber \\
\end{equation}\begin{equation}
v=\frac{\text{dC}_{\text{Ag}}}{\text{dt}}={{-k}_{1}}^{*}{C_{\text{Ag}}}^{n}+{{k_{-1}C}_{\text{Ag}^{+}}}^{n}\nonumber \\
\end{equation}\begin{equation}
{k_{1}}^{*}=k_{1}{C_{H_{2}O}}^{m}C_{O_{2}}\nonumber \\
\end{equation}\begin{equation}
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ v=\frac{\text{dC}_{\text{Ag}}}{\text{dt}}={{-k}_{1}}^{*}C_{\text{Ag}}+{k_{-1}C}_{\text{Ag}^{+}}\ \ \ \ (for\ n=1)\nonumber \\
\end{equation}