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\begin{document}

\title{Methyl Iodide Adsorption on Reduced Silver-Functionalized Silica
Aerogel: How Temperature Impacts the Adsorption?}



\author[1]{Siqi Tang}%
\author[1]{Seungrag Choi}%
\author[1]{Lawrence Tavlarides}%
\affil[1]{Syracuse University}%


\vspace{-1em}



  
  \date{June 14, 2024}


\begingroup
\let\center\flushleft
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\maketitle
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\selectlanguage{english}
\begin{abstract}
To understand the effect of temperature to the adsorption, 104 ppbv and
1044 ppbv methyl iodide (CH\textsubscript{3}I) adsorptions on reduced
silver-functionalized silica aerogel (Ag\textsuperscript{0}-Aerogel) at
100, 150 and 200  were performed. In the experiments, a significantly
high uptake rate (3 -- 4 times higher than that at 100 and 150 ) was
observed for the 104 ppbv adsorption at 200 . To explain such behavior,
a potential reaction pathway was proposed and multiple physical analyses
including nitrogen titration, x-ray photoelectron spectroscopy (XPS) and
scanning electron microscopy (SEM) were performed. Based on the results,
the contributing factors appear to be the formation of different Ag-I
components induced by temperature, higher silver site availability,
decreasing diffusion limitation, and increasing reaction rate described
by the Arrhenius relationship.%
\end{abstract}%



\sloppy


Methyl Iodide Adsorption on Reduced Silver- Functionalized Silica
Aerogel: How Temperature Impacts the Adsorption?

Siqi Tang, Seungrag Choi, and Lawrence L. Tavlarides\textsuperscript{*}

Department of Biomedical and Chemical Engineering, Syracuse University,
329 Link Hall, Syracuse, NY 13244, USA

\subsection*{Abstract}

{\label{abstract}}

To understand the effect of temperature to the adsorption, 104 ppbv and
1044 ppbv methyl iodide (CH\textsubscript{3}I) adsorptions on reduced
silver-functionalized silica aerogel (Ag\textsuperscript{0}-Aerogel) at
100, 150 and 200  were performed. In the experiments, a significantly
high uptake rate (3 -- 4 times higher than that at 100 and 150 ) was
observed for the 104 ppbv adsorption at 200 . To explain such behavior,
a potential reaction pathway was proposed and multiple physical analyses
including nitrogen titration, x-ray photoelectron spectroscopy (XPS) and
scanning electron microscopy (SEM) were performed. Based on the results,
the contributing factors appear to be the formation of different Ag-I
components induced by temperature, higher silver site availability,
decreasing diffusion limitation, and increasing reaction rate described
by the Arrhenius relationship.

\textbf{Topical Heading:} Separations: Materials, Devices and Processes

\textbf{Keywords:} Adsorption, Iodine Removal, Separation, Silver
Aerogel

\subsection*{Introduction}

{\label{introduction}}

Since 1951, when the first nuclear power plant was built in Idaho, the
nuclear waste treatment arose as a crucial difficulty and environmental
concern.\textsuperscript{1} During the nuclear fission and the
successive aqueous reprocessing of the radioactive
waste,\textsuperscript{129}I was released in both organic and inorganic
forms to off-gas streams, along with
\textsuperscript{85}Kr,\textsuperscript{14}C, \textsuperscript{3}H
etc.\textsuperscript{2-4}According to Jubin and
Strachan\textsuperscript{4}, the radioactive iodine (both inorganic and
organic forms) mainly exists in dissolve off-gas (DOG) and vessel
off-gas (VOG), which contain 5-10 ppmv and 20-30 ppbv respectively.
Unlike I\textsubscript{2}, it is more difficult to study the organic
iodides because of their additional alkyl groups and the low
concentrations. Multiple forms of organic iodides (from
CH\textsubscript{3}I to C\textsubscript{12}H\textsubscript{25}I) were
observed, and among these organic iodides, CH\textsubscript{3}I and
C\textsubscript{12}H\textsubscript{25}I were reported to be the two most
abundant ones.\textsuperscript{5-10}

To remove the radioactive iodine, multiple adsorbents were developed and
studied including reduced silver-containing materials such as silver
functionalized silica aerogel
(Ag\textsuperscript{0}-Aerogel)\textsuperscript{11}, hydrogen reduced
silver exchanged mordenite
(Ag\textsuperscript{0}Z)\textsuperscript{12,13}, silver nitrate
impregnated alumina (AgA)\textsuperscript{14}; bismuth-containing
materials such as
Bi-Bi\textsubscript{2}O\textsubscript{3}-TiO\textsubscript{2}-C\textsuperscript{15},
bismuth-decorated electrospinning carbon nanofiber\textsuperscript{16};
and other organic materials such as graphene
aerogel\textsuperscript{17}, nitrogen-rich covalent organic framework
(SCU-COF)\textsuperscript{18} and metal organic frameworks
(MOF)\textsuperscript{19}. Among these materials, the silver-containing
ones are the most matured and commonly used. To provide references and
information for the design and future industrial application of
Ag\textsuperscript{0}-Aerogel, the adsorption experiments of 104 ppbv
and 1044 ppbv CH\textsubscript{3}I on Ag\textsuperscript{0}-Aerogel at
100, 150 and 200  were conducted. During the experiments, an abnormally
high uptake rate was observed for 104 ppbv CH\textsubscript{3}I
adsorption at 200 , and multiple physical analyses including nitrogen
titration, scanning electron microscopy (SEM) and x-ray photoelectron
spectroscopy (XPS) were performed. Based on the data collected and
theoretical analyses, the factors impacting the uptake rate appear to
be, unusual reactions and products, difference in silver site
availability, change of diffusion limitation and impact of temperature
to reaction rate described by the Arrhenius relationship.

\subsection*{Method}

{\label{method}}

\subsubsection*{Continuous Flow Adsorption
System}

{\label{continuous-flow-adsorption-system}}

The organic iodide adsorption experiments were performed using a
continuous flow adsorption system. The system includes the
Dynacalibrator (VICI, Model 450 and 500), adsorption column, furnace,
microbalance and the corresponding data acquisition system.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

Figure 1. Schematic diagram of the continuous flow adsorption system.

As Figure 1 shows, a permeation tube containing CH\textsubscript{3}I was
placed in the Dynacalibrator, which air (Airgas Inc. Air, Ultra Zero)
flowed through as the carrier gas. The mixture then passed through the
pre-heating coil around the adsorption tube (inner diameter = 30mm) and
reached the adsorbent placed in the tray. During the adsorption process,
the mass change was measured by the microbalance and the data were
recorded by the computer.

Additionally, to prevent the counterweight from being oxidized, the
continuously flowing nitrogen (Airgas Inc. Nitrogen, Ultra High Purity)
was used as the protective gas. The temperature of the adsorption system
was controlled by the temperature controller and the connected furnace;
the flow rate of the adsorbate mixture was controlled by the mass flow
controller.

\subsubsection*{Silver Functionalized Silica
Aerogel}

{\label{silver-functionalized-silica-aerogel}}

In this presented work, silver functionalized silica aerogel
(Ag\textsuperscript{0}-Aerogel) was selected to be the adsorbent for its
high silver concentration and high aging
resistance.\textsuperscript{20}The shape and size of
Ag\textsuperscript{0}-Aerogel is relatively uneven and the average
density and diameter of the material is 0.58 g/cm\textsuperscript{3} and
0.2 cm, respectively. The iodine adsorption capacity was measured
experimentally to be approximately 37-38 wt\%.

The compositions of the as-received Ag\textsuperscript{0}-Aerogel
measured by SEM-EDX and XPS are listed in Table 1.\selectlanguage{english}
\begin{longtable}[]{@{}llllll@{}}
\toprule
& C (wt\%) & O (wt\%) & Si (wt\%) & S (wt\%) & Ag (wt\%)\tabularnewline
\midrule
\endhead
SEM-EDX & 12.0 & 32.5 & 18.3 & 5.7 & 31.5\tabularnewline
XPS & 11.2 & 15.4 & 34.5 & 5.2 & 33.7\tabularnewline
\bottomrule
\end{longtable}

Table 1. Chemical composition of the Ag\textsuperscript{0}-Aerogel
determined by SEM-EDX and XPS.

The results in the first row were measured by Backscattered electron
composition (BEC) mode of scanning electron microscopy (SEM, JEOL JSM
IT100LA) with energy dispersive x-ray analysis (EDX). During the
analysis, unlike reduced silver exchanged mordenite\textsuperscript{13},
no obvious silver cluster in micrometer scale was observed on the pellet
surface. The second row provides the composition measured by x-ray
photoelectron spectroscopy (XPS, Scienta Omicron ESCA-2SR).

The reactions between Ag and organic iodides were proposed by Scheele et
al.\textsuperscript{21}; using CH\textsubscript{3}I as an example, the
reaction is,\(\mathrm{2Ag\ +\ 2C}\mathrm{H}_{\mathrm{3}}\mathrm{I(g)\ \leftrightarrow\ 2AgI\ +\ }\mathrm{C}_{\mathrm{2}}\mathrm{H}_{\mathrm{6}}\mathrm{(g)}\). In this reaction, iodine binds with
silver and the organic groups are released to the off-stream in gas
form, which was also suggested by Zhou et al.\textsuperscript{22}

\subsubsection*{Procedure Description}

{\label{procedure-description}}

Using the continuous flow adsorption system, the mass changes of
Ag\textsuperscript{0}-Aerogel were recorded and the kinetic adsorption
curves can be generated. In this presented work, the adsorption
experiments of 104 ppbv and 1044 ppbv of CH\textsubscript{3}I at 100,
150 and 200  were performed. Since reaching equilibrium is not
realistic at ppbv level concentrations, the experiments were stopped at
approximately 300 hours.\textsuperscript{23} To satisfy the superficial
velocity of 1.1 m/min,\textsuperscript{24} the flow rate of the gas
through the adsorption column was set at 500 sccm (standard cubic
centimeter per minute) for all experiments. Additionally, to prevent the
concentration difference between the pellets, a single layer of
Ag\textsuperscript{0}-Aerogel (0.1-0.2 g) was carefully placed in the
tray.

Before the start of the organic iodide adsorption, the pellets were
air-dried at the same temperature as that of the adsorption experiment
until the mass change in the past 24 hours is lower than 0.005 wt\%
(approximately 1/5 of the adsorption rate of 104 ppbv
CH\textsubscript{3}I at 150 ). Especially, at 200, the drying process
induced the loss of organic moiety of up to 9 -10 wt\%, which a similar
observation was reported in Maty\selectlanguage{ngerman}á\selectlanguage{polish}š \selectlanguage{english}and Engler's thermogravimetric
analysis (TGA).\textsuperscript{25}

Therefore, to determine the effect of organic moiety loss, the
comparison experiments were performed at 104
ppbv-CH\textsubscript{3}I-150 and 1044 ppbv-CH\textsubscript{3}I-150 
using the Ag\textsuperscript{0}-Aerogel with and without the organic
moiety loss. The results showed no significant difference in the uptake
curves (in wt\%). To further accelerate the drying process (which
usually takes weeks) and removing the organic moiety for all
experiments, the pellets were vacuum dried overnight at 350  using the
degas function of Surface Area and Porosity Analyzer (Micromeritics,
ASAP 2020) and stored in N\textsubscript{2} after the treatment.
Similarly, after degassing, the adsorption curves (in wt\%) and the
maximum iodine capacities (approximately 37 -- 38 wt\%, measured by 50
ppmv I\textsubscript{2} adsorption at 150 ) are similar to the
untreated adsorbent. It is important to notice that during the 350 
treatment, the organic moiety loss results in approximately 10 \% loss
of pellet mass. Therefore, the similar uptake rate by pellet mass
indicates an approximately 10\% loss of uptake rate by silver mass.
However, this loss could be considered as a `worthy cost' due to the
successive significant increase of the organic iodide uptake rate at 200
, which will be discussed in the following sections.

\subsection*{Results and Discussion}

{\label{results-and-discussion}}

\subsubsection*{Adsorption Kinetics}

{\label{adsorption-kinetics}}

The 104 ppbv and 1044 ppbv CH\textsubscript{3}I adsorptions on
Ag\textsuperscript{0}-Aerogel at 100, 150 and 200  were performed using
the continuous flow adsorption system. For consistency purposes, pellets
used for all trials were vacuum dried at 350  before the adsorption.
After the pre-dry process, the pellets were moved to the adsorption
system and the final water equilibrium process was performed before
starting the adsorption. Once the mass change of the pellets in the past
24h was less than 0.005 wt\%, the CH\textsubscript{3}I adsorption was
started. During the CH\textsubscript{3}I adsorption, no significant mass
gain/loss was observed neither in the initial part (first 1-2 days) nor
after the adsorption ended and the desorption started, which indicating
the physisorption of CH\textsubscript{3}I on
Ag\textsuperscript{0}-Aerogel is relatively minor.

The kinetic curves are shown in Figure 2, at 100 and 150 , the tendency
agrees well with the previous studies of I\textsubscript{2} adsorption
on Ag\textsuperscript{0}Z\textsuperscript{24}, that the adsorption rates
increase slightly as the temperature increases. However, at 200 , the
uptake rate increases significantly (3 -- 4 times higher) at 104 ppbv,
and the curvature of the curve decreases at 1044 ppbv. To analyze such
abnormal behaviors, the shrinking core model (SCM) was applied.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

Figure 2. The adsorption curves of 104 ppbv (a) and 1044 ppbv (b) at
100, 150 and 200 .

The SCM (Eq. 1) consists of three terms, the gas film diffusion term
(Eq. 2), the pore diffusion term (Eq. 3) and the reaction term (Eq.
4).\textsuperscript{26}

\emph{q} is the average sorbate concentration (mol/g) at time
\emph{t}(s) and \emph{q\textsubscript{e}} is the equilibrium sorbate
concentration (mol/g), \selectlanguage{greek}\emph{τ\textsubscript{1}}\selectlanguage{english}
,\selectlanguage{greek}\emph{τ\textsubscript{2}}\selectlanguage{english} , and \selectlanguage{greek}\emph{τ\textsubscript{3}}\selectlanguage{english} are gas film
diffusion term, pore diffusion term, and reaction term
respectively,\emph{R\textsubscript{a}} is the radius of the pellet
(cm),\selectlanguage{greek}\emph{ρ\textsubscript{p}}\selectlanguage{english} is the density of the pellet
(g/cm\textsuperscript{3}), \emph{C\textsubscript{b}} is the bulk
adsorbate concentration
(mol/cm\textsuperscript{3}),\emph{k\textsubscript{f}} is the gas film
mass transfer coefficient (cm/s), \emph{D\textsubscript{p}} is the pore
diffusivity (cm\textsuperscript{2}/s), \emph{k\textsubscript{s}} is the
reaction rate constant (cm/s) and \emph{b} is the stoichiometric
coefficient of Ag in Ag-CH\textsubscript{3}I reaction, which is 1.
Additionally,\emph{q} and \emph{q\textsubscript{e}} are sometimes
represented in wt\% for convenience.

The \emph{k\textsubscript{f}} in Eq. 2 can be approximated theoretically
using Eq. 5-8.\textsuperscript{24}

\emph{Sh} , \emph{Sc} , and \emph{Re} are Sherwood number, Schmidt
number, and Reynolds number respectively, \emph{D\textsubscript{AB}} is
the binary diffusivity (cm\textsuperscript{2}/s), \emph{T} is the
temperature (K), \emph{P} is the pressure (bar), \emph{M} is the
molecular mass of CH\textsubscript{3}I (A) and air (B). \selectlanguage{greek}\emph{ν} \selectlanguage{english}is the
atomic diffusion volume (cm\textsuperscript{3}), which = 52.63
cm\textsuperscript{3} and = 19.7
cm\textsuperscript{3}.\textsuperscript{27}

The \emph{AARD} 's (absolute average relative deviation) were determined
using Eq. 9,

where \emph{N} is the number of data points and \emph{exp, model} denote
the experiment results and model fitting results.

The parameters and results determined using the SCM are listed in Table
2. At 104 ppbv, the \emph{D\textsubscript{p}} 's were not determined
since no significant pore diffusion processes were observed during the
experiments.\selectlanguage{english}
\begin{longtable}[]{@{}llllll@{}}
\toprule
Concentration (ppbv) & Temperature () & \emph{k\textsubscript{f}}
(cm/s) & \emph{D\textsubscript{p}} (cm\textsuperscript{2}/s) &
\emph{k\textsubscript{s}} (cm/s) & \emph{AARD} (\%)\tabularnewline
\midrule
\endhead
104 & 100 & 2.18* & N.D** & 0.17 & 0.05\%\tabularnewline
& 150 & 2.71* & N.D** & 0.24 & 3.97\%\tabularnewline
& 200 & 3.29* & N.D** & 0.67 & 3.40\%\tabularnewline
1044 & 100 & 2.18* & 3.41\selectlanguage{ngerman}×10\textsuperscript{-4} & 0.30 &
0.03\%\tabularnewline
& 150 & 2.71* & 6.58\selectlanguage{ngerman}×10\textsuperscript{-4} & 0.43 &
0.84\%\tabularnewline
& 200 & 3.29* & 5.70\selectlanguage{ngerman}×10\textsuperscript{-3} & 0.29 &
0.77\%\tabularnewline
Calculated theoretically using Eq. 5-8. & *Calculated theoretically
using Eq. 5-8. & *Calculated theoretically using Eq. 5-8. & *Calculated
theoretically using Eq. 5-8. & &\tabularnewline
*Not determined. & & & & &\tabularnewline
\bottomrule
\end{longtable}

Table 2. Parameters and results of the SCM.

It can be visualized that, at 200 , certain abnormal behaviors exist
for both 104 and 1044 ppbv CH\textsubscript{3}I adsorption. To explain
such observation, the nitrogen titration, XPS and SEM-EDX analyses were
performed and a potential reaction pathway was proposed.

\subsubsection*{Water Equilibrium in Drying
Process}

{\label{water-equilibrium-in-drying-process}}

Because of multiple factors including the pellet size of
Ag\textsuperscript{0}-Aerogel, the internal structure of
Ag\textsuperscript{0}-Aerogel, etc., the water concentration in the
pellets after 350  vacuum drying may not be constant. Therefore, a
final drying is still required before the CH\textsubscript{3}I
adsorption and the pellets may adsorb or desorb water in different
trials. The water adsorbed was from the trace amount of moisture
contained in the carrier gas (Airgas Inc. Air, Ultra Zero). According to
the manufacturer, the air contains approximately 2 ppmv of water and the
value was also validated by experimental measurement using a dewpoint
meter. By selecting a water adsorption curve with the highest uptake
(therefore the initial water concentration in the pellet can be assumed
to be zero) , the water adsorption process can be modeled using multiple
models including the 1-D spherical Fick's Law\textsuperscript{26} (Eq.
10), differential form of the diffusion term of the shrinking core model
(SCM)\textsuperscript{26} (Eq. 11), and the micropore term of the pore
diffusion model (Micro PD)\textsuperscript{13} (Eq. 12). For Fick's law
and the shrinking core model, it is assumed that an equilibrium is
established on the surface immediately.

\emph{q(r,t)} is the sorbate concentration (mol/cm\textsuperscript{3})
at radius \emph{r} (cm) at time \emph{t} (s), and the average sorbate
concentration \emph{q(t)} can be calculated using . \emph{D} is the pore
diffusivity (cm\textsuperscript{2}/s), \emph{r} is the radius at
time\emph{t} , \emph{V} is the volume of the pellet
(cm),\emph{D\textsubscript{i}} is the micropore diffusivity
(cm\textsuperscript{2}/s) and \emph{R\textsubscript{i}} is the radius of
the micropore (cm). \emph{R\textsubscript{i}} was measured by the
nitrogen adsorption method using ASAP 2020 and the value is
approximately 6.6 .\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image18/image18}

\end{center}
\end{figure}

\par\null

Figure 3. The adsorption curve and the modeling results of the water
adsorption process. (Fick's Law and Micro PD are overlapped)

The adsorption curve and the modeling results are shown in Figure 3. The
diffusivities determine using Fick's Law, SCM and Micro PD are
9.6\selectlanguage{ngerman}×10\textsuperscript{-9} cm\textsuperscript{2}/s,
2.6×10\textsuperscript{-8} cm\textsuperscript{2}/s and
4.4×10\textsuperscript{-21} cm\textsuperscript{2}/s respectively. By
comparing with multiple literature works\textsuperscript{28,29}, the
values of the diffusivities clearly fit in the range of micropore
diffusion, indicating that the water adsorption/desorption in
Ag\textsuperscript{0}-Aerogel is a micropore diffusion process.

\subsubsection*{Nitrogen Adsorption
Analyses}

{\label{nitrogen-adsorption-analyses}}

Since the carrier gas contains approximately 2 ppmv of water, the
Ag\textsuperscript{0}-Aerogel tends to reach moisture equilibrium with
the ambient air during the adsorption of CH\textsubscript{3}I. The
moisture levels in the pellet at 100, 150, 200\selectlanguage{english} were measured using the
pre-dried pellet and the continuous flow adsorption system. The
pre-dried (350 \selectlanguage{english} degassed) pellets were placed into the adsorption
system with identical settings except flowing pure air instead of
air/CH\textsubscript{3}I mixture. The temperature of the adsorption
column was firstly set at 200 \selectlanguage{english}, and the pellets started to adsorb water
from the ambient air, with the mass change collected continuously. Once
the mass change in the past 24h was less than 0.005 wt\%, the
temperature was decreased to 150 \selectlanguage{english} and further down to 100 \selectlanguage{english} when the
same criterion was met. The time to settle a new equilibrium was 100 --
150 hours.

The results indicated that the differences in water concentration
between each temperature were approximately 0.15 -- 0.2 wt\%. In other
words, if the water concentration in the pellets at 200 \selectlanguage{english} was set as the
zero point, the water adsorbed at 150 and 100 \selectlanguage{english} were approximately 0.2
and 0.4 wt\%. To examine such observation, the water desorption
experiment in the reverse temperature order was also performed and the
differences between each level were comparable.

In order to determine the effect of different concentrations of moisture
in the pellets at various temperatures, the nitrogen adsorption analyses
were performed using the Surface Area and Porosity Analyzer
(Micromeritics, ASAP 2020). Traditionally, the samples used for nitrogen
adsorption analysis were fully dried to prevent any residual water to
influence the results. Since the standard drying conditions for
Ag\textsuperscript{0}-Aerogel were not reported, the fully dried result
was the one with the highest pore volume and surface area, selected from
multiple 350 \selectlanguage{english} degassed trials.

Instead, to determine the surface area and pore volume at real
adsorption temperatures, the Ag\textsuperscript{0}-Aerogel was air dried
using the adsorption column at the target temperatures (100, 150 and 200
\selectlanguage{english}) with the same criterion described above. Once the drying process was
completed, the pellets were transferred to ASAP 2020 as quickly as
possible (2-3 min). To minimize the potential water gain/loss during the
analyses, multiple methods were applied including, minimize the time of
transferring sample, measure the free volume of the test tube in advance
(therefore, exposing the dried sample under vacuum at room temperature
could be avoided), submerge the sample in liquid nitrogen immediately,
only start the vacuum pump after the sample was submerged, and minimize
the analysis time by selecting the minimal amount of sample points. Once
the analysis was completed, the sample was transferred back to the
adsorption column to measure the mass change during the porosity
analysis. Since no significant mass changes were observed, the water
gain/loss during the analysis appears to be minor.

As a reference of the highest level of water that could be contained in
the pellet during actual industrial usage, the nitrogen adsorption
experiment without any sample pretreatment was also performed using
normally stored Ag\textsuperscript{0}-Aerogel (named as Room Condition
Equilibrium in Figure 4, short as RC.EQ). The storage conditions
measured by laboratory thermometer and hydrometer are, 20 -- 23 \selectlanguage{english} and 20
-- 30\% humidity.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image19/image19}

\end{center}
\end{figure}

Figure 4. The surface area and pore volume of micropores, macropores and
total pores measured using nitrogen titration method at different drying
conditions.

The micro, macro and total pore surface area and volume are plotted in
Figure 4. The total pore surface area of the 350  degassed sample is
297.6 m\textsuperscript{2}/g and the total pore volume is 0.34
cm\textsuperscript{3}/g, which are comparable with the trends of surface
area and pore volume to silver composition in silica aerogel reported by
Balkis Ameen et al.\textsuperscript{30} Additionally, the plot shows
that as the temperature decreases and the in-pellet water concentration
increases, both pore surface area and pore volume decrease. As the
temperature decreases to 100 , the micropores are significantly blocked
by water and become fully blocked at room condition equilibrium.

Moreover, the diffusion of CH\textsubscript{3}I and related gas form
products in Ag\textsuperscript{0}-Aerogel may also be impacted by the
porosity change. The porosity (\selectlanguage{greek}\emph{ε} \selectlanguage{english}= total pore volume / density)
of the pellet is larger at higher temperature, and an experimental
relationship between pore diffusivity and porosity is given
as,\textsuperscript{31}

where \emph{m} is usually between 2 -- 4.5 depending on the material.
This relationship indicates that the pore diffusivity of both
CH\textsubscript{3}I and gas form products may increase with increasing
temperature, and therefore decreasing the diffusion limitations and
accelerating the adsorption process.

\subsubsection*{Pore Distribution and Silver Sites
Availability}

{\label{pore-distribution-and-silver-sites-availability}}

Shown in Figure 4, the drying temperature impacts the pore surface area
and the pore volume of the pellets by changing the water concentration
in the pellet. When temperature decreases to below 100 , the micropores
are significantly impacted. This can be further visualized by comparing
the pore distribution plots of the Barrett-Joyner-Halenda (BJH)
desorption method and the density function theory (DFT) of 350 
degassed and room condition equilibrium samples.

The pore distribution plots (Figure 5) show that the
Ag\textsuperscript{0}-Aerogel mostly consists of mesopores (20-500 )
and micropores (\textless{}20 ) with a limited amount of macropores
(\textgreater{} 500 ), which agree with the SEM images that no
significant structure was observed in the micrometer scale. Comparing
the two curves in Figure 5. b, two sharp peaks at approximately 6 and 12
 were observed only in the fully dried sample, whereas the room
condition equilibrium one only contained a small peak at 15-17 . A
similar trend is also revealed in Figure 5. a: the 350  degassed sample
contains a `tail' at 20-25 .

Such observation further supports that the micropores (\textless{} 2 nm)
are mostly blocked as the in-pellet water concentration increases
(Discussed in Nitrogen Adsorption Analyses ) and the water
adsorption/desorption process in Ag\textsuperscript{0}-Aerogel is a
micropore diffusion process (Discussed in Water Equilibrium in Drying
Process ).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image21/image21}

\end{center}
\end{figure}

Figure 5. The BJH (a) and DFT (b) pore distribution plots of 350 
degassed sample and room condition equilibrium (RC.EQ).

Since both pore surface area, pore volume and the amount of micropores
decrease as the adsorption temperature decreases, the availability of
silver sites may decrease due to the increasing water coverage.

\subsubsection*{Potential Reaction Pathway and Diffusion
Limitation}

{\label{potential-reaction-pathway-and-diffusion-limitation}}

For the chemisorption with gas phase product generated, Zhou and
White\textsuperscript{32} and Robb and
Harriott\textsuperscript{33}suggested that the formation of gases and
the successive diffusion limitations may result in a fractional order
reaction, which has been observed in the CH\textsubscript{3}I adsorption
on Ag\textsuperscript{0}-Aerogel by Tang et al.\textsuperscript{23} To
explain this observation, a potential reaction pathway is proposed.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image22/image22}

\end{center}
\end{figure}

Figure 6. The proposed reaction pathway between CH\textsubscript{3}I and
Ag in Ag\textsuperscript{0}-Aerogel.

In the shrinking core model, the reactions only happen on the reacting
surface, which separates the reacted layer and the unreacted core. Once
the Ag sites on one surface are fully consumed, the reactions proceed to
the next surface. As Figure 6 shown, during the adsorption,
CH\textsubscript{3}I first diffuses through the reacted layer and
reaches the reacting surface (0). On the reacting surface,
CH\textsubscript{3}I breaks reversibly into two free radicals (1),
CH\textsubscript{3}\textsuperscript{*} and I\textsuperscript{*}. Two
CH\textsubscript{3}\textsuperscript{*} radicals bind with each other and
form C\textsubscript{2}H\textsubscript{6} (2);
I\textsuperscript{*}radical binds with Ag and forms AgI (3); and
C\textsubscript{2}H\textsubscript{6} diffuses out through the reacted
layer (4). In this process, to satisfy the observed 1.4 reaction order
by Tang et al.\textsuperscript{23}, the reaction order of
CH\textsubscript{3}I is assumed to be \emph{n} ; the orders of other
reactions are 1 to each component; and the reason will be discussed in
the following contents.

The formation/consumption rates of the components can be written as,

\par\null\par\null

where \emph{k} 's are the reaction rate
constant,\emph{D\textsuperscript{*}} is the diffusivity of
C\textsubscript{2}H\textsubscript{6}, and \emph{L} is the thickness of
the reacted layer. The stoichiometric coeffecient of
C\textsubscript{2}H\textsubscript{6} is ignored in the equations since
it does not impact the results.

Assuming pseudo-equilibrium, the steady state is established immediately
after the reactions proceed to the next surface,
CH\textsubscript{3}\textsuperscript{*}, I\textsuperscript{*} and
C\textsubscript{2}H\textsubscript{6} may not accumulate on the reacting
surface and the rates, , , and should be 0. Therefore, the and in Eq. 14
can be rewritten in term of constants and (the detailed procedure can be
found in the Supplementary Materials ) which is,

where \selectlanguage{greek}\emph{Φ} \selectlanguage{english}is similar to the Thiele modulus, the ratio of the
reaction rate to the diffusion rate.\textsuperscript{34}

As more than five parameters are included, determining the step-wise
would be impracticable. Considering two limiting cases, when , the
reaction rate would be proportional to; if , would be proportional to.
Since the reaction order would be between \emph{n/} 2 and \emph{n} , the
integer that satisfies the observed 1.4 order is \emph{n} = 2.

Additionally, Eq. 18 indicates that the temperature change may impact
the reaction rate. Generally, the relationship between \emph{k}
(or\emph{D} ) and \emph{T} can be written as Eq. 20,

which implies that the temperature change may impact the overall
reaction rate by changing the magnitude of .

\subsubsection*{Arrhenius Relationship and Eyring
Equation}

{\label{arrhenius-relationship-and-eyring-equation}}

The well-known Arrhenius relationship is commonly used in describing the
temperature dependence of reaction rate constant and diffusivity, which
is, \textsuperscript{35}

and the linear form is,

Where \emph{k\textsubscript{s}\textsuperscript{0}} is the
pre-exponential factor (unit same as \emph{k\textsubscript{s}}
),\selectlanguage{greek}\emph{ΔE}\selectlanguage{english} is the activation energy (kJ/mol) and \emph{R} is the gas
constant (kJ/mol/K). Reported by Tang et al.\textsuperscript{23}, the
CH\textsubscript{3}I adsorption on Ag\textsuperscript{0}-Aerogel may be
a 1.4 order shrinking core process, where the
calibrated\emph{k\textsubscript{s}\textsuperscript{*}}((cm/s)[?](mol/cm\textsuperscript{3})\textsuperscript{1-n})
can be represented as . Therefore, the Arrhenius equation was applied to
the calibrated \emph{k\textsubscript{s}\textsuperscript{*}} and the plot
including the fitting results are shown in Figure 7.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image45/image45}

\end{center}
\end{figure}

Figure 7. The Arrhenius plot of 104 and 1044 ppbv CH\textsubscript{3}I
adsorptions on Ag\textsuperscript{0}-Aerogel at 100, 150 and 200 .

By fitting all three data points at each concentration, the \selectlanguage{greek}\emph{ΔE}\selectlanguage{english} 's
are 21.0 and 1.34 kJ/mol for 104 and 1044 ppbv adsorptions respectively.
As stated above, both adsorption behaviors at 200  are relatively
abnormal. If excluding the 200  data and consider the 100 and 150 
results only, the \selectlanguage{greek}\emph{ΔE}\selectlanguage{english} 's of 104 and 1044 ppbv adsorptions are
well-agreed. The activation energy determined using 100 and 150 data of
104 ppbv adsorption is 10.4 kJ/mol, that of 1044 ppbv adsorption is 10.8
kJ/mol and the pre-exponential factors are 1.80\selectlanguage{ngerman}×10\textsuperscript{5}and
1.47×10\textsuperscript{5}(cm/s)\selectlanguage{english}[?](mol/cm\textsuperscript{3})\textsuperscript{1-n}
respectively. In previous studies of CH\textsubscript{3}I adsorption on
Ag-ZSM-5, Park et al.\textsuperscript{36} report the activation energy
of 2.57 kJ/mol and Scheele et al.\textsuperscript{21} proposed 20 -- 40
kJ/mol for CH\textsubscript{3}I adsorption on Ag\textsuperscript{0}Z.

Another model describing the relationship between temperature and
reaction rate constant is the Eyring equation,\textsuperscript{37}

where \emph{k} is the reaction rate
(s\textsuperscript{-1}),\emph{k\textsubscript{B}} is Boltzmann's
constant, \emph{h} is Planck's constant and \selectlanguage{greek}\emph{ΔG}\selectlanguage{english} is the Gibbs free
energy of activation. Since the unit and the physical meaning of
\emph{k} are different from\emph{k\textsubscript{s}} determined using
SCM, a quantified result may not be given. However, some valuable trends
and predictions can be interpreted. Representing the Gibbs free energy
of the activation of the reaction between iodoalkane and
Ag\textsuperscript{0}-Aerogel as\selectlanguage{greek}\emph{ΔG}\selectlanguage{english} , \emph{dk/dT} may be written
as,

Eq. 24 indicates that the dependency of \emph{k} to \emph{T} may vary
as\selectlanguage{greek}\emph{ΔG/R}\selectlanguage{english} changes. For example, given a range of
temperature\emph{T\textsubscript{1}} to \emph{T\textsubscript{3}} ,
Figure 8 shows that how -\selectlanguage{greek}\emph{ΔG/R}\selectlanguage{english} changes the dependency of \emph{k}
to \emph{T} . When -\selectlanguage{greek}\emph{ΔG/R}\selectlanguage{english} \textless{} \emph{T\textsubscript{1}} ,
\emph{dk/dT}\textgreater{} 0, indicating the increasing temperature
increases the reaction rate; when -\selectlanguage{greek}\emph{ΔG/R}\selectlanguage{english}
\textgreater{}\emph{T\textsubscript{3}} , \emph{dk/dT} \textless{} 0,
and the reaction rate may decrease with increasing temperature.
Interestingly, if\emph{T\textsubscript{1}} \textless{} -\selectlanguage{greek}\emph{ΔG/R}\selectlanguage{english}
\textless{}\emph{T\textsubscript{3}} , a minimum value of \emph{k} may
be observed at \emph{T} = -\selectlanguage{greek}\emph{ΔG/R}\selectlanguage{english} . Generally, the \selectlanguage{greek}\emph{ΔG}\selectlanguage{english} is
represented as a positive number, but can it be negative in some
circumstances?

Proposed in the section above, iodoalkane molecules may cleave into free
radicals and produce alkanes and AgI in the re-bindings of radicals. The
negative activation energies have been reported in some radicals-engaged
reactions.\textsuperscript{38,39} Therefore, in the adsorptions of
iodoalkanes with larger alkane groups (e.g.
C\textsubscript{6}H\textsubscript{13}I,
C\textsubscript{12}H\textsubscript{25}I, etc.), the \selectlanguage{greek}\emph{ΔG}\selectlanguage{english} 's may
decrease (or become negative) due to their
instabilities,\textsuperscript{40} and the rough estimation above
suggests that the dependency of \emph{k} to \emph{T} may vary at certain
circumstances.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image48/image48}

\end{center}
\end{figure}

Figure 8. An example of the Eyring equation, how \selectlanguage{greek}\emph{ΔG/R}\selectlanguage{english} changes the
dependency of \emph{k} to \emph{T}(curves have been rescaled and
repositioned to clarify the tendencies).

\subsubsection*{XPS and SEM-EDX Analyses}

{\label{xps-and-sem-edx-analyses}}

To determine the compounds formed during the adsorptions, XPS analyses
were performed using, fresh Ag\textsuperscript{0}-Aerogel, 350 
degassed Ag\textsuperscript{0}-Aerogel, CH\textsubscript{3}I fully
loaded (9585 ppbv, powdered adsorbent) Ag\textsuperscript{0}-Aerogel,
I\textsubscript{2} fully loaded (50 ppmv, powdered adsorbent)
Ag\textsuperscript{0}-Aerogel, 104 ppbv CH\textsubscript{3}I adsorbed
(partially loaded) Ag\textsuperscript{0}-Aerogel at 100, 150 and 200 ,
and 1044 ppbv CH\textsubscript{3}I adsorbed (partially loaded)
Ag\textsuperscript{0}-Aerogel at the same temperatures. Since the first
scan of the 104 ppbv/200  was questionable, a rescan was performed
using the identical sample and settings (marked as SC1 and SC2 in the
spectra).

The XPS analyses were performed using the Scienta Omicron ESCA-2SR at
Cornell University. The operating pressure is
1\selectlanguage{ngerman}×10\textsuperscript{-9}Torr, and the monochromatic Al K\selectlanguage{greek}α \selectlanguage{english}x-rays (1486.6
eV) were generated at 300W (15 kV; 20mA).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image49/image49}

\end{center}
\end{figure}

Figure 9. Regional scans of Ag (a), I (b) XPS spectra of 104 ppbv
CH\textsubscript{3}I adsorbed Ag\textsuperscript{0}-Aerogel and Ag (c),
I(d) of 1044 ppbv CH\textsubscript{3}I adsorbed
Ag\textsuperscript{0}-Aerogel, with fresh, 350  degassed,
CH\textsubscript{3}I fully loaded at 150  and I\textsubscript{2} fully
loaded Ag\textsuperscript{0}-Aerogel at 150  as references.

The XPS spectra collected are shown in Figure 9. The fresh
Ag\textsuperscript{0}-Aerogel obtains the Ag3d\textsubscript{5/2} peak
located at approximately 368.6 eV and the Ag3d\textsubscript{3/2} peak
at approximately 374.6 eV, which are comparable to the binding energy
(BE) reported by Maty\selectlanguage{ngerman}á\selectlanguage{polish}š \selectlanguage{english}et al.\textsuperscript{20} After being degassed
at 350 , the Ag BE decreases to 368.1 and 374.1 eV, indicating that
certain amount of Ag\textsubscript{2}S nanoparticles may be generated in
this process.\textsuperscript{41,42} After reacting with
CH\textsubscript{3}I at different concentrations and temperatures, most
of the Ag peaks shift to approximately 368.2 and 374.2 eV except those
of the pellets at 104 ppbv/ 200  condition. The trend of iodine BE is
slightly different from that of Ag, CH\textsubscript{3}I fully loaded
sample contains the I3d\textsubscript{5/2} and
I3d\textsubscript{3/2}peaks at approximately 619.6 and 631.1 eV
respectively, I\textsubscript{2} fully loaded sample contains
I3d\textsubscript{5/2}and I3d\textsubscript{3/2} peaks at approximately
619.3 and 630.8 eV, and the peaks of remaining CH\textsubscript{3}I
reacted samples located in between the values above except the 104 ppbv/
200  case.

However, the spectra of the 104 ppbv/200  CH\textsubscript{3}I adsorbed
Ag\textsuperscript{0}-Aerogel are significantly different. Both
Ag3d\textsubscript{5/2} and Ag3d\textsubscript{3/2} split to at least
two peaks, locating at approximately 366.6, 369.5, 372.6 and 375.5 eV
and I3d\textsubscript{5/2} and I3d\textsubscript{3/2} at 618.1, 620.9,
629.6 and 632.4 eV. The variations of the Ag and I spectra at 104 ppbv/
200  condition indicate the Ag-I compounds formed may be different.

The SEM-EDX analyses were also conducted to measure the element
compositions and potential structure changes on the pellet surface. The
SEM-EDX analyses were performed using JEOL JSM IT100LA at SUNY College
of Environmental Science and Forestry (SUNY-ESF). The acceleration
voltage was 10-15 kV and the probe current is 20-30 mA for secondary
electron detector (SED) mode and 55-65 mA for backscattered electron
composition (BEC) mode.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image50/image50}

\end{center}
\end{figure}

Figure 10. The SEM images including SED, BEC, Ag mapping and I mapping
of (a) fresh, (b) 104 ppbv/150  CH\textsubscript{3}I partially loaded,
(c) 1044 ppbv/150  CH\textsubscript{3}I partially loaded, (d) 9585
ppbv/150  CH\textsubscript{3}I fully loaded and (e) 50 ppmv /150 
I\textsubscript{2} fully loaded Ag\textsuperscript{0}-Aerogel. (Full
resolution images are available in Supplementary Materials )

The SED and BEC (including the corresponding mappings of Ag and I)
images are shown in Figure 10. The images show that the fresh
Ag\textsuperscript{0}-Aerogel (a) does not contain any notable Ag
clusters in the micrometer scale on the surface. After reacting with 104
(b) and 1044 ppbv (c) CH\textsubscript{3}I (partially loaded), the
surfaces of the adsorbent become coarser, whereas the distributions of
Ag and I remain relatively uniform. As the concentration of the
adsorbate increases, certain surface structures were formed and some
bright spots can be observed in the SED image of the 9585 ppbv
CH\textsubscript{3}I fully loaded Ag\textsuperscript{0}-Aerogel(d).
These spots appear to be AgI clusters since the same spots were also
observed in the BEC image and the corresponding Ag and I mappings. The
change of surface structure is more significant for the 50 ppmv
I\textsubscript{2} fully loaded sample. A layer consisting of AgI in
polygon shape may be formed during the adsorption process.

\subsubsection*{Surface Composition}

{\label{surface-composition}}

Observed in the XPS results (Figure 9), the spectra of 104 ppbv/ 200 
CH\textsubscript{3}I adsorbed Ag\textsuperscript{0}-Aerogel are
significantly different from all others, which may further explain the
abnormal high uptake rate. Figure 11 is the Ag(a) and I(b) regional
scans of the 104 ppbv/200  CH\textsubscript{3}I adsorbed pellets with
the spectra of CH\textsubscript{3}I fully loaded sample as references.
Both Ag and I spectra of 104 ppbv/ 200 sample consist of three groups
of peaks, which are marked as 1, 2 and 3 in the figure. For Ag spectrum,
3 Ag3d\textsubscript{5/2} peaks are located at 366.6, 368.2 and 369.45
eV, which the second group is well agreed with the peaks of
CH\textsubscript{3}I fully loaded sample. Similarly, the I spectrum also
contains 3 groups of peaks and the binding energies of the second group
are close to those of the fully loaded sample. The compositions of three
groups of peaks were also determined, and the results are, approximately
52-55\%, 15-20\% and 28-29\% for group 1, 2 and 3 respectively. Since
the compositions acquired in both fittings are relatively similar, the
additional peaks appear to be some form of Ag-I (not AgI, silver iodide)
compounds.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image51/image51}

\end{center}
\end{figure}

Figure 11. The regional scans of Ag(a), I(b) and the curve fits of the
104 ppbv/ 200  CH\textsubscript{3}I adsorbed
Ag\textsuperscript{0}-Aerogel.

Reported in multiple studies,\textsuperscript{43-47} the Ag BE tends to
decrease as the oxidation state increases. For example, the
Ag3d\textsubscript{5/2} BE of metallic Ag is approximately 368.1, and
this value decreases to 367.7-367.9 eV for Ag\textsuperscript{+} and
367.3-367.6 eV for Ag\textsuperscript{2+}. Admittedly, the instrument
deviations and data calibration standards may vary the BE measured, but
the trend indicates that a certain amount of Ag\textsuperscript{2+} may
be formed in 104 ppbv CH\textsubscript{3}I adsorption at 200 , whereas
the peak group 3 remains questionable.

The Ag and I concentrations can be interpreted from the XPS and SEM-EDX
spectra, where the results are listed in Table 3. To compare the iodine
concentrations between samples, the iodine compositions have been
calibrated as additional mass, which the summations of all other
elements are 100\%. It is important to noticed that the
Ag\textsuperscript{0}-Aerogel is a highly heterogeneous material; the Ag
coverage on the pellets is uneven, and the values measured by SEM-EDX
and XPS may vary based on the specific location scanned.

\textbf{Conditions}

\textbf{Temperature}

()

\textbf{SEM-EDX}

\textbf{SEM-EDX}

\textbf{SEM-EDX}

\textbf{SEM-EDX}

\textbf{XPS}

\textbf{XPS}

\textbf{XPS}

\textbf{XPS}

\textbf{Iodine Uptake}

(wt\%)

Ag (wt\%)

I (wt\%)

I:Ag\textsuperscript{(2)} (mol)

I:Ag\textsuperscript{(3)} (wt)

Ag (wt\%)

I (wt\%)

I:Ag\textsuperscript{(2)} (mol)

I:Ag\textsuperscript{(3)} (wt)

Fresh

31.5

33.7

350  Degas

34.0

30.2

CH\textsubscript{3}I F.L.\textsuperscript{(1)}

150

29.1

32.3

0.94

1.11

29.2

28.3

0.82

0.97

38.31

I\textsubscript{2} F.L. \textsuperscript{(1)}

150

--

--

--

--

26.9

27.1

0.86

1.01

37.24

104 ppb

100

39.0

0.9

0.02

0.02

27.7

1.8

0.05

0.06

0.29

150

38.5

1.2

0.03

0.03

28.0

2.5

0.08

0.09

0.42

200

41.9

2.6

0.05

0.06

28.7

5.8

0.17

0.20

1.15

1044 ppb

100

40.6

4.8

0.10

0.12

27.9

6.0

0.18

0.21

2.84

150

34.3

5.0

0.12

0.15

27.8

12.4

0.38

0.45

3.71

200

47.9

6.4

0.11

0.13

33.1

13.1

0.34

0.40

4.31

(1) Fully Loaded

(1) Fully Loaded

(2) Molar ratio of I and Ag

(2) Molar ratio of I and Ag

(3) Mass ratio of I and Ag

(3) Mass ratio of I and Ag

Table 3. The Ag and I concentrations measured by SEM-EDX and XPS (I
compositions have been calibrated as additional mass).

Both SEM-EDX and XPS are the surface analysis techniques whereas the
penetration depth of XPS is approximately 5-10 nm and that of SEM-EDX is
1-10 \selectlanguage{greek}μ\selectlanguage{english}m.\textsuperscript{48,49} Therefore, the higher iodine
compositions for partially loaded Ag\textsuperscript{0}-Aerogel observed
by XPS indicate the existence of a strong concentration gradient in the
pellet during the CH\textsubscript{3}I adsorption. Additionally, it can
also be visualized that the concentrations of I on the surface are much
higher than the experimental measured iodine uptakes (same as
CH\textsubscript{3}I uptake, assuming CH\textsubscript{3} group diffuse
out in C\textsubscript{2}H\textsubscript{6} form), which further
supports the existence of the surface reaction proposed by Tang et
al.\textsuperscript{23}

\subsection*{Conclusion and
Recommendation}

{\label{conclusion-and-recommendation}}

Traditionally, after the adsorption, Ag\textsuperscript{0}-Aerogel will
be consolidated by compressing at high temperature, and removing the
organic moieties at 350  before compressing benefits the consolidation
results (higher product density and lower
porosity).\textsuperscript{25}In this presented work, a novel
pre-treating method was applied. The Ag\textsuperscript{0}-Aerogel was
vacuum dried at 350  before the CH\textsubscript{3}I adsorption to
remove the organic moieties, and the uptake rate and maximum iodine
adsorption capacity remain similar to the untreated one. Therefore,
removing the organic moieties before the adsorption could be a
practicable alternative, and the potential iodine contamination during
the traditional organic moieties removing process could be avoided.

In the 104 and 1044 ppbv CH\textsubscript{3}I adsorptions on
Ag\textsuperscript{0}-Aerogel at 100, 150 and 200 , an abnormal
behavior was observed in 104 ppbv adsorption at 200 ; the uptake rate
was approximately 3 -- 4 times higher than those of 100 and 150 
adsorptions at the same concentration. The most intuitive explanation is
the well-known Arrhenius relationship, the increase of temperature
results in the increase of reaction rate and diffusivity.

Additionally, more potential explanations are proposed based on
successive experimental and theoretical analyses. The nitrogen
adsorption analyses were performed using the pellets at different drying
conditions, and the results indicated that the increasing temperature
decreases the water concentration in the pellet and therefore may
increase the silver sites availability and the pore diffusivities of
CH\textsubscript{3}I and the gas form product. The gas form product,
believed to be C\textsubscript{2}H\textsubscript{6}, is considered as a
`diffusion limitation' for the adsorption process in the proposed
reaction pathway, and the increase of its diffusivity may vary the
reaction rate in another perspective.

Moreover, the XPS and SEM-EDX analyses were also performed and the
results indicated that at 104 ppbv/ 200 condition, some additional Ag-I
compounds were generated. By comparing the binding energies of the peaks
with previous studies, we presumed that the additional Ag-I compounds
may contain a certain amount of Ag\textsuperscript{2+}. However,
identifying the peak group 3 in Figure 9 remains unsolved. To further
determine the composition formed in CH\textsubscript{3}I adsorption
process, performing additional physical analyses such as regional scans
of other elements in XPS, x-ray absorption spectroscopy (XAS) and Raman
spectroscopy is recommended.

In the presented work, we observed an unusually high uptake rate for 104
ppbv CH\textsubscript{3}I adsorption on Ag\textsuperscript{0}-Aerogel at
200 , and suggested multiple explanations for this behavior. Our
discoveries offer a new perspective in determining the optimum
temperature for CH\textsubscript{3}I adsorptions, whereas a commonly
used temperature is 150 . However, for the purpose of carefulness and
accuracy, we may not recommend 200  as the optimum adsorption
temperature until further evidence has been revealed.

\subsection*{Acknowledgement}

{\label{acknowledgement}}

This research was funded by the Nuclear Energy University Program of the
U.S. Department of Energy, Office of Nuclear Energy (Grant No.
DE-NE0008761). A portion of the presented work may be used in Siqi
Tang's Ph.D. thesis and the technical report submitted to DOE.

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{\label{literature-cited}}

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