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\begin{document}

\title{Photoisomerization of cis- to trans-cyclooctene: integration of a
micro-flow reactor \& separation by specific adsorption}



\author[1]{Elnaz Shahbazali}%
\author[2]{Emilie Billaud}%
\author[3]{Jan Meuldijk}%
\author[4]{Guy Bormans}%
\author[3]{Timothy Noel}%
\author[5]{Volker Hessel}%
\affil[1]{University of Technology Eindhoven Department of Chemical Engineering and Chemistry}%
\affil[2]{KU Leuven}%
\affil[3]{Eindhoven University of Technology}%
\affil[4]{Katholieke Universiteit Leuven}%
\affil[5]{The University of Adelaide}%


\vspace{-1em}



  
  \date{May 15, 2024}


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\selectlanguage{english}
\begin{abstract}
Liquid-phase adsorption has hardly been established in micro-flow,
although this constitutes an industrially vital method for product
separation. A micro-flow UV-photo isomerization process converts
cis-cyclooctene partly into trans-cyclooctene, leaving an isomeric
mixture. Trans-cyclooctene adsorption and thus separation was achieved
in a fixed-bed micro-flow reactor, packed with AgNO3/SiO2 powder, while
the cis-isomer stays in the flow. The closed-loop recycling-flow has
been presented as systemic approach to enrich the trans-cyclooctene from
its cis-isomer. In-flow adsorption in recycling-mode has hardly been
reported so that a full theoretical study has been conducted. This
insight is used to evaluate three process design options to reach an
optimum yield of trans-cyclooctene. These differ firstly in the
variation of the individual residence times in the reactor and
separator, the additional process option of refreshing the adsorption
column under use, and the periodicity of the recycle flow.%
\end{abstract}%



\sloppy


\section*{Introduction}

{\label{introduction}}

In cancer discovery research, radiolabeled monoclonal antibodies
directed against tumor-associated antigens have been developed as
promising vectors to visualize or to treat tumors, mostly owing to their
high affinity and specificity {[}1{]}, {[}2{]}. Since antibodies have a
long biological half-life, it takes a long time (in the order of days)
to clear the antibodies from plasma. The half-life of radionuclides that
are used to radiolabel antibodies should be sufficiently long
(\textgreater{}12h) to allow clearance of the radiolabeled antibody from
plasma prior to acquire high signal-to-noise ratio tumor PET images. The
use of long lived radionuclides (e.g.
\textsuperscript{64}Cu,\textsuperscript{124}I, \textsuperscript{89}Zr)
will however result in prolonged exposure to radiation and a high
absorbed radiation dose. Fluorine-18 (F-18) is the most frequently used
radionuclide for positron-emission tomography (PET) {[}3{]}--{[}5{]}
radioisotopes due to its favorable physical properties (e.g. half-life
of 109.8 min) {[}6{]}.

Application of shortlived F-18 for in vivo visualization of antibodies
can be achieved by pretargeting approaches based on high yield in vivo
click reaction using e.g. \textsuperscript{18}F-labeled\emph{trans}
-cyclooctene (TCO) or tetrazine derivatives {[}7{]}. This reaction
strategy has been used for both \emph{in vitro} and \emph{in vivo}
applications {[}5{]}, {[}8{]}, {[}9{]}.

\emph{Trans} -cyclooctene has a high reactivity due to the release of
high strain energy upon the click reaction providing a well-defined
chiral structure which makes it interesting for stereocontrolled
synthesis. Therefore, radiolabeled TCOs are good candidates for
bio-orthogonal chemistry {[}10{]}.

There are many routes to synthesize a \emph{trans-} cyclooctene. A
common and elegant way is the photoisomerization of \emph{cis}
to\emph{trans} -cyclooctene {[}11{]}. Yet, the photoisomerization is
not irreversible and thus removal of the \emph{trans} -isomer from the
equilibrium \emph{cis} and \emph{trans} mixture is required to shift the
equilibrium. Fox et al. have proposed an elegant procedure for the
photochemical synthesis of TCO {[}12{]}. In this method, TCO was
produced via photoisomerisation of \emph{cis-} cyclooctene by exposure
to UV light (254 nm) in a batch vessel. The reaction mixture was
continuously passed through a bed of silver nitrate impregnated on
silica gel. Subsequently, the TCO is selectively retained by silver
nitrate and the remaining \emph{cis} -cyclooctene-containing solution is
recycled to the photochemistry batch vessel. This is a very unique
method yet the total yield was 66\% and the total reaction time was
relatively long, i.e. 12 hrs.

Recently, the sustainable production of active pharmaceuticals and
excipients in a has received a lot of attention {[}13{]}. Novel
bioprocesses, continuous-flow processing, process integration and
intensification and green chemistry are the main assets of sustainable
processes. Flow chemistry, especially micro-flow technology, is a high
potential platform in terms of equipment size reduction, energy
efficiency , and reduced solvent usage to achieve process
intensification and thereby performing more sustainable processes in
fine chemistry {[}14{]}, {[}15{]}.

More specifically, for photochemical reactions, microreactors have
several advantages compared to batch processes such as improved photon
transport, energy efficiency and better mixing {[}16{]}--{[}18{]}. The
constricted diameter of the microreactors (shorter photon diffusion
pathway) allows better use of the irradiated light efficiently reducing
the total exposure time, which leads to shorter reaction time and
possibly reduced byproduct formation {[}19{]}, {[}20{]}.

Beyond microfabricated channels, and microcapillaries, mini-scale
packed-bed reactors allow to form micro-flow in their void spaces.
Indeed, enhanced reaction rates, higher conversions and selectivities
were found as well and can be attributed to the reduced mass-transfer
limitations {[}21{]}, {[}22{]}. This, in combination with the high
surface-to-volume ratio, makes the packed-bed reactor suited for
performing biphasic reactions in multiple-repeated reentrance-flow mode
or for heterogeneous catalytic reactions {[}23{]}. Adsorption (and
desorption) is an essential step in heterogeneous catalysis. Hern\selectlanguage{ngerman}ández
Carucci et al. proposed a model based on the competitive adsorption of
ethylene and molecular oxygen over a silver surface of microchannels at
260 °C as part of a precise kinetic model for the ethylene oxide
formation {[}24{]}.

Accordingly, it stands to reason that sole adsorption processes (without
catalysis) might be intensified in micro-flow. Microspheres have been
reported and termed as adsorption `microreactors' and indeed use the
same transfer intensification by size reduction {[}25{]}. Rutin-Cr(III)
loaded alginate microspheres were designed to reduce Cr(VI) to Cr(III)
through adsorption and recover it. Yet, true micro(channel)reactors and
micro-flow packed bed reactors have been hardly applied for adsorption
so far.

Recently, we reported on the combination of a nucleophilic substitution
to the thermal-Claisen rearrangement and also to photo-Claisen
rearrangement in micro-flow {[}26{]}, {[}27{]}. The motivation was to
integrate two processes and to address the resulted challenging issues
towards orthogonality. Also, here, we would like to design and integrate
two processes, photoreaction and adsorption, yet with more in depth
theoretical study for each process.

Therefore, the aim of this study is to develop a photo micro-flow
process for the photochemical isomerization of \emph{cis} -cyclooctene
to TCO and its subsequent in-flow separation to isolate isomerically
pure TCO derivatives. Such a compact integration of small devices fed
with minute volumes provides opportunities for synergism between
reaction and separation, which is a means of process intensification and
was termed process-design intensification {[}28{]} as one arms of novel
process windows {[}29{]}--{[}31{]}.

More specifically, we focus in this work on the experimental procedures
(batch as well as flow) for the photoisomerisation, and the design and
operation of the adsorption column. Furthermore, the theoretical
concepts behind these operations are explained and relevant models for
both sections are developed. Finally, the results of the experiments and
theoretical modeling are presented and discussed.

\section*{Experimental section}

{\label{experimental-section}}

\textbf{2.1 Chemicals}

\emph{Cis} -cyclooctene, methyl benzoate, n-dodecane,
AgNO\textsubscript{3}/Silica (10\% loading, +230 mesh size), ammonium
hydroxide (28\% NH\textsubscript{3} in H\textsubscript{2}O), 1,3,5
trimethoxy benzene, n-hexane, diethyl ether and dichloromethane were
purchased from Sigma-Aldrich chemical company and used as received. The
solvent purity were all according to HPLC grade (\textgreater{}95\%).
Ultrapure water (HPLC grade, 18.2 M\selectlanguage{english} at 25degC) was used.

\textbf{2.2 \emph{Trans}-cyclooctene preparation}

The general procedure to produce \emph{trans} -cyclooctene (TCO) was
followed by using the setup which was applied in case 3 (section 4.5.1).
In the photoisomerisation of \emph{cis} into \emph{trans} -cyclooctene,
0.06 g (0.55 mmol) of TCO and 0.136 g (1mmol) of methyl benzoate were
dissolved in 25 ml of (1: 99 diethyl ether: n-hexane) solvent. The
solution was stirred in the inlet vessel and pumped through the micro
flow setup (case 3). On average, each 70 minutes the packed bed was
changed to a fresh bed. Prior to discharge of the used column, the bed
was flushed with solvent (1\% ether in n-hexane), dried with compressed
air and stored in an Erlenmeyer flask. Each packed bed approximately
contained 200-220 mg of AgNO\textsubscript{3} impregnated silica gel and
was mixed with 1 mm borosilicate glass beads in a mass ratio 1.66:1. The
experiment was carried out for about 3 hours and the final yield was
above 80\% (using n-dodecane as internal standard).

\emph{Trans} -cyclooctene adsorbed on packing powder was extracted by
the following procedure. First, the powder was stirred with a mixture of
10 ml ammonium hydroxide solution (28\% NH\textsubscript{3} in
H\textsubscript{2}O) and 10 ml of dichloromethane for about 5 min. Then,
the powder was filtered and the filtrate was transferred to a separating
funnel. The organic layer was separated and the aqueous phase was
extracted by dichloromethane three times (each time 10 ml). The organic
layers were combined, washed with water and dried by using
MgSO\textsubscript{4}. After filtration, the residue was concentrated
under reduced pressure to provide concentrated \emph{trans}
-cyclooctene. The yield (80\%) was determined by
\textsuperscript{1}H-NMR using 1,3,5 trimethoxybenzene as an internal
standard.

\textbf{2.3 Batch operation for determination of the adsorption
isotherm}

The batch adsorption experiment was performed in 25 ml glass Erlenmeyer
flask at a fixed temperature, 23\selectlanguage{english}@C. The first experiment was done by
concentrating the pure TCO in n-hexane to a volume of approximately 5
ml. Then 0.192 mmol of 1,3,5 trimethoxybenzene (internal standard
for\textsuperscript{1}H-NMR) was added. Based on
the\textsuperscript{1}H-NMR result, the amount of TCO was calculated.
Then, a fixed amount (0.2 g) of AgNO\textsubscript{3}/silica was added
to the solution. Subsequently, the Erlenmeyer was shaken at 100 rpm in a
temperature controlled shaker, for a period of 4 hours. Next, the
mixture was kept in stagnant mode to let the particles sediment. From
the solution a sample (0.2 ml) was taken for \textsuperscript{1}H-NMR
analysis. The result is one point in the TCO adsorption isotherm.
Afterwards, 3 ml of n-hexane was added to the solution and was shaken
again at the same condition as previous for a period of 4 hours and
consequently another sample was taken for \textsuperscript{1}H-NMR
analysis. This procedure was repeated for several times and every time a
certain amount of solvent was added and after shaking a sample was taken
for \textsuperscript{1}H-NMR analysis.

The amount of solute (B) adsorbed per gram dry of adsorbent at
equilibrium, \(q_{B}\) (g\textsubscript{B}/g), was calculated
according to Eq. 2.1.

\(q_{B}=\frac{V}{W}\left(C_{B_{0}}-C_{B_{e}}\right)\) (2.1)

Where, \(C_{B_{0}}\) (g/dm\textsuperscript{3}) and
\(C_{B_{e}}\)(g/dm\textsuperscript{3}) are respectively the initial
and equilibrium concentrations of the solute (B) in the liquid
phase,\(V\)(dm\textsuperscript{3}) is the solution volume,
and W (g) is the weight of the dry adsorbent.

\textbf{2.4 Continuous Flow Setup}

The experimental setup used for micro-flow based photoisomerization and
in-flow separation process is presented in supporting information
(section S1). The solution is pumped from the inlet solution vessel
using an HPLC pump (Knauer Azura P4.1S). The outlet stream from the pump
is fed to FEP (fluorinated ethylenepropylene copolymer, IDEX 1548 L)
capillary tubular reactor (ID 0.02'', OD 1/16'', length 5 m) which is
wound around a cylindrical UV light source placed inside a closed oven.
Irradiation is carried out using a low-pressure amalgam lamp (TS23-212;
Dinies Technologies GmbH). The outlet then flows to the packed bed. The
packed bed (stainless steel, ID 4.5 mm, L 25 mm) is packed with 200-220
mg of AgNO\textsubscript{3} impregnated silica gel (as packing or
adsorbent) with a mesh size of 230+ (Sigma-Aldrich). The
AgNO\textsubscript{3}/silica particles are mixed with 1 mm borosilicate
glass beads in a mass ratio 1.66:1 and then introduced to the packed bed
with a funnel. The inert glass beads are applied to prevent particle
agglomeration which results in channeling of the flow inside the packed
bed (for more information on micropacked beds and the assembling
process, we refer to {[}32{]}--{[}34{]}).The inlet and outlet of the
packed bed have attached separately two frits with a pore size of 10 \selectlanguage{greek}μ\selectlanguage{english}m
to keep the packing material inside the reactor. The outlet of the
packed bed is recycled to the inlet solution vessel through a 0.2 m long
FEP capillary tube. Samples are collected exactly before the recycle
stream enters the inlet solution vessel. The inlet solution vessel is
stirred with a magnetic stirrer bar to ensure a uniform concentration in
the vessel. In a general micro-flow based photoisomerization and an
in-flow separation experiment, \emph{cis} -cyclooctene (0.06 g, 0.55
mmol), methyl benzoate as a singlet sensitizer (0.136 g, 1mmol) and
n-dodecane as the internal standard for GC analysis (0.017g, 0.1 mmol)
are dissolved in 25 ml n-hexane (with 1\% diethyl ether) as solvent and
mixed in the same vessel (volumetric flask of 50 ml) and from this
vessel the solution is pumped to the flow setup.

\emph{2.4.1. Photo-microreactor kinetics study experiment}

In order to perform a kinetic study of the
photoisomerization,\emph{cis-} cyclooctene (0.0234 g, 0.2 mmol), methyl
benzoate (0.054 g, 0.4 mmol) and n-dodecane (0.014 g, 0.082 mmol ) are
dissolved in 10 ml n-hexane and mixed well. This solution is pumped in
to the photo-microreactor (FEP tubing, 2m) without passing the packed
bed. The reaction mixture is not recycled. The flow rate is varied
between 0.02-1.0 ml/min, corresponding to mean residence times of
10-0.20 min. The samples are collected for GC analyses at the outlet of
photo-microreactor for each flow rate.

\emph{2.4.2. Breakthrough curve prediction experiment}

The experiment was done by concentrating pure TCO in n-hexane to a
volume of 12.75 ml. Then 0.02141 g 1,3,5 trimethoxybenzene (internal
standard for \textsuperscript{1}H-NMR) was added. Based on
the\textsuperscript{1}H-NMR result, the amount of TCO was calculated
which was equal to 0.04 g (0.028 mol/dm\textsuperscript{3}). Then the
solution was diluted to 20 ml ({[}TCO{]}, 0.018
mol/dm\textsuperscript{3}). The packed bed (stainless steel, ID 4.5 mm,
L 25 mm) was packed with 0.2 g AgNO\textsubscript{3}/silica and 0.12 g
glass beads (1 mm), similarly to the previous section. The inlet
solution is pumped through the packed bed at the flow rate of 1 ml/min.
The outlet of the packed bed was connected to a FEP tube, from which
samples were collected for analyses. All packed bed space times have
been determined assuming a bed porosity of 0.5.

\textbf{2.5 Characterization}

Results of the flow experiments were characterized by gas chromatography
(GC-FID; Varian 430-GC) equipped with a CP-Sil 5 CB capillary column,
length 30 m (0.25 mm ID, film thickness 1 \selectlanguage{greek}μ\selectlanguage{english}m). The carrier gas was
helium (1 mL/min, split ratio 1:80). The oven temperature was maintained
at 50 \selectlanguage{ngerman}°C for 5 min and then increased to 200 °C at a rate of 10 °C/min.
The injector temperature was fixed at 250 °C, and the detector
temperature at 275 °C. The results from batch experiments and
breakthrough curve experiments were characterized by nuclear magnetic
resonance spectroscopy (\textsuperscript{1}H-NMR). Nuclear magnetic
resonance spectra were recorded on a Varian 400 MHz instrument.
All,\textsuperscript{1}H-NMR are reported in chemical shift (\selectlanguage{greek}δ, \selectlanguage{english}part per
million (ppm)), and were measured relative to the signal of
tetramethylsilane (0 ppm) in the deuterated solvent, unless otherwise
stated.

\section*{Theoretical study}

{\label{theoretical-study}}

\textbf{3.1 Photoreactor}

It is known from the literature {[}11{]}, {[}35{]}, {[}36{]} that the
photoisomerization of \emph{cis} to\emph{trans} -cyclooctene is an
equilibrium reaction. However, we could not find an in depth kinetic
study about this photoisomerization. To investigate the kinetics of the
equilibrium reactions, the conversion time histories have been
monitored. The results reveal the existence of equilibrium between the
\emph{cis} and \emph{trans} -isomers.

\textbf{Kinetics of the photoisomisation}

When it is assumed that intrinsic kinetics is obeyed and that the
photoreaction follows the first order kinetics, the photoisomerization
of \emph{cis} -cyclooctene to \emph{trans} -cyclooctene is represented
in scheme 1:

Scheme 1. \textbf{Photo isomerisation of \emph{trans}
from\emph{cis}-cyclooctene}

For a first order reversible reaction {[}37{]}, the concentration of
the\emph{cis} -cyclooctene \(C_{\text{cis}}\) as a function of time
obeys Eq 3.1. For a batch process, the conversion time histories have
been monitored:

\begin{equation}
\frac{C_{cis,(\tau)}\ }{C_{cis,(0)}\ }=\left[\frac{1}{k_{1}+k_{-1}}\left(k_{1}e^{-\tau\left(k_{1}+k_{-1}\right)}+k_{-1}\right)\right]\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (3.1)\nonumber \\
 \end{equation}

In this equation \(C_{cis,(0)}\) represents the concentration
of\emph{cis} at the start of reaction. See supplementary material S1 for
the derivation.

\textbf{3.2.1 Adsorption Isotherm}

An experimental adsorption isotherm correlates the adsorbed amount of
the adsorbate (\emph{trans} -cyclooctene) onto the adsorbent
(AgNO\textsubscript{3}) with the concentration of the adsorbate in
solution at equilibrium at a fixed temperature.

\textbf{3.2.2 Langmuir isotherm}

The Langmuir isotherm is one of the adsorption models that describe
physisorption of neutral molecules onto adsorption sites {[}38{]},
{[}39{]}. Based on the Langmuir model assumption, adsorption takes place
on homogeneously distributed adsorbent sites by monolayer adsorption.

The nonlinearized Langmuir equation is expressed as:

\begin{equation}
q_{\text{Be}}=\frac{b{q_{\max}C}_{B_{e}}}{1+bC_{B_{e}}}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\ \ \ \ \ \ \ \ \ \ \ \ \ \ (3.2)\nonumber \\
 \end{equation}

where \(q_{\text{Be}}\) (mg/g) is the amount of TCO adsorbed by
AgNO\textsubscript{3} at equilibrium, \(q_{\max}\) (mg/g)
represents the maximum adsorption capacity, \(C_{B_{e}}\)
(g/dm\textsuperscript{3}) is the equilibrium concentration of the
adsorbate in solution, and \(b\)(dm\textsuperscript{3}/ mg)
is a constant that amongst others is related to the heat of adsorption.

Moreover, Eq. 3.2 can be expressed as Eq. 3.3.

\begin{equation}
\frac{C_{B_{e}}}{q_{\text{Be}}}=\frac{C_{B_{e}}}{q_{\max}}+\frac{1}{q_{\max}b}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (3.3)\nonumber \\
 \end{equation}

Plotting \(\frac{C_{B_{e}}}{q_{\text{Be}}}\) against \(C_{B_{e}}\), allows the
calculation of the parameters, \(b\) and
\(q_{\max}\).

\textbf{3.2.3 Packed bed Modeling}

In order to predict the dynamic behavior of the adsorption column, a
mass balance over the liquid phase of an infinitesimal sized slice of
the packed bed leads with perfect radial mixing and negligible pressure
drop to Eq. 3.4, see {[}40{]}--{[}42{]}.

\begin{equation}
D_{\text{ax}}\frac{\partial^{2}C_{i}}{\partial z^{2}}-v\frac{\partial C_{i}}{\partial z}-\frac{1-\varepsilon_{b}}{\varepsilon_{b}}N_{i}=\frac{\partial C_{i}}{\partial t}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\ \ \ \ \ \ \ \ \ \ \ (3.4)\nonumber \\
 \end{equation}

In Eq. 3.4 \(C_{i},\)\(D_{\text{ax}},\ v,\ \varepsilon_{b},\ and\ N_{i}\) are the concentration of
TCO in the liquid phase, the axial dispersion coefficient, the
interstitial liquid velocity\emph{,} the bed porosity, and the mass
transfer rate into the particle per unit volume of the particle phase,
respectively\emph{.} The first and second term in Eq. 3.4 stand for the
dispersive transport and the convective transport in the column,
respectively. The third term represents the mass transfer between liquid
phase and adsorbent. The last term is related to accumulation of the
adsorbate. This model is based on the following assumptions: isothermal
adsorption and spherical adsorbent particles packed uniformly in the
bed.

As it was stated, \(N_{i}\ \)is the mass transfer rate between
solid and fluid phase and can be represented as {[}40{]}--{[}42{]}:

\(N_{i}=\rho_{p}\frac{\partial q_{i}}{\partial t}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\ \ \ \ \ \ \ \ \ \ \ (3.5)\)

\(q_{\text{i\ }}\left[\frac{\text{mol}}{\text{kg}_{s}}\right]\)is the concentration of TCO on the adsorbent surface
and\(\rho_{p}\left[\frac{\text{kg}_{s}}{\text{dm}_{s}^{3}}\right]\)is the adsorbent particle density. In order to
define\(\frac{\partial q_{i}}{\partial t}\) mathematically, it is important to know whether
the mass transfer resistance or the intrinsic adsorption kinetics
dominates the adsorption rate.

\textbf{Mass transfer resistance and intrinsic adsorption rate}

A useful approach to investigate and to compare the mass transfer
resistance with the kinetic resistance is by comparing\(\frac{1}{k_{c}\text{.a}}\)
with \(\frac{1}{k_{\text{ads}}}\) , i.e. the time constant for mass transfer and
adsorption, respectively. Since the diameter of adsorbent particle is
small, 60 microns, and the AgNO\textsubscript{3} layer thickness is much
smaller than the silica particle diameter, the internal mass transport
through the pores of the adsorbent has been neglected (For more
information see supplementary material, S2). Therefore, the mass
transfer resistance calculation is only based on the external mass
transfer from the bulk fluid to the adsorbent surface.

In order to determine \(k_{c}\ \)first the Reynolds number based
on the particle diameter,\selectlanguage{ngerman} Re, should be investigated. The
calculated Reynolds number, Re, in our system is smaller
than 2. From the literature {[}43{]} for low Re number,
the Sherwood number can be defined as

\begin{equation}
Sh=\frac{k_{c}d_{p}}{D}=\frac{\phi_{s}}{6\left(1-\varepsilon_{b}\right)\xi}\frac{ud_{p}}{D}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (3.6)\ \nonumber \\
 \end{equation}

where \(\phi_{s}\), \(u{,\ d}_{p}\),\(\xi,\ \text{and}\ \text{D\ }\)represent
particle sphericity factor, the superficial liquid velocity, the
particle diameter, the channeling factor and the diffusion coefficient
of TCO in the solvent. In the Eq. 3.6, it is assumed that particles are
spherical; so\(\ \phi_{s}=1\). Unfortunately, the \(\xi\)
value cannot be estimated exactly. However, in literature {[}43{]} the
value of \(\xi\) has been predicted to be in the range of
1-10. Here the worst case value, \(\xi\)=10 (the case that
gives highest mass transfer resistance) has been considered.

\(D\) is estimated on the basis of values in the similar
systems{[}44{]}. As the fluid phase is very diluted, parameters such as
density and viscosity are approximated based on solvent characteristics
(n-hexane) at 25@\selectlanguage{english}C.

On the other hand, in order to determine \(\frac{1}{k_{\text{ads}}}\)which has
the dimension of time, an adsorption experiment can be performed in
batch in a way that mass transfer resistance is eliminated as much as
possible. By this experiment, the time to reach 50\% of the equilibrium
adsorption (\(t_{\frac{1}{2,\ ads}}\)) is calculated which can be considered
to be \(\frac{1}{k_{\text{ads}}}\). Lastly,\(k_{\text{ov}}\) is calculated
according to:

\begin{equation}
\frac{1}{k_{\text{ov}}}=\frac{1}{k_{\text{ads}}}+\frac{1}{k_{c}\text{.a}}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\ \ \ \ \ \ \ \ \ \ (3.7)\nonumber \\
 \end{equation}

In the mentioned experiment (adsorption of TCO on AgNO\textsubscript{3})
the batch vessel was well stirred so it is assumed that there is no
external mass transfer limitation (more details on the experiment can be
found in experimental section). Adsorption is an equilibrium process.
According to the results, by plotting TCO concentration versus time it
is possible to record \(t_{\frac{1}{2,\ ads}}\).

\textbf{Breakthrough curve prediction}

The common available models in reported literature for breakthrough
curve prediction are divided into two main categories based on the
existence of a mass transfer resistance between the adsorbent particles
and fluid phase or local adsorption assumption between adsorbent
particle and bulk phase, i.e. by using intrinsic adsorption kinetics
{[}45{]}.

\textbf{Local adsorption model-local equilibrium theory}

Local adsorption theory is divided into two sets of models depending on
the rate of adsorption- local equilibrium theory and local kinetic
theory {[}45{]}, {[}46{]}.

Local equilibrium theory is based on the existence of equilibrium
between adsorbate and fluid concentration, and how fast the equilibrium
is reached in each stage in the packed bed column.
Thus\(\ \frac{\partial q_{i}}{\partial t}\) is defined by using the Langmuir isotherm as
follows:

\begin{equation}
\frac{\partial q_{i}}{\partial t}=\frac{\partial q_{i}}{\partial C_{i}}\times\frac{{\partial C}_{i}}{\partial t}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\ \ \ (3.8)\nonumber \\
 \end{equation}

and

\begin{equation}
\frac{\partial q_{i}}{\partial C_{i}}=\frac{q_{\max}b}{{(1+bC_{i})}^{2}}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\ \ \ \ \ \ \ \ \ (3.9)\nonumber \\
 \end{equation}

where\(\text{\ q}_{\max}\ \)and \(b\) are from Langmuir isotherm
model, see Eq. 3.2.

The local kinetic theory is based on a non-equilibrium adsorption
reaction. It is expressed based on the rate of adsorption and desorption
of the adsorbate on the surface of adsorbent particles.

In this work an equilibrium surface reaction is governing, so the only
model that has been applied is the local equilibrium theory. For the
local kinetic theory, see the related literature {[}45{]}, {[}46{]}.

Therefore, Eq. 3.4 becomes

\begin{equation}
D_{\text{ax}}\frac{\partial^{2}C_{i}}{\partial z^{2}}-v\frac{\partial C_{i}}{\partial z}=\left[1+\rho_{p}\frac{\left(1-\varepsilon_{b}\right)}{\varepsilon_{b}}\times\frac{q_{\max}b}{\left(1+bC_{i}\right)^{2}}\right]\frac{\partial C_{i}}{\partial t}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\ \ \ \ (3.10)\ \nonumber \\
 \end{equation}

For the model calculations the partial differential equation (3.10) has
to be solved. Eq 3.10, is discretized using finite differences and
solved using MATLAB\selectlanguage{ngerman}® with implicit PDEPE solvers.

The initial condition is a packed bed filled with solvent. Then, at the
inlet of the column a step change is applied. The applied boundary
conditions are of Danckwert's type conditions {[}47{]} and used at the
inlet (z=0) and at the outlet (z=L) of the column (Eq. 3.11).

\begin{equation}
\frac{\partial C_{i}}{\partial z}|_{z=0}=\frac{v}{D_{\text{ax}}}\left(C_{i}-C_{i,feed}\right);\ \ \ \frac{\partial C_{i}}{\partial z}|_{z=l}=0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (3.11)\ \nonumber \\
 \end{equation}

The initial conditions are given by Eq. 3.12

\begin{equation}
C_{i}\left(z,t=0\right)=0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\ \ \ \ \ \ \ \ \ \ \ \ \ (3.12)\nonumber \\
 \end{equation}

\textbf{3.3} \textbf{Modeling the combination of the photo-microreactor
and the adsorption column}

In this section it is aimed to predict the \emph{cis} -cyclooctene
conversion when there is a continuous closed system of the
photo-microreactor with an integrated adsorption column and recycling
the unreacted \emph{cis} -isomer to the reactor feed solution (Figure
1). In order to mathematically model the system, two control volumes are
selected: the photo-microreactor and the packed bed (1), and the stirred
vessel with solution to be fed to the photoreactor (2).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

Figure 1 \textbf{Schematic overview of the complete photo-microreactor
and the adsorption system control volumes; (1): photo-microreactor and
packed bed, (2): inlet vessel with reactor feed solution}

The rate of photoisomerization of the \emph{cis} -isomer into
the\emph{trans} -isomer has been given in the previous section (3.1). It
is assumed that the amount of the \emph{cis} - isomer adsorbed in the
packed bed is negligible. Therefore, for the first control volume and a
single pass of the flow, if \(C_{t}=\frac{n_{\text{cis}}}{V}\), where\(\ n_{\text{cis}}\)
denotes the molar amount of the\emph{cis} -isomer in the inlet vessel
and\selectlanguage{ngerman} V the volume of the photo-microreactor, the rate
equation becomes (only if the outlet concentration of the \emph{trans}
-isomer from the packed bed is zero):

\begin{equation}
-\frac{dC_{\text{cis}}}{\text{dt}}={(k}_{1}+k_{-1})\times C_{\text{cis}}-k_{-1}\times\frac{n_{\text{cis}}}{V}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (3.13)\nonumber \\
 \end{equation}

In order to model the second control volume, a mass balance is set up
over the inlet vessel, see Eq. 3.14. The inlet vessel is assumed to be
ideally mixed.

\begin{equation}
\left[n_{\text{cis}}\right]_{t+t}-\left[n_{\text{cis}}\right]_{t}=Q\times C_{cis,\ iv}\times t-Q\times\frac{n_{\text{cis}}}{V}\times t\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\ \ \ \ \ \ \ \ \ \ \ \ \ (3.14)\nonumber \\
 \end{equation}

where \(\text{Q\ }\text{and}\ C_{cis,\ iv}\) stand respectively for the total volumetric
flow rate and the \emph{cis} concentration at the inlet of the vessel.
Division the right and left hand side of Eq. 3.18
by\(t\ \)and taking the limit \(t\ \rightarrow 0,\) leads to:

\begin{equation}
\frac{dn_{\text{cis}}}{\text{dt}}+\frac{Q}{V}n_{\text{cis}}=Q\times C_{cis,\ iv}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (3.15)\nonumber \\
 \end{equation}

Eq. 3.15 expresses the change in the amount of \emph{cis} -isomer with
respect to time. The concentration of \emph{cis} -isomer at the outlet
of the first control volume, (i.e. the outlet of the packed bed
for\emph{trans} -isomer adsorption) is equal to the concentration of
the\emph{cis} -isomer at the inlet of control volume 2, (i.e. the vessel
with the reactor feed solution)\(\ C_{cis,\ iv}=C_{\text{cis}}\).

Eq. 3.13 and 3.15 are first order ordinary differential equations (ODEs)
which are solved simultaneously by employing numerical methods (in
MATLAB\selectlanguage{ngerman}®) whereby the final concertation of \emph{cis} -isomer or the
final conversion of the \emph{cis} -isomer with respect to time is
obtained. The initial values for numerically solving Eq. 3.13 and 3.15
are \(C_{\text{cis}}=C_{0}\) and \(n_{\text{cis}}=\frac{C_{0}}{V}\), where
\(C_{0}\) is the initial concentration of the \emph{cis}
-isomer in the reactor feed vessel.

\section*{Results and Discussion}

{\label{results-and-discussion}}

\textbf{4.1.1 Kinetic study of photoisomerisation}

The photoisomerization of \emph{cis} -cyclooctene into\emph{trans}
-cyclooctene has been investigated in detail in photo-microreactor. In
order to determine the optimal reaction condition, the
photoisomerisation was performed at varoius residence times (for more
details see experimental section). The results are presented in Figure
2. Figure 3 shows that conversion is limited by equilibrium to
approximately 28\%.

\textbf{4.1.2 k\textsubscript{1} and k\textsubscript{-1} determination}

The experimental data points in Figure 2 have been fitted to Eq. 3.1. A
regression analysis is carried out in MATLAB® (see Figure 2).
k\textsubscript{1} and k\textsubscript{-1} at 23°C are calculated to be
0.45 and 1.23 (1/min), respectively. For 23°C the equilibrium constant
is\(K=\left(\frac{C_{\text{trans}}}{C_{\text{cis}}}\right)_{\text{eq}}=\frac{k_{1}}{k_{-1}}=0.36\).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

Figure 2. \selectlanguage{ngerman}\textbf{Results of regression analysis for calculating
k\textsubscript{1} and k\textsubscript{-1}. X\textsubscript{eq}=0.28 at
23°C, ( ): experimental points; calculated line with Eq. 3.1 and
k\textsubscript{1}=0.45 (1/min) and k\textsubscript{-1}= 1.23 (1/min).}

\textbf{4.2 Adsorption isotherm}

As stated before, the experimental adsorption isotherms represent the
balance between adsorbent and adsorbate at equilibrium conditions.
Figure 3 shows the adsorption isotherm for \emph{trans} -cyclooctene on
AgNO\textsubscript{3}/silica at 23\selectlanguage{english}@C. Provided that the adsorption
isotherm obeys the Langmuir isotherm type, \(\frac{C_{B_{e}}}{q_{B}}\)versus
\(C_{B_{e}}\)should represent a linear behavior.
Furthermore,\(\frac{C_{B_{e}}}{q_{B}}\) versus \(C_{B_{e}}\) has been
plotted, from which it can be observed that \(\frac{C_{B_{e}}}{q_{B}}\) is a
linear function of \(C_{B_{e}}\). The results indicate that the
adsorption of TCO on AgNO\textsubscript{3} obeys the Langmuir isotherm
model and the highest adsorption capacity was recorded at 43.089 mg/g at
initial concentration of 5.85 g/dm\textsuperscript{3}.

{[}CHART{]}{[}CHART{]}

Figure 3. \textbf{Adsorption isotherm of \emph{trans}-cyclooctene on the
AgNO\textsubscript{3}/SiO\textsubscript{2} at 23@C,
W\textsubscript{AgNO3}=0.175 g,}\selectlanguage{english}\(\frac{\mathbf{C}_{\mathbf{\text{Be}}}}{\mathbf{q}_{\mathbf{\text{Be}}}}\mathbf{=17.515}\mathbf{C}_{\mathbf{B}_{\mathbf{e}}}\mathbf{+20.529,\ }\mathbf{R}^{\mathbf{2}}\mathbf{=0.965}\)\textbf{; (a)
nonlinearized form and (b) linearized form (Eq. 3.3 ), for calculated
parameters b and q\textsubscript{Bmax}, see Table 1}

Accordingly, the Langmuir model parameters, \(b\) and
\(q_{B_{\max}}\), have been calculated see Table 1.

Table 1 \textbf{Langmuir isotherm parameter b and
q\textsubscript{Bmax}for TCO adsorption on AgNO\textsubscript{3}/silica
at 296.15 K}\selectlanguage{english}
\begin{longtable}[]{@{}ll@{}}
\toprule
b = 0.85 (dm\textsuperscript{3}/g\textsubscript{trans}) &
\(\mathbf{q}_{\mathbf{B}_{\mathbf{\max}}}\) = 57.1 \selectlanguage{ngerman}× 10\textsuperscript{-3}
(g\textsubscript{trans}/g\textsubscript{AgNO3})\tabularnewline
\bottomrule
\end{longtable}\selectlanguage{ngerman}

\textbf{4.3 Adsorption kinetics}

Adsorption kinetics of TCO on to AgNO\textsubscript{3}/silica was
studied by performing an experiment in batch. In that experiment a known
amount of AgNO\textsubscript{3}/silica, (0.175g) was suspended in the
solution of TCO, C\textsubscript{0}=8.06 g/dm\textsuperscript{3} in
n-hexane. The time history of the liquid concentration of TCO was
recorded, see Figure 4. In order to prevent any external mass transfer
limitation, the suspension was stirred intensively. The experimental
data were analyzed using (pseudo-)first-order and (pseudo-)second-order
kinetics {[}48{]}--{[}52{]}, see Eq. 4.1 and 4.3, respectively:

\begin{equation}
\frac{dq_{t}}{\text{dt}}={k\left(q_{\max}-q_{t}\right)}^{n}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (4.1)\nonumber \\
 \end{equation}

n=1 for (pseudo-)first-order and n=2 for (pseudo-)second-order

\begin{equation}
\ln\frac{\left(q_{B_{e}}-q_{B_{t}}\right)}{q_{B_{e}}}=-k^{\prime}t\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (4.2)\nonumber \\
 \end{equation}\begin{equation}
\frac{1}{q_{B_{t}}}=\frac{1}{k"q_{B_{e}}^{2}\text{.t}}+\frac{1}{q_{B_{e}}}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (4.3)\nonumber \\
 \end{equation}

Where \emph{k'} (min\textsuperscript{-1}) is the rate constant for the
(pseudo-)first-order and \(k"\) (g
mg\textsuperscript{-1}min\textsuperscript{-1}) is the rate constant for
the (pseudo-)second-order kinetic models.\emph{q\textsubscript{Be}}
and\emph{q\textsubscript{Bt}} are the amount of the \emph{trans} -isomer
adsorbed per gram AgNO\textsubscript{3} at equilibrium and at time t,
respectively. The constants can be calculated from the intercepts and
slopes of the linear plots of \(\ln{(q_{B_{e}}-q_{B_{t}})}\)versus\selectlanguage{ngerman} t
and \(t/q_{B_{t}}\) versus \(t\), respectively (Figure
4).

Figure 4a shows that adsorption of \emph{trans} -cyclooctene proceeds
rapidly during the first 30s and becomes almost constant after 1 min.
The adsorption rate constants and linear regression values are collected
in Table 2. The results in Figure 4 and Table 2 reveal that adsorption
obeys a (pseudo-)second order rate law. Also the experimentally observed
value of \(q_{B_{e}}\) is equal to 44.3 ×
10\textsuperscript{-3}g\textsubscript{trans}/g\textsubscript{AgNO3} and
it can be easily observed that it is very close to \(q_{B_{e}}\)
calculated from pseudo-second order kinetic model This fact suggests
that the adsorption rate of \emph{trans} -cyclooctene is dependent on
the adsorption site availability on AgNO\textsubscript{3} rather than
the\emph{trans} -cyclooctene concentration in solution {[}53{]},
{[}54{]}. Initially, there are many adsorption sites are available,
however with the prolonging time the sites have been occupied, hence,
limited free sites for molecule to be adsorbed on {[}53{]}, {[}55{]}.

Table 2 \selectlanguage{english}\textbf{pseudo-second-order rate constant for adsorption of TCO
onto AgNO\textsubscript{3} at 23@C}\selectlanguage{english}
\begin{longtable}[]{@{}lll@{}}
\toprule
\begin{minipage}[b]{0.30\columnwidth}\raggedright\strut
Models\strut
\end{minipage} & \begin{minipage}[b]{0.30\columnwidth}\raggedright\strut
Model parameters\strut
\end{minipage} & \begin{minipage}[b]{0.30\columnwidth}\raggedright\strut
R\textsuperscript{2}\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.32\columnwidth}\raggedright\strut
(pseudo-)first-order\strut
\end{minipage} & \begin{minipage}[t]{0.32\columnwidth}\raggedright\strut
\(q_{B_{e}}\) =15.87 mg/g \(k^{\prime}\)
=8.8\selectlanguage{ngerman}×10\textsuperscript{-3} min\textsuperscript{-1}\strut
\end{minipage} & \begin{minipage}[t]{0.32\columnwidth}\raggedright\strut
0.69\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.32\columnwidth}\raggedright\strut
(pseudo-)second-order\strut
\end{minipage} & \begin{minipage}[t]{0.32\columnwidth}\raggedright\strut
\(q_{B_{e}}\) =44.25 mg/g \(k"\)
=0.51\selectlanguage{ngerman}×10\textsuperscript{-3} g\textsubscript{AgNO3}
mg\textsuperscript{-1}\textsubscript{trans}
min\textsuperscript{-1}\strut
\end{minipage} & \begin{minipage}[t]{0.32\columnwidth}\raggedright\strut
0.9924\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

{[}CHART{]}{[}CHART{]}

Figure 4 \textbf{(a) Liquid phase concentration
of\emph{trans}-cyclooctene in a stirred vessel with a suspension of
AgNO\textsubscript{3}/SiO\textsubscript{2} in n-hexane (1\% diethyl
ether) W\textsubscript{AgNO3/SiO2}=0.175 g, C\textsubscript{0}=8.06
g/dm\textsuperscript{3} at 23@C, (b) (pseudo-)second-order kinetics for
adsorption of \emph{trans}-cyclooctene onto
AgNO\textsubscript{3}/SiO\textsubscript{2}}\selectlanguage{english}

\textbf{4.4 Packed bed}

\textbf{4.4.1 Breakthrough model validation}

In order to validate the model (see Eq. 3.8-3.12), the obtained results
from the adsorption breakthrough curve model are compared with the
experimental results, see Figure 5. The calculated breakthrough curve
agrees reasonably well with the experimentally observed curve. The
proposed breakthrough curve model is able to predict the saturation
time, t\textsubscript{s}, of the adsorption column. t\textsubscript{s}is
the time at which \(\frac{C_{\text{trans}}}{C_{trans0}}=0.05\).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image5/image5}

\end{center}
\end{figure}

Figure 5 \selectlanguage{ngerman}\textbf{Calculated and experimental breakthrough curve at 23°C,
W\textsubscript{AgNO3}=0.2 g, volumetric flow rate= 1 ml/min,
C\textsubscript{trans0}=1.99 gr/dm\textsuperscript{3}}

\textbf{4.5 Process design for integration of a photo-microreactor and
adsorption for the isomerization of \emph{cis}-cyclooctene in
to\emph{trans}-cyclooctene}

After optimizing each sub process, i.e. photoisomerisation and
adsorption, in this section, the process configuration for
photoisomerisation of \emph{cis} into \emph{trans} -cyclooctene is
presented for three different cases. These three cases were
experimentally tested. The model for the adsorption column that was
presented earlier in this paper, can be used to estimate saturation time
and the operational parameters such as the temperature for the
adsorption of \emph{trans} -cyclooctene. Later in the text the validity
of the model as described in section 3.3 is confirmed with the
experimental results.

\textbf{4.5.1 Solvent selection}

The selection of a proper solvent is crucial in any (photo)chemical
reaction. Here, this is even more significant as the solvent should play
a role in different process steps. First, it should be able to
solubilize the cyclooctene (both \emph{cis} - and \emph{trans} -) and
the sensitizer. Also, the solvent has to be transparent at the required
wavelength, 245 nm. On the other hand, it should not dissolve the
packing powders (AgNO\textsubscript{3}/silica). If AgNO\textsubscript{3}
dissolves, the \emph{trans} -complex will not be collected in packed bed
and there is no separation of the\emph{trans} -isomer from the
\emph{cis} -isomer. This means that there is no equilibrium shift in the
direction of the \emph{trans} -isomer. Considering the features
mentioned, n-hexane or cyclohexane seem to be proper choices.
Cyclohexane has a higher boiling point than n-hexane. Since to desorb
\emph{trans} -cyclooctene from
AgNO\textsubscript{3}/SiO\textsubscript{2} there is an elution step
needed which is not included in this process design. Therefore, as the
solvent of this process, n-hexane is preferred. Also, in order to
increase the solubility of \emph{cis} and \emph{trans} -cyclooctene 1\%
of diethyl ether is added. It is worth mentioning that diethyl ether
dissolves AgNO\textsubscript{3}, so it is recommended not to increase
the ratio of diethyl ether to n-hexane to more than 5:95 (volume ratio).

\textbf{4.5.2 Process configurations}

\textbf{Case (a)} . This case concerns the basic continuous flow setup
in which a photo-microreactor of 5 m length and an adsorption column of
5 cm length packed with AgNO\textsubscript{3}/SiO\textsubscript{2}
powders are used (Figure 6a). The flow rate is set to 0.2 ml/min. As
reported earlier in section 2.4, in all cases the outlet flow from the
packed bed is recycled to the vessel with the reactor feed solution.

\textbf{Case (b).} Since, our system is a closed-loop recycle flow
system, it is important that as soon as photoreaction takes place the
molecules are transferred to the separation unit and from there quickly
recycled to the feed vessel .Therefore, the key in this design (case
(b)) is to reduce the residence time of the flowing fluid in the
connecting tubes and parts between the feed vessel, the
photo-microreactor(s) and the packed bed.

In this case, we applied the concept of symmetrical flow splitting by
using a T-micromixer placed in reverse mode to act as flow splitter in a
bifurcate fashion the feed flow rate is directed towards two
photo-microreactors of 5 m length which are wound around one UV light
and placed in parallel (Figure 6b). With this design, it is possible to
double the main flowrate while keeping the residence time in the
photo-microreactor the same as in case (a).

Therefore, the total flow rate is raised to 0.4 ml/min which speeds up
the flow in connecting parts, and by symmetrical flow splitting, the
flow rate is kept 0.2 ml/min in each photo-microreactor.

\textbf{Case (c).} This case is similar to the case (b). Again, two
parallel photo-microreactors are used. But, the main difference is that
in this configuration more than one packed bed, each with a length of
2.5 cm, are installed in parallel, see Figure 6c. This adds the function
of refreshing the adsorption column under use, by switching between two
columns set in parallel -- one for the closed-loop flow and the other in
a wait position, being re-activated. Such an integrated flow
configuration for purification following micro-flow reaction was already
proposed by us in a recent paper, using a fixed-bed column packed with
Amberlyst resin for an ion-exchange based purification of the product
mixture {[}26{]}.

In the operational mode, the parallel packed beds are connected to the
photoreactor by a switching valve. While one packed bed is in use to
adsorb the \emph{trans} -isomer, the other is in the waiting mode. As
soon as the first column reaches saturation, the flow is switched to
pass through a fresh packed bed. Based on the amount of the
inlet\emph{cis} -cyclooctene, in this case, three parallel packed beds
are used. Also, the flow rate is increased to 0.66 ml/min.

\textbf{Hosted file}

\verb`image7.emf`  available at \url{https://authorea.com/users/319031/articles/448823-photoisomerization-of-cis-to-trans-cyclooctene-integration-of-a-micro-flow-reactor-separation-by-specific-adsorption}

\textbf{Hosted file}

\verb`image8.emf`  available at \url{https://authorea.com/users/319031/articles/448823-photoisomerization-of-cis-to-trans-cyclooctene-integration-of-a-micro-flow-reactor-separation-by-specific-adsorption}

Figure 6 \textbf{Three different process configuration for
photoisomerisation of \emph{cis} to \emph{trans}-cyclooctene. case (a),
case (b), case (c).}

\textbf{4.5.3 Validation of the model in the combination of micro
photoreactor and adsorption column}

The results in Figure 7 demonstrate that the conversion of\emph{cis}
-cyclooctene as a function of the process time obtained from solving the
model discussed in section 3.3. This model has been solved and sketched
for different total flow rates and compared with each experimental case.
Here, time is the total operational time.

In case (a) after 400 min almost 70\% conversion is achieved. This time
is the total required time of operation since this is a closed-loop
system operating in a recycling mode. In the case (b), as stated earlier
the total flow rate is doubled to 0.4 ml/min, while the residence time
in each photoreactor is the same as in case (a). Figure 7b shows that
there is a small deviation between the results of the model calculations
and the experimental results. Besides, upon increasing the total
operational time, the deviation increases and at some point the
experimental results tend to reach a plateau earlier than with the
predicted model. Since the total flow rate is doubled, the flow rate
inside the packed bed is also doubled. Therefore, the packed bed reaches
saturation earlier in case (b) than in case (a). With prolonging time,
the packed bed becomes saturated with TCO and TCO molecules are not
adsorbed anymore and recycled in the system which also affects the
photoreaction process to reach equilibrium faster. As a result, the
total conversion of \emph{cis} -cyclooctene is not improved anymore and
therefore the experimental points tend to reach a plateau and deviate
from the model.

In case (c), there is less deviation between the experimental points and
the results of the model calculations (Figure 7c). The first switching
towards a fresh packed bed was at 75 min operational time and the second
switch was at 180 min. As indicated in Figure 7c, after 50 min the
packed bed tends to reach saturation. Therefore there is a plateau
before the fresh packed bed was in use (75 min) which explains the small
deviation between the experimental results and the results of model
calculations. Also, it is important to note that this is a closed system
and the concentration of the \emph{cis} -isomer is getting less with
respect to the operational time. Therefore, the first packed bed is
saturated in less time than the ones used later, so as time increases
the packed bed saturation time also increase due to the smaller
concentration of \emph{cis} -isomer in the flowing fluid. In case (c)
90\% conversion is achieved after 250 min.

According to the results, case (c) shows a massive improvement compared
to the first two cases. Primarily, using the packed bed with smaller
volume gives the chance to quicker recycle the \emph{cis} -isomer. This
results in an improvement of the total conversion at any certain time.
Also, changing the packed bed as soon as it reaches its saturation
point, improves the process performance in terms of an increasing rate
of production of the \emph{trans} -isomer. Table 3 summarizes the
performance of the different design cases. To give better comparison, we
calculate the total conversion divided by the total time of operation
for each case which can be correlated to the overall reaction rate of
the closed-loop system. As it is expected this number is much higher in
case (c), 0.36 (min\textsuperscript{-1}) compared to the case (a) and
(b), which are 0.175 and 0.2 (min\textsuperscript{-1}), respectively.

Table 3 Summary of different configuration's performance\selectlanguage{english}
\begin{longtable}[]{@{}llllll@{}}
\toprule
& Total flow rate (ml/min) & Time of operation (min) & Time of operation
(min) & Total conversion (\%) & Conv./time of operation
(min\textsuperscript{-1})\tabularnewline
\midrule
\endhead
Case (a) & 0.2 & 0.2 & 400 & 70 & 0.175\tabularnewline
Case (b) & 0.4 & 0.4 & 365 & 75 & 0.2\tabularnewline
Case (c) & 0.66 & 0.66 & 250 & 90 & 0.36\tabularnewline
\bottomrule
\end{longtable}

It is worth mentioning that the outcome of this process configuration
has been successfully applied for the photoisomerisation of
functionalized TCO in our research {[}56{]}.

\textbf{Flow rate effect}

As can be seen in Figure 7d and be expected for a closed-loop recycle
flow system, for a certain time of operation, larger flow rates result
in a higher conversion. For instance, if the total flow rate is equal to
0.66 ml/min, after almost 3hr, more than 80\% of \emph{cis} -cyclooctene
is converted. While, if we double the total flow rate to 1.2 ml/min, a
conversion of more than 90 \% can be reached within 3 hr. On the other
hand, if the flow rate is kept lower, for instance 0.2 ml/min, after 3
hrs, only 50 \% of \emph{cis} -cyclooctene is converted. By increasing
the total flow rate, although the stable equilibrium may not be reached
in photo-microreactor, we get benefit from recycling the feed faster and
the whole process speeds up. Therefore, comparing the higher flow rate
case with the lower flow rate cases, indicates that in less time of
operation, higher conversion is achieved.

\textbf{Hosted file}

\verb`image9.tiff`  available at \url{https://authorea.com/users/319031/articles/448823-photoisomerization-of-cis-to-trans-cyclooctene-integration-of-a-micro-flow-reactor-separation-by-specific-adsorption}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image10/image10}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image11/image11}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image12/image12}

\end{center}
\end{figure}

Figure 7 \textbf{Validation of the model of combination of the
photoreactor and adsorption column and comparing the results with three
process configuration, (a) case 1, (b) case 2, (c) case 3, (d) Total
flow rate (ml/min) effect on \emph{cis}-cyclooctene conversion}

\section*{Conclusion}

{\label{conclusion}}

In this paper, an integrated photo micro-flow adsorption was developed
for product separation, with the option to do that in recycle mode. This
was investigated to produce \emph{trans} -cyclooctene from its\emph{cis}
-isomer. Here, the thermodynamic equilibrium is shifted by inserting an
in-flow separation in a recycling flow mode, which makes better use of
the given photoenergy (transport intensification). Further, a full
theoretical study of in-flow separation in a recycling flow mode has
been conducted. Moreover, different process design options to reach an
optimum yield of \emph{trans} -cyclooctene are proposed and
experimentally tested. Radiolabeled \emph{trans-} cyclooctenes are
valuable in vivo click synthons for PET imaging.

First, the kinetics of the photoisomerisation of \emph{cis} -
to\emph{trans} -cyclooctene was investigated in a microreactor. Results
confirm that the conversion is limited by equilibrium to nearly 28\%.
The comparison of the reaction rate constants, k\textsubscript{1} and
k\textsubscript{-1}, shows that the reaction rate from \emph{trans} -
to\emph{cis} - is higher than \emph{cis} - to \emph{trans} -cyclooctene.

Moreover, an in-depth study of the TCO adsorption on
AgNO\textsubscript{3}/SiO\textsubscript{2} was done. The results
indicate that the adsorption of TCO on AgNO\textsubscript{3} follows the
Langmuir isotherm model. The reaction rate is governed by the
equilibrium surface reaction. The analysis of the adsorption kinetic
data demonstrated that the kinetics can be approximated with a
pseudo-second order rate equation. The maximum adsorption capacity of
the \emph{trans} -isomer adsorbed per gram AgNO\textsubscript{3} is
equal to 44.25 mg\textsubscript{trans}/g\textsubscript{silvernitrate} .

The dynamic behavior of the adsorption column was experimentally studied
and modeled according to the local equilibrium theory. The results of
the model calculations show good agreement with the experimental data.
Based on the model, it is possible to predict the breakthrough curve and
saturation time of the mentioned adsorption column.

Finally, after optimization of each sub process, i.e photoisomerisation
and adsorption, three different integrated process designs for
photoisomerisation of the \emph{cis} to \emph{trans} -isomer was
mathematically modeled. According to the calculated model, it is
important to remark that by increasing the flow rate a higher conversion
of \emph{cis} -isomer was achieved. By increasing the total flow rate,
the time that the flow is passing through connecting parts is reduced
and also, speeding up the feed recycling gives an advantage.
Furthermore, the three different process configurations were tested
experimentally. Comparing three cases, case (c) (Figure 6), shows
improvement of the total conversion of the \emph{cis} -isomer. 90\%
conversion was achieved after 250 min. In case (c) two parallel
photo-microreactors and parallel packed beds in switching mode were
applied. Switching the packed bed as soon as it reaches saturation
results in obtaining higher conversion in less time. Numbering up the
sub processes gives a good promise for scaling up this integrated
process.

It is worth mentioning that in this closed-loop system, solvent can be
added only once at the beginning. In this system solvent is only carrier
medium and is not consumed or converted, thus by recycling, solvent is
also recovered and transferred back to the system. As soon as the amount
of \emph{cis} -isomer reaches to 0.05 of initial concentration, fixed
amount of \emph{cis} -isomer can be added to the initial feed vessel
which already contains enough solvent. Therefore, with this closed-loop
design, it is possible to reduce the amount of solvent usage to only
once.

\section*{Acknowledgements}

{\label{acknowledgements}}

We kindly acknowledge the European Research Council for the Advanced
Grant on ``Novel Process Windows---Boosted Micro Process Technology'' No
267443.

\section*{References}

{\label{references}}

{[}1{]} E. D. G. Fleuren \emph{et al.} , ``Theranostic applications of
antibodies in oncology,'' \emph{Molecular Oncology} , vol. 8, no. 4. pp.
799--812, 2014.

{[}2{]} L. E. Lamberts \emph{et al.} , ``Antibody positron emission
tomography imaging in anticancer drug development,'' \emph{J. Clin.
Oncol.} , vol. 33, no. 13, pp. 1491--1504, 2015.

{[}3{]} R. J. Hargreaves, ``The role of molecular imaging in drug
discovery and development,'' \emph{Clinical Pharmacology and
Therapeutics} , vol. 83, no. 2. pp. 349--353, 2008.

{[}4{]} H. H. Pien, A. J. Fischman, J. H. Thrall, and A. G. Sorensen,
``Using imaging biomarkers to accelerate drug development and clinical
trials,'' \emph{Drug Discov. Today} , vol. 10, no. 4, pp. 259--266,
2005.

{[}5{]} C. Denk \emph{et al.} , ``Development of a
\textsuperscript{18}F-Labeled Tetrazine with Favorable Pharmacokinetics
for Bioorthogonal PET Imaging,'' \emph{Angew. Chemie Int. Ed.} , vol.
53, no. 36, pp. 9655--9659, 2014.

{[}6{]} K. Serdons, A. Verbruggen, and G. M. Bormans, ``Developing new
molecular imaging probes for PET,'' \emph{Methods} , vol. 48, no. 2. pp.
104--111, 2009.

{[}7{]} M. L. Blackman, M. Royzen, and J. M. Fox, ``Tetrazine ligation:
Fast bioconjugation based on inverse-electron-demand Diels-Alder
reactivity,'' \emph{J. Am. Chem. Soc.} , vol. 130, no. 41, pp.
13518--13519, 2008.

{[}8{]} N. K. Devaraj, R. Upadhyay, J. B. Haun, S. A. Hilderbrand, and
R. Weissleder, ``Fast and sensitive pretargeted labeling of cancer cells
through a tetrazine/trans-cyclooctene cycloaddition,'' \emph{Angew.
Chemie - Int. Ed.} , vol. 48, no. 38, pp. 7013--7016, 2009.

{[}9{]} E. M. F. Billaud \emph{et al.} , ``Pretargeted PET Imaging Using
a Bioorthogonal (18)F-Labeled trans-Cyclooctene in an Ovarian Carcinoma
Model.,'' \emph{Bioconjug. Chem.} , vol. 28, no. 12, pp. 2915--2920,
2017.

{[}10{]} C. Wolf, \emph{Dynamic Stereochemistry of Chiral Compounds} .
2007.

{[}11{]} J. S. Swenton, ``Photoisomerization of cis-cyclooctene to
trans-cyclooctene,'' \emph{J. Org. Chem.} , vol. 34, no. 10, pp.
3217--3218, 1969.

{[}12{]} M. Royzen, G. P. A. Yap, and J. M. Fox, ``A Photochemical
Approach to Functionalized trans -Cyclooctenes Driven by Metal
Complexation,'' pp. 1--30.

{[}13{]} C. Jimen\selectlanguage{ngerman}éz-Gonzalez \emph{et al.} , ``Key green engineering
research areas for sustainable manufacturing: A perspective from
pharmaceutical and fine chemicals manufacturers,'' \emph{Org. Process
Res. Dev.} , vol. 15, no. 4, pp. 900--911, 2011.

{[}14{]} P. Poechlauer \emph{et al.} , ``Pharmaceutical Roundtable Study
Demonstrates the Value of Continuous Manufacturing in the Design of
Greener Processes,'' \emph{Org. Process Res. Dev.} , vol. 17, no. 12,
pp. 1472--1478, 2013.

{[}15{]} L. Vaccaro, D. Lanari, A. Marrocchi, and G. Strappaveccia,
``Flow approaches towards sustainability,'' \emph{Green Chem.} , vol.
16, no. 8, pp. 3680--3704, 2014.

{[}16{]} E. E. Coyle and M. Oelgemöller, ``Micro-photochemistry:
photochemistry in microstructured reactors. The new photochemistry of
the future?,'' \emph{Photochem. Photobiol. Sci.} , vol. 7, no. 11, p.
1313, 2008.

{[}17{]} J. P. Knowles, L. D. Elliott, and K. I. Booker-Milburn, ``Flow
photochemistry: Old light through new windows,'' \emph{Beilstein J. Org.
Chem.} , vol. 8, pp. 2025--2052, 2012.

{[}18{]} Y. Su, N. J. W. Straathof, V. Hessel, and T. Noël,
``Photochemical Transformations Accelerated in Continuous-Flow Reactors:
Basic Concepts and Applications,'' \emph{Chem. -- A Eur. J.} , vol. 20,
no. 34, pp. 10562--10589, 2014.

{[}19{]} D. Cambié, C. Bottecchia, N. J. W. Straathof, V. Hessel, and T.
Noël, ``Applications of Continuous-Flow Photochemistry in Organic
Synthesis, Material Science, and Water Treatment,'' \emph{Chem. Rev.}

{[}20{]} T. Noël, \emph{Photochemical Processes in Continuous-Flow
Reactors} . World Scientific, 2017.

{[}21{]} M. W. Losey, M. A. Schmnidt, and K. F. Jensen,
``Microfabricated multiphase packed-bed reactors: Characterization of
mass transfer and reactions,'' \emph{Ind. Eng. Chem. Res.} , vol. 40,
no. 12, pp. 2555--2562, 2001.

{[}22{]} K. F. Jensen, ``Microreaction engineering --- is small
better?,'' \emph{Chem. Eng. Sci.} , vol. 56, no. 2, pp. 293--303, 2001.

{[}23{]} M. Shang, T. Noël, Y. Su, and V. Hessel, ``High Pressure Direct
Synthesis of Adipic Acid from Cyclohexene and Hydrogen Peroxide via
Capillary Microreactors,'' \emph{Ind. Eng. Chem. Res.} , vol. 55, no.
10, pp. 2669--2676, 2016.

{[}24{]} J. R. H. Carucci \emph{et al.} , ``Ethylene oxide formation in
a microreactor: From qualitative kinetics to detailed modeling,''
in\emph{Industrial and Engineering Chemistry Research} , 2010, vol. 49,
no. 21, pp. 10897--10907.

{[}25{]} M. Jiang, Y. Qi, Y. L. Cui, L. Zhao, and S. Liu, ``Removal and
Recovery of Chromium from Aqueous Solutions by Reduction-Absorption
Microreactor,'' \emph{Water. Air. Soil Pollut.} , vol. 228, no. 1, 2017.

{[}26{]} E. Shahbazali, M. Spapens, H. Kobayashi, S. Ookawara, T. Noël,
and V. Hessel, ``Connected nucleophilic substitution-Claisen
rearrangement in flow -- Analysis for kilo-lab process solutions with
orthogonality,'' \emph{Chem. Eng. J.} , vol. 281, pp. 144--154, 2015.

{[}27{]} E. Shahbazali, T. Noel, and H. Volker, ``Photo-claisen
rearrangement of allyl phenyl ether in micro-flow: influence of phenyl
core substituents and vision on orthogonality,'' \emph{J. Flow Chem.} ,
vol. 6, no. 3, pp. 252--259, 2016.

{[}28{]} V. Hessel, I. Vural Gürsel, Q. Wang, T. Noël, and J. Lang,
``Potential Analysis of Smart Flow Processing and Micro Process
Technology for Fastening Process Development: Use of Chemistry and
Process Design as Intensification Fields,'' \emph{Chemical Engineering
and Technology} , vol. 35, no. 7. pp. 1184--1204, 2012.

{[}29{]} V. Hessel, I. Vural Gürsel, Q. Wang, T. Noël, and J. Lang,
``Potential Analysis of Smart Flow Processing and Micro Process
Technology for Fastening Process Development: Use of Chemistry and
Process Design as Intensification Fields,'' \emph{Chem. Eng. Technol.} ,
vol. 35, no. 7, pp. 1184--1204, Jul. 2012.

{[}30{]} V. Hessel, ``Novel Process Windows - Gate to Maximizing Process
Intensification via Flow Chemistry,'' \emph{Chem. Eng. Technol.} , vol.
32, no. 11, pp. 1655--1681, Nov. 2009.

{[}31{]} V. Hessel, D. Kralisch, N. Kockmann, T. No??l, and Q. Wang,
``Novel process windows for enabling, accelerating, and uplifting flow
chemistry,'' \emph{ChemSusChem} , vol. 6, no. 5. pp. 746--789, 2013.

{[}32{]} T. Noël, T. J. Maimone, and S. L. Buchwald, ``Accelerating
palladium-catalyzed C-F bond formation: Use of a microflow packed-bed
reactor,'' \emph{Angew. Chemie - Int. Ed.} , vol. 50, no. 38, pp.
8900--8903, 2011.

{[}33{]} J. R. Naber and S. L. Buchwald, ``Packed-bed reactors for
continuous-flow C-N cross-coupling,'' \emph{Angew. Chemie - Int. Ed.} ,
vol. 49, no. 49, pp. 9469--9474, 2010.

{[}34{]} T. Noël, S. Kuhn, A. J. Musacchio, K. F. Jensen, and S. L.
Buchwald, ``Suzuki-miyaura cross-coupling reactions in flow: Multistep
synthesis enabled by a microfluidic extraction,'' \emph{Angew. Chemie -
Int. Ed.} , vol. 50, no. 26, pp. 5943--5946, 2011.

{[}35{]} Y. I. Hiroshi Tsuneishi, Tadao Hakushi, ``Singlet- versus
triplet-sensitized enantiodifferentiating photoisomerization of
cyclooctene: remarkable effects of spin multiplicity upon optical
yield,'' \emph{J. Chem. SOC., Perkin Trans. 2} , pp. 1601--1605, 1996.

{[}36{]} M. R. Wilson and R. E. Taylor, ``Strained alkenes in natural
product synthesis,'' \emph{Angew. Chemie - Int. Ed.} , vol. 52, no. 15,
pp. 4078--4087, 2013.

{[}37{]} E. J. Molga and K. R. Westerterp, ``Principles of chemical
reaction engineering,'' \emph{Ullmann's Encycl. Ind. Chem.} , 2013.

{[}38{]} H. S. Fogler, ``Elements of chemical reaction
engineering,''\emph{Chem. Eng. Sci.} , vol. 42, p. 1000, 1999.

{[}39{]} K. Y. Foo and B. H. Hameed, ``Insights into the modeling of
adsorption isotherm systems,'' \emph{Chem. Eng. J.} , vol. 156, no. 1,
pp. 2--10, 2010.

{[}40{]} J. Aracil, J. L. Casillas, and M. Martinez, ``Modelling and
Solving Fixed-bed Adsorption,'' vol. 1, no. January 1992, pp. 533--544,
1993.

{[}41{]} C. Costa and A. Rodrigues, ``Design of cyclic fixed\selectlanguage{english}-bed
adsorption processes. Part I: Phenol adsorption on polymeric
adsorbents,'' \emph{AIChE J.} , vol. 31, no. 10, pp. 1645--1654, 1985.

{[}42{]} L. Fournel, P. Mocho, R. Brown, and P. Le Cloirec, ``Modeling
breakthrough curves of volatile organic compounds on activated carbon
fibers,'' \emph{Adsorption} , vol. 16, no. 3, pp. 147--153, 2010.

{[}43{]} A. A. C. M. B. K.R. Westerterp, W. P. M. van
Swaaij,\emph{Chemical reactor design and operation} . Wiley, 1991.

{[}44{]} T. FUNAZUKURI, N. NISHIMOTON, and N. WAKAO, ``Binary
Diffusion-Coefficients of Organic-Compounds in Hexane, Dodecane, and
Cyclohexane at 303.2-333.2-K and 16.0 Mpa,'' \emph{J. Chem. Eng. Data} ,
vol. 39, pp. 911--915, 1994.

{[}45{]} M. Siahpoosh, S. Fatemi, and A. Vatani, ``Mathematical modeling
of single and multi-component adsorption fixed beds to rigorously
predict the mass transfer zone and breakthrough curves,'' \emph{Iran. J.
Chem. Chem. Eng.} , vol. 28, no. 3, pp. 25--44, 2009.

{[}46{]} C. L. Chuang, P. C. Chiang, and E. E. Chang, ``Modeling VOCs
adsorption onto activated carbon,'' \emph{Chemosphere} , vol. 53, no. 1,
pp. 17--27, 2003.

{[}47{]} J. F. Wehner and R. H. Wilhelm, ``Boundary conditions of flow
reactor (Reprinted from Chem Engng, vol 6, pg 89-93, 1956),''\emph{Chem.
Eng. Sci.} , vol. 50, no. 24, pp. 3885--3888, 1995.

{[}48{]} J. Lin and L. Wang, ``Comparison between linear and non-linear
forms of pseudo-first-order and pseudo-second-order adsorption kinetic
models for the removal of methylene blue by activated
carbon,''\emph{Front. Environ. Sci. Eng. China} , vol. 3, no. 3, pp.
320--324, 2009.

{[}49{]} J. P. Simonin, ``On the comparison of pseudo-first order and
pseudo-second order rate laws in the modeling of adsorption
kinetics,''\emph{Chem. Eng. J.} , vol. 300, pp. 254--263, 2016.

{[}50{]} Y. S. Ho and G. McKay, ``Pseudo-second order model for sorption
processes,'' \emph{Process Biochem.} , vol. 34, no. 5, pp. 451--465,
1999.

{[}51{]} H. Qiu, L. Lv, B. Pan, Q. Q. Zhang, W. Zhang, and Q. Q. Zhang,
``Critical review in adsorption kinetic models,'' \emph{J. Zhejiang
Univ. Sci. A} , vol. 10, no. 5, pp. 716--724, 2009.

{[}52{]} T. Shahwan, ``Sorption kinetics: Obtaining a pseudo-second
order rate equation based on a mass balance approach,'' \emph{J.
Environ. Chem. Eng.} , vol. 2, no. 2, pp. 1001--1006, 2014.

{[}53{]} X. Song, Y. Zhang, C. Yan, W. Jiang, and C. Chang, ``The
Langmuir monolayer adsorption model of organic matter into effective
pores in activated carbon,'' \emph{J. Colloid Interface Sci.} , vol.
389, no. 1, pp. 213--219, 2013.

{[}54{]} M. U. Dural, L. Cavas, S. K. Papageorgiou, and F. K. Katsaros,
``Methylene blue adsorption on activated carbon prepared from Posidonia
oceanica (L.) dead leaves: Kinetics and equilibrium
studies,''\emph{Chem. Eng. J.} , vol. 168, no. 1, pp. 77--85, 2011.

{[}55{]} Y. Matsui, N. Ando, H. Sasaki, T. Matsushita, and K. Ohno,
``Branched pore kinetic model analysis of geosmin adsorption on
super-powdered activated carbon,'' \emph{Water Res.} , vol. 43, no. 12,
pp. 3095--3103, 2009.

{[}56{]} E. M. F. Billaud \emph{et al.} , ``Micro-flow photosynthesis of
new dienophiles for inverse-electron-demand Diels--Alder reactions.
Potential applications for pretargeted in vivo PET imaging,''\emph{Chem.
Sci.} , vol. 8, no. 2, pp. 1251--1258, 2017.

{[}57{]} M. A. Vannice and W. H. Joyce, ``Acquisition and Evaluation of
Reaction Rate Data,'' pp. 38--86, 2005.

{[}58{]} M. A. Vannice, \emph{Kinetics of catalytic reactions} .
Springer, 2005.

{[}59{]} P. Y. Lanfrey, Z. V. Kuzeljevic, and M. P. Dudukovic,
``Tortuosity model for fixed beds randomly packed with identical
particles,'' \emph{Chem. Eng. Sci.} , vol. 65, no. 5, pp. 1891--1896,
2010.

{[}60{]} J. H. Dymond and L. A. Woolf, ``Tracer diffusion of organic
solutes in n-hexane at pressures up to 400 MPa,'' \emph{J. Chem. Soc.
Faraday Trans. 1 Phys. Chem. Condens. Phases} , vol. 78, no. 3, p. 991,
1982.

{[}61{]} J. H. Dymond and L. a. Woolf, ``Tracer diffusion of organic
solutes in n-hexane at pressures up to 400 MPa,'' \emph{J. Chem. Soc.
Faraday Trans. 1} , vol. 78, no. 3, p. 991, 1982.

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