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\DOI{10.5802/crchim.324}
\datereceived{2024-02-19}
\daterevised{2024-05-15}
\datererevised{2024-06-17}
\dateaccepted{2024-06-19}
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\begin{document}
%\copyeditor{RK}
\begin{noXML}

%\makeatletter
%\def\TITREspecial{\relax}
%\def\cdr@specialtitle@english{French Network on Solvation (GDR 2035 SolvATE)}
%\def\cdr@specialtitle@french{R\'eseau th\'ematique sur la solvatation (GDR 2035 SolvATE)}
%\makeatother

\CDRsetmeta{articletype}{research-article}

\title{On the phase behavior of sorbitol/water/H\textsubscript{2}/CO\textsubscript{2}
mixtures at high pressures and temperatures by in~situ infrared
spectroscopy}

\alttitle{Thermodynamique des m\'{e}langes
sorbitol/eau/H\textsubscript{2}/CO\textsubscript{2} \`{a} haute pression et haute
temp\'{e}rature par spectroscopie infrarouge in situ}

\author{\firstname{Isaline} \lastname{Bonnin}}
\address{Institut des Sciences Mol\'{e}culaires (ISM), Univ. Bordeaux,
CNRS, Bordeaux INP, ISM, UMR 5255, F-33400 Talence, France}
\address{Institut de Chimie des Milieux et Mat\'{e}riaux de Poitiers
(IC2MP), Univ. de Poitiers, UMR CNRS 7285, 1 rue Marcel Dor\'{e}, 86073 Poitiers Cedex 9, France}

\author{\firstname{Rapha\"{e}l} \lastname{Mereau}\CDRorcid{0000-0002-0357-4654}}
\addressSameAs{1}{Institut des Sciences Mol\'{e}culaires (ISM), Univ.
Bordeaux, CNRS, Bordeaux INP, ISM, UMR 5255, F-33400 Talence, France}

\author{\firstname{Karine} \lastname{De Oliveira Vigier}\CDRorcid{0000-0003-3613-7992}}
\addressSameAs{2}{Institut de Chimie des Milieux et Mat\'{e}riaux de
Poitiers (IC2MP), Univ. de Poitiers, UMR CNRS 7285, 1 rue Marcel
Dor\'{e}, 86073 Poitiers Cedex 9, France}

\author{\firstname{Thierry~}\lastname{Tassaing}\CDRorcid{0000-0003-4114-170X}\IsCorresp}
\addressSameAs{1}{Institut des Sciences Mol\'{e}culaires (ISM), Univ.
Bordeaux, CNRS, Bordeaux INP, ISM, UMR 5255, F-33400 Talence, France}
\email[T. Tassaing]{thierry.tassaing@u-bordeaux.fr}

\shortrunauthors

\thanks{Region Nouvelle Aquitaine, University of Poitiers, MITI of
CNRS, INCREASE Federation, GDR 2035 SolvATE}

\begin{abstract}
The thermodynamic behavior of multi-component system, which
includes sorbitol dissolved in water under CO\textsubscript{2} and
H\textsubscript{2} pressure, is investigated by {in situ}  infrared spectroscopy.
Our study focuses on the gas phase of binary, ternary, and quaternary
systems at temperatures ranging from 40~\textdegree{}C to 
220~\textdegree{}C and at CO\textsubscript{2} pressures between 30 and 120 bar,
while maintaining a constant pressure of H\textsubscript{2} at 30 or 60 bar. The
influence of addition of sorbitol in the liquid aqueous phase and
of H\textsubscript{2} in the CO\textsubscript{2}-rich gas phase on the mutual solubility of
CO\textsubscript{2} and water is evaluated. In our experimental conditions
(\textit{T}< 220~\textdegree{}C and \textit{P}< 120 bar), it is found
that in such multi-component system, a water-rich liquid phase always
coexists with a CO\textsubscript{2}-rich gas phase. Presence of sorbitol
in the water-rich phase and H\textsubscript{2} in the CO\textsubscript{2}-rich phase has a
limited impact on the mutual solubility of water and CO\textsubscript{2}.
Furthermore, sorbitol is not soluble in the CO\textsubscript{2}-rich phase and
instead remains in the water-rich liquid phase over the thermodynamic
range investigated. 
\end{abstract}

\begin{altabstract}
Le comportement thermodynamique du syst\`{e}me multi-composants, qui
comprend du sorbitol dissous dans l'eau sous pression de CO\textsubscript{2}
et H\textsubscript{2}, est \'{e}tudi\'{e} par spectroscopie infrarouge in situ.
Notre \'{e}tude se concentre sur la phase gazeuse des syst\`{e}mes
binaires, ternaires et quaternaires dans une large gamme de
temp\'{e}ratures allant de 40~\textdegree{}C \`{a} 220~\textdegree{}C
et sous une pression de CO\textsubscript{2} comprise entre 30 bar et 120 bar,
tout en maintenant une pression constante de 30 ou 60 bar de H\textsubscript{2}
L'influence de l'addition de sorbitol dans la phase aqueuse liquide
et de H\textsubscript{2} dans la phase gazeuse riche en CO\textsubscript{2} sur la
solubilit\'{e} mutuelle du CO\textsubscript{2} et de l'eau est
\'{e}valu\'{e}e. Dans nos conditions exp\'{e}rimentales (\textit{T}<
220~\textdegree{}C et \textit{P}< 120 bar), nous constatons que dans un tel
syst\`{e}me multi-composants, une phase liquide riche en eau coexiste
toujours avec une phase gazeuse riche en CO\textsubscript{2}. La pr\'{e}sence de
sorbitol dans la phase riche en eau et de H\textsubscript{2} dans la phase riche
en CO\textsubscript{2} a un impact limit\'{e} sur la solubilit\'{e} mutuelle de
l'eau et du CO\textsubscript{2}. De plus, le sorbitol n'est pas soluble dans
la phase riche en CO\textsubscript{2} et reste dans la phase liquide riche en
eau dans la gamme thermodynamique \'{e}tudi\'{e}e.
\end{altabstract}

\keywords{\kwd{Sorbitol}
\kwd{CO\textsubscript{2}}
\kwd{Hydrogen}
\kwd{Water}
\kwd{High pressures}
\kwd{Infrared spectroscopy}}

\altkeywords{\kwd{Sorbitol}
\kwd{CO\textsubscript{2}}
\kwd{Hydrog\`{e}ne}
\kwd{Eau}
\kwd{Hautes pressions}
\kwd{Spectroscopie infrarouge}}

\maketitle

\vspace*{20pt plus 1pt minus 1pt}

\twocolumngrid

\end{noXML}

\section{Introduction}

In the context of biomass valorization towards substitution of
petroleum-based materials, sorbitans represent bio-sourced alternatives
to a large number of petroleum-based molecules; and can be used in a
wide range of applications such as additives, pharmaceuticals and
monomers for polymer industries~\cite{1,2,3,4}. In particular, the
hydrogenation of glucose into sorbitol and the dehydration of sorbitol 
with various catalytic systems have been studied in depth~\cite{5,6}. 
However, the synthesis of these diols remains, to
this day, a technological challenge due to the cost of energy-consuming
processes, use of expensive and toxic solvents as well as the intensive
\mbox{purification} steps.

To this regard, it is worthwhile to develop ``one-pot'' protocols for
the obtention of sorbitans starting from glucose combining
heterogeneous catalytic hydrogenation and an acid-catalyzed dehydration
reaction~\cite{5,7}. Conventionally, strong mineral acids are used and they
limit the selective obtention of sorbitans to favor its dehydration
to isosorbide (produced by double dehydration of sorbitol). Being
non-toxic and non-corrosive, gaseous CO$_{2}$ has attracted attention in
replacing environmentally unsafe mineral acid catalysts thanks to
the reversible control of reaction mixture's~pH.

In order to study this one-pot reaction (hydrogenation and
dehydration), we combined in situ spectroscopic analysis with
molecular modeling to better understand the mechanisms and the kinetics in the 
formation of different reactions' intermediates~\cite{8,9,10}. However, the
thermodynamics of these multi-component mixtures are not clearly known.
We recall that the aqueous dehydration of sorbitol was
performed under H$_{2}$ and CO$_{2}$ pressure (between 30 and 120 bar); and
at high temperature (up to 220~\textdegree{}C). The phase behavior and 
the mutual solubility of all the components of this multi-component mixture 
depend strongly upon the pressure/temperature conditions which in turn can
significantly influence the selectivity and yield of the sorbitans
synthesis during hydrogenation and dehydration occurring in the
liquid phase.

The aim of this paper is to determine the
thermodynamic behavior of binary, ternary, and quaternary systems
composed of sorbitol/water/H$_{2}$/CO$_{2}$ at
temperatures ranging from 40~\textdegree{}C to 220~\textdegree{}C;
at CO$_2$ pressure between 30 bar to 120 bar; H$_{2}$ pressure at 30
or 60 bar. Additionally, we have focused our investigation on the
gas phase using infrared spectroscopy which performs well
{in situ} and {in operando} investigations. Of particular note, the evolution 
of the intensity of selected vibrational modes of CO$_{2}$ 
and H$_{2}$O have also been analyzed as a function of 
temperature and pressure in order to determine the evolution of
H$_{2}$O and CO$_{2}$ concentrations in binary, ternary, and quaternary
mixtures. From the results obtained, it was possible to show that in such
multi-component system, a water-rich liquid phase coexists with a
CO$_{2}$-rich gas phase under our experimental conditions ($T <
220$~\textdegree{}C and $P < 120$ bar). In addition, it was found that
sorbitol remains in the water-rich liquid phase over the thermodynamic
range investigated.\looseness=-1 

\section{Experimental setup}

\subsection{High pressure in situ infrared absorption setup}

The {in situ} analysis of sorbitol--water--CO$_{2}$--H$_{2}$
mixture was done with IR spectroscopy in one\break high-pressure cell
({Figure~\ref{fig1}}). Due to strong absorption of water,
the liquid-phase analysis is best performed using ATR-FTIR equipment which 
can withstand high temperature and pressure. Due to the lack of such equipment, we have focused our study on the gas phase
using a home made HP cell which can withstand high temperature of about
250~\textdegree{}C and pressure up to 20 MPa. The home-made stainless-steel
cell is composed of three cylindrical windows (one sapphire window for
visual observation and two silicon windows for IR absorption with a
pathlength of 26 mm). Windows were positioned on the flat surface of an
inconel plug with a Kapton foil placed between the window and the
plug to compensate for imperfections at the two surfaces
(unsupported area principle). Flat Kapton rings were used to ensure
sealing between the plug and the cell body. Heating was achieved
using four cartridge heaters inside the body of the cell and a
thermocouple located close to one cartridge was used to regulate the
temperature with an accuracy of ${\rmDelta}T = \pm
0.5$~\textdegree{}C. The cell was connected via a stainless capillary to a
pressurizing system which allows the regulation of pressure with an
accuracy of $\rmDelta P = \pm 0.1$ bar.

\begin{figure*}
{\vspace*{1pt}}
\includegraphics{fig01}
\caption{\label{fig1}Design of the high-pressure experimental device
with a high-pressure cell coupled with IR spectrometer for the
{in situ} measurements of the CO$_{2}$-rich phase of the
sorbitol/water/H$_{2}$/CO$_{2}$ mixtures.}
\end{figure*}

For IR absorption measurements, a Nicolet 6700 FTIR spectrometer
equipped with a Globar source, a KBr/Ge beamsplitter and a DLaTGS/KBr
thermal detector was used to determine the spectral range, from 400 to
6500 cm$^{-1}$. Single beam spectra with 4 cm$^{-1}$ resolution were
obtained by Fourier transformation of 100 accumulated interferograms in
order to improve the signal to noise ratio.

\subsection{Experimental procedure}

For the quaternary mixture, the lower part of the cell was filled with
1~ml of an aqueous solution of 30 wt\% of sorbitol (purchased from
Sigma Aldrich (${>}$98\% purity)). The experiments were
performed by initially adding a predetermined pressure of H$_{2}$ (purchased from
Air Liquid (99.9999\% purity)); CO$_{2}$ (purchased from Air Liquid
(99.95\% purity)) was then added to this high-pressure cell using a
manual pump (TOP industrie) up to the desired pressure. We mention that
the notation 30/30 bar CO$_{2}$/H$_{2}$ means that 30~bar of H$_{2}$ is
introduced and then the cell was filled with CO$_{2}$ until the total
pressure reached 60 bar. Making the hypothesis that both CO$_{2}$ and
H$_{2}$ behave as ideal gases and that their pressures can be added, we
assumed that 30 bar of CO$_{2}$ was added to the cell. The cell volume
(8~ml) is fixed and only the pressure can be adjusted.

{\vspace*{3pt}}

\subsection{Infrared absorption spectra and calibration}

{\vspace*{3pt}}

{Figure~\ref{fig2}} illustrates (for the case of a binary
H$_{2}$O/CO$_{2}$ mixture) the spectral changes of the infrared
absorption spectra in the CO$_{2}$-rich phase that occur with an
increase of the temperature from 40 to 220~\textdegree{}C at a constant
pressure of 60 bar. 

\begin{figure*}
\includegraphics{fig02}
\caption{\label{fig2}Infrared spectra of the CO$_{2}$-rich phase of the
H$_{2}$O--CO$_{2}$ binary system at a constant pressure of CO$_{2}$ of
60 bar; and temperature from 40~\textdegree{}C to 220~\textdegree{}C.}
\end{figure*}

In that region, fundamental and combination bands of CO$_{2}$ and
H$_{2}$O were observed. However, only the spectral range between 2500 and
3200 cm$^{-1}$, and between 4500 and 7500 cm$^{-1}$ are of
interest for our purpose under our experimental conditions. Indeed, the
strong absorption of CO$_{2}$ and H$_{2}$O precludes any quantitative
analysis outside this spectral range.

For CO$_{2}$, the region from 4750 to 5200 cm$^{-1}$ with overlapping
peaks of CO$_{2}$ at 4800 cm$^{-1}$, 4950~cm$^{-1}$ and 5100 cm$^{-1}$
are of interest and correspond to the combination modes
$4\nu _{2}+ \nu _{3}$, $\nu _{1}+ 2\nu _{2}+ \nu
_{3}$ and $2\nu _{1}+ \nu _{3}$, respectively. $\nu _{1}$, $\nu _{2}$ 
and $\nu _{3}$ are the fundamental
vibrational modes of CO$_{2}$ with \mbox{symmetric} stretch, bending
mode and antisymmetric stretch, respectively~\cite{11,12,13,14}. The weak
peak observed at 6950 cm$^{-1}$ is assigned to the $3\nu _{3}$
overtone of~CO$_{2}$.\looseness=-1

For H$_{2}$O, the band at 1600 cm$^{-1}$ which is saturated at 
temperatures above 120~\textdegree{}C is related to the bending mode $\nu
_{2}$ of water~\cite{15}. The profile at 5300~cm$^{-1}$ having an
increasing intensity with the temperature, is assigned to the $\nu
_{2}+ \nu _{3}$ combination mode of water~\cite{16,17}. In 7000--7500 cm$^{-1}$ spectral range, the profile with a
doublet structure observed at 7200~cm$^{-1}$ with an enhanced
intensity with temperature is assigned to the $2\nu _{3}$ overtone
of water.

In order to quantify the concentration of CO$_{2}$, we selected
the vibrational mode $2\nu _{1}+ \nu _{3}$ of CO$_{2}$ and determined
its epsilon value from its integrated area (from 4900 to 4740 cm$^{-1}$).
This was selected as it negligibly overlaps with any contribution
of water. We, then measured the infrared absorption spectra of neat
gaseous CO$_{2}$ at constant pressures of 30, 60 and 120 bar at 40, 80,
120, 160, 200 and 220~\textdegree{}C. Knowing the concentration of
CO$_{2}$ (in mol${\cdot}$L$^{-1}$) from the NIST database (NIST Chemistry
Webbook~\cite{18}), the pathlength of the cell ($l$) and measuring the
integrated area ($A$) in 4900 to 4740 cm$^{-1}$ range; the molar
extinction coefficient (epsilon $=$\ $\varepsilon{}$) values are then
calculated by applying the Beer--Lambert law: $A = \varepsilon\cdot l\cdot c$ (see
Table~\ref{tab1}). For all temperatures and pressures, it can be seen 
that there is a significant variation of the epsilon values with increase in pressure. 
Hence, these values are used as reference for the same given temperature and
pressure to determine CO$_{2}$ concentration in all analyzed mixtures. 

\begin{table*}
\caption{\label{tab1} Molar extinction coefficients (in
L${\cdot}$mol$^{-1}{\cdot}$cm$^{-2}$) of the $2\nu_{1}+ \nu_{3}$ mode of
CO$_{2}$~integrated in 4900 to 4740 cm$^{-1}$ range}
\begin{tabular}{lcccccc} 
\thead
& {40~\textdegree{}C} & {80~\textdegree{}C} & {120~\textdegree{}C} & {160~\textdegree{}C} & {200~\textdegree{}C} & {220~\textdegree{}C} \\
\endthead
{30 bar CO}$_{2}$ & 2.010 & 2.101 & 2.114 & 2.014 & 1.931 & 1.806 \\
{60 bar CO}$_{2}$ & 1.916 & 2.013 & 1.970 & 1.903 & 1.791 & 1.675 \\
{120 bar CO}$_{2}$ & 1.341 & 1.645 & 1.688 & 1.646 & 1.532 & Saturate
\botline
\end{tabular}
\end{table*}

By the same token, to quantify the concentration of water, selecting a vibrational mode of water and determining its
epsilon value is required. In water--CO$_{2}$ mixtures, the molar
fraction of CO$_{2}$ can be calculated from the concentration of
CO$_{2}$ and water. We selected the $\nu_{2} + \nu_{3}$
combination mode of water and used its integrated area from 5800 to 5347
cm$^{-1}$ to calculate the concentration of water. We emphasize that
only the high frequency wing of the mode of water has been considered
for integration as the low frequency range is superimposed with a
contribution of CO$_{2}$. Then, the epsilon of this band associated
with water is fitted to obtain an experimental molar fraction of water
calculated from the experimental water and CO$_{2}$ concentration, that
is consistent with the molar fraction in the literature~\cite{19,20}.
As shown in the {Figure~\ref{fig3}}, a good fit is obtained in the
whole temperature and pressure range specific to this study when a unique epsilon
value of water is used and found to be equal to 
140~L${\cdot}$mol$^{-1}{\cdot}$cm$^{-2}$. 
Thus, we have evaluated a relative uncertainty
of ${\pm}$5\% on the concentration measurements using our setup
and data processing methodology.

\begin{figure}
%\vspace*{-2pt}
\includegraphics{fig03}
%\vspace*{-2pt}
\caption{\label{fig3}Comparison of the molar fraction of CO$_{2}$ in
the CO$_{2}$-rich phase of H$_{2}$O--CO$_{2}$ mixtures calculated from
our infrared spectra with literature data.}
%\vspace*{-4pt}
\end{figure}

Finally, it is worth noting that if sorbitol is soluble in the CO$_{2}$-rich phase, one should observe a peak in the alkane region (in the
range 2800--3000 cm$^{-1}$) related to C--H stretching vibrations with
a detection limit of about
10$^{-4}$--10$^{-5}$\ $g_{\mathrm{sorbitol}}/g_{\mathrm{CO}_{2}}$. We
emphasize that the initial total amount of sorbitol is excessive
in comparison to the minimum amount of sorbitol that could be detected.

In a few experiments, the collision-induced IR spectral band of H$_{2}$
is also observed at about 4150~cm$^{-1}$ 
(see Figures~\ref{fig5} and~\ref{fig12} in the
results and discussion section). This band has been reported
previously for H$_{2}$ diluted in monoatomic gases under high pressure
conditions~\cite{21,22}. Indeed, as the H$_{2}$ stretching vibration is
inactive in IR spectroscopy, the observed H$_{2}$ spectrum in the
CO$_{2}$-rich phase is due to an induced dipole moment of the H$_{2}$
molecule that results from its interaction with the surrounding
CO$_{2}$ molecules. Therefore, the induced molar extinction coefficient
of the H$_{2}$ peak strongly depends on the temperature and 
pressure and precludes the use of this peak for quantitative 
analyses~\cite{23}.



\section{Results and discussion}

\subsection{H$_2$O--CO$_{2}$ binary system}

Preliminary studies are done in H$_2$O--CO$_{2}$ binary system 
to analyze the influence of water on the CO$_{2}$ concentration in
the CO$_{2}$-rich phase based on the pressure of CO$_{2}$ and 
temperature. Infrared spectra of the gas phase of the binary system are
illustrated in {Figure~\ref{fig2}} and has been described in 
earlier sections. Beer--Lambert law is applied to determine the evolution of the concentration
of CO$_{2}$ in the CO$_{2}$-rich phase of the H$_{2}$O--CO$_{2}$ binary
mixture and compare it with the concentration of neat CO$_{2}$ in the
same thermodynamic range from 40 to 220~\textdegree{}C at constant
CO$_{2}$ pressures (30, 60 and 120 bar as shown in {Figure~\ref{fig4}}).

\begin{figure}
\includegraphics{fig04}
\caption{\label{fig4}Temperature versus CO$_{2}$  concentration at
constant pressure in neat CO$_{2}$ and in the CO$_{2}$-rich phase of
the binary system H$_{2}$O--CO$_{2}$.}
\end{figure}

Looking initially at CO$_{2}$ alone ({Figure~\ref{fig4}}, dotted lines),
it can be inferred that the concentration of CO$_{2}$ gas decreases when the temperature rises.
This~effect is very pronounced at high pressure of 120~bar and less
marked at 60 and 30 bar. In the presence of water ({Figure~\ref{fig4}},
solid line), the same effect is observed but between 160 and
220~\textdegree{}C, the concentration of CO$_{2}$ decreases further.
This effect can be explained by two phenomena: as temperature 
increases, CO$_{2}$ dissolves in water and consequently, its concentration in
the gas phase decreases and concomitantly, water is ``evaporated'' in
the gas phase leading to a decrease in CO$_{2}$ concentration. Both
phenomena governing the mutual solubility of water and CO$_{2}$ are
consistent with data reported in the literature~\cite{19,20}.

\begin{figure*}
\includegraphics{fig05}
\caption{\label{fig5}Infrared spectra of the binary system
CO$_{2}$--H$_{2}$ at 90 bar from 40~\textdegree{}C to
220~\textdegree{}C.}
\end{figure*}

\subsection{CO$_2$--H$_2$ binary system}

The evolution of the infrared spectra of the binary mixture CO$_{2}$/H$_{2}$ 
(30 bar/60 bar) with temperature is elucidated in
{Figure~\ref{fig5}}. We emphasize that above the critical point of CO$_2$,
the binary mixture H$_{2}$/CO$_{2}$ displays only one gas phase as
previously reported in thermodynamic studies on H$_{2}$/CO$_{2}$
mixtures~\cite{24,25,26}. Interestingly, a barely detectable band at 4100 cm$^{-1}$ 
in neat H$_{2}$ is clearly observed after adding  CO$_{2}$ 
in the cell at 40~\textdegree{}C. Then, its intensity
decreases continuously as the temperature rises. This band is
assigned to the vibrational stretching mode (vibron) of H$_{2}$
interacting with surrounding CO$_{2}$ molecules and the effect of
CO$_{2}$ on this band has been discussed by
our group in a recent article~\cite{23}. As the intensity of this band is related to
``induced'' effects, it is not possible to accurately 
calculate the concentration of H$_{2}$ in the mixture.

However, in order to determine the effect of H$_{2}$ on the CO$_{2}$
concentration, we determined the evolution of the concentration of
CO$_{2}$ in the H$_{2}$--CO$_{2}$ binary mixture and compared it with the
concentration of neat CO$_{2}$ in the same thermodynamic range (from 40
to 220~\textdegree{}C) at constant pressures of CO$_{2}$ (30 and 60~bar)
as shown in Figure~\ref{fig6}. The concentration of CO$_{2}$ appears to
decrease at 60 bar of H$_{2}$ (yellow line in Figure~\ref{fig6}),
while at 30 bar (of H$_{2}$) negligible effect is observed (grey line
in Figure~\ref{fig6}). When the pressure of CO$_{2}$ is doubled from 30 to 60
bar while keeping the pressure of H$_{2}$ at 30 bar results in a weak decrease of the
concentration of CO$_{2}$ in comparison with neat CO$_{2}$ at low
temperature (below 120~\textdegree{}C). This effect could be attributed to the 
intermolecular interactions between H$_{2}$ and CO$_{2}$ as evidenced
by ``induced'' effects on the vibrational stretching mode of H$_{2}$.

\begin{figure}
\includegraphics{fig06}
\caption{\label{fig6}Temperature versus CO$_{2}$ concentration at
constant pressure in neat CO$_{2}$ and in the CO$_{2}$-rich phase of
the binary system CO$_{2}$--H$_{2}$.}
\end{figure}

\subsection{H$_2$O--CO$_2$--H$_2$ ternary system}

The binary system comprising CO$_{2}$ and H$_{2}$
is compared to the ternary system where water is added to the
high-pressure cell at a given pressure of H$_{2}$ and CO$_{2}$
({Figure~\ref{fig7}}). At temperatures below 150~\textdegree{}C,
concentration of CO$_{2}$ in the H$_{2}$/CO$_{2}$ binary mixture is
similar to that of the ternary mixture with water. However, at
temperatures above 150~\textdegree{}C, a significant decrease in 
CO$_{2}$ concentration is observed in the CO$_{2}$-rich phase of the
ternary mixture when compared to CO$_{2}$-rich phase of the binary system \mbox{CO$_{2}$--H$_{2}$.}

\begin{figure}
\includegraphics{fig07}
\caption{\label{fig7}Temperature {versus}  CO$_{2}$
concentration at constant pressure in the CO$_{2}$-rich phase of the
binary (CO$_{2}$--H$_{2}$) and ternary 
(H$_{2}$O--CO$_{2}$--H$_{2}$) systems.}
\end{figure}

To determine if the
presence of H$_{2}$ has a significant effect on the solvation of water
in the gas phase, for a given ratio H$_{2}$/CO$_{2}$ (see {Figure~\ref{fig8}}), the evolution
of water concentration according to the temperature for the binary
(H$_{2}$O--CO$_{2}$) system is compared with the ternary
system (H$_{2}$O--CO$_{2}$--H$_{2}$). First, the increase of the CO$_{2}$
pressure from 30 bar to 60 bar slightly increases the concentration of
water (dotted lines). For example, at a constant temperature of
200~\textdegree{}C, the \mbox{water} concentration in the vapor phase is 
0.36~mol${\cdot}$L$^{-1}$ and 0.41 mol${\cdot}$L$^{-1}$ for 30 bar and 60 bar of
CO$_{2}$, respectively. When H$_{2}$ is added to the system
(full lines), negligible effect is seen when 30 bar of
CO$_{2}$ mixes with 30 bar of H$_{2}$ (yellow line). However,
in the system comprising 60 bar of CO$_{2}$, the addition of 30 bar of
H$_{2}$ leads to a slight decrease of the solubility water in the
CO$_{2}$ phase (orange lines) and is similar to
that measured with 30 bar of CO$_{2}$. Thus, the lower solubility of
water in the CO$_{2}$ phase in the presence of H$_{2}$ could be due to
the lower CO$_{2}$ concentration in the CO$_{2}$ phase as shown for the
binary system CO$_{2}$--H$_{2}$ (cf.\ {Figure~\ref{fig7}}) as well as to
the fact that H$_{2}$ is a highly hydrophobic molecule that is expected
to limit the solubility of water in the CO$_{2}$ phase. 

\begin{figure}
\includegraphics{fig08}
{\vspace*{-2pt}}
\caption{\label{fig8}Temperature versus H$_{2}$O concentration at
constant pressure in the CO$_{2}$-rich phase of the binary 
(H$_{2}$O--CO$_{2}$) and ternary (H$_{2}$O--CO$_{2}$--H$_{2}$) systems.}
{\vspace*{-2pt}}
\end{figure}

\subsection{H$_2$O--sorbitol--CO$_2$ ternary system}

{Figure~\ref{fig9}} displays the infrared spectra of the gas phase of
a ternary system, an aqueous solution of 30 wt\% of
sorbitol under CO$_{2}$ pressure. It is worth noting that the
evolution of the profiles is similar to that observed when the
temperature is increased in H$_{2}$O--CO$_{2}$ binary system (cf.\ 
{Figure~\ref{fig2}}). This suggests that sorbitol is not detected in
the CO$_{2}$-rich phase (under our detection limit of 10$^{-4}$--10$^{-5}$\ $g_{\mathrm{sorbitol}}$/$g_{\mathrm{CO}_2}$) as we
have not observed any new peaks related to sorbitol 
between 2900~cm$^{-1}$ and 1100 cm$^{-1}$.

\begin{figure*}
{\vspace*{-2pt}}
\includegraphics{fig09}
{\vspace*{-2pt}}
\caption{\label{fig9}Infrared spectra of the CO$_{2}$-rich phase of the
ternary system H$_{2}$O--sorbitol--CO$_{2}$ at 60 bar from
40~\textdegree{}C to 220~\textdegree{}C.}
{\vspace*{-2pt}}
\end{figure*}

The CO$_{2}$ concentration in the CO$_{2}$-rich phase of the
H$_{2}$O--sorbitol--CO$_{2}$ ternary mixture is compared to that of the
H$_{2}$O--CO$_{2}$ binary system ({Figure~\ref{fig10}}). No 
significant difference in the CO$_{2}$ concentration was seen at 30 or 60 bar of CO$_{2}$. However, at a
higher CO$_{2}$ pressure of 120 bar, the concentration of CO$_{2}$
slightly increases (green, full line) when sorbitol is added to water.
It can be inferred that the presence of sorbitol in water has no effect on the
CO$_{2}$ concentration in the gas phase at low CO$_{2}$ pressures and higher pressure of 120 bar, sorbitol modifies the
water--CO$_{2}$ equilibrium.\looseness=-1

\begin{figure}
\includegraphics{fig10}
{\vspace*{-1pt}}
\caption{\label{fig10}Temperature {versus} CO$_{2}$
concentration at constant pressure in the CO$_{2}$-rich phase of the
binary (H$_{2}$O--CO$_{2}$) and ternary (sorbitol--H$_{2}$O--CO$_{2}$) systems.}
{\vspace*{-1pt}}
\end{figure}

In order to assess the modification of the water--CO$_{2}$ equilibrium
due to the presence of sorbitol in the aqueous phase, the evolution of the concentration of water in the CO$_{2}$-rich phase
for the H$_{2}$O--sorbitol--CO$_{2}$ ternary mixture with temperature is 
observed (see {Figure~\ref{fig11}}) and compared with the results obtained for the
H$_{2}$O--CO$_{2}$ binary system. As shown in
Figure~\ref{fig10}, no effect is seen at CO$_{2}$ pressure ${<}$ 60~bar, as the concentration of water in the CO$_{2}$-rich phase is
similar for the binary and ternary systems. However, at CO$_{2}$ pressure 
of 120 bar, the water concentration decreases from 0.3 mol${\cdot}$L$^{-1}$ to 
0.24~mol${\cdot}$L$^{-1}$ at 160~\textdegree{}C. Therefore, it
can be inferred that sorbitol prevents the solvation of water in the
CO$_{2}$-rich phase by ``keeping'' water in the liquid phase and
leads to a higher concentration of CO$_{2}$ in the
CO$_{2}$-rich phase. 

\begin{figure}
{\vspace*{2pt}}
\includegraphics{fig11}
{\vspace*{2pt}}
\caption{\label{fig11}Temperature versus H$_{2}$O concentration at
constant pressure in the CO$_{2}$-rich phase of the binary 
(H$_{2}$O--CO$_{2}$) and the ternary (sorbitol--H$_{2}$O--CO$_{2}$) systems.}
\end{figure}

\subsection{H$_{2}$O--sorbitol--CO$_{2}$--H$_{2}$ quaternary system}

{Figure~\ref{fig12}} shows the evolution of the infrared spectra in the
CO$_{2}$-rich phase as a function of temperature of the quaternary
system comprising an aqueous solution of 30 wt\% of sorbitol and the
mixture of CO$_{2}$ and H$_{2}$ gases. The ``induced'' peak of H$_{2}$
at 4150~cm$^{-1}$ is only observed at low temperatures. With
increase in temperature, the band of water increases and overlaps H$_{2}$ while the bands of CO$_{2}$ decrease. As seen in the ternary
system ({Figure~\ref{fig9})}, sorbitol is not detected in the
CO$_{2}$-rich phase.

\begin{figure*}
\includegraphics{fig12}
\caption{\label{fig12}Infrared spectra of the CO$_{2}$-rich phase of
the quaternary system H$_{2}$O--sorbitol--CO$_{2}$--H$_{2}$ at 90~bar at temperatures from
40~\textdegree{}C to 220~\textdegree{}C.}
\end{figure*}

In Figure~\ref{fig13}, the concentration of CO$_{2}$ in the CO$_{2}$-rich phase for the quaternary mixture is compared with the ternary system H$_{2}$O--CO$_{2}$--H$_{2}$. It appears that at the
pressure range investigated (corresponds to conditions used for the
catalytic reactions reported previously~\cite{8,10}), the addition of
sorbitol does not have a significant effect on the CO$_{2}$
concentration in the presence of H$_{2}$. 

\begin{figure}
\includegraphics{fig13}
\caption{\label{fig13}Temperature  {versus} CO$_{2}$
concentration at constant pressure in the CO$_{2}$-rich phase of the
ternary (H$_{2}$O--CO$_{2}$--H$_{2}$) and quaternary 
(H$_{2}$O--sorbitol--CO$_{2}$--H$_{2}$) systems.}
\end{figure}

By the same token, the quaternary system is compared to the ternary
system H$_{2}$O--sorbitol--CO$_{2}$ to study the effect of H$_{2}$ on
water concentration in the CO$_{2}$-rich phase (cf.\ 
{Figure~\ref{fig14}}). Almost no effect is observed, which is
consistent with the results reported in {Figure~\ref{fig13}.}

\begin{figure}
{\vspace*{-1pt}}
\includegraphics{fig14}
{\vspace*{-1pt}}
\caption{\label{fig14}Temperature  versus H$_{2}$O concentration at
constant pressure and increasing temperature in the
CO$_{2}$-rich phase of the ternary (H$_{2}$O--sorbitol--CO$_{2}$)
and quaternary  (H$_{2}$O--sorbitol--CO$_{2}$--H$_{2}$) systems.}
{\vspace*{-1pt}}
\end{figure}

Therefore, at the pressure and temperature range investigated where
two distinct water-rich and CO$_{2}$-rich phase are observed, the
presence of sorbitol in the water-rich phase and H$_{2}$ in the
CO$_{2}$-rich phase have a limited impact on the mutual solubility of
water and CO$_{2}$.

\section{Conclusion}

The aim of this paper was to investigate, using {in situ}
infrared spectroscopy, the thermodynamic behavior of the
H$_{2}$O--sorbitol--CO$_{2}$--H$_{2}$ system which is involved in the one-pot 
catalytic reaction for hydrogenation of glucose to sorbitol and
the acid-catalyzed dehydration of sorbitol by CO$_{2}$~\cite{8,10}. 
Specifically, our study focused on the gas phase of
binary, ternary and quaternary mixtures and selected vibrational modes
of CO$_{2}$ and H$_{2}$O that have been analyzed in order to determine
the evolution of the H$_{2}$O and CO$_{2}$ concentrations as a function
of the temperature and pressure.

At a given pressure of CO$_{2}$, with increasing temperature, the 
concentration of water in the gas phase increases with
a concomitant decrease of the CO$_{2}$ concentration when compared with
neat CO$_{2}$. Addition of H$_{2}$ at a pressure of 30 bar to 
H$_{2}$O/CO$_{2}$ binary system lowered the concentration of both CO$_{2}$ and
water in the gas phase. On the other hand, the addition of
sorbitol to water appears to prevent the mutual solubility of CO$_{2}$
and water, an effect that is significant only at
high CO$_{2}$ pressure (120 bar) investigated in this study.

Finally, the purpose of these thermodynamic measurements was to
determine whether sorbitol, present in the liquid water phase at high
temperature, could dissolve in the gas phase and reduce the sugar
concentration in water, thus affecting the catalytic reactions
mentioned earlier. However, an inverse relationship was observed, where
both sorbitol and H$_{2}$ limited the water solubility
in the gas phase to some extent. Therefore, we confirm that under our experimental
conditions ($T< 220$~\textdegree{}C and $P< 120$ bar), the ternary and
quaternary mixtures display two distinct phases, sorbitol/water-rich
liquid and CO$_{2}$/H$_{2}$-rich gas phase, both reactions of
hydrogenation and dehydration taking place in the liquid phase.

\section*{Declaration of interests}

The authors do not work for, advise, own shares in, or receive funds
from any organization that could benefit from this article, and have
declared no affiliations other than their research organizations.

\section*{Funding}

The authors acknowledge the Region Nouvelle Aquitaine and the
University of Poitiers for their financial support (funding of the PhD
of IB). The authors are also grateful to the program ``Instrumentation
in situ en conditions extr\^{e}mes'' of the MITI of CNRS {for 
financial support towards infrared and Raman equipment,} the INCREASE
Federation and the GDR 2035 SolvATE.

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