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\DOI{10.5802/crchim.300}
\datereceived{2023-11-01}
\daterevised{2023-12-08}
\dateaccepted{2024-02-09}
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\dateposted{2024-04-22}
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%\def\cdr@specialtitle@english{GDR-SolvATE}
%%\def\cdr@specialtitle@french{GDR SolvATE}
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\CDRsetmeta{articletype}{research-article}

\title{How NaCl addition destabilizes ionic liquid micellar suspension
until phase separation}

\alttitle{Comment l'ajout de NaCl d\'estabilise une suspension
micellaire de liquide ionique jusqu'\`a la s\'eparation de phase}

\author{\firstname{Jean-Fran\c{c}ois} \lastname{Dufr\^eche}\CDRorcid{0000-0001-8422-3639}}
\address{ICSM, Univ Montpellier, CEA, CNRS, ENSCM, Bagnols-sur-C\`eze, France}
\email[J.-F. Dufr\^eche]{jean-francois.dufreche@icsm.fr}

\author{\firstname{Marie} \lastname{Plazanet}\CDRorcid{0000-0002-7041-8299}\IsCorresp}
\address{Laboratoire Interdisciplinaire de Physique, LIPhy, CNRS \& Univ. Grenoble-Alpes, Grenoble, France}
\email[M. Plazanet]{marie.plazanet@univ-grenoble-alpes.fr}

\author{\firstname{Gautier} \lastname{Meyer}}
\addressSameAs{2}{Laboratoire Interdisciplinaire de Physique, LIPhy, CNRS \& Univ. Grenoble-Alpes, Grenoble, France}
\email[G. Meyer]{gautier.meyer@univ-grenoble-alpes.fr}

\author{\firstname{Isabelle} \lastname{Billard}\CDRorcid{0000-0002-2842-7706}}
\address{Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, Grenoble INP, LEPMI, 38000 Grenoble, France}
\email[I. Billard]{isabelle.billard@grenoble-inp.fr}

\keywords{\kwd{Aqueous biphasic solution}
\kwd{Extraction}
\kwd{Ionic liquid}
\kwd{Regulation charge theory}}

\altkeywords{\kwd{Syst\`eme biphasique aqueux}
\kwd{extraction}
\kwd{liquide ionique}
\kwd{th\'eorie de la r\'egulation de charge}}

\thanks{French National Agency for Research (Grant No.
ANR-ITALLIX-22-CE29-0023-01)}

\shortrunauthors

\begin{abstract}
The ionic liquid tributyltetradecylphosphonium chloride
([P\textsubscript{4,4,4,14}]Cl) forms micelles in water, with a very low CMC,
below 1~wt\%. The solution is macroscopically homogeneous, even large
amounts of [P\textsubscript{4,4,4,14}]Cl in water do not induce any phase
separation. The ternary system [P\textsubscript{4,4,4,14}]Cl/NaCl/H\textsubscript{2}O instead
displays a LCST (Lower Critical Separation Temperature) behavior, being
monophasic at low \textit{T} and experiencing phase separation when \textit{T} is
increased. This phenomenon has been ascribed to the \textit{T}-increased
adsorption onto the micellar surface of these additional chloride ions.
The lowering of the repulsive interactions between micelles finally
allows coalescence and thus phase separation.  In this work, we explore
the impact of NaCl addition onto the phase separation, at fixed \textit{T}.
Specific chloride electrode allows the determination of chloride
counterion adsorption for different samples in the phase diagram, all
of them being single-phase. A simple theory based on the
Poisson--Boltzmann equation and with charge regulation is proposed. The
only fitted parameter is the chloride adsorption constant. It enables
to model the different populations of ions in the solution and at the
micelle surface in different conditions. Considering the effective
charge of the micelles with respect to the ionic strength of the
solution, it moreover provides a key element in the prediction of phase
separation.
\end{abstract}

\begin{altabstract}
Le liquide ionique chlorure tributylt\'etrad\'ecylphosphonium
([P\textsubscript{4,4,4,14}]Cl) forme des micelles dans l'eau, avec une concentration
micellaire critique tr\`es faible, inf\'erieure \`a 1~wt\%. La solution
est macroscopiquement homog\`ene, m\^eme de larges fractions de
[P\textsubscript{4,4,4,14}]Cl dans l'eau n'induisent pas de s\'eparation de phases. Le
syst\`eme ternaire [P\textsubscript{4,4,4,14}]Cl/NaCl/H\textsubscript{2}O, par contre, pr\'esente une
LCST (Lower Critical Separation Temperature), \'etant monophasique \`a
temp\'erature ambiante et subissant une s\'eparation de phase lorsque
la temp\'erature augmente. Ce ph\'enom\`ene a \'et\'e attribu\'e \`a
l'adsorption accrue par la temp\'erature des ions chlorure sur la
surface des micelles, diminuant ainsi les interactions r\'epulsives
entre les micelles, permettant finalement la coalescence et donc la
s\'eparation de phase. Dans ce travail, nous explorons l'impact de
l'ajout de NaCl sur la s\'eparation de phase, \`a  \textit{T} constante. Une
\'electrode sp\'ecifique au chlorure permet de caract\'eriser
l'adsorption du contre-ion chlorure pour diff\'erents \'echantillons
dans le diagramme de phase, tous \'etant monophasiques. Une th\'eorie
simple bas\'ee sur l'\'equation de Poisson--Boltzmann et une
r\'egulation de charge est propos\'ee. Le seul param\`etre ajustable
est la constante d'adsorption des chlorures. Cette th\'eorie permet de
mod\'eliser les diff\'erentes populations d'ions dans la solution et \`a 
la surface de la micelle dans diff\'erentes conditions. Compte tenu de
la charge effective des micelles par rapport \`a la force ionique de la
solution, elle fournit en outre un \'el\'ement cl\'e dans la
pr\'ediction de la s\'eparation de phase.
\end{altabstract}

\maketitle
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\section{Introduction}\label{sec1}

Aqueous biphasic systems (ABS) recently deserve a lot of attention
thanks to their \mbox{environmental} friendly composition, with a large 
water  content. They have been investigated for multiple extraction purposes
in order to substitute the use of traditional highly polluting organic
solvents~\cite{Gonzalez-Valdez2018,karmakar2019}. Among ABS, the family
comprising  the ionic liquid (IL) tributyltetradecylphosphonium
chloride ([P$_{4,4,4,14}$]Cl) mixed with water and a strong acid has
been proposed for metallic ion extraction~\cite{Gras2018-angew,
Schaeffer2019, CARREIRA2022}. Metallic ions have preferential phases,
as for example Co(II) prefers the \mbox{upper,} ionic liquid-rich phase while
Ni(II) prefers the lower highly acid solution.~Beside the interest in
metal extraction, these ternary systems are surprising with a very rich
phase diagram, either in presence of a strong acid or a salt (for
example, HCl or NaCl). The solutions are thermomorphic, i.e.\ reversibly
change from a monophasic to a biphasic liquid state with temperature,
and with the particularity to separate upon an increase of temperature,
meaning that the biphasic region of the phase diagram increases with
temperature, therefore also having a \textit{Lower Solution Critical
Temperature} (LCST). The mono- or biphasic states are related to the
composition and, at any fixed temperature, the increase of both IL or
salt/acid content triggers the phase separation. The metallic ions
extracted will therefore play themselves a determinant role in their
own extraction~\cite{Dupont2015, Sinoimeri2023, Sinoimeri2020}.
Understanding the mechanisms of phase separation in such family of
systems is therefore a challenging task that we partially address in
this paper. Our previous investigation~\cite{Meyer2022} was focused on
the structural organization of the acidic (HCl, H$_{2}$SO$_{4}$)
solutions with concentration and temperature. We highlighted that the
IL [P$_{4,4,4,14}$]Cl, which could be assimilated to a cationic
surfactant, forms spherical micelles in solution. Upon temperature
rise, the micelles aggregate until eventually causing the phase
separation. The aggregation is due to an adsorption of chloride ions at
the micelles surface with temperature, as proved by the titration of
free chloride ions in solution: the adsorption of ions causes a
variation in the Electric Double Layer (EDL) composition around the
micelles and a screening of electrostatic repulsion bewteen micelles.
Our previous structural investigation also shows an aggregation of the
micelles when the acid content increases. Here, we question the
similarity of the phase separation with temperature and salt
concentration in the system. Using the former chloride titration
technique at fixed temperature but variable salt content, we aim at
rationalizing the electrostatic interactions responsible for the state
of the solution. After describing the experimental methods, we present
the experimental results: the investigated points are presented in the
Figure~\ref{fig:figure1} on the phase diagram of the particular
solution investigated here: [P$_{4,4,4,14}$]Cl, NaCl and water. We then
detail the theoretical approach based on a classical charge regulation
theory to model the results. We eventually discuss the validity and
limits of the model.

\begin{figure}
\includegraphics{fig01}
\caption{Binodal curve of the system [P$_{4,4,4,14}$]Cl, NaCl and
water, and points investigated by chloride titration. Binodal data
(black squares) from~\cite{Schaeffer2018}. The three
series of points correspond to the following IL wt\%: 8.12 (blue
squares), 14.55 (red circles) and 20.48\% (green triangles).
\label{fig:figure1}}
\end{figure}

\section{Materials and methods}

\subsection{Chemicals}
Tributyltetradecylphosphonium chloride
([P$_{4,4,4,14}$]Cl) has been provided by Interchim, while NaCl was
purchased from Honeywell. All chemicals were used as received. All
samples were made using ultra-pure water (Millipore system, 18~M$\Omega$).

\subsection{Samples} Desired amounts of NaCl and of a concentrated aqueous
solution of [P$_{4,4,4,14}$]Cl were weighted in a {10~mL}  gauged flask
and then ultra-pure water was added to the line. The composition of all
the samples can be found in the ESI.

\subsection{Apparatuses and methods}
A balance (Fisherbrand, Analytical
Series,  precision 0.0001 g) was used to prepare the samples. Free
chloride ions concentration (M) was determined by use of a chloride
specific electrode (ThermoScientific,  chloride half cell Orion 9417SC
and reference cell), which was calibrated by seven standard aqueous
solutions of NaCl with concentrations ranging from $6\times 10^{-3}$~M to 
$1.1~\mathrm{mol}{\cdot}\mathrm{L}^{-1}$. The calibration was found
linear with very good regression parameter and under the experimental
procedure followed, reproducibility is within ${\pm} 2\%$. For both
calibration and measurement of the samples, temperature was controlled
at $T = (25 \pm 0.5)$~\textdegree C~by a thermostated bath. Densities
at $T = 25$~\textdegree C~were measured by use of a density-meter
(Anton-Paar, DMA 4001, precision
$10^{-4}~\mathrm{g}{\cdot}\mathrm{cm}^{-3}$). Concentrations in moles per
liter (M) were calculated from the weighted masses and flask volume
while NaCl and [P$_{4,4,4,14}$]Cl wt\% were calculated from added
masses, density and flask volume. Samples are sorted within three
series, for which a fixed mass of IL is mixed with increasing amounts
of NaCl. To label the series, we use the IL wt\% in the absence of
NaCl, i.e.\ 8.12/14.55/20.48 wt\% of IL. This corresponds respectively
to 0.185, 0.329 and $0.462~\mathrm{mol}{\cdot}\mathrm{L}^{-1}$. 

The binodal data obtained by Schaeffer \etal~\cite{Schaeffer2018} have
been obtained with Iolitech as the IL provider, while our samples are
prepared with an Interchim batch of IL. Nevertheless, both data sets
agree very well in terms of monophasic domain (see
Figure~\ref{fig:figure1}). In addition, we prepared one sample
supposedly being biphasic and very close to the binodal, according to
the data by Schaeffer \etal~and it actually appears to be biphasic (see
ESI).

\section{Experimental results}

In the Figure~\ref{fig:figure2} are plotted the experimental
measurements of the chloride concentrations in the solutions. 
{The first point of each experimental series corresponds
to the case without any addition of NaCl and the horizontal lines are
the experimental averages of each series. The line $x = y$ would be the
behavior without any adsorption at the micelle surface (see caption).}
The chloride specific electrode is sensitive to the chemical potential
of the ion, which is converted directly into the equivalent
concentration of chloride ion in an aqueous electrolyte solution in
equilibrium with the system. By neglecting the activity coefficient
corrections, which are relatively small in this chloride concentration
range~\cite{Lobo}, one can consider that this quantity corresponds to
the bulk free chloride ion concentration $[\mathrm{Cl}^-]_{\mathrm{free}}$,
{i.e.}\ the $\mathrm{Cl}^-$ concentration far away from the micelles. The
quantity of chlorides adsorbed at the micelle surface is therefore
equal to
$[\mathrm{Cl}^-]_{\mathrm{ads}}=[\mathrm{Cl}^-]_{\mathrm{tot}}
-[\mathrm{Cl}^-]_{\mathrm{free}}$. The data
are presented up to the limit of linearity of the electrode, that does
not allow a reliable measurement of the region too close to the binodal
line. For this reason, more points are plotted in the
Figure~\ref{fig:figure1} than in the Figure~\ref{fig:figure2}.  

\begin{figure}
\includegraphics{fig02}
\caption{Chloride titration for three different ionic liquid contents,
as a function of total amount (in $\mathrm{mol}{\cdot}\mathrm{L}^{-1}$) 
of chloride. The
$[\mathrm{Cl}^-]_{\mathrm{free}}$ are directly measured and the
$[\mathrm{Cl}^-]_{\mathrm{ads}}$ are deduced from the measurement by
the relation $[\mathrm{Cl}^-]_{\mathrm{tot}}=[\mathrm{Cl}^-]
_{\mathrm{ads}}+[\mathrm{Cl}^-]_{\mathrm{free}}$. The line $x = y$
would be the behavior without any adsorption at the micelle surface.
\label{fig:figure2}}
\end{figure}

As observed in the Figure~\ref{fig:figure2}, without any addition of
NaCl, about 40\% of the $\mathrm{Cl}^-$ are free in the solution, whatever the
mass fraction of ionic liquid. {More precisely, the fraction of
adsorbed chloride at the surface follows the linear behaviour given by
the equation: $[\mathrm{Cl}^-]_{\mathrm{ads}}=0.39\cdot[\mathrm{LI}]
+0.071$, both concentration
in $\mathrm{mol}{\cdot}\mathrm{L}^{-1}$. The micelles therefore carry
an effective charge for any fraction of IL. This result is consistent
with the structural characterization of the binary mixture (IL ${+}$
water)~\cite{Meyer2022}, where a strong correlation peak between
micelles is observed, arising from the electrostatic repulsion between
the objects in solution in absence of additional charges.} Upon
addition of NaCl, the adsorbed quantity of chloride is constant, all
the ions are dispersed into the solution, in opposition to what is
observed with temperature.

\section{Theory}

As previously expressed, we consider that the quantity measured by the
electrode corresponds to the bulk free chloride ion concentration far
away from the micelles, where the aqueous solution plays the role of a
reservoir. The measurement can therefore be used to establish a link
between the total concentration of introduced chlorides
$[\mathrm{Cl}^-]_{\mathrm{tot}}$ and $[\mathrm{Cl}^-]_{\mathrm{free}}$.

This result can then be compared with those obtained using an
Electrical Double Layer (EDL) model with charge regulation. The total
chloride concentration reads
{\begin{equation}
[{\mathrm{Cl}}^-]_{\mathrm{tot}}= [{\mathrm{Cl}}^-]_{\chi}
+ [{\mathrm{Cl}}^-]_{\mathrm{EDL}}+ [{\mathrm{Cl}}^-]_{{\infty}}
\label{eq3}
\end{equation}}\unskip
where $[{\mathrm{Cl}}^-]_{\chi}$ represents the concentration of the ions
that are specifically bound to the surface, on particular adsorption
sites. $[{\mathrm{Cl}}^-]_{\mathrm{EDL}}$ is the excess concentration of
chlorides in the electrical double layer. This corresponds to the ions
electrostatically bound to the surface, beyond the Stern layer
represented by  $[{\mathrm{Cl}}^-]_{\chi}$.
$[{\mathrm{Cl}}^-]_{{\infty}}$ is the global concentration of the
free ions far away from the micelle. It is not exactly equal to the
reservoir concentration $[\mathrm{Cl}^-]_{\mathrm{free}}$ because the free
ions cannot penetrate the micelles.

The mass action law for the equilibrium between free ions and ions
bound specifically to the surface reads as follows:
{\begin{equation}
\rho^S_\chi= K\text{\textdegree}  C_0 {\mathrm{e}}^{\frac{e \psi_S}{k_{\mathrm{B}T}}}
\end{equation}}\unskip
$\rho^S_\chi$ is the area number density ({i.e.}\ the number of
bound ions per unit area).  $e$ is the elementary charge,
$k_{\mathrm{B}}T$ is the thermal energy and $\psi_S$ is the electrostatic
potential at the micelle surface. $K$\textdegree~is the mass action law
constant of the adsorption reaction.  $C_0=
[{\mathrm{Cl}}^-]_{\mathrm{free}}$ is the chloride concentration in the
reservoir where the electrostatic potential $\psi_S=0$.  We consider 
the regime~\cite{Jardat09} of strong electrostatic screening for which
$\kappa R >1$ where $R$ is the micelle radius and $\kappa$ the Debye
parameter. If $R \approx 2$~nm, this corresponds to the case where the
salt concentration is greater than $2\times
10^{-2}~\mathrm{mol}{\cdot}\mathrm{L}^{-1}$.  In this regime the
interface is almost flat compared to the Debye distance. Thus the
Gouy--Chapman solution of the Poisson--Boltzmann equation can be used.

The SI practical unit of the mass action law constant $K$\textdegree~is
meter if the reservoir salt concentration $C_0=
[{\mathrm{Cl}}^-]_{\mathrm{free}}$ is the volume number density ({i.e.}\ 
the number of electrolyte per unit volume). The effective charge of the
micelles is then:
{\begin{equation}
\sigma^{\mathrm{eff}} = \sigma - e  
K\text{\textdegree} C_0 {\mathrm{e}}^{\frac{e \psi_S} 
{k_{\mathrm{B}}T}}
\label{eq1}
\end{equation}}\unskip
with $\sigma$ the bare charge. The diffusive part of the EDL is
modelled by the Poisson--Boltzmann equation. Thus the effective charge
can also be calculated thanks to the Grahame equation:
{\begin{equation}
\sigma^{\mathrm{eff}} = \sqrt{8 \epsilon_0 \epsilon_r 
k_{\mathrm{B}}T C_0 } \sinh{\left( \frac{e \psi_S}
{2k_{\mathrm{B}}T }  \right)}
\label{eq2}
\end{equation}}\unskip
$\epsilon_0 \epsilon_r=\epsilon$ is the permittivity of water. The two
equations (\ref{eq1}) and (\ref{eq2}) have to be solved numerically to
obtain $\sigma^{\mathrm{eff}}$ and $\psi_S$. We finally obtain from this
self-consistent calculation:
{\begin{equation}
\rho^S_\chi= \frac{\sigma - \sigma^{\mathrm{eff}} }{e}
\end{equation}}\unskip

Then we calculate the chloride excess in the EDL. Considering the
Gouy--Chapmann equation~\cite{Lyklema} yielding the anion concentration
$C_{-}(x)$ as a function of the position $x$ with respect to the
surface, we obtain the excess chloride area number density
{\begin{equation}
\rho^S_{\mathrm{EDL}}=\int_0^{+\infty} (C_-(x)-C_0) 
\, \mathrm{d}x=\frac{4AC_0}{(1-A)\kappa}
\end{equation}}\unskip
with $A=\tanh{\sofrac{e\psi_S}{4k_{\mathrm{B}}T }}$ and the Debye parameter
$\kappa= \sofrac{2e^2C_0}{\epsilon_0 \epsilon_r k_{\mathrm{B}}T}^{1/2}$. 

These area number densities $\rho^S_\chi$ and  $\rho^S_{\mathrm{EDL}}$
must then be transformed into volume number densities to obtain the
total experimental concentration $[{\mathrm{Cl}}^-]_{\mathrm{tot}}$. So
multiplying by the specific surface area of the micelles 
$S_V^{\mathrm{mic}}$, we finally obtain from (\ref{eq3}):
{\begin{equation}
[{\mathrm{Cl}}^-]_{\mathrm{tot}}=  S_V^{\mathrm{mic}}  
\left( \rho^S_\chi +   \rho^S_{\mathrm{EDL}}\right) +(1-\eta) C_0 
\end{equation}}\unskip
where $\eta$ is the volume fraction of the micelles supposed to be
spherical. Here are the model parameters we used. Scattering
experiments~\cite{Meyer2022} allow us to specify the radius of the
micelles $R=18$~\AA, the aggregation number $N_{\mathrm{agg}}=30$. The
resulting volume fractions $\eta$ for the three series are 9.1, 16.1
and 22.7\% and the resulting  surface charge density is
$\sigma=eN_{\mathrm{agg}}/ 4\uppi R^2=0.737~\mathrm{e}
{\cdot}\mathrm{nm}^{-2}$. The only
unknown parameter in the model is therefore the adsorption constant
$K$\textdegree. This value has been fitted from the experimental curve at
the lower IL concentration (8.16~wt\%). We obtained
$K\text{\textdegree}=1$~nm. The other curves are therefore true
predictions, since they were calculated without any adjustable
parameters. 

In the Figure~\ref{fig:figure3}, we inverted the axes in order to stick
to the experimental observables. Despite the simplicity of the model we
have a quantitative agreement with the data for the range of chloride
and ionic liquid concentrations investigated, although some deviations
are observed and discussed below.

\begin{figure}
\includegraphics{fig03}
\caption{Free chloride in the solution ({i.e.}\ chloride concentration
in the reservoir) as a function of total amount of chloride in the
systems, as measured by titration and computed, for the three sets of
samples (different colors/symbols). \label{fig:figure3}}
\end{figure}
 
\section{Discussion}

The Figure~\ref{fig:figure4} enables to analyse the different chloride
populations. When no salt (NaCl) is added to the solution, the
reservoir salt concentration $C_0= [{\mathrm{Cl}}^-]_{\mathrm{free}}$ is
0. In this limit the model is not rigorously valid for two reasons.
First, as long as the salt concentration is less than
$2\times 10^{-2}~\mathrm{mol}{\cdot}\mathrm{L}^{-1}$, the strong
electrostatic screening regime is not reached. Second we neglected the
critical micellar concentration (cmc) and the concentration of free IL
in solution. The cmc of [P$_{4,4,4,14}$]Cl was evaluated from the
variation of the surface tension as a function of IL wt\% in aqueous
mixture, measured by pending drop method (see SI). It was found to be
equal to $0.05 \pm 0.02$~wt\%, and drops consequently (${<}0.02$~wt\%) when
acid or salt is added to the solution. There is therefore a proportion
of free chloride not taken into account by the model for these two
effects for low salt concentration $C_0=
[{\mathrm{Cl}}^-]_{\mathrm{free}}$, as shown in Figure~\ref{fig:figure3}.

\begin{figure}
\includegraphics{fig04}
\caption{Different chloride populations (colors/groups) for three
solutions of various IL mass fraction (full, dashed and dotted lines)
as function of the free chloride in the solution (chloride
concentration in the reservoir). \label{fig:figure4}}
\end{figure}

Adding more chloride into the solution, therefore having more chloride
into the reservoir, leads to a slight increase of the bounded ions
while the concentration into the EDL decreases. For a reservoir
concentration of $1.25~\mathrm{mol}{\cdot}\mathrm{L}^{-1}$, the EDL
concentration $ [{\mathrm{Cl}}^-]_{\mathrm{EDL}}$ even becomes negative.
$ [{\mathrm{Cl}}^-]_{\mathrm{EDL}}$ is actually an excess term with
respect to bulk concentration. This means that above this limit,
adsorption onto the surface is strong enough so that it reverses the
surface charge, which becomes negative. {We note that in absence of
well-defined adsorption sites, there is no chemical saturation of the
surface. Adsorption is therefore not limited and inversion is
possible.} In practice, this means that the electrostatic repulsion
between micelles breaks down. The system can then become destabilised
because the attractions due to Van der Waals forces are no longer
counterbalanced by electrostatic forces. Phase separation is then
possible. This is precisely what happens experimentally. Despite its
simplicity, the model allows us to represent the destabilisation
mechanism of the solutions and the appearance of this phase separation.
At some chloride addition, the effective charge of the micelles becomes
very small, leading to a complete screening of the electrostatic
repulsion between the objects and therefore a flocculation of the
micelles followed by the phase separation.

This effect is due to the increase in $[\mathrm{Cl}^-]_{\chi}$ population.
Although the increase in $[\mathrm{Cl}^-]_{\chi}$ population in the
Figure~\ref{fig:figure4} is fairly small, it is enough to neutralise
the charge on the micelles. Because of the high charge of the micelles
due to their high aggregation number, adsorption is already high in the
absence of salt, even if the $K$\textdegree~constant is low. The addition
of chloride further increases this phenomenon and the charge is
eventually reversed.

We eventually examined the influence of the bounding constant
$K$\textdegree. The Figure~\ref{fig:figure5} shows the effect of varying the
binding constant between 0.5 and 10 on the solution at 8.6~wt\% of IL.
The figure is understandable if we remember that
$[\mathrm{Cl}^-]_{\mathrm{free}}=C_0$ is the concentration of chloride in an
electrolyte solution in equilibrium with the system. Thus the free ions
far from the micelles $[{\mathrm{Cl}}^-]_{\infty}$ are directly
proportional to it and do not depend on the adsorption constant which
only controls the adsorbed ${\mathrm{Cl}}^-$ and the ions in the Debye
EDL. Overall, an increase in $K$\textdegree~logically increases chloride
ions adsorption. This then reduces the counter-ions concentration and
the co-ion depletion in the EDL: the effective charge being lower,
fewer counter-ions are needed to screen the micelles and the repulsive
force on cations is\break weaker.

\begin{figure}
\includegraphics{fig05}
\caption{Different chloride populations (colors/groups) for the the
20.65 wt\% IL solution as functions of the free chloride in the
solution (chloride concentration in the reservoir). The values are
given for different binding constants $K$\textdegree~(full, dashed, dotted
or dash-dotted lines). \label{fig:figure5}}
\end{figure}

We first remark that increasing the value of $K$\textdegree~indeed increases
the slope of $[{\mathrm{Cl}}^-]_{\chi}$ with the chloride reservoir
concentration, as previously mentioned. But the main effect is that
increasing the binding constant will increase $[{\mathrm{Cl}}^-]_{\chi}$,
reducing the effective potential at the micelle surface, therefore
shifting to lower concentration the EDL and the term
$[{\mathrm{Cl}}^-]_{\mathrm{EDL}}$. This leads to the effective charge of
the micelle to be screened at lower NaCl addition, then the phase
separation to be induced at lower NaCl or acid content. This behaviour
is exactly what is observed upon increase of temperature, where the
free \mbox{chloride} \mbox{concentration} decreases with temperature until phase
separation. The higher is the temperature, the lower the salt (or acid)
addition needed to observe the phase separation. The increase of
temperature can therefore be modelled by an increase of $K$\textdegree.
All this means that the adsorption reaction is favoured at high
temperature and is therefore endothermic. It is this phenomenon that
allows us to understand why this system shows a \textit{Lower Solution
Critical Temperature} (LCST). Eventually, we could assume that if
$K$\textdegree~increases enough, i.e.\ at high enough temperature, the
charge inversion of the micelles could lead to repulsion again and the
system would turn homogeneous again upon NaCl addition. This was
however never tested experimentally, since the solubility of NaCl
limits the phase\break diagram.



\section{Conclusion}

The aqueous biphasic systems formed by the mixture of the ionic liquid
[P$_{4,4,4,14}$]Cl with salt or acid present a strong interest from a
fundamental as well as potential application point of view. The phase
diagram is complex, with self aggregation and organisation varying with
the addition of charges and temperature in different ways. Following a
detailed structural investigation of acidic solutions with temperature
and an insight into the phase transition mechanisms upon heating, we
complete here our rationalisation of electrostatic effects. We propose
a simple still relevant charge regulation model to describe the
electrical double layer and screening of electrostatic interactions in
the solution with addition of ions. The only fitted parameter is the
binding constant taking into account the chemically or, in this case,
physically bound ions to the micelle surface. The model is not
rigorously valid at low salt concentration. Nevertheless, it provides a
qualitative but strong insight into the mechanisms at play between the
micelles upon addition of charges or increase of temperature, leading
to the phase separation.

This approach could therefore be the first step in describing the phase
diagram and thermodynamics of these complex systems, for which
electrolyte theory can explain their behaviour and in particular their
phase diagram. It would thus be possible to take into account more
complex geometries of aggregates ({e.g.}, beyond a spherical
organisation) or to look at the limit of weaker electrostatic screening
and the influence of the non-micellised part of the ionic liquid. A
model combining the DLVO approach and Hamaker's constant could thus
enable the full prediction of the phase diagram versus ions
concentration and temperature. Investigating the effect of salt versus
acid, H$^+$ versus Na$^+$ or other ions, will eventually lead to
another world of physical\break chemistry.

\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*{Dedication}

The manuscript was written through contributions of all authors. All
authors have given approval to the final version of the manuscript.

\section*{Funding}

This research was funded by the French National Agency for Research
(Grant No. ANR-ITALLIX-22-CE29-0023-01). A CC-BY public copyright
license has been applied by the authors to the present document and
will be applied to all subsequent versions up to the Author Accepted
Manuscript arising from this submission, in accordance with the
grant's open access conditions. \eject

\CDRGrant[ANR]{ANR-ITALLIX-22-CE29-0023-01}

\back{}

\section*{Supplementary data}
Supporting information for this article is available on the journal's
website under \printDOI\ or from the author.  

\CDRsupplementaryTwotypes{supplementary-material}{\cdrattach{crchim-300-suppl.pdf}}

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