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\DOI{10.5802/crchim.310}
\datereceived{2023-10-23}
\daterevised{2024-04-23}
\dateaccepted{2024-04-08}
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%\makeatletter
%\def\TITREspecial{\relax}
%\def\cdr@specialtitle@english{GDR Prom\'eth\'ee - French Research Network on \textit{Hydrometallurgical Processes for Primary and Secondary Resources}}
%\def\cdr@specialtitle@french{GDR Prom\'eth\'ee - Groupement de Recherche sur les Proc\'ed\'es Hydrom\'etallurgiques pour la Gestion Int\'egr\'ee des Ressources Primaires ...}
%\makeatother

\CDRsetmeta{articletype}{research-article}

\title{Solubilisation--microstructure relationship of trivalent salts
in hydrotropic ternary systems}

\alttitle{Relation microstructure-activit\'{e} de sels trivalents
s\'{e}par\'{e}s par des syst\`{e}mes ternaires hydrotropiques}

\author{\firstname{Asmae} \lastname{El Maangar}}
\address{ICSM, Univ. Montpellier, CEA, CNRS, ENSCM, Marcoule, France}

\author{\firstname{Johannes} \lastname{Gram\"{u}eller}}
\address{Institute of Organic Chemistry, Faculty of Chemistry and
Pharmacy, University of Regensburg, D-93040 Regensburg, Germany}

\author{\firstname{Verena} \lastname{Huber}}
\address{Institute of Physical and Theoretical Chemistry, Faculty of
Chemistry and Pharmacy, University of Regensburg, D-93040 Regensburg,
Germany}

\author{\firstname{Pierre} \lastname{Degot}}
\addressSameAs{3}{Institute of Physical and Theoretical Chemistry,
Faculty of Chemistry and Pharmacy, University of Regensburg, D-93040
Regensburg, Germany}

\author{\firstname{Didier}\nobreakauthor\lastname{Touraud}\CDRorcid{0000-0002-2243-9781}}
\addressSameAs{3}{Institute of Physical and Theoretical Chemistry,
Faculty of Chemistry and Pharmacy, University of Regensburg, D-93040
Regensburg, Germany}

\author{\firstname{Ruth} \lastname{Gschwind}}
\addressSameAs{2}{Institute of Organic Chemistry, Faculty of Chemistry
and Pharmacy, University of Regensburg, D-93040 Regensburg, Germany}

\author{\firstname{Werner} \lastname{Kunz}\CDRorcid{0000-0002-9463-632X}}
\addressSameAs{3}{Institute of Physical and Theoretical Chemistry,
Faculty of Chemistry and Pharmacy, University of Regensburg, D-93040
Regensburg, Germany}

\author{\firstname{Thomas} \lastname{Zemb}\CDRorcid{0000-0001-8410-6969}\IsCorresp}
\addressSameAs{1}{ICSM, Univ. Montpellier, CEA, CNRS, ENSCM, Marcoule,
France}
\email[T. Zemb]{thomas.zemb@icsm.fr}

\shortrunauthors

\keywords{\kwd{Separation chemistry}
\kwd{Critical fluctuations}
\kwd{Sodium salicylate}
\kwd{Lanthanides}
\kwd{Pre-Ouzo \mbox{effect}}
\kwd{Hydrotropes}}

\altkeywords{\kwd{Chimie s\'{e}parative}
\kwd{Fluctuations critiques}
\kwd{Salicylate de sodium}
\kwd{Lanthanides}
\kwd{Effet pr\'{e}-Ouzo}
\kwd{Hydrotropes}}

\thanks{CNRS through the International Research Project ``NISI''
program, Fonds der Chemischen Industrie.}

\begin{abstract}
We show here that there are four different regimes of pronounced
mesoscopic structuring in the monophasic region of the water/sodium
salicylate/ethyl acetate ternary phase diagram. Surprisingly, the
solubility of various lanthanides is highest in these regimes
containing pre-nucleation clusters and not in the complexation regime.
All four local maxima of solubility are characterised by their
scattering and explained in terms of the driving forces behind the
structuring and as a function of the added ions. The position of the
critical point was determined by regions where critical opalescence is
maximal. After centrifugation, the points located at the boundary of
the diphasic zone separate into two immiscible fluids of equal volumes.

While the highest solubility of metal ions is found in the region of
critical fluctuations, a still high solubility combined with a
significant selectivity was found in the region of the pre-nucleation
clusters. This new and previously unknown feature can also be explained
and may pave the way for a new, green procedure of selective rare-earth
metal recovery.
\end{abstract}

\begin{altabstract}
Nous montrons ici que la r\'{e}gion monophasique du diagramme de phase
ternaire eau/salicylate de sodium/ac\'{e}tate d'\'{e}thyle pr\'{e}sente
quatre r\'{e}gimes de forte structuration m\'{e}soscopique. De
mani\`{e}re surprenante, la solubilit\'{e} de divers lanthanides est la
plus \'{e}lev\'{e}e dans ces r\'{e}gimes contenant des agr\'{e}gats de
pr\'{e}-nucl\'{e}ation et non dans le r\'{e}gime de complexation. Les
quatre maxima locaux de solubilit\'{e} sont caract\'{e}ris\'{e}s par
leur diffusion et expliqu\'{e}s en termes des forces mol\'{e}culaires
\`{a} l'origine de la structuration et en fonction des ions
ajout\'{e}s. La position du point critique a \'{e}t\'{e}
d\'{e}termin\'{e}e par les r\'{e}gions o\`{u} l'opalescence critique
est maximale. Apr\`{e}s centrifugation, les points situ\'{e}s en limite
de zone diphasique se s\'{e}parent en deux fluides immiscibles de
volumes \'{e}gaux. Alors que la solubilit\'{e} la plus \'{e}lev\'{e}e
des ions m\'{e}talliques se trouve dans la r\'{e}gion des fluctuations
critiques, une solubilit\'{e} encore \'{e}lev\'{e}e combin\'{e}e \`{a}
une s\'{e}lectivit\'{e} significative a \'{e}t\'{e} trouv\'{e}e dans la
r\'{e}gion des agr\'{e}gats de pr\'{e}-nucl\'{e}ation. Cette
caract\'{e}ristique nouvelle et inconnue jusqu'\`{a} pr\'{e}sent peut
\'{e}galement \^{e}tre expliqu\'{e}e et pourrait ouvrir la voie \`{a}
de nouveaux proc\'{e}d\'{e}s produisant moins d'effluents toxiques pour
la r\'{e}cup\'{e}ration s\'{e}lective des m\'{e}taux des terres rares.
\end{altabstract}

\maketitle

\twocolumngrid

\end{noXML}

\section{Introduction}

Ternary systems comprising a short-chain amphiphilic molecule called
``hydrotrope'' and two immiscible fluids are considered as powerful
solubilisation media avoiding the use of surfactants
\mbox{\cite{1,2,3}}. Hydrotropes are small, usually water-soluble,
organic molecules~\cite{4}.\ They comprise hydrophilic and hydrophobic
moieties, with the hydrophobic moiety being too small to induce micelle
formation~\cite{5}.\ Typical examples include neutral compounds such as
short-chain alcohols like ethanol, but also charged molecules, usually
anionic compounds composed of an aromatic ring with an additional
sulfate, sulfonate, or carboxylate group. Typical examples of
hydrotropes are sodium \mbox{salicylate} (NaSal), which is widely used
in the pharmaceutical and body care industry, sodium xylene sulfonate
(SXS), sodium cumene sulfonate (SCS) or sodium toluene sulfonate
(NaTS). The existence of well-defined mesoscale inhomogeneities in
macroscopically transparent solutions was shown to be often responsible
for such unexpected solubilisation capacity. Such mesoscale
inhomogeneity phenomena of oil-rich and water-rich domains are
comparable to the microdomains observed in the classical
water/oil/surfactant ternary systems (direct, bicontinuous, and reverse
microemulsions)~\cite{1,3,6,7}, and therefore we call the corresponding
systems surfactant-free microemulsions (SFME).

The concept of hydrotropy, defined by Neuberg in 1916~\cite{8,9},
outlines the capability of short-chain amphiphilic molecules to
solubilise hydrophobic compounds in a hydrophilic solvent. In SFME
showing the compartmentation of hydrophilic and hydrophobic domains,
the hydrotrope accumulates mostly at the interface between water-rich
and oil-rich domains. The interface between the oil-rich and water-rich
domains is usually considered as a kind of highly flexible film in
dynamic exchange with the surrounding medium~\cite{3,10}. 

In contrast to surfactants, the amphiphilic character of hydrotropes is
usually considered to be insufficiently pronounced to promote
micellisation or self-aggregation of the hydrotrope itself in
water~\cite{11}. However, they are able to form loose or ill-defined
aggregates at higher concentrations (${\sim}$1~M) than those that would
be necessary for surfactants ($10^{-2}$--$10^{-3}$~M). Sometimes the
loose aggregation only happens when a hydrophobic solute is present.
The solute is solubilised in binary or ternary solvents as isolated
molecules, and it is not clear until now how aggregation enhances
solubilisation~\cite{12}.\ Shimizu \mbox{et~al.}\ described
theoretically this hydrotropic solubilisation using an approach derived
from pure statistical thermodynamics. They considered hydrotropic
solubilisation to be the result of a subtle balance between
hydrotrope--hydrotrope interaction and solute--hydrotrope interaction.
In other studies, the authors argued that strong hydrotrope--hydrotrope
interactions, resulting in a pre-structuring of the hydrotrope in
H$_{2}$O, diminish the solubilisation efficiency of
solutes~\cite{13,14}. However, the opposite was also
found~\cite{7}.\ This solubilisation efficiency could also come from an
\mbox{entropic} effect in the bulk of the solvent by preferential
adsorption as recently shown by Spadian {et~al.}~\cite{15}. As we will
see in the following, things are even more complex.

Various examples of solubilisation with anionic hydrotropes are
described in the literature: Theneskumar {et~al.}\ have solubilised a
highly hydrophobic compound, lauric acid, in water using different
hydrotropes such as SCS, SXS and NaTS~\cite{16}. A high amount of
hydrotrope (over 0.5~mol/L) was necessary to enhance the solubility of
lauric acid by a factor of 6 at room temperature. The same hydrotropes
also enhance the solubility of the water-insoluble
hydroxyacetophenones~\cite{17}. NaSal was used to increase the
solubility of salicylic acid in water~\cite{18} and is widely used in
the pharmaceutical industry as hydrotrope~\cite{19,20,21}.

\looseness=-1
From the phase diagram consisting of water, NaSal, and ethyl acetate
(EA), as studied by El Maangar {et~al.}, it can be deduced that the
hydrotrope is not soluble in the organic phase~\cite{22}. However, a
monophasic domain was found, which is enclosed by a liquid/liquid and a
solid/liquid two-phasic system (see Figure~\ref{fig1}). The monophasic
area was examined using density excess, X-ray, and neutron scattering
techniques, and they evidenced three major facts. First, in an ethyl
acetate saturated aqueous solution, the hydrotrope NaSal can indeed
form aggregates which are reminiscent of micelles. Second, the critical
point was determined to be close to the EA-rich corner of the phase
diagram, surrounded by asymmetrical tie lines, and around the critical
point neither a pre-Ouzo structuring nor a spontaneous Ouzo effect
could be evidenced. This suggests that there is only a ``normal''
critical point in this phase diagram. Finally, in a domain near the
liquid/solid phase boundary, X-ray, light, and neutron scattering
combined with a density excess determination proved the presence of
dynamic aggregates reminiscent of pre-nucleation clusters
(PNC)~\cite{23}. These aggregates are stabilised without any
surfactants but by selective solvation of ethyl acetate. These findings
are intriguing and triggered the detailed examination of the
nanostructuring occurring in the monophasic region as well as the
evolution of the solubilisation capacity of charged trivalent
electrolytes---lanthanide salts---by this ternary system in the
single-phase region. 

\begin{figure}
\includegraphics{fig01}
{\vspace*{-.25pc}}
\caption{\label{fig1}Ternary phase diagram of water, sodium salicylate,
and ethyl acetate, showing the single phase-region present is separated
by a binodal line from the 2-pahse region and a S/L region with an
excess precipitate that is rich in sodium salicylate. The red dot
indicates the critical point. The figure is adapted from~\cite{22}.}
{\vspace*{-.25pc}}
\end{figure}

Our goal is to establish a structure--function relationship and to
determine to what extent the microstructure influences the
solubilisation of solutes and how this will be different for
electrolytes and non-electrolytes.

\section{Experimental section} \label{sec2}
\subsection{Materials} \label{sec2.1}

\looseness=-1
Ethyl acetate (EA) (purity ${&gt;}$ 99.9\%) was purchased from Merck.\ 
Sodium salicylate (NaSal) (purity ${&gt;}$ 99.5\%) was purchased from Sigma
Aldrich.\ All samples were prepared with deionised water using a
Millipore Milli-Q purification system (Merck Millipore.\ Billerica.\ MA).
All other chemicals were purchased from Sigma Aldrich: lanthanum (III)
nitrate hexahydrate La(NO$_3$)$_3{\cdot}6$H$_2$O (purity ${&gt;}$ 99.99\%),
neodymium (III) nitrate hexahydrate Nd(NO$_3$)$_3{\cdot}6$H$_2$O
(purity {${&gt;}$} 99.9\%), europium (III) nitrate hexahydrate
Eu(NO$_3$)$_3{\cdot}6$H$_2$O (purity {${&gt;}$} 99.9\%), dysprosium (III)
nitrate hexahydrate Dy(NO$_3$)$_3{\cdot}6$H$_2$O purity {${&gt;}$} 99.9\%),
and ytterbium (III) nitrate hexahydrate Yb(NO$_3$)$_3{\cdot}6$H$_2$O
(purity 99.9\%). All chemicals were used without further purification.

\subsection{Phase diagrams} \label{sec2.2}

All phase diagrams were determined with the cloud point
method~\cite{24}, by initially mixing sodium \mbox{salicylate} with one
of the other two solvents, then adding the third one dropwise to the
solutions, until a visible change in the phase behaviour occurred. The
initial phase diagrams were determined in mass fractions $w_{i}$. To
obtain the phase diagrams in molar fractions $x_{i}$, the molar masses
of the pure solvents were used. All phase diagrams were determined at
25~{\textdegree}C, and the phase transitions were determined with the
naked eye and through two cross-polarised filters to check the presence
of liquid crystals.

We define compositions in the monophasic region based on a mass
fraction relative to binary fluids: ${\alpha}$ is the mass fraction of
EA in the water/EA binary mixture, not taking into account the amount
of hydrotrope present in the sample for the determination 
{of}~${\alpha}$. 
All additions were measured by weight with a laboratory scale.
Solutions were prepared at room temperature.
{\vspace*{-.2pc}}

\subsection{Density measurement and tie-line{\hfill\break}
determination in the miscibility gap} \label{sec2.3}

Solution densities were determined using a vibrating tube density meter
(DMA 5000~M. Anton Paar. Austria) at ($25 \pm 0.005$)~{\textdegree}C
with a nominal precision of ${\pm}5\times 10^{-6}$~g/mL. Calibration
was performed using air and pure water at 25~{\textdegree}C.
Calibration was checked using pure water and between each measurement
against air (allowed deviation: ${\pm}5\times 10^{-5}$~g/ml).

The determination of the density allows determining the two extremities
of the tie-lines in the biphasic liquid/liquid region very precisely,
i.e., the phase boundary actually corresponds to the binodal
(compositions of phases in contact at equilibrium). To this purpose, a
mapping of more than a hundred samples was used after interpolation of
the measured densities as explained in the work of El Maangar
{et~al.}~\cite{22}, and thus the compositions of the two phases at
equilibrium are obtained.{\vspace*{-.2pc}}

\subsection{Conductivity measurements} \label{sec2.4}

Conductivity measurements were carried out in a thermostatic
measurement cell (25.0~{\textdegree}C) under permanent stirring and if
necessary, manual mixing using a low-frequency WTW inoLab Cond 730
conductivity meter connected with a WTW TetraCon 325 electrode
(Weilheim, Germany). 20~g of initial sample were placed in the
measurement cell and \mbox{successively} diluted either with pure water
or ethyl acetate. The electrode was calibrated with potassium chloride,
and a cell constant of $R = 0.472$~cm$^{-1}$ was \mbox{determined}.

\subsection{Diffusion-ordered NMR(DOSY) experiments} \label{sec2.5}

Diffusion-ordered NMR spectroscopy experiments were performed on a
Bruker Avance~III HD 600~MHz spectrometer, equipped with a 5~mm CPPBBO
BB-${}^{1}$H/${}^{19}$F probe. All measurements were performed at
298~K, and the temperature was controlled by a BVT 3000 and a BVTE 3900
temperature unit. NMR data were processed, evaluated, and plotted with
the TopSpin~3.2 software.

Deuterated solvents were not employed, and no field-frequency lock was
established. Due to the rather short measurement times, no drift of the
chemical shifts was observed due to a missing field-frequency lock. To
establish magnetic field homogeneity, shimming was performed on the 
${}^{1}$H~NMR signals (either on the singlet of H$_{2}$O or ethyl
acetate). ${}^{1}$H NMR signals were not referenced.

Measurements were performed in the monophasic region (depicted in
Figure~\ref{fig3}). To this purpose 5~g samples were prepared and
centrifuged at 4300~g for 10~min. Then the solutions were transferred
to standard NMR tubes.

The DOSY measurements were performed with the convection-suppressing
DSTE (double stimulated echo) pulse sequence developed by Jerschow and
M\"{u}ller in a pseudo 2D mode~\cite{25}. The diffusion time delay was
set to 45~ms. Smoothed square (SMSQ10.100) gradient shapes and a linear
gradient ramp with 20 increments between 5\% and 95\% of the maximum
gradient strength (5.35~G/mm) were used. For the homospoil gradient
strengths, values of~100, ${-}$13.17, 20, and ${-}$17.13\% were used.
For each compound in the sample, gradient pulse lengths were first
optimised to obtain a sigmoidal signal decay for increasing gradient
strength, with gradient pulse lengths ranging from 0.75 to 3.3~ms. NMR
spectra were processed with Bruker TopSpin~3.2 (T1/T2 relaxation
package), and diffusion coefficients were derived according to Jerschow
and M\"{u}ller~\cite{25}.

\subsection{X-ray fluorescence (XRF) measurements} \label{sec2.6}

For ternary systems containing organic compounds, X-ray fluorescence
(XRF) is a precise and suitable method to quantify the elements present
in the solution. The commercial XRF spectrometer used to analyse the
samples after solubilising lanthanides is a SPECTRO XEPOS (AMETEK)
model. It is commercially equipped with an energy dispersive X-ray
analyser (ED-XRF) that uses the energy loss of the X photon in a
silicon material to determine the spectrum by suitable signal
processing. Secondary targets reduce background noise compared to the
output signal from the tube and improve fluorescence detection. Liquid
samples were placed in 6~mm diameter cups, the bases of which consisted
of a 4~mm-thick proline film. The XRF spectrometer was used to analyse
a series of eleven cups in sequence, using a rotating carousel that
positions the samples to be measured above the inverted optical part. A
volume of 200~$\upmu$L of each of the samples was placed in the
microcups for analysis for a duration of 40~min. The X-ray tube
generator was set at 40~kV and an intensity of 0.160~mA. The zirconium
secondary target was monitored between 15 and 17~keV to visualise the
fluorescence of all lanthanides and between 4~keV and 10~keV for iron.

In order to quantify the elements from the raw spectra, we used a
calibration procedure described and further detailed in the Supporting
Information. In other words, one XRF spectrum yields a concentration
value after processing with the calibration. Calibration was carried
out using commercial ICP-OES standard solutions. 

\subsection{Small- and wide-angle X-ray scattering{\hfill\break}
(SWAXS) experiments} \label{sec2.7}

Small- and wide-angle X-ray scattering experiments were carried out on
a bench, built by Xenocs using X-ray radiation from a molybdenum source
($\lambda = 0.71$~\AA), delivering a 1~mm-large circular beam of
17.4~keV. The scattered beam was recorded by a large on-line scanner
detector (MAR Research~345) which was located 750~mm from the sample
stage. Off-center detection was used to cover a large $q$ range
simultaneously ($0.2~\mathrm{nm}^{-1} &lt; q &lt; 30~\mathrm{nm}^{-1}$,
$q=(4\uppi/\lambda)\sin (\theta/2)$).

Collimation was applied using a 12:${\infty}$ multilayer Xenocs mirror
(for Mo radiation), coupled to two sets of Forvis scatterless slits,
which provides a 0.8~mm ${\times}$ 0.8~mm X-ray beam at the sample
position. A~high-density polyethylene sample (from Goodfellow) as a
calibration standard was used to obtain absolute 
\mbox{intensities.} Silver
behenate in a sealed capillary was used as scattering vector
calibration standard. Integration of the two-dimensional spectra was
performed, using the FIT2D software. Data were normalised considering
the electronic background of the detector, transmission measurements,
and empty cell subtraction. The acquisition time was 1800~s per sample.

Fitting of the spectra was done with the SasView package~\cite{26},
assuming two different models. On the one hand, an Ornstein--Zernike
formula was used for composition fluctuations which gives information
about the pseudo-phase domain size~\cite{27}, on the other hand, a
simple sphere model was used to fit mainly the spectra near the EA-rich
region where little aggregates are observed. More detailed information
can be found in the manual~\cite{26}.

\section{Results and discussion} \label{sec3}
\subsection{Conductivity experiments} \label{sec3.1}

In order to investigate the structuring of the ternary mixtures
H$_{2}$O/NaSal/EA, conductivity measurements were
performed first. Conductivity measurements provide detailed information
on the mobility of charge carriers and yield insight into the local
structuring of a system~\cite{6,28,29,30,31}. Conductivity measurements
in the domain of microemulsions are a common and very well-known method
to distinguish between regions of w/o, o/w and bicontinuous
microemulsions~\cite{24,32}. In order to obtain meaningful and
conclusive results, the conductivity must be measured by diluting with
water but also by diluting with the solvent (EA). In both cases, the
polar fraction contains all the charge carriers.

Two different dilution lines (see the phase diagram on
Figure~\ref{fig2}a) as a function of $\alpha$ are depicted in
Figure~\ref{fig2}a. $\alpha$ is calculated in the investigated
samples using the following equations:
{\begin{equation} \label{eq1}
\alpha =\frac{w_{\mathrm{EA}}}{w_{\mathrm{EA}}+w_{\mathrm{water}}}
\end{equation}}\unskip
where $w_{i}$ is the weight fraction of molecule $i$ in the ternary
mixture.

\begin{figure*}
\includegraphics{fig02}
\caption{\label{fig2}(a)~Conductivity, (b)~reduced conductivity
measured along the two dilution lines represented in the phase diagram
as a function of ${\alpha}$ that is the mass fraction of water versus
ethyl acetate, not taking into account the mass of hydrotrope. The
insert is a scaled-up graph of the reduced conductivity of the dilution
line with ethyl acetate. The black dashed line on the phase diagram
shows that two samples with different compositions (red and blue
crosses) can have the same ${\alpha}$ value.}
\end{figure*}

It should be noted that the same alpha value can be obtained for two
samples with different compositions (see Figure~\ref{fig2}a). So, the
reader is kindly invited to refer both to the alpha value but also to
the color code of the graphs and dilution lines. The water dilution
line is shown in blue and the solvent dilution line is shown in red. 

In Figure~\ref{fig2}a, the red curve shows a decrease in conductivity
when $\alpha$ increases. At $\alpha$ values above~0.9, the polar volume
fraction is too small to obtain significant conductivity values (a
few~$\upmu\mathrm{S}{\cdot}\mathrm{cm}^{-1}$) but a flat rise in the
conductivity with decreasing ${\alpha}$ values is observed (at low
water content). Below~0.9, the charge carriers are released (increase
in the polar fraction), and a linear increase in conductivity is
observed. A strong linear increase in conductivity with increasing
water content is observed followed by a change in slope at $\alpha
=0.4$. It should be noted that this slope change at ($\alpha=0.4$)
corresponds to the pre-nucleation cluster (PNC) region~\cite{22}. 

In order to determine the origin of the sharp increase in conductivity
as well as for a better understanding of the curve shape, conductivity
was normalised to the reduced equivalent conductivity. It should be
noted that the conductivity depends on two critical factors:
\begin{itemize}
\item the concentration of charge carriers present in the solution
\item the volume in which these charge carriers can move.
\end{itemize}

Thus, we normalised the experimentally determined specific conductivity
${\sigma}$ and translated it to the reduced equivalent conductivity
$\Lambda^{*}$, according to:
{\begin{equation} \label{eq2}
\Lambda^{*}=\frac{\sigma}{c(\mathrm{NaSal})\cdot\phi_{\mathrm{polar}}^*}
\end{equation}}\unskip
where $\phi_{\mathrm{polar}}^{*}$ is an estimation of the polar volume
fraction taking into account the distribution coefficient of the three
components. The polar volume fractions were calculated in the
investigated samples using the following equation:
{\begin{equation} \label{eq3}
\phi_{\mathrm{Polar}}=0.1\cdot v_{\mathrm{EA}}+0.96\cdot
v_{\mathrm{water}}+0.9\cdot v_{\mathrm{NaSal}}
\end{equation}}\unskip
where $v_{i}$ is the volume fraction of molecule $i$ in the ternary
mixture.

We call $\Lambda^{*}$ the ``reduced conductivity'' or ``reduced
equivalent conductivity'' of the system, in order to avoid confusion
with notations of the equivalent conductivity~$\Lambda$.\ This
normalisation is based on the conductivity introduced in the
charge-fluctuation model presented by Eicke {et~al.}~\cite{33}, where
the specific conductivity is normalised by the volume \mbox{fraction}
of water. Further, the background to normalise the conductivity by the
NaSal concentration stems from the classical aqueous model, which has
also been adapted in one of Eicke's earlier works~\cite{28}.\ This
reduced conductivity is thus the contribution of a single charge
carrier to the total conductivity.

Figure~\ref{fig2}b shows the reduced conductivity $\Lambda^{*}$ as a
function of ${\alpha}$ for the same two dilution lines depicted in the
phase diagram. For ${\alpha}$ below~0.6, the reduced conductivity
depends weakly on the amount of solvent present, i.e.\ the majority of
mobile ions are free to move. The maximum of reduced conductivity
occurs when charged PNCs are detected by their scattering pattern.

The conductivity of the dilution line towards water is shown in
Figure~\ref{fig2}a in blue. The curve is bell-shaped, characteristic
of pre-Ouzo aggregates showing an increase towards low water
contents~\cite{7}. With an increasing water content, a maximum is
reached before the conductivity decreases again due to excessive
dilution of the present charge carriers $(0&lt; \alpha &lt; 0.2)$. For the
reduced conductivity, a slope change is observed below $\alpha = 0.1$,
demonstrating the dissociation of the pre-Ouzo aggregates present near
the phase boundary.

For $\alpha &gt; 0.9$, the slope of reduced conductivity is smaller than
in the water corner: charge carriers could be aggregates.

\subsection{NMR experiments} \label{sec3.2}

Figure~\ref{fig3} shows the self-diffusion coefficients of the three
molecules composing the ternary system: NaSal, EA, and water as a
function of~${\alpha}$. These self-diffusion coefficients allow us to
see the interactions of each molecule with the others. The
self-diffusion coefficients were measured along the two dilution lines
(the numbered samples on the phase diagram, see Figure~\ref{fig3}a).

\begin{figure*}
{\vspace*{-2pt}}
\includegraphics{fig03}
{\vspace*{-3pt}}
\caption{\label{fig3}\fontsize{9.8}{11.76}\selectfont 
Self-diffusion coefficients as a function of the
water/EA mass ratio $\alpha$ of (a)~sodium salicylate, (b)~ethyl
acetate, (c)~water, as well as (d)~the effective charge derived from
the ratio of conductivity to self-diffusion along the water (blue) and
EA (red) dilution lines at the positions shown in the phase diagram.}
{\vspace*{-3pt}}
\end{figure*}

Figure~\ref{fig3}a shows the self-diffusion coefficient of NaSal
along the two dilution lines. Starting from the EA-rich corner (red
curve, $\alpha =0.93$), we can see that in an organic medium, the NaSal
molecule cannot move freely compared to the water-rich corner (blue
curve, $\alpha \approx 0$), where NaSal is more mobile with a 50-fold
increase in diffusion coefficient. This value decreases with the
decrease in $\alpha$ (from sample 11 to 20 on the phase diagram,
Figure~\ref{fig3}a) passing through the PNC region, already discussed
in a previous paper~\cite{1}, and then towards the solid/liquid region
where the value of D is minimal. For the water dilution line, the
difference in diffusion coefficients between the two extremities of the
curve (between sample~1 and~9) is more pronounced compared to the red
dilution line (between sample~11 and~20) with a minimum reached near
the PNC region ($\alpha =0.4$). This indicates that the NaSal molecules
(or their ions) are distributed between water and EA with a
\mbox{preference} for water. This is consistent with the slope of
tie-lines observed in the biphasic region and with the fact that ethyl
acetate acts as a weak antisolvent. This is also in agreement with the
results obtained in a previous publication concerning the same ternary
system, where using optical density we noticed that in EA-saturated
water (20~wt\%), sodium salicylate micellises like a medium-chain
classical surfactant~\cite{22}.

Figure~\ref{fig3}b and~c represent the self-diffusion coefficients
of EA and water, respectively. The trends are quite similar. In the
EA-rich corner, the EA curve reaches its maximum (red curve, $\alpha
=0.93$) and then decreases exponentially with decreasing ${\alpha}$
passing by the PNC region and approaching the solid/liquid phase
separation limit. In the blue dilution line, the $D$ value of EA
decreases with increasing ${\alpha}$ (from sample~9 to~1 on the phase
diagram) and remains \mbox{constant} for $\alpha &lt; 0.4$. For water and
in the water-rich corner, the $D$ values decrease considerably with
increasing ${\alpha}$ until it reaches a constant value at $\alpha
=0.4$. Concerning the red curve, the $D$ of water decreases from sample
20 to 11, but this decrease is not pronounced compared to the decrease
of $D$ of EA. It should be pointed out that in the PNC region, where the
two dilution curves cross, we notice that NaSal and EA have
approximately the same value of $D$. This is not the case for water,
which confirms that the EA and NaSal molecules are confined in the same
small aggregates and that water is the main component of the
``external'' solvent as already reported~\cite{22}.

Figure~\ref{fig3}d shows the effective charge as a function of
$\alpha$ for each point where self-diffusion coefficients were
measured. The effective charge $Z$ was calculated assuming that NaSal
is the only charge carrier according to the equation:
{\begin{equation} \label{eq4}
Z=\sqrt{\frac{kT\sigma }{e^{2}DC}}
\end{equation}}\unskip
where $k$ (joules per Kelvin) is the Boltzmann constant, $T$ (Kelvin)
is the temperature, $\sigma$ (milliSiemens per centimetre) is the
conductivity, $e$ (coulombs) is the elementary charge, $D$ is the
self-diffusion coefficient in cm$^{2}$/s and $C$ is the solute
concentration in molecules per~m$^{3}$.

In Figure~\ref{fig3}d, we can see that the effective charge of the
main charge carrier near the PNC as well as the pre-Ouzo region is
above~1. Near the EA corner, NaSal is only partially dissociated or
forms neutral clusters. The calculation of the effective charge gave us
the approximate average charge in the pre-Ouzo region as well as in the
PNC region. As these PNCs are negatively charged aggregates with a
charge ranging from~1.5 to~2, we wondered what would happen if we added
a trivalent ion (for example a lanthanum) to a ternary mixture of a
given composition in the monophasic region.

{\vspace*{-2pt}}

\subsection{Solubilisation map} \label{sec3.3}

{\vspace*{-1pt}}

Figure~\ref{fig4} shows the saturation concentration of
lanthanum---converted to solubilisation efficiency ($E\%$)---in the
monophasic region as a function of the location in the phase diagram.
The solubilisation experiments were performed in vials by adding
lanthanum salt to a given ternary mixture. Different compositions of
the ternary mixtures in the monophasic region were tested to obtain a
mapping of solubilisation efficiency as shown in Figure~\ref{fig4}. A
stirring bar was added to the solution, and the lanthanum was added
gradually to the solution until a solid/liquid separation occured,
i.e., the solution was saturated with lanthanum. The vials were then
closed with a sealed lid. The mixtures were stirred for 15~h at room
temperature. Afterwards, the vials were centrifuged for 10~min at
5300~rpm. The concentrations were obtained after filtration of the
solid residue and measurement of the remaining liquid by XRF. The
solubilisation efficiency ($E\%$) is defined as:
{\begin{eqnarray}
{\small E\%=\frac{\text{Amount of metal in the solution}}
{\text{Total amount of metal in the solution and residue}}.}\nonumber\\
\label{eq5}
\end{eqnarray}}\unskip
\par\vspace*{-.4pc}\noindent
As shown in Figure~\ref{fig4}, we can distinguish four regions where
the solubilisation of lanthanum, and consequently the saturation
concentration are high. 
\begin{enumerate}[(1)]
\item The region near the critical point, which is a classical critical
point. No pre-transition effect due to heterophase fluctuation was
\mbox{observed.} It is known that critical fluctuations can lead to a
remarkable enhancement of the solubility~\cite{1,34,35}. The
solubilisation regime in this region is governed by critical
fluctuations and thus by entropy linked to concentration fluctuations
of NaSal~\cite{36}.
\item The second region is the region previously called ``pre-Ouzo''
region which was observed first by conductivity measurements (and
confirmed later by SAXS). These are dynamic aggregates in the
water-rich region at the phase separation boundary.
\item The third region with high solubilisation is the region where
prenucleation clusters (PNC) are formed. As mentioned before, these
PNCs with inter-aggregate distance of 2.5~nm possess an effective
charge of~2. Thus, solubilisation in this case is mainly governed by
electrostatic interactions between the charged aggregates and the
trivalent lanthanum.
\item And finally, a region close to the oil-rich corner. In this
region, reverse aggregates coexist in equilibrium with monomers, and a
more detailed study of this region will be the focus of the following
part of this paper.
\end{enumerate}

\begin{figure}
\includegraphics{fig04}
\caption{\label{fig4}Solubilisation map of lanthanum in the
water/NaSal/EA ternary system. The colour scale relates to a relative
value of solubilised lanthanum nitrate observed in the presence of a
small excess of solute.}
\end{figure}

It has been shown in several studies that salicylate and lanthanides
form stable complexes of different stoichiometry~\cite{37,38,39,40,41}.
Aoyagi {et~al.}\ reported a stability constant only for the 1:1
complex~\cite{38}. Hasegawa {et~al.}\ determined the stability constants
of complexes with 1:1 and 1:2 metal-to-ligand ratios and also
thermodynamic data (but only the reaction enthalpy) of these two
complexes in the case of europium only~\cite{42,43}. Irving and Sinha
reported additionally the thermodynamic data of the neutral 1:3 complex
Eu(Sal)$_{3}$, detected with solvent extraction~\cite{39}. A crystal
structure of the 1:3 complex was published by Kuke {et~al.}~\cite{37}.
However, in solution they assume the existence of only the 1:1 and 1:2
complexes. Also, a theoretical study concerning possible structures of
the 1:1 complex in an aqueous phase has been published~\cite{40}.
Wujuan {et~al.}\ have studied a series of rare earth complexes using
different spectroscopy techniques. They demonstrate that the lanthanide
ions coordinate with salicylate via the carboxyl group. They also
showed that energy transfer between the salicylate and the rare-earth
ions is the primary process and that the heavier the rare earth, the
higher the efficiency of intermolecular energy transfer~\cite{44}.

However, these four solubilisation regimes cannot be explained with
only a complexation mechanism between lanthanum and salicylate. If this
was the case, there should be a correlation between the solubilisation
efficiency and the amount of NaSal in the ternary solution. In other
words, a better solubilisation with high quantities of NaSal could be
expected since there will be more free sites to complex the lanthanum.
On the other hand, a sharp decrease should occur when the ternary
mixture contains less NaSal, i.e., less complexing sites. This
correlation between the amount of NaSal and solubilisation is not
observed and we can reach $E\%$ values higher than 50\% even with small
amounts of NaSal in the region called pre-Ouzo and the EA-rich region
(see Figure~\ref{fig4}). To understand the origin of these
solubilisation regimes, we investigated the structuring of these
ternary systems using scattering techniques. The aim was to see if
there is a solubilisation--structure relationship that can explain
these observed regimes.

It should be noted that theses solubilisation regimes were not found in
the case of curcumin solubilisation, which is effective only near the
critical point~\cite{45}. This is maybe due to the fact that curcumin
is a large uncharged molecule and thus difficult to solubilise compared
to rare-earth salts which are electrolytes involving a first layer of
highly bound solvating water molecules
($\mathrm{V}_{\mathrm{curcumin}}=4.701\times 10^{2}$~\AA$^{3} &gt;
V_{\mathrm{lanthanum}}=3.757\times 10^{1}$~\AA$^{3}$).

The solubilisation of lanthanum salts was investigated in the
monophasic region above the liquid/liquid miscibility gap of the
ternary system. Whenever solubilisation is efficient near a
liquid/liquid miscibility gap, separation and purification processes in
the biphasic region can be performed via liquid/liquid equilibria,
which will be the focus of a next paper.\looseness=-1

\subsection{Small-angle X-ray scattering (SAXS) of{\hfill\break}
ternary mixtures and microstructures{\hfill\break} inferred from them}
\label{sec3.4}

To better understand the link between solubilisation and
microstructure, SWAXS experiments were carried out on the different
regions where lanthanum solubility was at its maximum.

The primary subject of this study was a detailed characterisation of
the microstructures in the monophasic region of the water/NaSal/EA
system. X-ray techniques are among the few suited methods for probing
structure transitions. SWAXS is particularly appropriate, as it gives
multiscale information from atomic scale up to colloidal scale. In
previous work, investigations of microstructures in ternary mixtures of
the considered water/NaSal/EA system focused only on the so-called
``Pre-Nucleation Cluster'' region near the solid/liquid boundary. The
current work aims to cover the entire monophasic region of the phase
diagram in order to understand the relationship between the
solubilisation of trivalent ions and the microstructure. The samples
chosen are illustrated in Figure~\ref{fig5} with the corresponding
SWAXS spectra.

\begin{figure*}
\includegraphics{fig05}
\caption{\label{fig5}Experimental small and wide angle X-ray scattering
(SWAXS{\textdegree} curves and their corresponding location on the
phase diagram for: (a)~the region near the critical point, (b)~the
region of pre-Ouzo aggregates, (c)~the region of pre-nucleation
clusters (PNC), i.e., ternary aggregates involving typically 6 to 20 EA
molecules associated with NaSal and water, and (d)~the region of weak
reverse w/o aggregates. In the four figures, the light blue spectrum
corresponds to pure water, while the orange one corresponds to pure EA
for comparison. Figure~(a) is dominated by critical scattering,
Figure~(b) by OZ behaviour far from the critical point corresponding to
polydisperse surfactant-free microemulsions (SFME), while Figure~(d) is
typical scattering from supramolecular stoichiometric complexes.}
\end{figure*}

In order to determine the correlation length and the radii of the
aggregates, an Ornstein--Zernike (OZ) formalism was used for data
fitting in the low-$q$ range (0.2--4~nm$^{-1}$). The OZ function can be
converted into an effective radius of gyration
$R_{\mathrm{G}}$ of{\break} the aggregates by:
{\begin{equation} \label{eq6}
I(q)=\frac{I_{0}}{1+\xi^{2}q^{2}}=\frac{I_{0}}
{1+\frac{{R}_{\mathrm{G}}^{2}q^{2}}{3}}
\end{equation}}\unskip
where $\xi$ is the correlation length and $I_{0}$ the intensity for
$q=0$. The spherical radius $R_{\mathrm{S}}$ of all identical compact
spherical aggregates stands as:
{\begin{equation} \label{eq7}
R_{\mathrm{G}}^{2}=\tfrac{3}{5}{R}_{\mathrm{S}}^{2}.
\end{equation}}\unskip
In this case, the link between correlation length and the spherical
radius of the aggregate is valid:
{\begin{equation} \label{eq8}
R_{\mathrm{S}}=2.24\cdot \xi.
\end{equation}}\unskip

\begin{table*} %tab1
\caption{\label{tab1}Structural parameters obtained from fitting the
spectra near the critical point as well as those in the pre-Ouzo
region\vspace*{3pt}}
\begin{tabular}{cccccccc}
\thead
&amp; \multicolumn{3}{c}{Critical point region} &amp;&amp;
\multicolumn{3}{c}{Pre-Ouzo region}\\
\cline{2-4}\cline{6-8} 
&amp;
\parbox[t]{1.4cm}{\centering Red sample} &amp;
\parbox[t]{1.4cm}{\centering Green sample} &amp;
\parbox[t]{1.4cm}{\centering Blue sample} &amp;&amp;
\parbox[t]{1.4cm}{\centering Red sample} &amp;
\parbox[t]{1.4cm}{\centering Green sample} &amp;
\parbox[t]{1.4cm}{\centering Blue sample}\vspace*{2pt}\\
\endthead
Forward scattering $I_{0}$ (cm$^{-1}$) &amp; 4.53 &amp; 2.65 &amp; 1.13 &amp;&amp; 2.6 &amp; 4.2 &amp; 1.88\\
Correlation length (\AA) &amp; 32 &amp; 25 &amp; 14.5 &amp;&amp; 25 &amp; 35 &amp; 29\\
Background (cm$^{-1}$) &amp; 0.01 &amp; 0.01 &amp; 0.01 &amp;&amp; 0.015 &amp; 0.014 &amp; 0.01\\
$R_{\mathrm{S}}$ &amp; 71.68 &amp; 56 &amp; 32.48 &amp;&amp; 56 &amp; 78.4 &amp; 64.96
\botline
\end{tabular}
\vspace*{3pt}
\end{table*}

In Figure~\ref{fig5}a, different SWAXS experimental spectra are shown
in log--log scale for the critical point as well as for pure water and
pure EA. The colour of each of the spectra corresponds to the colour of
the sample presented in the associated phase diagram. In the WAXS
regime, above 7~nm$^{-1}$, the curves converge and a peak is visible.
This broad peak is linked to different packings of aliphatic chains. We
have not observed any peak linked to crystallinity~\cite{46}. In the
small-angle regime below 7~nm$^{-1}$, all spectra show an intense OZ
signal ($I_{0} &gt; 1~\mathrm{cm}^{-1}$) which weakens with the distance
from the critical point. Table~\ref{tab1} shows the values of the
correlation length ($\xi$) as well as the radius of the aggregates
($R_{\mathrm{S}}$), which effectively {decreases} from
$\xi=32$~\AA\ to $\xi=14.5$~\AA. This means that critical fluctuations
persist event far from the critical point (dark blue sample on
Figure~\ref{fig5}a). This confirms that critical fluctuations, driven
by entropy, govern the \mbox{solubilisation} regime in this region as already
mentioned (see Figure~\ref{fig4}).\looseness=1

In Figure~\ref{fig5}b, SWAXS experiments are performed in the second
region, where solubilisation of lanthanum is maximal, called ``pre-Ouzo
region''. As in Figure~\ref{fig5}a, the curves converge in the WAXS
regime above 7~nm$^{-1}$. While the WAXS local correlation peak of
ethyl acetate can be found around 14~nm$^{-1}$, the signature peak of
water is located at 20~nm$^{-1}$ (the spectra of the pure solvents are
plotted in each case of Figure~\ref{fig5} (the light blue spectrum is
for water and the orange one is for ethyl acetate). The position of the
peaks in Figure~\ref{fig5}b are slightly shifted towards higher $q$
values ($q=17.9~\mathrm{nm}^{-1}$), due to higher water content compared
to the samples of Figure~\ref{fig5}a, where the opposite was found.
Indeed, the peak remains at $q=14~\mathrm{nm}^{-1}$ due to the low amount
of water in the ternary solution. Diat {et~al.}\ have shown that the WAXS
signal for mixtures of three solvents can be approximately estimated by
superposition of the pure solvent spectra~\cite{10}. At low $q$ values
($q &lt; 7~\mathrm{nm}^{-1}$), a strong OZ behaviour is also observed even
far from the critical point, as it is expected in the case of
heterophase fluctuation due to pre-transition effects called pre-Ouzo
effect previously~\cite{47}. These signals indicate the formation of
dynamic aggregates at the nanometre scale. To estimate the size of
these aggregates, the Ornstein--Zernike equation was applied (see
Equation~(\ref{eq6})). We obtained a value $I_{0}$ between 1.88 and
4.2~cm$^{-1}$ for the zero-angle intensity, and a value of $\xi$
between 25 and 35~{\AA} for the correlation length, which is a measure
for the size of the aggregates. Thess results prove the presence of
mesoscopic objects, which are larger than in the case of the
well-studied water/ethanol/1-octanol system~\cite{3,48,49}. This
difference in correlation lengths is related to the miscibility of
water in ethyl acetate that is larger than in 1-octanol~\cite{50}.

In Figure~\ref{fig5}c, SWAXS spectra are shown for the third
solubilisation region, which is the pre-nucleation clusters (PNC)
region.\ The spectra in this region show a particular forward scattering
behaviour: a broad peak corresponding to a distance in real space
derived from the peak position of 2~nm is detected. This result is in
good agreement with {reports} in the previous work of El Maangar
{et~al.}\ which was devoted to this PNC region~\cite{22}. Using SWAXS and
small angle neutron scattering (SANS) measurements, the presence of
aggregates was confirmed, with an inter-aggregate distance of 2~nm in a
region where density anomalies were observed. These PNC aggregates
contain 12 NaSal molecules and a mole ratio of 1 NaSal to 2 EA inside
the aggregates~\cite{22}. Their effective average charge is 2 (see
Figure~\ref{fig3}d) corresponding to a dissociation of approximately
16\% of the sodium salt included in a PNC, which is consistent with the
dressed model of micelles~\cite{51}. Thus, it can be concluded that
solubilisation in this domain is dominated by electrostatic
interactions between negatively charged aggregates with a surface
charge of 0.15~e/nm$^{2}$ and trivalent cations.\looseness=-1

Figure~\ref{fig5}d shows the SWAXS spectra of the fourth
solubilisation domain in the EA-rich region. In the WAXS regime, the
curves converge, and a peak is visible at $q = 14~\mathrm{nm}^{-1}$,
which corresponds to the peak of pure EA. This is due to the low amount
of water in this region and already observed in the case of the
critical fluctuation region (cf.\ Figure~\ref{fig5}a). At low $q$
values, a signal close to what is observed for the well-described weak
w/o aggregates is measured~\cite{52}. The scattering intensity at low
$q$ values increases only slightly ($I_{0} = 0.2$) when approaching the
phase boundary. The intensity values at low $q$ are within the range of
a ternary solution that contains weak aggregates. 

These spectra show an organisation of NaSal molecules in EA. Indeed,
with the addition of water to the ``blue'' sample, an increase at small
angles appears which is more marked for the ``red'' sample than for the
``green'' sample. The increase in intensity indicates that the
aggregation of salicylates is favoured by the addition of water, which
favours the organisation of small inverse aggregates of salicylate
molecules. These aggregates are therefore either more numerous or
larger with the addition of water. The effect of water on the size of
the aggregates' polar core has already been studied in the case of
aggregates of extractants like DMDOHEMA for example~\cite{53}. It has
been shown that the amount of water co-extracted in the polar core of
the w/o reverse aggregates of extractants influences their size and
thus the extraction performances, since more ions in the core require a
higher dilution in order to reach a stable form. The water extraction
and its influence on stabilisation of the aggregate core are often
reported in the literature~\cite{54,55,56,57}. These results prove the
presence of small w/o inverse aggregates in the EA-rich side, which are
more stable with the addition of water. These results are in perfect
agreement with the previous work of El Maangar {et~al.}\ where they found
by using optical density measurements of added DR-13 dye that NaSal
already starts to ``micellise'' in the presence of water saturated with
ethyl acetate much as a medium-chain classical surfactant. This
confirms the antisolvent effect of ethyl acetate for NaSal~\cite{22}.

In this case, form factors, modified by a Baxter interaction term if
necessary, are more suited than an OZ fit in absolute scale. The form
factor $P(q)$ was taken as a simple sphere without attraction, since
there is no hard sphere effect when aggregates are produced by
fluctuation. Details of equation are given in the Supplementary
Material. $P(q)$ depends on the aggregates' radii and their scattering
length density. The latter was estimated by taking into account the
``lowest aggregation concentration'' (LAC) of NaSal, which corresponds
to the concentration of monomers in equilibrium with the aggregates as
well as the solubility of water in EA. Details of calculation and
estimated values are also shown in the Supplementary Material.

Overall, all the quantities are fixed thanks to the sample composition
already determined, and the only variable is the aggregation number
$N_{\mathrm{agg}}$.

Figure~\ref{fig6} shows the experimental spectrum (same as the red one
in Figure~\ref{fig5}d) as well as the calculated spectra for
different aggregation numbers $2&lt; N_{\mathrm{agg}}&lt; 10$. Imposing a
priori histograms of aggregates size would require too many
parameters~\cite{3}. In~binary systems, an approximation is usually
made: an aggregate of $N$ molecules produces a form factor with $N$
times the molecular volume. We have extended this approximation to
ternary systems with the known water-to-NaSal ratio for each sample.
The multiple-equilibria model requires that aggregates of
$N_{\mathrm{agg}}$ molecules must coexist with aggregates of
$N_{\mathrm{agg}}-1$ and $N_{\mathrm{agg}}+1$~\cite{58}. The size
distribution function depends on the exact form of the free energy
linked to stacking or packing and cannot be derived quantitatively.
Figure~\ref{fig6} shows the calculated spectra for monodisperse
aggregates from $N_{\mathrm{agg}}=2$ to $N_{\mathrm{agg}}=10$ as well
as the spectrum that best fits the experimental result. This spectrum
$I_{\mathrm{cal}}$ is obtained by minimising the following equation:
{\begin{equation} \label{eq9}
I_{\mathrm{cal}}-I_{\mathrm{exp}}=0
\end{equation}}\unskip
with:
{\begin{equation} \label{eq10}
I_{\mathrm{cal}}(q)=\sum_{N_{\mathrm{agg}}=2}^{N_{\mathrm{agg}}=10}
x_{{N_{\mathrm{agg}}}}\cdot I_{{N_{\mathrm{agg}}}}(q)
\end{equation}}\unskip
$x_{{N_{\mathrm{agg}}}}$ is the proportion of aggregates with
$N_{\mathrm{agg}}$ NaSal molecules in the sample, and
$I_{{N_{\mathrm{agg}}}}(q)$ is the calculated spectrum for monodisperse
aggregates with an aggregation number of~$N_{\mathrm{agg}}$.

\begin{figure}
\includegraphics{fig06}
\caption{\label{fig6}Experimental and theoretical Small Angle X-ray
Scattering (SAXS) curves for the complexes formed in the EA-rich region
represented in logarithmic scale.}
\end{figure}

The result of this equation shows that the sample contains mainly
aggregates with $N_{\mathrm{agg}} &lt; 5$, and the tetramers (i.e.,
aggregates of four NaSal molecules) are the dominant species. So they
are indeed small w/o aggregates with an aggregation number below~5.

To conclude the first part of this work, the experimental analysis
allowed us to confirm that four solubilisation regimes exist in the
monophasic region. Furthermore, SWAXS measurements give proof that
these four regimes correspond to four different microstructures:
pre-nucleation clusters (PNC), critical fluctuations (CF), direct
pre-Ouzo aggregates (PO), and reverse aggregates (RA). This allows us
to define a mapping of the monophasic domain as depicted in
Figure~\ref{fig7}. Note that, in addition to the data shown here, other
compositions were investigated with the help of SWAXS experiments. The
results and discussion of these data are given in Figures~S1 and~S2.

\begin{figure}
\includegraphics{fig07}
\caption{\label{fig7}Schematic view of the mesoscopic structuring in
the ternary phase diagram water/NaSal/EA. The region around the
liquid/liquid phase transition border is dominated by three different
regimes: the regime where pre-Ouzo aggregates are dominant (PO),
critical fluctuations (CF) and supramolecular complexes (RA) are close
to the L/L miscibility gap while pre-nucleation clusters (PNC) are
close to the solid/liquid phase separation boundary, while one further
regime exists near the solid/liquid phase boundary. The white
monophasic region corresponds to a simple molecular solution.}
\end{figure}

\subsection{Effect of lanthanum salt on miscibility gap and tie-lines}
\label{sec3.5}

A striking observation is the shift in the liquid/liquid phase boundary
of the miscibility gap and a variation of the slope of tie-lines when
adding lanthanum salt to water. A similar effect was initially observed
by Tobias and coworkers when adding sulfuric acid to the
water/ethanol/1-octanol ternary system~\cite{48}.

As shown in Figure~\ref{fig8}, the monophasic region is growing
slightly on the water-rich side of the phase diagram with increasing
concentration of lanthanum salt, ranging from 0 to 100~mM. By contrast,
the biphasic region grows in the EA-rich side. There is a crossing of
the binodals reflecting the change in partition of the hydrotrope
(NaSal). The critical point is experimentally identical to the point
marked in red for low concentrations of lanthanum.

\begin{figure}
\includegraphics{fig08}
\caption{\label{fig8}Phase diagram of EA/NaSal/aqueous solution of
lanthanum. The phase diagrams are plotted in weight fractions wt\%. The
boundary in black is without lanthanum nitrate; 0.01, 0.05 and
$0.1~\mathrm{mol}{\cdot}\mathrm{L}^{-1}$ are shown in green, blue and red
respectively. Rare-earth salts produce salting-in on the water-rich
side and salting out on the EA-rich side of the phase boundary while
the critical point remains indifferent to the addition of rare-earth
nitrate.}
\end{figure}

The maximum amount of added NaSal is reduced from 20~wt\% for pure
water to 16~wt\% for aqueous solutions containing 30~mM of lanthanum
salt. The increase seems to be proportional to lanthanum salt
concentration. 

Considering the different types of mesoscale structuring introduced in
the first part of this work, the lanthanum salt stabilises the pre-Ouzo
aggregates, while it reduces the region where critical fluctuations and
w/o tetramers are observed. Addition of electrolytes reduce the
stability of w/o aggregates regardless of the electrolyte considered.
This is due to the Born energy of the electrolyte in EA~\cite{59}.

The displacement to the right of the binodal lines is thus the result
of two opposing features: the additional stabilisation (salting in) in
the water-rich region and the salting out of water out of ethyl acetate
in the EA-rich region. The partition of NaSal is significantly shifted
towards a higher NaSal concentration in the aqueous phase. This can be
seen by the change in the slope of the tie-lines, as represented in
Figure~\ref{fig9}.

\begin{figure}
\includegraphics{fig09}
\caption{\label{fig9}Pseudo-ternary phase diagram of lanthanum aqueous
phase/NaSal/EA in wt\%. The phase transition is given in blue for pure
water, in red for 0.1~mol/L of lanthanum salt. Three tie-lines are
given for each case: tie-lines rotate counterclockwise around the
critical point that remains invariant in position.}
\end{figure}

To check whether the four different regimes are still present after
addition of lanthanum salt or if they experience serious structural
rearrangements, SWAXS spectra have been recorded in each of the four
regimes. The compositions corresponding to the investigated samples are
shown in the phase diagrams depicted in Figure~\ref{fig10}, where the
amount of water (in wt\%) is replaced by the same amount of an aqueous
solution of lanthanum (also in wt\%). It should be noted that the
significant amount of salt slightly changes the sample density, which
would lead to different points in diagrams based on volume or mole
fractions. As depicted in Figure~\ref{fig10}, the shape of the spectra
remains roughly the same and thus confirms that the aggregates are
still present up to 30~mM of lanthanum salt. All spectra have a higher
intensity in the low-angle scattering regime, except in the critical
fluctuation regime, compared to the ternary systems without lanthanum
salt. The introduction of an electron-dense component enhances the
scattering contrast, which leads to an increase in intensity.

\begin{figure*}
{\vspace*{1pt}}
\includegraphics{fig10}
{\vspace*{1pt}}
\caption{\label{fig10}SWAXS spectra in the presence of lanthanum salt
in the four solubilisation regimes: (a)~critical fluctuations, (b)~w/o
reverse aggregates, (c)~pre-nucleation clusters (PNCs) and (d)~pre-Ouzo
aggregates dominant in the scattering patterns.}
{\vspace*{2pt}}
\end{figure*}

Figure~\ref{fig10}a shows the SAXS spectra obtained near the critical
point with and without lanthanum salt. The darkest red indicates the
spectrum without lanthanum salt and the lighter shades the spectra at
growing lanthanum concentrations in the aqueous phase. The addition of
0.1~M of lanthanum salt corresponds to an average distance between
trivalent cations of 4~\AA. Any fluctuation of more than 4~{\AA} is
quenched, because it implies modification of the distance between
highly repulsive charged ions (0.105~nm). The location of the critical
point is not noticeably changed, since it corresponds to the
fluctuation concentration of NaSal.

Figure~\ref{fig10}b shows that the main dominant aggregates are
tetramers with or without lanthanum salt. The presence of trivalent
salts increases the number of aggregates and reduces the critical
micelle concentration (CMC). Attraction between the aggregates' cores
is responsible for the smaller domain of \mbox{stability}~\cite{52}.

Figure~\ref{fig10}c shows that adding lanthanides in the PNC region
(1~trivalent cation per cluster) produces an increase in cluster volume
since the composition is the same. In the absence of lanthanum, the
cluster contains 12 NaSal molecule, and the average \mbox{distance} between
clusters is 2~nm. The addition of lanthanum produces a shift of the
peak to the left and a corresponding distance of 2.5~nm between the
clusters. Therefore, the average aggregation number increases from 12
to~24. The electrostatic interaction between the trivalent cation and
monovalent salicylate favours larger PNC aggregates. This explains the
high efficiency of solubility in this region.

Figure~\ref{fig10}d shows that in the pre-Ouzo region, the
correlation length increases when adding lanthanum salt. Lanthanum
salts favour large pre-Ouzo aggregates. Values of correlation length
are shown in the Supplementary Material. As in the case of the PNCs,
this is a molecular mechanism responsible for the higher solubility in
this domain. In between the PNC and pre-Ouzo domain, there is no local
structuring that can be stabilised by lanthanide salts: this is the
origin of the minimum of solubilisation observed between the pre-Ouzo
and PNC region in Figure~\ref{fig4}.

So far, we have only focused on lanthanum as a trivalent ion. However,
for a future application, selectivity is a key parameter to implement a
separation process. The solubilisation of four other rare-earths salts
in addition to lanthanum nitrate was investigated in the two regions
where solubilisation is maximal (see Figure~\ref{fig4}), i.e., in the
PNC and CF region. The results are summarised in Table~\ref{tab2}. It
can be seen that this ionic hydrotrope-based system can solubilise both
light and heavy rare earths. A very slight selectivity is observed in
the case of solubilisation in the region close to the critical point.
This selectivity increases significantly in the PNC region. This is
related to the solubilisation mechanism. In contrast to PNCs, the
critical fluctuations do not induce differences between the solubility
of ions, because the solubilisation mechanism is governed by entropy,
which is not the case in the PNC~region, where \mbox{interactions}
between molecules are involved. These results strengthen the interest
of this eco-compatible system which can solubilise rare earths and in
addition induce selectivity as well.

\begin{table} %tab2
\caption{\label{tab2}Solubilisation efficiency of rare-earths elements}
\begin{tabular}{cccccc}
\thead
\xmorerows{1}{Sample} &amp; \multicolumn{5}{c}{Solubilisation efficiency}\\
\cline{2-6}
&amp; $\%E_{\mathrm{La}}$ &amp; $\%E_{\mathrm{Nd}}$ &amp;
$\%E_{\mathrm{Eu}}$ &amp; $\%E_{\mathrm{Dy}}$ &amp; $\%E_{\mathrm{Yb}}$\\
\endthead
PNC &amp; 73.6 &amp; 80.9 &amp; 91.4 &amp; 95.2 &amp; 97.1\\
CF &amp; 80.1 &amp; 81.9 &amp; 80.3 &amp; 84.1 &amp; 86.7
\botline
\end{tabular}
\end{table}

\section{Conclusion} \label{sec4}

The solubilisation--structuring relationship in the monophasic region
of the water/NaSal/EA ternary system was investigated. By performing
conductivity, DOSY, SWAXS, and XRF measurements on different monophasic
mixtures, we revealed fundamental changes in the nanostructuring of the
system considered.

Four differently structured regions were detected and could be related
to increased solubilisation regimes: 
\begin{itemize}
\item Region CF is a region dominated by critical fluctuations, where
entropy is the dominant driving force. In this region, the presence of
trivalent ions quenches critical fluctuations.
\item Region PNC containing pre-nucleation clusters, where charged
aggregates of typically 12 EA molecules exist. In this case,
solubilisation of rare-earth salts is enhanced by surface
electrostatics of the prenucleation clusters and lanthanides increase
their aggregation number.
\item Region PO far from the critical point where small dynamic
pre-Ouzo aggregates are present on the water-rich phase separation
boundary. The aggregates in this region increase in volume upon
solubilisation of rare-earth salts facilitated by the PO aggregates
(also known as SFME or even UFME for ultra-flexible microemulsions).
This mechanism is also known as mesoscale solubilisation.
\item The diluted region on the EA-rich side, where reverse aggregates
consisting mainly of tetramers coexist with monomers. The presence of
lanthanides in this case increases the number of aggregates present,
transforming them in supramolecular complexes. This is the only region
for which the standard theory, taking only into account the
complexation Gibbs energy difference combined with the mass action law,
applies quantitatively. This complexation was the only theory for
liquid/liquid extraction before the availability of the
\textit{ienaics} theory.
\end{itemize}

These different structure--solubilisation regimes and their
modifications in the presence of electrolytes may have significant
consequences on various applications~\cite{60}. The selectivity induced by this
system may lead to a potential application in the field of rare-earth
recovery, but this will be the topic of future research.

\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*{Acknowledgements}

We thankfully acknowledge the CNRS for financial support through the
International Research Project ``NISI'' program. JG thanks the Fonds
der Chemischen Industrie for funding. We thank M.-H. Heng\'{e} for
critical proof-reading of the manuscript.

\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-310-suppl.pdf}}

\printbibliography
\refinput{crchim20230940-reference.tex}

\end{document}
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