# Interface-templated crystal growth in sodium dodecyl sulfate solutions with
NaCl

Anna Kharlamova  Université Paris-Saclay, CNRS, Laboratoire de Physique des
Solides, 91405, Orsay, France.  Synchrotron SOLEIL, L’Orme des Merisiers,
Départementale 128, 91190, Saint-Aubin, France.  François Boulogne  Université
Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405, Orsay, France.
Philippe Fontaine  Synchrotron SOLEIL, L’Orme des Merisiers, Départementale
128, 91190, Saint-Aubin, France.  Stéphan Rouzière  Université Paris-Saclay,
CNRS, Laboratoire de Physique des Solides, 91405, Orsay, France.  Arnaud
Hemmerle  Synchrotron SOLEIL, L’Orme des Merisiers, Départementale 128, 91190,
Saint-Aubin, France.  Michel Goldmann  Synchrotron SOLEIL, L’Orme des
Merisiers, Départementale 128, 91190, Saint-Aubin, France.  Institut des
NanoSciences de Paris, Sorbonne Université, 4 Place Jussieu, 75005 Paris,
France.  Anniina Salonen  Université Paris-Saclay, CNRS, Laboratoire de
Physique des Solides, 91405, Orsay, France.  Corresponding author:
<EMAIL_ADDRESS>
###### Abstract

Many ionic surfactants, such as sodium dodecyl sulphate (SDS) crystallize out
of solution if the temperature falls below the crystallization boundary. The
crystallization temperature is impacted by solution properties, and can be
decreased with the addition of salt. We have studied SDS crystallization at
the liquid/vapor interfaces from solutions at high ionic strength (sodium
chloride). We show that the surfactant crystals at the surface grow from
adsorbed SDS molecules, as evidenced by the preferential orientation of the
crystals identified using grazing incidence X-ray diffraction. We find a
unique timescale for the crystal growth from the evolution of structure,
surface tension, and visual inspection, which can be controlled through
varying the SDS or NaCl concentrations.

Keywords: Crystal, surfactant, interface, Krafft boundary, structure, Grazing
Incidence X-ray Diffraction

## Introduction

Many surfactants crystallize out of solution at low temperatures or in the
presence of salts [1]. This can be a problem for the stability of
formulations, as crystallization can lead to a diminished visual aspect or a
decreased foamability [2]. However, solution crystallization is by no means
always undesired. It is an important step in a number of manufacturing
processes [3, 4], and surfactant crystals have been shown to act as effective
foam stabilizers if they adsorb onto the bubble surfaces [5, 6].

Solid particles have been used to create highly stable foams, through the
practically irreversible adsorption of particles at the liquid/vapor
interfaces (given suitable particle size and wetting conditions) [7, 8]. Such
systems are particularly interesting for applications where foam lifetime is
crucial. We showed that the crystallization of sodium dodecyl sulphate (SDS)
or potassium dodecyl sulphate (KDS) with the addition of either sodium or
potassium chloride to SDS during foam generation leads to highly stable foams,
which could be destroyed by heating them above the melting temperature of the
crystals [5]. The criteria for foam stability have been explored, and the
first requirements are a crystallization process which is fast compared to the
foam destabilization processes, and a sufficient quantity of crystals [9].
Jiang et al. [10] studied foam stability as different salts were added to SDS
solutions (NaCl, KCl or CaCl2). They suggest a link between foam stability and
crystal structure formed, with higher packing densities improving foam
stability. Binks and Shi [11] used magnesium nitrate hexahydrate to
crystallize the solutions of SDS. They saw a correlation between the size of
crystals, foamability and foam stability, with the intermediate size of
crystals being the most efficient. This was in agreement with suggestions when
a series of alkali salts had been used for the precipitation [12].

Although the crystal structure, size of crystals and the rate of
crystallization have been identified as important parameters in the capacity
of the crystals to stabilize foams, there are few studies of SDS
crystallization at liquid/vapor surfaces. In the bulk the crystallization of
SDS has been studied, and it is known that a number of crystal structures can
be formed, depending on the degree of hydration [13, 14, 15]. Howevever, as
recently as in 2021, a novel hydrate form of SDS crystal was discovered [16].
Recently, Khodaparast et al. explored the impacts of confinement and surfaces
on the crystallization of SDS [17]. The use of microvolumes allowed them to
study the impact of surface roughness and surface energy on crystallization.
They showed that increasing the surface energy decreased nucleation times.

The crystallization of surfactants is different from the surface freezing
phenomenon. Long-chain alkanes have been shown to undergo a surface freezing
transition, where at temperatures above bulk freezing they form a nanometric
crystal-layer at alkane/water interfaces [18, 19]. Surface freezing has also
been used to shape emulsion drops [20, 21]. Such a transition has been shown
to occur at gas/oil interface in the presence of a long-chain surfactant [22].
In surface freezing the systems are kept above bulk crystallization
temperature, however the role of surfaces in the crystallization of
surfactants is still an open question.

In order to study SDS crystallization at liquid/vapor surfaces, we have used
varying concentrations of NaCl to modulate the temperature of crystallization
and hence the kinetics of crystal formation. The addition of salt screens the
electrostatic repulsion between the surfactant headgroups and promotes
precipitation. This increases the crystallization temperature, so that
crystals form at room temperature. We measure the crystal structure at the
surface using grazing incidence X-ray scattering, and follow the kinetics of
crystallization with surface tension and imaging methods.

## Materials and methods

### Materials

The surfactant sodium dodecyl sulfate (SDS, purity $\geq 99.0\%$) and the salt
sodium chloride (NaCl, purity $\geq 99.0\%$) are purchased from Sigma. The SDS
powder is used as received and the NaCl powder is roasted in an oven at
650–700 ∘C for 16-20 hours to remove any possible organic impurities.

### Preparation of SDS solutions with NaCl

Solutions are prepared in the concentration range 0.5–6.0 mM for SDS and
350–600 mM for NaCl volumetrically at 20 ∘C. These concentrations were chosen
to observe crystallization on reasonable timescales. Required amounts of SDS
and NaCl powders are transferred into a 500 mL or 1 L flask and diluted with
ultrapure water (18.2 M$\Omega\cdot$cm). The precipitate forming in the
solutions during preparation is solubilized by increasing the temperature to
25–30 ∘C (depending on the NaCl concentration) in a water bath (Memmert WNE 10
equipped with a cooling Peltier). The temperature is then gradually decreased
back to 20 ∘C, which requires 30–40 minutes. All prepared solutions were
homogeneous and transparent prior to the start of the experiments, and are
analyzed immediately after preparation.

### The Krafft boundary determination

The Krafft boundary is determined for solutions with [SDS] = 1, 5, 10 and 100
mM and [NaCl] from 50 to 1000 mM. The mixtures with different surfactant/salt
concentrations are prepared from stock solutions of SDS and NaCl in 20 mL
glass bottles. The mixtures are heated at approximately 40 ∘C until the
precipitate is solubilized to ensure homogeneity and placed in a fridge at 4
∘C overnight. The bottles are then gradually heated in a water bath (VWR
1137-1P circulating water bath) starting from 4 ∘C with the rate 1 ∘C per 2
hours. The Krafft boundary is considered as the lowest temperature at which
all precipitate appears dissolved by visual inspection. We estimate the
uncertainty of the melting temperature measurement in $\pm$1 ∘C. The measured
temperatures are shown in Supporting Information Figure S1, and all the data
points are shown in Table S1. The measured values are in good agreement with
the study of Illous et al. [23]. The Krafft boundary does not depend on the
concentration of SDS, but the temperature increases weakly with [NaCl]. With
100 mM NaCl the crystals melt at 20 ∘C, while at 1 000 mM the melting
temperature is around 32 ∘C.

### Crystallization kinetics

The kinetics of crystallization at the interface of salt-surfactant mixtures
is characterized using a polytetrafluoroethylene Langmuir trough (Kibron
microtrough) 80 mm $\times$ 206 mm equipped with two polyoxymethylene barriers
(width 20 mm) that are immobile during the measurement. The surface area of
the trough is therefore 132.8 cm2. The trough is equipped with a balance
holding a sensor – the DyneProbe, made of a metal alloy with a hydrophilic
oxide, ensuring negligible contact angle with the solution. The trough
operates in an acrylic cover box preventing perturbations during measurements.
The temperature in the trough is regulated with a water bath at 20 ∘C. The
sensor is cleaned from organic residues by heating with a flame torch and
calibrated with 100 mL of ultrapure water at 20 °C before each measurement.
Then 100 mL of freshly prepared SDS + NaCl solution at 20 ∘C is poured into
the trough and the time evolution of the surface tension is recorded. The
surface tension is initially stable and is followed by a sharp drop after
crystallization at the interface. For each measurement, we determined the
characteristic time of the surface tension drop $\tau_{\gamma}$ as the
inflection point between the plateau and the slope.

To correlate the percolation of crystals at the interface with the surface
tension measurements, crystallization kinetics for solutions with 500 mM NaCl
was also followed by taking photographs of the solution interface in a glass
Petri dish (diameter: 11 cm, surface area 95 cm2) placed in the Kibron trough.
The Petri dish was colored with black paint on the outside for easier
observation of the crystallization process. The trough was filled with water
at 20 °C that surrounded the bottom of the dish for temperature regulation.
The DyneProbe, cleaned with a flame torch, was calibrated with 100 mL of
ultrapure water poured into the dish that was then substituted with 100 mL of
the SDS + NaCl solutions prepared as described above. The surface tension was
measured as function of time and grayscale photographs of the solution
interface were taken every minute with a Basler acA3800-14uc USB 3.0 camera
placed at approximately 45° angle with the liquid interface. The percolation
time $\tau_{perc}$ is determined from the movies by eye as the time at which
the movement at the interface stopped due to its complete coating with
crystals. We estimate the uncertainty of the values to be $\pm 10$ min. We
verified with image analysis in MATLAB that the values determined by the eye
correspond to the time to reach the plateau of total pixel intensity at the
water interface (the result is not shown).

To obtain colorful images of the evolution of the crystal growth, we filmed
solutions (100 mL) in an open Petri dish (diameter: 11 cm), colored black from
the outside, in a lab with air temperature control (20 °C). The images were
taken every minute with a USB 2.0 camera (uEye UI-1495LE-C-HQ).

### X-ray Scattering

X-ray scattering experiments are carried out at the SIRIUS beamline at SOLEIL
Synchrotron (Saint-Aubin, France). Details of the beamline optics can be found
in the literature [24]. The X-ray beam energy is fixed by a Silicon (111)
Double Crystal Monochromator (DCM) at 8 keV ($\lambda=0.155$ nm). The beam
size is fixed horizontally by optical slits and vertically by a focalizing
mirror at $0.1\times 0.5$ mm2 (V $\times$ H) for Grazing Incidence X-ray
Diffraction (GIXD) experiments and $0.1\times 2$ mm2 for X-ray diffraction
measurements in the vertical plane of incidence.

#### GIXD experiments

For Grazing Incidence X-ray Diffraction (GIXD) experiments, the water surface
is illuminated at an incident angle of $2$ mrad below the critical angle
($2.7$ mrad) of total external reflection on the air/water interface so that
the incident wave is almost totally reflected. In this regime, the refracted
wave is evanescent, probing the interface with a penetration depth of a few
nanometers. The diffracted X-ray beam intensity is recorded by a Pilatus3 1M
2D detector (Dectris, Switzerland) as a function of the horizontal in-plane
scattering angle $2\theta$ between the incident beam and the scattered beam.
The in-plane resolution ($\Delta 2\theta=0.06^{o}$) is defined by a Soller-
Collimator (JJ X-ray, Denmark) located in front of the Pilatus3 1M detector. A
home-made Langmuir trough of total area 800 cm2 and with 400 mL volume is used
for these surface crystallization experiment combined with X-ray measurements.
It is enclosed in a temperature-controlled sealed chamber and flushed with
helium gas during data collection in order to lower scattering and sample
damage. The helium is saturated with water before entering the trough
enclosure in order to avoid water evaporation during the measurements. The
surface pressure is measured in this trough by the Wilhelmy plate method,
using a filter paper plate and a Riegler and Kirstein Gmbh (Berlin, Germany)
surface pressure sensor.

#### Diffraction in the vertical plane of incidence

Out-of-plane diffraction (i.e. in the plane containing the incident beam and
its specular reflection) measurements were performed in an original geometry
initially developed for X-ray reflectivity at liquid-air interfaces. In this
setup, the incidence angle on the last deflecting mirror of the SIRIUS
beamline is varied to scan the incidence angle on the water surface between 0
and 2∘. The upper limit of 2∘ on the water surface is determined by the
critical angle of total external reflection of the mirror of approximately
0.5∘, given by its external coating of 80 nm platinum. When the incidence
angle on the mirror exceeds this threshold, the intensity of the reflected
X-rays decreases significantly, with almost no X-rays being reflected for
angles greater than 1∘ on the mirror, equivalent to 2∘ on the water surface.
The intensity of the incident beam $I_{0}$ is monitored by an ionization
chamber (IC PLUS 50, FMB Oxford, England) placed right before the liquid
surface for proper normalization of the reflected beam. In this particular
geometry, as the incident angle increases, it becomes necessary to lower the
liquid surface to follow the incident beam. This adjustment is achieved by
vertically translating the sample stage of the diffractometer, which has a
wide range of motion ($150$ mm) and an excellent repeatability ($1$ $\mu$m).
The signal reflected by the interface is measured by the Pilatus3 1M detector,
which is moved vertically to ensure that the reflected spot remains at the
same position on the detector. For every data point of the experimental curve,
the signal is measured by summing the intensity of each pixel within a Region
Of Interest (ROI) that is centered around the reflected beam. Background
subtraction is then performed by calculating the average signal from the ROIs
located immediately on the left and on the right of the ROI containing the
reflected beam. Finally, the signal is divided by a measurement of the direct
beam on the detector, along with a proper normalization by the $I_{0}$
intensity.

## Results and discussion

Figure 1: Time series of the surface of a glass Petri dish with an SDS-NaCl
mixture at 20 ∘C with (a) 500 mM NaCl and 0.6 mM SDS at 0, 8, 13.5 and 20
hours and (b) 500 mM NaCl and 1 mM SDS at 0, 1, 2 and 5 hours. (c) Close up of
the crystal surface with 500 mM NaCl and 0.6 mM SDS after 15 hours. (d) Close
up of the crystal surface with 500 mM NaCl and 1 mM SDS after 15 hours. The
scale bar is 2 cm in all the photographs. See movies in Supplementary
materials.

### Macroscopic observation of the surfaces

We observe the evolution of solutions of SDS in Petri dishes. At the SDS
concentrations studied, and at room temperature, the surfactant will not
precipitate without the addition of salt. The addition of 500 mM NaCl will
decrease the solubility of SDS and the critical micelle concentration (CMC)
falls to around 0.5 mM [25]. We are working at the concentrations above this
concentration. We observe crystal-formation, as the melting temperature of SDS
crystals is around 25 ∘C as shown the Supporting Information Figure S1. We
have selected images of the time-evolution of the surface of a Petri dish with
two different solutions at 0.6 mM (Figure 1a) and 1.0 mM (Figure 1b) SDS
solution with 500 mM of NaCl. The videos from which the images are extracted
are available as supplementary materials. In both samples the surface is free
from any visible crystals after pouring the solution in the Petri dish.
Eventually, crystals will appear in both samples, however, the timescales of
the process are different.

For the sample with 0.6 mM SDS (Figure 1a), we need to wait several hours
before the appearance of crystals (the second photograph of the series was
taken 8 hours after preparation). The crystals formed are large, several
millimeters in size and with varying colours. This means that they have a
typical thickness of hundreds of nanometers at this moment. Over several
hours, the crystals continue to grow in number and in size until reaching an
almost full coverage of the Petri dish. Their motion ceases as they percolate
through the surface. At longer times the visual aspect changes very little,
although it continues to become more homogeneous in hue.

Increasing the concentration of SDS to 1.0 mM (Figure 1b) leads to a much
faster formation of crystals, which are also much smaller (millimetric). After
1 hour (2nd photograph) large numbers of sub-millimetric crystals can be seen
at the sample surface. These continue to grow in number, and in size until
they cover the full surface. As the crystal layer continues to thicken, the
brightly colored crystals thicken and the film becomes colorless.

In both cases, the surfaces are very mobile during the growth of the crystals,
due to convection, however, once the surface density of crystals becomes
sufficiently high all motion arrests and the surfaces become jammed. This is
not the end of the evolution, and the thickness of the layers continues to
increase.

The impact of the SDS concentration can also be seen in photographs of a
smaller region of the surfaces, as shown in Figure 1c and d, for the 0.6 mM
and 1.0 mM SDS respectively, both taken after 15 hours. We can again note the
difference in the size of the crystals, as those formed in the 0.6 mM SDS are
much larger than with 1.0 mM SDS. This is typical of the samples, where
smaller SDS concentrations form larger crystals. We have not explored the
control over the crystal size, however the use of salts has been shown to be
an interesting way to control crystal size [26].

### Crystal structure at the surfaces

Figure 2: (a) $Q_{z}$-Integrated Grazing Incidence X-ray Diffraction spectra
measured on a $1.5$ mM SDS and $500$ mM NaCl solution 12 hours after the
SDS:NaCl solution was poured into the trough. This time frame corresponds to a
later stage, following the complete coverage of the surface by crystals. Peaks
are indexed by a rectangular 2D structure with $a=1.032$ nm and $b=1.641$ nm.
(b) $Q_{xy}$–$Q_{z}$ intensity map of diffraction peaks $22$ and $04$.

In order to determine the structure and, eventually, the nature of the
crystals that form at the surface of SDS solution in presence of high
concentration of NaCl, we performed GIXD and diffraction in the vertical plane
of incidence. Figure 2-a presents the $Q_{z}$–integrated diffraction spectrum
measured after the complete covering of the free surface of an SDS solution
(1.5 mM) and NaCl (500 mM). A very large $Q_{xy}$–range is scanned and
revealed a high number of diffraction peaks. The $Q_{xy}-Q_{z}$ intensity map
(Figure 2-b) clearly demonstrates that the vertical structure of the
diffraction peaks corresponds to modulated diffraction rods indicating that
the crystals are oriented with a defined lattice plane always parallel to the
surface. Since the crystals are oriented by the interface, it also suggests
that the crystal growth occurs at the solution-air interface. In Figure 2-a
all diffraction peaks are indexed on a two-dimensional rectangular lattice
with $a=1.032$ nm and $b=1.641$ nm. To obtain this lattice, we started from
the structures of SDS powder proposed by Smith et al. [13], who determine the
crystallographic structure of SDS crystals with different degrees of
hydration. The structure is always composed of lamellae of SDS molecules
crystallizing in bilayers formed by alternate layers. We calculate the peak
position for each structure proposed by Smith et al., with different amounts
of water in the unit cell, using the xrayutilities python library [27]. To
compare with our 2D diffraction peaks, $\mathbf{a}$ and $\mathbf{b}$ vectors
were ascribed to the 2D structure parallel to the lamellae, and the
$\mathbf{c}$ – to the pile-up of the lamellae. We then only keep the $hk0$
peaks to compare with the experimental peak positions. Among the different
hydration levels of the SDS crystals, the ${\rm SDS}:1/8~{}{\rm H}_{2}{\rm O}$
gives parameters $a=1.022$ nm and $b=1.641$ nm that allow a very good
adjustment to the peaks in Figure 2-a. Only a small variation of $a$ to 1.032
nm is necessary to fully reproduce the measured peak positions. Several
reasons may explain this difference: the experimental resolution of the
instrument is about 0.05 nm-1 and leads to an uncertainty in distance
determination roughly equivalent to the measured difference; also the
hydration level is neither controlled and nor measured and could be slightly
different from the crystals of Smith et al. [13].

In order to determine the vertical structure and the distance between lamellae
we performed X-ray diffraction in the vertical plane of incidence using the
same experimental geometry as X-ray reflectivity measurement (XRR). The main
feature of the diffraction spectra in the vertical plane is the presence of
two Bragg peaks as shown in Figure 3 located at $q_{1}=1.603\pm 0.002$ nm-1
and $q_{2}=3.172\pm 0.022$ nm-1. The ratio of these two positions is about two
and can thus be attributed to the diffraction peaks of a multi-layer with a
period of $2\pi/q_{1}=3.9$ nm. In the inset of figure 3, we have plotted the
first order peak (001) measured with time. Its intensity is growing while the
other parameters remain constant, showing that the amount of crystallized
matter is increasing with time. The Gaussian shape of the diffraction peaks
suggest that they are limited by the instrument resolution. The $w=0.07~{}{\rm
nm}^{-1}$ width of the diffraction peaks is indeed around the expected
experimental resolution. This suggests that the correlation length $\xi$ is
more than $80{\rm nm}$ in the vertical direction according to the Debye-
Scherrer formulae ($\xi\approx 0.9\times 2\pi/w)$ [28, 29].

Figure 3: X-ray diffraction measured in the plane of incidence with the X-ray
Reflectivity geometry on a solution of SDS 1.5 mM SDS and 500 mM NaCl. Inset:
Intensity as function of time expressed in hours in the legend in the
$Q_{z}$-range of the (001) peak for a solution of 1.0 mM SDS and 500 mM NaCl.
Lines are a Gaussian fit of the experimental data.

The X-ray diffraction studies of the crystalline layer formed at the free
surface of SDS/NaCl solutions with time demonstrates that the formed structure
corresponds to hydrated SDS crystals oriented by the interface since the SDS
lamellae formed are parallel to the surface. Comparing the structure obtained
with literature data[13], the in-plane rectangular structure and its
parameters $a$ and $b$ compared well with the lattice parameters $b=1.02$ nm
and $c=1.64$ nm and the $\alpha=90^{\circ}$ angle of the 2D structures of the
lamellae of the ${\rm SDS}:1/8~{}{\rm H}_{2}{\rm O}$ hydrated structure
evidenced by Sundell et al. [14]. For the third parameter corresponding to the
lamellar periodicity, the $3.9$ nm periodicity we found is exactly half of the
$a=7.8$ nm lattice parameter of the ${\rm SDS}:1/8~{}{\rm H}_{2}{\rm O}$
hydrated structure [14, 13]. In both papers, Sundell et al. and Smith et al.
pointed out the fact that for this hydration ratio, the unit cell contains 32
SDS molecules and 4 molecules of water, resulting in two bilayers in the unit
along the axis perpendicular to the lamellae [14, 13]. This double bilayer
cell is mandatory to account for an alternating displacement of adjacent
molecule perpendicular to the layer place [14]. However we do not have enough
measured peaks in the limited Qz-range explored to perform such a refined
analysis of the structure. Therefore we have simply indexed the peaks $q_{1}$
and $q_{2}$ as (001) and (002) with $c=3.9$ nm, but they could also be indexed
(002) and (004) with the double lattice parameter $c=7.8$ nm. We can conclude
that the formed crystals at the concentrated salt / SDS solution interface are
hydrated SDS crystals with a proportion of $1/8$ ${\rm H}_{2}{\rm O}$
molecules.

Apart from anhydrous SDS crystals, several hydrates have been identified in
the water / SDS phase diagram in the literature: ${\rm SDS}:1/8~{}{\rm
H}_{2}{\rm O}$ [14], ${\rm SDS}:1/2\ {\rm H}_{2}{\rm O}$, monohydrate [13],
dihydrate [15]. The water molecules exhibit strong interactions with the polar
head groups of SDS molecules and are located between the lamellae in the
lamellar phase [13, 15]. In the SDS / water phase diagram, the ${\rm
SDS}:1/8~{}{\rm H}_{2}{\rm O}$ hydrate appears at low water fractions (above
90wt % SDS concentration) [15]. At first glance, it may seem surprising to
discover the hydrate with the least amount of water in a system that contains
a large reservoir of water. However, we should remember that we are working at
high salt concentration (500 mM NaCl). The SDS hydrate structure can be
modified through changing solvent conditions, such as using acetone as an
antisolvent to produce ${\rm SDS}:1/8~{}{\rm H}_{2}{\rm O}$ crystals [30].
Indeed, we show in Fig. S2 of the Supplementary materials that the lamellar
spacing of the bulk crystals shifts in the presence of NaCl. The lamellar
spacing measured with 600 mM NaCl is 3.9 nm in agreement with the structure
measured at the surface.

### Crystal growth kinetics

Figure 4: (a) Amplitude of the (001) diffraction peaks obtained by fitting the
intensity of Figure 3-Inset by a Gaussian function as function of time for a
$1.0$ mM SDS and $500$ mM NaCl solution. The horizontal bars indicate the time
over which the measurement is performed. The red line shows the simultaneous
measurement of the surface tension $\gamma$ for which the time $\tau_{\gamma}$
is indicated by a read arrow. (b) Percolation time $\tau_{\rm perc}$ as a
function of $\tau_{\gamma}$ for five different SDS concentrations and $[{\rm
NaCl}]=500$ mM. The black solid line represents equality between axes.

To have a more quantitative description of the interface-templated crystal
growth phenomenon, we have combined the visual inspection of the surface, the
measurement of the time-evolution of the surface tension $\gamma$, and the
intensity of the (001) peak obtained in diffraction in the vertical plane of
incidence. Results obtained for the same SDS and NaCl solution as in Figure 1
are plotted in Figure 4-a. The time to measure a single spectrum of
diffraction in the vertical plane of incidence is about 45 min, which explains
the low time resolution in Figure 4-a. However, the depicted evolution is
typical of the studied samples. It initiates with the appearance of a peak
with low intensity. Around the percolation time $\tau_{\rm perc}$, the
intensity of the (001) peak significantly increases and subsequently decreases
to approximately 60 % of its maximum value. It remains stable for a period and
then shows a further increase over longer times. While the increase at longer
times can be attributed to the thickening of the interfacial layer, explaining
the peak intensity maximum at the percolation of the layer poses a greater
challenge.

One possible explanation could be sample degradation, as the crystals at the
interface undergo percolation and the two-dimensional diffusion is halted,
resulting in continuous irradiation of the same crystals. This phenomenon may
induce irradiation damage, causing a decrease in peak intensities. However,
typically, this would also result in an increase in peak width, which is not
observed in this case. Furthermore, the subsequent increase in intensity over
longer times does not support this explanation.

An alternative explanation could arise from the observation that at the
percolation time, the surface is relatively flat, and the crystals align well
with the solution’s surface. This ideal scenario facilitates the measurement
of diffraction from a two-dimensional, surface-oriented powder. However, after
percolation, the roughness of the surface increases, and crystals may become
misaligned, resulting in a smaller diffraction signal.

The evolution of the reflected intensity is mirrored in the response of the
surface tension measurements. Initially, the surface tension is about
$31.5~{}\textrm{mN}\cdot\textrm{m}^{-1}$ far below the surface tension of
ultrapure water ($72~{}\textrm{mN}\cdot\textrm{m}^{-1}$ at 20 ∘C). At a given
time $\tau_{\gamma}\approx 3$ h, a decrease followed by a sharper drop of the
surface tension occurs concomitantly with the end of the crystal expansion at
the surface as illustrated in Figure 1. Indeed, the measurement of the surface
tension, performed by a Wilhelmy plate, is unreliable when the liquid surface
becomes rough, as expected when completely covered by solids domains. Thus,
surface tension values obtained after $t=\tau_{\gamma}$ are not usable. Data
collecting continued after this time to allow us to accurately determine
$\tau_{\gamma}$, Figure 4a.

In addition, the diffraction measurements indicate an absence of the (001)
peak just after the sample preparation, supporting the absence of crystals at
the interface. Then, the peak intensity increases with the growth of crystals
and reaches a maximum correlated with the decrease of the surface tension.
After this time, no drastic change of the intensity is measured. Even if
visual observations evidence a thickening of the crystalline layer, GIXD
cannot measure it due to the limited penetration of X-rays for thick layers,
only the diffraction in the vertical plane of incidence is still sensitive at
long time.

The temporal evolution of the intensity is typical for all the samples with
different SDS concentrations. They show the appearance of an intense
diffraction peak at percolation. The peak intensity decreases just after,
followed by a slow increase at longer times.

The characteristic time-scales linked to structural evolution and surface
tension measurements are in close agreement (Figure 4a). From the images taken
of the interfaces, as shown in Figure 1 we can also fix a characteristic time
$\tau_{\rm perc}$ defined as the time for the crystals to percolate through
the interface. At $\tau_{\rm perc}$ the highly mobile surface suddenly slows
down as the crystal coverage become sufficiently high to block the mobility.
In Figure 4b a comparison between $\tau_{\rm perc}$ and $\tau_{\gamma}$ is
shown. The equivalence between the times indicates that we can define a single
characteristic time-scale for the development of the surface crystals at the
vapor/water interface, which gives rise to a response in surface tension,
local structure and macroscopic appearance.

Figure 5: Surface tension drop time $\tau_{\gamma}$ as a function of SDS
concentration for four NaCl concentrations. Lines are guides for the eye.

Then, we focus on the effect of salt and surfactant concentrations on the
crystal growth kinetics. In Figure 5, we have plotted the time $\tau_{\gamma}$
based on the surface tension measurements as a function of the SDS
concentration for different salt concentrations. For each salt concentration,
the evolution is characterized by a sharp decrease as SDS concentration
increases followed by a constant time $\tau_{\gamma}$ at high surfactant
concentration that increases with the reduction of the amount of SDS in the
solution. As the salt concentration increases from 350 to 600 mM the melting
temperature of the crystals increases from 23 to 26∘C, and the CMC decreases
from 0.6 to 0.4 mM [25, 31]. This leads to a higher degree of supersaturation,
which will increase the rate of crystal formation. However, an increase in the
NaCl concentration also leads to a higher surfactant surface coverage as the
repulsion between the surfactant headgroups is screened. Both of these effects
can increase the kinetics of crystallization at the surface.

## Conclusion

We have studied the crystallization of SDS at the vapor/water interface as we
precipitate the surfactant from salt solution (NaCl). We measure the structure
of the surface layers using a combination of GIXD and diffraction in the
vertical plane of incidence, to access both the in-plane and out-of-plane
structure. We show that crystals are formed from adsorbed SDS molecules, and
that they are oriented parallel to the surface. We can match the crystal
structure to that of a poorly hydrated SDS (${\rm SDS}:1/8~{}{\rm H}_{2}{\rm
O}$ hydrate), despite the dilute conditions and contact with a water bath.
This is because the presence of salt changes the equilibrium bulk crystal
structure to a less hydrated form.

We analyze the kinetics of crystal growth by combining the structural
evolution with surface tension measurements and visual observations. We show
that a single characteristic time defines the evolution of the crystals. The
visual percolation of the surface is accompanied by a sudden decrease of the
measured surface tension, and an increase of the (001) peak intensity.

The characteristic time for the precipitation of SDS is long compared to the
characteristic timescales linked to foam stability (hours compared to tens of
minutes). This is probably why the use of NaCl to precipitate SDS for the
generation of stable foams is less frequent, and potassium or magnesium
chlorides are much more efficient[5, 11]. However, this system shows variation
in crystal size, which would be interesting to explore and to link to bubble
stability.

## Supporting Information

Two videos of the surface crystallization. The data on the Krafft boundary.
Bulk wide-angle X-ray scattering spectra of the precipitate.

## Acknowledgments

We thank Fabrice Cousin, François Muller, Patrick Kékicheff and Matthieu Roché
for fruitful discussions. We also thank Zhizhong Li for his assistance on salt
purification. We gratefully acknowledge SOLEIL synchrotron for provision of
beamtime on SIRIUS Beamline. This work is supported by “Investissements
d’Avenir” LabEx PALM (ANR-10-LABX-0039-PALM) project "Interfreeze".

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See pages 1- of SI.pdf