Bridging the Gap between Osmotic and Crystalline Swelling in 2D Layered Materials Using Levitated Droplets

Abstract

The swelling behavior of smectite clay minerals is known to have two distinct regimes. The crystalline swelling involves the incorporation of a few water sheets between clay layers while the osmotic swelling corresponds to the complete delamination of clay layers in a solvent. Although a linear transition between osmotic and crystalline swellings is proposed, a complete description of smectite swelling has never been achieved. Here, acoustic levitation coupled with Small Angle X‐ray Scattering (LevSAXS) is proposed to follow the evolution of the interlayer space of a smectite in a single levitated droplet. The advantage is to track fast non‐equilibrium phenomena over a wide concentration range, while avoiding anchoring effects during drying. The results reveal a gradual shift from osmotic to crystalline swelling, marked by a transition from a pure nematic glass to a coexistence zone where the nematic phase contracts and a saturated crystalline phase emerges. This transition occurs through a continuous process, forming interstratified structures ultimately progressing to an unsaturated crystalline state. Applied to the emblematic case of clay swelling, LevSAXS opens new perspectives to investigate or reconsider the swelling mechanisms of other low‐dimensional 2D materials.

A complete description of smectite swelling from the dilute regime up to the dry is proposed by performing time‐resolved X‐ray scattering on self‐standing droplets. A continuous evolution of the interparticle distance down to 30 Å is evidenced. Beyond, a transition zone occurs where the delaminated phase contracts to a saturated crystalline phase, leading to the unexpected coexistence of interstratified layers.

1. Introduction

Clay minerals are lamellar aluminosilicates, naturally present in most soils and used since early prehistoric times for their unique physical and chemical properties.^{[ 1 ]} Among these properties, some clay minerals have the ability to accommodate water within their sheets, leading to significant swelling properties. These swelling clay minerals, such as the smectite group, are constituted by 2:1 (TOT) layer whose structure consists of a parallel stacking of one octahedral sheet (O) sandwiched between two tetrahedral sheets (T). The presence of isomorphic substitutions by cations of lower valency induces a permanent negative structural charge, either in the tetrahedral or in the octahedral sheet. This charge is compensated by cations present in the interlayer space with a charge per half unit cell ranging from 0.2 to 0.6.^{[ 2 ]} The swelling capacity of smectites then strongly depends on the solvation of these counterions, which is a direct result of their nature and their valency, as well as the ionic strength of the aqueous medium.^{[ 3} , ^{4 ]} The swelling properties of smectites have been long recognized, arousing the interest not only of geologists but also of chemists, physicists and biologists from both fundamental and applied point of view due to their numerous industrial and environmental applications.^{[ 5} , ⁶ , ⁷ , ⁸ , ⁹ , ^{10 ]} Notably, swelling properties of smectites are used to predict the impact of soil modification due to moisture on constructions or for their use as barriers for the disposal of industrial or nuclear wastes.^{[ 11 ]} The modification of the swelling behavior and therefore of the underlying rheological properties is behind their massive use in industry.^{[ 12} , ¹³ , ^{14 ]}

The swelling of smectites is divided into two main regimes most often qualified as crystalline and osmotic swellings.^{[ 15} , ¹⁶ , ^{17 ]} The layer‐to‐layer distance for smectites at the dry state (0W layer) is around 10 Å. Since the pioneer works of Bradley et al. in 1937, the crystalline swelling corresponds to a 1D expansion of the clay layer‐to‐layer distance by incorporation of water sheets into the interlayer space.^{[ 18 ]} It is now well‐established that the interlayer space can incorporate several water sheets, increasing the layer‐to‐layer distance to 12.3–12.7 Å for one (1W), 15.2–15.8 Å for two (2W) and 18.0–19 Å for three sheets of water (3W) depending on the nature of the interlayer cation (size, valency).^{[ 19} , ²⁰ , ²¹ , ²² , ^{23 ]} The possibility of a 4W hydration state with layer‐to‐layer distance beyond 20 Å remains rarely observed, only in systems of montmorillonite samples (low‐charged smectite with octahedral layer charge).^{[ 16} , ²⁴ , ^{25 ]} The second regime is the so‐called osmotic swelling, which occurs at higher water content. This state corresponds to a complete delamination of the material into individual platelets, typically by dispersing powder samples into ultrapure water.^{[ 26} , ^{27 ]} When the water content is increased, there is a difference in ion concentration between the interlayer space and the bulk water, resulting in the formation of an osmotic pressure gradient and a reduction of the platelets cohesion.^{[ 28 ]} In addition, the cations present in the interlayer space are hydrated and therefore mobile, meaning that water molecules can penetrate the interlayer space to balance the difference in osmotic pressure. The osmotic swelling is possible only for low bonding energy cations, i.e., in the case of smectites homoionized with monovalent cations such as Li⁺ or Na⁺.^{[ 3} , ^{16 ]} Furthermore, the charge density could also prevent the full delamination due to strong electrostatic attractions,^{[ 29 ]} but this effect can be overcome with the help of hydrophilic organo‐cations.^{[ 30 ]} The layer‐to‐layer distance increases until the platelets are fully dispersed, forming colloidal sols, whose stability is governed at the first order by the range of electrostatic interactions between the clay platelets.

The colloidal stability of smectites dispersions has been extensively studied both theoretically and experimentally to explain particle organization as a function of the clay concentration reported as volume fraction (ϕ). Smectites dispersions form an isotropic phase at low volume fraction, which corresponds to a 3D osmotic swelling. Above a critical volume fraction (typically a few percent), the platelets show rotational and translational arrested motion into a glass‐like state displaying a nematic‐like ordering with local organization of platelets in face‐face configuration (1D osmotic swelling).^{[ 31} , ³² , ³³ , ^{34 ]} Liquid‐crystalline phase may also appear due to a competition between orientational entropy and packing entropy governed by excluded volume interactions.^{[ 35} , ^{36 ]} The isotropic/nematic (I/N) transition has been demonstrated in colloidal dispersions of natural (nontronite,^{[ 7 ]} beidellite^{[ 37 ]}) or synthetic (fluorohectorites^{[ 38 ]}) low‐charged smectites.

To probe the structure evolution during hydration or drying, the most appropriate approach is to perform in situ small‐angle X‐ray (SAXS) or neutron scattering experiments.^{[ 39} , ⁴⁰ , ^{41 ]} Smectites have been studied through two distinct approaches, either by adding water to the system or by removing it. As early as 1954, Norrish^{[ 16 ]} suggested a jump in interlayer spacing between the linear evolution of crystalline and osmotic swelling. However, this fundamental question has never been explored experimentally until now because of the difficulty of investigating the transition between fully dispersed and fully dry nanosheet states in a single experiment. We propose to bridge this gap by drawing on recent developments in acoustic levitation.^{[ 42} , ^{43 ]} This approach allows conducting in situ studies on self‐standing droplets, enabling real‐time kinetic analysis of homogenous drying in substrate‐free conditions. The immobilization of droplets is typically achieved at the nodes of an acoustic standing wave between an ultrasonic transducer and a reflector.^{[ 44} , ^{45 ]} The combination of SAXS with acoustic levitation can address a variety of scientific challenges, including the investigation of the self‐assembly of colloids or proteins,^{[ 46} , ⁴⁷ , ^{48 ]} out‐of‐equilibrium phenomena and revisiting phase diagrams.^{[ 49 ]}

In this study, the dehydration process of a levitated droplet of smectite suspensions is investigated using time‐resolved Small Angle X‐ray Scattering coupled with an acoustic levitator (LevSAXS). In this configuration, we have been able to fully capture the evolution of layer‐to‐layer distances from the dilute regime (isotropic/nematic transition and liquid/glass transition) to the concentrated crystalline regime and ultimately the dry state. Notably, this investigation reveals the gradual transition from osmotic to crystalline swelling, defining the various hydration states of smectites, details the evolution of layer‐to‐layer distances, the relative proportions of platelets involved in each process, and the transitions between these states.

2. Results and Discussion

2.1. Microstructure under Osmotic Swelling Regime

We selected a standard beidellite from Idaho (SBId‐1, i.e., low‐charged smectite with tetrahedral layer charge), which is known to display a rich colloidal behavior in dilute conditions with a transition from isotropic to nematic liquid‐crystalline phase before forming an arrested phase for ϕ ≈1%.^{[ 37 ]} Dispersions of size‐selected beidellite were prepared using established procedures (see Experimental Section). We assessed the microstructure evolution during the evaporation process by using a dedicated LevSAXS set‐up as illustrated in Figure 1 . In situ LevSAXS measurements have been performed every second on the levitated droplet, under controlled relative humidity (RH = 70 or 30%). The initial volume fractions of the dispersions were selected to be either in a dilute isotropic phase (ϕ _initial = 0.1%), close to the I/N phase transition (ϕ _initial = 0.4%) or in a nematic liquid (ϕ _initial = 0.55%).^{[ 37 ]} For each sample, a droplet of 1µL in volume was placed at one node of the acoustic standing wave between the transducer and the reflector.

Figure 1.

Photograph of the acoustic levitator implemented on the SAXS beamline (SWING, Synchrotron SOLEIL) equipped with an in‐house humidity regulator. Samples droplets are placed between the transducer and the reflector of the acoustic levitator. The images are captured in real time with the on‐axis visualization (OAV) camera while recording the 2D‐SAXS patterns on a hybrid photon counting detector.

An example of temporal evolution of the droplet is shown in Figure 2A for ϕ _initial = 0.55% at RH = 70%. The volume fraction over time was determined from the image analysis of the droplet recorded with an on‐axis visualization (OAV) camera while recording simultaneously the SAXS pattern. As shown previously,^{[ 50 ]} the SAXS diagrams of beidellite dispersions present a monotonous decay of the scattered intensity I with scattering vector Q, that scales as I(q) ≈ Q ⁻². A representation in the form of a Kratky plot Q² .I(Q) provides a better view of the appearance of correlation peaks related to short‐range positional order of the clay platelets. For the most diluted sample (ϕ _initial = 0.1%), the 2D SAXS images are isotropic (Video S1, Supporting Information). The corresponding SAXS diagrams only display a Q⁻² slope (Figure 2B), characteristic of the form factor of individual and non‐interacting 2D platelets. At a certain stage of evaporation (t = 866s), the 2D SAXS patterns become anisotropic with the appearance of two facing circle arcs at higher volume fraction and display periodic oscillations with Q‐value following a 1:2:3… progression characteristic of a local lamellar order of the platelets. The average interparticle distance, estimated from the position of the first maximum as: d ≈ (2π)/(Q _max), occurs at an interparticle distance of 58.5 nm. Given that the estimated volume fraction ϕ _866s is 1%, this transition is more related to the liquid/glass transition determined from rheological measurements performed at thermodynamic equilibrium.^{[ 51 ]} The same experiment was then conducted with initial volume fractions (ф _initial) of 0.4% and 0.55% in order to test whether the initial organization of the platelets has an influence on the evolution of osmotic swelling under levitation. For ф _initial = 0.4%, the first SAXS patterns are isotropic then rapidly display preferential orientation with the appearance of broad oscillations (Figure 2C; Video S2, Supporting Information). This effect is all the more marked when the initial suspension is already in the I/N coexistence concentration range as illustrated for ф _initial = 0.55% (Video S3, Supporting Information). The corresponding SAXS diagrams present the characteristic periodic modulation of the scattered intensity related to the liquid nematic phase (Figure 2D). The variation in phase transitions depending on the initial volume fraction is probably due to constant mixing within the droplet, driven by acoustic pressure forces, which prevents the formation of the liquid nematic phase. In both cases, a transition occurred upon drying around 0.9%, as shown by integrating parts of the SAXS images obtained after t = 515s (Figure S1, Supporting Information). This analysis reveals two distinct structural organizations within the droplets with a first broad peak at Q = 0.01 Å⁻¹ (d = 62.8 nm) and a series of 3 peaks following a 1:2:3 progression with the first peak at Q = 0.0136 Å⁻¹ (d = 46.1 nm). This can be due to a heterogeneous distribution of the platelets inside the droplet at a certain stage of drying. Indeed, the evaporation time is large compared to the diffusion of the particles inside the droplet, leading to a Péclet number Pe >> 1 and thus to a preferential organization of the platelets at the interface of the droplet during drying. This distinguishes the face‐to‐face platelets stacking at the interface with a smaller inter‐particle distance from the “bulk” at the center of the droplet with larger inter‐particle distances. From ϕ _632s = 1.12% (d = 55.5 nm), the SAXS patterns display periodic oscillations as well as anisotropic 2D SAXS images showing two facing circle arcs or dots (Video S2, Supporting Information), characteristic of the presence of a nematic glass. Overall, regardless of the initial volume fraction, the system appears to undergo a transition around 1%, either evolving into a nematic glass or forming a biphasic system.

Figure 2.

LevSAXS on aqueous dispersions of beidellite. a) Snapshots of the time evolution of droplet drying under levitation (ϕ _initial = 0.55%). b–d) Evolution of the structures factors Q²I(Q) with the evaporation time for a 1 µL droplet of SBId‐1 dried under acoustic levitation at 70% of relative humidity. The initial SBId‐1 volume fraction ϕ _initial is set at a) 0.1%, b) 0.4%, and c) 0.55%. The curves have been shifted vertically for the sake of the clarity.

From these levSAXS patterns, we can extract the swelling law relating the evolution of the average interparticle distance as a function of the volume fraction. Figure 3 presents the corresponding swelling laws of beidellite during evaporation for the different initial volume fraction. All data point scale on a master curve, whose slope evolves as ф ⁻¹, reflecting a local lamellar order of the beidellite platelets. This is in agreement with the trend observed on beidellite dispersions characterized by SAXS and polarized optical microscopy at thermodynamic equilibrium on capillaries,^{[ 37 ]} added for comparison in Figure 3, and for aqueous dispersions of 2D nanoparticles in general.^{[ 7} , ²⁶ , ⁵² , ^{53 ]} At thermodynamic equilibrium, the swelling laws at low volume fractions show a ф ^−1/3 dependence with the interparticle distance characteristic of the 3D swelling of the noninteracting platelets. This regime is not observed by acoustic levitation probably due to the constant mixing within the droplet driven by acoustic pressure forces. However, our results make it possible for the first time to continuously explore the high‐volume fraction regime (ϕ > 5%), in which the ϕ ⁻¹ dependence on interparticle distance diverges. This discrepancy could be related to concentration heterogeneities of particles within the droplet during the drying process. A more likely scenario would be the onset of the transition to crystalline swelling.

Figure 3.

Evolution of the interparticle distance deduced from SAXS (round symbols) and WAXS (square symbols) curves as a function of SBId‐1 volume fraction. The dotted line corresponds to the dependence of the interparticle distance as a function of ϕ ⁻¹. Evolution of the interparticle distance deduced from SAXS measurements on capillaries of various smectite suspensions concentrated by osmotic stress at various ionic strength from^{[ 37 ]} are added for comparison.

2.2. Probing In Situ the Crystalline Swelling of Clay Nanosheets

As the system dries, the layer‐to‐layer distance decreases, shifting the nematic peak toward higher Q‐values. To probe this transition with better accuracy, we conducted the same LevSAXS measurements but at a smaller sample‐to‐detector distance in order to reach larger scattering vectors (see Experimental Section). The evolution of the SAXS curves as a function of the evaporation time has been investigated first at RH = 70% for both ϕ _initial = 0.1% (Figure S2, Supporting Information) and ϕ _initial = 0.55% (Figure 4 ). At the beginning, only the nematic peak described previously is observed. At a certain time of the evaporation process, sharp diffraction peaks appear clearly on the SAXS curves in addition to the characteristic nematic glass pattern (Videos S4 and S5, Supporting Information). This corresponds to the crystalline compression, i.e., face‐to‐face stacks of clay layers with water sheets in between. Before reaching the complete dry state (i.e., 0W layer, with a layer‐to‐layer distance of ≈10 Å), the system undergoes a dehydration process marked by complex transitions, with the presence of different discrete hydration states (Figure 4).

Figure 4.

Evolution of the SAXS curves with the evaporation time for a 1 µL droplet of SBId‐1 (ϕ _initial = 0.55%) dried under acoustic levitation at a) RH = 70% and b) RH = 30%. The discrete hydration states corresponding to one (1W), two (2W), three (3W) and 4 water layers (4W) are highlighted.

Here again, by plotting the curves in the form of a Kratky plot, it is possible to better distinguish the transitions of the different hydration states (Figures S3 and S4, Supporting Information). For all initial volume fractions investigated, the 001 reflections related to 4W (≈20.8 Å) and 3W (≈18.2 Å) hydration states appear in addition to the broad nematic peak, quickly followed by the appearance of a peak corresponding to 2W layers (≈15.1 Å). We observe the coexistence of these three different hydration states for a few seconds followed by the disappearance of the 4W peaks and the coexistence of both 3W and 2W hydration states. At the end of the drying process, we only have the presence of the 2W layers reflection. It has already been shown that the crystalline dehydration is a continuous process due to layer charge heterogeneities, leading to the coexistence of clay layers having different hydration states in the same crystal, leading to the so‐called mixed‐layer structures.^{[ 54} , ⁵⁵ , ⁵⁶ , ⁵⁷ , ^{58 ]} Note however that in the present case, the presence of typical 4W, 3W, and 2W hydrations states on the same experimental SAXS patterns is rather unusual, for high water contents an homogenous 3W hydration state being commonly reported.^{[ 20 ]} We have also performed the same experiment at 30% of relative humidity (Figure 4; Figures S2, S5, S6 and Videos S6 and S7, Supporting Information), showing similar continuous process, except that in this case the final state is the 1W layer (≈12.2 Å). Accordingly, the different experiments show a similar trajectory with no influence of surrounding relative humidity but rather a change in overall water content. The coexistence of discrete 4W, 3W, 2W and 1W hydrations states, in addition to nematic contribution, likely reflects a heterogeneous distribution of water content within the droplet.

2.3. Modeling of SAXS Profiles During Crystalline Swelling

To derive quantitative information regarding the evolution of the different hydrates in both osmotic and crystalline regime, the sample at ϕ _initial = 0.55% was modeled for selected evaporation times with a fitting procedure considering mixed‐layer structures using a trial and error approach.^{[ 21 ]} For the crystalline swelling, this procedure considers an interstratified mixed‐layer structure that could be composed of up to five discrete states of hydration: dehydrated (0W, with layer‐to‐layer distance at 9.6 Å), 1 (1W at ≈12.2 Å), 2 (2W at ≈15.1 Å), 3 (3W at ≈18.1 Å) and 4 water sheets (4W at ≈21.0 Å). The number of mixed‐layer structures, the relative proportions of the different types of layers, and the mean number of layers N in the coherent scattering domain size along the c* axis are adjusted to fit the experimental SAXS data (Figure 5 ). For all fitted patterns, the N values are 6 ± 0.5 for the different crystalline hydrates. To account for the low‐angle region associated to the nematic phase, the strategy of Wilson et al.^{[ 56 ]} is also considered. Accordingly, several discrete structures with layer‐to‐layer distances ranging from 24 to 75 Å, with a step size of 3 Å are first generated, considering a mean number of layers in the coherent scattering domain size N = 2.5. This set of obtained XRD patterns were then averaged considering a normal distribution around a mean dn value, representative of mean layer‐to‐layer distance in the osmotic regime. This value and the relative proportion of the nematic structure relative to the crystalline structures are thus adjusted to reproduce the experimental patterns as shown in Figure S7 (Supporting Information).

Figure 5.

Comparison between experimental (red curves) and calculated Q²I(Q) SAXS patterns (black curves) including all individual contributions (colored curves) leading to the calculated pattern of the sample at ϕ _initial = 0.55% dried under acoustic levitation at 70% of relative humidity for selected evaporation times with a fitting procedure considering mixed‐layer structures. Grey rectangles highlight the theoretical peak positions corresponding to 4W, 3W, 2W, 1W and 0W. The misfit located at the low‐Q value is related to the scattering of water that is not accounted for in the modeling exercise.

2.4. A General Description of Smectite Swelling

Our original approach, combining acoustic levitation with SAXS, allows investigating for the first time the evolution of the interlayer space of a smectite from dilute regime to the unsaturated state by focusing on the transition between osmotic swelling and crystalline swelling (Figure 6 ). During the evaporation, whatever the initial concentration, the evaporation leads to a transition toward an arrested phase (nematic‐like glass) at around 1% in volume fraction. Above this critical concentration, our results enabled us to follow the evolution of this nematic peak over time, revealing a transition zone where the nematic phase contracts and a saturated crystalline phase emerges leading to the coexistence of interstratified layers until reaching an unsaturated crystalline state.

Figure 6.

General mechanism of smectite dehydration. This scheme summarizes the evolution of the microstructure of smectites from dilute dispersions to the dry state probed by acoustic levitation.

The evolution over time during evaporation in relative proportion for the nematic phase and the different hydrates (i.e., 0W, 1W, 2W, 3W, and 4W) is shown in Figure 7A. The average distance between platelets in the nematic phase (dn) can be plotted as a function of its relative proportion (Figure 7B).

Figure 7.

Proportion of the different hydrates obtained from SAXS modeling. (a) Relative proportion of each hydration states as well as the nematic state as a function of time of evaporation. (b) Average distance between platelets in the nematic phase as a function of its relative proportion.

The distance decreases until a noticeable change in slope occurs when the system reaches 60% nematic phase and 40% crystalline phase. Beyond this point, the average distance remains relatively constant at ≈30 Å, until the nematic phase fully disappears. This indicates that during the drying process, the nematic phase undergoes a contraction to a metastable state at ≈30 Å. Interestingly, this mean distance between platelets at ≈30 Å is consistent with the pioneer study of Norrish^{[ 16 ]} for Na‐smectite performed in static conditions. However, the advantage of the levSAXS approach is that it can probe non‐equilibrium phenomena that are fast and impossible to identify using conventional static experiments. Our measurements demonstrate that the transition between crystalline and osmotic swelling is a continuous process that does not imply a jump in the interlayer spacing as suggested previously.^{[ 16 ]} The contraction of the nematic phase is followed by a shift toward a saturated crystalline swelling regime, and ultimately progresses to an unsaturated crystalline state. The existence of the 4W, which has been seldom reported in literature in the case of montmorillonite‐type of smectite is evidenced here for the first time in the case of beidellite. This 4W hydration state can be fully assigned to the crystalline swelling regime owing to the similar coherent scattering domain size (N = 6±0.5) as for other crystalline hydrates, whereas for the nematic phase the number of layers in the stack is significantly decreased (N = 2.5). The crystalline regime follows a continuous process, with the coexistence of the nematic phase alongside 4W, 3W, 2W, 1W, and 0W layers. The final analysis at the end of evaporation indicates the coexistence of 1W and 0W layers that is fully consistent with the final relative humidity reached (i.e., 70% RH).

3. Conclusion

In summary, we report the first complete description of smectite swelling from the dilute regime up to the dry state. The originality of our approach was to combine self‐standing droplets under acoustic levitation with time‐resolved X‐ray scattering. Beidellite dispersions with initial volume fractions ranging from the isotropic regime (0.1%) to the nematic phase (0.55%) were levitated and monitored during drying. SAXS analysis revealed a progressive transition from isolated, non‐interacting platelets to short‐range ordered structures, characterized by anisotropic SAXS patterns and lamellar stacking at volume fractions approaching 1%. At this critical concentration, a nematic glass‐like arrested state consistently formed, regardless of initial conditions. We unambiguously evidenced a continuous evolution of the interparticle distance down to 30 Å upon drying. Beyond, a transition zone occurs where the delaminated phase contracts to a saturated crystalline phase, leading to the coexistence of interstratified layers. Remarkably, the presence of a four water sheets hydration state, suspected but seldom observed, was clearly identified. Beyond beidellite, the levSAXS approach represents a powerful tool to investigate rapid, non‐equilibrium phenomena over a wide concentration range, while eliminating the need to produce a set of samples with variable concentrations. Applied here to the emblematic case of clay swelling, it opens new perspectives to investigate or reconsider the transition from crystalline to osmotic swelling and to achieve controlled exfoliation for other low‐dimensional 2D materials, such as for instance titanates,^{[ 59} , ^{60 ]} MXenes^{[ 61 ]} or graphene oxides nanosheets.^{[ 62 ]}

4. Experimental Section

Sample Preparation

Beidellite (SBId‐1) was purchased from the Source Clays Minerals Repository of the Clay Mineral Society at Purdue University, Indiana. The structural formula is (Si_7.27Al_0.73)(Al_3.77Fe³⁺ _0.11Mg_0.21)O₂₀(OH)₄Na_0.67. Before use, the clay sample is purified of accessory minerals and Na‐saturated according to previously established procedure.^{[ 63 ]} Then, a size fractionation is applied by successive centrifugation at various speed and redispersion in ultrapure water, resulting in a dispersion of discoidal particles with a average diameter of 210 nm and and an average thickness of 0.6 nm.^{[ 37 ]}

Levitation under Small‐Angle X‐Ray Scattering (LevSAXS)

Small‐Angle X‐ray scattering (SAXS) experiments are performed at the SWING beamline, SOLEIL synchrotron (Saint‐Aubin, France) using a fixed energy of 12 keV. The scattering patterns are recorded on an EigerX4M (Dectris Ltd.) with two sample‐to‐detector distances of 6 and 0.5 m to access a q‐range of 0.0011–0.15 Å⁻¹ and 0.12–1.26 Å⁻¹, respectively. A commercial acoustic levitator (tec5, 100 kHz free jet nozzle) is implemented on the translation table of the SWING beamline. The setup is equipped with an in‐house humidity regulator based on a proportional integral‐derivative (PID) controller adjusting the relative humidity by injecting either dry or water‐saturated (compressed air bubbling in pure water) air inside the levitator chamber. Gas flow is insured by two mass‐flow meters/controllers (Bronkhorst). For LevSAXS experiments, a droplet of 1 µL of beidellite suspension is placed using a syringe into the acoustic levitator, at a distance of 1.8 mm between the transducer and the reflector while the ultrasonic power level is set at 4 W. The relative humidity is maintained at 70% to ensure the drying of the droplet over one hour. An OAV and its source of white light is used to monitor the dimensions of the droplet throughout the experiment. A MATLAB code is used for determining the volume and the volume fraction of the sample at each step of the evaporation process. Briefly, this code consists of fitting the shape of an ellipse to the droplet contour and to retrieve the lengths of the major a and minor semi axes b of this ellipse. From these data, the volume of the droplet V is determined as $V=\frac{4}{3}\pi \times a\times a\times b$, assuming an axial symmetry around the minor semi axis, and the volume fraction as $\varphi =\frac{{\varphi }_{\mathrm{initial}}\times V_{\mathrm{initial}}}{V}$.

Conflict of Interest

The authors declare no conflict of interest.

Supporting information

Supporting Information

Supplemental Video 1

Supplemental Video 2

Supplemental Video 3

Supplemental Video 4

Supplemental Video 5

Supplemental Video 6

Supplemental Video 7

Hotton C., Bizien T., Hamon C., Ferrage E., and Paineau E., “Bridging the Gap between Osmotic and Crystalline Swelling in 2D Layered Materials Using Levitated Droplets.” Small 21, no. 33 (2025): 21, 2505038. 10.1002/smll.202505038

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.