Introduction

Clays have always been used as a material by humans [1]. Clays are 2D nano-lamellar materials [2, 3], and as such, they offer an array of possible applications, for instance, as barrier coatings [4,5,6,7,8], hydrogels [9,10,11], capture and storage of gasses [12,13,14], as well as photonic crystals producing structural colors [15].

Almost a century has passed since Langmuir’s experiments discussing clay colloidal suspensions in terms of liquid crystal structures [16]. Such experiments were the basis for Onsager’s seminal paper on the first purely entropy-driven nematic phase transition [17]. Later several experimental studies of colloidal platelet suspensions have been performed, for instance by Lekkerkerker and collaborators [18,19,20]. This has inspired renewed interest in anisometric clay platelets in suspensions and their liquid crystalline phase behavior [20,21,22,23,24]. When the concentration of suspended clay nanosheets is increased, typically the system forms a gel [23, 25,26,27] with a yield stress preventing flow [24]. It has been debated how gelation might interfere with the formation of liquid-crystalline structuring [28,29,30,31,32].

Clay-based platelets can come in two versions [33], either as stacked nano-lamellar (> 20 nm thick) flat particles [34,35,36,37], or as delaminated thin nanosheets (ca. 1 nm for a monolayer) in aqueous suspension [38]. In the former case, gravity in combination with container confinement and particle to wall anchoring [39] are responsible for sorting clay particles, allowing for observation of the nematic-isotropic transition in the same sample tube [34,35,36,37, 40].

High aspect ratio (lateral size of 20 μm and thickness of 1 nm) [41] synthetic sodium fluorohectorite (NaHec) with a nominal formula unit of \({\left[\text{N}{\text{a}}_{0.5}\right]}^{\text{i}\text{n}\text{t}\text{e}\text{r}}{\left[\text{M}{\text{g}}_{2.5}\text{L}{\text{i}}_{0.5}\right]}^{\text{o}\text{c}\text{t}} {\left[\text{S}{\text{i}}_{4}\right]}^{\text{t}\text{e}\text{t}} {\text{O}}_{10}{\text{F}}_{2}\) [42] can delaminate into a mixture of nematic domains and metastable colloidal accordions where the single layers are separated to uniform distances defined by the amount of water and electrostatic interactions governing the separation [2, 38]. These lamellae stacks bear similarities with a smectic liquid-crystalline phase [43]. By adjusting the ratio of NaHec/water, it is even possible to separate the single layers (SGL) to distances comparable with the wavelengths of visible light allowing for structural colors. Fixation of these tuned layer-separation distances in (polymeric) matrices could open the way to tunable bright coloration for nowadays applications. Recently, it was shown that the brightness is significantly increased for dispersions of double layered clay nanosheets (DBL) [15]. Figure S1 in the supplementary information shows typical reflectance spectra in the visible range for the herein investigated DBL suspensions, in agreement with literature [15]. The DBLs were obtained from NaHec, following a protocol which includes a partial ion exchange of interlayer sodium cations with cesium cations leading to an ordered interstratification of Cs+- and Na+-interlayers. As Cs+ has a substantial lower hydration enthalpy than Na+ only along the later interlayers delamination is observed upon immersion of the ordered interstratification into deionized water (Fig. 1).

Fig. 1
figure 1

Production of SGL and DBL clay suspensions. The swelling behavior of NaHec is modified when Na+ (yellow) is partially exchanged with Cs+ (green). NaHec delaminates into single lamellae (SGL) upon immersion in water. In contrast, ordered interstratification enables delamination of double layered clay nanosheets (DBL) pinned together by cesium ions. Additionally, the general structure of a silicate layer in NaHec is shown (more details in Fig. S2 in the supplementary information)

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NaHec changes its swelling behavior in dependence of the volume fraction: The first steps of layer separation occur via discrete hydration steps (crystalline swelling, regime I). With further uptake of water, a gel phase is obtained, in which the layers of a tactoid are still positionally strongly correlated and localized in well-defined distances d (Wigner crystal, regime II). For even lower volume fractions, a transition to a more disordered regime takes place due to the increasing loss of correlation between the adjacent platelets (osmotic swelling regime III, lattice melting) [42]. Because of the huge lateral expansion, in all phases individual clay nanosheets are forced in coplanar arrangement in statistically oriented domains originating from the pristine non-hydrated layered crystals. The individual layers in the coplanar arrangement, however, partially translate, tilt and wrinkle to gain conformational entropy resulting in certain deviations from perfect coplanarity. This leads to a significant reduction of the coherent correlation length in the ordered domains. Nevertheless, the swelling regime is still characterized by a power law scaling with the volume fraction ϕ, e.g., the layer separation distance d scales with ϕ−x. Previous small angle X-ray scattering (SAXS) measurements indicate a crossover from a power law exponent x = −0.66 at low ϕ (in the range 0.2 to 2 vol%) to x = −1 at higher ϕ (in the range 2 to 10 vol%) for SGL suspensions [42], whereas observations of structural coloration from DBL suspensions at low ϕ indicated a power law of x = −0.84 (in the ϕ range 0.67 to 1.34 vol%) [15]. Due to the extreme aspect ratio of the silicate layers, an isotropic suspension with freely rotating individual nanosheets can only be obtained for very low concentrations (ϕ < 0.0001).

We note that in the previous works different confinement geometries were used for the suspensions, cylindrical capillaries [42] or flat cuvettes [15], respectively. However, they were not directly compared and, as demonstrated in this paper, this can impact on the results of the studies. Therefore, in the present work, SAXS is used to investigate highly diluted SGL and DBL suspensions in different sample container geometries in a concentration regime allowing for structural color. We find that the confinement geometries yield power law ϕ behaviors that are consistent with the dependencies reported in previous publications [15, 42].

Samples and experiments

Fluorohectorite

Melt synthesis and long-term annealing of the synthetic sodium fluorohectorite \(({\left[\text{N}{\text{a}}_{0.5} \right]}^{\text{i}\text{n}\text{t}\text{e}\text{r}}{\left[\text{M}{\text{g}}_{2.5}\text{L}{\text{i}}_{0.5}\right]}^{\text{o}\text{c}\text{t}}{\left[\text{S}{\text{i}}_{4}\right]}^{\text{t}\text{e}\text{t}}{\text{O}}_{10}{\text{F}}_{2}\)) (NaHec) was performed according to literature procedures [44]. The material featured a cation exchange capacity of 1.27 mmol/g and a density of 2.73 g/cm3. CsCl (ReagentPlus, ≥ 99.9%), NaCl (EMSURE ACS, ISO, Reag. Ph. Eur, ≥ 99.5%) were used as obtained. The clay suspensions were diluted to the targeted concentrations using stock solutions (ϕ = 1 vol% for SGLs, and ϕ = 2 vol% for DBL), which were prepared by spontaneous delamination of NaHec tactoids in water due to the repulsive interactions between the interlayers. The average platelet dimensions were ⁓ 20 μm in lateral size and 1.0 nm in thickness for the SGL and 2.1 nm for the DBL (see Fig. S3 in supplementary information). The stock solutions appear fluid and transparent to the eye, suggesting that the delamination was homogeneous. Before the transfer to the sample containers, the diluted suspensions were put in an overhead shaker (Trayter D, IKA) at 80 rpm for 16 h. It was confirmed that the diluted suspensions were not gelled, as seen in Fig. S4 in the supplementary information. The clay suspensions were inserted by means of a syringe (0.8 mm ø needle) in the respective sample containers, either a capillary (Hilgenberg, diameter 2 mm, product code: 4,007,620) or a flat cell (Hellma quartz cuvette with 1 mm thickness and 9.5 mm width, product code: Z803111). Afterwards, to check for structural coloration photos were taken using an iPhone 13 Pro camera as shown in Fig. 2.

Fig. 2
figure 2

Structural coloration from DBL and SGL suspensions. The DBL suspensions in (a) cuvettes (1.0 mm × 9.5 mm) (1.15 vol%, 0.92 vol%, and 0.68 vol%, respectively) and (c) capillary (0.48 vol%, 2.0 mm ø). The SGL suspensions in (b) cuvettes (0.48 vol%, 0.40 vol%, and 0.28 vol%, respectively) as they were measured at the ESRF DUBBLE beamline. The DBL suspensions display bright structural colors in contrast to the very weak colors for the SGL samples

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Small angle X-ray scattering

The SAXS experiments were performed at the European Synchrotron Radiation Facility (ESRF, BM26 DUBBLE beamline). For the X-ray scattering pattern acquisition, a fixed wavelength λ = 1.03 Å was used, with a beam size of 0.8 mm × 3.2 mm (VxH). The scattering intensities were recorded by a Pilatus 1 M detector (Dectris, pixel size 172 × 172 μm [2], with an active area of 168 mm × 179 mm) placed at a distance from the sample of 9.34 m, resulting on a q-range from 2.2·10−2 to 1.3 nm−1 (where q = 4π/λ sin(θ) and 2θ is the scattering angle). A simple representation of the irradiation geometry and the characteristic 2D SAXS images are shown in Fig. 3. Due to the container orientational confinement, it is important to keep in mind the direction of the beam relative to the clay nanosheet orientations. For the cuvettes, the setup at the beamline blocked the beam at the lowest q values.

Fig. 3
figure 3

Irradiation geometry, sample container, and characteristic 2D SAXS images. A simple representation of the beam direction for the two investigated geometries, cuvettes (a) and capillaries (b). Examples of obtained diffractograms are shown for both geometries. The X-ray path length through the suspension was 9.5 mm for the cuvettes, whereas for the capillaries it was 2.0 mm

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The 2D diffractograms were converted by 360° azimuthal integration into their 1D representations (\(I\left(q\right)\;\mathrm{vs}.\;q\)) following the beamline’s standard procedure. 1D data were fit using the Förster model [45], previously used for similar studies on clay systems [42]. In this model, the intensity \(I\left(q\right)\) is given by:

$$I\left(q\right)={b}^{2}\rho P\left(q\right)\left[1+{\upbeta }\left(q\right)\left(Z\left(q\right)-1\right)G\left(q\right)\right]$$
(1)

where \(b\) is the scattering contrast between the clay nanosheets and the solvent, \(\rho\) the number density of the layers, \(q\) the scattering vector, and \(P\left(q\right)\) the form factor of disks. The terms inside the square brackets constitute the structure factor, where \(Z\left(q\right)\) is the lattice factor determining the distance \(d\) of adjacent nanosheets in the liquid, \(G\left(q\right)\) is the Debye–Waller factor, and \(\beta \left(q\right)\) is a polydispersity factor [45].

In order to crosscheck the Förster model, we also tested the more commonly used SasView [46]. See supplementary information.

Results and discussion

The experimental results of the SAXS are summarized in Fig. 4, where the plots for DBL and SGL suspensions in cuvettes and capillaries are shown with their respective fits using the Förster model (disks separated by distance d).

Fig. 4
figure 4

1D I(q) vs. q for DBL and SGL suspensions. The colored plots in the top row show the 1D diffractograms for DBL suspensions and the corresponding fits. The agreement between both is reasonable. The bottom black and white plots show the 1D diffractograms for SGL suspensions and the corresponding fits. Curves are shifted vertically with an arbitrary scaling factor for clarity

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The results for the distances d are summarized in Fig. 5 and can be found as well in Table S1 in the supplementary information. The estimated correlation lengths are in the range of 200 to 500 nm. Note that as shown in Fig. S5 for the capillary case, the contribution from the scattering volume is related to the packing of the suspension in the central region of the capillary, and the packing itself is a result of the wall anchoring.

Fig. 5
figure 5

Power law behavior of d-spacing, d vs. volume %, ϕ shown as log-log plots for DBL and SGL suspensions with their respective fits (straight lines), both for cuvettes (gray lines) and capillaries (black lines)

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The behavior of the d-spacing as a function of sheet type (SGL or DBL), concentration and cell geometry is shown in Fig. 5.

The log-log plots in Fig. 5 suggest power laws for d vs. ϕ for DBL and SGL suspensions. Note that somewhat surprisingly the power law exponent depends on the geometry of the sample container, being significantly higher for cuvettes than for capillaries. These results are, however, in very good agreement with previous results obtained from DBL structural coloration in cuvettes [15] and with SAXS studies of SGL suspensions in capillaries [42]. Modeling using SasView gives approximately the same result (Fig. S6 in supplementary information).

Comparison of the 2D patterns, right column of Fig. 6, shows that the data taken in cuvettes are more anisotropic than in capillaries. Thus, the (local) spatial and orientational distribution of high aspect ratio nanosheets in suspension is largely defined by the border slip conditions induced by the confinement geometry of the sample container (giving the boundary conditions for swelling). Whereas for the cuvette there is only one main orientation direction, for the capillaries, more than one main orientation direction is observed. The texture of the samples is better visible and quantifiable in the azimuthal plots, also given in Fig. 6. The liquid crystalline domains are better oriented in flat cuvettes as can be seen from the significantly smaller FWHM of the Lorentzians. The FWHM are ca. 12° and ca. 50° for blue DBL (1.5 vol%) sample in cuvette and capillary, respectively. See Figs. S7 and S8 in supplementary information for the azimuthal angle plots for all DBL in cuvettes and capillaries, as well as for SGL case.

Fig. 6
figure 6

Normalized intensity vs. azimuthal angle for blue DBL suspensions in different sample containers. On the left column are the azimuthal plot for blue DBL in cuvette (top) and capillary (bottom). As expected, there is a sharp alignment (texture) in the cuvette case. On the right column are enlarged image sections of the respective 2D SAXS patterns

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Referring to Table S1, the relative displacement (Δd/d) is noticeably smaller for DBL (in average 12 ± 1.5%) when compared to SGL (in average 18 ± 2.5%), and it is similar between the two geometries. This can possibly be associated with differences in bending rigidity, which is higher for DBL than for SGL [47]. Our observed relative displacement values are higher than 10% which is above the Lindemann criterion [48] for lattice melting as discussed previously by Rosenfeldt et al. [42]. Swelling to structural coloration is in the melted regime, in which the platelets are still correlated in plane, but are not anymore ideally stiff and strictly coplanar. Dislocations by sliding or tilting of planes as well as bending of sheets may become important and can influence the local order of colloidal accordions. These transitions most likely influence the spatial and the orientational distribution of the platelets.

For capillary containers, the behavior of the d-spacing as a function of the volume fraction follows a power law previously shown to be ϕ−1 for concentrated SGL suspensions (Wigner crystals, d < 30 nm, and ϕ−0.66 for more dilute suspensions, d > 30 nm) [42]. In the present work, these power law dependencies are shown to be closer to ϕ−1 for DBL samples compared to SGL samples, which we attribute to the higher stiffness of DBL nanosheets. Also, it seems evident that the power law dependency is closer to ϕ−1 for cuvette than for capillary containers, presumably because nanosheets may “pack” more efficiently in flat cuvettes.

The internal domain nanosheet d-spacing increases with decreasing ϕ, as consistent with previous observations [15, 42]. The measured d-spacings of samples in capillaries are smaller than the ones in cuvettes for all cases. This difference can be up to 15% and is consistent for both, SGL and DBL, due to different domain alignments in the capillaries and the cuvettes. Although we are not in a position to reach a final explanation of this, we suggest that this could be related to the platelet anchoring and the container geometry (flat or cylindrical) which is translated throughout the sample, in accordance with previous results from nematic organization of non-delaminated clay particles [39]. Another factor that possibly could play a role here is the container material, for instance in our experiments the capillaries were made from borosilicate glass whereas the cuvettes are made from quartz, and these materials could possibly have different influence on the clay anchoring and packing density. Pre-aligning due to shear forces during filling may also play a role.

NaHec tactoids originally consist of N ~ 500 nanosheets, which are forced to separate while being forced into coplanar arrangement and at the same time align to the container during swelling. Also, we note that the size of the beam ensures that a large amount of the nematic domains are fully inside the scattering volume. Nanosheets originating from one tactoid lose correlation to each other to a certain degree as the domains swell. In consequence, the coherent correlation size (measure for averaged strictly coplanar stacked monolayers in the domain) determined by modeling the tactoids in the suspension as stack of coplanar oriented disks must decrease. Indeed, in the investigated concentration regime these correlation lengths are in the order of 200–500 nm, which corresponds to ca. 2 to 5 layers only and suggests pronounced local disorder in the melting regime. These results are summarized in Table S1 and in Fig. 7, which shows a representation of the nanosheet organization in the two geometries that we have investigated here. Figure 7 suggests correlation lengths in particle stacks that extend up to about 500 nm, with well-oriented stacks of particles extending over very much larger distances up to the millimeter range. This is illustrated by optical microscopy observations of accordion suspensions, see Fig. S9.

Fig. 7
figure 7

Sketch of nanosheet organization in two different types of confinement. The SAXS results suggest domain organizations as sketched for both investigated geometries, flat cuvettes and cylindrical capillaries, including both inter domain and coherent intra-domain lamellar organization. For both type of containers, a lamellar correlation length of approximately 200 to 500 nm is found from the fits (Fig. 5), whereas the azimuthal plots (Figs. 6, S7, and S8) suggest that the domain orientations are quite different for the two types of confinement. The illustration is out of proportion with respect to nanosheet diameter compared to container dimensions

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The purpose of Fig. 7 is to illustrate the liquid crystalline organization in the two different geometries. In addition to sliding of platelets, we suggest a correlated lamellar liquid crystalline organization with disorder, due to nanosheets twisting, buckling, or wrinkling.

We suggest that this local disorder within long-range ordered nematic domains is directly related to the non-iridescent structural coloration observed in this system [15]. This is illustrated in Movie S1 in the supplementary information (rotating the capillary seen in Fig. 2b by 180° around its axis), which clearly demonstrates an angle independent behavior, despite the pronounced texture and the suggested wall-anchoring illustrated in Fig. 7. This also demonstrates that the structural coloration comes from Bragg interference and not from refraction, which would result in iridescence during such a rotation.

Conclusions

We have demonstrated that the geometry of the container used for suspensions of 2D nanosheets, NaHec in our case, directly affects the alignment of nanosheets and their effective d-spacing, as measured by SAXS. We find that the clay nanosheets form nematically ordered flat coherent subdomains. The lamellar intra-domain organization of nanosheets being forced in approximately coplanar arrangement by steric restrictions warrants interference with visible light. At the same time, the local disorder by tilting, translation, and undulation of flexible nanosheets limits the coherence length as observed with X-rays to a few monolayers. This study aids in understanding the factors that influence the internal organization in these nanosheet suspensions, and thus opens for the possibility of controlled color variation by systematic adjustment of the geometry that encapsulates the suspension and/or the characteristics of the individual nanoparticles.

In the present work, we used the same type of cuvettes that were previously used for analysis of structural colors. In the future, we plan to study suspensions in specially designed cuvettes, with both different geometries and different material types. In future works, magnetic or electric fields should be applied to assist orientation of nematic domains. Also, investigations of influence of flow, of confinement geometries as well as aqueous ionic strength should be performed. It could also be of interest to study these systems using scattering beams with a smaller or larger cross-sectional area in order to look for any structural ordering at different length scales.

Spatial and orientational distribution of high aspect ratio platelets in suspension is largely defined by filling conditions and the confinement of sample container. This knowledge enables the targeted design of hectorite-based templates showing structural color. Maybe even the degree of iridescence (higher for non-bending/non-undulating platelets) may be tuned. Our findings greatly enhance the understanding of the interplay between orientation in suspension, swelling behavior, and sample container geometry, thus providing a rationale for controlling the alignment in new materials/application, for instance in coating fabrication.