Liquid crystalline structuring in dilute suspensions of high aspect ratio clay nanosheets

Aqueous liquid suspensions of high-aspect ratio 2D clay nanosheets were investigated using small angle X-ray scattering (SAXS). The high aspect ratio of synthetic �uorohectorite clays allows for investigation of liquid crystalline orientational order for relatively large nanosheet spacings, in the range which can produce structural coloration, thus providing two handles for determining the nanosheet spacings: SAXS and visible color. Various clay concentrations were investigated, and good agreement with previous work on structural coloration from such suspensions, was obtained. Particular attention is given to the con�nement caused by the container geometry, where both cylindrical and �at con�nements were investigated. In both cases, the SAXS data suggest coherent regions that have a nematic inter-orientational distribution that surprisingly is linked to the container geometry, which apparently determines the e�ciency of packing of the suspension. For both geometries the analysis suggests that these coherent regions have a 1D lamellar periodic intra-structure with uniform nanosheet spacing determined by the clay concentration and a typical coherence length in the range of 200 to 500 nm.


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, 4-8 hydrogels, [9][10][11] capture and storage of gases, [12][13][14] as well as photonic crystals producing structural colors. 15most a century has passed since Langmuir's experiments discussing clay colloidal suspensions in terms of liquid crystal structures. 16Such experiments were the basis for Onsager's seminal paper on the rst purely entropy-driven nematic phase transition. 171][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 ow. 24[30][31][32] Clay based platelets can come in two versions, 33 either as stacked nano-lamellar (> 20 nm thick) at particles, [34][35][36][37] or as delaminated thin nanosheets (ca. 1 nm for a monolayer) in aqueous suspension. 38][37]40 High aspect ratio (lateral size of 20 µm and thickness of 1 nm) 41 synthetic sodium uorohectorite (NaHec) with a nominal formula unit of , 42 can delaminate into a mixture of nematic domains and metastable colloidal accordions where the single layers are separated to uniform distances de ned by the amount of water and electrostatic interactions governing the separation. 2,38These lamellae stacks bear similarities with a smectic liquid-crystalline phase. 43By 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 signi cantly increased for dispersions of double layered clay nanosheets (DBL). 15Fig. S1 in the supplementary information shows typical re ectance spectra in the visible range for the herein investigated DBL suspensions, in agreement with literature. 15The 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 interstrati cation 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 interstrati cation into deionized water (Fig. 1).
NaHec changes its swelling behavior in dependence of the volume fraction: The rst 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-de ned 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). 42Because 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 signi cant 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 vol% to 2 vol%) to x = -1 at higher ϕ (in the range 2 vol% 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 vol % 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 con nement geometries were used for the suspensions, cylindrical capillaries 42 or at 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 nd that the con nement geometries yield power-law ϕ behaviors that are consistent with the dependencies reported in previous publications. 15,42amples and experiments Fluorohectorite Melt synthesis and long term annealing of the synthetic sodium uorohectorite ) (NaHec) was performed according to literature procedures. 44e material featured a cation exchange capacity of 1.27 mmol/g and a density of 2.73 g/cm 3 .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 uid 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 con rmed 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: 4007620) or a at 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.

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 xed 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 1M detector (Dectris, pixel size 172 x 172 µm 2 , with an active area of 168 mm x 179 mm) placed at a distance from the sample of 9.34 m, resulting on a q-range from 2.2•10 − 2 nm − 1 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 con nement, 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.The 2D diffractograms were converted by 360° azimuthal integration into their 1D representations ( ) following the beamline's standard procedure (see details in supplementary information).1D data were t using the Förster model, 45 previously used for similar studies on clay systems. 42In this model, the intensity is given by: ( where, is the scattering contrast between the clay nanosheets and the solvent, the number density of the layers, the scattering vector, the form factor of disks.The terms inside the square brackets constitute the structure factor, where is the lattice factor determining the distance of adjacent nanosheets in the liquid, is the Debye − Waller factor and is a polydispersity factor. 45 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 ts using the Förster model (disks separated by distance d).
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 coherence 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.
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 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 signi cantly 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. 42Modeling 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 de ned by the border slip conditions induced by the con nement 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 quanti able in the azimuthal plots, also given in Fig. 6.The liquid crystalline domains are better oriented in at cuvettes as can be seen from the signi cantly smaller FWHM of the Lorentzians.The FWHM are ca.10° and ca.50° for blue DBL (1.5 Vol %) sample in cuvette and capillary, respectively.See Fig. S7 and Fig. S8 in supplementary information for the azimuthal angle plots for all DBL in cuvettes and capillaries, as well as for SGL case.
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 in uence the local order of colloidal accordions.These transitions most likely in uence 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 e ciently in at cuvettes resembling the nanosheet morphology than in capillaries.
The internal domain nanosheet d-spacing increases with decreasing ϕ, as consistent with previous observations. 15,42The 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 nal explanation of this, we suggest that this could be related to the platelet anchoring and the container geometry ( at or cylindrical) which is translated throughout the sample, in accordance with previous results from nematic organization of non-delaminated clay particles. 39Another 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 in uence on the clay anchoring and packing density.Pre-aligning due to shear forces during lling 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 loose 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 modelling the tactoids in the suspension as stack of coplanar oriented discs 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.The purpose of this gure 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 withing long-range ordered nematic domains is directly related to the non-iridescent structural coloration observed in this system. 15This is illustrated in Movie S1 in the supplementary information (rotating the capillary seen in Fig. 2 (b) by 180 ° around its axis), which clearly demonstrates an angle independent behavior, despite the pronounced texture and the suggested wallanchoring 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 nd that the clay nanosheets form nematically ordered at 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 exible nanosheets limits the coherence length as observed with X-rays to a few monolayers.This study aids in understanding the factors that in uence 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 elds should be applied to assist orientation of nematic domains.Also, investigations of in uence of ow, of con nement 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 de ned by lling conditions and the con nement 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 ndings 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.

Declarations Con icts of interest
There are no con icts to declare.

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