Iridescence in nematics: Photonic liquid crystals of nanoplates in absence of long-range periodicity

Significance

The striking colors of organisms, like butterflies, have sparked tremendous research interest in developing artificial photonic crystals with extraordinary optical properties. In most cases, the color of photonic crystals originates from the periodic microstructure that manipulates light through optical interference. Here, we report a photonic structure that does not rely on long-range periodic arrangements. Instead, such structural color comes from the nematic liquid crystals of nanodiscs as opposed to the conventional achiral nematic phases that are colorless under white light. This finding challenges the stereotypical design of photonic liquid crystals based mainly on periodically layered or helical structures. We expect that the concept of nematic photonic nanoparticles may open research opportunities for developing advanced photonic materials.

Abstract

Photonic materials with positionally ordered structure can interact strongly with light to produce brilliant structural colors. Here, we found that the nonperiodic nematic liquid crystals of nanoplates can also display structural color with only significant orientational order. Owing to the loose stacking of the nematic nanodiscs, such colloidal dispersion is able to reflect a broad-spectrum wavelength, of which the reflection color can be further enhanced by adding carbon nanoparticles to reduce background scattering. Upon the addition of electrolytes, such vivid colors of nematic dispersion can be fine-tuned via electrostatic forces. Furthermore, we took advantage of the fluidity of the nematic structure to create a variety of colorful arts. It was expected that the concept of implanting nematic features in photonic structure of lyotropic nanoparticles may open opportunities for developing advanced photonic materials for display, sensing, and art applications.

Followed by the rise of graphene, significant advances have been witnessed in the field of 2D nanomaterials (1). This has led to particular research interest in understanding the collective behaviors of 2D nanomaterials in suspension (2). Like other anisotropic particles (e.g., rods), 2D nanomaterials can form liquid-crystal (LC) phases when dispersed in a solvent (3). Driven by entropic interaction, the self-assembly of 2D nanodiscs can produce a fascinating variety of LC structures ranging from orientationally ordered nematic (N) to positionally ordered structures, including lamellar (L) and columnar (C) phases with positional order in 1 and 2 dimensions, respectively (4). These superstructures with controlled ordering have emerged as promising paradigms addressing challenges in energy storage (5), controlled drug delivery (6, 7), and self-healing materials (8). For example, by controlling liquid-crystalline alignment of 2D titanium carbide (MXene), researchers have demonstrated thickness-independent capacitance of vertically aligned nanosheet-based film (5). Additionally, the integration of LC ordering of 2D nanomaterials and additive manufacturing techniques (e.g., 3D printing), may enable advanced assembly technology for fabricating flexible and wearable electronics (9, 10). Therefore, developing approaches of understanding and manipulating the mesoscopic ordering of nanodiscs will significantly forward practical application of 2D nanomaterials.

Among various types of ordered nanoarchitectures, photonic liquid crystals (PLCs) of 2D nanomaterials have attracted recent attention owing to the ability of dynamically interacting with the light of interest to achieve brilliant reflection colors (11). Generally, the color of PLCs originates from the periodic structures with long-range positional ordering, such as lamellar or helical arrangement (12–17). In particular, lamellar structure is one of the most studied designs for fabricating photonic materials of 2D building blocks due to the structural similarity to natural nacre and pearls (18). For example, several lamellar 2D monolayers, including graphene oxide and titanium oxide nanosheets (19, 20), have been developed into colorful PLCs. By contrast, forming visible color by nematic structure is notoriously difficult due to the lack of long-range periodicity in most nematic phases. Most theories of lyotropic nematic phase have focused on its orientationally ordered features (21, 22), while the possibility of structural coloration has yet to elicit much attention. To date, the only colorful nematic materials were found to be chiral nematic (N*) phase with the prerequisite of a chiral structure (23), which limits the choices of nanoscale building blocks. In addition, the colorful chiral phase has been mainly found in small-molecule thermotropic LC systems, while it remains debated if colorful N* phase of nanosheets is feasible (23). In consequence of smaller order parameter (i.e., less crystalline), the nematic phase may allow higher flexibility and larger directional diffusivity (24, 25), and thus is promising for dynamic chemical/biological sensing, which would be complementary to existing photonic materials with prolonged response to stimuli (26, 27). In addition, as lamellar structure requires high monodispersity in nanoplate thickness, toxic chemicals or strong oxidizers are often necessary to prepare monolayers during exfoliation (19, 20, 28), while the less-ordered nematic structure may circumvent such requirement (29). Despite these advantages, however, developing a photonic structure based on achiral nematic phase remains a formidable task, as the nematic platelets dispersion must be developed in a way that can selectively reflect light in absence of long-range periodicity.

Here, we report a photonic crystalline dispersion based on unexfoliated 2D materials (zirconium hydrogenphosphate, ZrHP) without involving any strong long-range positional ordering. Instead of developing a lamellar structure by monolayers, we took advantage of the local correlation of nematic nanodiscs with controlled size and polydispersity, resulting in reflecting a broad reflection wavelength with vivid color. The ZrHP platelets with low polydispersity were prepared by a method involving gravity-driven size segregation followed by centrifugation of selected fractions (Fig. 1A). Under gravity, the size segregation occurs as larger particles tend to sediment faster due to Stokes’ law, where the terminal sedimentation velocity increases as the square of particle size (R²) for spherical particles (30). As shown in Fig. 1B, we loaded the nanodisc suspension into a cylindrical glass vial, allowing gravitational fractionation for 20 h, after which the desired fractions of suspension were collected and centrifuged to yield the final product. A much longer sedimentation time was also performed on ZrHP samples, where we observed an iridescent layer at the top of the sediments. The size segregation was confirmed using scanning electron microscopy (SEM). As shown in Fig. 1C, the pristine ZrHP platelets showed a polydisperse morphology, whereas a much-narrowed distribution of platelet size was seen for fractionated ZrHP (Fig. 1D). Quantitatively, the fractionation process caused a significant reduction in platelet polydispersity (σ) from 0.58 to 0.13, while a similar decrease in diameter was also observed (SI Appendix, Fig. S1). Measured by atomic force microscopy, the average thickness of ZrHP platelets was 46.6 nm of ZrHP (SI Appendix, Figs. S2 and S3). Remarkably, we observed that an iridescent structure started to form when the fractionation experiment proceeded at high volume fraction (ϕ > 15%, Fig. 1 D, Inset). These suspended colloidal nanoplates strongly diffract visible light and render the solution vivid and monochromic colors. Such diffraction of visible light can originate from the positional order of lamellar structure or local correlation of nematic nanodiscs (Fig. 1E). Despite increasing advances in colorful lamellar structure (19, 20), direct evidence of photonic structure based on local correlation of nematic nanodiscs has not been experimentally proven yet.

Fig. 1.

The gravity-driven fractionation of ZrHP platelets. (A) Schematic illustration of fractionation process under gravity. (B) Digital camera images of ZrHP suspension: (A) t = 0 min; (B) t = 4 min; (C) t = 5 h; (D) t = 9 h; (E) t = 20 h; (F) t = 100 h. (C and D) SEM images of (C) pristine ZrHP and (D) fractionated ZrHP. (D, Inset) The dispersions of fractionated ZrHP in water. The concentration of ZrHP in dispersion increases from left to right, showing a blue shift in structural color. (E) Schematic illustration of proposed color mechanisms of lamellar and nematic colors. The color of lamellar structure comes from the multilayer interference, while the local alignment of nematic nanoplates may also produce structural color under suitable conditions.

To investigate the color behavior of the ZrHP platelets, we suspended platelets at various concentrations in water. To reduce the background scattering effect and enhance the color contrast, we added a small amount of carbon black (0.1 wt %) into the ZrHP dispersions. As shown in Fig. 2A, a variety of structural colors (including red, green, and blue) were seen upon increasing the platelet volume fraction. By changing [ZrHP] from 29.7 to 14.8%, the structural color of ZrHP can be smoothly modulated from the blue (497 nm) to green (559 nm) and to red (644 nm) in a wide spectral range (Fig. 2B). It was found that the UV-vis reflection peaks throughout the system are quite broad, signaling the presence of short-range order of nematic phase since scattering pattern of nematic phase is typically much wider than that of lamellar phase (Fig. 2 B, Inset) (4). The uniform and single color throughout the system suggests the formation of an ordered structure that follows Bragg–Snell equation λ_max = 2(d/m)(n² − sin²θ)^1/2, where d is the average lattice spacing, m is the order of the Bragg reflection, θ is the incidence angle of light, and n is the average refractive index of the suspension (19, 31). Fig. 2C shows the peak wavelength (λ_max) of ZrHP dispersion as a function of (1 − ϕ)/ϕ; a linear correlation was observed, which is comparable with small-molecule photonic system (32). The interlayer spacing (d) was also estimated by Bragg’s equation (Fig. 2C), showing a similarly linearly proportional relation to (1 − ϕ)/ϕ. To calculate water layer thickness, we applied a modified Bragg’s equation for a two-component system (SI Appendix, Fig. S4). It was found that the water layer thickness was in the range of 130 to 200 nm; such bulky interparticle distance (10² nm) is much larger than the intermolecular distance of thermotropic LC (∼1 nm) (33, 34). Despite that the colors can be tuned by particle concentration, we found the color is not highly sensitive to surface anchoring. Upon shearing with different types of substrates, the PLC shows no significant change in color intensity or wavelength (additional discussion on ZrHP color under shearing/disturbance can be found in SI Appendix, Figs. S5 and S6).

Fig. 2.

The structural colors of platelet suspensions. (A) Digital camera images of colorful ZrHP drops with different concentrations: (A) ϕ = 0.15; (B) ϕ = 0.23; (C) ϕ = 0.28; (D) ϕ = 0.32; (E) ϕ = 0.39; (F) ϕ = 0.39 (unfractionated ZrHP). (B) UV-vis spectra of platelet suspensions showing a wide range of colors. The inset proposes different scattering patterns from nematic (N) and lamellar (L) phases. (C) The maximum reflection wavelength (black) and calculated average d spacing (blue) of platelets with different volume fraction.

Based on UV-vis analysis, we expected the structural color of ZrHP origins from the long-range positional ordering, e.g., smectic or columnar phases. To understand the self-assembly of nanodiscs, we used field-emission SEM to analyze the photonic structure in microscale. As the electrostatic repulsion between ZrHP platelets would disappear with the evaporation of water, the microstructure of PLC dispersion would completely lose its initial alignment. To prevent the collapse of ZrHP nanodiscs, we introduced a freeze-drying process to preserve the structural features of ZrHP dispersion followed by SEM analysis of cross-section samples. As shown in Fig. 3A, no long-range ordered lamellar structure was observed in the samples. Instead, the SEM image revealed a rather twisting and bending structure showing elongation with periodic lines in some local regions. Such alignment of platelets was in direct contrast to the positional-ordered lamellar structure with long-range periodicity (e.g., smectic structure) (4). Furthermore, one of the most conclusive tools to determine colloidal structure is the small-angle scattering techniques (35). In particular, the small-angle neutron scattering (SANS) was preferred for our unexfoliated nanodiscs, as SANS has a higher penetration of bulk unexfoliated samples than small-angle X-ray scattering. As shown in Fig. 3B, the formation of high positional ordering was also disapproved as there is no observable signal of long-range positional ordering within the q range investigated despite varying of the vol % of ZrHP from 0.1 to 31.4%. This suggests that there is no visible smectic layer ordering with a long correlation length in the ZrHP dispersion. At the highest concentration of 31.4%, a small peak around q = ∼0.9 Å⁻¹ was observed, whose length scale $\left(\frac{2\pi }{q}=\sim 7\mathrm{\AA }\right)$ reasonably agrees with the well-known interlayer distance of ZrHP (36). Since the contrast for this interlayer structure is not strong enough, similar peaks were not observed in the lower concentrations. For positional-ordered lamellar structure, a series of sharp scattering peaks were expected with a q ratio of 1:2:3. To rule out the possible positional ordering in a larger length scale, we also performed extended q-range SANS. As shown in SI Appendix, Fig. S7, no observable peak of significant positional ordering was found. This was also confirmed by 2D SANS measurements (SI Appendix, Fig. S8).

Fig. 3.

Structure characterization of platelet suspensions. (A) Field-emission SEM images of freeze-dried platelet samples. (B) SANS measurements of platelet suspensions. (C) Theoretical prediction of phase diagram of discotic particles. (D) Polarized light microscopy of an as-prepared platelet suspension showing flow-induced birefringence. A nematic defect can be observed after equilibrating overnight (Inset). (E) UV-vis reflection spectra of platelet suspensions showing the structural colors tuned by NaCl (long dash) and NaH₂PO₄ (short dash). (F) Reflection spectra of platelet suspensions showing the structural colors tuned by charged polymer. (Inset) The structural color blue-shifting with CNC concentration. (Scale bars in A, Inset and D, Inset are 5 and 10 µm, respectively.)

To identify the phase details of ZrHP, we next investigated the LC feature of nanodisc dispersion by polarized optical microscopy (POM). As shown in Fig. 3D, the POM image of ZrHP suspension revealed a strong anisotropic texture upon loading samples due to the shear-induced birefringence. After equilibrating the sample overnight, a characteristic nematic texture was seen (Fig. 3 D, Inset) (37, 38). No focal conical defect or oily streak defect, typical defects for smectic or cholesteric phase, was observed. The POM results were well consistent with SANS results where no significant positional ordering was found. In fact, theoretical works have made extensive effort on predicting LC phase formation for a specific shape and volume fraction of nanoplates. Based on Onsager’s second virial theory, Wensink and Lekkerkerker studied the hard colloidal platelet phase diagram for different aspect ratios using the Parson–Lee decoupling approximation for multiple-body interactions (39). The phase diagram predicts liquid-crystalline phase formation: isotropic, nematic, and columnar phases. As the volume fraction increases, an I-N-C phase transition would be expected (Fig. 3C). In our study, the aspect ratio was estimated to be 0.031 and the volume fraction of nanodisc suspension ranged from 0.15 to 0.40, which falls into the nematic region in the phase diagram and confirms our experimental observation.

The structural color that we observed in nematic phase is sort of counterintuitive considering that nematic mesogens possess solely long-range orientational order and lack periodically positional order. Here we attributed the structural color to the strong stacking of the nematic nanodisc that forms local order. Such nematic phase, often called cybotactic or columnar nematic, consists of platelets that tend to stack over short distances, forming locally aligned structure (4). Although the detailed reason remains unclear, we hypothesize that the large plate size and low thickness polydispersity might improve interlayer interactions, producing a stable smectic-like layer ordering with a short correlation length in the N phase. Such locally aligned structure of neighboring flakes forms an average stacking distance that is at the same length scale of visible-light wavelength (∼10² nm, Fig. 2C). In contrast to ZrHP-based LC, the spacing of small-molecule nematic LCs is several orders of magnitude smaller than the wavelength of visible light, and thus these LCs usually do not show structural color. The distinctive optical behavior of nematic ZrHP dispersion highlights the difference of discotic particle-based LCs from small-molecule LCs. The cybotactic nematic structure was confirmed by SEM images: The platelets situated far apart are not correlated in long range, while it is evident that some neighboring flakes are locally stacked. In addition, the UV-vis reflection peaks throughout the system are considerably broad, confirming a marked positional short-range order of nematic phase. As ZrHP are charged plates (zeta potential = −31.0 ± 8.5 mV), we expected that a change of the Debye length induced by ionic concentration may offer a versatile approach to manipulate the self-assembling color. To quantify it, we adjusted the ionic strength of nanodisc suspension by varying salt concentration with different anions including Cl⁻ and H₂PO₄⁻. As shown in Fig. 3E, the structural color of PLC suspension blue-shifted sharply with increasing NaCl concentration from zero to 0.2 mM and then to 2 mM; this indicated that strong electrolyte NaCl induced a Debye screening of charged platelets, and thus decreased average d spacing. The addition of NaH₂PO₄ showed a similar trend of color shift, although the change of color was less significant. In addition to the small-molecule electrolyte, we also studied the effect of polymer electrolyte on the structural color of ZrHP, in which we added the cellulose nanocrystals (CNC) with the charged sulfate groups (-OSO₃-). Upon increasing the CNC content, the peak wavelength decreased continuously (Fig. 3F), allowing for PLCs with optically tunable red, green, and blue color, as demonstrated in Fig. 3F (Inset). It is worth noting that CNC can form chiral nematic alignment, and even achieve various structural colors at high concentration (>50 wt %) owing to its periodical pitch at high concentration (40). However, as the added CNC concentration is relatively low throughout our system (<2 wt %), we can ignore the intrinsic color of CNC in the CNC/ZrHP mixture (41).

As the discotic nematic PLC is not composed of monolayers, we expected an improved thermal stability in our PLCs. It was reported that conventional heating/drying processes of monolayer-based LC material can cause irreversible structural change to PLCs of 2D monolayers (31, 42). First, we evaluated the thermal stability of unexfoliated ZrHP dispersion by multiple heating–cooling cycles. In each heating–cooling cycle, the sample was held first at 20 °C for 10 s, then heated to 80 °C at a rate of 1 °C/s, followed by being held at 80 °C for 10 s, and finally cooled to 20 °C at a controlled rate of 1 °C/s. Despite multiple heating–cooling cycles, the color of PLCs remained almost unchanged after 200 and 400 cycles, as shown in Fig. 4A. This indicates the exceptional color stability of the nematic dispersion over this temperature range. For comparison, monolayer-based PLCs were prepared and evaluated under heating–cooling cycles, showing an obvious change in color intensity (SI Appendix, Fig. S9). In addition, we found the ZrHP showed an even higher thermal stability. After thermally treating ZrHP powder at 200 °C for 100 h, the dispersion of these particles (Fig. 4 B, Right) demonstrated the almost identical color feature in comparison with the as-prepared one (Fig. 4 B, Left). It is worth mentioning that the ZrHP dispersion becomes blue-shifting at 80 °C in comparison with its structural color at room temperature (20 °C), as shown in SI Appendix, Fig. S10. This can be explained by the fact that heating process promotes the dissociation of ion pairs on the ZrHP surface to enhance the ionic strength, leading to a decrease in Debye length and a blue-shifting structural color (19).

Fig. 4.

Thermal stability of ZrHP platelets and their suspension. (A) The thermal stability of ZrHP dispersion. A colorful droplet after 200 and 400 heating–cooling cycles showed the same blue color without observable change. The PLC droplets were sealed in centrifuge tubes during the thermal cycling to prevent possible H₂O evaporation. (B) The thermal stability of ZrHP particles over 100 h. Upon dispersion in water, the ZrHP particles showed the almost same color before (Left) and after thermal treatment (Right) at 200 °C for 100 h.

The low elasticity and high flexibility of PLC enabled the possibility of developing colorful “inks” and “papers” using the same material. As different structural colors can be seen under different ZrHP concentration, a photonic palette including the pigments with red, yellow, green, and blue colors was obtained by simply adding the proper amount of water into concentrated ZrHP suspensions (Fig. 5A). These photonic inks can be manipulated with different shapes and angles, allowing direct ink writing on a glass substrate (Fig. 5B, Lower). Meanwhile, owing to the stimuli-responsive nature of photonic inks, a small amount of dopant CNC can be used to control on-demand the color of writing (Fig. 5B, Upper). To obtain a photonic paint, we employed a strategy involving pretreated glass as the art template (see details in SI Appendix, Fig. S11). A selected pattern was first taped on a glass substrate before a commercially available hydrophobic coating was applied. After removing the templates, the photonic ink can be readily applied on the glass, forming a photonic “wave” pattern with good resolution (Fig. 5C). In addition to direct ink writing on glass, a “water marbling” can be obtained by applying shearing force on the surface of photonic ink. Such idea is “borrowed” from ancient Japanese art, i.e., so-called suminagashi, in which a shear force was skillfully applied to the surface of the ink. Without applying any shear force, the PLCs automatically aligned at the air/water interface, forming a “blank state” (Fig. 5D). By applying a shear force to stir photonic ink (ϕ = 0.32) using a plastic stick, a heart-shape suminagashi with blue color was obtained. In addition, a cyan suminagashi of “flower” can also be made by changing the platelet content to ϕ = 0.30, demonstrating water-based photonic arts with different structural colors.

Fig. 5.

Photonic patterning and coffee art by platelet suspension. (A) A color palette obtained by ZrHP with different volume fractions. (B) Iridescent “TAMU” and “123” made by ZrHP suspension on glass substrate. (C) Photonic pattern before (Left) and after adding ZrHP suspension (Right) on glass substrate with hydrophobic coating (Scale bar, 1 cm.) (D) The dispersion of ZrHP in water showing various drawings in comparison with coffee art.

In summary, we demonstrated that nonperiodic nematic LCs of nanoplates can show iridescent color. Despite the nematic mesogens possessing solely long-range orientational order, the large platelet size and improved polydispersity favored interlayer interactions, yielding locally aligned structure in the length scale of visible wavelength. This finding reshaped the stereotypical design of PLCs based mainly on periodically layered or helical structures. Furthermore, we demonstrated that such structural colors are highly tunable and can be readily assembled into different photonic patterns. Due to the high stability of unexfoliated nematic flakes, we showed the structural color was stable after 400 heating–cooling cycles. The research offers a facile, straightforward, and highly flexible approach of assembling 2D nanomaterials into nematic photonic liquid, which is expected to find applications in chemical sensors, optical display, and biological indictors.

Materials and Methods

Materials.

Crude ZrHP powder was obtained from Sunshine Factory Co., Ltd. Sodium chloride (98%) was purchased from Avantor Performance Materials. Sodium dihydrogen phosphate (99%) was obtained from Sigma-Aldrich. Carbon black (99.9%) was purchased from Alfa Aesar. CNC was obtained from UMaine Process Development Center.

Fractionation of ZrHP.

First, 5 g of pristine ZrHP powder was dispersed in 20 mL deionized H₂O. Then, the ZrHP dispersion was vortexed for 1 min, followed by sonication for 30 s, allowing the ZrHP platelets to be fully homogenized in aqueous suspension. Next, the resulting white dispersion was transferred into a cylindrical glass vial before the fractionation occurred. After 20 h, the resulting suspension was separated into different fractions to obtain fractionated platelets. Of the liquid, 20–80% fractions were collected and centrifuged, whereas the other fractions were discarded. Finally, the obtained ZrHP was dried at 65 °C in an oven before usage. To enhance the structural color, 0.1 wt % of carbon black particles was added.

Photonic Arts.

For the photonic ink experiments, we prepared different concentrations of ZrHP in water as paints, where a small amount of carbon black was added to enhance color contrast. The photonic arts were achieved by simply dropping ZrHP paint on a pretreated glass substrate on which template tapes and hydrophobic coating were applied.

SANS Measurement.

SANS measurements were conducted at the Spallation Neutron Source at the Oak Ridge National Laboratory using extended q-range SANS diffractometer (beam line 6) (43, 44). To cover the q range (0.003 Å⁻¹ < q < 1 Å⁻¹), three configurations were used at sample-to-dectector distances of 1.3, 2.5, and 4 m, with wavelength bands defined by minimum wavelength of 2.5, 2.5, and 10 Å. Samples were loaded to 1-mm quartz cells. The empty cell scattering was subtracted from all data. Measured data have been corrected for detector sensitivity, dark current noise, angle-dependent transmission, and time-of-flight corrections using MantidPlot software package (45).

Characterization.

The reflection colors of platelets were measured by UV-vis spectra (Hitachi U-4100 UV-Vis-NIR spectrophotometer). A field-emission SEM (JEOL JSM-7500F) was used to obtain SEM images of samples. The thermal cycling test was performed using a Px2 thermal cycler (Thermo Electron Corporation). To prevent possible H₂O evaporation, PLC samples were loaded in 0.2-mL plastic tubes which were then sealed for thermal cycling analysis.