High-Angle Structural Color Scattering Features from Polymeric Photonic Structures

Abstract

Three-dimensional goniometric measurements of structural color from melt-sheared polymer nanoparticle composites is presented revealing high-angle features arising from Bragg scattering. These features are presented in terms of ‘scattering cones’ from full 180° hemispherical scans showing the spectroscopic and angular properties of these scattering spots. This work identifies the Miller indices of the photonic crystal planes responsible for these features and makes further observations as to the appearance of this scattering in the context of these structures as quasi-ordered systems. We probe structural color metrics such as peak wavelength and the tunability of reflectance intensities. As such, this report contributes towards an improved understanding of Bragg scattering and structural color from structures with inherent disorder. The complexity and specificity of color quality across the scattering hemisphere is an important consideration for practical uses such as in sensing applications, and we suggest that soft photonics, in particular, are strong candidates in high-angle color uses.

1. Introduction

The origins of brilliant structural color from photonic crystals (PCs) are well understood in terms of strong light–matter interactions in the form of photonic bandgaps, initially put forth by Yablonovitch and John [1,2]. These stem from the resonance of light with nanoscale dielectric periodicities [3,4,5]. Sanders [6] was among the first to recognize that the characteristic iridescence of precious opal gemstones stems from the Bragg diffraction of light from the three-dimensional repetition of the constituent silica nanospheres, producing intense coloration that changes with viewing angle. This structural color appears throughout the natural world, with the distinctive tree-like repetitions within the wings of Morpho butterflies [7,8] among the most reported on structures in the photonic crystal literature. This has given rise to ‘bioinspired’ photonic crystal devices aiming to replicate the mechanisms of nature in the development of structurally colored materials. Within the field of PCs, soft photonic systems in particular are of emerging importance [9,10]. As PCs find wider application, polymeric materials are particularly strong candidates as smart materials [11,12,13,14] on account of their robustness, viscoelasticity, and capacity for large-scale fabrication by means of roll-to-roll (R2R) processing [14,15,16], which allows for consistent and inexpensive fabrication over the scale of many m².

Polymer opal (PO) thin films are, therefore, highly relevant systems in which to understand the crystallographic origins of structural color. These core-interlayer-shell nanoparticle composites are ordered by R2R melt shear fabrication [16], whereby order iterates from the outer surfaces of the films as the particle cores self-assemble into twinned fcc arrangements. During shear, a region of melt flow is continually present in the bulk—resulting in structures with inherent disorder. This is compounded by the lack of next-nearest neighbor interaction [17,18] due to the ‘sticky’ PO shells.

The structural color of POs has been extensively reported on previously [19,20,21,22,23]. However, this has been primarily in terms of the primary Bragg feature occurring from the periodicity of the {111} plane. Other Bragg features have been reported on elsewhere [24]; although, this is specifically in the context of mechanical symmetry-breaking effects [25]. Here we report on additional Bragg features present across the hemisphere of scattering, as measured with three-dimensional reflectance goniophotometry. These features are presented in terms of ‘scattering cones’ showing the spectroscopic reflectivity of the films as a function of ordering depth and viewing angle, and this scattering response is mapped to the Bragg-Snell law in order to ascertain the Miller indices of the plane(s) this scattering originates from. This work builds towards an improved understanding of the structural color of POs and additionally highlights previously unreported high-angle coloration effects from these films.

The nature of structural color stemming from photonic crystals as permanent and resistant to photo bleaching is central to its appeal in aesthetic applications, compared to traditional pigments which lack longevity and tunability. This is in addition to the environmental benefits over potentially toxic dyes, furthermore in terms of photonic crystals as solvent-free systems. In particular, high-angle structural color is pertinent to a range of device, display, and aesthetic applications. For example, Ji and colleagues [26,27] report on high-angle structural color for application in viewing-invariant color filters, and elsewhere geometry dependent photonic crystals have been touted as potential dynamic color filters [28,29]. In the latter works, structural color remained intense up to viewing angles of 60–70°. In terms of other applications, Wu et al. [30] discuss the potential of high-angle structural color PCs as anticounterfeiting mechanisms. They show how the color appearance of silica bilayer crystals was highly saturated up to viewing angles of 55–65°.

However, the vast majority of this existing work relies on multilayer films fabricated by either deposition techniques or ablation methods such as electron beam lithography, neither of which are readily compatible with mass production. Such methods can also be expensive. There remains a lack of literature pertaining to high-angle structural color from materials which can easily be applied with R2R methods, and/or harness the mechanical robustness of flexible photonic devices, which could be applied to a wider range of substrates and surfaces. Furthermore, polymer opals are materials which do not require deposition or bonding to surfaces, as they simply behave like decals or stickers. This makes them able to be installed to surfaces retroactively, and easily removed—with the possibility of being recycled if the film is in good condition. For these reasons, in addition to the inherent disorder of POs, we believe this work represents a step change away from the usual high-angle structural color paradigm in terms of reporting on materials with a notable versatility.

2. Materials and Methods

2.1. Thin Film Fabrication and Ordering Chracterization

The polymer opals reported here were fabricated from 223 nm diameter particles which comprise a polystyrene (PS) core, a poly(methyl methacrylate) (PMMA) interlayer, and a poly(ethyl acrylate) (PEA) shell in a 34:16:50 volume ratio. These particles were synthesized by starve-fed, multistage seeded emulsion polymerization [31], whereby surfactant quantity can be altered to tune final particle size and, hence, resultant color appearance. Following synthesis, the particle slurry was dried into precursor material, which was then extruded into 1 mm thick ribbons with a Haake MiniLab co–rotating screw extruder. The ribbons were laminated together between PET strips and compressed to form POs (Figure 1a) with a bespoke kit. At this stage, the films are highly disordered and characterized by a milky-blue appearance originating from the structural correlation length [32].

The POs are then ordered by Bending-Induced Oscillatory Shear (BIOS), first proposed by Zhao et al. [16]. The films, of approximately 100–150 µm thickness, are drawn over 1 cm diameter rollers, heated to 100 °C at a shear rate of 1 cm s⁻¹, with the shear direction ĝ indicated. This is repeated 0–40 times in order to obtain improved sample ordering, which is optimal at 40 BIOS iterations (see illustrated inset). The cross-linked PS cores remain rigid as they are forced by the compression to flow through the soft poly(ethyl acrylate) matrix. The end result is rubbery, free-standing films displaying intense structural color which changes with viewing angle and illumination, pictured rightmost in Figure 1a. With the resulting peak wavelength of color appearance dependent on the CIS particle diameter, this process has previously been tuned to engineer POs reflecting in the UV [33] through to red [21] and near-infrared part of the spectrum.

BIOS processed POs have been extensively reported and have been characterized using electron microscopy [20] and small-angle X-ray scattering (SAXS) [34] among other techniques, which have hinted that optical features away from the {111} direction should be visible. Further transmission electron microscopy (TEM) reported in Figure 1b–d validates the expected ordering of these structures as a baseline of efforts to begin probing these other planes. Microscopy was performed with a Thermo Scientific Talos L120C G2 operating at 120 kV in Montage Mode. The films were microtomed into 60–80 µm thickness slices using a Leica EM UC7 & FC7 diamond knife at −60 °C. This was perpendicular to the shear direction to obtain a series of film cross sections, in order to probe the inner ordering mechanics of BIOS where it is well understood that, due to the melt shear nature of the process, a disordered region remains in the center of the film. The slices were stained with RuO₄ vapor on copper grids. Figure 1b–d shows the internal structure of 0, 20, and 40 BIOS POs, respectively, with the film surfaces shown at the top of the images. These images have been digitally enhanced for improved clarity to account for staining difficulties. This microscopy clearly shows that structural order begins at the outer surfaces of the films and propagates inwards with successive shear—although, bulk ordering is not achieved (not shown). A high degree of ordering is observed in 40 BIOS opals (Figure 1d), with the PS cores arranged in straight layers. This is seen to occur over the regime of many particles, with ordering depths having previously being shown to extend past the Bragg penetration depth [20]. This is in agreement with separate studies [16] which showed these structures to demonstrate twinned face-centered cubic (fcc) packing [17,18,35].

2.2. Reflectance Characterization

Three-dimensional relative reflectance goniophotometry was undertaken with a Reflet 180S in a dark box. This is illustrated in Figure 2 in order to elucidate the co-ordinate geometries. The collection optics can move freely within any values of measurement, or viewing angle θ_m, and viewing plane angle ϕ_m in the upper hemisphere of the instrumentation. This allows a number of planes of scattering to be studied and the viewing angle dependency of the resultant color appearance to be fully examined. θ_m and the incident illumination angle θ_I are defined as 0° at the zenith, whereas ϕ_m is defined as ±90° in the plane of illumination. The sample stage height is adjustable to align the focusing optics and incident light with the sample surface.

The spectrometer was calibrated with respect to a 99% Lambertian reflectance standard and dark background. The measured values of light intensity are then applied, whereby the dark background is subtracted from the measured intensity, with this divided by the reflectance profile of the Lambertian standard and then multiplied by 100% to give relative reflectance. To calibrate with respect to a mirror or light source would cause relative reflectance values to be very low outside of the specular direction. Hence, calibration with respect to an omnidirectional scatterer alleviates this issue to bring values into the normal range, important for the consideration of structural color visible at high angles away from the specular. As a caveat, care should be taken with this technique as around the specular direction values become very high and, thus, are removed from the spectra in postprocessing.

The PO films are aligned with the shear direction ĝ parallel to the plane of illumination, ϕ_m = ±90°. A collimated 3200K halogen tungsten bulb was incident on the films in a spot size of approximately 8 mm, with the angle of illumination given as displacement from the zenith. Scattered light was collected by the detector, with a collection solid angle of 3.3 × 10⁻⁴ Sr, which was fiber coupled to a CCD spectrometer. The light source and detector rotate approximately 20–25 cm from the center of the instrument. Measurements were taken over complete viewing hemispheres −90° ≤ θ_m ≤ 90° in 0.1° angle increments, with spectrometer collection taken over the complete visible wavelength range of 380–780 nm in increments of 1 nm. This was fully automated within the Reflet 180S software which returned this data as a complete matrix of relative reflectance over the viewing hemispheres.

3. Results and Discussion

Hemispherical scans of relative reflectance are shown in Figure 3 for polymer opals of 0, 20, and 40 BIOS passes, showing the change in structural color properties as a function of increasing structural order and ordering depth [20]. These represent the stacked spectra collected at every viewing angle between ±90°, where the opal is illuminated from the zenith. The scattering features of interest are shown enlarged for each opal, with these rescaled for clarity in Figure 3d–f. Relative reflectance can be seen to exceed 100% due to measurements having been taken with reference to a Lambertian scatterer which scatters omnidirectionally as discussed, compared to polymer opals which by their nature as photonic crystals display preferential scattering directionality. The most intense specular scattering around the 0° viewing direction has been removed, in addition to detector obscuration.

One can observe the high-angle scattering feature to be of low intensity relative to the wider scattering envelope (see Figure 3a) for a 0 BIOS film. However at 20 BIOS, Figure 3b, this feature has fully come into focus, and intensity was seen to peak at 40 BIOS passes (Figure 3c). This feature is visible over viewing angles 70° to 20°, in line with the highest viewing angles of structural color reported in the literature; although, closer to the specular the scattering is rapidly superseded in intensity by a central scattering feature originating from the {111} plane. As shown in Figure 3c, the symmetry of the high-angle scattering feature is shown to degrade as viewed either side of the specular, illustrated by the difference in appearance of scattering around the θ_m = ±50° directions. This is likely to be the result of the competitive ordering–disordering of the BIOS process, whereby the melt shear process eventually begins to degrade the structural crystallinity. These structural changes also serve to affect the shape of the scattering feature, shown particularly clearly by Figure 3e,f. The peak wavelengths of the high-angle feature and central scattering cone around 0° were extracted in 10° increments, and fitted to the Bragg-Snell law:

$$m\lambda =2d\sqrt{n_{eff}{}^2-{\sin }^2{\theta }_I},$$

(1)

where the value of effective refractive index n_eff is taken from the literature to be 1.52 [36]. The plane spacing d₁₁₁ was calculated from the peak wavelengths extracted from the primary scattering feature shown around the 0° viewing angle from the {111} plane. This is carried out by fitting Voigt functions away from the specular at a viewing angle where both the {111} and high-angle feature have distinct intense peaks in the spectra in order to give the most accurate result.

Extraction of the peak wavelength allowed for calculation of the lattice parameter a:

$$d=\frac{a}{\sqrt{h^2+k^2+l^2}}$$

(2)

which varies slightly as a function of BIOS as the crystal experiences deformation, taking on calculated values between 343 and 352 nm. For example, for 40 BIOS, the central wavelength of the 1st order reflectance peak from the {111} plane for θ_m = −40° is 552 nm, which according to the Bragg-Snell in calculating d₁₁₁:

$$d_{111}=\frac{\lambda }{2\sqrt{n_{eff}{}^2-{\sin }^2{\theta }_I}}=\frac{552 \mathrm{nm}}{2 \sqrt{{1.52}^2-{\sin }^2\left(-40\right)}}=200.4 \mathrm{nm} \pm 2.3.$$

(3)

Inserting the calculated value of d₁₁₁ to calculate the lattice parameter a:

$$a=d_{111}\sqrt{h^2+k^2+l^2}=200.4 \mathrm{nm}\ast \sqrt{3}=347 \mathrm{nm} \pm 4.$$

(4)

Given the core-shell particle diameter of 233 nm, the calculated values of a are in the expected range for a face-centered cubic crystal. Reversing this process in order to calculate the Miller indices for the high-angle scattering features, for 40 BIOS one extracts the central peak wavelength at the same viewing angle of θ_m = −40° of 452 nm in order to calculate the plane spacing:

$$d_{???}=\frac{452 \mathrm{nm}}{2 \sqrt{{1.52}^2-{\sin }^2\left(-40\right)}}=164.1 \mathrm{nm} \pm 2.3.$$

(5)

The usual crystallographic relationship between lattice parameter a, plane spacing d, and Miller indices was then applied to find the Miller indices corresponding to the peak wavelengths of the high-angle scattering feature. The relationship between d_??? and a = 347 nm as calculated previously is given by:

$$\sqrt{h^2+k^2+l^2}=\frac{a}{d}=\frac{347}{164}=2.12 \pm 0.04 \approx 2$$

(6)

with the only allowed combination of h, k, and l for the face-centered cubic lattice case being given by the {002} plane group. In the same manner, peak wavelengths were extracted prior with the fitting of Voigt functions; this is carried out for viewing angle values from −80° to 80° in 10° increments, where possible. This fits to values expected in accordance with the Bragg–Snell law, as shown by Figure 4. The central specular feature given by the {111} plane is denoted in red, with the {002} plane group feature shown in blue, and the dashed lines corresponding to the Bragg-Snell law behavior. Error is seen to be somewhat greater for the {002} feature due to the difficulty in accurate peak wavelength extraction where intensity is markedly lower. Nevertheless, these calculated values of h, k, and l show a good fit to the Bragg-Snell law and this data conclusively evidences the Bragg scattering origins of this high-angle structural color. Although the level of fit is seen to depreciate past approximately 50°, the fit remains acceptable up to around 70° for 20 and 40 BIOS. Our previous work [20] has highlighted that good structural ordering is seen to reach the Bragg penetration depth of around 10 µm for approximately 10 BIOS, and this is the primary suggestion as to why the fit with Bragg-Snell is particularly poor for 5 BIOS. This is most pertinently the case around the specular direction, illustrated by a dip in the peak wavelengths (Figure 4a). Here, the measured light penetrates deepest into the sample before reflection, so this corresponds with the viewing direction where the measured scattering is most sensitive to the crystalline disorder that persists in the film at this stage in processing. This is, furthermore, evidenced by that seen for 10 BIOS, where around the specular viewing direction the fit to Bragg-Snell is markedly improved in line with reasoning that ordering has now permeated down to the Bragg penetration depth. This figure additionally elucidates other structural changes that occur as BIOS advances—for example, the Bragg-Snell fit for the {002} plane is shown to reach an optimal point at 10 BIOS. Asymmetry in peak wavelength is clearly evident for 20 BIOS at viewing angles of ±20°, and this area of the fit continues to depreciate for 40 BIOS over the range ±10–30°. This is likely caused by the innate disordering mechanisms of shear [16] beginning to affect the outer layers of the crystal, because one can also observe how the {111} fit drifts from the expected behavior, albeit slightly. Indeed, this suggestion is also evidenced by the discrepancies in the calculated values of the lattice parameter indicate deformation competing with self-assembly. Further work is necessary in optimizing the ordering depth obtained from BIOS in line with desired application, and mapping this in further detail to other structural color metrics such as reflectance intensity and color purity, in addition to quantification of the color appearance.

Figure 5 provides further insight regarding the interplay of the two scattering features, with spectroscopic data shown for the (a) θ_m = 70° and (b) −10° viewing angles. It was not possible to observe the specular direction for illumination from the zenith due to obscuration by the detector. With successive structural ordering, the {111} reflectance peak is shown to become the dominant scattering feature, and reference to Figure 3 indicates this occurs around viewing angles of approximately 20–30° displaced from the zenith. The wavelength FWHM of the {111} seen to sharpen as order permeates the structure, in line with expectation. Whilst direct evaluation of the {002} peak FWHM above the background continuum is difficult, the reflectance intensity increases significantly with viewing angle towards the center of the feature at approximately 50°. Additional understanding of the tuning of this peak could be used as a potential ordering parameter for the system, for example, in terms of FWHM or in terms of comparison with the {111} peak. Further work in optimizing the BIOS process could lead to the enhancement of the {002} reflectance relative to the background, which would evidently be a necessary factor in polymer opals finding high-angle applications.

4. Conclusions

In conclusion this work presents new insights regarding high-angle scattering features from polymer opals, melt-shear-ordered photonic crystals. These features are shown to appear up to 70° removed from the specular viewing direction. Evidence is presented as to their origin associated with the {002} plane group of the twinned fcc structure, determined from the good agreement with the Bragg-Snell law across the viewing plane. The relative reflectance intensity is seen to increase as structural order is gradually introduced into the films. Further data is presented showing the interplay of the {111} and {002} reflectance peaks which features as a function of structural order, and results from the complex ordering–disordering mechanisms stemming from melt shearing. An improved understanding of Bragg scattering from structures with some inherent disorder, and the complexity of structural color quality across the scattering hemisphere, lends itself to such materials being developed as a low-cost, readily scalable, soft photonics approach finding applications as diverse as antiforgery and sensing devices. This is important on account of the understanding of systems with an inherent compatibility with roll-to-roll processes.