Structurally colored silica foams using colloidal templating

Abstract

We produce solid silica dry foam structures that exhibit structural color. For this purpose, we use densely packed colloidal microgels decorated with silica nanoparticles that are much smaller than the microgels. By concentrating and overpacking the microgel particles, we can control their morphology so that the silica nanoparticles spontaneously form honeycomb-like structures or networks. We obtain pure silica dry foam structures by burning the organic polymer, leaving behind silica networks. The resulting foams exhibit vivid structural colors. We can control the color by changing the microgel particles’ size and degree of compression. Furthermore, thanks to the softness of the particles, compression can also lead to the appearance of facets. This faceting behavior distinguishes microgels from hard spherical particles. We present details about the synthesis and fabrication strategies and report on a comprehensive characterization of optical and structural properties. Our study provides insight into the fabrication of innovative self-assembled materials with structural colors by colloidal templating.

1 Introduction

Solid foams are materials typically made by dispersing gas bubbles in a matrix that is subsequently solidified. Such materials are used in various fields, including food, acoustics, cosmetics, gas filters, construction, and insulation, making them an important class of materials in industry Liu et al. (2006); Yan et al. (2011). The pore sizes of foams can range from a few nanometres to hundreds of micrometres Luc et al. (2014). Foam structures are divided into two main groups: open cell and closed cell. In closed-cell foams, the cells are separated from each other by enclosing walls. Open-cell foams are made of struts and the cells are connected; they have holes through which liquid and air can easily travel Banhart (2001). Depending on the bubble size and the structure of foams the applications are different. For instance, closed-cell foams are shown to have better energy and sound absorption characteristics Du et al. (2020). They also make strong, durable, rigid materials that do not absorb water, for example, in athletic shoes. For photonics, it has been suggested that open-cell foams or network structures made of dielectric materials can exhibit a photonic band gap Klatt et al. (2019); Ricouvier et al. (2019); Maimouni et al. (2020), as opposed to closed-cell foams Bergman et al. (2022). Photonic applications in the visible range require small pore sizes. Researchers often opt for a sacrificial template method instead of directly foaming a material to achieve this. In this templating approach, small particles are dispersed in a matrix instead of air bubbles and subsequently removed. By manipulating the quantity, size, polydispersity, and shape of the sacrificial particulate materials, the foam’s structure and morphology can be fine-tuned Yu et al. (2021).

While some foams are colored due to absorption by chemical compounds or pigments Członka et al. (2019); Kim et al. (2009), nature offers another method of coloration through structural correlations at the nano- and mesoscale of dielectric materials. These so-called “structural colors” are non-fading and can be more environmentally friendly than pigment-based colors Chan et al. (2022); Galisteo-López et al. (2011). Structural colors originate from interactions between light waves scattered coherently by nanoscale structures. This phenomenon is widely seen in nature, for example, in opals, beetles, and the brilliant feathers of birds Zhao et al. (2012), Li et al. (2023). In 1998, Prum et al. first explained the color in the blue feather barbs of the plum-throated cotinga, consisting of a keratin matrix with air vacuoles of uniform diameter and spacing Prum et al. (1998). Dielectric materials arranged in a crystalline fashion produce angle-dependent structural color like in opals, whereas angle-independent structural color is produced when the materials have short-ranged order at the nanoscale and no long-ranged order Kawamura et al. (2016).

Blue and green structural colors are widely found in nature. Several groups have been successful in making synthetic structural colors, for instance, with polystyrene or silica particles Forster et al. (2010), Rojas-Ochoa et al. (2004)Demirörs et al. (2022), Højlund-Nielsen et al. (2014), Yazhgur et al. (2022), Wang et al. (2022). However, synthesizing materials with longer-wavelength colors like red and yellow has been more challenging. Researchers have set to understand why it is difficult to make red structural color and why it is absent in nature Magkiriadou et al. (2014); Jacucci et al. (2020). Later on, red photonic glass has been reported Kim et al. (2017) in inverse structures, i.e., structures that have low-refractive-index dielectric materials embedded in a matrix of higher-refractive-index dielectric materials. Dry foams can be considered as inverse structures, which makes them relevant for structural color applications. Moreover, they have the potential to show a photonic band gap when made from materials with a refractive index contrast greater than ≈ 2.5 Klatt et al. (2019).

In previous work, we reported the fabrication of macroporous silica foams by templating soft colloids Bergman et al. (2022) but we did not target nor characterize the structural color spectra of the materials. We have shown the synthesis of soft colloids, the fabrication of foams, and the relevance of these foams for photonic applications. Through simulations, we have confirmed that open-cell foams can show a photonic bandgap. In our experiments we used microgel colloidal particles as the sacrificial template. Microgel particles typically have diameters between one hundred nanometers and about 1 μm Saunders et al. (2009). Poly-NiPAm-based microgels are particularly appealing as building blocks of a colloidal template, because they are temperature sensitive: they undergo a volume phase transition at ≈ 32°C, corresponding to the polymer’s lower critical solution temperature (LCST). These microgels swell by about a factor of two in size when the temperature is decreased below °C. Importantly, swollen microgel particles are soft and can be compressed to high effective volume fractions greater than 1, developing facets. Therefore, when they are used as sacrificial particles to fabricate inverse structures, the resulting air voids resemble the pores of dry foams Conley et al. (2017, 2019).

In the present work we report on synthesizing dry silica foam-like materials with structural colors that span the visible spectrum. Our approach begins by synthesizing microgel particles surrounded by inorganic silica nanoparticles. These composite particles are small enough that, when compressed, they become comparable in size to the wavelength of visible light. We take advantage of the microgels’ compressibility to produce disordered foam-like structures whose cells have flattened facets. After these are formed, we remove most of the organic polymer through calcination and obtain dry silica foams. We leave residues of carbonised polymer in the sample, which then act as light absorbers Demirörs et al. (2022). These foams exhibit vibrant structural colors. We show that the central resonant wavelength determining the color of the silica foams depends on the nanostructures’ characteristic length scale. In turn, this length scale is set by the size of the microgels, which allows us to target the color of the foam.

2 Results and discussion

2.1 Synthesis of silica-decorated microgels

We chose microgel colloids as the template for fabricating silica foams because of their softness, enabling the formation of flat walls between the cavities when the microgels are compressed. We synthesized thermoresponsive microgel particles with a shell composed of silica nanoparticles. The microgel particles are based on Poly-(N-isopropyl acrylamide) (PNiPAm) crosslinked with N,N’-methylenebis-(acrylamide) (BIS). A water-soluble initiator, Potassium PerSulphate (KPS), was used to initiate the reaction. We followed the semi-batch polymerization process described by Still et al. (2013), which results in microgel particles with a homogeneous crosslinking. The synthesis was divided into two parts. The initial part involved the growth of microgel particles that were uniformly crosslinked using NiPAm and BIS monomers. Subsequently, in the following part, we added a positively charged co-monomer, N-(3-aminopropyl)methacrylamide hydrochloride (APMA), and commercially available silica nanoparticles (LUDOX AS-40, ≈ 20 - 24 nm diameter, aqueous dispersion), Figure 1A. LUDOX AS-40 are negatively charged, with a zeta potential −47 mV measured on Litesizer (Anton Paar GmbH, Austria). The electrostatic interactions between the co-monomer and the silica nanoparticles allowed us to incorporate the silica into the microgel network. Our synthesis protocol follows the one described in our earlier work Bergman et al. (2022).

FIGURE 1

Bergman et al. (2022) [adapted from Bergman et al. (2022) licensed CC-BY-NC]. The right half of the panel on the right shows an enlarged scanning electron microscope image of one of the resulting structures, where the individual silica nanoparticles can be distinguished. Scale bar: 0.5 μm.

We have synthesized silica-decorated microgel particles of various sizes. The mole ratios of NiPAm:BIS and APMA:NiPAm, as well as the monomer:silica mass ratios, are kept nearly constant in all the syntheses, as shown in Table 1, in order to maintain similar internal architecture in all the samples. This approach allows for the creation of particles with different hydrodynamic radii by adjusting the feeding time while maintaining the same monomer ratios.

We present results for three different synthesis batches of silica-decorated microgel particles, named sample k₁, k₂, k₃. The detailed syntheses are described in the Supplementary Material S1. We characterized the particle size in the swollen state by Static and Dynamic Light Scattering measurements (for details see Section 4.2). We find that the particles have average hydrodynamic radii of 344 ± 4 nm , 394 ± 20 nm, and 581 ± 38 nm, measured by Dynamic Light Scattering (DLS), and polydispersities of 0.04, 0.07, and 0.12 respectively, estimated by fitting the form factor from static light scattering (SLS). The SLS data of samples k₁, k₂, k₃ were fitted using the well-known fuzzy-sphere model Stieger et al. (2004) for the radial density distribution profile that describes the form factor of microgels (Supplementary Figure S1A). The hydrodynamic radii measured by SLS and DLS are found to be in good agreement with each other (Supplementary Figure S1B).

2.2 Fabrication of solid foams

For the production of silica foams we proceeded as follows. First, a ∼0.5 mL suspension of silica microgel particles was centrifuged at room temperature for 15 min at 16,200 g and then the supernatant was carefully removed. The centrifugation process caused the particles to become densely packed and lightly compressed. The remaining residue was then placed in an oven at 70°C for 2 min, a temperature that exceeds the volume phase transition temperature of PNiPAm microgels. The microgels expelled water at this temperature, leading to particle shrinkage but also weak attraction and aggregation. The suspension was subsequently centrifuged again at 16,200 g for 5 min, and the supernatant was immediately removed. This second step compressed the shrunken particles even more. As they returned to room temperature they swelled, however constrained by the available water volume per particle. The result was a solid plug of gel, visible at the bottom of the Eppendorf tube, as illustrated in Supplementary Figure S2. In the process of compression and re-swelling, the microgel particles develop facets as shown in Figure 1B, which allows the silica shells around them to form cellular foams with faceted interfaces.

The compressed gel was calcined in a tubular oven, to remove the organic polymer and to obtain solid silica foams. When burnt at temperatures greater than 530°C, the organic phase is almost fully removed, and the remaining samples appear whitish due to multiple scattering of light Forster et al. (2010). Therefore, the temperature during calcination was adjusted in such a way that some amount of carbon remains inside the sample after calcination, with the aim to enhance broadband absorption and thus diminish multiple scattering. Samples k₁, k₂, k₃ were calcined at 500°C–530°C (see experimental Section 4.1). After removal of the polymer we are left with solid silica foams that show color, Figure 2A. In the calcined samples we noticed some non-uniformity in the color, that could be explained by uneven compression during the centrifugation or heating of the particles, resulting in air pores of varying sizes. Another possible explanation is that the binding of silica nanoparticles may not be uniform for all microgel particles, leading to stratification and different silica filling fractions through the foam. We have not further explored the origins of these color variations and in the following we present our observations corresponding to the dominant colors in samples k₁, k₂, and k₃, which are blue, green, and a mixture of pink and red color. The latter is represented by the RGB values (197, 136, 148), a hue referred to as “King’s cloak”. The colors of the samples shifted towards red when the hydrodynamic radius, R_H, increased, as indicated above Figure 2A.

FIGURE 2

We examined the internal nanoscale features of our samples with focused ion beam (FIB) milling and a scanning electron microscope (SEM, see experimental Section 4.4 for details). As shown in Figure 2B, the analysis revealed porous nanostructures. In the insets of Figure 2B, we plot the Fourier power spectrum of the cross-section micrographs versus the spatial frequency Prum and Torres (2003). We observe a clear decrease in the size of the correlation ring, consistent with the visible increase in the pore size. To quantify the structural correlation length, we performed tomography on the samples before calcination and obtained the 3D power spectrum by fast Fourier transform (FFT) of the 3D reconstructions (explained in Section 2.4). For all three samples, we then calculated the azimuthal average of the power spectrum (see Supplementary Figure S4D). From the locations of its peak values, q_max, we find the following correlation lengths: for sample k₁, d = 206 nm, k₂, d = 277 nm and k₃, d = 339 nm. These values are overall consistent with the pore-to-pore distances measured directly from the images.

2.3 Optical characterization

Before the removal of the polymer from the compressed silica-decorated microgel packing we observed a translucent gel that was not colored, as illustrated in Supplementary Figure S2E. While the refractive index contrast between the polymer (with n = 1.5) and the silica nanoparticles (with n = 1.475) was insufficient to produce colors prior, this changed after calcination. When the polymer was removed, the pores were filled with air (with n = 1), creating a refractive index contrast between air and silica that was sufficient to produce color as presented in Supplementary Figure S3. After calcination, no organic material was present in the sample except for some carbon residues.

We studied the optical properties of the colored samples through bright-field reflection microscopy and spectrometry, both in co-polarized and cross-polarized configurations, as detailed in the experimental Section 4.3 and shown in Figure 3. The co-polarized spectrum comprises of singly scattered and multiply scattered light, Figure 3A, while the crosspolarized spectrum contains only multiply scattered light, Figure 3B. By subtracting the cross-polarized spectrum from the co-polarized spectrum, we can isolate the features that are primarily due to single scattering, and which arise from constructive interference of light scattered from the nanostructures within our samples, Figure 3C (Noh et al., 2010; Hwang et al., 2020). We obtained spectra from five different areas on each sample and averaged them. We observe one distinct reflection peak for each sample, as depicted in Figures 3A, C. The peak wavelength red-shifts with the controlled increase in the correlation length d, Figure 3C. The values of the peak wavelengths are listed in Table 2. These observations confirm the structural origin of the color. We used the measured reflection spectra in Figure 3A to calculate the standard RGB colors, with standard illuminant D65 as the light source, in Matlab Guo (2023); CIE (2023). The calculated colors agree well with the colors we observe (Insets in Figure 2A).

FIGURE 3

Previous studies have suggested that producing red structural color is difficult due to the occurrence of additional reflection peaks at shorter wavelengths. When creating blue structural color these peaks are in the ultraviolet range, invisible to the human eye, and they do not interfere with the perceived color of blue. In the case of red color, however, they can lead to the appearance of mixed colors. These shorter-wavelength peaks can arise from either single-particle resonances in direct structures (i.e., particle packings) Magkiriadou et al. (2014), or from structural correlations Jacucci et al. (2020). It has been suggested that better red hues can be obtained with inverted structures than direct structures. These findings were supported by theoretical Magkiriadou et al. (2014) and numerical analysis Jacucci et al. (2020). Later on, Kim et al. Kim et al. (2017) and Wang et al. Wang et al. (2022) experimentally demonstrated the advantage of inverse structures in achieving red hues. Consistent with the above, in our system of inverse structures with controlled deformation of the silica walls acquired by microgel templating, we observed only a gentle scattering peak in the blue spectral region for sample k₃, as shown in Figures 3A, C clearly dominant reflection peak in the red. The peak intensity ratio of reflection peaks at 687 nm and 457 nm is ≈ 2.6 : 1, leading to a stronger contribution of red to structural color over the aforementioned works Xiao et al. (2015).

We studied the angular dependence of the scattering properties of these colored foams by capturing their scattering profiles in k-space, called scatterograms Stavenga et al. (2009). We illuminated the samples in wide-angle and collected scattered light with a ×50 objective. The resulting scattering angles range from 0° to 53.15°. In Figure 4 optical micrographs are shown in the left panel and the corresponding scatterograms in the right panel. These scatterograms exhibit uniform color across the angles, marked with circles, which shows the angle-independent nature of the color. This feature is consistent with the structural disorder observed in the 3D reconstructions (Supplementary Figure S4). And with the small-angle X-ray scattering (SAXS) analysis explained in Section 2.4.

FIGURE 4

To better understand the structural colours of our samples and relate them to their nanostructure, we need to estimate their effective refractive index. This, in turn, requires estimating the refractive index of the silica walls, which are themselves a packing of silica nanoparticles in air. We assume random close packing of silica NPs, as the particles need temperatures as high as 1300°C to be fully sintered Hamzah et al. (2023), and moreover from our SEM images we can confirm that the particles remain distinct (Figure 1B, rightmost panel; Supplementary Figure S5). Assuming that the silica nanoparticles have a refractive index of 1.45 and are arranged in random close packing inside the walls at a volume fraction of 0.64, the Maxwell Garnett equation predicts an effective refractive index of 1.27 for the walls. From 3D reconstruction analysis, the volume fraction occupied by silica walls in the samples is approximately 0.45 (as explained in Section 4.6). Therefore, using again the Maxwell Garnett equation, the effective refractive index of the sample is calculated to be 1.12. For backscattering, the maximum reflection is at λ_max = 4πn_eff/q_max, where n_eff is the effective refractive index of the material and q_max is the wavevector corresponding to the material’s characteristic lengthscale, given by the location of the structure factor peak. For a disordered dense packing of spheres, the structure factor peak is around q_max ≈ 2.2π/dLiu et al. (2000). Assuming a disordered packing of air spheres in the silica matrix for our case, we can use the above expressions with n_eff ≈ 1.12, and we obtain λ_max/d ≈ 2.03. To compare this to our data, we normalize the reflectance data for single scattering (C_p - C_r in Figure 3C) and plot it against λ/d in Figure 3D. This data indicates an approximate ratio of λ_max/d listed in Table 2, which is similar to the λ_max/d value calculated above assuming a dense packing of air spheres in a porous silica matrix.

2.4 Structural analysis

To examine the structure and correlations of silica foams, we utilized a 3D reconstruction technique (outlined in Section 4.6) on pre-calcined samples. Figure 5A presents an example of such tomography reconstruction of sample k₁ that was derived from focused ion beam milling and scanning electron microscopy sequences Groeber et al. (2006); Supplementary Figures S4B, S4C present the reconstruction of samples k₂ and k₃ respectively. The filling fractions (volume occupied by silica walls) for samples k₁, k₂ and k₃ are 45%, 46% and 46% respectively, determined from tomographic reconstruction. From the 3D reconstructions we also calculated and analyzed the Fourier power spectra, , where q denotes the spatial frequency. is proportional to the modulus squared of the numerical fast Fourier transform (FFT) derived from two-dimensional images or three-dimensional tomographic reconstructions as discussed in Prum and Torres (2003). In the presence of structural correlations we find a peak in , which defines a correlation length d via the relation q_max ≈ 2.2π/dLiu et al. (2000).

FIGURE 5

We performed 3D FFT on the reconstructions of pre-calcined samples to calculate the correlation length (d), listed in Table 2. We also examined one cross-section in the xy, yz, xz planes of k₁ and k₃ from the generated 3D FFTs. The correlation lengths calculated from the FFT in the xy, yz, xz planes of k₁ and k₃ are comparable in all planes, as shown in Supplementary Figures S6D, S7D (FFT spectra of the respective planes are included in the Supplementary Figures S6, S7). Although the correlation lengths are similar, the ring in the FFT spectra appears elongated for samples k₁ and k₃ (Supplementary Figures S6, S7). This might be an artifact in reconstructions which we have not analysed further.

To provide additional information about the structure of the samples, we utilized small angle X-ray scattering (SAXS) on calcined sample k₁. The results of this analysis are presented in Figure 5B, which displays concentric rings of uniform intensity in the scattering pattern. These rings suggest that the structure of the sample is not crystalline but has short-range order, as no Bragg peaks are visible. Notably, the SAXS pattern in Figure 5B bears a resemblance to the FFT spectrum (in the xy plane) obtained from the 3D reconstruction of k₁, as depicted in Figure 5C. The azimuthal average of the SAXS pattern, the azimuthal average of the FFT spectrum and the normalised single-scattering reflection spectrum of k₁ (Figure 3C), converted to reciprocal or q-space, are plotted together in Figure 5D. In these plots, it can be seen that the first peak occurs at q = 0.03048 nm⁻¹ from the 3D reconstruction, q = 0.03241 nm⁻¹ from the SAXS analysis and q = 0.03346 nm⁻¹ from the reflectance measurements. All these values agree well and correspond to correlation length scales of 206 nm, 193 nm, and 181.5 nm, respectively. This allows us to conclude that the structural colors originate from constructive interference.

In photonic foam materials or phoamtonics Klatt et al. (2019), the opening of the photonic band gap is found in open-cell structures or networks Ricouvier et al. (2019); Klatt et al. (2019); Bergman et al. (2022). Although both open and closed-cell foams should exhibit structural color, the distinct cell topologies observed in our study are still worth discussing. To provide additional clarity regarding the inherent structure of our silica foams, we focus on a specific region within the three-dimensional rendered images of k₁ and k₃. In k₁ (Figures 6A, B), we see that the foams have closed cells, except for a small region (Figure 6A, circled in green) where there is an opening in the cell. In k₃ (Figures 6C, D), it is interesting to note that the foams have larger openings in the cell compared to k₁ (Figure 6C, circled in green). In Figures 6B, D, the circled areas in red highlight the walls of the cell foams. k₁ has smaller pores compared to k₃ and the cell openings are narrower than in k₃.

FIGURE 6

The synthesis of the silica-decorated microgel particles can explain this. k₁ has a hydrodynamic radius of 344 nm, and the silica shell is thicker in relation to the microgel core. In comparison, k₃ has a hydrodynamic radius of 581 nm and the silica nanoparticles are distributed over a larger surface area, resulting in a comparably thinner shell. The openings in the cell may then be caused by an inhomogeneous distribution of silica on the microgel particles or by stresses during drying and calcination. Therefore, it is possible that our foams have (partially) open cell structures. By controlling the silica content, we can possibly adapt foams to have either open-cell or closed-cell structures. A systematic analysis of how to control the cell topology is beyond the scope of the present work.

3 Summary and conclusion

In summary, this study demonstrates how microgel colloidal templating can be used to assemble silica nanoparticles in foam-like structures with structural color. We obtain pure silica dry foams by calcining the silica-decorated microgel polymer, and removing water and the polymer. The structural colors of the samples are vivid. The primary color can be adjusted by controlling the size and degree of compression of the microgel particles. This work demonstrates the feasibility of self-assembling foams at length scales comparable to visible wavelengths.

Previous work has shown that silicon dioxide can be reduced to pure silicon by a magnesiothermic reaction, potentially increasing the refractive index from 1.45 to 3.6 Ibisate et al. (2009). The implementation of this approach in developing silicon foam structures has the potential to facilitate the development of photonic foam materials that possess a photonic band gap. This possibility has been demonstrated through numerical analysis conducted by Bergman et al. (2022), for a near-infrared silicon refractive index contrast of 3.6. Furthermore, the silica nanoparticles used in this study are building blocks of foam structures and can be exchanged for any other type of nanoparticle with different functions. This possibility suggests that our method can be used as a general and simple way to obtain mesoscale foam structures of many materials, from high refractive index to magnetic or plasmonic nanoparticles.

4 Experimental section

4.1 Sample preparation

An Eppendorf tube containing 1 mL of the microgel colloids (2–5 wt%) was centrifuged at 16,200 g at room temperature for 15 min and subsequently the supernatant was removed. The sample was then placed in an oven at 70°C for 2 min to induce the microgel deswelling. The sample was immediately centrifuged (16,200 g for 5 min) at room temperature and the supernatant was removed again. The resulting monolith (non-calcined samples) was glued on an aluminium stub with conducting silver paste and left to dry in the oven at 70°C for electron microscopy analysis. The monoliths were calcined in an open tubular oven to remove the microgel template from the networks. The samples were heated to 500°C–530°C (ramp—100°C/hour) and left for 7 h, followed by cooling to 40°C (150 °C/hour) Silencieux et al. (2015).

4.2 Light scattering analysis

A glass vial with a dilute suspension of 10 μL stock solution plus 500 μL de-ionized water was placed inside a 3D—DLS light scattering spectrometer (LS Instruments, Switzerland) operating at a laser wavelength of 660 nm Block and Scheffold (2010). The scattered intensity was collected at angles 15°–135° with step size 3°–5°. Measurements were preformed in 3D—modulated cross correlation mode which suppresses multiple scattering if present. Three measurements were obtained at each angle with a duration of 60 s or 120 s. The hydrodynamic radius was calculated via a standard first cumulant fit on the auto-correlation functions.

4.3 Spectral measurements

To characterize the reflection spectra of the samples, the measurements were performed using a Zeiss Axio Scope. A1 light microscope (Carl Zeiss AG, Oberkochen, Germany) outfitted with a CCD camera (GS3-U3-28S5C-C, FLIR Integrated Imaging Solutions Inc., Richmond, Canada). The calcined samples were analyzed in bright field with a halogen white lamp (Zeiss HAL100) using a Zeiss, EC Epiplan-Neofluar 10X, NA = 0.25 objective, capturing spectra (400 nm–800 nm) from the point of interest. The reflected light was collected by an optical fiber (Ocean Optics QP230-2-XSR, 230 μm core) with a spot size of 25 μm at a magnification of ×10. The collected light was analyzed with an Ocean Optics Maya2000 Pro spectrometer (Ocean Optics, Dunedin, FL, United States). The reflectance spectra were normalized with respect to a white Spectralon diffuse reflectance standard (Labsphere). The spectra were obtained in Oceanview software. The optical micrographs and the scatterograms were captured with the CCD camera; for the micrographs the samples were placed on a black background. For the polarization measurements, one polarizer was placed in front of the light source that illuminates the sample, and another polarizer in the direction of backscattered light.

4.4 Electron microscopy and tomography

The dried-out monolith or calcined sample was sputter-coated with platinum to minimize charging and imaged in a Scios 2 Focused Ion Beam SEM, ThermoFisher. To access the interior network for SEM imaging, the region of interest was chosen and cross-sectioned using a focused ion beam (FIB). A focused beam of gallium ions (voltage 30 kV, current 0.3–0.5 nA) was chosen to mill the region of interest perpendicularly to the surface of the sample. Cross-sectional images were acquired using an electron beam (voltage 5 kV, current 0.2–0.4 nA) under OptiTilt mode with different detectors.

Tomography of the pre-calcined samples was performed using FIB-SEM. The region of interest (ROI) was coated with Pt using built-in Pt deposition induced by ion beam, so that the ROI was not destroyed during tomography. A rough cut was milled in front of the ROI to expose the imaging plane and trenches were milled on the sides to provide a deposition site for the milled material and prevent re-deposition on the exposed section. A fiducial marker was created near the ROI, to monitor drift. The tomography was performed in Auto Slice and View Software (4.2). Slices of 10 nm or 15 nm thickness were milled with a Galium ion beam set at 30 kV acceleration voltage and 0.3 nA beam current. Images were captured after each slice in the OptiTilt configuration using the built-in SEM Everhart-Thornley (ETD, secondary electrons) and T1 detector (back-scattered electrons) set to a voltage of 5 kV and current of 0.2–0.4 nA.

4.5 Small angle X-ray scattering (SAXS) analysis

SAXS X-ray scattering measurements were performed on calcined samples with a Xeuss 3.0 UHR SAXS system (Xenocs SAS, Grenoble, France) equipped with a GeniX 3D Cu Kalpha radiation source (λ ≈ 1.54 Å) and a Q-Xoom in-vacuum motorized Eiger2 R 1 M detector (Dectris Ltd., Switzerland) for data collection. The reduction of 2D data into 1D plots of the scattering intensities, I (q), was performed automatically using the Xenocs XSACT software. The scattering vector q was calculated using the relation q = 4π sin θ/λ where θ is half the scattering angle.

4.6 3D reconstruction and image analysis

Image processing was done in Fiji ImageJ Schneider et al. (2012) and Matlab 2021a (MathWorks Inc., United States) MATLAB (2010). The raw image stack was drift-corrected using the Fiji StackReg plug-in Jain and Healey (1998). The stack was analysed using image analysis scripts in Matlab. The images were resized in the y direction to compensate for the image distortion induced by the acquisition at a 52° angle between the sample and the SEM column. The drift was removed again by calculating the correlation between consecutive slices. Later, the images were resized in the x and y directions as in the z direction, so as to have a cubic voxel. The 3D reconstruction was converted into a 3D matrix. n-dimensional fast Fourier transform (fftn) with absolute squared intensities in log scale was applied separately to these 3D matrices to generate the 3D FFT of the images. The structural correlation lengths were calculated for xy, yz and xz planes on one cross-section picked from the centre of the matrix. The 2D FFTs in all planes were azimuthally averaged to obtain the structural correlation length. For the filling fraction calculation, the images were binarized using adaptive thresholding.

References

• 1

  BanhartJ. (2001). Manufacture, characterisation and application of cellular metals and metal foams. Prog. Mater. Sci.46, 559–632. 10.1016/S0079-6425(00)00002-5

  • CrossRef
  • Google Scholar
  • View reference in article

• 2

  BergmanM. J.García-AstrainC.FuchsN.ManneK.YazhgurP.Froufe-PérezL. S.et al (2022). Macroporous silica foams fabricated via soft colloid templating. Small Methods6, 2101491. 10.1002/smtd.202101491

  • CrossRef
  • Google Scholar
  • View reference in article

• 3

  BlockI. D.ScheffoldF. (2010). Modulated 3d cross-correlation light scattering: improving turbid sample characterization. Rev. Sci. Instrum.81, 123107. 10.1063/1.3518961

  • CrossRef
  • Google Scholar
  • View reference in article

• 4

  ChanC. L. C.LeiI. M.van de KerkhofG. T.ParkerR. M.RichardsK. D.EvansR. C.et al (2022). 3d printing of liquid crystalline hydroxypropyl cellulose—Toward tunable and sustainable volumetric photonic structures. Adv. Funct. Mater.32, 2108566. 10.1002/adfm.202108566

  • CrossRef
  • Google Scholar
  • View reference in article

• 5

  CIE (2023). CIE standard illuminant D65. http://cie.co.at/datatable/cie-standard-illuminant-d65.

  • Google Scholar
  • View reference in article

• 6

  ConleyG. M.AebischerP.NöjdS.SchurtenbergerP.ScheffoldF. (2017). Jamming and overpacking fuzzy microgels: deformation, interpenetration, and compression. Sci. Adv.3, e1700969. 10.1126/sciadv.1700969

  • CrossRef
  • Google Scholar
  • View reference in article

• 7

  ConleyG. M.ZhangC.AebischerP.HardenJ. L.ScheffoldF. (2019). Relationship between rheology and structure of interpenetrating, deforming and compressing microgels. Nat. Commun.10, 2436–2438. 10.1038/s41467-019-10181-5

  • CrossRef
  • Google Scholar
  • View reference in article

• 8

  CzłonkaS.SienkiewiczN.KairytėA.VaitkusS. (2019). Colored polyurethane foams with enhanced mechanical and thermal properties. Polym. Test.78, 105986. 10.1016/j.polymertesting.2019.105986

  • CrossRef
  • Google Scholar
  • View reference in article

• 9

  DemirörsA. F.PoloniE.ChiesaM.BargardiF. L.BinelliM. R.WoigkW.et al (2022). Three-dimensional printing of photonic colloidal glasses into objects with isotropic structural color. Nat. Commun.13, 4397. 10.1038/s41467-022-32060-2

  • CrossRef
  • Google Scholar
  • View reference in article

• 10

  DuZ.YaoD.XiaY.ZuoK.YinJ.LiangH.et al (2020). Highly porous silica foams prepared via direct foaming with mixed surfactants and their sound absorption characteristics. Ceram. Int.46, 12942–12947. 10.1016/j.ceramint.2020.02.063

  • CrossRef
  • Google Scholar
  • View reference in article

• 11

  ForsterJ. D.NohH.LiewS. F.SaranathanV.SchreckC. F.YangL.et al (2010). Biomimetic isotropic nanostructures for structural coloration. Adv. Mater.22, 2939–2944. 10.1002/adma.200903693

  • CrossRef
  • Google Scholar
  • View reference in article

• 12

  Galisteo-LópezJ. F.IbisateM.SapienzaR.Froufe-PérezL. S.BlancoÁ.LópezC. (2011). Self-assembled photonic structures. Adv. Mater.23, 30–69. 10.1002/adma.201000356

  • CrossRef
  • Google Scholar
  • View reference in article

• 13

  GroeberM.HaleyB.UchicM.DimidukD.GhoshS. (2006). 3D reconstruction and characterization of polycrystalline microstructures using a FIB–SEM system. Mater. Charact.57, 259–273. 10.1016/j.matchar.2006.01.019

  • CrossRef
  • Google Scholar
  • View reference in article

• 14

  GuoT. (2023). Color calculation from spectrum. https://www.mathworks.com/matlabcentral/fileexchange/98289-convert-spectrum- to-color.

  • Google Scholar
  • View reference in article

• 15

  HamzahM. S.WildanM. W.Kusmono SuharyadiE. (2023). Effect of sintering temperature on physical, mechanical, and electrical properties of nano silica particles synthesized from Indonesia local sand for piezoelectric application. J. Asian Ceram. Soc.11 (1), 178–187. 10.1080/21870764.2023.2173851

  • CrossRef
  • Google Scholar
  • View reference in article

• 16

  Højlund-NielsenE.WeirichJ.NørregaardJ.GarnaesJ.Asger MortensenN.KristensenA. (2014). Angle-independent structural colors of silicon. J. Nanophot.8, 083988. 10.1117/1.jnp.8.083988

  • CrossRef
  • Google Scholar
  • View reference in article

• 17

  HwangV.StephensonA. B.MagkiriadouS.ParkJ. G.ManoharanV. N. (2020). Effects of multiple scattering on angle-independent structural color in disordered colloidal materials. Phys. Rev. E101, 012614. 10.1103/PhysRevE.101.012614

  • CrossRef
  • Google Scholar
  • View reference in article

• 18

  IbisateM.GolmayoD.LópezC. (2009). Silicon direct opals. Adv. Mater.21, 2899–2902. 10.1002/adma.200900188

  • CrossRef
  • Google Scholar
  • View reference in article

• 19

  JacucciG.VignoliniS.SchertelL. (2020). The limitations of extending nature’s color palette in correlated, disordered systems. Proc. Natl. Acad. Sci. U. S. A.117, 23345–23349. 10.1073/pnas.2010486117

  • CrossRef
  • Google Scholar
  • View reference in article

• 20

  JainA.HealeyG. (1998). A multiscale representation including opponent color features for texture recognition. IEEE Trans. Image Process.7, 124–128. 10.1109/83.650858

  • CrossRef
  • Google Scholar
  • View reference in article

• 21

  KawamuraA.KohriM.MorimotoG.NannichiY.TaniguchiT.KishikawaK. (2016). Full-color biomimetic photonic materials with iridescent and non-iridescent structural colors. Sci. Rep.6, 33984–34010. 10.1038/srep33984

  • CrossRef
  • Google Scholar
  • View reference in article

• 22

  KimS.-H.MagkiriadouS.RheeD. K.LeeD. S.YooP. J.ManoharanV. N.et al (2017). Inverse photonic glasses by packing bidisperse hollow microspheres with uniform cores. ACS Appl. Mater. Interfaces9, 24155–24160. 10.1021/acsami.7b02098

  • CrossRef
  • Google Scholar
  • View reference in article

• 23

  KimS.BarrazaH.VelevO. D. (2009). Intense and selective coloration of foams stabilized with functionalized particles. J. Mater. Chem.19, 7043–7049. 10.1039/b908054f

  • CrossRef
  • Google Scholar
  • View reference in article

• 24

  KlattM. A.SteinhardtP. J.TorquatoS. (2019). Phoamtonic designs yield sizeable 3D photonic band gaps. Proc. Natl. Acad. Sci. U. S. A. 116, 23480–23486. 10.1073/pnas.1912730116

  • CrossRef
  • Google Scholar
  • View reference in article

• 25

  LiF.FenW.HongjieL.BoxinQ. (2023). Review of recent advancements in the biomimicry of structural colors. Dyes Pigments210, 111019. 10.1016/j.dyepig.2022.111019

  • CrossRef
  • Google Scholar
  • View reference in article

• 26

  LiuJ.SchöpeH.-J.PalbergT. (2000). An improved empirical relation to determine the particle number density of fluid-like ordered charge-stabilized suspensions. Part. Part. Syst. Charact.17, 206–212. 10.1002/1521-4117(200012)17:5/6<206:aid-ppsc206>3.0.co;2-c

  • CrossRef
  • Google Scholar
  • View reference in article

• 27

  LiuY. M.FengW. L.LiT. C.HeH. Y.DaiW. L.HuangW.et al (2006). Structure and catalytic properties of vanadium oxide supported on mesocellulous silica foams (MCF) for the oxidative dehydrogenation of propane to propylene. J. Catal.239, 125–136. 10.1016/j.jcat.2005.12.028

  • CrossRef
  • Google Scholar
  • View reference in article

• 28

  LucS.GuilhemM.MathieuS.ArianeM.RémyD.Jean-JacquesB. (2014). Processing and structures of solids foams. Comptes Rendus Phys.15, 662–673. 10.1016/j.crhy.2014.10.006

  • CrossRef
  • Google Scholar
  • View reference in article

• 29

  MagkiriadouS.ParkJ. G.KimY. S.ManoharanV. N. (2014). Absence of red structural color in photonic glasses, bird feathers, and certain beetles. Phys. Rev. E - Stat. Nonlinear, Soft Matter Phys.90, 062302–062308. 10.1103/PhysRevE.90.062302

  • CrossRef
  • Google Scholar
  • View reference in article

• 30

  MaimouniI.MorvaridiM.RussoM.LuiG.MorozovK.CossyJ.et al (2020). Micrometric monodisperse solid foams as complete photonic bandgap materials. ACS Appl. Mater. Interfaces12, 32061–32068. 10.1021/acsami.0c04031

  • CrossRef
  • Google Scholar
  • View reference in article

• 31

  MATLAB (2010). MATLAB version: 10 (R2020b). Natick, MA: The MathWorks Inc.

  • Google Scholar

• 32

  NohH.LiewS. F.SaranathanV.PrumR. O.MochrieS. G. J.DufresneE. R.et al (2010). Contribution of double scattering to structural coloration in quasiordered nanostructures of bird feathers. Phys. Rev. E81, 051923. 10.1103/PhysRevE.81.051923

  • CrossRef
  • Google Scholar

• 33

  PrumR. O.TorresR. H. (2003). A fourier tool for the analysis of coherent light scattering by bio-optical nanostructures. Integr. Comp. Biol.43, 591–602. 10.1093/icb/43.4.591

  • CrossRef
  • Google Scholar

• 34

  PrumR.TorresR.WilliamsonS.DyckJ. (1998). Coherent light scattering by blue feather barbs. Nature396, 28–29. 10.1038/23838

  • CrossRef
  • Google Scholar

• 35

  RicouvierJ.TabelingP.YazhgurP. (2019). Foam as a self-assembling amorphous photonic band gap material. Proc. Natl. Acad. Sci. U. S. A.116, 9202–9207. 10.1073/pnas.1820526116

  • CrossRef
  • Google Scholar

• 36

  Rojas-OchoaL. F.Mendez-AlcarazJ.SáenzJ.SchurtenbergerP.ScheffoldF. (2004). Photonic properties of strongly correlated colloidal liquids. Phys. Rev. Lett.93, 073903. 10.1103/physrevlett.93.073903

  • CrossRef
  • Google Scholar

• 37

  SaundersB. R.LaajamN.DalyE.TeowS.HuX.SteptoR. (2009). Microgels: from responsive polymer colloids to biomaterials. Adv. colloid interface Sci.147, 251–262. 10.1016/j.cis.2008.08.008

  • CrossRef
  • Google Scholar

• 38

  SchneiderC.RasbandW.EliceiriK. (2012). Nih image to imagej: 25 years of image analysis. Nat. Methods9, 671–675. 10.1038/nmeth.2089

  • CrossRef
  • Google Scholar

• 39

  SilencieuxF.BouchouchaM.MercierO.TurgeonS.ChevallierP.KleitzF.et al (2015). Mesoporous silica nanoparticles under sintering conditions: A quantitative study. Langmuir31, 13011–13021. 10.1021/acs.langmuir.5b02961

  • CrossRef
  • Google Scholar

• 40

  StavengaD.LeertouwerH.PirihP.WehlingM. (2009). Imaging scatterometry of butterfly wing scales. Opt. Express17, 193–202. 10.1364/OE.17.000193

  • CrossRef
  • Google Scholar

• 41

  StiegerM.RichteringW.PedersenJ. S.LindnerP. (2004). Small-angle neutron scattering study of structural changes in temperature sensitive microgel colloids. J. Chem. Phys.120, 6197–6206. 10.1063/1.1665752

  • CrossRef
  • Google Scholar

• 42

  StillT.ChenK.AlsayedA. M.AptowiczK. B.YodhA. (2013). Synthesis of micrometer-size poly (n-isopropylacrylamide) microgel particles with homogeneous crosslinker density and diameter control. J. colloid interface Sci.405, 96–102. 10.1016/j.jcis.2013.05.042

  • CrossRef
  • Google Scholar

• 43

  WangZ.ChanC. L. C.HaatajaJ. S.SchertelL.LiR.van de KerkhofG. T.et al (2022). Deconvoluting the optical response of biocompatible photonic pigments. Angew. Chem. - Int. Ed.61, e202206562. 10.1002/anie.202206562

  • CrossRef
  • Google Scholar

• 44

  XiaoM.LiY.AllenM. C.DeheynD. D.YueX.ZhaoJ.et al (2015). Bio-inspired structural colors produced via self-assembly of synthetic melanin nanoparticles. ACS Nano9, 5454–5460. 10.1021/acsnano.5b01298

  • CrossRef
  • Google Scholar

• 45

  YanX.ZhangL.ZhangY.QiaoK.YanZ.KomarneniS. (2011). Amine-modified mesocellular silica foams for CO2 capture. Chem. Eng. J.168, 918–924. 10.1016/j.cej.2011.01.066

  • CrossRef
  • Google Scholar

• 46

  YazhgurP.MullerN.ScheffoldF. (2022). Inkjet printing of structurally colored self-assembled colloidal aggregates. ACS Photonics9, 2809–2816. 10.1021/acsphotonics.2c00627

  • CrossRef
  • Google Scholar

• 47

  YuC.NannanW.OluwafunmilolaO.YongdeX.YanqiuZ. (2021). Porous ceramics: light in weight but heavy in energy and environment technologies. Mater. Sci. Eng. R Rep.143, 100589. 10.1016/j.mser.2020.100589

  • CrossRef
  • Google Scholar

• 48

  ZhaoY.XieZ.GuH.ZhuC.GuZ. (2012). Bio-inspired variable structural color materials. Chem. Soc. Rev.41, 3297–3317. 10.1039/c2cs15267c

  • CrossRef
  • Google Scholar