Deconvoluting the Optical Response of Biocompatible Photonic Pigments

Abstract To unlock the widespread use of block copolymers as photonic pigments, there is an urgent need to consider their environmental impact (cf. microplastic pollution). Here we show how an inverse photonic glass architecture can enable the use of biocompatible bottlebrush block copolymers (BBCPs), which otherwise lack the refractive index contrast needed for a strong photonic response. A library of photonic pigments is produced from poly(norbornene‐graft‐polycaprolactone)‐block‐poly(norbornene‐graft‐polyethylene glycol), with the color tuned via either the BBCP molecular weight or the processing temperature upon microparticle fabrication. The structure–optic relationship between the 3D porous morphology of the microparticles and their complex optical response is revealed by both an analytical scattering model and 3D finite‐difference time domain (FDTD) simulations. Combined, this allows for strategies to enhance the color purity to be proposed and realized with our biocompatible BBCP system.

then stirred for 24 h at room temperature. The reaction mixture was filtered to remove any precipitate and the filtrate was added to a 10-fold excess of cool diethyl ether to precipitate the product as a white solid. Two more precipitations in diethyl ether were carried out to remove excess NB-COOH. The white solid was dried in a vacuum oven at 40 °C for 24 h (Mn = 2.4 kg mol -1 ).
Synthesis of [(H2IMes)(3-Br-py)2(Cl)2Ru=CHPh] (Third generation Grubbs catalyst, G3) 3-Bromopyridine (0.34 mL, 3.5 mmol, 10 eq.) was added to G2 catalyst (0.3 g, 0.35 mmol, 1 eq.) in a 20 mL vial with a snap cap; no additional solvent is required. The reaction was stirred at room temperature in air for 10 min during which a color change from red to bright green was observed. Pentane (20 mL) was added to the green solution, leading to the precipitation of a green solid. The vial was subsequently capped under air and cooled to ~ -20 °C overnight (freezer). The green precipitate was collected using vacuum filtration, washed with 4 × 10 mL of pentane, and dried under vacuum to afford the product as a green powder.
Synthesis of poly(NB-PCL)-b-poly(NB-PEG) block copolymers via ring opening metathesis polymerization (ROMP). In a typical experiment, 315 mg of NB-PCL (3.1 kg mol -1 , 0.01 mmol) and 220 mg of NB-PEG (2.4 kg mol -1 , 0.009 mmol) were added separately into vials, which were degassed and backfilled with nitrogen. Anhydrous dichloromethane (DCM), which was degassed via three freeze-pump-thaw cycles, was added to the two vials resulting in macromonomer solutions between 0.1-0.2 M. At room temperature, the polymerization of NB-PCL was initiated by adding the precise volume of G3 catalyst as a solution in DCM solution (1.8 mg mL -1 ), using a syringe pump. After 3 min, the solution of the second macromonomer (NB-PEG) was injected into the reaction mixture. This solution was allowed to stir at room temperature for an additional 2 h. The reaction was then quenched with ethyl vinyl ether, diluted with DCM and precipitated into cold methanol. The produced BBCP was dried overnight in a vacuum oven at 50 °C. The desired degree of polymerization was achieved by maintaining the same quantities of macromonomers and varying the volume of G3 catalyst solution. The amount of catalyst added for each polymer and the resultant Mn are reported in Table S2.
Preparation of BBCP microemulsions via a microfluidic device. Monodisperse microdroplets were generated within a hydrophilic, etched-glass microfluidic device (Dolomite #3000158, Droplet Junction Chip with 100 µm etch depth). The discontinuous phase was prepared by dissolving the block copolymers (CLEG1-4) in toluene (30 mg mL -1 ) For polymer-macromonomer mixtures, the solutions were prepared by dissolving 6-36 mg NB-PCL into 1 mL of CLEG1 or 4 solution (30 mg mL -1 ) , i.e. a macromonomer loading of 20-120 wt.% relative to the BBCP. The continuous phase contained polyvinyl alcohol (PVA, 200 mg) as a stabilizer, dissolved in Milli-Q water (10 mL). To form a toluene-in-water microemulsion, the aqueous PVA solution (2 w/v%) and the BBCP solution in toluene were injected into the microfluidic device using two syringe pumps with flow rates of 500 and 200 μL h -1 , respectively.
At the junction, the toluene-in-water emulsions were formed by the shear forces, leading to stable droplets with diameter, Ø ≈ 170 μm. The droplets (ca. 23 μL) were collected into a vial (7 mL) filled with PVA solution (ca. 2 mL) for further solvent evaporation.
Preparation of BBCPs photonic microparticles. For CLEG1, vials containing polymer-toluene droplets were placed in a pre-heated water bath at a defined temperature (30, 40, 50, 60, 70 and 80 °C). For investigation of the effect of molecular weight, droplets containing CLEG2-4 were evaporated at 50 °C. For polymer-macromonomer mixtures, the droplets were evaporated in 60, 65, 70, and 75 °C. In all cases, discrete polymer microparticles were formed after loss of toluene.
Once dry, the microparticles dispersed in water (typically Ø ≈ 70 μm) were washed with Milli-Q water to remove residual PVA surfactant.

Section S2: Additional characterization methods
Optical microscopy and micro-spectroscopy were performed on a customized Zeiss Axio Scope A1 microscope fitted with a CCD camera (Eye IDS, UI-3580LE-C-HQ, calibrated with a white diffuser) using a halogen lamp (Zeiss HAL100) as a light source. To perform microspectroscopy, the microscope was coupled to a spectrometer (Avantes, AvaSpecHS2048) using an optical fiber (Avantes, FC-UVIR200-2, 200 µm core size). The reflectance spectra were normalized against a white diffuser (Labsphere USRS-99-010). The BBCP microspheres dispersed in water were analyzed using a water immersion objective (Zeiss, W N-Achroplan 40x/0.75 M27 (FWD=2.1mm)). The collected spectra are analyzed based on the methodology presented in Section S3, Supporting Information. Optical photographs were taken using Canon EF 50mm f/1.8 II lens with Kenko 12 mm extension tube mounted to Canon EOS-1D Mark III body.
Scanning electron microscope (SEM) images were collected with a Mira3 system (TESCAN) operated at 3 kV and a working distance of 3 -6 mm. The samples were mounted on aluminum stubs using conductive carbon tape and coated with Pt (10 nm) using a sputter coater (Quorum Q150T ES). The samples were obtained by lyophilizing the microparticle suspensions. The samples were fractured mechanically using a microspatula to expose the cross-section. 1 H NMR spectroscopy was recorded in CDCl3 using a Bruker 400 MHz Avance III HD Spectrometer.
Cryogenic Scanning electron microscopy (Cryo-SEM) was performed at the Cambridge Advanced Imaging Centre using an FEI Verios 460 scanning electron microscope, equipped with a Quorum cryo-transfer system (PP3010T). Samples were washed with Milli-Q water to remove surfactant. A small amount of this suspension of microspheres in water was then placed on top of a freezing rivet mounted on the specimen holder, forming a spherical droplet. The specimen holder with sample was then plunge frozen in liquid ethane and transferred to a specimen preparation chamber cooled to −140 °C. The droplets were then freeze-fractured, exposing the internal structure of the microspheres. Samples were then sublimed at −90 °C for 10 minutes and subsequently sputter-coated with platinum. Imaging was performed at 2.00 kV acceleration voltage with a 13 pA probe current.
Gel permeation chromatography (GPC) was used to determine the molecular weights of the macromonomers and the block copolymers. GPC was carried out in DMF (eluent flow rate of 1.0 mL min -1 ) using three PLgel 10 µm mixed-B LS columns (Polymer Laboratories). For macromonomers (NB-PCL), the molecular weights were obtained relative to a series of polystyrene standards. For block copolymers, their absolute molecular weights were determined by combining GPC and light scattering technique, which is widely used to measure polymers with a non-linear architecture. The GPC was connected in series with a DAWN HELEOS multi-angle light scattering (MALS) detector and a refractive index (RI) detector.
The dn/dc values were first measured by injecting 5 concentrations of polymer solutions directly into RI detector without passing through the columns. From the dn/dc values, the absolute molecular weights were obtained by analysis of the signals obtained from the MALS detector.
Optical Microscopy with an inverted microscope (Zeiss Axio Vert.A1) connected with a CCD camera (Pixelink PL-D725CU-T) was used to monitor the preparation process of the microdroplets.
Dynamic Light Scattering (DLS) was performed with a glass cuvette with round aperture on a ZETASIZER NANO-ZS with 633nm He-Ne LASER (Malvern Panalytical). The polymertoluene solutions (1 mL, 5 mg mL -1 ) were added in the cuvette and equilibrated for 5 min at a specific temperature (22, 30, 40, 45, or 50 °C) and water (200 μL) at the same temperature was added to initiate the measurements. Before each measurement, the mixture was gently shaken to obtain a uniform micelle suspension. Measurement angle, position, and the attenuator were fixed at 173°, 6.5 mm, and 11, respectively. Constant refractive indices for the material (1.

Dynamic Interfacial tension (IFT) was measured in a Contact Angle and Surface Tensiometer
(First Ten Ångstroms 100) via pendant drop shape analysis. Typically, a drop of BBCP toluene solution (30 mg mL -1 ) was suspended in water, which formed an inverted droplet because of the lower density of toluene compared to water. A series of images were recorded by a camera at an interval of 2 s over 5 min. By fitting the droplet shape with the associated software, the values of the interfacial tension were obtained.

Section S3: Spectra and image analysis
The reflectance spectrum of 50 photonic microparticles was collected with the setup in Methods. The mean of these spectra was used to plot the representative spectrum in Figure 4, and also Figure S10, S24, S28, S29, and S30. The colored band represents the standard deviation of these 50 spectra. The optical spectra were analyzed by first correcting for the baseline. The baseline was taken as the spectrum of a water layer on a glass slide, which was deducted from each spectrum. The position of the peak at large wavelength was extracted by peak-picking. The position of the first structural peak was obtained by fitting the spectra with Lorentzian distributions. For spectra that appear as a bimodal distribution or a unimodal distribution with a shoulder, the spectra were modelled as the sum of two Lorentzian distributions while spectra with only one peak (without a shoulder) were described by one Lorentzian distribution. The form of each Lorentzian curve was taken as where the peak position is given by . The presented positions for each sample were averages calculated using values extracted from 50 measurements, while the errors were calculated from the standard deviation.
For structural analysis, let ( ): ℝ → (0,1) denote binarized 2D images and 3D volumes for n=2 and n=3, respectively. The 2-point correlation function (structure factor) is then defined where = | |, and the angular brackets denote ensemble averages and the correlation length is defined as For experimental data, SEM micrographs were segmented to I(x) using the trainable WEKA segmentation tool in ImageJ. [1] The correlation length was then calculated using fast Fourier techniques in Matlab, and the pore sizes were calculated using ImageJ particle analysis tools after removing noise from the images via the "remove outliers tool" in ImageJ. [2] The extracted apparent pore size ( Figure S15a) was analyzed using a Matlab code developed by Depriester and Kubler based on the Saltykov method. [3] Excluding outlying pore sizes with radii above 300 nm, a histogram (with 25 bins) of the real pore size was accordingly generated ( Figure S15b). The bin centers and heights were subsequently fitted to a log-normal distribution with the form Thus, the histogram could be approximated as a continuous probability density function, of which the median can be taken as the average pore size | |. The error in the average pore size was approximated from the distribution fitting by the confidence bound at a level of 95%.
The full width at half maximum probability of the pore size distribution curves √ − √ was taken as the pore size distribution width (wr).

Section S4: 3D simulation
Let ( ) ∶ ℝ → ℝ represent a continuous field. The structural simulations were carried using a phase-field crystal model approach suggested by Guttenberg et al. [4] The following equation of motion: where = 20 is the undercooling parameter, and the mean density 〈 〉 = 2 − 1, = 0.23, was solved by using a spectral method to simulate the time evolution of the system. [5] The simulations were performed in a simulation box with grid points under periodic boundary conditions, and the scale of the structures were controlled by varying between 500 to 700.
The 3D surface models (Figure 2a, c, e, g) representing the photonic structures were then obtained by using a level-set scheme: where is the threshold value, using UCSF Chimera, [6] and then imported to Lumerical FDTD solver as 5 µm × 5 µm × 5 µm volumes. The FDTD simulations were carried out using Section S5: Analytical model of scattering Calculating the Mie-scattering cross section of a single sphere: For a plane wave scattered by a spherical particle the scattering cross section is given by: [7] = 2 (2 + 1)(| | + | | ) with and the Mie coefficients calculated with the use of Bessel functions of first and second order.

Multiple light scattering in the diffusive regime
In the multiple scattering regime the transport mean free path * , as a microscopic property, can be directly related to the reflection R of a system via R=1-T (where T is transmission, assuming no absorption) with [8] ~ * The mean free path connects to the scattering cross section via * ~ 1 Where is the number density of scatters and is the scattering cross section. The scattering cross section can be expressed in terms of the form factor F(θ) (scattering properties of the single sphere) and the structure factor S(θ) (collective scattering of the sample) [7,9] = ( ) ( ) sin Calculating the structural correlation for a random packing of hard spheres: For randomly packed hard spheres, one can calculate the structure factor ( ) (collective scattering of the sample) using the Percus-Yevick approximation: [10] ( ) = 1/(1 − ( )) Here q = 2k sin /2 with k = 2 / and the wavelength of the light in the surrounding medium.
( ) can be calculated via the Ornstein-Zernike equation and = (6 )/ is the number density that can be expressed via the volume fraction and the scatterer radius .

Section S6: Color saturation and purity
To better quantify how the pigments appear to the human eye, their coordinates in the CIELAB color space were calculated from the reflection spectra using a standard observer (CIE 1931 2°) and relative to a standard illuminant (Daylight D65). [11] As shown in Figure S32a, this chromaticity diagram has three coordinates representing lightness (L*, between 0 and 100), the position between red and green (a*, green when a*< 0, red when a*> 0), and the position between yellow and blue (b*, blue when b*< 0, yellow when b*> 0) of the color, which allows for detecting perceptual color difference between any two colors. The coordinates are calculated according to an open-source Python package. [12] The chroma (C*) is calculated according to: * = * + * which is conceptually close to saturation, representing the purity of the color. [13] The values from different photonic pigments prepared in different temperatures or with different BBCPs were normalized and compared in Figure S32b.

Section S7: DLS analysis
The amphilicity of CLEG1, as validated by interfacial tension measurements (see Figure S12, Video S1), can promote the formation of BBCP micelles, the presence of which can be monitored in real time by DLS. When CLEG1 was dissolved in pure toluene, no micelles were detected, even at high BBCP concentrations (e.g., 30 mg mL -1 ). However, once the homogenous BBCP solution was exposed to a water drop, subsequent diffusion into the toluene phase stimulated their formation. As reported in Figure S13b, when the experiment was carried out at 22°C, initially nothing was detected by DLS, but after 5 minutes, micelles started to form in the solution and their number increased rapidly as more water diffused into the toluene. In parallel, their size decreased as more micelles formed until a dynamic equilibrium was finally reached, in which the size and number of the micelles was relatively stable ( Figure S13b-c).
Notably, the dispersity of the micelle size sharpened during the early stages of this process and increased slightly as the micelles swelled ( Figure S13d). The resulting narrow distribution in size supports the mechanism of micelles first forming upon emulsification of the BBCP toluene solution in water, and then geometrically packing upon subsequent toluene evaporation to yield the uniform porous structures observed in Figure 1d, with the BBCP shells of the micelles fusing upon final drying to form the extended polymer matrix. Repeating the DLS measurement at a higher temperature resulted in a smaller number of micelles, but of a larger size ( Figure   S13b-c), which is attributed to the increased solubility of water in toluene. [14] Importantly, this phenomenon can explain the increase in pore size and corresponding redshift in the color of the photonic pigments.
Section S9: Additional tables Section S10: Additional video Video S1: When the toluene solution of NB-PEG (30 mg mL -1 ) was added in water by the pendant drop method during the interfacial tension measurements, small droplets were formed in the pendant toluene droplet as water was absorbed into the droplet.        block. The integral ratio between PEG and PCL is calculated to be 3.28. Combined with the 1 H NMR spectra of the NB-PCL and NB-PEG in Figure S2-3, the DPs for each block can be obtained as shown in Table S2. Figure S9. Optical transmission micrograph of the generation of toluene-in-water microdroplets containing 30 mg mL -1 CLEG1, using a hydrophilic flow-focusing microfluidic device. Figure S10. (a) Reflectance spectra and (b) the corresponding peak wavelengths or the high wavelength peak if there are two peaks in the spectra for the microspheres suspended in water.
The intensity was measured relative to a white Lambertian diffuser. Figure S11. Cryo-SEM image of the sublimated microparticle cross section prepared with CLEG1 at 60 °C. By manually measuring the center-to-center distance, the correlation length was evaluated as 144 ± 18 nm from this image. This value is higher than that measured for the freeze-dried sample (105 ± 4 nm, see Figure 1 and S15), which can be explained by a degree of shrinkage of the entire microparticle during the freeze-drying process. While this shrinkage can underestimate the correlation length and pore size, the high contrast of such images combined with the complete removal of water importantly allows for automated determination of important structural parameters with high precision. In contrast, the sublimation process used in cryo-SEM is complicated and uncontrollable, which can lead to the presence of residual water in the pores, overestimating the filling fraction. Therefore, in this study, we chose to match the experimental spectra directly with the simulated spectra, rather than to simulate the optical response of a reconstructed nanostructure using the parameters from the SEM analysis.   extracted from the analysis of the fitted spectra, plotted against the values from simple peak picking (Pp), taking the high wavelength peak if there are two peaks in the spectra, see Figure   S10.          As shown in Figure S24, a microsphere prepared at 50°C without any MM has a correlation length of 100 nm and a filling fraction of 42%, leading to a green color with a reflection intensity of 0.2 ( Figure S24e). When 40 wt.% MM relative to the mass of BBCP was blended into the initial toluene solution, ( Figure S24i, j), the filling fraction of the resultant microparticles increases to 52% with only a slight decrease in correlation length (95 nm). As a result, the particle shows a 1.8 fold increase in reflectance to 0.35 in the first structural peak ( Figure S24f).
This increase in reflectance can also be explained by a narrowed pore size distribution which is reflected by decreased wr from 114 to 89 nm. Further increasing the filling fraction should lead to larger improvements in the color quality, but systematically increasing the amount of MM to 120 wt.% resulted in a deterioration of the short-range order in the porous structure and a large shrinkage in the size of the irregular pores, reducing the correlation length ( Figure S24k-l). As such, further enhancement of the first structural peak reflectance was not observed.        pigments prepared with CLEG1 at 60 °C and 80 °C have better color purity than for comparably colored pigments respectively prepared from the higher molecular weight CLEG3 and CLEG4 at 50 °C. In addition, the color from the particle obtained with CLEG2 at 50 °C is purer than that from the higher molecular weight CLEG1 at lower temperature (22 °C). This suggests that a single low molecular weight BBCP combined with temperature modulation is a more optimal approach to produce a wide range of colored pigments with good color purity.