\chapter{Full-Spectrum Photonic Pigments with Non-Iridescent Structural Colors through Colloidal Assembly}\label{chap:HighD}
\label{ch:photonic_balls}
\graphicspath{{figures/ch3/}} 

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%\begin{abstract} 
%A major challenge in this work has been the fabrication of structurally-colored materials that can mimic the appearance of absorbing pigments through the visible range. Such structurally colored materials have long been sought after as replacements for dyes and conventional pigments in many applications. In this chapter, we demonstrate a type of “photonic pigment” consisting of a microcapsule containing a dense amorphous packing of core-shell colloidal particles. Our microcapsules show non-iridescent structural colors that are independent of the viewing angle -– a critical requirement for applications such as displays or coatings. Moreover, our microcapsules are specifically designed to suppress incoherent and multiple scattering, allowing us to make photonic pigments with colors spanning the visible spectrum. Our findings should provide new insights into the design and synthesis of materials with structural colors.
%\end{abstract}

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\section{Introduction}

As we have seen, there are two major challenges in making isotropic structural coloration through colloidal assembly: independent control of the resonances due to single-particle scattering from the resonances due to inter-particle correlations, and control over multiple scattering. If the size of the colloidal particles is too large, the structural resonance at long wavelengths is compromised by single-particle scattering resonances at shorter wavelengths~\cite{Takeoka2013}. If the particle aggregate is too thick, white color from multiple scattering dominates, compromising the color saturation~\cite{Forster2010}. Therefore, control over both single-particle and multiple scattering is necessary to realize photonic pigments with pronounced structural colors that cover the visible range. 
 %\todo[inline]{comment somewhere that scatterers can neither be too large NOR too small}

In this chapter we present a new colloidal assembly method to fabricate micro-encapsulated photonic pigments that cover the full spectrum. Our approach combines the flexibility of the soft core-shell particles that we described in Chapter \ref{ch:core-shell} with a technique that allows precise control over the total sample size. Hence, our design has three structural length scales, each of which is primarily associated with a different scattering process that affects structural color. The scatterer size, set by the cores, determines the resonances of the form factor; the inter-scatterer distance, set by the shells, determines the resonances of the structure factor; and the sample size, set by the capsule size, determines the amount of multiple scattering. It is particularly important that, in this system, the core particles, which dominate the scattering, can be small compared to the shells. This has a twofold benefit: first, it allows blueshifting of the form factor resonances that can interfere with long-wavelength structural color, as we have seen in Chapter~\ref{ch:absence_of_red}; second, it mitigates multiple scattering, since small particles scatter less. In this way, coherent scattering due to the structure factor dominates, and we are finally able to make photonic pigments with isotropic structural colors throughout the visible range.  

\section{Methods}

We use microfluidic techniques to produce spherical microcapsules approximately 100 $\mathrm{\mu}$m in diameter that contain densely packed, amorphous arrays of colloidal particles. The encapsulated particles are polystyrene/poly (N-isopropylacrylamide-co-acrylic-acid) (PS/poly-NiPAm-AAc) core-shell particles with shells that are closely index-matched to the surrounding water, as described in Chapter \ref{ch:core-shell}. 

We start with an aqueous suspension of PS/poly-NiPAm-AAc core-shell particles synthesized through seeded emulsion polymerization~\cite{Perro2009}, using polystyrene nanoparticles of hydrodynamic radius $R_{\mathrm{h, PS}} = 78$ $\pm$ 5 nm as seeds. The ratio of NiPAm monomer to seed particle, which controls the thickness of the soft polyNiPAm shell, is 0.5$\%$ w/w, yielding a core-shell hydrodynamic radius $R_{\mathrm{h, core-shell}} = 168$ $\pm$ 17 nm. We match the refractive index of the shell to that of the suspension medium by co-polymerizing 4.0$\%$ w/w of acrylic acid (AAc) in the polyNiPAm shell. We then encapsulate this suspension in the innermost phase of water-in-oil-in-water double-emulsion droplets using a capillary microfluidic device, as shown in Figure~\ref{fig:microfluidics_schematic_colors_and_SEM}(a)~\cite{Kim2011}. The aqueous suspension and an oil phase containing a UV-curable monomer, ethoxylated trimethylol-propane triacrylate (ETPTA), are injected simultaneously through a hydrophobic capillary, creating a train of suspension droplets in the continuous monomer flow. The hydrophobicity of the capillary prevents the droplets from wetting. This core-sheath is then emulsified into the continuous phase, aqueous poly(vinyl alcohol) (PVA, 10$\%$, w/w), at the tip of the capillary, yielding water-in-oil-in-water double-emulsion drops where the innermost phase is the particle suspension and the middle phase is an ultra-thin shell of oil, as shown in Figure~\ref{fig:microfluidics_schematic_colors_and_SEM}(b). These droplets are the precursors to our photonic microcapsules.

\begin{figure}
\centering
\includegraphics[scale = 0.15]{microfluidics_schematic_colors_and_SEM}
\caption{\label{fig:microfluidics_schematic_colors_and_SEM} Fabrication of photonic pigments. a) Schematic of a capillary microfluidic device for the production of water-in-oil-in-water double-emulsion droplets with a thin ethoxylated trimethylolpropane triacrylate (ETPTA) membrane. b) Optical micrograph showing generation of uniform water-in-oil-in-water droplets. The innermost phase contains an aqueous suspension of core–shell particles with a volume fraction $\phi_{\mathrm{core–shell}}) \sim 0.28$. c) Time-series optical micrographs of osmosis-driven condensation of droplets at 340 mOs/mL, where $t_{1}$, the elapsed time for microscope analysis, is about 5 minutes. d) Schematic of the structure of particles during osmosis-driven condensation. e,f) A photograph and an optical micrograph of the photonic pigments in water after UV-curing of the ETPTA shell. The sample is compressed at 440 mOs/m L. A few capsules show yellow spots due to local deformation of the polymer shell. g) Scanning electron micrograph of a cross-section of a cryogenically fractured photonic pigment microcapsule prepared under compression at 440 mOs/m L. The field of view is 20 $\mathrm{\mu}$m wide. The inset in (g) is the two-dimensional Fourier power spectrum derived from (g), with a 220 $\mathrm{\mu}^{-1}$m field of view.}
\end{figure}

The precursor droplets are designed to facilitate the preparation of amorphous nanostructures. The double emulsion makes it possible to concentrate the suspension by an osmotic pressure gradient~\cite{Kim2013}. Furthermore, the softness of the particle shells inhibits crystallization during concentration~\cite{Mattsson2009}. We concentrate the particles by placing the water-in-oil-in-water droplets into an aqueous solution of PVA and sodium chloride (NaCl), creating a positive osmotic pressure difference that forces the water out through the thin ETPTA membrane and causes the droplets to shrink isotropically, as shown in Figure~\ref{fig:microfluidics_schematic_colors_and_SEM}(c). As the droplets shrink, they develop color that blue-shifts with increasing concentration (Figure~\ref{fig:microfluidics_schematic_colors_and_SEM}(c)). We then polymerize the ETPTA layer by exposing it to ultraviolet light for 30 seconds, as illustrated in Figure~\ref{fig:microfluidics_schematic_colors_and_SEM}(d). The ETPTA layer ($n_{\mathrm{ETPTA}} = 1.4689$) yields a 0.8-$\mathrm{\mu}$m-thick, optically transparent shell after curing. The resulting microcapsules are monodisperse and display non-iridescent structural colors, as shown in Figures~\ref{fig:microfluidics_schematic_colors_and_SEM}(e) and (f). 

The internal structure of these photonic pigments is random and isotropic, as we see in the scanning electron microscope image of a cryogenically fractured microcapsule in Figure~\ref{fig:microfluidics_schematic_colors_and_SEM}(g). The two-dimensional power spectrum of a 20 $\mathrm{\mu}$m $\times$ 20 $\mathrm{\mu}$m cross-section is in the inset. We observe a ring pattern; as we discussed in the Introduction, this indicates that the structure is isotropic, with a characteristic lengthscale of short-range order that we calculate to be 217 nm.  
\begin{figure}
\centering
\includegraphics[width = \textwidth]{spectra}
\caption{\label{fig:spectra} Control of structural colors through osmotic pressure. a) Reflectance spectra of the microcapsules equilibrated under different osmotic pressures. b) Plots of peak positions (dark squares) and normalized full-width at half maximum (FWHM; open circles) of the microcapsules as a function of osmotic pressure. c) Estimated concentration of PS scatterers (dark squares) and average spacing between PS scatterers (open circles) as a function of osmotic pressure. Insets are bright-field (reflection) optical micrographs of red, yellow, and green microcapsules prepared under 180 mOsm/ L, 260 mOsm/ L, and 440 mOsm/ L, respectively. The field of view for the insets is 100 $\mathrm{\mu}$m wide. d) Co-polarization (lines) and cross-polarization (dots) reflection spectra of red (upper) and green (lower) photonic microcapsules.}
\end{figure}

We can control the colors by changing the average distance between the polystyrene cores, which are the primary scatterers. The inter-scatterer distance depends on the degree of droplet compression, which depends on the osmotic pressure difference used to concentrate the particles. For example, we can prepare red microcapsules at 180 mOsm/L, yellow ones at 260 mOsm/L, and green ones at 440 mOsm/L. At each osmolarity, we incubate emulsion droplets containing core-shell particles with $R_{\mathrm{h, core-shell}} = 168$ $\pm$ 17 nm for two hours to equilibrate the osmotic pressure before we polymerize the ETPTA shell. As we see in the reflectance spectra of the resulting microcapsules, shown in Figure~\ref{fig:spectra}(a), the characteristic peak shifts from 610 nm to 550 nm as the osmotic pressure increases, but the normalized full width at half-maximum $\Delta\lambda / \lambda_{\mathrm{max}}$, shown in Figure~\ref{fig:spectra}(b), remains almost constant, indicating that the shrinking leads to rescaling of the structures without inducing any qualitative change.  

\section{Results and Discussion}

To understand the relation between the optical properties of the photonic balls and the structures they contain, we first estimate the inter-scatterer distance $d$ from the reflection spectra. For simplicity, we assume back-reflected light, namely a scattering angle $\theta=$ 180 degrees. Then, from Equation~\ref{eq:resonant_wavelengths} 
%
\begin{equation}
\label{eq:resonant_wavelength_backscattering}
d = 0.6 \lambda_{\mathrm{o}} / n_{\mathrm{medium}}
\end{equation}
%
where $\lambda_{\mathrm{o}}$ is the resonant wavelength and $n_{\mathrm{medium}}$ is the effective refractive index of the medium, which depends on the volume fraction of the polystyrene cores via the Maxwell-Garnett relation (Equation \ref{eq:Maxwell-Garnett}). The factor of 0.6 in Equation~\ref{eq:resonant_wavelength_backscattering} comes from the average spacing between particles in a colloidal glass of hard spheres with volume fraction $\phi=$ 0.65. Our particles are soft, however this serves as a useful starting point. Because we do not know a priori the volume fraction of polystyrene, we calculate $d$ using an iterative process: We first use Equation \ref{eq:resonant_wavelength_backscattering} to calculate $d_{\mathrm{0}}$ with $n_{\mathrm{medium, 0}}$ equal to the refractive index of water, then we use $d_{\mathrm{0}}$ to estimate the volume fraction of polystyrene, $\phi_{\mathrm{PS}} = (d_{\mathrm{core}} / d_{\mathrm{0}})^3$, and a new effective $n_{\mathrm{medium, 1}}$, and from Equation \ref{eq:resonant_wavelength_backscattering} we calculate a new $d_{\mathrm{1}}$ from $n_{\mathrm{medium, 1}}$. The values for $d$ converge quickly, and we find a reasonable $n_{\mathrm{medium}} \sim 1.39$. From this calculation, we estimate the number density of polystyrene scatterers and the average distance between them as a function of osmotic pressure, shown in Figure~\ref{fig:spectra}(c). We find that, for the green microcapsules, the inter-scatterer distance calculated from the spectrum (236 nm) agrees reasonably well with that obtained through Fourier analysis of an SEM image of the same sample (217 $\pm$ 14 nm). On the basis of the spectra, calculations, and SEM analysis, we conclude that the particles are compressed into roughly 35$\%$ of their original volume at 440 mOsm/L. 

In all of these samples, coherent scattering from the inter-particle correlations dominates over single-particle scattering and over multiple scattering. We characterize all scattering away from the structure factor resonance by the intensity at short wavelengths (420–-435 nm), where it contributes the most. The ratio of the peak intensity on the structure factor resonance to the background intensity, $I_{\mathrm{max, S}} / I_{\mathrm{background}}$ shown in Figure~\ref{fig:spectra}(a), increases from 1.35 for red photonic microcapsules to 1.83 for green. This quantity is one measure of color saturation: the lower the value, the whiter the sample, due to mixing of the resonant color with blue light. Although the background scattering is not negligible, particularly for red microcapsules, it is significantly less than scattering due to inter-particle correlations for all the samples. Moreover, for all microcapsules, this background scattering is drastically less than it is for the more conventional colloidal glasses of poly-methylmethacrylate particles discussed in Chapter~\ref{ch:absence_of_red}. For comparison, the corresponding ratio $I_{\mathrm{max, S}} / I_{\mathrm{background}}$ for those is 1.24 for the green sample and 0.74 for the purple sample. In the last case it is even less than one; as we have already discussed, for particles larger than $\sim$240 nm the second-order form factor resonances can be much stronger than the structure factor resonances and prevent entirely structural color of longer wavelengths. Using smaller scatterers, we have demonstrated a way to blueshift the second-order form factor resonances away from the visible spectrum and thus to decrease their effect on structural color: for a $d = $ 156 nm polystyrene particle in this system, the second-order form factor resonance occurs at 305 nm, and only the much weaker first-order form factor resonance is within the visible.

\begin{figure}
\centering
\includegraphics[width = \textwidth]{microscope_polarization_setup}
\caption{\label{fig:microscope_polarization_setup} A schematic illustration of our spectrometry setup for measuring the co-polarized and cross-polarized reflection spectra of the photonic microcapsules.}
\end{figure}

We isolate the contribution of multiply scattered light to the background scattering by measuring the polarization dependence of the reflection spectra, since multiply scattered light loses memory of its original polarization. We linearly polarize the incident light and place another linear polarizer in front of the detector, as shown in Figure~\ref{fig:microscope_polarization_setup}. The resulting spectra, shown in Figure~\ref{fig:spectra}(d), are very different. When the two polarizers are parallel, we observe a single spectral peak at approximately 560 nm for the green and 600 nm for the red microcapsules; whereas when the two polarizers are crossed the spectra for both samples are nearly flat. From these measurements we calculate the ratio of singly to multiply scattered light at the resonant wavelength, assuming that the cross-polarized signal is due to multiple scattering and that the contribution of multiple scattering to the signal is the same in both the co- and cross-polarized spectra. We find values of 16.2 for the green and 17.3 for the red microcapsules, indicating that multiple scattering does not contribute significantly to the color. We also calculate the contribution of multiple scattering to the background from the average reflectivity through crossed ($I_{\mathrm{crossed}}$) and parallel ($I_{\mathrm{parallel}}$) polarizers at short wavelengths (420-435 nm), $I_{\mathrm{crossed}} / (I_{\mathrm{crossed}} + I_{\mathrm{parallel}})$. We find that multiple scattering accounts for only 23$\%$ of the background intensity in green and 24$\%$ in red microcapsules, indicating that the primary source of background scattering is single-particle scattering from the polystyrene cores. From these measurements we conclude that multiple scattering does not compromise the color saturation in our system, in contrast to other systems with isotropic structural colors where multiple scattering has to be suppressed through absorption~\cite{Takeoka2009, Forster2010, Jiang1999, Norris2004, Velev2000}.

\begin{figure}
\centering
\includegraphics{RGB}
\caption{\label{fig:RGB} Photonic microcapsules with blue, green, and red structural colors prepared with different shell thicknesses of core–shell particles. a) Bright-field (reflection) and b) dark-field (reflection) optical micrographs of photonic microcapsules. c) Reflectance spectra of the microcapsules. All droplets are incubated at 440 mOsm /L for one hour before ETPTA polymerization.}
\end{figure}
To complete the color spectrum, we make microcapsules from core-shell particles of different sizes. We use the same osmotic compression and cores for all samples, so that the inter-scatterer distance is controlled by the thickness of the particle shells. We obtain blue photonic microcapsules with $R_{\mathrm{h, core-shell}} = 135$ $\pm$ 24 nm, green with $R_{\mathrm{h, core-shell}} = 168$ $\pm$ 17 nm, and red with $R_{\mathrm{h, core-shell}} = 210$ $\pm$ 15 nm, as shown in Figure~\ref{fig:RGB}. 

\begin{figure}
\centering
\includegraphics[scale = 0.25]{glasses_and_crystals}
\caption{\label{fig:glasses_and_crystals} Photonic microcapsules show uniform structural colors under different illumination directions. Bright-field (reflection) optical micrographs of (a) photonic microcapsules and (b) crystalline balls. (c) Schematic of the apparatus used to measure the reflection spectra of a single microcapsule or ball. (d,e) Reflectivity (yellow: 100$\%$, blue: 0$\%$) of a microcapsule (d) and a crystalline ball (e) as a function of position (x), where x=0 at the center and x=1 at the edge.}
\end{figure}

The optical properties of our amorphous microcapsules are qualitatively different from those of crystalline structures, even for samples prepared with comparable particle sizes. For comparison, we prepare crystalline photonic balls with a diameter of about 90 $\mathrm{\mu}$m through consolidation of 250 nm polystyrene spheres in W/O droplets~\cite{Kim2006}. Reflection optical micrographs in Figure~\ref{fig:glasses_and_crystals}(a) and (b) show the dramatic differences between the two samples: the amorphous microcapsules show colors that are uniform across each capsule and from capsule to capsule, whereas the crystalline balls show patches of different colors and variations between balls. To quantify these differences, we measure the spectra of single microcapsules and crystalline balls as a function of position ($x$) with our microscope-mounted, fiber-optic spectrometer (Figure~\ref{fig:glasses_and_crystals}(c)). The position of the spectral peak remains constant for the microcapsule (Figure~\ref{fig:glasses_and_crystals}(d)), while in the crystalline ball it shifts by 40 nm or more (Figure ~\ref{fig:glasses_and_crystals}(e)). This behavior arises from the anisotropy of the crystal, which leads to a variation in the resonant condition with angle. At the same time, the incompatibility of crystalline order with the spherical symmetry of the droplet likely leads to the formation of grain boundaries, which could account for the variation in colors from ball to ball. Our measurements highlight the trade-off in optical performance between crystalline and isotropic structures: while the crystalline ball has sharper resonant peaks at some locations, the isotropic microcapsule shows a broader but more consistent peak across a wide range of positions. We also measure the reflectivity of the microcapsules at various angles by rotating the sample stage. As shown in Figure~\ref{fig:rotated_spectra}, the peak moves less than 10 nm and is independent of the viewing angle. Plots of as a function of angle in Figure~\ref{fig:rotated_spectra} confirm that the optical properties of our microcapsules are independent of orientation.

\begin{figure}
\centering
\includegraphics[width = \textwidth]{rotated_spectra}
\caption{\label{fig:rotated_spectra} (a) Reflectance spectra of the photonic pigments at various viewing angles. (b) Peak position ($\lambda_{\mathrm{max}}$, dark squares) and normalized full-width at half-maximum ($\Delta\lambda / \lambda_{\mathrm{max}}$, open circles) of each peak at various angles. In this measurement we varied the angles of the sample stage with respect to the normal to the substrate.}
\end{figure}

In conclusion, we have demonstrated a new colloidal assembly method to fabricate photonic microcapsules with non-iridescent structural colors that cover the entire visible range. The length scales of our system are such that both single-particle and multiple scattering is suppressed, so that resonant scattering from the inter-particle correlations is the dominant process determining color. In this way, this design has enabled the creation of structural colors that were inaccessible with conventional colloidal particles. We note that this system is optimized for structural inks that remain in a fluid medium. Pigments than can be dried might be made using a more rigid microcapsule. Another challenge is to further increase the saturation across the visible range; as our experiments show, red microcapsules are not as saturated as green or blue ones due to scattering at short wavelengths. Our system provides several potential ways to reduce incoherent scattering; for example, one could vary the refractive indices of the core and shell, or optimize the ratio of the core size to the inter-particle spacing. The ability to independently tune refractive indices and length scales to optimize the color -- all while maintaining the ability to form amorphous packings -- make this a promising system for mass-produced photonic pigments. 

This chapter is based on the following publication: Jin-Gyu Park, Shin-Hyun Kim, Sofia Magkiriadou, Tae Min Choi, Young-Seok Kim, and Vinothan N. Manoharan, ``Full-spectrum photonic pigments with non-iridescent structural colors through colloidal assembly,'' Angewandte Chemie, 126(11):2943–2947, 2014 \cite{Park2014}.

%\begin{figure}[hbtp]
%\centering
%\includegraphics[scale=1]{}
%\caption{\label{fig:}}
%\end{figure}



%\begin{equation}
%4 \pi n/\lambda_r = 2 \pi/a_r = q
%\label{eq:resonance}
%\end{equation}


%\begin{equation}
%  n = n_\mathrm{water} \sqrt{\frac{2 n_\mathrm{water}^{2} +
%     n_\mathrm{PS}^{2} +  2 \phi (n_\mathrm{PS}^{2} -
%      n_\mathrm{water}^{2} )} {2 n_\mathrm{water}^{2} + n_\mathrm{PS}^{2} - \phi (n_\mathrm{PS}^{2} - n_\mathrm{water}^{2})}}
%\label{eq:Maxwell-Garnett}
%\end{equation}

