\chapter{Conclusion and Outlook}
\label{chap:HighD}
\graphicspath{figures/conclusion/}

In this thesis we have studied the optical properties and colors of colloidal photonic glasses. In the theoretical part of our work, we have constructed the first model that accurately predicts the absolute reflectivity of a colloidal glass; we have provided a reason to explain the difficulty in making red color; and we have preliminary results to suggest that the range of possible colors far exceeds what has so far been created in the lab. In the experimental part of our work, we have created and studied novel colloidal systems that offer a high degree of control over scattering: glasses of core-shell particles with scattering cores and transparent shells, where the hue can be tuned independently of saturation; encapsulated suspensions of these particles, or photonic balls, in which incoherent scattering can be suppressed, leading to the first observation of a full-spectrum photonic glass system; and inverse glasses, where we expect to see more saturated, long-wavelength colors.

In subsequent work, the potential of inverse glasses needs to be investigated further. In particular, it will be interesting to use the core-shell architecture in an inverse system. This could be achieved in numerous ways. Our calcination method for creating inverse glasses could easily be modified to include core-shell polymer-silica particles in the template, instead of simple polymer particles, leading to inverse structures where the size of the air cores can be controlled independently of the spacing between them. Such particles have already been synthesized~\cite{Lu2004}; our collaborator Gi-Ra Yi and his students are currently working on providing us with a batch for structural color applications. Similarly, our infiltration protocol can as easily be applied to glasses of core-shell particles with low-index cores. My colleague Jin-Gyu Park has already synthesized polymer particles with low refractive index, on the order of 1.38, using a fluorinated monomer, 1H,1H-heptafluorobutylmethacrylate. Covering these particles with a polymer shell has turned out to be challenging due to their different wetting properties, and further experiments on synthesis are required to find a material for the shell that is compatible. Along similar lines, Dr. Park has also synthesized polystyrene-poly(tert buthylmethacrylate) core-shell particles, which, if the sequence of materials can be inverted, can also be used in infiltrated inverse glasses. 

A natural extension to particles with two layers is particles with many layers. One idea we originally had to obtain structural red color was to include in our glasses multi-layered particles as anti-reflection coatings for blue wavelengths. We have since analytically shown and independently learned that a stack of dielectrics on a spherical surface cannot establish perfect destructive interference~\cite{Small2005}. Regardless, a multi-layer architecture can offer even more precise control over the form factor. The potential advantages of this approach can be checked readily, as our code for calculating the single particle scattering cross section can be applied to particles with an arbitrary number of layers.

At a higher level, we have not at all investigated whether a glassy structure is optimal for angle-independent structural color. Are there other structure factors that lead to more saturated colors? By symmetry, we know that, to obtain angle-independent structural color, we need an isotropic material with long-range disorder -- unless we wait for a complete band gap to be realized with a photonic crystal in the visible. From Fourier theory, we also know that we need some degree of order, characterized by some lengthscale, in order to have constructive interference and color. But we do not currently know whether there is an optimum value for the spatial extent of the short-range order, or an optimum class for its local symmetries. In glassy packings of spherical particles, the pockets of order usually have the form of slightly distorted hexagonal packings. This local geometry defines the location of the first peak of the structure factor, since it determines the average spacing between coordination shells. It is conceivable, then, that the first peak of the structure factor could be controlled by imposing a different geometry of short-range order, for example by randomly packing particle \textit{clusters} instead of individual particles. This is certainly within the realm of possibility, since techniques for the assembly of colloidal clusters of various sizes and shapes have already been established~\cite{Manoharan2003, Sacanna2011, Schade2013}.

Turning more directly to applications, another open question pertains to the optimal thickness of a photonic glass. It has already been discussed that, if the samples are too thick, incoherent multiple scattering overwhelms coherent single scattering, bleaching any structural color~\cite{Forster2010}. But the converse question has not been answered: how \textit{thin} can a photonic glass be and still have a saturated, visible color? This is particularly relevant for coating applications, where the film thickness cannot exceed a few dozen micrometers. Our newest recruit, Victoria Hwang, is currently addressing this question experimentally, with microfluidic techniques that allow her to create colloidal glasses with precisely controlled thickness.

Moreover, a striking feature of structural colors that cannot be matched with conventional pigments is their potential to be interactive and dynamically tunable. We have begun exploring this feature with temperature-tunable photonic crystals of core-shell particles that can be synthesized to span the visible range over a variety of temperature ranges~\cite{Park2014inprep}. This concept can be extended to temperature-tunable glasses. Other ways to make tunable structural colors could be by embedding small magnets in them, or using dielectrophoretic materials that, when placed between two electrodes, can either be displaced or swollen, leading to a change in appearance -- for instance, in the pixel of a reflective electronic display. 

Finally, no application of photonic pigments will be very appealing if their colors are not comparable to what we already have with absorbing dyes. To ensure that the color-fastness and dynamic tunability of structural colors does not come with aesthetic compromises, we hope that our calculations of the RGB colors of colloidal glasses will inspire a more thorough chromaticity study aimed at identifying the key parameters for color saturation and hue. 

While this work has helped elucidate some aspects of the physics behind the colors of photonic glasses, we hope to have also shown that these can be just the first steps of an exciting quest.    

%difference between crystal and glass: second peak in crystal is further away, or more narrow? 
% later - appendix with non AR coatings from spheres

%near-fields 

%\begin{figure}
%\centering
%\includegraphics[width = \textwidth]{colormaps_vs_rcore_rshell}
%\caption{\label{fig:colormaps_vs_rcore_rshell} Our model predicts that colloidal glasses can produce a wide range of structural colors. Calculated sRGB colorsfor colloidal glasses of core-shell particles as a function of core and shell diameter. We used a thickness of 15$\mathrm{\mu}$m and a volume fraction $\phi=0.5$, and we have index-matched the shells to the medium. (a) Air-silica core-shell particles in silica. The colors are primarily determined by the shell diameter, indicating that the form factor does not have strong features in the visible. (b) Polystyrene scatterers in water. (c) Silica scatterers ($n$=1.4) suspended in air. In (b) and (c), the range of colors is fairly wide and the hue can be tuned with both the shell and the core diameter. (d) Titania cores in silica. While the refractive index contrast here is the same as in (c), the range and saturation of colors is limited.} 
%\end{figure}


%\section{Conclusion}


%\section{The Inverse Problem: From Color to Structure}



%simplest: vary the volume fraction
%figure of color vs volume fraction?

%control the structure factor by mixing in clusters to control short-ranged order

%\section{Conclusion}

%Photonic glasses have the potential to provide a wide range of colors, of controllable hue and saturation, that cover the visible spectrum. Promising something something applications. 

%The work we presented here is by no means complete. A lot of questions remain unanswered: 

%We hope it will inspire a further study into the potential of photonic glasses as pigments 

%chromaticity study


