Light Manipulation with Photonic Fibers and Optical Light Guides: Dynamic Structural Color and Light Distribution in Microalgae Cultures

Joseph D. Sandt

B.S. Mechanical Engineering University of Kansas, 2013

S.M. Mechanical Engineering Massachusetts Institute of Technology, 2015

Submitted to the Department of Mechanical Engineering in Partial Fulfillment of the Requirements for the Degree of

Doctor of Philosophy

at the

Massachusetts Institute of Technology

February 2020

Signature of Author Department of Mechanical Engineering January 15th, 2020

Certified by Mathias Kolle Professor of Mechanical Engineering Thesis Supervisor

Accepted by Nicolas Hadjiconstantinou Professor of Mechanical Engineering Chairman, Committee on Graduate Students

Light Manipulation with Photonic Fibers and Optical Light Guides: Dynamic Structural Color and Light Distribution in Microalgae Cultures

Joseph D. Sandt

Submitted to the Department of Mechanical Engineering on January 15th, 2020 in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Mechanical Engineering

ABSTRACT

Optical and photonic fibers represent versatile systems for light manipulation. They are used to guide, reflect, emit, and absorb light, and can be designed to alter the light’s spectral composition in any of these light-matter interactions. Additional functionality arises from the combination of these effects in single fibers, and the ability to employ fibers as individual strands, or as woven networks. Two distinct light-manipulating-fiber systems are the focus of this thesis: (1) photonic fibers, which have vivid structural color that changes reversibly in response to mechanical or electrical stimuli, and (2) leaky light guides, which emit light along their length when illuminated from one end.

Mechanochromic fibers that convert a mechanical perturbation into an optical response can be used, standalone or integrated into textiles, as easy-to-read strain sensors. Such fibers respond to elongation with a gradual shift in their reflected color through the visible range of light. In particular, their use in compressive bandages – discussed in detail in this thesis – could greatly improve the efficiency of compression therapy for chronic venous ulcers and other vascular maladies. Electrochromic fibers exploit the electrochemically-tunable absorption of poly(3,4-ethylenedioxythiphene) polystyrene sulfonate, a common conducting polymer, to design devices that can be flipped between a vivid, structurally colored state, and a dull, absorption-colored state. Custom optical multilayer and lumped parameter models are used to analyze the behavior of these fibers.

Leaky light guides, by distributing light throughout volumes of algae culture, could yield greater productivity in microalgae cultivation, while lowering energy requirements. The combination of these factors could enable the economically favorable generation of algal biomass for fuels, feedstock, pharmaceuticals, and many other uses. A passive system for distributing light throughout culture volumes, by selectively scattering light out of light-guiding fibers, is developed and implemented. The process of designing and manufacturing these leaky light guides, and their use in a variety of laboratory- scale bioreactors with live microalgae cultures, are described.

Thesis Supervisor: Mathias Kolle

Title: Associate Professor of Mechanical Engineering

Table of Contents

Introduction: Stimuli-Responsive Photonic Fibers and Leaky Light Guides ...... 6

Chapter 1: Dynamic Structural Color in Stimuli-Responsive Photonic Fibers ...... 9

1.1 Sensing with Structural Color ...... 9

1.2 Mechanochromic Photonic Fibers ...... 11

1.2.1 Sensor Concept ...... 11

1.2.2 Manufacture and Characterization of Mechanochromic Fibers ...... 12

1.2.3 Mechanochromic Fibers as Sub-Bandage Pressure Sensors ...... 18

1.2.4 Other Applications of Mechanochromic Fibers ...... 23

1.2.5 Summary and Perspective for Project Continuation ...... 24

1.3 Electrochromic Photonic Fibers ...... 25

1.3.1 Sensor Concept ...... 26

1.3.2 Manufacture and Characterization of Electrochromic Fibers ...... 27

1.3.3 Circuit Modeling of Electrochromic Fibers ...... 32

1.3.4 Optical Modeling of Electrochromic Fibers ...... 37

1.3.5 Continuation ...... 43

1.4 Outlook ...... 44

Chapter 2: Leaky Light Guides for Microalgae Cultivation ...... 45

2.1 The Promise of Microalgae ...... 45

2.2 Optical Concepts...... 47

2.2.1 Total Internal Reflection and Light Guiding ...... 47

2.3 Modeling and Realization of Uniform Light Emission ...... 48

2.3.1 Modeling of Light Scattering from Leaky Light Guides ...... 48

2.3.2 Laser Ablation of Transparent, Cylindrical Light Guides ...... 50

2.3.3 Manufacture of Uniformly-Emitting Leaky Light Guides ...... 56

2.4 Implementation of Leaky Light Guides in Algae Cultures...... 57

2.5 Characterization of the Influence of Leaky Light Guides on Microalgae Growth ...... 58

2.5.1 Bubble Column Bioreactors at Arizona State University ...... 58

2.5.2 Photoelectrochemical Cells at Arizona State University...... 60

2.5.3 In-lab Bioreactors with Chlamydomonas reinhardtii ...... 61

2.6 Discussion ...... 62

2.6.1 Manufacturability of Leaky Light Guides ...... 62

2.6.2 Outlook and Next Steps ...... 63

Conclusion: Structural Manipulation of Light in Fiber-Based Technologies ...... 64

References ...... 66

Introduction: Stimuli-Responsive Photonic Fibers and Leaky Light Guides

Consider light traveling through some uniform, isotropic optical medium (Figure 1a). This medium has some refractive index n, defined as the ratio of the speed of light in a vacuum to the speed of light in the medium, and it might have some extinction coefficient k, associated with attenuation of electromagnetic radiation. Both of these quantities may vary with wavelength, e.g. red light may travel faster than blue light through one medium, or all visible wavelengths besides green light might be absorbed in another. In this uniform, isotropic medium, light will travel in a straight line. For spectral ranges for which the medium is non-absorbing, light will do so indefinitely. This is immensely important to life on Earth (it's how light and heat from the Sun can travel nearly 100 million miles to Earth), but not particularly interesting for many engineering applications.

Figure 1: Light and Interfaces. a) Light traveling, in a straight line forever, through some medium with refractive index n1. b) A single, flat interface between regions of distinct refractive index results in the reflection and refraction of an incident ray of light. c) Multiple interfaces between regions of distinct refractive index result in multiple reflections and refracted rays. The separation between the two interfaces, and the refractive indices, can be tuned to strongly reflect particular ranges of visible light.

By introducing structure (i.e. inhomogeneity or anisotropy of optical properties) into the medium light is traveling through, it is possible to manipulate and tune visible light in myriad ways by its interaction at interfaces. In one of the simplest cases, light traveling through a volume with some refractive index could encounter a flat interface with a volume with some other refractive index (Figure 1b). At such an interface, some incident light is reflected, and some is transmitted through the interface. The angles these rays make with respect to a line normal to the interface is defined by Snell's Law, and the Fresnel equations indicate how much incident light is reflected and how much is refracted. If multiple such interfaces are placed in the path of some incident light, there is reflection and refraction each time light interacts with any interface (Figure 1c). A fascinating result of such a structure, is that if these multiple interfaces are

6 separated by an appropriate distance (typically tens or hundreds of nanometers), interference between different rays reflected by the structure results in the strong reflection of particular ranges of visible light. This can be seen in asphalt parking lots following rain showers - oil from vehicles forms thin films on top of water puddles, which are observed to have bright, iridescent colors.

This thesis will discuss the use of two particular types of structured optical media in fiber formats, for simple sensing of sundry stimuli and even emission of essential light for environment-embracing energy. Optical and photonic fibers are extremely versatile – their constituent materials and design can be selected to engineer a wide variety of light-matter interactions with light incident on the fibers’ ends or sides. This can result in fibers that guide light along their length, fibers that reflect or absorb incident light, and fibers that emit and scatter light with spectral and spatial control. More than one of these interactions can be incorporated into the same fiber, and additional functionality can be attained by joining multiple fibers together into a rope or cord, or weaving fibers into a fabric.

Even greater functionality can be realized in optical and photonic fibers via the inclusion of nontraditional materials. Traditional optical structures rely almost entirely on glasses and metal oxides – materials that are well-understood and well-suited to the manufacture of most optics, but have inherent limitations in terms of their ability to stretch, take on water or other fluids, react in the presence of vapors, or respond to electrical and magnetic signals. Introducing elastomers, hydrogels, and other transparent materials into familiar optical architectures could give rise to simple optical sensors, light guides with unique properties, or other potentially useful modifications on extant technology.

Mechanochromic and electrochromic fibers, described in Chapter 1, are examples of both the versatility of fiber structures and the benefits of creating optical structures with nontraditional optical materials. The cladding of these fibers consists of a nanoscale multilayer geometry, often referred to as a Bragg stack, constructed using highly stretchable, transparent elastomers, or a material with tunable absorption. The results are fibers that respond to mechanical or electrical stimuli with a noticeable change in their vivid structural coloration. Such fibers are demonstrated to be useful sensors on the laboratory scale; future efforts in scalable manufacturing could enable the development of the fibers into functional and aesthetic fabrics and devices.

In parallel to broadening the application scope of optical and photonic fibers by the introduction of new constituent materials, a range of applications can be unlocked by considering nontraditional and emerging fields, which present specific light management challenges. One such field is microalgae cultivation, in

7 which biomass is grown and harvested to be processed into fuel, feedstock, food, pharmaceuticals, and other products. Cultivation of microalgae could be made more energy efficient and cost effective by more evenly distributing light throughout culture volumes. Light can be controllably emitted from simple, light- guiding fibers by introducing small pits in the fiber surface by laser ablation; the intensity of emitted, scattered light can be adjusted by changing the depth and density of these pits, to form “leaky light guides” with approximately uniform emission over lengths of tens of centimeters. The utility of such light guides is explored in a variety of laboratory-scale bioreactors for microalgae cultivation.

Chapter 1: Dynamic Structural Color in Stimuli-Responsive Photonic Fibers

1.1 Sensing with Structural Color Color is typically produced in one of two ways: absorption or interference of light. Absorption-based color relies on the attenuation of ranges of wavelengths of visible light within a material. This is what makes the stems and leaves of most plants green, and is responsible for the colors of most clothes. Interference- based color relies instead on the combination of multiple reflections of light off distinct interfaces within a structure, resulting in constructive or destructive interference observed as strong reflection of specific ranges of visible light (and weak or absent reflection of others). This type of coloration is prevalent in the natural world (peacock feathers, many beetle carapaces and butterfly wings, and the iridescent seeds of the fruits of Margaritaria nobilis plants are examples), and is observed in an ever-expanding set of man- made materials and devices1.

Interference-based color is often referred to as structural color, since a material’s observed color depends on its micro- and nano-scale structure. A material with a periodic arrangement of optical interfaces in one, two, or three dimensions that induces structural color is often referred to as a “photonic crystal”. The simplest photonic crystal to describe, and the one that will be relevant for the devices discussed herein, is a one-dimensional periodic structure often called a Bragg reflector. Such a structure typically consists of a stack of alternating layers of two materials with different refractive indices (Figure 2a). Often, all the layers of each material will have a consistent thickness. Light incident on any arbitrary interface within this stack partially reflects off that interface, with the remainder of the light

Figure 2: Bragg reflector. a) Incident light is reflected refracting into the next medium. For white light off many interfaces within a periodic multilayer incident on the structure, the total observed reflection structure. b) Calculated reflection spectra, with light incidence and observation normal to the surface, off is summed up from all of the light that reflected off a structure consisting of 45 stacks of a bilayer consisting of a 111 nm film with n = 1.5 and a 104 nm each interface in the stack, and made it back to the film with n = 1.4. The bounding medium is air (n = 1).

9 initial surface. Light waves that were reflected by different interfaces will have acquired some phase difference, which is determined by the variation in optical path length between any two waves’ transit into and out of the structure. This phase difference depends on the indices of refraction of the constituent materials, the thicknesses of the stacked layers, and the angle of the incident light with respect to the surface of the stack. In a carefully designed “quarter wavelength” structure, also known as an ideal multilayer structure, the thickness of each layer is equal to one quarter of a wavelength of visible light in

that material (i.e. λ0/n, where n is the refractive index of the material and λ0 is the wavelength in air). All waves of light of that wavelength, incident on and reflected by such a structure, are constructively interfered. Other wavelengths, to varying degrees, experience destructive interference. The end result is a structure which, when illuminated with white light, strongly reflects a limited part of the visible spectrum, observed as a particular color (Figure 2b).

The application of a rigorous formalism to this structure results in the observation of a photonic bandgap2. This explains why the sides of structural color reflectance peaks are typically quite steep (Figure 2b). Photons with energy that falls within the bandgap are barred from traveling through the structure, in a similar manner to how electronic bandgaps forbid the existence of electrons in particular energy states in materials. This bandgap gets narrower, resulting in the reflection of a more pure color, as the difference between the two materials’ refractive indices shrinks. Simultaneously, though, decreasing the refractive index contrast means more layers are required to achieve strong reflectance.

Structural colors are typically quite striking – a complete photonic bandgap results in the reflection of all incident light of certain wavelengths, making colors appear much brighter than most absorption-based coloration. The absence of pigments or dyes also means that structural color cannot be bleached – as long as the fine structure responsible for the interference remains intact, the coloration will persist. As an example, berries of the Pollia condensata plant have been known to retain their iridescent, blue appearance for decades after being picked.3

The color reflected by a photonic crystal is determined by the optical path difference between different light waves that interact with the structure. Photonic crystals composed of metal oxides and similar materials can be fabricated with a vast array of reflection spectra, but one made, their layers and indices are typically fixed, which prevents any potentially desirable changes in color. Similar structures, made with materials that respond to some external stimulus with predictable changes in their optical properties, layer thickness, or other properties that can influence the optical path difference within a photonic crystal, could respond to the aforementioned stimulus with an observable change in their coloration. If this color

10 shift is small, it could be measured precisely with a spectrometer or other specialized equipment. More usefully, if such a color shift can be made large, then it can be noticed directly by a human observer. Many such structures have been made that respond to changes in temperature, humidity, electric and magnetic fields, mechanical deformation, and other phenomena with a measurable change in their structural color4–6. In this chapter, two such systems are studied: strain-responsive mechanochromic fibers,7 and electrochromic fibers with structurally enhanced optical contrast. For each system, working principles are specified, manufacturing and characterization processes are detailed, potential applications are discussed, and remaining work is outlined.

1.2 Mechanochromic Photonic Fibers 1.2.1 Sensor Concept The structure of the mechanochromic photonic fibers discussed herein was initially inspired by the coiled cellulose sheets found in the skin cells of Margaritaria nobilis seeds.8 They consist of a concentric, cylindrical multilayer cladding comprised of alternating layers of transparent elastomers with distinct refractive indices, arranged around an opaque elastomer core fiber. In a fiber’s unstretched state, its cladding strongly reflects light within a narrow spectral range, observed as a vivid color. As a fiber is stretched, the layers in the cladding get thinner. This thickness change reduces the wavelength around which a fiber’s photonic bandgap is centered, resulting in a blue shift of its observed color (Figure 3).

Assuming normal light incidence, the central wavelength of the mth spectral peak of the reflection spectrum of an ideal periodic multilayer (with refractive indices ni and layer thicknesses ti) is given by

= (1) 4𝑛𝑛𝑖𝑖𝑡𝑡𝑖𝑖 𝜆𝜆𝑚𝑚 𝑚𝑚

Figure 3: Mechanochromic photonic fiber, consisting of a concentric cylindrical multilayer cladding of transparent elastomers, around an opaque elastomer core fiber. Elongation of the fiber induces a thinning of all cladding layers, which reduces the central wavelength of the multilayer’s photonic bandgap. This change is reversible up to stretching the fiber to 2 – 3 times its original length.

The evolution of this central wavelength as fibers are elongated and relaxed can be understood, by

defining how layer thicknesses ti change upon elongation. Longitudinal strain εl and radial strain εr are related by the Poisson’s ratio ν of a material (true, or logarithmic, strain is defined below).

ln = ln = = = ln (2) 𝑟𝑟 𝑡𝑡 𝑙𝑙 � � � � 𝜀𝜀𝑟𝑟 −𝜈𝜈𝜀𝜀𝑙𝑙 −𝜈𝜈 � � 𝑟𝑟0 𝑡𝑡0 𝑙𝑙0 We can rearrange Equation 2 to define the thickness upon elongation t as a function of the initial layer thickness t0, the longitudinal strain, and the Poisson’s ratio.

= (3) −𝜈𝜈𝜀𝜀𝑙𝑙 𝑡𝑡 𝑡𝑡0𝑒𝑒 Plugging this relation back into Equation 1, we can define the central wavelength λc of the first order reflectance peak of an ideal multilayer structure as it is elongated. The central wavelength of the first order peak at zero strain is represented by λ0. = (4) −𝜈𝜈𝜈𝜈 𝜆𝜆C 𝜆𝜆0𝑒𝑒 It will be shown in the latter portion of Section 1.2.2 that this color change is predictable, reversible, and repeatable even as a fiber is stretched to over twice its initial length several thousand times.

We sought to exploit the mechanochromic properties of these fibers to create colorimetric strain sensors, which would allow an observer to quickly estimate the degree to which some material or structure had been stretched, merely by determining its color at a glance. Flat multilayer structures in this context could cause some confusion, as the strong dependence of their observed reflectance color on angles of light incidence and observation could result in false signals if illumination or observers are improperly aligned. The cylindrical symmetry of the fiber cladding structure of these fibers reduces the dependence of their observed color on these angles, further enhancing their utility in sensing applications. With illumination and an observer fixed, the fiber can be rotated about its longitudinal axis without exhibiting any apparent change in color. In the case of uniform illumination from all directions, the fiber will appear the same color no matter where the observer stands, as long as they maintain a fixed angle with respect to the surface normal of the fiber.

1.2.2 Manufacture and Characterization of Mechanochromic Fibers The fibers we synthesized and studied featured claddings comprised of polydimethylsiloxane (PDMS, refractive index n ≈ 1.41) and a polystyrene-polyisoprene triblock copolymer (PSPI, n ≈ 1.55). These materials form transparent thin films that exhibit an elastic response up to at least 350% elongation, and

12 possess similar Poisson’s ratios, which reduces the chance that individual cladding layers will delaminate during elongation and relaxation. Their refractive index contrast is both sufficient for strong reflection with only a few tens of layers, and small enough that the resulting bandgaps are suitably narrow to enable well-defined reflected colors and useful strain sensitivity.

Figure 4: Modular manufacture of mechanochromic fibers. a) Depiction of the spin coating process, and a plot demonstrating the relationship between spin speed ω and resulting film thickness t (red for PSPI, 4(w/w)% in toluene; yellow for PDMS, 4(w/w)% in heptane). Error bars indicate standard deviation from n = 4 data points for each solution at each spin speed. b) Depiction of core fiber extrusion process, images of extruded fiber cores (lower left, note how opacity and thickness are controllably varied in the rightmost two samples), and two images (lower right, scale bars 100 µm) showing how absorbing cores preserve reflection colors (upper) by eliminating light that is transmitted through the cladding and would pass through a transparent core (lower). c) Depiction of fiber rolling process, in which a spin-coated bilayer of transparent elastomers is wrapped around an elastomer core fiber to form a multilayer cladding. We fabricate stretchable colorimetric fiber sensors by wrapping a thin bilayer of PDMS and PSPI (100-300 nm layers) 30-60 times around an extruded PDMS core filament (Figure 4c). The core filament is rendered light-absorbing by adding a black dye prior to extrusion, which attenuates light in the spectral range transmitted by the cladding to ensure that its bright reflection colors are not obscured (Figure 4b). By separately manufacturing and subsequently assembling the fiber core and cladding, we independently control the structure of each component. For example, the thicknesses of the individual layers within the cladding can be controlled by varying the polymer concentration in solution and the spinning speed used in the coating process (Figure 4a). The thickness of these cladding layers dictates the fiber cladding’s zero- strain color and the range of colors observed as they are strained. The core filaments can be fabricated so that their geometric, optical, and mechanical properties vary along their length (Figure 4b). It is therefore possible to create fiber sensors that exhibit varying sensitivity to applied forces along their length, enhance or counteract the angular dependency of observed color, or transmit or absorb light not reflected by the cladding. During fiber assembly, the rolling process can be modified to form multilayer claddings with multiple distinct periodicities, chirped layered architectures, and other engineered cladding designs,

13 which lead to more complex spectral landscapes of light reflected by these fibers (Figure 5). Representative fibers with distinct coloration obtained by varying the aforementioned parameters in cladding and core design are highlighted in Figure 5e. Moreover, a wide range of elastomeric and stimuli-responsive materials could be assembled into multilayer architectures by this approach. Figure 5: Variations in fiber rolling. a) Depiction of different possible means of rolling bilayer claddings around core fibers. From top to bottom: free rolling To quantitatively assess the fibers’ optomechanical from one end (used to create fibers studied herein), free rolling from a line not at the end of the bilayer performance, we subjected them to many cycles of (results in two distinct regions with different stretching and relaxation. Using a custom-made periodicity), and fixed rolling from one end (results in a chirped multilayer, in which each subsequent layer optical setup, we simultaneously measured the fibers’ is thinner than the underlying layer). b) Several manufactured fibers. Different colors are achieved by stress-strain behavior, reflection spectra, and varying spin coating conditions during bilayer microscale optical appearance over a wide range of formation. The multicolored fiber was rolled around a core fiber with variable diameter – upon elongation, controlled deformations to determine whether their thicker regions stretch less than thinner regions, resulting in variation in strain that matches variation vivid, colorimetric response is altered or diminished in fiber diameter (scale bar 1 mm). with repeated exposure to large strains. The fiber stretching apparatus (Figure 6) consisted of a Thorlabs MTS50-Z8 motorized translation stage (“Stretching Motor”), used to apply a controlled strain to fibers; an LCM Systems UF1 force sensor (“Load Cell”), for detecting the corresponding forces to be converted into stresses; and a Prior H101A motorized XY microscope stage (“Motorized Stage”), to control the position of the stretching motor and load cell with respect to a custom-assembled microscope. The microscope has one optical fiber input for illumination (light provided by a Thorlabs SLS201 stabilized broadband light source), one optical fiber output to an Ocean Optics Maya2000 Pro spectrometer, and a Tucsen IS300 camera in its image plane. Necessary manual adjustment stages are included to allow for the alignment of fiber samples parallel to the direction of travel of the Thorlabs motorized stage, and to center points of interest in the microscope’s focal plane. Control and automation of the stretching motor and positioning stage, and readout of the strain level, force values, and reflection spectra of fibers, was done with WaveMetrics Igor Pro software.

Figure 6: Mechanochromic fiber characterization apparatus. A custom microscope has optical fiber input for illumination, optical fiber output to a spectrometer, and a camera for recording observed images. The stretching motor and load cell enable controlled application and detection of strain and stress, while the motorized stage keeps one or more points of interest on the fiber in the focus of the microscope.

Cyclic deformation of fiber samples was carried out by repeatedly stretching specimens to a prescribed level of strain, and then returning to a zero-strain state. During analyzed cycles, instead of applying this strain in a single step, strain is applied in 0.05 increments, and stretching is briefly paused after each step. During each pause, the microscope stage moves the fiber to ensure the same point of interest along its length is in the focus of the microscope, and force data and reflection spectra are recorded. Fibers were subjected to 10,000 cycles of stretching up to 0.75 true strain (which corresponds to 1.12 engineering strain, i.e. an elongation of the fibers to over twice their original length). These tests reveal that the fibers’ optical and mechanical response to strain is both remarkably consistent and robust (Figure 7). Importantly, the spectral position of the fibers’ reflection peak at each strain is consistent between cycles: the central wavelength of reflection peaks for arbitrary levels of strain shift by less than 5 nm over 10,000 cycles (Figure 8). Converting the measured spectra to points on the CIE x-y chromaticity diagram9 (a common way of representing the gamut of hues humans can perceive) further demonstrates the consistency of reflected colors over cyclic stretching, with points at comparable levels of strain from different cycles clustered together (Figure 8). After 10,000 cycles, the fibers’ average reflection strength diminished from 86% to 73%, a relative drop of about 15%, which initiates only after more than 1000 stretch cycles (Figure 8). Nonetheless, even after 10,000 cycles, the fibers are highly visible and appear brighter than conventional means of textile coloration, such as pigments or dyes.

Figure 7: Characterization of mechanochromic fibers. a) Strain, stress, and reflection spectra from one point on a fiber at cycles 1, 10, 100, 1000, and 10,000 of being stretched to 75% true strain and returned to a relaxed state. b) Reflection spectra at increasing (yellow) and decreasing (red) levels of strain during the first stretching cycle. Spectra are vertically offset from each other for clarity. Numbers indicate alignment with spectra shown in (a).

Figure 8: Repeatability of mechanochromic response. a) Fiber hue as a function of strain plotted in the CIE x-y color space. Fiber colors were obtained from observed spectra using the CIE 1931 2o Standard Observer color matching functions. Clustering of differently colored rings at each level of strain indicates the similarity of the fiber’s color over several thousand stretch cycles. b) Reflectivity of the fiber, averaged over all strain levels, in each examined cycle. Error bars represent standard deviations calculated from n = 21 distinct strain states. c) Deviation from initial central peak wavelength (difference in central wavelength of peaks at Cycle 1 and later cycles, averaged across all strain levels) in each examined cycle. Error bars represent standard deviations calculated from n = 21 points, as in (b).

In order to be useful for sensing applications, each fiber should ideally reflect the same color from any point along its length. To assess their color consistency, both spectra and microscopy images were recorded along the length of several fibers at prescribed strains. Instead of tracking a single point of interest as before, the position of 15-24 points (spaced approximately 1 mm apart at zero Figure 9: Uniformity of mechanochromic fibers. a) Fiber with low defect density (scale bar 100 µm). b) Fiber with a strain) were tracked, and moved into the focus of higher defect density (scale bar 100 µm). c) Color the microscope at each level of strain to collect trajectory of a high-quality fiber in response to various applied levels of strain, plotted in the CIE x-y color space. reflection spectra. While well-manufactured fibers Opaque circles represent arithmetic means of n = 15 points collected from equally-spaced points along the exhibited homogenous coloration along their fiber; semi-transparent ovals represent standard lengths (Figure 9a,c), we did find that defects deviations (from the same 15 points) in coordinate systems aligned to linear regressions of the cluster of introduced via the spin coating or fiber rolling points at each strain level. The consistency of reflected colors are seen in the tight ovals that align with the path processes reduced color uniformity (Figure 9b,d). of the color change. d) Color trajectory of a fiber with a Yet even defective fibers exhibited well-defined higher number of defects. Arithmetic means and standard deviations for n = 15 points are plotted as in (c). The color trajectories as a function of strain (Figure 9d, greater defect density is seen in the larger, less-aligned in which the fiber transitions from blue to green via ovals indicating greater, more arbitrary variation in color along the fiber at each level of strain. violet, red, orange, and yellow). The color variability along a given fiber at arbitrary strains is significantly lower for well-manufactured samples, as seen by comparing the standard deviations in Figure 9c,d.

Finally, we calculated color trajectories of model fibers in the CIE color space to predict the color response of possible fibers and guide future manufacturing and assembly efforts. Figure 10 shows a selection of three simulated color trajectories and their corresponding spectra as a function of strain. Given the independent control over the material and morphology of the core fiber and cladding-forming bilayer, it is possible to design a wide variety of tailored color responses for specific strain levels. The ability to fine- tune the film thicknesses in the fibers’ multilayer claddings during manufacture is critical for designing fibers that display specific color variations in response to relevant levels of strain. While the physics underlying the fibers’ color-changing mechanism prescribe a shift of the fibers’ reflection peaks to lower wavelengths (a “blue shift”) with increasing strain, it is possible to design fibers with multiple, carefully positioned reflection peaks, to create an apparent shift to red hues. Such fibers would appear to transition from a blue or green coloration to a red or orange hue at some prescribed strain, as predicted by the

17 second and third CIE color space trajectories shown in Figure 10. This could boost sensor utility by aligning the fibers’ color trajectory with the human perception of signal colors by indicating dangerous levels of strain with bright red hues, as red stimuli have been shown to receive an attentional advantage.10 Alternatively, fibers can be designed to turn yellow at an important level of strain – yellow occupies the narrowest bandwidth of colors, and so is most easily distinguished from its neighbors, green and orange.

Figure 10: Modeling of ‘color paths’ of possible mechanochromic fibers. a) Theoretical color trajectories for three fibers with different multilayer morphologies. Trajectory 1 shows a typical blue shift mechanochromic response. Trajectories 2 and 3 exploit thicker elastomer films and claddings with multiple periodicities to introduce multiple reflection peaks around the visible range, enabling apparent red shifts with increasing strain. b) Reflection spectra isolated from the simulated color trajectories in (a); arrows indicate increasing strain.

1.2.3 Mechanochromic Fibers as Sub-Bandage Pressure Sensors The mechanochromic response of the aforementioned fibers makes them superb candidates for strain sensors, particularly when circumstances require the repeated achievement of high strains and a simple method of estimating the level of strain. A variety of medical and biomechanical devices, processes, and observations could be improved by the implementation of such a sensing system; we focused our efforts on integrating fibers into elastic bandages used in compression therapy.

Engineered medical textiles11,12 are widely employed in compression therapy, in which a well-controlled pressure gradient is applied to a patient’s limb or other body part. This approach is used to treat a broad array of medical conditions, including post-surgical hematoma, burn-related wounds, lymphedema, scarring, and chronic venous ulceration.13 Optimal pressure ranges that promote healing have been estimated to vary between 30 and 50 mmHg gauge pressure (i.e., 4.0 – 6.7 kPa),14 but the correct “dosage” for compression therapy varies between patients based on their body structure and medical condition.15 Beyond this relatively narrow pressure range, compression therapy becomes ineffective and could potentially result in further injury to the patient.15–17 Over one percent of all people in industrialized countries suffer from venous leg ulcers,18 which are typically treated by compression therapy. For over

600,000 patients in the United States alone, ineffective treatment leads to the loss of around two million work days and unnecessary additional health care costs of up to five billion dollars each year.19,20 Chronic venous ulceration is increasingly prevalent in persons over 65 years of age, and with a growing and aging world population, there is a pressing need to improve compression treatment.19,20

While the design and mechanics of compressive medical textiles have improved,21 they still do not provide quantitative, localized feedback regarding the pressure exerted by a bandage on a patient’s body.14,16 One common strategy is to limit the maximal pressure that a textile can exert on an underlying limb.13 However, these pressure-limiting textiles are difficult to manipulate at high strains, and cannot be adjusted to suit individual patients. While thin sensors can be placed under bandages or directly onto a patient’s skin to determine the applied pressure,22,23 they can only provide information for particular regions of a treated area, and may themselves affect the pressure being applied. Moreover, if the sensors are removed, they cannot provide pressure information throughout bandage use.

Figure 11: Fiber bandage concept. a) There is a well-defined relationship between the level of strain of an elastic bandage, and the sub-bandage pressure it applies to a patient’s limb. b) A mechanochromic fiber is affixed to an elastic bandage with stitching. As the bandage is stretched, the fiber stretches with the bandage, and indicates approximate levels of strain. c) In an idealized concept, a mechanochromic fiber is integrated into the full length of an elastic bandage, enabling the simple, colorimetric readout of sub-bandage pressure anywhere on a patient’s leg.

The interdependence observed in mechanochromic fibers between an applied load, its corresponding strain, and the observed color change can be harnessed in integrated fiber-based sensors that provide real-time feedback for applied pressure in compression therapy, since the pressure exerted by an elastic bandage on a patient’s body is related to the strain in that bandage (Figure 11).16 By directly monitoring the reversible color shift of these optomechanical fibers integrated into compressive medical textiles, it becomes possible to quickly, locally, and accurately quantify sub-bandage pressure anywhere along a bandage.

Figure 12: Bandage pressure measurement apparatus. a) Pressure measurement device, consisting of a sealed bladder connected to a pressure gauge and an air-filled syringe for calibration. When the bladder is compressed, the gauge reveals the pressure applied to the bladder. b) Pressure device from (a) is integrated into a bandage pressure measurement apparatus. A bandage is affixed to a simulated leg and an adjustable crossbar. After initially stretching the bandage to some prescribed strain, a rack and pinion (with the pinion concentric with the simulated leg) allow the bandage to be wrapped around the simulated leg while holding the initial applied strain. An optical fiber allows for illumination of a fiber specimen in the bandage, and readout of reflection spectra from that specimen. A camera mounted on the setup enables the capture of photographs of the fiber in the bandage. This apparatus enables the measurement of sub-bandage pressure and bandage-integrated mechanochromic fiber appearance and reflection spectra at any level of strain.

As a simple proof-of-concept, we stitched the fibers onto single-component elastic compression bandages and validated their function as integrated sensors for sub-bandage pressure measurements using a custom-built apparatus (Figure 12). This apparatus allows an elastic bandage to be wrapped around a simulated leg at well-controlled strains. A compressible bladder is attached to a pressure gauge to measure sub-bandage pressure, while an integrated camera and optical fiber spectrometer enable the collection of images and reflection spectra from the textile-integrated fiber sensors, in conjunction with the acquisition of strain and pressure data. Using this device, we first determined the relationship between bandage strain and sub-bandage pressure (Figure 11a), and then confirmed that a direct link between fiber color and sub-bandage pressure could be established in fiber-integrated bandages (Figure 13). Importantly, these integrated fiber sensors retain their strong colorimetric response to applied strain when incorporated into compression bandages, and provide a clear colorimetric indication of the pressure beneath the bandage.

Figure 13: Preliminary results with fiber-integrated bandages. a) Central wavelengths of reflection peaks of a mechanochromic fiber integrated into an elastic bandage, as the bandage is stretched to apply varying levels of pressure. The green highlighted area indicates the approximate pressure range that leads to remedial effects when used in compression therapy. Numbers correspond to spectra and images in (b). b) Reflection spectra, and images, of a fiber sample integrated into an elastic bandage, as the bandage is stretched to apply varying levels of pressure. Of particular importance is the distinction in observed color between pressures in and around the remedial range.

To assess the efficacy of bandages within integrated fiber sensors, we subjected a group of volunteers to compression therapy (applied by other volunteers) with varying target pressures applied to different locations on their legs using three different bandages: a plain bandage (unmarked, first control), a bandage with geometric markings that indicate when a given target pressure is reached (second control), and a prototype bandage with integrated color-changing fibers. For this prototype bandage, volunteers were provided with a color chart that relates the observed fiber color to the applied pressure. Using the same pressure measurement bladder described before, we determined the precision with which volunteers applied desired levels of pressure. The results indicate that each volunteer was able to apply pressures considerably closer to target values when using bandages with integrated fiber sensors (Figure 14). For each target pressure, the measured pressures applied by different bandage systems are generally found to be statistically different (p < 0.02 for seven of nine comparisons; p ≈ 0.05 for comparing pressures applied by the geometric bandage and fiber bandage on the mid-calf; p < 0.10 for comparing the plain bandage to the fiber bandage on the ankle). More statistical details can be found in Table 1 below. The bias is estimated for each bandage system and application location (Figure 14b). Bias is defined the difference of the means and the desired target pressures; a bias of zero indicates a measurement that exactly corresponds to the actual value. All biases for the plain bandage are significantly different from zero, while two of three biases for the bandage with geometric pressure indicators are significantly different from zero. However, none of the three biases for mechanochromic fiber-integrated bandages are significantly different from zero. Additionally, the distributions for pressures applied with fiber- integrated bandages had comparable, or smaller, standard deviations, than both control bandages tested.

In practice, these results show that compression therapy administered using mechanochromic fiber- sensor integrated bandages should yield more efficient and successful compression therapy treatment.

Figure 14: Results of bandage mock trial. a) Data from mock trial, in which student volunteers attempted to apply specific target pressures to three different leg locations with three different elastic bandages (gray – plain bandage, beige – geometric bandage, green – prototype bandage). Mean pressures are plotted as bars, with error bars indicating standard deviations. Red dashed lines indicate target pressures. b) Estimated bias in each bandage system, with error bars indicating 95% confidence bounds, at each experimental bandage location. As in (a), gray – plain bandage, beige – geometric bandage, and green – prototype bandage.

Table 1: Results of statistical analysis of bandage application experiment. t-values, degrees of freedom ν, and p- values are shown for all comparisons between different bandages (Ctrl 1 – plain bandage, Ctrl 2 – bandage with rectangular markings, Fiber – the prototype fiber-integrated bandage).

Mid-Calf (Target: 40 Knee (Target: 30 mmHg) Ankle (Target: 50 mmHg) mmHg)

Ctrl 1 Ctrl 1 Ctrl 2 Ctrl 1 Ctrl 1 Ctrl 2 Ctrl 1 Ctrl 1 Ctrl 2 vs vs vs vs vs vs vs vs vs Ctrl 2 Fiber Fiber Ctrl 2 Fiber Fiber Ctrl 2 Fiber Fiber

t 7.67 1.77 5.30 4.63 3.94 2.10 4.56 2.67 2.86

ν 17.3 18.8 15.3 14.9 19.3 13.2 14.3 19.9 14.8

p 0.05 - 0.05 - 0.01 - 0.01 - <0.001 <0.001 <0.001 <0.001 <0.001 0.10 0.10 0.02 0.02

1.2.4 Other Applications of Mechanochromic Fibers A separate exploration of the utility of these mechanochromic fibers involved mapping strain in complex tangled structures. Knots are widely relied on in medicine, sailing, construction, and other pursuits; while there is a wealth of knowledge based on decades, centuries, or millennia of human experience with the use of knots in these contexts24,25, it is not well understood how the layout of an arbitrary knot can be used to predict how it might perform in particular applications. Tying knots in mechanochromic fibers allows for the facile determination of strain at any visible point along the knotted fiber, by recording variations in observed color. This behavior was exploited to visualize the distribution of strain in two common knots: a trefoil and a figure-eight (Figure Figure 15: Comparison of model and experimental 15b,d). Trefoil knots are simple knots that can be used knots. a) Simulation of stress in trefoil knot, colored as building blocks in larger, more complicated knots; by converting stress to strain and using the colormap (color as a function of strain) of the mechanochromic figure-eight knots are frequently employed as effective fiber in (b) and (d). b) A trefoil knot tied in a mechanochromic fiber. c) Simulation of stress in stopper knots, which aim to prevent the line they are figure-eight knot, colored by the same technique as tied in from passing through narrow openings. the knot in (a). d) A figure-eight knot tied in a mechanochromic fiber. The coloration of the experimental knots in (b) and (d) closely matches the Collaborators Vishal Patil and Prof. Jörn Dunkel, in computation prediction in (a) and (c). MIT’s Department of Mathematics, developed a mathematical model to describe the mechanical behavior of knots tied in elastic fibers. The model could be compared to empirical observations by artificially coloring simulated knots according to their strain and angles of observation of their visualization. The model was used to simulate trefoil and figure-eight knots in a material with mechanical properties and dimensions based on those of the mechanochromic fibers (Figure 15a,c), and it was observed that the model agrees well with the strain estimated by the mechanochromic fiber knots. With this validation in hand, the model could be extended to more complicated families of knots, and simple counting rules were identified that give good indication of the relative stability of various knots26.

These newly-developed rules help explain the difference in performance of superficially similar knots, such as the reef, granny, thief, and grief knots (their common names indicate that performance disparities have been known for some time, but the model provides insight as to why these differences exist in knots with effectively identical silhouettes). Further measured the load at which a small perturbation caused different knots to unravel (similar to the classical “prison escape” problem). These values matched qualitatively with model predictions of friction and compressive force within the different knots26.

The aforementioned model and experiments take a big step toward being able to identify knots that are suitable for specified applications, and enabling the design of arbitrary knots to achieve specified goals. Fortuitously, the understanding gained about these knots relies on concepts in topology and elasticity, which can be applied across a wide range of length scales. This means that the model could be used to explore and explain the behavior of phenomena as far ranging as tangled fluid vortices, microscopic knots in biomolecules and macromolecules, and knitted fabrics26.

1.2.5 Summary and Perspective for Project Continuation Thanks to the structure of their photonic cladding, these mechanochromic fibers respond to applied strain with a predictable, reversible, and easily observed color change that persists over several thousand cycles of deformation. This color shift is preserved upon integration of fibers into elastic textiles and knotting of fibers. It has been demonstrated that laboratory-scale strain-sensitive colorimetric fibers can be used to estimate strain in knots, and could facilitate the application of more consistent and accurate compression therapy, potentially saving billions of dollars, and countless hours of patient and healthcare provider productivity, while improving patient outcomes. Generally, we anticipate that stretchable, colorimetric fiber sensors could be used in a variety of biomedical devices, athletic wear, and other applications that require stimuli-responsive, color-changing textiles. However, for the fibers to be truly useful on a larger scale, they need to be manufactured on a larger scale.

Our laboratory process of spin coating and rolling does not scale directly, though a similarly solvent-based method for producing thin polymer films could be implemented in a roll-to-roll-style process (Figure 16). We took first steps in testing the feasibility of this approach, as well as thermal drawing with cylindrically concentric multilayer and photonic crystal fiber structures, but further work is necessary to demonstrate the viability of such a technique. Given that the strain-sensitive color change effect can be achieved with any transparent, stretchable materials with refractive index contrast that can be formed into a nanoscale-

24 periodic structure, it is likely that a set of materials, and corresponding manufacturing method, exists that can enable the production of meters and kilometers of mechanochromic fibers. When production is realized on such a scale, mechanochromic fibers will be excellent candidates for novel devices that could have a positive impact in a variety of medical, aesthetic, and other applications.

Figure 16: Scaled solvent-based manufacture of mechanochromic fibers ("Flow Coating"). a) Schematic of how Flow Coating works – reservoirs containing different polymers in solution dispense their contents on a slowly flowing water surface. The slow flow of this water brings the solution, which becomes a polymer thin film by evaporation of the solvent, toward a core fiber that collects and rolls two films (one from each side) into a concentric, periodic multilayer structure. Inset image shows how, by bringing formed films toward the core fiber at some angle, it is possible to create a multilayer structure while continuously pulling the rotating core fiber through the apparatus. b) Photograph of a prototype Flow Coating device, with a single channel for film formation. The device was designed to allow for independent control of core fiber rotation and travel across the setup: un-clad core fiber would start on one spool, be drawn through the setup, and be collected after being clad on the opposite spool. Spools were driven by gears from one motor, while another motor rotated large discs that the spools and their frame were mounted on. The flow rate of polymer solution onto the water surface was controlled by using a pressure regulator to drive flow from a reservoir of solution at a fixed pressure. Separate infrastructure was put in place to circulate water between the channel and a basin that collected runoff from the channel.

1.3 Electrochromic Photonic Fibers In the previous sections, the development, characterization, and application of photonic fibers that respond to strain with an observable change in their structural color were discussed. Those fibers rely on a change in the dimension of periodicity of their nanoscale multilayer cladding, induced by elongation of fibers, to cause their color change. While interesting and useful, this is only one example of a broad array of potential colorimetric sensors made possible by the fabrication of structurally colored devices with stimuli-responsive materials. Other similar devices could exhibit a clear color change in response to changes in temperature, humidity, or other physical phenomena – in particular, the following sections discuss the working principles, development, and characterization of a fiber sensor that responds to electrical stimuli with a stark shift in its observed color.

1.3.1 Sensor Concept These electrochromic fibers are based on the aforementioned mechanochromic fibers, with two changes to enable an entirely different mode of actuating a color change. First, one of the transparent elastomers is replaced by poly(3,4-ethylenedioxythiophene) polystyrene sulfonate (PEDOT:PSS), a conducting polymer known for appearing mostly transparent and light blue when oxidized, and more opaque and dark blue when reduced. Second, the black-dyed PDMS core fiber is replaced by a carbon nanotube (CNT) ribbon, which is still highly optically absorbing, but can also conduct electricity to facilitate contact with the coiled PEDOT:PSS film. Integrated into a cylindrically concentric multilayer structure, the expectation was that it could be possible to rapidly switch between two distinct states. One state would feature an entirely transparent multilayer that would exhibit structural color; the second state would feature a multilayer in which every other layer was dark blue, which would drastically reduce the influence of interference effects responsible for structural color.

It was hypothesized that a functional fiber constructed in this manner would need only the application or reversal of an electrical or chemical potential to flip between exhibiting vivid color, determined by the thickness of the layers in its cladding, and appearing a muted blue hue (Figure 17). Such a fiber enhances

Figure 17: Electrochromic fiber sensing concept. a) Chemical structure of PEDOT:PSS in its reduced and oxidized states, along with depictions of sensing fibers, with concentric multilayer claddings including PEDOT:PSS, exhibiting “structurally enhanced” color contrast between reduced and oxidized states. b) Photographs of thin films of oxidized (top) and reduced (bottom) PEDOT:PSS (scale bars 5 mm), and associated absorption spectra (darker line indicates reduced PEDOT:PSS, lighter line indicates oxidized PEDOT:PSS). c) Photographs of multilayer-clad fibers (scale bars 1 mm) with oxidized (top) and reduced (bottom) PEDOT:PSS layers. Reflection spectra, normalized to complete reflection of all incident light, are shown for a fiber with oxidized (red line) and reduced (dark blue line) PEDOT:PSS films in its multilayer cladding.

26 the intrinsic difference in optical appearance between oxidized and reduced PEDOT:PSS. This renders any electrochemically induced variation in the optical properties of PEDOT:PSS more noticeable and allows for this more overt color shift to be tuned. This enhancement and selection of the color contrast between electrical states should make the system more useful in sensing, particularly in notifying observers that a change has occurred. Among other potential applications, this specific type of system could be used as a simple, analog warning of the presence of oxygen in anaerobic environments.

Fibers based on this hypothesized functionality were ideated, formulated, and characterized in collaboration with Carsten Dingler and Prof. Dr. Sabine Ludwigs, from the Institute of Polymer Chemistry (IPOC) at the University of Stuttgart in Stuttgart, Germany.

1.3.2 Manufacture and Characterization of Electrochromic Fibers Electrochromic fibers were manufactured in the same manner as mechanochromic fibers, with PDMS and PEDOT:PSS as the constituent materials deposited on top of a sacrificial layer of PSS. The multilayer film was rolled around a CNT ribbon such that the PEDOT:PSS film was the innermost layer, in contact with the CNT ribbon core (Figure 18a). Oxidized PEDOT:PSS is still somewhat absorbing in the visible range, so films of this material were made as thin as possible, to ensure the best chance at obtaining structural color in at least the oxidized state. For this reason PEDOT:PSS films were manufactured to be approximately 20 nm thick, and spin coating of PDMS layers was tuned to make the multilayer stack reflect light around 700 nm (red), for greater contrast with the blue, reduced state. This minimization of the thickness of the PEDOT:PSS film causes the multilayer structure to be strongly non-ideal, which necessitates the use of many more layers than an ideal (quarter wavelength) structure to exhibit strong

Figure 18: Manufacture of electrochromic fibers. a) Depiction of the immersion of a silicon wafer, with thin films of PSS, PDMS, and PEDOT:PSS deposited by spin coating, into a water bath. This immersion dissolves the PSS layer, leaving the PDMS and PEDOT:PSS films floating on the water surface, where they can be collected and rolled onto a core fiber consisting of a CNT ribbon. b) Photograph of a manufactured electrochromic fiber (scale bar 1 cm). c) Micrograph of fiber photographed in (b) (scale bar 200 µm).

27 reflectance. Fortunately, as seen by the manufactured fiber in Figure 18b,c, it was still possible to collect enough layers to create a sample with vibrant structural color.

Figure 19: Characterization apparatus for electrochromic fibers. A custom microscope with optical fiber light input, optical fiber output to a spectrometer, and a camera in its image plane was used to collect data regarding the optical behavior of electrochromic fibers subjected to various electrochemical stimuli. These stimuli were applied (and electrical behavior was analyzed) via a special three electrode cell attached to a potentiostat. An additional camera allowed for recording of the appearance of the entire fiber within the electrochemical cell as it was switched between oxidized and reduced states.

To characterize the electrochromic fibers’ optical and electrochemical response, the custom microscope used to study mechanochromic fibers was adapted to collect reflection spectra and optical micrographs from electrochromic fibers in a special three-electrode electrochemical cell (Figure 19). The cell consisted of an electrochromic fiber specimen as a working electrode, a silver/silver chloride reference electrode, and a platinum counter electrode, all immersed in a 0.1 M solution of tetrabutylammonium hexafluorophosphate within a narrow, rectangular quartz cuvette. The three-electrode cell was connected to a Princeton Applied Research VersaSTAT 3 potentiostat. This device applies a potential between the working and reference electrodes, and measures the current that flows through the system in response to different and variable applied potentials via the counter electrode. With the potentiostat, it is possible to collect temporally resolved current and voltage data, which can be recorded while reflection spectra and images are collected with the custom microscope. A representative set of data collected in the aforementioned apparatus is shown in Figure 20.

There are two primary modes of electrochemical stimulus: chronoamperometry and cyclic voltammetry. In chronoamperometry, a fixed potential is applied between the working and reference electrodes, and the current that flows in response to this fixed potential is recorded. Often such a current will be a

Figure 20: Electrochromic fiber characterization. a) Applied potential over time, showing two periods of chronoamperometry (negative potential to induce reduction of PEDOT:PSS films in an electrochromic fiber, positive potential to induce oxidation). b) Reflection spectra collected every eight seconds during reduction of an electrochromic fiber, and images of the fiber at select points (red, black, and blue photo outlines correspond to similarly colored spectra and highlighted points between 400 and 500 s in (c)). c) Current over time, showing two transient responses upon application or changing of a fixed potential. Highlighted points correspond to images and spectra in (b) and (d). d) Reflection spectra collected every eight seconds during oxidation of an electrochromic fiber, and images of the fiber at select points (red, black, and blue photo outlines correspond to similarly colored spectra and highlighted points between 500 and 600 s in (c)). transient response, decaying toward zero from some relatively large initial value at the onset of the applied potential. Cyclic voltammetry involves the gradual ramping of applied potential between two extremes, instead of rapidly applying a potential or switching between distinct potentials. As in chronoamperometry, the response current is measured. This type of experiment is frequently used to ascertain information about dissolved analytes or species adsorbed onto an electrode, by studying a plot of current against potential. This type of standard electrochemical analysis is not particularly relevant to our use of the technique, as PEDOT:PSS is well understood in this context. In this study, cyclic voltammetry is used to further an exploration of an analysis of electrochromic fibers from a systems perspective. This will be explained further in Section 1.3.3.

Through chronoamperometry (Figure 21a,c,e,g), it is possible to study the response of an electrochromic fiber to sudden shifts between extended periods of forced oxidation and forced reduction. Switching between a potential of 1.08 V (known to induce oxidation) and a potential of -1.52 V (known to induce

29 reduction) led to brief surges in current that decayed exponentially to small, persistent baseline values. A baseline value is present in the system even after complete oxidation or reduction of a PEDOT:PSS structure, and is related to the meager charge flow that is able to pass between separate electrodes through the electrolyte solution. This behavior is analogous to a capacitor with a leakage current. By eye, and through spectrometer measurements, a strong shift in observed color was evident between the oxidized state (vivid red) and the reduced state (dull). This shift in color appeared to happen more quickly for oxidation than reduction, and occurred during all three cycles of reduction and oxidation that were observed. There is also evidence of a reduction in reflectance over multiple cycles of reduction and oxidation – this will be discussed in a moment.

Figure 21: Results of chronoamperometry and cyclic voltammetry. a) Applied potential over time for chronoamperometry, in which an electrochromic fiber was put through three cycles of reduction and oxidation. b) Applied potential over time for cyclic voltammetry, in which an electrochromic fiber was put through five cycles of gradual ramping between the same potentials used for reduction and oxidation in (a). c) Current over time for three cycles of reducing and oxidizing chronoamperometry. d) Current over time for five cycles of cyclic voltammetry. e) Maximum reflectance of an electrochromic fiber over time for three cycles of reducing and oxidizing chronoamperometry. f) Maximum reflectance of an electrochromic fiber over time for five cycles of cyclic voltammetry. g) Wavelength of maximum reflectance peak over time for three cycles of reducing and oxidizing chronoamperometry. h) Wavelength of maximum reflectance peak over time for five cycles of cyclic voltammetry. All data in a, c, e, and g were collected simultaneously; separately, all data in b, d, f, and h were collected simultaneously. The same fiber was used in both experiments.

Cyclic voltammetry experiments (Figure 21b,d,f,h) were conducted to analyze how an electrochromic fiber behaves in response to a gradual shift between reducing and oxidizing environments. As is typical of cyclic voltammetry, the first cycle has a slightly different current signature than the other cycles, which are very similar to each other. The same color change as before was evident, but occurred more smoothly. There is a clear signal in the reflection peak wavelength that aligns with the linearly varying electrochemical stimulus, but this signal is quite small and would not result in any observable change in the fiber’s color. There is still evidence of a reduction in reflectance over multiple cycles of reduction and oxidation, but the trend is less overt than the observed decline in chronoamperometry tests.

The decrease in reflectance, of any point observed through the microscope over multiple cycles of reduction and oxidation, has a few potential causes. The simplest explanation may be that the fiber moves during the experiments, and a loss of focus, or focus on a dimmer spot of the fiber, is responsible for the decrease in observed reflection peak intensity. This had been observed in preliminary experiments, but multiple measures were taken to minimize the chance that such drift could occur in the reported experiments. Additionally, upon the conclusion of experiments with an electrochromic fiber specimen, no areas with strong reflection could be found, despite searching along the length of the fiber with the microscope.

Another potential cause could be the slow swelling of one or both cladding constituent materials with the electrolyte solvent, acetonitrile. Acetonitrile must be able to readily diffuse into PEDOT:PSS, or else the ions it carries would not be able to enter and exit the material to balance charges while PEDOT:PSS is reduced or oxidized. The polymer-solvent interaction parameter, which can be estimated via Hansen Solubility Parameters27 (see Equation 5 and Table 2), roughly indicates the quality of a solvent for different polymers. The approximate value of 1.7 for PDMS in acetonitrile indicates that while acetonitrile would not readily dissolve PDMS, it would potentially swell the polymer. Acetonitrile diffusing into both materials in the multilayer cladding would diminish the refractive index contrast between the two materials, weakening the reflectance of the multilayer stack. As with the fiber motion explanation, however, this would not explain why an electrochromic fiber, put through a few dozen cycles of reduction and oxidation, would retain its diminished reflectance after being removed from the electrochemical cell and dried for several days.

( ) ( ) ( ) + + (5) 4 2 4 2 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑀𝑀𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 2 𝛿𝛿𝑃𝑃 − 𝛿𝛿𝑃𝑃 𝛿𝛿𝐻𝐻 − 𝛿𝛿𝐻𝐻 𝜒𝜒𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 ≈ � 𝛿𝛿𝐷𝐷 − 𝛿𝛿𝐷𝐷 � 𝜌𝜌𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑅𝑅𝑅𝑅

Table 2: Hansen solubility parameters for PDMS and acetonitrile; molar mass and mass density of acetonitrile.

3 Property δD δP δH M (g/mol) ρ (g/cm )

PDMS 15.9 0.1 4.7 - - Acetonitrile 15.3 18.0 6.1 41.05 0.79

An alternative explanation is that the fibers are degraded by ion transport during cycles of reduction and oxidation. Large tetrabutylammonium ions must diffuse into the PEDOT:PSS film in order to balance charges upon reduction, and then evacuate the film when it is oxidized; these molecules may be driven to travel ballistically through the thin films, damaging them and diminishing the reflectance of the multilayer stack. Other processes associated with reduction and oxidation (rearrangement of molecules within PEDOT:PSS layers, etc.) could similarly have a detrimental effect on the stability of individual layers or the periodic nature of the multilayer structure. Such effects would, in turn, hamper the structural color of the fiber.

1.3.3 Circuit Modeling of Electrochromic Fibers Models can further understanding of principles and mechanisms behind the response of electrochromic fibers to electrochemical stimuli, and enable the tailored design of sensors with reflection spectra and electrical responses suited to specified applications. Two models were developed, to gain insight into the behavior of these electrochromic fibers. The first of these was a circuit model that represents an electrochromic fiber as a simple RC circuit. The quantifiable circuit elements in this model (capacitance, charging resistance, and leakage resistance) can be related to underlying characteristics of the sensing fiber structure. This simple circuit consists of a capacitor C in series with a charging resistance RC, and a leakage resistance RL in parallel with both of these elements (Figure 22). The capacitance represents the PEDOT:PSS film, which takes on electrons when reduced, and evacuates them when oxidized. The leakage current, which flows across RL when the capacitor is fully charged or discharged, corresponds to the miniscule electron flow that persists during long cycles of reduction or oxidation, after the film is completely altered. With this simple linear model, an equation can be defined that relates the input voltage to the output current. Fitting this equation to measured data for voltage and current, it becomes

possible to see how the lumped parameters C, RC, and RL vary between reduction and oxidation, and how they change over multiple cycles of electrochemical stimulation.

Ohm’s Law (Equation 6) defines the relationship between current and voltage for a circuit, which depends on the impedance Z of that circuit. Calculations were carried out in Laplace space, which simplifies several of the steps necessary to generate a function to fit to measured current and voltage values. Laplace space is defined with a complex variable s

Figure 22: Circuit model. A potential v(t) is applied, (often complex frequency); the Laplace Transform and a current i(t) is measured or predicted. Physical converts a function of some real variable t (often time) origins of resistive and capacitive terms are discussed in the text. into a function of s. The Inverse Laplace Transform accomplishes the inverse conversion, which we will use to turn our derived current I(s) in Laplace space to a time-domain equation for current i(t), which we can fit to data. The impedance, the potential V(s) applied across this circuit, and the current I(s) that runs through the circuit are related by

( ) = ( ) ( ) (6)

𝑉𝑉 𝑠𝑠 𝐼𝐼 𝑠𝑠 𝑍𝑍 𝑠𝑠 The impedance of each circuit element is defined as follows:

1 = = = (7)

𝑍𝑍𝑅𝑅𝐿𝐿 𝑅𝑅𝐿𝐿 𝑍𝑍𝑅𝑅𝐶𝐶 𝑅𝑅𝐶𝐶 𝑍𝑍𝐶𝐶 It is possible to define the inverse of the equivalent impedance of this𝑠𝑠𝑠𝑠 circuit by combining these terms.

1 1 1 = + (8) ( ) 1 + 𝐿𝐿 𝑍𝑍 𝑠𝑠 𝑅𝑅 𝑅𝑅𝐶𝐶 In order to calculate current, it is necessary to define an applied𝑠𝑠𝑠𝑠 potential in the complex frequency domain. For chronoamperometry, the applied potential is analogous to a square wave input when cycled between reduction and oxidation. The input voltage for any given cycle of reduction or oxidation can be

represented as a step function, where V0 represents the fixed voltage of the cycle.

( ) = (9) 𝑉𝑉0 𝑉𝑉 𝑠𝑠 Rearranging Equation 6 and solving for current, the following𝑠𝑠 equation is derived:

1 1 1 1 1 1 1 ( ) = + = + = + (10) 1 + 1 0 + + 𝑉𝑉 0 𝐶𝐶 0 𝐼𝐼 𝑠𝑠 � � � 𝐿𝐿 � 𝑉𝑉 � 𝐿𝐿 𝑐𝑐 � 𝑉𝑉 � 𝐿𝐿 𝐶𝐶 1 � 𝑠𝑠 𝑅𝑅 𝑅𝑅𝐶𝐶 𝑅𝑅 𝑠𝑠 𝑅𝑅 𝐶𝐶𝐶𝐶 𝑅𝑅 𝑠𝑠 𝑅𝑅 �𝑠𝑠 𝑅𝑅𝐶𝐶𝐶𝐶� Taking the Inverse Laplace Transform,𝑠𝑠𝑠𝑠 the current can be defined in the time domain (t > 0).

1 1 ( ) ( ) = + −𝑡𝑡 11 𝑅𝑅𝐶𝐶𝐶𝐶 𝑖𝑖 𝑡𝑡 𝑉𝑉0 � 𝑒𝑒 � 𝑅𝑅𝐿𝐿 𝑅𝑅𝐶𝐶 This makes intuitive sense: the current in response of the model circuit to an applied, fixed voltage should start strong and decay as the capacitor charges up, until it reaches a stable value equal to the applied potential divided by the leakage resistance once the capacitor no longer passes current.

The electrical current in response to reduction and oxidation was recorded for three full cycles (applying a fixed potential to force reduction for 100 seconds, then applying a fixed potential to force oxidation for 100 seconds). Equation 11 was fit to each cycle of this data to quantify model parameters. Curve fits for all six periods of chronoamperometry (three each to induce reduction and oxidation) match quite well with experimental data – these fits, and trends in circuit parameters, are shown in Figure 23. Breaking down the changes in fit parameters, several intriguing trends emerge. Capacitance C, which is assumed to be the storage of charge in the coiled PEDOT:PSS film, is always greater during oxidation than reduction,

but in both cases it increases over multiple cycles. The opposite is true for the charging resistance RC: this value is always lower for oxidation than reduction, and decreases over cycles (note that the value is very similar for reduction and oxidation by the third cycle). The leakage resistance RL decreases over cycles, but maintains a similar gap between reduction (with a high resistance, between 45 and 50 kΩ) and oxidation (with a lower resistance, around 35 kΩ).

Some conclusions can be drawn about the physical behavior of the electrochromic fibers based on these trends in the simple circuit model. An increase in capacitance over cycles, and a decrease in charging resistance over cycles, both point to the travel of ions into and out of the coiled PEDOT:PSS film being made easier as their forced entry into, and exit from, the film is repeated. This could correspond to tunnels being formed through the films over time, where the first “trailblazer” ions have to force their way through to unreached parts of the film, but ions in subsequent cycles are able to more freely travel at least as far as ions have previously reached. The gradual swelling of both PDMS and PEDOT:PSS films with the electrolyte solvent, acetonitrile, could also make this charge transfer easier over time. That this charge

Figure 23: Circuit model fit to chronoamperometry data. a) Applied potential during three cycles of reduction and oxidation by chronoamperometry. b) There is good overlap between the fits (orange and blue lines) and experimental data (black dots) for all cycles of reduction and oxidation. c) Change in model capacitance C over cycles. C is always higher for oxidation than reduction, but in both cases it increases over multiple cycles. d) Change in model resistance RC over cycles. RC is always higher for reduction than oxidation, though in both cases it drops significantly (and approaches similar values). e) Change in model resistance RL over cycles. RL is always higher for reduction than oxidation; this offset remains roughly constant while the value decreases for both states. transfer is faster and more voluminous during oxidation, as compared to reduction, implies that the PEDOT:PSS film exhibits a preference to be oxidized. This preference could potentially stem from the relative increase in stability of oxidized PEDOT:PSS, as opposed to its reduced form.

The same model can be applied to find a fit for cyclic voltammetry data, by replacing a fixed V(s) with a function that corresponds to a straight line with some slope m in the time domain (t > 0).

( ) = ( + ) = + = ( ) (12) 𝑉𝑉0 𝑚𝑚 ℒ�𝑣𝑣 𝑡𝑡 � ℒ 𝑉𝑉0 𝑚𝑚𝑚𝑚 2 𝑉𝑉 𝑠𝑠 35 𝑠𝑠 𝑠𝑠

As done before in Equations 8-10, we use this V(s) and the effective impedance of our model circuit to determine an equation for the current that flows in response to the applied potential.

+ 1 1 1 1 1 1 ( ) = + = + + + (13) + + + 𝑉𝑉0𝑠𝑠 𝑚𝑚 𝑉𝑉0 𝑚𝑚 𝑉𝑉0 𝑚𝑚 2 1 2 1 1 𝐼𝐼 𝑠𝑠 � 𝐿𝐿 𝐶𝐶 � 𝐿𝐿 𝐿𝐿 𝐶𝐶 𝐶𝐶 𝐶𝐶 𝑠𝑠 𝑅𝑅 𝑅𝑅 𝐶𝐶𝐶𝐶 𝑅𝑅 𝑠𝑠 𝑅𝑅 𝑠𝑠 𝑅𝑅 𝑠𝑠 𝑅𝑅 𝐶𝐶 𝑅𝑅 𝑠𝑠 �𝑠𝑠 𝑅𝑅𝐶𝐶𝐶𝐶� ( ) = ( ) + + + = + + + −𝑡𝑡 𝑡𝑡 −𝜏𝜏 −𝑡𝑡 −𝜏𝜏 𝑡𝑡 0 0 𝑅𝑅𝐶𝐶𝐶𝐶 𝑅𝑅𝐶𝐶𝐶𝐶 0 0 𝑅𝑅𝐶𝐶𝐶𝐶 𝑅𝑅𝐶𝐶𝐶𝐶 𝑉𝑉 𝑚𝑚 𝑉𝑉 𝑚𝑚 𝑉𝑉 𝑚𝑚 𝑉𝑉 𝑚𝑚 𝐶𝐶 𝑖𝑖 𝑡𝑡 𝐿𝐿 𝑢𝑢 𝑡𝑡 𝐿𝐿 𝑡𝑡 𝐶𝐶 𝑒𝑒 𝐶𝐶 �0 𝑒𝑒 𝑑𝑑𝑑𝑑 𝐿𝐿 𝐿𝐿 𝑡𝑡 𝐶𝐶 𝑒𝑒 𝐶𝐶 �−𝑅𝑅 𝐶𝐶𝑒𝑒 �0 ( ) 𝑅𝑅 𝑅𝑅 𝑅𝑅 = 𝑅𝑅 −𝑡𝑡 + 𝑅𝑅+ 𝑅𝑅+ 𝑅𝑅 𝑅𝑅 14 𝑉𝑉0 𝑅𝑅𝐶𝐶𝐶𝐶 𝑚𝑚 𝑉𝑉0 � − 𝑚𝑚𝑚𝑚� 𝑒𝑒 𝑡𝑡 𝑚𝑚𝑚𝑚 𝑅𝑅𝐶𝐶 𝑅𝑅𝐿𝐿 𝑅𝑅𝐿𝐿 The response of the same electrochromic fiber tested above was measured for five cycles of cyclic voltammetry, in which the potential was ramped at a fixed rate back and forth between the same maximum and minimum potentials applied in the forced reduction and oxidation cycles. This is analogous to a triangle wave input, and can be split into a series of ten linear ramps. Unfortunately, the fit of this model to the data was poorer than the good fits observed in chronoamperometry (Figure 24a). By fixing the initial potentials and rate of change of potential for each ramp to the known, controlled values, it was possible to replicate part of the curvature of the current data curve, but not its magnitude or inflection point. The inflection Figure 24: Circuit model fit to cyclic voltammetry data. a) point is actually impossible to fit with this model, The fit is poor when the applied potential is set to match which consists of the summation of a first-degree the values from the experiment. b) The fit can be improved by allowing the initial potential to vary, but this polynomial and an exponential expression. is non-physical and no conclusions are drawn from any parameter values. Allowing the initial potential to vary, instead of fixing it at the controlled value, generates a fit that much more closely matches the data (Figure 24b), but is nonphysical. Accordingly, no conclusions about fit parameters were drawn from the application of the model to cyclic voltammetry current response data.

It is possible to extend this model to establish a relationship between input voltage and output reflectance. Changes in absorption of PEDOT:PSS during reduction and oxidation coincide with the flow of electrons into (reduction) and out of (oxidation) an electrochromic fiber’s multilayer cladding, which is measured as the current flowing through the three-electrode electrochemical cell. By quantifying the amount of charge that flows into, or out of, a fiber in each period of reduction or oxidation, it should be possible to estimate the level of oxidation or reduction in the PEDOT:PSS in its multilayer cladding, and subsequently how transparent or absorbing PEDOT:PSS layers in the cladding will be. Even if such a calculation does not align with measured changes in reflectance, comparing expected reflectance against measured reflectance could lead to the emergence of clearer trends that indicate what might be the cause of the dimming of the electrochromic fibers over multiple cycles of reduction and oxidation.

The circuit model will gain further utility when its lumped parameters can be conclusively linked to material properties, device dimensions, or other physical phenomena. In that case, the design of electrochromic fibers could be adapted to tune their response to various applied potentials. Film thicknesses, doping of PEDOT:PSS films, properties of the CNT ribbon, and other parameters could be controlled to produce devices that respond as quickly or slowly as is desired to a variety of electrochemical stimuli. In this scenario, however, it is important to ensure that the optical response of the fibers is also thoroughly understood, so that changes are not made to a fiber that improve its electrical response at the expense of its optical behavior.

1.3.4 Optical Modeling of Electrochromic Fibers The second model quantifies light interference within a multilayer stack of materials with complex refractive indices to account for absorption. This optical model predicts the reflection spectrum of an electrochromic fiber as a function of the morphology of the multilayer cladding and optical properties of its constituent materials. The model is based on Rouard’s technique, as described in Chapter 4 of O.S. Heavens’ Optical Properties of Thin Solid Films.28 First, a single thin film is considered, with refractive index

n1 and thickness d1, which is bounded below by some substrate with refractive index n2, and above by some medium with refractive index n0 (Figure 25a). It is possible to compute the Fresnel coefficients r and t for both interfaces in this hypothetical structure, with subscripts indicating the medium a ray originates from, and refracts into or reflects from (e.g. r01 indicates the coefficient of reflection for light traveling in the medium and reflecting off the top surface of the film). A wave that travels through a film of thickness d1, at some angle φ1 with respect to a surface normal acquires some phase δ1.

Figure 25: Setup for optical model of electrochromic fibers. a) Reflections from a ray of light incident on a single thin film with refractive index n1 and thickness d1, bounded below by some substrate with refractive index n2 and bounded above by some medium with refractive index n0. If all of these values are known, it is possible to exactly calculate the summation of all light that is reflected by the film, meaning the film can be represented as a single interface with an effective coefficient of reflection. b) A stack of k thin films, each with refractive index nk and thickness dk. The reflectance of the entire structure can be calculated iteratively, from the bottom up. The reflectance of the bottom film is determined, and converted to an effective coefficient of reflection that allows for the determination of the reflectance of the next lowest film. This process is repeated until the reflectance of the top film (including all films below, which have been incorporated as effective coefficients of reflection) can be calculated.

2 = cos( ) (15) 𝜋𝜋 𝛿𝛿1 𝑛𝑛1𝑑𝑑1 𝜙𝜙1 The summation of all rays that comprise the reflection𝜆𝜆 of light off the film and substrate is built up.

= + + + + (16) 2𝑖𝑖𝛿𝛿1 4𝑖𝑖𝛿𝛿1 6𝑖𝑖𝑖𝑖1 𝑅𝑅 𝑟𝑟01 𝑡𝑡01𝑟𝑟12𝑡𝑡10𝑒𝑒 𝑡𝑡01𝑟𝑟12𝑟𝑟10𝑟𝑟12𝑡𝑡10𝑒𝑒 𝑡𝑡01𝑟𝑟12𝑟𝑟10𝑟𝑟12𝑟𝑟10𝑟𝑟12𝑡𝑡10𝑒𝑒 ⋯ This can be re-written as a convergent geometric series, for which there is a finite sum

= + ∞ = + (17) 1 2𝑖𝑖𝑖𝑖1 2𝑖𝑖𝑖𝑖1 2𝑖𝑖𝛿𝛿1 𝑛𝑛 𝑡𝑡01𝑟𝑟12𝑡𝑡10𝑒𝑒 01 01 12 10 10 12 01 2𝑖𝑖𝛿𝛿1 𝑅𝑅 𝑟𝑟 �𝑡𝑡 𝑟𝑟 𝑡𝑡 𝑒𝑒 � ��𝑟𝑟 𝑟𝑟 𝑒𝑒 � 𝑟𝑟 10 12 𝑛𝑛=0 − 𝑟𝑟 𝑟𝑟 𝑒𝑒 Exploiting the relations in Equations 18-19, Equation 20 shows how the reflectance of the film can be defined by only the reflection coefficients from its top and bottom interfaces, the film thickness, the refractive index of the film, and the angle that the incident light makes with the films’ surface normal.

= 1 (18) 2 𝑡𝑡01𝑡𝑡10 − 𝑟𝑟01 = (19)

10 01 𝑟𝑟 +−𝑟𝑟 = (20) 1 + 2𝑖𝑖𝛿𝛿1 𝑟𝑟01 𝑟𝑟12𝑒𝑒 𝑅𝑅 2𝑖𝑖𝛿𝛿1 𝑟𝑟01𝑟𝑟12𝑒𝑒 The transmitted amplitude T of a film can be calculated by a similar method.28

With the above relation to calculate the effective reflection coefficient of a single film bounded by two

media, the wavelength-dependent reflectance of a stack of k films, with refractive indices n1 through nk,

bounded by some substrate with index nk+1 and some medium with index n0 (Figure 25b) can be deduced. Looking only at the bottom film, Equation 20 is used to determine the effective coefficient of reflection (with real part ρ and phase Δ) for the combination of its top and bottom interfaces.

+ = (21) 1 + 2𝑖𝑖𝛿𝛿𝑘𝑘 𝑖𝑖∆𝑘𝑘 𝑟𝑟𝑘𝑘 𝑟𝑟𝑘𝑘+1𝑒𝑒 𝜌𝜌𝑘𝑘𝑒𝑒 2𝑖𝑖𝛿𝛿𝑘𝑘 𝑟𝑟𝑘𝑘𝑟𝑟𝑘𝑘+1𝑒𝑒 Using this term as the effective reflection coefficient for the bottom two interfaces, the effective reflection coefficient of the bottom three interfaces can be calculated in a similar manner.

+ = (22) 1 + 𝑖𝑖∆𝑘𝑘 2𝑖𝑖𝑖𝑖𝑘𝑘−1 𝑖𝑖∆𝑘𝑘−1 𝑟𝑟𝑘𝑘−1 𝜌𝜌𝑘𝑘𝑒𝑒 𝑒𝑒 𝜌𝜌𝑘𝑘−1𝑒𝑒 𝑖𝑖∆𝑘𝑘 2𝑖𝑖𝛿𝛿𝑘𝑘−1 𝑟𝑟𝑘𝑘−1𝜌𝜌𝑘𝑘𝑒𝑒 𝑒𝑒 This technique can be applied moving up the entire structure, defining the effective coefficient of reflection of each layer based on the calculation of the effective coefficient of reflection of all the layers

beneath it. This is done iteratively until ρ1 and Δ1 are defined. The reflectance of the structure R = R1 can then be calculated by multiplying the complex effective coefficient of reflection with its complex conjugate. R1 is equal to the square of ρ1 for transparent media, for which the phase change is purely real.

When incorporating the capacity to account for absorption in layers in this calculation, it simplifies the equations to restrict light to normal incidence, eliminating the dependence of the phase change (and now absorption) on φ. Absorbing materials have a nonzero extinction coefficient k, and the complex refractive index of such a material is defined in Equation 23.

+ (23)

𝒏𝒏𝑘𝑘 ≡ 𝑛𝑛𝑘𝑘 𝑖𝑖𝑘𝑘𝑘𝑘 This complicates the calculation of the Fresnel reflection coefficient r at interfaces, which can be represented as the complex quantity defined in Equations 24-26.

= + (24)

𝑘𝑘 𝑘𝑘 𝑘𝑘 𝑟𝑟 𝑔𝑔 +𝑖𝑖ℎ = (25) ( 2 + )2 + ( 2 + 2 ) 𝑛𝑛𝑘𝑘−1 − 𝑛𝑛𝑘𝑘 𝑘𝑘𝑘𝑘−1 − 𝑘𝑘𝑘𝑘 𝑘𝑘 2 2 𝑔𝑔 𝑘𝑘−1 𝑘𝑘 𝑘𝑘−1 𝑘𝑘 𝑛𝑛 2( 𝑛𝑛 𝑘𝑘 )𝑘𝑘 = (26) ( + ) + ( + ) 𝑛𝑛𝑘𝑘−1𝑘𝑘𝑘𝑘 − 𝑛𝑛𝑘𝑘𝑘𝑘𝑘𝑘−1 ℎ𝑘𝑘 2 2 𝑛𝑛𝑘𝑘−1 𝑛𝑛𝑘𝑘 𝑘𝑘𝑘𝑘−1 𝑘𝑘𝑘𝑘 39

The phase term now includes a real term, which is a value between 0 and 1, due to absorption. A value of 0 in this term indicates that all the light in the considered wave has been attenuated; a value of 1 indicates the absence of absorption.

= (27) −4𝜋𝜋 4𝜋𝜋 𝑘𝑘 𝑘𝑘𝑘𝑘𝑑𝑑𝑘𝑘 𝑖𝑖𝑖𝑖𝑘𝑘𝑑𝑑𝑘𝑘 2𝑖𝑖𝛿𝛿 𝜆𝜆 𝜆𝜆 Equipped with these definitions, Equation𝑒𝑒 21 can𝑒𝑒 be used𝑒𝑒 as before, iteratively moving upward through the stack from the bottommost layer. The multiplication of the effective reflection coefficient of the top layer (and all layers below it) by its complex conjugate yields the reflectance R of the stack of films.

The above technique was implemented in a computational MATLAB model to determine the reflectance of multilayer stacks of absorbing materials. Prior to any analysis of the PEDOT:PSS/PDMS multilayer system, three test cases were simulated, to verify that the code was working as expected (Figure 26). First, a multilayer stack of two transparent materials was modeled, as had been done accurately in the past using extant code passed down within the Laboratory for Bioinspired Photonic Engineering at MIT29. The predicted reflectance was found to overlap exactly with the prediction of the extant code. Next, a “mirror” was simulated, as a single layer of a transparent material resting on a highly absorbing substrate. The code predicted, as expected, that a sufficiently absorbing substrate caused the structure to reflect all light, regardless of wavelength. Finally, multiple thin films of metals (silver, cobalt, and copper) of varying thickness were simulated, using n and k values taken from Filmetrics’ publicly available tables and the Refractive Index Database. The model closely matched the Filmetrics online Spectral Reflectance Calculator30 when Refractive Index Database31 values were used, and exactly matched the Filmetrics calculator when the Filmetrics values32 were used to simulate reflection.

Figure 26: Validation of optical model. a) The model agrees excellently with an extant simulation used to predict the reflectance of transparent multilayer stacks. b) The model simulates a mirror by placing a thin transparent film on top of a highly absorbing substrate. c) The model agrees excellently with the online Filmetrics Spectral Reflectance Calculator for a single thin (15 nm) film of copper on silicon and absorbing substrates.

Having validated the model, it was used to predict the reflectance of an electrochromic fiber. In a somewhat surprising turn, the experimental results and model predictions were in remarkably poor agreement, but incremental changes to the model improved the degree to which experimental and computational reflectance spectra matched. Accounting for the variation in film thickness across a wafer after spin coating broadened formerly sharp reflection peaks and introduced undulations toward higher wavelengths; swelling of one or both layers with the electrolyte solvent can account for the disparity between the target wavelength for the reflection peak (700 nm) and the wavelength location of observed reflection peaks. The model was also made into a Graphical User Interface (Figure 27), in which materials can be chosen for films, medium, and substrate, and layer thicknesses and the thickness distribution across all the layers can be programmed. This GUI simplifies the adjustment of model parameters, which helped to elucidate several relationships between the optical properties and structural parameters of a multilayer, and its total reflectance (Figure 28).

Figure 27: Screenshot of interactive optical model. Different materials can be selected; the user chooses whether to use reported values for n and k, or input custom (non-wavelength-dependent) values. Medium and substrate materials can be altered within a predefined range of relevant options. Multilayer parameters (film thicknesses, number of layers, variation in thickness across layers, swelling of films by solvent) can be carefully tuned to match recorded or hypothetical manufacturing and experimental conditions.

The primary disagreement between the experimental and computational reflectance values, is whether the reflected light is stronger in the oxidized or reduced state. The model predicts that, for very thin films, an increase in absorption can actually boost the overall reflectance of a multilayer stack. While counterintuitive, this is possible – an increase in absorption means that more light is attenuated within each layer, but it also makes the reflection at each interface stronger. For a finite stack of sufficiently thin layers, there could be a layer thickness below which the lost light due to absorption is balanced out, or outweighed, by increases in reflectance at interfaces. The PEDOT:PSS films were estimated to be 14 nm thick, which is extraordinarily thin, even for multilayer reflectors. This could be why the model predicts the reduced (higher absorption) state to exhibit stronger reflectance than the oxidized state, counter to our experimental observations.

Another possible explanation is that the change in absorption is not as important as the change in refractive index between oxidized and reduced PEDOT:PSS. The refractive index of PDMS, the other material in the multilayer stack, is approximately 1.41, and it is estimated that the refractive index of

Figure 28: Observations from optical model. a) Experimental data for reflectance of an electrochromic fiber as a function of wavelength in oxidized (red line) and reduced (blue line) states. b) Simulation with preliminary values for complex refractive index of PEDOT:PSS. The locations of spectral peaks are in good agreement with the experiment, but the magnitude of reflectance is considerably off, and predicted reflection peaks are more agitated than observed. c) Altering indices of refraction (nOx=1.7, nRed=1.5) can lead to a closer match in reflectance magnitude between experiments and the model, but there is no physical justification for these values. d) Increasing k can smooth out the oscillations in peaks, but reduces the difference between oxidized and reduced states.

42 oxidized PEDOT:PSS is around 1.5 through most of the visible range. Even a small decrease in the refractive index of PEDOT:PSS upon reduction (whether due to conformational change of its constituent polymers, or the possible influx of lower refractive index acetonitrile electrolyte solvent) can significantly reduce the refractive index contrast, and so overall reflectance, of a multilayer stack. If the model is correctly describing the effects of increased reflectance in very thin PEDOT:PSS layers, it is possible that the dramatic color switch observed is influenced primarily by changes in the refractive index, and is only minimally affected by changes in absorption.

Of course, another simple explanation of the mismatch between experimental observations and model predictions is that inaccurate values are used for the refractive index and extinction coefficient of PEDOT:PSS in its oxidized and reduced states. Further investigation of these parameters is underway, with collaborators in Stuttgart carrying out in-situ ellipsometry during electrochemical experiments. These tests are a big step toward defining the complex refractive index of PEDOT:PSS during and after reduction and oxidation.

We are confident, given the validation of the optical model under a variety of conditions with known material parameters, that the model will enable further insights into the observed color change of electrochromic fibers, and provide the means to design similar fibers that switch from dull blue to vivid green, yellow, or any other desired color. The optical and circuit models of the behavior of the electrochromic fiber system, functioning in concert, will expedite the exploration of design parameter spaces, and enable the careful design of fibers ideally tuned to match a variety of response profiles.

1.3.5 Continuation An electrochromic fiber was demonstrated that could be controllably switched between a bright, structurally colored state and a dark, absorption-based color state by applying or reversing an electric potential. This change was shown to be reversible and repeatable, though some degradation in the reflectance of fibers was observed over time and with cycles of reduction and oxidation. This degradation still needs to be explored and quantified in greater detail. Two models, of the electrical and optical behavior of electrochromic fibers, were developed to gain further insight into the behavior of the system, which could be expanded in the future with the collection of more data (improved optical properties for PEDOT:PSS, and current and reflectance information from more cycles of reduction and oxidation).

This work was a first step, and in the future, it could serve as a foundation for simple oxygen sensors. Scaling of the manufacturing process will not be necessary for the implementation of electrochromic fibers in this application, but could be useful for reducing costs and making the technology viable. If these fibers can be manufactured efficiently enough to allow them to be disposable, the issue of degradation over time will become less problematic. Otherwise, it will be necessary to find a way to minimize or eliminate this reduction in the reflectance of a fiber with time and cycling of reduction and oxidation.

1.4 Outlook Designed structural color is a relatively young concept; the design of structures comprised of nontraditional optical materials, even more so. This chapter has discussed systems that use dynamic structural color to respond to mechanical deformation and electrochemical stimuli with observable, repeatable changes in their vivid coloration. The manufacturing process used to make both the mechanochromic and electrochromic fibers is modular and versatile, and could be used to create similar structures with a host of possible materials and morphologies. Appropriate selection of constituent materials could enable the production of photonic fiber-based sensors that respond to thermal gradients, the presence of solvent vapors, stimulation by electromagnetic fields, and other phenomena with a predictable, observable change in their vivid coloration.33–39

Efforts to implement colorful sensors for all of these phenomena and more are, and have been, underway, and it is exciting to imagine a future where simple sensors translate danger, completeness, and other everyday occurrences into easily readable hues. Continued expansion of materials used in photonic crystals will brighten our lives with colorful clothing and accessories. There are many obstacles to overcome, first among them scaling of manufacturing processes used to make these structures (particularly for the sensing fibers we described), but the potential of these devices to simplify and enhance our lives is too great to not strive to bring their ideas to fruition.

Chapter 2: Leaky Light Guides for Microalgae Cultivation

2.1 The Promise of Microalgae Provision of sufficient food and fresh water for Earth’s human population is an extant and widespread problem, which will not get any easier as the number of our planet’s inhabitants is expected to exceed nine billion by the year 205040. It is estimated that crop yields will need to double in order to feed this expanded population in a similar manner to how developed countries eat today41, largely due to the inefficient conversion of animal feed into livestock42. At the same time, regions suitable for farming are shifting, and could potentially shrink, as a result of climate change, and vast swaths of arable land are used only to grow corn, soy, or other crops to be processed into biofuels and feedstock. Less than one third of all crop calories produced in the United States go directly toward feeding people.43

Microalgae are unicellular photosynthetic organisms, which could prove useful in overcoming many of the challenges outlined briefly above (Figure 29). They are similar to plants in that they convert sunlight and nutrient gases (typically carbon dioxide) into energy and biomass, but they generate biomass orders of magnitude more quickly and efficiently because they do not need to develop and maintain roots, stems, and leaves.44 Microalgae are also staggeringly diverse – while many species are suitable for cultivation of biomass for processing into biofuels and similarly plant-based products, others have high lipid and/or protein content and can be converted into nutritious feedstock and human supplements, some produce compounds utilized in pharmaceuticals, and a few can even extract heavy metals and other toxins from wastewater streams.45–47 Additionally, many species of microalgae thrive in brackish water, and require sufficient and consistent exposure to sunlight typically only available in arid regions unsuitable to more traditional agriculture; these factors combine to dramatically reduce competition for resources between algae farming and crops like corn and wheat.48

While microalgae show great promise as an efficient, renewable source of a variety of useful products and precursors, the way in which they grow has limited their capacity to realize their potential. Microalgae grow fastest near the surface of bodies of water, where they receive sufficient sunlight and can exchange gases with the atmosphere. Algae are self-shading, though, and at depths as shallow as a few feet, there may not be enough unabsorbed, photosynthesis-stimulating light remaining to promote growth. Algae stuck at the surface of a body of water can also be bleached by overexposure to sunlight. These detrimental effects are normally countered in algae farming by growing algae cultures in shallow (approximately 0.3 m deep) ponds and narrow tubes, and by constantly churning the algae via large paddlewheels or pumps. While a small amount of this churning is necessary in any case, to prevent less

Figure 29: Interconnected impact of microalgal generation of biomass. Microalgae can serve as efficient sources of biomass for conversion into fuels, feedstock, food, and more. Use of algae for biofuels and feedstock reduces the need to use arable land to grow corn, soy, or other crops for this purpose, freeing up farmland to grow crops for human consumption. Many strains of algae do not compete with traditional crops for freshwater, and others can turn industrial exhaust and other waste streams into useful products, offering some cleaning and filtering along the way. In short, microalgae have great potential to approach the manifold, linked challenges presented by human population growth and climate change, if they can be grown and processed in an economical and energetically viable manner. buoyant strains of algae from settling to the bottom of the culture, the bulk of effort is required just to ensure that all algae in a culture are exposed to healthy amounts of light and nutrient gases. Along with energy-intensive processes used to convert dilute algae cultures into useable biomass, these constraints restrict energetically and economically viable microalgal cultivation to the production of high-value products like pharmaceuticals. In order to expand this viability to more strains of algae, it is imperative to find a way to reduce the input cost and energy necessary to grow algae.

We have explored one possible method of tilting the economic and energetic balance more in favor of the cultivation of microalgae for a variety of end uses: “leaky light guides”, illuminated at one end (by solar collection or artificial light), that passively distribute light throughout volumes of microalgae cultures. A brief discussion of the optics knowledge necessary to understand their functionality, and a more in-depth consideration of our efforts to create and implement these devices, follows.

2.2 Optical Concepts 2.2.1 Total Internal Reflection and Light Guiding

When a ray of light within a medium with refractive index n1 is incident upon an interface with some medium with refractive index n2, the angles between the incident and refracted rays with respect to the surface normal of the interface are related by Snell’s Law, which states

sin( ) = sin( ) (28)

𝑛𝑛1 𝜃𝜃1 𝑛𝑛2 𝜃𝜃2 If n2 < n1, then there exists some critical angle ϴ1= ϴc for which ϴ2=90°, indicating that refracted light travels along the interface between the two media. If ϴ1 is increased beyond this critical angle, then ϴ2 is undefined. In this case, all incident light is reflected, in a condition known as “Total Internal Reflection”

(TIR). These angles (ϴ1,2 in the diagram is equivalent to ϴ1 in Equation 28) are shown in Figure 30.

TIR can be exploited to create optical waveguides, referenced herein as “light guides”, which confine light within some medium with a higher refractive index than the surrounding environment. This is the basis for optical fibers, which transmit light great distances along narrow, transparent fibers surrounded by a low-index cladding. For any light guide, there exists a range of input angles of light that will be subject to TIR within the structure, often characterized as a numerical aperture (NA, which is defined as the product of n0 and the largest possible sinϴ0). The NA of an optical fiber can conveniently be defined solely as a function of its core and cladding refractive indices (Equation 32).

Figure 30: Cross-section of the input end of a fiber (material with refractive index n1) immersed in some medium with refractive index n2. The relationship between various angles and refractive indices is defined in the text. When ϴ2 is 90 degrees, further increasing ϴ1,2 results in total internal reflection within the fiber. The extension to the input into the fiber from the medium with refractive index n0 demonstrates how this principle can be used to define the angle of acceptance for a light guide.

sin( ) = sin , = cos( ) (29)

𝑛𝑛0 𝜃𝜃0 𝑀𝑀𝑀𝑀𝑀𝑀 𝑛𝑛1 �𝜃𝜃1 0 𝑀𝑀𝑀𝑀𝑀𝑀� 𝑛𝑛1 𝜃𝜃𝐶𝐶 sin( ) = sin sin( ) = (30) 2 𝜋𝜋 𝑛𝑛2 𝑛𝑛1 𝜃𝜃𝐶𝐶 𝑛𝑛2 � � ⇒ 𝜃𝜃𝐶𝐶 𝑛𝑛1 sin( ) = cos( ) = (1 sin( ) ) = 1 (31) 2 2 2 2 2 2 2 2 𝑛𝑛2 𝑛𝑛0 𝜃𝜃0 𝑀𝑀𝑀𝑀𝑀𝑀 𝑛𝑛1 𝜃𝜃𝑐𝑐 𝑛𝑛1 − 𝜃𝜃𝐶𝐶 𝑛𝑛1 � − 2� 𝑛𝑛1 sin( ) = = (32) 2 2 𝑛𝑛0 𝜃𝜃0 𝑀𝑀𝑀𝑀𝑀𝑀 𝑁𝑁𝑁𝑁 �𝑛𝑛1 − 𝑛𝑛2 2.3 Modeling and Realization of Uniform Light Emission In order to create leaky light guides that are useful for homogeneously distributing light in microalgae cultures, it is helpful to model how the concentration of scatterers must vary in a light guide in order to emit uniform light intensity along its length. In parallel, it is necessary to determine how process parameters relevant to the studied approach for creating such light guides influences their spatially varying scattering coefficient. Taken together, these steps enable the informed design of approximately uniformly emitting leaky light guides, for implementation in lab-scale microalgae cultures.

2.3.1 Modeling of Light Scattering from Leaky Light Guides

Consider a one-dimensional light guide of length L, exposed to light of intensity Io input at one end (Figure 31). Without any scatterers, all input light will propagate along the entire light guide and be emitted out the other end. However, if some scattering s(x), defined as the fraction of input light emitted from an infinitesimal length via scattering, is included along the light guide, then a nonzero amount of light is emitted from any arbitrary segment, as defined below.

( ) = ( ) ( ) (33)

𝐸𝐸 𝑥𝑥 𝑑𝑑𝑑𝑑 𝑠𝑠 𝑥𝑥 𝐼𝐼 𝑥𝑥 Assuming no light is lost to absorption, E(x) can also be related to the intensity of light propagating within the light guide before and after some differential length dx by the equation

( ) = ( ) ( + ) (34)

𝐸𝐸 𝑥𝑥 𝑑𝑑𝑑𝑑 𝐼𝐼 𝑥𝑥 − 𝐼𝐼 𝑥𝑥 𝑑𝑑𝑑𝑑 Equation 34 can be rearranged as the definition of a derivative.

( + ) ( ) ( ) = = (35) 𝐼𝐼 𝑥𝑥 𝑑𝑑𝑑𝑑 − 𝐼𝐼 𝑥𝑥 𝑑𝑑𝑑𝑑 −𝐸𝐸 𝑥𝑥 48𝑑𝑑 𝑑𝑑 𝑑𝑑𝑑𝑑

Figure 31: Model for scattered emission from a light guide. A light guide of length L, with input intensity I0 and emission per unit length E is shown. Consideration of a differential length dx, and the light intensity that is input into this segment, scattered from this segment, and propagated to the next segment allows for the derivation of an equation for scattering that varies along the length of the fiber, in order to make E uniform along the fiber.

In the general case, this shows that

( ) = ( ) (36)

𝐼𝐼 𝑥𝑥 � −𝐸𝐸 𝑥𝑥 𝑑𝑑𝑑𝑑 For the specific case where all input light is emitted, and emission is constant, E(x) is equal to Io/L, and

( ) = = + (37) 𝐼𝐼𝑜𝑜 𝐼𝐼𝑜𝑜 𝐼𝐼 𝑥𝑥 � − 𝑑𝑑𝑑𝑑 − 𝑥𝑥 𝐶𝐶 𝐿𝐿 𝐿𝐿 Knowing that the initial input intensity is Io, we can solve for C, which tells us that

( ) = 1 (38) 𝑥𝑥 𝐼𝐼 𝑥𝑥 𝐼𝐼𝑜𝑜 � − � Equation 33 can be rearranged to define a desired scattering𝐿𝐿 profile as a function of propagated and emitted light along the length of a light guide.

( ) ( ) = (39) ( ) 𝐸𝐸 𝑥𝑥 𝑑𝑑𝑑𝑑 𝑠𝑠 𝑥𝑥 In the special, uniform-emission case outlined above, this𝐼𝐼 𝑥𝑥 becomes

( ) = = (40) 𝐼𝐼𝑜𝑜 1𝑑𝑑𝑑𝑑 𝐿𝐿 𝑑𝑑𝑑𝑑 𝑠𝑠 𝑥𝑥 𝑥𝑥 𝐼𝐼𝑜𝑜 � − � 𝐿𝐿 − 𝑥𝑥 49 𝐿𝐿

Thus, for a light guide of length L and control over the amount of scattering with spatial resolution dx, it is possible to prescribe the variable scattering s(x) that leads to uniform emission. In order to understand how s(x) corresponds to physical parameters, it can be related to an exponential scattering coefficient σ by considering a differential length dx with uniform scattering (s and σ are constant across dx). The intensity of light that propagates out of this small section, I(x+dx), can be defined in two ways. First, rearranging Equation 34 and plugging in Equation 33 yields a definition in terms of s(x).

( + ) = ( ) ( ) = ( )(1 ) (41)

𝐼𝐼 𝑥𝑥 𝑑𝑑𝑑𝑑 𝐼𝐼 𝑥𝑥 − 𝐸𝐸 𝑥𝑥 𝑑𝑑𝑑𝑑 𝐼𝐼 𝑥𝑥 − 𝑠𝑠 Losing a fixed fraction of something per unit step in space or time is one definition of exponential decay, which enables the second definition of propagated light.

( + ) = ( ) (42) −𝜎𝜎𝜎𝜎𝜎𝜎 𝐼𝐼 𝑥𝑥 𝑑𝑑𝑑𝑑 𝐼𝐼 𝑥𝑥 𝑒𝑒 We can use these two definitions to determine σ as a function of s:

= 1 (43) −𝜎𝜎𝜎𝜎𝜎𝜎 𝑒𝑒 = ln(1− 𝑠𝑠 ) (44)

−𝜎𝜎𝜎𝜎𝜎𝜎 ln(1 − 𝑠𝑠) = (45) − − 𝑠𝑠 𝜎𝜎 Using the equations derived above, it is possible to estimate𝑑𝑑𝑑𝑑 how the scattering coefficient of a leaky light guide must vary along its length in order to emit approximately similar amounts of light from any section along its length.

2.3.2 Laser Ablation of Transparent, Cylindrical Light Guides Scattering was introduced into our light guiding materials (6-13 mm diameter cylindrical rods of glass and acrylic) via laser engraving, an idea first proposed by Seiji Engelkemier, a UROP who assisted with the research on this project. Laser pulses incident on the surface of one of these rods cause the formation of small craters, networks of cracks, and other defects on the surface of the light guide. The density and size of defects formed can be controlled by adjusting several machine-dependent laser machining parameters.

Light guiding rods were modified with a Universal Laser Systems VLS3.60 laser engraver with a 30 Watt

CO2 laser tube, equipped with high power density focusing optics for the finest possible resolution and a rotary attachment to simplify the uniform modification of the surfaces of cylindrical light guides (Figure 32). There were four means of controlling the density of defects on a machined part: “Image Density” (ID),

50 laser power, laser speed, and gray value (GV). Image Density controls the resolution of the rastering, which defines how many points are available to be exposed (or not exposed) to the laser in a given area. This resolution varies from 83 lines per inch (lpi) at ID 1 up to 1000 lpi at ID 7, and is fixed when a black-and- white image is sent to the laser engraver software. Laser power straightforwardly controls the power of each laser pulse, specified as a percentage of the engraver’s maximum possible power. Laser speed similarly controls the rate of travel of the laser carriage, specified as a percentage of the machine’s maximum achievable velocity. Together, laser power and speed determine the size and character of defects created at each pulsed point in a raster pattern. These parameters are variable after having sent an image to the engraving software, but are fixed for each “job”, which is defined as the engraving of one part using a printed file. Gray Value is an 8-bit grayscale characterization of the color of each pixel in a raster pattern. GV 0 for laser engraving is represented as white, and leads to no engraving; GV 255 is represented as black, and leads to the pulsing of all possible points (determined by Image Density) with the laser. Gray Value is the only laser engraving parameter that is variable within each job. In addition to

Figure 32: Universal Laser Systems (ULS) VLS3.60 laser engraver with rotary attachment and custom fixturing. A ULS rotary attachment was modified to enable the consistent patterning of long, relatively narrow rods of glass and acrylic to be used as leaky light guides.

51 these four parameters, there are different dithering patterns that convert GV graphics into clusters of laser pulses. An ideal surface for this application would have evenly distributed scatterers that vary in density along the length of a light guide – as such, the “Error Diffusion” dithering algorithm was chosen. Error Diffusion uses a random scatter filter to place pixels according to GV, and mostly avoids the larger- scale pattern repetition observed with halftones and other dithering methods.

The characterization of the amount of scattering induced by different combinations of laser engraving settings was accomplished using a custom-built setup, named the “Heptapod” (Figure 33). This apparatus consists of a standard optical components frame supporting a 3D-printed fitting that holds seven optical fibers normal to the surface of, evenly spaced around, and equidistant from a cylindrical object. Leaky light guides could be translated through this setup, allowing for the collection of a circumferential average of emitted light at any point along the length of a laser-modified fiber. For light guides subject to uniform rastering, we expected and observed an exponential decay in emitted light along their length. This emission could be fit to the Beer-Lambert Law (Equation 46), in order to determine the effective scattering coefficient σ.

( ) = (46) −𝜎𝜎𝜎𝜎 𝐼𝐼 𝑥𝑥 𝐼𝐼𝑜𝑜𝑒𝑒 The influence of the four laser engraving parameters discussed above on the effective scattering coefficient of leaky light guides was studied for guides made of soda-lime glass (Figure 34) and extruded acrylic (Figure 35). While the full parameter space is somewhat vast, in both cases a narrower, more easily tested subset of this space could be defined and explored. For both materials, a fixed combination of ID, power, and speed was identified that enabled the achievement of a wide, utile range of scattering coefficients simply by varying GV within each job. In this way, complete leaky light guides could be made in single jobs of laser rastering.

In general, it was hypothesized that ideal surface patterning would result in an even distribution of very small (on the order of the wavelength of visible light) defects. While laser engraving glass rods, it was quickly discovered that the material could endure the engraver’s maximum resolution without being undesirably deformed, and that the smallest achievable defects were obtainable by maximizing laser speed. With these two parameters fixed, uniformly scattering leaky light guides were manufactured with a variety of combinations of laser power and Gray Value. A monotonic, proportional, and nonlinear

Figure 33: Characterization of scattered light emission from leaky light guides. a) A photograph of the setup affectionately known as “The Heptapod”. It relies on a custom-designed, 3D-printed part that holds seven optical fibers equally spaced around, and normal to, a leaky light guide. The surrounding infrastructure allows for the measurement of emission at any arbitrary point along the length of the light guide. b) Schematic of The Heptapod. Colored dots link components in the photograph and schematic. c) A representative light spectrum collected with The Heptapod. d) Reducing spectra like the one shown in (c) to a single point by integrating under each one’s spectral curve, the amount of light emitted out of a leaky light guide along its length can be characterized. relationship was observed between Gray Value and effective scattering coefficient, while increases in power were found to first increase scattering, then have the opposite effect as power was increased further. A polynomial surface (second order with respect to laser power, third order with respect to Gray Value) was fit to the data, and indicated that maximum and minimum achievable scattering coefficients

Figure 34: Laser rastering of glass rods. a) Surface fit to scattering coefficients measured from glass rods with uniform rastering at different fixed combinations of laser power and gray value. The surface fit is a second order polynomial with respect to laser power and a third order polynomial with respect to gray value. b) Isolating the curve along laser power = 35% from the surface fit in (a) yields manufacturable scattering coefficients as a function of gray value. c) Scattering coefficient plotted against length for leaky light guides. Green lines indicate theoretically ideal variation in scattering coefficient, in order to induce uniform emission, along leaky light guides in 10, 50, and 100 cm lengths. The blue shaded region indicates the range of scattering coefficients that are manufacturable, according to (b).

could be reached by varying Gray Value at around 35% power. Leaky light guides manufactured according to this insight are discussed in Section 2.3.3 below.

Unlike glass, extruded acrylic could not endure high-resolution laser rastering – attempting to engrave features at maximum Image Density led to the removal of egregious amounts of material, and the formation of poorly defined features. It is hypothesized that this is because the heat-affected zone during laser machining is larger for acrylic than for glass, meaning that the thermal fields induced by laser pulses that are close in space and time are more likely to overlap, resulting in the formation of defects with less sharp features. A brief survey of engraving parameters revealed that the optimal ID was 4 (corresponding to 250 lpi), though a fixed, optimal value could not be found for power or speed. As such, a subset of power and speed combinations were examined near extrema of Gray Value, in an attempt to identify fixed Figure 35: Laser rastering of acrylic rods. a) After identifying ID = 4 as the optimal resolution for combinations that could successfully induce a wide modification of acrylic rods, power and speed were swept through relevant parts of their full ranges at fixed low and variety of scattering coefficients with varying GV. high gray value. Empty cells indicate no modification; gray Two combinations of power and speed were cells indicate appropriate modification at one GV; red cells indicate excessive modification; green and yellow cells identified, that could induce visible scattering at correspond to the two power and speed combinations that resulted in appropriate modification at both GV GV 45, and not overwhelm the material at GV 210. settings. b) Green and yellow squares and Xs correspond Both of these combinations were used to to the power and speed settings identified above. Squares indicate settings that resulted in observable exponential manufacture test leaky light guides with a range of decay after uniform patterning; Xs indicate non- exponential behavior. An exponential function was fit to Gray Values, and one combination (20% power, the green boxes at GV 75, 120, and 165, to predict 40% speed) exhibited a meaningful correlation scattering as a function of GV and inform the manufacture of approximately uniform leaky light guides. between Gray Value and scattering coefficient. As with glass, acrylic leaky light guides whose manufacture was informed by this relationship are discussed in Section 2.3.3 below.

Soda-lime glass and extruded acrylic were analyzed for this project. Certain types of soda-lime and flint glass, if metallic impurities present in the mixture were not properly eliminated during manufacture, absorbed light in the same bandwidths as most chlorophylls, making them uniquely unfit for use in our

55 proposed systems. Borosilicate glass (used to make Pyrex dishes) was found to respond undesirably to laser ablation, and many plastics (polyvinyl chloride, PVC; polystyrene; polyethylene; polycarbonate; and others) were not considered because they release particularly noxious fumes when laser machined. There are still several materials that we did not examine that are transparent, could guide light when immersed in water, and are laser-machinable. Cast acrylic is chief among these, and its unique behavior in response to laser engraving (commonly referred to as “frosting”) could potentially diffuse the effects of surface modification, giving rise to useful variation in scattering at lower powers and Gray Values.

2.3.3 Manufacture of Uniformly-Emitting Leaky Light Guides Theoretical understanding of how the scattering coefficient should vary along a leaky light guide and empirical understanding of how laser engraving parameters affect the scattering coefficient were combined to manufacture leaky light guides with approximately uniform emission. For both soda-lime glass and extruded acrylic, the scattering coefficient had been determined as a function of Gray Value for some fixed combination of ID, laser power, and laser speed. In order to make a uniformly-emitting leaky light guide of some length L, Equations 40 and 45 were used, setting dx equal to the resolution of the laser engraver for the material being modified. Each ideal scattering coefficient was rounded to its closest manufacturable match, and these scattering coefficients were then converted to relevant Gray Values, which could be output as an image with width equal to the length of the desired fiber and height equal to the circumference of the light guide to be modified. This image file was then printed to the laser engraver, where it could be positioned on as many unmodified light guides as desired to convert them into approximately uniform leaky light guides. We manufactured such light guides up to 50 cm in length, from glass and acrylic fibers. Figure 36 shows the overlap between the model expectation for emission, and measured emission, from a shorter (approximately 13.5 cm) uniform-emitting leaky light guide.

Figure 36: Relative emission strength vs. position along a leaky light guide. The black line shows the model prediction, given achievable scattering coefficients, for a 13.5 cm-long leaky light guide. The green dots show emitted light measured from an experimentally realized light guide manufactured to match the modeled emission profile.

Emission from these leaky light guides is significantly more uniform than emission from light guides imbued with uniform scattering. Ultimately, there is a limit in practically achievable uniformity of emission, which arises from the discrete nature of the set of manufacturable scattering coefficients – scattering is varied by changing the gray value, which can only be one of 256 integer values. Finer differences between achievable scattering coefficients, and the realization of greater and lesser values of scattering, could both help make manufactured leaky light guides more uniform in their emission. However, it is hypothesized that the observed emission is uniform enough to prove or disprove the concept of using leaky light guides to passively distribute light throughout volumes of algae culture.

2.4 Implementation of Leaky Light Guides in Algae Cultures There are two challenges associated with illuminating algae cultures with leaky light guides. First, light has to be coupled, in a controlled manner, into the leaky light guide to maximize the amount of the light’s output that will propagate along the light guide by TIR. Second, the intensity of light emitted at any point along the leaky light guide, in the spectral range relevant to photosynthesis, has to be sufficiently high to promote growth in the algae culture. Additional concerns include thermal regulation (ensuring that the heat of the light source does not negatively impact the light guide or the fixture that couples the light into the fiber), material compatibility (glass is fairly nonreactive and can be autoclaved for sterility, but is brittle and prone to shattering into dangerously sharp shards; acrylic is less stable than glass and cannot be autoclaved, but is considerably safer in most environments), power consumption and efficiency of the light source, and dimensional constraints on leaky light guides in different bioreactors and experimental setups.

A succession of iterative improvements in the fixtures used to hold leaky light guides has led to the apparatus depicted in Figure 37. Earlier versions used exclusively light guides with diameters between 6 and 6.4 mm, and smaller LED illuminators; these were found to provide insufficient illumination for microalgae (more details in Section 2.5). Consequently, more powerful LEDs were acquired. These larger light sources improved the illumination out of the older light guides, they also wasted a great deal of energy generating light that could not be coupled into these smaller fibers. To capture the light from these larger light sources more efficiently, acrylic rods with a larger cross section of approximately 13 mm were modified as before to create leaky light guides. One of these rods is pictured in Figure 37.

Figure 37: Leaky light guide fixture. a) A representative fixture with a ½”-diameter acrylic leaky light guide, with the LED light source turned off. The box and breadboard in the background are used to drive the LED with a constant current. b) The same fixture as in (a), with the LED turned on. Note that the rod appears uniform by eye, but with the camera we can detect slight changes in scattering near the end of the rod, and see the decay in emission (due to a single scattering coefficient being used) along the first ~3/4 of the light guide (starting at the end closest to the fixture).

2.5 Characterization of the Influence of Leaky Light Guides on Microalgae Growth Various fixtures were designed to work in different experimental setups, aimed at quantifying the effects of light-distributing leaky light guides on the growth of microalgae. These experiments fall into one of two main categories: comparing growth of algae in bioreactors with leaky light guides to those illuminated only near the surface, and using modified cyanobacteria in an electrochemical setup to precisely quantify the electron transport induced by different lighting conditions. We collaborated with Christine Lewis, Everett Eustance, Ph.D., and Prof. Bruce Rittmann at Arizona State University for the work described in Sections 2.5.1-2. Stefan Kolle at Harvard University, and Everett Eustance, contributed advice and assistance with the work described in Section 2.5.3.

2.5.1 Bubble Column Bioreactors at Arizona State University The simplest test of whether or not leaky light guides enable more efficient cultivation of microalgae, is to grow microalgae with only the source of light being different between samples for comparison. In this

58 regard, experiments were conducted in collaboration with Everett Eustance at Arizona State, in which cultures of Scenedesmus acutus were grown in large, glass tube bioreactors illuminated by prototype leaky light guides (Figure 38). Scenedesmus strains of microalgae are non-motile green algae that are commonly grown to produce biomass for fuels.

Figure 38: Bubble column bioreactors with S. acutus (Arizona State University). a) Two bubble column bioreactors, seeded with Scenedesmus acutus, illuminated by early prototype leaky light guides (soda-lime glass, 6 mm diameter). b) Density of each of the two cultures, recorded over a period of three days. The inset image shows samples taken from column 1 on each day.

The first experiments were conducted in March 2019, with light-emitting, but appreciably non-uniform light guides immersed in the reactors. The light guides were illuminated by a halogen illuminator, via two gooseneck fibers. The reactor tubes were not shielded from external illumination by the fluorescent lights in the laboratory, but prior knowledge of the researchers at ASU indicated that these room lights were insufficient for growth of microalgae. In this round of experiments, growth was observed during each of three days of experiments in two bioreactors, including one bioreactor where the rate of growth also increased each day. While these initial results were promising, the growth rates were slower than those typically observed when reactors are illuminated by a large bank of fluorescent lights.

Refined, more uniformly emitting light guides were sent, along with small LED illuminators, late in the summer of 2019. Upon implementation in a similar manner as before, it was discovered that the light

59 emitting from these rods, while more uniform, was considerably dimmer than the light that was emitted by the first rods in March. This revelation drove us to identify and procure larger, much brighter LEDs, and identify means of integrating them into light fixtures without damaging the light guides, the fixture, or related experimental apparatus due to overheating or excess illumination. After testing out a variety of optics to collimate and focus down the emission from the LEDs, it was decided that the simplest solution was likely just the modification of larger (1/2”-diameter) acrylic rods. These rods were acquired and modified as before, with the relationship between GV and scattering coefficient for acrylic scaled to the gray values that induced maximal and minimal scattering from the new, larger light guides. These uniform, bright light guides have been shipped to ASU for further experimentation.

2.5.2 Photoelectrochemical Cells at Arizona State University Another experiment, which is carried out at Arizona State University by Christine Lewis, involves the use of a photoelectrochemical cell to quantify the quantum efficiency of photon utilization by genetically modified cyanobacteria. Their photosynthetic chains are modified such that one stage of electron transport is replaced by an electron carrier in the electrochemical cell. By quantifying the illumination incident on the cell, and the current that flows through it, it is possible to determine the efficiency with which incident light is actually turned into energy (and therefore growth) for the microalgae.

Glass light guides are necessary for these experiments, since glass enables greater sterility (ensuring that all microbes in the cell are only the genetically modified microbes) and does not react with any other components of the experiment. In a round of experiments in March 2019, acrylic was found to adsorb the electron carrier present in the electrolyte, which hampered the cell’s ability to carry out the critical step of photosynthesis. Tests carried out in September 2019 with the improved light guides proved promising, showing a large increase in current generated in response to illumination by leaky light guides, but even greater light levels were desired. As such, the larger LEDs were also acquired for use in this setup. Larger glass rods, akin to the large acrylic rods that take in more of the large LED’s emission, are not feasible in the small electrochemical cells. As such, light coupling into the thinner glass rods from the large LEDs was maximized, while ensuring that the excess illumination would not damage any of the relevant equipment. This was accomplished by including a light blocking ring around the fiber in the light fixture; these new setups have been shipped to ASU for further experimentation.

Figure 39: Photoelectrochemical experiments. a) Photograph of two photoelectrochemical cells, wrapped in aluminum foil to prevent non-leaky light guide illumination from affecting the cyanobacteria within the cells. b) Plot of measured current magnitude over time, as lights were cycled on and off. There is a notable jump in current flow (analogous to photosynthetic activity) whenever the light guides are illuminated, which decays down to near zero when the lights are shut off. 2.5.3 In-lab Bioreactors with Chlamydomonas reinhardtii In addition to sending materials to our algae expert colleagues at Arizona State, a different strain of microalgae, Chlamydomonas reinhardtii, was cultivated in the Laboratory for Bioinspired Photonic Engineering at MIT. This enabled a more rapid turnaround on testing new iterations of leaky light guide fixturing, and allowed for experiments with a second species of algae to test, and quantify the effects of, illumination with leaky light guides. Stefan Kolle and Everett Eustance provided critical help in starting and maintaining these critical experiments. In addition to light and gas exchange, C. reinhardtii require a nutrient mixture, consisting of soil extract, a variety of salt solutions, and water as described in UTEX Soil Extract Medium.10

In these tests, custom bioreactors were designed that enabled the bubbling of air from the bottom of the reactor for gas exchange, freeing the entire top of the reactor for affixing of a light fixture. Illumination for all reactors came from identical LEDs driven at the same current level. This light was coupled into a large acrylic rod, which was either truncated just below the surface of the growth medium in the bioreactor (for control cultures), or extended and modified to radially emit approximately uniform light

Figure 40: In-Lab microalgae bioreactors. (a)-(d) show four bioreactors in various stages of preparation: a) media has been loaded; b) all reactors are inoculated with algae from extant culture; c) lights are turned on in cultures (two feature leaky light guides for illumination, the others are fiber-illuminated at the top of the culture); d) all reactors are foil-wrapped to ensure that algae are only exposed to light provided to each reactor by LED and fiber or leaky light guide. along its length. Two reactors with each illumination style have been left to grow until all present nutrients are consumed, and the rates of growth and peak productivity will be compared between the two styles of setup.

2.6 Discussion 2.6.1 Manufacturability of Leaky Light Guides While demonstrating the effectiveness of this type of technology leaps one hurdle toward its future implementation, the affordability of integrating leaky light guides into various algae farming systems will play a large role in whether they can realize their potential and positively impact the monetary and energetic balance of microalgae cultivation. There are two ways to look at this, enabled by the two styles of experiment that were carried out. On a very small scale, the quantum efficiency of microbes illuminated by leaky light guides can be used, along with the efficiencies of power conversion into light, and light coupling into the leaky light guide, to determine the cost, per kWh, of a unit of microbe growth. On a more general scale, the growth rate of microbes in a bioreactor illuminated by a leaky light guide can be used, with the efficiencies related to conversion of power into light guide-propagating illumination as before, to generate a related measure for energy cost per unit growth. These relationships, along with the sale price of a particular strain of algae, would indicate what the cost of manufacturing and maintaining leaky light guides for illumination in microalgae cultivation would need to be, in order to break even (or turn a profit) farming algae for pharmaceuticals, biofuels, feedstock, food, and other uses.

The costs associated with manufacture and maintenance of leaky light guides will depend on light guide material cost; capital, resource (compressed air, energy, time/labor), and maintenance cost of laser engravers suited to patterning light guides; cleaning and sterilization of light guides used in bioreactors; provision of energy to illuminate light guides or mechanisms to collect and distribute sunlight to light guides; and other miscellaneous expenses. Some of these costs will be reduced in the transition from laboratory scale to industrial scale manufacture: raw materials will become cheaper per unit length as more are ordered, and LEDs specifically designed to efficiently convert electricity into light that can be coupled into (and propagated along) the light guides could be designed in collaboration with Bridgelux, Cree, or another company. Additional benefits could be realized by identifying a different manufacturing method to produce similar leaky light guides at greater scales. Laser machining is well-suited to laboratory study because it is quickly and simply modified, capable of a wide range of impacts on acrylic and glass rods, and highly controllable and repeatable. Some expenses, such as costs associated with the upkeep and replacement of leaky light guides and their relevant infrastructure, are harder to predict without large-scale studies.

2.6.2 Outlook and Next Steps It has been demonstrated that some simple optical light guides can be modified with laser rastering, in order to create fibers that emit light approximately uniformly along their length. Herein, these were manufactured in lengths up to 50 cm, but the technique is applicable to leaky light guides multiple meters in length, with appropriate laser machining infrastructure. Growth of microalgae was spurred by the inclusion of these leaky light guides in laboratory-scale bioreactors, but further analysis is necessary to determine whether, and by how much, growth is increased when leaky light guides are used, with respect to external illumination. Additional studies would shed more light on whether any increase in biomass productivity is worth the increased infrastructure, maintenance, and power supply costs.

Different strains of algae could represent an array of excellent solutions to multifaceted problems associated with food and water security and climate change, particularly as the human population continues to grow. Identifying and implementing means of boosting the efficiency of microalgae cultivation takes important steps toward ensuring our future on Earth. With any luck, and some perseverance, leaky light guides like the ones discussed herein could be implemented on an industrial scale to aid in the provision of carbon-neutral liquid fuels, nutritious feedstock, and pharmaceutical compounds.

Conclusion: Structural Manipulation of Light in Fiber-Based Technologies

In all the projects described in this document, careful control of the micro- or nanoscale structure in an optical or photonic fiber enables that fiber to interact with and manipulate light in a useful manner. The functionality of these fibers stems from their manufacture with elastomers, conducting polymers, and other materials not traditionally used in optical devices, and their fiber architecture will allow for great flexibility with their eventual incorporation into a variety of technologies.

Mechanochromic and electrochromic fibers predictably and repeatably convert different stimuli (strain and electrochemical potential) into color changes that are easily detected by the human eye. These fibers demonstrate the effectiveness of colorimetric sensors, and the great potential of simple sensors based on the fabrication of photonic crystals with materials that respond to physical phenomena with a predictable change in their optical or mechanical properties. The colorimetric fibers described above could enhance the application of compression therapy for millions of patients and provide clear indications when anaerobic environments are exposed to oxygen; countless other sensing fibers could be made to detect changes in temperature and humidity, magnetic fields, or almost any other parameter. In addition to all these potentially impactful applications, photonic fibers look great, and could easily find extensive use in art, apparel, and other aesthetic endeavors.

Leaky light guides can be manufactured by blasting small craters into the surface of glass and acrylic rods by laser engraving; these light guides can then be used to more evenly distribute light within cultures of microalgae, potentially enabling them to become energetically and economically viable sources of biomass. A complex web of problems confront humanity as our population continues to grow and the full extent of the detrimental impacts from powering modern society with fossil fuels is revealed. Microalgae show promise as a potential solution to many of these interconnected challenges, if their cultivation can be made sufficiently efficient.

The work reported in the previous chapters comprehensively describes the functionality of multiple optical and photonic fibers that derive some useful functionality from the inclusion of fine structure to manipulate light. While the study of these structures was thorough, and their many potential applications were discussed, they represent a small fraction of the nigh-endless possibilities of forming and exploiting micro- and nanoscale features to interact with light in ways that introduce beneficial effects. The continued exploration of this broad parameter space, by curiosity-driven researchers around the world, will surely yield additional fascinating and utile devices and systems.

References

1. McDougal, A., Miller, B., Singh, M. & Kolle, M. Biological growth and synthetic fabrication of structurally colored materials. JOURNAL OF OPTICS 21, (2019). 2. Johnson, S. G. & Joannopoulos, J. D. Photonic crystals : the road from theory to practice. (Boston : Kluwer Academic Publishers, c2002., 2002). 3. Vignolini, S. et al. Pointillist structural color in Pollia fruit. Proceedings of the National Academy of Sciences 109, 15712–15715 (2012). 4. Qin, M., Sun, M., Hua, M. & He, X. Bioinspired structural color sensors based on responsive soft materials. Current Opinion in Solid State and Materials Science 23, 13–27 (2019). 5. Dong, X. et al. Solvatochromism based on structural color: Smart polymer composites for sensing and security. Materials & Design 160, 417–426 (2018). 6. Rezaei, S. D. et al. Tunable, Cost-Effective, and Scalable Structural Colors for Sensing and Consumer Products. Advanced Optical Materials 7, 1900735 (2019). 7. Sandt, J. D. et al. Stretchable Optomechanical Fiber Sensors for Pressure Determination in Compressive Medical Textiles. Advanced Healthcare Materials 7, 1800293 (2018). 8. Kolle, M. et al. Bio-inspired band-gap tunable elastic optical multilayer fibers. Advanced Materials 25, 2239–2245 (2013). 9. Gupte, V. G. Expressing colors numerically. in Color Measurement: Principles, Advances and Industrial Applications (ed. Gulrajani, M. L.) (Woodhead Publishing, 2010). 10. Elliot, A. J. Color and psychological functioning: a review of theoretical and empirical work. Front Psychol 6, (2015). 11. Kaufmann, J. Advances In Medical Textile Applications. Textile World 166, 36–39 (2016). 12. Ng, J. L., Collins, C. E. & Knothe Tate, M. L. Engineering mechanical gradients in next generation biomaterials – Lessons learned from medical textile design. Acta Biomaterialia 56, 14–24 (2017). 13. Ramelet, A.-A. Compression Therapy. Dermatologic Surgery 28, 6–10 (2002). 14. Zarchi, K. & Jemec, G. B. E. Delivery of compression therapy for venous leg ulcers. JAMA Dermatology 150, 730–736 (2014). 15. Moffatt, C. Variability of pressure provided by sustained compression. Int. Wound J. 5, 259–265 (2008). 16. Mosti, G. Elastic stockings versus inelastic bandages for ulcer healing: a fair comparison? Phlebology 27, 1–4 (2012). 17. Keller, K., Krenzer-Scheidemantel, G. & Meyer, T. A Systematic Analysis of the Compression Pressure in the Compression Therapy for Scars in Childhood with the Help of the Kikuhime® Pressure Device. Zentralbl Chir 139, 638–642 (2014). 18. O’Meara, S., Cullum, N., Nelson, E. A. & Dumville, J. C. Compression for venous leg ulcers. Cochrane Database Syst Rev. CD000265 (2012) doi:10.1002/14651858.CD000265.pub3. 19. Sen, C. K. et al. Human skin wounds: a major and snowballing threat to public health and the economy. Wound Repair And Regeneration: Official Publication Of The Wound Healing Society [And] The European Tissue Repair Society 17, 763–771 (2009). 20. Mousa, A. Y., Richmond, B. K. & AbuRahma, A. F. Review and update on new horizon in the management of venous ulcers. Vascular And Endovascular Surgery 48, 93–98 (2014). 21. Partsch, H. Compression for the management of venous leg ulcers: which material do we have? Phlebology 29, 140 (2014). 22. Partsch, H. & Mosti, G. Comparison of three portable instruments to measure compression pressure. Int. Angiol. 29, 426–430 (2010).

23. Brophy-Williams, N., Driller, M. W., Halson, S. L., Fell, J. W. & Shing, C. M. Evaluating the Kikuhime pressure monitor for use with sports compression clothing. Sports Eng 17, 55–60 (2014). 24. Ashley, C. W. The Ashley book of knots. (1944). 25. History and science of knots. vol. 11 (World Scientific Publishing Co., Inc., River Edge, NJ, 1996). 26. Patil, V. P., Sandt, J. D., Kolle, M. & Dunkel, J. Topological mechanics of knots and tangles. Science 367, 71–75 (2020). 27. Hansen, C. M. Hansen solubility parameters : a user’s handbook. (Boca Raton : CRC Press, c2007., 2007). 28. Heavens, O. S. Optical Properties of Thin Solid Films. (1955). 29. Kolle, M. Photonic structures inspired by nature. [electronic resource]. (Berlin ; Heidelberg ; New York : Springer, c2011., 2011). 30. Spectral Reflectance Calculator for Thin-Film Stacks. https://www.filmetrics.com/reflectance- calculator?wmin=300&wmax=995&wstep=1&angle=0&pol=mixed&units=nm&mat[]=Air&d[]=0 &mat[]=Cu&d[]=15&mat[]=Air&d[]=0&sptype=r. 31. RefractiveIndex.INFO - Refractive index database. https://refractiveindex.info/. 32. Refractive Index Database – Table of Refractive Index Values for Thin Film Thickness Measurement. https://www.filmetrics.com/refractive-index-database. 33. Aguirre, C. I., Reguera, E. & Stein, A. Tunable Colors in Opals and Inverse Opal Photonic Crystals. Adv. Funct. Mater. 20, 2565–2578 (2010). 34. Nair, R. V. & Vijaya, R. Photonic crystal sensors: An overview. Progress in Quantum Electronics 34, 89–134 (2010). 35. Applegate, M. B. et al. Silk: A Different Kind of “Fiber Optics”. Optics & Photonics News, OPN 25, 28–35 (2014). 36. Zhao, Y., Ying, Y. & Wang, Q. Latest research progress on methods and technologies for tunable photonic crystals. Optics & Laser Technology 64, 278–287 (2014). 37. Yue, Y. & Gong, J. P. Tunable one-dimensional photonic crystals from soft materials. Journal of Photochemistry and Photobiology C: Photochemistry Reviews 23, 45–67 (2015). 38. Kamita, G. et al. Biocompatible and Sustainable Optical Strain Sensors for Large-Area Applications. Advanced Optical Materials 4, 1950–1954 (2016). 39. Piriya V.S, A. et al. Colorimetric sensors for rapid detection of various analytes. Materials Science and Engineering: C 78, 1231–1245 (2017). 40. FAO’s Director-General on How to Feed the World in 2050. Population and Development Review 35, 837–839 (2009). 41. Tilman, D., Balzer, C., Hill, J. & Befort, B. L. Global food demand and the sustainable intensification of agriculture. Proceedings of the National Academy of Sciences of the United States of America 108, 20260–20264 (2011). 42. Feeding 9 Billion - National Geographic. Feeding 9 Billion - National Geographic http://www.nationalgeographic.com/foodfeatures/feeding-9-billion/. 43. Cassidy, E. S., West, P. C., Gerber, J. S. & Foley, J. A. Redefining agricultural yields: from tonnes to people nourished per hectare. Environ. Res. Lett. 8, 034015 (2013). 44. Greenwell, H. C., Laurens, L. M. L., Shields, R. J., Lovitt, R. W. & Flynn, K. J. Placing microalgae on the biofuels priority list: a review of the technological challenges. J. R. Soc. Interface 7, 703–726 (2010). 45. Mata, T. M., Martins, A. A. & Caetano, Nidia. S. Microalgae for biodiesel production and other applications: A review. Renewable and Sustainable Energy Reviews 14, 217–232 (2010). 46. Becker, E. W. Micro-algae as a source of protein. Biotechnology Advances 25, 207–210 (2007).

47. Spolaore, P., Joannis-Cassan, C., Duran, E. & Isambert, A. Commercial applications of microalgae. Journal of Bioscience and Bioengineering 101, 87–96 (2006). 48. Greene, C. et al. Marine Microalgae: Climate, Energy, and Food Security from the Sea. Oceanog 29, (2016).