The present teachings relate generally to colloidal geodes based on nanowires and, more particularly, to tunable nanowire geode-based colloidal materials.
A longstanding problem in the design of optical materials is engineering the response over multiple spectral bands. Solving this problem is an important component to manufacturing functional materials for energy harvesting, thermal management, and functional coatings. Materials for radiative cooling, for example, must strongly scatter visible wavelengths while strongly absorbing (and re-radiating) mid-infrared (IR) radiation, and ultraviolet (UV)-protective coatings must absorb or reflect UV light while remaining transparent in the visible. To engineer a response in multiple bands, one must combine components that have optical resonances in different spectral regions. Because the choice of components and the way they are combined generally depend on the application, it is slow to fabricate and deploy such materials.
There is a current need for extending the palette of available materials, understanding and designing the optical response of individual materials, understanding the optical response of assemblies of such materials, exploring the fundamental limits on what optical properties can be programmed, and what emergent properties might lie with-in a given design space, while establishing proof-of-concept in application areas, such as radiative cooling, UV-protection, and spectrally tuned/tunable camouflage. The availability of materials with fully prescribed optical responses in a window spanning UV (200 nm wavelength) to IR (20 μm or longer) would enable such applications or uses.
Therefore, it is desirable to evaluate, design, and fabricate nanowire geode-based materials with fully prescribed optical responses.
The following presents a simplified summary in order to provide a basic understanding of some aspects of one or more embodiments of the present teachings. This summary is not an extensive overview, nor is it intended to identify key or critical elements of the present teachings, nor to delineate the scope of the disclosure. Rather, its primary purpose is merely to present one or more concepts in simplified form as a prelude to the detailed description presented later.
An optically responsive material is disclosed, which includes a composite matrix and a plurality of colloidal nanowire geodes arranged within the composite matrix. The optically responsive material has an optical resonance in at least one spectral region. Implementations of the optically responsive material include where the composite matrix includes a polymer, such as polyvinylidene fluoride. Each of the plurality of colloidal nanowire geodes further may include a hollow colloidal microsphere, and a nanowire coupled to an inner surface of the hollow colloidal microsphere. The plurality of colloidal nanowire geodes is present in an amount from about 0.5% to about 30% based on a total weight of the optically responsive material. The hollow colloidal microsphere may include silicon dioxide. The hollow colloidal microsphere may include silicon nitride. The nanowire may include a semiconductor material. The nanowire may include silicon, phosphorous, boron, germanium, or a combination thereof. The nanowire can be doped with one or more impurities to modify a dielectric property of the colloidal nanowire geodes. The nanowire is selectively etched to scatter light in one or more spectral regions. Each of the plurality of colloidal nanowire geodes has an optical resonance in the ultraviolet spectral region. Each of the plurality of colloidal nanowire geodes has an optical resonance in the infrared spectral region. Each of the plurality of colloidal nanowire geodes has an optical resonance in the visible spectral region. The optically responsive material has an optical resonance in the ultraviolet spectral region, the infrared spectral region, the visible spectral region, or a combination thereof.
A colloidal nanowire geode is disclosed. The colloidal nanowire geode can include a hollow colloidal microsphere, and a nanowire coupled to an inner surface of the hollow colloidal microsphere. Implementations of the colloidal nanowire geode can include where the colloidal nanowire geode has an optical resonance in at least one spectral region. The colloidal nanowire geode has an optical resonance in the ultraviolet spectral region, the infrared spectral region, the visible spectral region, or a combination thereof. The hollow colloidal microsphere may include silicon dioxide. The hollow colloidal microsphere may include silicon nitride. The nanowire may include a semiconductor material. The nanowire may include silicon, phosphorous, boron, germanium, or a combination thereof. The nanowire is doped with one or more impurities to modify a dielectric property of the colloidal nanowire geodes. The nanowire is selectively etched to scatter light in one or more spectral regions.
A method of fabricating optically responsive materials is also disclosed. The method of fabricating optically responsive materials includes emulsifying a plurality of microscapsules from a hydrophobic silica in the presence of a hydrophilic metal nanoparticle in a water-in-oil media in a first emulsification process, emulsifying the plurality of microscapsules further in a water-in-oil-in-water media in a second emulsification process to produce a double emulsion; diluting the double emulsion to extract an oil portion of the double emulsion into a water phase to create a plurality of consolidated, porous microcapsule suspension, drying the suspension to produce a plurality of hollow microcapsules having metal nanoparticles disposed onto an interior surface of the plurality of hollow microcapsules, and depositing a nanowire onto the one or more metal nanoparticles to initiate and grow a plurality of nanowires disposed onto the interior surface of the plurality of hollow microcapsules. Implementations of the method of fabricating optically responsive materials can include selectively etching the plurality of nanowires to tune an optical resonance in at least one spectral region. The method of fabricating optically responsive materials may include filling one or more pores in an exterior surface of the plurality of microscapsules by atomic layer deposition. The plurality of nanowires may include silicon, phosphorous, boron, germanium, or a combination thereof. The plurality of nanowires is doped with one or more impurities to modify a dielectric property of the plurality of nanowires. The hydrophilic metal nanoparticles may include gold.
A method of programming optically responsive materials is also disclosed. The method of programming optically responsive materials includes inputting one or more structural parameters of a colloidal nanowire geode into a finite-element model simulation to predict an optical response result of the colloidal nanowire geode, synthesizing a colloidal nanowire geode according to the inputted structural parameters, measuring optical properties of the colloidal nanowire geode, and comparing the measured properties of the colloidal nanowire geodes to the predicted optical response result. Implementations of the method of programming optically responsive materials include where the finite-element model simulation can include a radiative-transfer approach or a Monte Carlo approach.
The features, functions, and advantages that have been discussed can be achieved independently in various implementations or can be combined in yet other implementations further details of which can be seen with reference to the following description.
The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments of the present teachings and together with the description, serve to explain the principles of the disclosure. In the figures:
It should be noted that some details of the figures have been simplified and are drawn to facilitate understanding of the present teachings rather than to maintain strict structural accuracy, detail, and scale.
Reference will now be made in detail to exemplary embodiments of the present teachings, examples of which are illustrated in the accompanying drawings. Wherever possible, the same reference numbers will be used throughout the drawings to refer to the same, similar, or like parts.
The present disclosure is directed to an enabling platform that provides: (1) an unprecedented combination of optical programmability and ease of fabrication: given a target optical response, it will be possible to specify a material structure that has the desired response, to fabricate it at scale, and to incorporate it into a functional material or device; (2) an understanding of the fundamental limits on what optical properties can be programmed in this hierarchical platform, and the new and unexpected properties that lie within the design space. The present teachings provide further understanding of and ability to model optical phenomena at multiple length scales, of soft and hard, ordered and disordered materials. Moreover, the present teachings focus on the fundamental and practical limitations of linear responses, as many applications would benefit from such control over multiple spectral ranges. Furthermore, this geode platform promises a marriage of optical functionality and processability not possible in currently known methods and materials. Such a capability can impact a broad range of technologies, including exterior coatings of space vehicles for heat management, broad spectrum camouflage, and radiatively cooled rooftop coatings. The present teachings can also provide a platform for using the geode-based concepts described herein to harness, for example, nonlinear or quantum optical effects.
The present teachings provide a paradigm for making materials with programmable optical response across multiple bands simultaneously: UV, visible, and IR. The present disclosure provides the use of a single materials platform that is versatile enough to address many different applications, making rapid design and deployment possible. To achieve this vision, two overarching challenges can be solved: (1) The engineering challenge is to combine programmability with ease of fabrication: given a target optical response, it must be possible to specify a structure that has that response, to fabricate it at scale, and to incorporate it into a functional material or device; (2) The scientific challenge is to understand the fundamental limits on what properties can be programmed with the platform, and what new and unexpected properties might lie within the design space.
Nanowire geodes are hollow colloidal particles with semiconductor nanowires decorating their interior, and whose composition and structure can be effectively “programmed” with nanoscale precision to yield a desired optical response. Because geodes combine the many optical properties of nanowires with the processability of conventional colloidal particles, they constitute a versatile photonic materials platform for a range of applications. Computation is essential because the parameter space is enormous, including the nanowire doping levels and morphologies, the sizes and volume fractions of the nanowires and microcapsules, the arrangement of the geodes in the final material, and the complex dielectric functions of all the components.
There is a current need for extending the palette of geode-based materials, understanding and designing the optical response of individual geodes, understanding the optical response of assemblies of geodes, exploring the fundamental limits on what optical properties can be programmed in the platform, and what emergent properties might lie with-in the design space, and establishing proof-of-concept in application areas, such as radiative cooling, UV-protection, and spectrally tuned/tunable camouflage. The availability of nanowire geode-based materials with fully prescribed optical responses in a window spanning UV (200 nm wavelength) to IR (20 μm or longer) would enable previously mentioned applications or uses.
To address the engineering challenge, hierarchically structured materials based on colloidal nanowire geodes (as shown in the top portion of
Geodes and composites thereof are structured hierarchically. Structure can be controlled at each length scale, which is critical to achieving our goal of programmability over multiple spectral bands. At the smallest scale are the nanowires, which can be grown and etched so that each nanowire has multiple segments with different doping levels, morphologies, and resonances. At the next scale are the geodes. Their microcapsules can be synthesized with different thicknesses and sizes, and the nanowires inside can be grown at different densities. At the largest scale is the composite material, consisting of many geodes. The density and arrangement of these geodes can be controlled, and a matrix material can be added. Each of these synthetic “control knobs” make orthogonal adjustments to the structure, in that the nanowire morphology can be tuned independently of the microcapsule size, for example.
However, the optical response is not orthogonal, which brings additional challenges in the development of such a system. For example, the cavity modes of the microcapsules can enhance, suppress, or augment the nanowire resonances. In assemblies of many geodes, the optical response depends on interference between waves scattered from individual nanowires and microcapsules as well as multiple scattering. Interference can give rise to additional resonances that can interact with the nanowire and cavity resonances. Multiple scattering can give rise to broad reflectance peaks in different spectral regions.
To address this scientific challenge—discovering what optical responses can be programmed and why others cannot—it can be helpful to understand the interplay between these effects. This provides further complications, particularly in the presence of multiple scattering. Computation is essential to achieving this goal because the parameter space is enormous, including the nanowire doping levels and morphologies, the sizes and volume fractions of the nanowires and microcapsules, the arrangement of the geodes in the final material, and the complex dielectric functions of all the components. But this complexity also opens the door to potentially unexpected and useful optical properties. For example, the coupling between multiple scattering and absorption allows corals to achieve nearly tenfold higher photosynthetic efficiency than terrestrial plants.
In the interest of enabling rapid discovery, design, and fabrication of geode-based materials with a prescribed optical response from the UV (200 nm wavelength) to the IR (20 μm or longer) further developmental alignment can be advantageous. Given a desired spectrum, it can be further advantageous to determine the material structure(s) that are closest to this spectrum. Where this is not possible, the physical reasons can be further studied. This aim can be aligned with four goals, as represented by the schematic in
Integration of experiment, computation, and theory. Ultimately, the goal is to minimize iteration between modeling and synthesis/assembly, where the ideal model is one that accurately predicts the response that the fabricated material will show. This is an achievable goal because the fundamental physical principles (Maxwell's equations) are known. Getting to an accurate and predictive model, however, will require iteration. To meet the fundamental aim of to deploy advanced materials at an accelerated pace with less cost, the computational approach must be efficient, which means approximations made should be tested in experiment. Furthermore, the scientific goal of discovering the fundamental limits on what responses are possible requires developing simplified, explanatory theories based on exploring the design space.
The integration of nanowire synthesis and characterization, colloids and emulsion templating, synthesis and characterization of hierarchically structured materials, and computational modeling of light-matter interactions combined with expertise and experimentation in different application areas, including radiative heat management, thermal emission, and structural color can further support the aforementioned goals.
As such, the major technical aims are to extend the palette of geode-based materials by developing new techniques for making geodes with controllable size and shell thickness and with different types of nanowires inside; to understand the optical response of individual geodes by developing models that describe the coupling between resonances at the nanowire and microcapsule scales and validating the models by comparison with experiment; to understand the optical response of assemblies of geodes by developing and validating models for multiple scattering and interference in assemblies of geodes; to explore the limits of what optical responses are possible by using the models developed to explore what optical responses can be programmed, given what is possible to synthesize; and further establishing proof of concept of these stated goals.
The development of theoretical models that explain limitations and tradeoffs in the geode platform can be generated, for example, given a particular coating thickness, determining a maximum possible radiative cooling achievable in the geode system, understanding the physics (e.g., Kramers-Kronig, multiple scattering) that governs this limit. Additionally, in a UV-protective coating, understanding a tradeoff between visible transparency and UV opacity, and what new emergent properties (e.g., absorption enhancement) may arise from the interplay of multiple scattering with the resonances. Once this is established as a proof of concept, methods for assembling geodes can be developed and, in concert with modeling and constrained optimization, used to build optimal geode-based structures for applications such as radiative cooling, UV protection, and broad-spectrum camouflage.
Semiconductor nanowires have arguably the most programmable optical response of any material system, but leveraging this versatility to make materials at scale is a difficult challenge. The geode platform addresses only part of that challenge, providing a way to make large quantities of nanowires and protect them. Further progress requires the understanding of how nanowires interact optically with the other components of the assembly. More broadly, the geode-based platform offers a compelling opportunity to explore fundamental and practical limitations of linear multispectral response.
Nanowire geodes are microcapsules with semiconductor nanowires filling their interior. In many ways, they are analogous to natural geodes—hollow rocks whose inner surface serves as a site for the nucleation and growth of crystalline minerals. Microcapsules are synthesized from silica particles via a double-emulsion-solvent-extraction scheme, drying, and calcination. The interior surface of the microcapsules is lined with metal nanoparticles that seed nanowire growth via the VLS mechanism. A microcapsule powder is then placed inside a chemical vapor deposition (CVD) reactor, where gaseous growth precursors diffuse through the porous microcapsule wall, decompose at the metal nanoparticles, resulting in nanowire growth.
Thus, the present teachings provide an optically responsive material made of a composite matrix, and a plurality of colloidal nanowire geodes arranged within the composite matrix, such that the optically responsive material has an optical resonance in at least one spectral region. The composite matrix can include a polymer, such as polyvinylidene fluoride, silicone, or others. In examples, each of the plurality of colloidal nanowire geodes further can include a hollow colloidal microsphere, and a nanowire coupled to an inner surface of the hollow colloidal microsphere. In other examples, the plurality of colloidal nanowire geodes is present in an amount from about 0.5% to about 30% based on a total weight of the optically responsive material. The hollow colloidal microsphere can include silicon dioxide, silicon nitride, combinations thereof or others. Nanowire material can include semiconductor materials, such as, but not limited to silicon, phosphorous, boron, germanium, or a combination thereof. In examples, these nanowires can be doped with one or more impurities to modify a dielectric property of the colloidal nanowire geodes. The nanowire is selectively etched, modified, or tailored to scatter light in one or more spectral regions, such as but not limited to the ultraviolet, infrared, visible, or a combination of the aforementioned spectral regions. Thus, the plurality of colloidal nanowire geodes has an optical resonance in these regions as well. The optically responsive material can include a colloidal nanowire geode including the materials or properties mention herein.
The present teachings described herein establishes two essential prerequisites: (1) the optical resonances of semiconductor nanowires can be programmed precisely over a wide spectral range; and (2) the nanowires can be grown inside spherical microcapsules to make geodes. There remain several open problems. The optical response of individual geodes—as well as assemblies of such—must be modeled and characterized. The toolkit for synthesizing geodes must be expanded to control the size and polydispersity of the microcapsules, as well as the structure and density of the nanowires within. New methods are also needed to assemble geodes in a matrix phase. After addressing these problems, the limits of the possible optical responses can be studied and this knowledge used to design optimal materials for applications.
A combination of existing capabilities will be completed to (i) synthesize geodes containing dopant-modulated nanowires, as previously shown in
The proposed optical programming will also require: (1) tuning geode dimensions (overall diameter, wall thickness) and internal nanowire density to generate the structures predicted from modelling, (2) “sealing” geodes against polymer infiltration, (3) independently engineering grooves and doping to simultaneously control both UV/visible and IR properties.
Geode diameter and wall thickness are set during the emulsion templating process and can be controlled via parameters such as particle weight fraction, surfactant weight fraction, and homogenization speed. While the density of dopant-modulated Si nanowires inside current geodes (2-5%) is already sufficient for the proposed work, nanowire density can be adjusted via Au nanoparticle density during emulsification.
Methods for fabricating optically responsive materials as provided herein include emulsifying a plurality of microscapsules from a hydrophobic silica in the presence of a hydrophilic metal nanoparticle in a water-in-oil media in a first emulsification process, emulsifying the plurality of microscapsules further in a water-in-oil-in-water media in a second emulsification process to produce a double emulsion, diluting the double emulsion to extract an oil portion of the double emulsion into a water phase to create a plurality of consolidated, porous microcapsule suspension, drying the suspension to produce a plurality of hollow microcapsules having metal nanoparticles disposed onto an interior surface of the plurality of hollow microcapsules, and depositing a nanowire onto the one or more metal nanoparticles to initiate and grow a plurality of nanowires disposed onto the interior surface of the plurality of hollow microcapsules. Examples of the methods of fabricating optically responsive materials can include selectively etching the plurality of nanowires to tune an optical resonance in at least one spectral region, or filling one or more pores in an exterior surface of the plurality of microscapsules by atomic layer deposition. In examples, the hydrophilic metal nanoparticles comprises gold. These optically responsive materials can be programmed by inputting one or more structural parameters of a colloidal nanowire geode into a finite-element model simulation to predict an optical response result of the colloidal nanowire geode, synthesizing a colloidal nanowire geode according to the inputted structural parameters, measuring optical properties of the colloidal nanowire geode, and comparing the measured properties of the colloidal nanowire geodes to the predicted optical response result. The finite-element model simulation can include a radiative-transfer approach or a Monte Carlo approach.
The synthesis process may be adapted to make smaller as well as more monodisperse geodes. The current approach for making geodes is efficient and scalable, but it works best for making geodes that are tens of micrometers, and it results in a polydisperse distribution. Interference effects and microcapsule resonances have broad peaks that occur at wavelengths comparable to the size of the capsule. To be able to tune these peaks throughout the visible and IR, capsules in the 1-10 μm range, or even smaller, are desired. The use of porous glass membranes, an established technique, can produce double emulsions with droplet diameters less than 10 μm. Incorporating silica or other nanoparticles inside the oil phase may lead to clogging, in which case different particle sizes, concentrations, and stabilizing agents can be explored to mitigate the problem. In parallel, the use of microfluidic methods can be used to reduce the polydispersity of geodes. These methods result in large (100-500 μm) droplets with low polydispersity, but the sizes can be reduced by subsequent application of the porous glass membrane technique. The resulting monodisperse geodes will be useful for applications in which the resonances of the microcapsules need to be precisely controlled or need to couple strongly to the nanowire resonances.
Maintaining a nanowire-air interface is important for many optical properties. While a porous microcapsule wall is essential for efficient precursor transport during nanowire growth, it can also allow for unwanted polymer infiltration upon composite formation. To prevent such infiltration, atomic layer deposition (ALD) can provide a route to “seal” geodes. ALD's self-limiting nature allows it to uniformly coat highly porous structures until pores are completely filled and precursor transport ceases. The choice of material can be dependent on the availability of ALD processes and its impact on the geode/composite optical properties. Materials used for this purpose can include Al2O3, TiO2, ZrO2, and HfO2.
Broad multispectral optical programming will ultimately require simultaneous control of nanowire groove dimensions as well as local carrier density. These parameters are strongly coupled in the baseline dopant-modulated Si system because segment doping is used to control the selective etch process, a situation that places undesirable constraints on geode design. Thus, the synthesis of geodes containing nanowires with a combination of Si and Ge segments can be done. In this system, the Si and Ge offer process orthogonality—Ge segments can be readily etched in H2O2 to create grooves (that dictate UV/visible response) while heavily doped Si segments (to control IR plasmonic response) are resistant to H2O2.
To understand the optical response at the largest scale of the system (assemblies of geodes) the response of an individual geode should be understood, which in turn depends on the response of the component nanowires and microcapsule. The calculated optical response for a geode can then be input into the calculation for microsphere packings. Models of the response of an individual geode are based on Mie theory for nanowires and microcapsules but will also account for the couplings between resonances.
Both approximate calculations and discrete simulations can be employed to calculate the optical properties of individual geodes. In the simplest approach, the response of the nanowires and microcapsules can be calculated separately to approximate the total response by combining the two. Next, the nanowires inside the microcapsules are treated as an effective medium, with a dielectric function determined by the density of nanowires (which can have a radial dependence) and their individual scattering and absorption cross-sections. In this mean-field approach, the cross-sections can be calculated directly from Mie theory for a layered sphere. The results from these approaches can be compared to numerical simulations in which the interaction of light with a discretized model of the entire geode is modeled. The use of finite-element methods, which are accurate and can account for large differences in scale (for example, between the size of the microcapsule and the modulations in the nanowire diameter in
To a first approximation, the behavior of light scattering/absorption of geodes in a matrix is a combined effect of the nanowire (
Finite-element simulations based on structures and parameters (density of nanowires, size of geode, etc.) from synthesis can be conducted. These results of these simulations can be compared to calculations using the approximate approaches in order to gauge the validity of the approximations. Where the approximations are valid, they will be used in the next two aims: understanding the response of assemblies of geodes and exploring the parameter space. The geodes will be synthesized, and the optical properties will be characterized and compared to predictions from the model. A microscope-based spectrometer that can measure the visible spectra of individual particles will be used, thus precluding any multiple scattering. A diffuse reflectance setup that can measure spectra from 400 nm to 50 μm will be utilized. To probe the full response, from the UV to mid-IR with a well-calibrated setup, instrumentation having a range of 200 nm to 20 μm which is temperature-controlled can be used. For these bulk measurements, dilute and/or thin powder samples of geodes are used to minimize multiple scattering.
To model the response of assemblies of geodes, the model for the optical properties of geodes is incorporated into models for multiple scattering and interference. Two approaches, including radiative-transfer theory and Monte Carlo simulations, are used. Both approaches take as input the phase function (angular scattering) and cross sections of individual geodes, and both make use of effective-medium (mean-field) theory.
With a radiative-transfer approach, light propagation in homogeneous random media can be described by the radiative transfer equation (RTE). The RTE is obtained from energy balance of scattered light intensity as:
where ŝ and ŝ′ are unit direction vectors, r is the position vector, Id is the diffuse specific intensity, ρ is the number density of scatterers, st is the extinction cross section, Itot is the total specific intensity, dω′ is the differential solid angle in the ŝ′ direction, and p(ŝ, ŝ′) is the phase function representing the probability density that light incident in the ŝ′-direction is scattered into the ŝ-direction. Equation (1) states that the ŝ-direction gradient in Id (left hand side) is due to the scattering of Id out of the ŝ-direction (ρst Id term) and the scattering of the total intensity from all other directions into the ŝ-direction (integral term). Within the radiative transfer model, light propagation is characterized by the extinction cross section (st), the phase function (ρ), and the scatterer density (ρ). Transmittance/reflectance/absorptance of a random media film are obtained by solving the RTE. The RTE can be simplified by the diffusion approximation, which assumes that Id is slowly varying over the space. The resulting diffusion equation provides an analytical solution for transmittance/reflectance/absorptance for a film.
The materials described previously can be characterized in terms of two lengths: transport mean free path (l*) and diffusive absorption mean free path (lda). l* is the length over which the direction of light propagation is randomized, and lda represents a length that diffusing light travels before being significantly absorbed. These lengths are obtained in terms of the RTE parameters by
where sa=st−ss is the absorption cross section with ss being the scattering cross section. l* and lda will be obtained by fitting experimentally measured transmittance and absorptance at different thicknesses to the solutions to the RTE or the diffusion equation. Alternatively, they can be determined from coherent backscattering measurement. When the random material is lossless, for a film of a thickness L>>l*, transmittance is roughly ˜l/L. When absorption is present, transmittance scales with thickness as exp(−kL), where k2=3(l*·lda).
The terms l* and lda can be calculated using mean-field theory, which is in general highly accurate in calculating scattering properties of optically dense media. Specifically, scattering units embedded in an effective medium are considered. For example, for randomly stacked non-overlapping monodisperse solid microspheres, the scattering units are a core-shell particle and an air volume. In the core-shell particle, the core is a solid microsphere and the shell is air; the air volume is a representative volume between the microspheres. In the mean-field approach, l* and lda of each scattering unit are calculated based on the Mie theory by taking an average scattering amplitude based on the volume fraction of each scattering unit.
The Monte Carlo approach is based on a scattering model. It is assumed that light interacts with randomly packed spherical particles. the differential cross-section as the product of a form factor F is calculated, which accounts for the scattering from individual particles and is calculated from Mie theory, and a structure factor S, which accounts for interference between waves scattered from different particles and is calculated using the Percus-Yevick approximation for the structure factor: dσ/dΩ=FS. The spheres are embedded in an effective medium whose refractive index comes from the Bruggeman approximation. This differential scattering cross section is used as input to the Monte Carlo simulation.
At each step in the simulation, photon packets move a random distance, sampled from an exponential distribution whose mean is the scattering length lscat=1/ρσ. After each step, they scatter into a random direction sampled from the phase function P(θ)=(dσ/dΩ)/σ. When any of the materials has a complex refractive index, the appropriate Mie solutions are calculated for absorbing materials. As the photons travel, their weights are reduced according to Beer's law, where lscat is replaced with the absorption length. The diffuse reflectance is then calculated by counting the trajectories that are scattered into the backward hemisphere. This simulation framework and results are illustrated in
Although previous studies show that the mean-field approach is a good approximation, even for dense and highly scattering samples, it is essential to account for the breakdown of mean-field theory at the boundary of the sample. When reflectance is calculated by solving Maxwell's equations on a supercell of the media, the interface effect is directly accounted for. But because such a direct calculation is computationally expensive, it is not practical, especially when calculations for many different design variables are required. Therefore, models of scattering from the interfaces of the samples should be developed and tested. These models also depend on the sample composition.
A theory is applied to model optical interaction at an interface of random media. Here Fresnel transmission/reflection at a boundary layer 910 of scattering media, geodes 908, is replaced by scattering within a finite region near the boundary defined as the optical boundary layer (OBL). In the air or polymer 904 super cell, incident light 902 is measured when transmitted through an optical boundary layer 910 and into/through an effective medium 912. The validity of the OBL theory was tested in experiment.
The OBL is used in concert with radiative-transfer theory to calculate reflectance and absorptance of assemblies of geodes for both top and bottom interfaces. The OBL calculation is integrated into the Monte Carlo method, in addition to the roughness calculation. To reduce computational time, the OBL approach can be simplified for material systems where optical interference effects can be ignored. In this case, light intensity reflected from the OBL into air and that transmitted from the effective medium through the OBL into air can be added and divided by the incident intensity to obtain reflectance.
The outcome of the experiments described above will be a set of multiscale models that can accurately predict the properties of any geode assembly. With such a model, the following three high-level aims can be pursued:
Exploring the parameter space and fundamental limits. It is important to understand which optical properties are and are not possible. To do this Bayesian optimization can be used to target specific desired extremal properties, such as complete visible transparency and complete UV opacity, or complete visible opacity and complete IR absorbance. An objective function is used such as a squared error over a broad spectrum. A large squared error suggests that some spectra cannot be accessed. It is important to understand the physical reasons for these limitations. Previous work has shown that this approach can lead to new physical understanding, which is useful in guiding the design of materials. For example, with solid microspheres, theory shows red hues cannot be accessed, owing to the tendency of solid microspheres to backscatter light more strongly in the blue. Based on this theory, a scheme of using hollow microspheres to generate red structural colors, has been devised and successfully implemented. A similar approach for the geode system can be utilized. Without seeking a general theory that would explain all possible limitations, instead, a simple and explanatory models that explain a specific limit or tradeoff is desired. The theoretical framework for setting the limit in such complex systems would be applicable to other systems as well and could suggest ways to circumvent the limitation (for example, changing the nanowire material).
Inverse design. The optimization approach also allows solving the inverse problem: for a given target response, determine the structure that can come closest to that response. An advantage of the radiative transfer/Monte Carlo multiscale modeling approach is that it is straightforward to incorporate constraints on what can be fabricated, because the models are specified in terms of experimental variables such as the volume fraction of geodes and the density of nanowires (note that this is not true of models such as finite-difference time-domain simulations). This approach will be used for proof-of-concept studies described herein.
Discovering novel properties. The determination of what unconventional optical responses lie within the design space is useful—for example, absorption enhanced by multiple scattering, or novel broadband properties arising from the coupling between resonances. Two areas are of interest: (i) geodes that are a few micrometers in size, in which case the capsule resonances may couple strongly to the nanowire resonances, and both interference and multiple scattering will be significant; and (ii) assemblies of different types of geodes (e.g., differing in capsule diameter or nanowire morphology).
Proof-of-concept studies are provided herein. The aim is to develop methods for assembling geodes and incorporating them into functional materials. This effort begins with experimentally characterizing optical properties (i.e., absorptance, transmission, and reflectance) of randomly packed hollow microspheres and then geodes, without matrix integration, to extract transport mean free path and diffusive absorption mean free path of the assembly. These optical measurements help identify and trace the source of resonant reflectance and absorptance peaks. The experimental measurements are then compared with computational modeling, which will either confirm robustness of the computational models or provide more accurate model parameters.
For alternate matrix integration, polymers, such as polyvinylidene difluoride (PVDF) and silicone may be used. The refractive index of PVDF (n˜1.4) and silicone (n˜1.4) and their optical transparency are important considerations. The requirements include (1) a matrix material that is compatible with or resistant to various terrestrial/extraterrestrial environmental stressors (e.g., UV, dust, temperature cycling, high-energy radiation) and (2) a facile geode incorporation process (i.e., easy mixing and even distribution) to enable large volume production. PVDF and silicone to meet many of these requirements. For ease of integration, low-viscosity PVDF solution and silicone monomers (before initiating polymerization) can be used to infiltrate the space between microspheres under vacuum and by capillary force. A planetary mixer can be used to homogenize the microsphere distribution in a polymer matrix.
For UV-protective coatings and spectrally tuned/tunable camouflage, the emergent cooperative optical properties of geodes could prove particularly advantageous. While the technique to integrate geodes into a polymer matrix would remain the same, geodes with strong UV absorption by capsule/nanowire resonance can be used for UV protection. Multiple scattering could then enhance the absorption in the UV. The geode capsule size can also be tuned to minimize visible scattering and thus maximize transmission in the visible. For spectrally tuned/tunable camouflage, the creation of geode/polymer composites with absorption bands selectively appearing in UV, visible, and/or IR, decoupled from high-reflectance spectral regions due to bulk light scattering can be employed. As an example, geode/polymer composites with high reflectance in IR with visible colors rendered by absorption due to capsule/nanowire resonance can be utilized.
While the present teachings have been illustrated with respect to one or more implementations, alterations and/or modifications may be made to the illustrated examples without departing from the spirit and scope of the appended claims. For example, it may be appreciated that while the process is described as a series of acts or events, the present teachings are not limited by the ordering of such acts or events. Some acts may occur in different orders and/or concurrently with other acts or events apart from those described herein. Also, not all process stages may be required to implement a methodology in accordance with one or more aspects or embodiments of the present teachings. It may be appreciated that structural objects and/or processing stages may be added, or existing structural objects and/or processing stages may be removed or modified. Further, one or more of the acts depicted herein may be carried out in one or more separate acts and/or phases. Furthermore, to the extent that the terms “including,” “includes,” “having,” “has,” “with,” or variants thereof are used in either the detailed description and the claims, such terms are intended to be inclusive in a manner similar to the term “comprising.” The term “at least one of” is used to mean one or more of the listed items may be selected. Further, in the discussion and claims herein, the term “on” used with respect to two materials, one “on” the other, means at least some contact between the materials, while “over” means the materials are in proximity, but possibly with one or more additional intervening materials such that contact is possible but not required. Neither “on” nor “over” implies any directionality as used herein. The term “conformal” describes a coating material in which angles of the underlying material are preserved by the conformal material. The term “about” indicates that the value listed may be somewhat altered, as long as the alteration does not result in nonconformance of the process or structure to the illustrated embodiment. The terms “couple,” “coupled,” “connect,” “connection,” “connected,” “in connection with,” and “connecting” refer to “in direct connection with” or “in connection with via one or more intermediate elements or members.” Finally, the terms “exemplary” or “illustrative” indicate the description is used as an example, rather than implying that it is an ideal. Other embodiments of the present teachings may be apparent to those skilled in the art from consideration of the specification and practice of the disclosure herein. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the present teachings being indicated by the following claims.
This application claims the benefit of U.S. Provisional Patent Application No. 63/376,794, filed on Sep. 23, 2022, which is hereby incorporated by reference in its entirety.
Number | Date | Country | |
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63376794 | Sep 2022 | US |