This work introduces formulae of Fresnel type related to reflection and transmission of a plane electromagnetic wave from a moving boundary separating two isotropic dielectrics. The dielectrics themselves remain immovable, so, the ensuing material formation represents an example of an activated dynamic material assembled from the LC-arrays serving as the discrete versions of each dielectric.

The recent development of materials with autonomous repair capabilities has opened an exciting new field of polymer science expected to impact nearly every facet of modern society. Similar to natural systems, these "self-healing" materials sense when their structural integrity has been compromised (e.g., due to wear or damage) and respond with a viable repair mechanism. Despite the extraordinary number of successes and advances in this area, a means to ascertain instantaneous knowledge of a material's structural integrity, and more importantly, when it has been compromised, remains a considerable challenge in current systems and materials. To address this challenge, we report recent efforts toward the development of an electronically conductive material that is structurally dynamic and responds to various types of external stimuli. In particular, we have developed new synthetic methodology to prepare a variety of organometallic polymers containing a novel benzobisimidazolylidene or bis(benzoimidazolylidene) ligand, which is comprised of two linearly opposed N-heterocyclic carbenes (NHCs) annulated to a common linker, and various types of transition metals in the polymer's main-chain. Using this approach, polymers with molecular weights up to 10⁶ Da were prepared and cast into robust thin films. Using four-point probe technique, the inherent conductivities of these materials were found to be on the order of 10⁻³ S/cm. Secondly, the dynamics of these polymers were probed in solution using gel permeation chromatography. At specific cross-linker loadings, thermally-responsive gels were obtained. Collectively, these experiments suggested that the essential features for a thermally-responsive, structurally dynamic, conjugated organometallic polymer were developed. Efforts toward probing their ability to display self-healing characteristics in the solid-state are described. The inherent conductivity of the polymers permitted the healing behavior of thin films to be observed by scanning electron microscopy in the absence of a dopant. Long range goals of implementing and utilizing these materials in electronic circuits and other advanced devices are also described. An additional approach towards a dynamic material utilized functional imidazolium-based ionic liquids. A series of functional ionic liquids were produced by appending N-substituents containing pendant halides, alkynes, azides, furans and maleimides. These functional groups allowed for polymerization and crosslinking. The physical properties of the imidazolium monomers, as well as the resulting polymers, could be tuned by altering the anion. When a trifunctional monomer is used in conjunction with the polymerization of difunctional ionic liquids an insoluble crosslinked material forms. This behavior, combined with NHCs ability to bind transition metals as ligands and catalyze various organic transformations, provides potential for this system to be used as a method for catalyst recovery and ultimately catalyst recycling. / text

"Recently, there has been some good interest in the field of Dynamic Materials, also referred to as Spatio-Temporal Composites. These materials have been theoretically attributed to show ability to switch their electromagnetic properties in time, as contrast to the spatial variations shown by regular materials of non-dynamic nature, existing naturally. Though there is no exhibition of dynamic material in nature yet, there are suggestions for its synthesis. This paper follows the idea of using standard lossless transmission line model approximating a material substance. Such a material though not truly homogeneous, could be made to vary its properties in time. The aim of this work is to test this idea for its functional efficiency in comparison to analytical results obtained from earlier works on the subject. We make use of Spice simulation for this. An important aspect of this work is to facilitate the dynamic operations in a static environment. Almost all the simulators available today like Spice, ADS, etc intrinsically provide no ability for parameter variations in time. Nonetheless, we make use of certain popular tricks to implement circuits imitating the dynamic circuit components we need. Such implementations are separately tested to demonstrate their success in providing us with the dynamic environment we desire. Finally, within the limitations of the computing capabilities, we could successfully show an agreement between the results obtained and the existing theory. "

This dissertation is composed of seven chapters, detailing advances within the area of sulfur polymer chemistry and processing, and highlights the relevance of the work to the fields of polymer science, energy storage, and optics that are enabled through the development of novel high sulfur-content copolymers as discussed in the following chapters. The first chapter is a review summarizing both the historical forays into utilization of elemental sulfur in high sulfur-content materials and the current research on the incorporation of sulfur into novel copolymers and composites for high value added applications such as energy production/storage, polymeric optical components, and dynamic/self-healing materials. Although recent efforts by the materials and polymer chemistry communities have afforded innovative sulfur containing materials, many studies fail to take advantage of the low cost and incredible abundance of sulfur by incorporating only minimal quantities into the end products. A fundamental challenge in the preparation of sulfur-containing polymers is simultaneous incorporation of high sulfur-content through facile chemical methods, to truly use the element as a novel feedstock in copolymerizations. Contributing to the challenge are the intrinsic limitations of sulfur (i.e., low miscibility with organic solvents, high crystallinity, and poor processability). The emphasis in chapter 1 is the critical development of utilizing sulfur as both a reagent and solvent in a bulk reaction, termed inverse vulcanization. Through this methodology we can directly prepare materials which retain the advantageous properties of elemental sulfur (i.e., high electrochemical capacity, high refractive index, and liable bond character), obviate the processing challenges, and enable precise control over composition and properties in a facile manner. The second chapter focuses on advancement in colloid synthesis, specifically an example mediated by in-situ reduction of organometallic precursors (ClAu^IPPh₃) by elemental sulfur at high temperatures. In chapter 2, elemental sulfur is employed both as a reactant and novel solvent, generating composite composed of well-defined gold nanoparticles (Au NPs) fully dispersed in a sulfur matrix. While the synthesis of Au NPs in molten sulfur was a novel development the challenge of analyzing the particles directly within the sulfur composite matrix by microscopy techniques required improvement of the composites mechanical properties. To overcome this issue, a one-pot reaction in which the Au NPs were initially synthesized, was vulcanized through an ambient atmosphere-tolerant bulk copolymerization by the addition of a difunctional comonomer (divinylbenzene). The improved composite integrity enabled microtoming and transmission electron microscopy analysis of the particles within the crosslinked reaction matrix. Due to the facile capabilities of directly dissolving the comonomers within the molten sulfur the inverse vulcanization methodology provides a simple route to prepare stable, high sulfur-content copolymers in a single one-pot reaction. The third chapter expands upon the methodology for direct dissolution of difunctional comonomers into molten elemental sulfur to afford chemically stable copolymer. A major challenge associated with the high temperature (i.e., 185 °C) bulk copolymerization reactions between sulfur and vinyl comonomers (i.e., divinylbenzene, DVB) is the high volatility of the organic monomers at elevated temperatures (BP of DVB = 195 °C). To obviate this problem required a novel monomer with an increased boiling point for successful scaling of the inverse vulcanization methodology. The work presented in chapter 3 details the employment of 1,3-diisopropenylbenzene (DIB, BP = 231 °C) to enable larger scale bulk inverse vulcanization reactions, allowing facile control over thermomechanical properties by simple variation in copolymer composition (50–90-wt% S₈, 10–50-wt% DIB). Poly(Sulfur-random-1,3-diisopropenylbenzene) ((poly(S-r-DIB)) copolymers prepared via the inverse vulcanization methodology possess substantially improved processing capabilities compared with elemental sulfur. A facile demonstration of improved processability is the generation of free-standing micropatterned structures using a high sulfur content liquid pre-polymer resin that can be poured into a mold and cured into the desired final form. The highest weight percentage copolymer (i.e., 90-wt% S₈) was also demonstrated to improve cycle lifetimes and capacity retention (823 mAh•g⁻¹ at 100 cycles) of a Lithium-Sulfur (Li-S) cell when the copolymer was utilized as the active material instead of elemental sulfur. Chapter four focuses on the optimization of Li-S cell performance as a function of copolymer composition and provides a more thorough understanding of the means by which copolymer active material improves battery performance. A substantial challenge associated with Li-S cells is the fast capacity fade and short cycle lifetimes that result from loss of the active material (i.e., sulfur) during normal cycling processes. The field has generally addressed these issues by encapsulation of the sulfur in a protective shell (e.g., polymeric, carbonaceous, or metal oxide in nature) in an attempt to sequester the active material. However, encapsulation of sulfur is non-trivial and leads to low loadings of sulfur, resulting in a low energy density within the final cell. To address the challenges associated with maintaining high capacity and long cycle lifetimes while employing an active material which is low cost, generated in a facile manner, and has a high sulfur content required a novel approach. In the work presented in chapter 4 we prepared high sulfur content copolymers via the inverse vulcanization methodology, which meet all the requirements necessary of an active material, and investigated the performance of Li-S batteries as a function of the copolymer composition. A survey of several poly(S-r-DIB) copolymer compositions were prepared with DIB compositions ranging from 1-50-wt% DIB (i.e., 50-99 wt% sulfur) and screened to determine optimal compositions for optimal Li-S battery performance. From this analysis it was determined that copolymers with 10-wt% DIB (90-wt% S₈) were optimal for producing Li-S batteries with high capacity and long cycle lifetimes. 10-wt% DIB copolymers batteries ultimately achieved long cyclic lifetimes and maintained high capacity (>600 mAh/g at 500 cycles). Chapter five details the optimization of conditions necessary to generate large scale (>100 g) inversely vulcanized sulfur copolymers and their application towards Li-S batteries. As previously stated a significant challenge in the Li-S battery field is the production of a Li-S active material with improved performance that is low cost, synthesized in a facile manner, and possesses high sulfur content. To date poly(S-r-DIB) copolymers prepared via the inverse vulcanization methodology afford some of the longest cycle lifetimes and highest capacity retention for polymeric active materials. However, initial inverse vulcanization reactions investigated for preparing active materials were performed on 10 gram scales. The goal of the work presented in chapter 5 was to prepare materials on a scale applicable to fabrication of several prismatic Li-S cells, each of which requires several grams of active material. However, scaling up of the reaction to a kilogram and utilizing the traditional inverse vulcanization conditions (i.e., 185 °C) results in catastrophic degradation as a consequence of the Trommsdorf effect. To address this challenge required decreasing the radical concentration within the bulk copolymerization, which necessitated performing the kilogram scale inverse vulcanization reactions at lower temperatures (i.e., 130 °C) over a longer reaction period. Decreasing the temperature generates materials that are nearly identical in thermomechanical properties to smaller scale samples and the battery performance is likewise comparable (>600 mAh/g at 500 cycles). The key advantage of performing the inverse vulcanization reaction at lower temperatures is that additional monomers, with lower boiling points or degradation issues, can be utilized and the increased gelation time, enables facile incorporation of additives (e.g., carbon black or nanoparticles) into the reaction. Chapter six focuses on the development of poly(S-r-DIB) copolymers as novel mid-infrared (mid-IR) transmitting materials and the analysis of the optical properties as a function of copolymer composition. A challenge in the optical science community is the limited number of materials applicable to the development of innovative optical components capable of functioning in the mid and far-IR regions. Semi-conductor and chalcogenide glasses have been widely applied as device components in infrared optics due to their high refractive indices (n ~2.0–4.0) and high transparency in the infrared region (1–10 μm). However, such materials are also expensive, difficult to fabricate, and toxic in comparison to organic polymers. On the other hand organic polymers are easily processed, low cost, and generated from easily accessible raw materials. Unfortunately, polymeric materials generally have low refractive indices (n<1.65) and are prepared from monomers with functional groups that are highly absorbing at mid-IR and longer wavelengths. Chapter 6 details the realization through the inverse vulcanization methodology of the first example of a material that is high refractive index and low mid-IR absorption, but also low cost and easily processable. Critical to achieving a polymeric material which was appropriate for mid-IR applications was the high sulfur content and the absence of functional groups, both of which are afforded by the facile copolymerization process. By simply controlling copolymer composition the optical properties of the material were tailorable; allowing adjustment of the refractive index from ~1.75 (50-wt% DIB) to ~1.875 (20-wt% DIB). Finally, through facile techniques, high quality copolymers lenses were prepared and we demonstrated the high optical transparency over several regions of the optical spectrum, from the visible (400–700 nm) all the way to the mid-IR (3–5μm). Poly(S-r-DIB) copolymers demonstrated high transparency to mid-IR light, but still maintain the processing capabilities of an organic polymer, the first example of such a material to possess both qualities. Ultimately the inverse vulcanization methodology offers a novel route to low cost, high refractive index, IR transparent materials, opening up unique opportunities for polymeric optical components within the optical sciences field. The seventh chapter discusses utilization of the inverse vulcanization methodology as a means to prepare and control the dynamic behavior of sulfur copolymers for potential applications towards self-healing materials. The incorporation of dynamic covalent bonds into conventional polymer architectures, either directly within the backbone or as side-chain groups, offers the stability of covalent bonds but with the ability of stimuli-responsive behavior to afford a change in chemical makeup or morphology. Traditionally the installation of such functionality requires the use of disparate, orthogonally polymerizable functional groups (i.e., vinyl) and discrete design of the comonomers utilized to generate a responsive copolymer. Therefore, a challenge in developing novel dynamic copolymers is the ability to install stimuli-responsive functionality directly as a result of the copolymerization without the need for rigorous synthetic monomer design and complex copolymerization techniques. In chapter 7 we discuss the analysis of poly(S-r-DIB) copolymers with rheological techniques to assess the composition dependent dynamic behavior. Aided by the bulk nature of copolymerization, the feed ratio of S₈ and DIB directly dictates copolymer microstructure; thus the sulfur rank between the organic groups (i.e., DIB) was tailorable from a single sulfur (thioether) to multiple sulfurs (pentasulfide). Control over sulfur content and number of S–S enables control over the dynamic behavior, as monitored via in-situ rheological techniques. The highest sulfur-content copolymers (80-wt% S₈, 20-wt% DIB) showed the fastest response when under shear stress due to the large number of S–S bonds. On the other hand when no dynamic bonds were present in the copolymer (i.e.; 35-wt% S₈, 65-wt% DIB) there is no dynamic behavior and full recovery of the pristine mechanical properties was not observed. The facile synthesis and simple control over copolymer microstructure affords the inverse vulcanization methodology an advantage over other dynamic materials, and provides potential secondary qualities (i.e., high refractive index) built directly into the structure.

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This work is a numerical and analytical study of wave motion through dynamic materials (DM). This work focuses on showing several results that greatly extend the applicability of the checkerboard focusing effect. First, it is shown that it is possible to simultaneously focus dilatation and shear waves propagating through a linear elastic checkerboard structure. Next, it is shown that the focusing effect found for the original €œperfect€� checkerboard extends to the case of the checkerboard with smooth transitions between materials, this is termed a functionally graded (FG) checkerboard. With the additional assumption of a linear transition region, it is shown that there is a region of existence for limit cycles that takes the shape of a parallelogram in (m,n)-space. Similar to the perfect case, this is termed a €œplateau€� region. This shows that the robustness of the characteristic focusing effect is preserved even when the interfaces between materials are relaxed. Lastly, by using finite volume methods with limiting and adaptive mesh refinement, it is shown that energy accumulation is present for the functionally graded checkerboard as well as for the checkerboard with non-matching wave impedances. The main contribution of this work was to show that the characteristic focusing effect is highly robust and exists even under much more general assumptions than originally made. Furthermore, it provides a tool to assist future material engineers in constructing such structures. To this effect, exact bounds are given regarding how much the original perfect checkerboard structure can be spoiled before losing the expected characteristic focusing behavior.