Nonlinear conduction via solitons in a topological mechanical insulator

Networks of rigid bars connected by joints, termed linkages, provide a minimal framework to design robotic arms and mechanical metamaterials built of folding components. Here, we investigate a chain-like linkage that, according to linear elasticity, behaves like a topological mechanical insulator whose zero-energy modes are localized at the edge. Simple experiments we performed using prototypes of the chain vividly illustrate how the soft motion, initially localized at the edge, can in fact propagate unobstructed all of the way to the opposite end. Using real prototypes, simulations, and analytical models, we demonstrate that the chain is a mechanical conductor, whose carriers are nonlinear solitary waves, not captured within linear elasticity. Indeed, the linkage prototype can be regarded as the simplest example of a topological metamaterial whose protected mechanical excitations are solitons, moving domain walls between distinct topological mechanical phases. More practically, we have built a topologically protected mechanism that can perform basic tasks such as transporting a mechanical state from one location to another. Our work paves the way toward adopting the principle of topological robustness in the design of robots assembled from activated linkages as well as in the fabrication of complex molecular nanostructures.Mechanical structures composed of folding components, such as bars or plates rotating around pivots or hinges, are ubiquitous in engineering, materials science, and biology (1). For example, complex origami-like structures can be created by folding a paper sheet along suitably chosen creases around which two nearby faces can freely rotate (2–4). Similarly, linkages can be viewed as 1D versions of origami where rigid bars (links) are joined at their ends by joints (vertices) that permit full rotation of the bars (Fig. 1 A–C). Some of the joints can be pinned to the plane while the remaining ones rotate relative to each other under the constraints imposed by the network structure of the linkage (5). Familiar examples include the windshield wiper, robotic arms, biological linkages in the jaw and knee, and toys like the Jacob’s ladder (6) and the Hoberman sphere. Moreover, linkages and origami can be used in the design of microscopic and structural metamaterials whose peculiar properties are controlled by the geometry of the unit cell (7, 8).Open in a separate windowFig. 1.The chain of rotors in the flipper phase. (A) The translation symmetric system with θ=θ¯ constant. We show a linkage made from plastic and metal screws. (B) A computer sketch of the elastic chain (11): The masses are blue, rigid rotors are black, and springs are dashed red lines. The green arrows depict the amplitude of displacement of each mass of the edge-localized zero mode of the system. (C) A configuration of the linkage showing a soliton as a domain wall between right-leaning and left-leaning states. (D) A computer-simulated static configuration. The arrows beneath show the x projections of each rotor.Many of these examples are instances of what mechanical engineers call mechanisms: structures where the degrees of freedom are nearly balanced by carefully chosen constraints so that the allowed free motions encode a desired mechanical function. However, as the number of components increases, more can go wrong: lack of precision machining or undesired perturbations. Robustness in this sense is a concern relevant to the design of complex mechanical structures from the microscopic to the architectural scale, typically addressed at the cost of higher manufacturing tolerances or active feedback.Here, we take an alternative approach inspired by recent developments in the design of fault tolerant quantum devices (9). Consider, as an example, the quantized Hall conductivity of a 2D electron gas that is topologically protected in the sense that it cannot change when the Hamiltonian is smoothly varied (10). In this article, we present a topologically protected classical mechanism that can transport a mechanical state across a chain-like linkage without being affected by changes in material parameters or smooth deformations of the underlying structure, very much like its quantum counterparts.Kane and Lubensky (11) recently took an important step toward establishing a dictionary between the quantum and classical problems. Their starting point, which seems at first disconnected from the linkages we study here, was to analyze the phonons in elastic systems composed of stretchable springs. In particular they derived a mathematical mapping between electronic states in topological insulators and superconductors (10) and the mechanical zero modes in certain elastic lattices (12). The simplest is the 1D elastic chain, shown in Fig. 1B, inspired by the Su–Schrieffer–Heeger (SSH) model for polyacetylene (13), a linear polymer chain with topologically protected electronic states at its free boundaries. In the mechanical chain, the electronic modes map onto zero-energy vibrational modes with a nontrivial topological index, whose eigenvectors represented as green arrows in Fig. 1B are localized at one of the edges (11). An intriguing question then arises: Could these zero-energy edge modes propagate through the system in the form of finite deformations?We address this question by building and analyzing a linkage of rigid bars as an extreme limit of the 1D lattice of springs. This linkage allows no stretching deformations, yet it still displays the distinctive zero-energy mode localized at the edges (Fig. 1 and Movie S1). By nudging the rotors along the direction of the zero-energy mode (Fig. 1B and Movie S2), we provide a vivid demonstration of how the initially localized edge mode can indeed propagate and be moved around the chain at an arbitrarily small energy cost. We then show analytically and numerically that the mechanism underlying the mechanical conduction is in fact an evolution of the edge mode into a nonlinear topological soliton, which is the only mode of propagation in the chain of linkages that costs zero potential energy. The soliton or domain wall interpolates between two distinct topological mechanical phases of the chain and derives its robustness from the presence of a band gap within linear elasticity and the boundary conditions imposed at the edges of the chain. Although the topological protection ensures the existence of a domain wall, the dynamical nature of the soliton falls into two distinct classes that can ultimately be traced to the geometry of the unit cell. The prototypes we built therefore provide simple examples of structures that we dub topological metamaterials whose excitations are topologically protected zero-energy solitons (9).     

Prosthetic rehabilitation of an orbital and facial defect: a clinical report

For patients undergoing radical head and neck surgery, the deformity or physical defect adds to the agony. Rehabilitation of patients with such deformities is a challenge for the maxillofacial prosthodontist to enhance the esthetics and give psychological strength to the patient. This clinical report describes the rehabilitation, using a silicone prosthesis, of a large facial and orbital defect due to mucoepidermoid carcinoma.     

Hybrid hollow silica particles: synthesis and comparison of properties with pristine particles

In the past decade, interest in hollow silica particles has grown tremendously because of their applications in diverse fields such as thermal insulation, drug delivery, battery cathodes, catalysis, and functional coatings. Herein, we demonstrate a strategy to synthesize hybrid hollow silica particles having shells made of either polymer-silica or carbon–silica. Hybrid shells were characterized using electron microscopy. The effect of hybrid shell type on particle properties such as thermal and moisture absorption was also investigated.

Hybrid hollow silica particles, which show different properties compared to their pristine counterparts, have been synthesized.

In the past decade, hollow particles have attracted a great deal of interest because of their unique properties (e.g., high surface area, low density, and encapsulated cavity) compared with their dense counterparts. Hollow particles of several materials, including polymers, silica, titania, carbon, and zinc oxide have been reported.^1–9 Among these, hollow silica particles have attracted great attention from scientists because of their low material cost; well understood chemistry; and potential applications in widespread areas such as thermal insulation, drug delivery, energy storage, phase change encapsulation, catalysis, and superhydrophobic coatings.^10–18 Hollow silica particles can be synthesized using various approaches, such as by employing polymer micelles, immiscible solvent emulsions, inorganic or polymer (e.g., polystyrene) particles, and bacterial or virus cells as templates; by etching solid silica particles; or by spray pyrolysis.^19–25 Polymer micelles or emulsions provide very small particles, but making larger particles and tuning particle size are challenges in this approach. Similarly, the obtained particles typically fuse with one another, and achieving individually separated particles is a challenging task. Inorganic template etching is a time-consuming process, and in many cases, rudiments of inorganic templates remain in the hollow particle cavity if etching is incomplete. Unconventional techniques such as spray drying are inexpensive, but particle size control is difficult. The use of polystyrene particles as templates is attracting much attention because polystyrene particles can be synthesized at low cost with controlled sizes. Polystyrene particle-based synthesis of hollow silica particles involves three steps: (1) synthesis of polystyrene particles, (2) deposition of silica shells on polystyrene particles, and (3) removal of the polystyrene core by burning or dissolving to obtain hollow silica particles.Synthesis of hollow silica particles having shells made of silica alone (pristine hollow particles) is well reported. Some previous efforts have been made to attach surfactant molecules to the surfaces of mesoporous (not hollow) hollow particles. For example, Zhang et al.²⁶ first made porous silica particles by using cetyltrimethylammonium bromide (CTAB) as the template. In the next step, sodium carbonate-based etching was used to create cavities inside the porous particles, thus leading to porous-hollow silica particles. Then, 3-mercaptopropyl-trimethoxysilane (MPTS) was used to attach thiol-group ending surfactants to the surface. Similarly, Ribeiro et al.²⁷ coated solid silica particles with poly(butyl methacrylate) to make superhydrophobic coatings. Similarly, hollow polymer particles have been reported by depositing a polymer layer around solid silica particles, followed by etching the silica core. The same hollow polymer particles were also converted to hollow carbon particles by pyrolysis of polymer.^28,31 However, in this work, shell is made of a single material – polymer or carbon.^28,31 To the best of our knowledge, no work has reported hollow particles with a hybrid shell – shell made of two layers of different materials (inner layer: silica and outer layer: polymer or carbon). Additionally, no previous report has investigated the effect of such an additional layer on the properties of the hollow silica particles. We envisage that such additional layers can change the properties, such as stability against moisture and thermal conductivity, of pristine hollow silica particles.We report the synthesis of hybrid hollow silica particles, characterize these hybrid particles, and compare their properties with the properties of pristine hollow silica particles. Our investigations reveal that by changing the coating material, several intrinsic properties of hollow silica particles can be modified.Hollow silica particles were synthesized by modifying previously reported strategies based on the use of polystyrene particles (synthesis details in ESI S1^†) as a template.¹ For synthesizing hollow silica particles, in a typical experiment, 0.25 g of polystyrene particles were mixed into 100 mL of ethanol/water (ethanol 80 mL, water 20 mL). A suitable amount of tetraethyl orthosilicate was added to make complete shells around the polystyrene particles. To increase the TEOS hydrolysis, 28–30% of ammonium hydroxide was used as a catalyst. Fig. 1a depicts a schematic of hollow particle formation. Fig. 1b shows an SEM image of the polystyrene particles used as templates, and Fig. 1c shows a transmission electron microscope (TEM) image of polystyrene core-silica shell particles. Fig. 1d shows an SEM and Fig. 1e shows a high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) image of hollow silica particles obtained after burning the polystyrene core by keeping the sample at 550 °C for 4 h.Open in a separate windowFig. 1(a) Schematic showing synthesis of hollow silica particles. (b) SEM image of polystyrene particles. (c) TEM image of polystyrene core coated with silica shell (core–shell). (d) SEM and (e) HAADF-STEM image of hollow silica particles.There are several polymers that can be used to form coatings on silica.^28–31 Among these, the use of resorcinol is well studied.^28,31 In a typical experiment, 0.25 g of hollow particles (0.25 g) were mixed in water (100 mL). Ammonium hydroxide (28–30%, 500 μL), resorcinol (0.1 g), and formaldehyde (150 μL) were added to this reaction mixture. The reaction was allowed to proceed overnight (≈16 h) to completion. Expected mechanism for polymer coating formation is explained in ESI S3.^†Fig. 2a shows a schematic of the process used to make a polymer (polyresorcinol) coating on a silica shell. Fig. 2b shows low-magnification (i) and high-magnification (ii) TEM images of polymer-coated hollow silica particles. The polymer coating can be clearly seen (light in contrast) around the silica shell (dense in contrast). Though TEM imaging confirmed the presence of a polymer coating on the surface of the silica, to further confirm the formation of the coating, we applied electron energy loss spectroscopy (EELS). Energy dispersive X-ray (EDX) imaging is easy to use and is a readily available technique for analysing materials; however, EDX has a very low sensitivity to low-atomic-weight elements such as carbon and oxygen. Therefore, it was not a suitable technique for confirming the polymer presence. In contrast, EELS is known for its high sensitivity to low-atomic-weight elements (e.g., carbon and oxygen). Fig. 2c shows scanning HAADF-STEM (i) and EELS (ii) images of the polymer-silica hybrid shell. The coating was quite uniform, with some thicker areas on the free surfaces of particles and some thinner areas at the joints in aggregated particles (ESI S2^†). Therefore, if individual uniform coatings are required, the original hollow particle samples must be properly disaggregated.Open in a separate windowFig. 2(a) Schematic showing the polymer coating process. (b) TEM images of polymer-coated silica particles. (c) HAADF-TEM (i) and EELS S map (ii) showing polymer and silica layers of hybrid shell.Additionally, we demonstrated the formation of hybrid hollow silica particles with outer layers made of carbon and inner layers made of silica. To form a carbon layer on a silica shell, the initial polymer coating was sintered in an inert atmosphere (argon) at 550 °C for 4 h. Fig. 3a shows a schematic of polymer layer conversion to a carbon layer. Under these conditions, polymer converts into carbon instead of being completely oxidized into carbon dioxide and water. After heating under an inert atmosphere, brown polymer-coated particles changed to black carbon-coated particles. Separate carbon (outer) and silica (inner) layers were observed in TEM (Fig. 3b) and EELS images (Fig. 3c).Open in a separate windowFig. 3(a) Schematic showing conversion of polymer coating to carbon coating. (b) TEM images of carbon-coated particles. (c) EELS element map showing the carbon layer on a silica shell.In addition to making hybrid shell hollow particles, we investigated whether the coating affected the properties (e.g., thermal conductivity and moisture absorption) of the pristine hollow silica particles. We measured the thermal conductivity of pristine, polymer-coated, and carbon-coated particles. The results showed that polymer-coated particles had the lowest thermal conductivity and carbon-coated particles had the highest thermal conductivity of the three types. The Fig. 4 plot shows the thermal conductivities of the three types of particles, and respective insets show photos of corresponding particle samples. More details of the measurements are provided in ESI-S3.^† As expected, the polymer silica particles had lower thermal conductivity (0.022 ± 0.002 W m⁻¹ K⁻¹) than pristine hollow particles (0.024 ± 0.002 W m⁻¹ K⁻¹), whereas carbon-coated particles had higher thermal conductivity (0.036 ± 0.004 W m⁻¹ K⁻¹) than both the pristine and the polymer-coated particles. This information provides a new tool to achieve or tune thermal properties of hollow silica particles as desired. For example, for high-thermal-insulation materials, polymer-coated particles are ideal; whereas carbon-coated particles are more suitable where somewhat higher thermal conductivity, but hydrophobicity is required. We were expecting that a carbon coating will increase electrical conductivity of hollow particles, however, we observed that even carbon coated particles had an electrical resistance in the megaOhm range, i.e., behave as electrically insulators (measurement details in ESI S3^†). Although the thermal conductivity of polymer-coated or carbon-coated hollow silica particles can be further modified by modifying the coating thickness, in the present work, we did not investigate the effect of coating thickness on thermal conductivity in detail. We expect the thinner the coating, the lower the thermal conductivity will be. We observed in both the polymer- and carbon-coated particles that the coatings were not uniform. Some particles had thick and others thin coatings, indicating that coating nucleation was not uniform, and the coatings may have begun forming earlier on some particles than on others. We observed that carbon–silica hollow particles are hydrophobic in nature, staying afloat on water for several hours (ESI Fig. S4^†) and mixing in water only after vigorous stirring. It appears that, with stirring, water molecules enter the hollow particle cavities through the pores present in the carbon and silica shells and wet the inner parts of the cavities, thus causing the particles to mix in water.Open in a separate windowFig. 4Effect of different types of coatings on the thermal conductivity of hollow silica particles. Insets show the photos of respective particles.Additionally, we compared the moisture absorption properties of pristine hollow silica particles with those of polymer- and carbon-coated hollow silica particles (Fig. 5). Moisture absorption/desorption experiments were performed using a dual vapor gravimetric sorption analyser. We observed that polymer-coated particles absorbed less humidity compared with pristine particles at the same relative humidity. However, both materials had similar isotherm profiles in which the moisture adsorption capacity increased at relatively higher moisture concentrations. The carbon-coated particles, on the other hand, showed a completely different isotherm behaviour: an immediate increase in adsorption capacity was observed between 30% and 50% relative humidity. A sharp increase in moisture absorption at higher relative humidity (between 30–50%) appears due to the entry of water vapors inside the particles because of porous nature of carbon layer. Similar shape of isotherms for pristine and polymer coated particles indicates that both of these particles had similar surface groups (–OH), but lower absorption in polymer coated particles compared to pristine particles indicates that its surface has a small number of moisture absorbing groups (–OH) compared to pristine particles. The hysteresis between adsorption and desorption isotherms was found to be minimal, indicating that the samples had similar performance for adsorption or desorption process. We expect this information to be helpful for applications such as developing water-stable coatings or insulation materials by using hollow silica particles.Open in a separate windowFig. 5Effect on moisture adsorption and desorption process. Plot showing behaviour of hollow particles under different relative humidity conditions for pristine and coated samples.