Topological mechanics of knots and tangles

Patil, Vishal; Sandt, Joseph D.; Kolle, Mathias; Dunkel, Jörn

doi:10.1126/science.aaz0135

Cited by 104 publications

(92 citation statements)

References 29 publications

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“…studied the topological mechanics of knots and tangles using the mechanochromic fibers, which was fabricated by cladding alternative layers with different refractive indexes on the elastic core. [ 131 ] Suffered from different strains, various structural colors were exhibited on the fiber due to the thickness change of cladded layers. Kinds of knots and tangles were achieved on the mechanically sensitive fibers, and their stress variation during tightening process could be analyzed according to the mechanochromic response ( Figure a).…”

Section: Applications Of Mechanochromic Structural‐colored Materialsmentioning

confidence: 99%

“…As discussed above, stress applied on the mechanochromic materials can triggered structural color shift, which is correlated with the stress intensity. Therefore, mechanochromic structural‐colored materials can be used as energy‐free mechanical sensors, serving various domains like physics, [ 131 ] healthcare, [ 43,62 ] and engineering. [ 132 ] For instance, Patil et al.…”

Section: Applications Of Mechanochromic Structural‐colored Materialsmentioning

confidence: 99%

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Mechanochromism of Structural‐Colored Materials

Chen

Hong

2020

Advanced Optical Materials

131

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In comparison with pigmentary colors, structural colors are with superior chemical stability and are resistant to photobleaching, making them promising candidates for color displays. What is more, the use of toxic dyes can be avoided by utilizing structural-colored materials to display various hues. Structural colors are widespread in nature and observed in opals, [3] beetles, [4] tropical fish, [5] peacock feathers, [6] chameleons, and similar iridescent materials. [7-9] Along with the growing understanding of the morphology and mechanism of natural structural-colored materials, their artificial counterparts have been manufactured with improved performance and functions consequently. Emerging structural-colored materials can be divided into three main categories according to their nanoscale architectures: photonic crystals (PCs), [10] liquid crystals (LCs), [11] and photonic glass. [12] Due to their ability to modulate visible light, the structural-colored materials have been applied in diverse domains such as optical waveguides, [13-16] luminescence enhancement, [17-19] photo electric devices, [20,21] photocatalysts, [22,23] anti-counterfeiting technologies, [24-26] and chemical and biological sensing. [27-29] With ingenious designs of nanostructures, a variety of responsiveness has been obtained on the structural-colored materials, corresponding to varying stimuli such as temperature, [30-32] solvent, [27] gases, [28] magnetic fields, [33] and external forces. [10-12] Among them, the mechanical responsive structural colors are able to visualize invisible stress in the materials, providing effective indicators for mechanical stimuli such as stretching, compression, or bending. Such mechanochromism can be directly achieved by the deformation-induced changes in periodic lattice constants of the structural-colored materials. [34,35] Recently developed mechanochromic structuralcolored materials have extended the responsive functions from conventional mechanical stimuli to complex signals such as electric stimuli. [10] In addition, although the color shift is a predominant method to achieve mechanochromic behavior, [34-36] increasing efforts have been made to develop mechanochromism based on polarization and transparence. [11,37,38] As one of the rapidly developing intelligent materials with multiresponse, [34,39,40] mechanochromic structural-colored materials have become promising in various applications, such as mechanical sensing, [11,41] colorful displays, [10,42] anti-counterfeiting, [26,37] and healthcare materials. [43,44] In this review, we summarize recent advances in mechanochromic structural-colored materials as shown in Figure 1.

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Section: Applications Of Mechanochromic Structural‐colored Materialsmentioning

confidence: 99%

Section: Applications Of Mechanochromic Structural‐colored Materialsmentioning

confidence: 99%

Mechanochromism of Structural‐Colored Materials

Chen

Hong

2020

Advanced Optical Materials

131

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“…Similar fibers also revealed the strain distributions in various knots, allowing their relative mechanical stability to be deduced. [ 76 ]…”

Section: Bottom‐up Approaches: Creating Structural Coloration Throughmentioning

confidence: 99%

Mechanochromism in Structurally Colored Polymeric Materials

Clough

Weder

Schrettl

2020

Macromol. Rapid Commun.

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of color in these materials has fascinated scientists for centuries, with early breakthroughs in understanding these phenomena made by Hooke, Newton [6] and Lord Rayleigh. [7] Another type of structural color arises from surface plasmon resonance, i.e., the resonant coupling between light and metallic nanostructures, which craftspeople have used since the Bronze age to impart color to ceramics and glass. [8,9] Over the past 30 years, fabricating structurally colored materials has been greatly facilitated by the rapid development of lithography-based technologies and directed self-assembly methodologies, which permit precise control of structural ordering at the nano-and microscale. Photonic and plasmonic materials can now be used to control and manipulate the flow of light in a plethora of colorful applications in the modern world, ranging from microoptical components [10] and lasing materials [11,12] to household products, such as nontoxic and photostable pigments for paints and cosmetics. [13-15] Artificial, structurally colored materials have been made predominantly from hard, rigid components. Their colors are stable as long as the nanostructure remains intact, but the application of excessive forces to these relatively brittle structures typically leads to an irreversible structural change and thus a change or loss of color. By contrast, many natural photonic coloration strategies are dynamic and responsive, such as in chameleons, [16] cephalopods, [17-20] tetra fish, [21] and the tortoise beetle. [22] For example, chameleon skin contains photonic arrays of high-refractive-index guanine nanocrystals that are embedded in a softer, low-refractive-index cytoplasmic matrix. [16] The reversible deformation of such composite structures enables the animal to reflect wavelengths of light in a spatially and spectrally selective manner for dazzling camouflage displays. Recent progress in synthetic approaches toward precisely ordered soft nanostructures has opened up a new class of structurally colored materials that also respond dynamically and reversibly to stimuli, such as pH, heat, light, and deformation. The design of responsive photonic structures has often been informed and inspired by natural coloration strategies. [3,23-25] To mimic natural materials and access responsive structural color, polymers are frequently employed as a component on account of their mechanical (low moduli and optionally elastic behavior) and optical (high transparency, low refractive Mechanochromic effects in structurally colored materials are the result of deformation-induced changes to their ordered nanostructures. Polymeric materials which respond in this way to deformation offer an attractive combination of characteristics, including continuous strain sensing, high strain resolution, and a wide strain-sensing range. Such materials are potentially useful for a wide range of applications, which extend from pressure-sensing bandages to anti-counterfeiting devices. Focusing on the materials design aspects, recent developments in this fi...

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“…Unlike the knotting mechanism of strings and ropes in daily life (e.g. Raymer & Smith 2007;Patil et al 2020), tying or untying knots in fluids with topological changes of vortex or magnetic field lines must go through the reconnection event (see Kida & Takaoka 1994;Yao & Hussain 2020). Magnetic reconnection (see Priest & Forbes 2000) is essential to alter the topology of field lines in MHD, and it is associated with extraordinary energy release (e.g.…”

Section: Introductionmentioning

confidence: 99%