different core block chemistry. The key point for choosing the different chemistries of the two hydrophobic blocks is that the two blocks experience a high degree of mutual immiscibility. In the current experiment, polystyrene (PS) and poly(2,3,4,5,6-pentafluorostyrene) (PPFS) were employed as the different, third hydrophobic blocks in the two triblock copolymers (PAA 94 -b-PMA 103 -b-PS 117 and PAA 93 -b-PMA 99 -b-PPFS 100 ) (29). Equal molar amounts of the two triblock copolymers with different respective third blocks were dissolved in pure THF. EDDA was then added to reach a final 1:1 molar ratio of amine groups to acid groups. The diamines underwent complexation with the PAA blocks, thereby forming aggregates with PAA-diamine cores. Notably, these aggregates contained each of the triblock copolymers with both PS and PPFS hydrophobic blocks because of the simple trapping of unlike hydrophobic blocks in the same aggregate by PAA-diamine complexation. Next, introduction of water into the THF solution to a final ratio of THF:water = 1:2 provided for the formation of cylindrical micelles. However, the existence of the original mixed triblock copolymer aggregates, as a result of PAA and diamine complexation, forced the local co-assembly of unlike third hydrophobic blocks into the same micelle core. In addition, the lack of chain exchange in solution that disallows global chain migration and maintains nonequilibrated micelle structures, combined with the fact that the PAA chains in the corona of the newly formed micelles were still complexed with diamines and were not freely mobile within the micelle, guarantee the stability of the mixed-core micelle. The immiscibility of the two different hydrophobic blocks, PS and PPFS, eventually resulted in internal phase separation on the nanoscale, producing multicompartment micelles. The images shown in Fig. 4, A to D were taken after 4 days of aging a solution of mixed hydrophobic core cylinders. Internal phase separation is clearly indicated by the strong undulations along the cylinder surfaces and the TEM contrast variation along the cylinders. The larger, darker, and more spherical regions within the cylinders are hypothesized to be regions that are concentrated in PAA 94 -b-PMA 103 -b-PPFS 100 triblock copolymer. First, there is a higher interfacial energy between PPFS and PMA, relative to PS and PMA, causing more chain stretching within PPFS-rich core domains so as to limit PPFS interactions with surrounding PMA blocks. Second, the greater electron density of the PPFS block provides a greater ability to scatter electrons and produce darker images in the TEM. The thinner region of the undulating cylinder would then be occupied primarily by PAA 93 -b-PMA 99 -b-PS 117 (Fig. 4G). This internal cylinder phase separation only occurred at relatively higher amounts of water in the mixed solvent solutions. Cryo-TEM showed uniform cylinders without undulation on the surface at only 40% water/THF solution after 4 days (Fig. 4E). However, multicompartment cylinders could be obser...

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Dielectric elastomer generators (DEGs) for harvesting electrical energy from mechanical work have been demonstrated but the energy densities achieved are still small compared with theoretical predictions. We show that significant improvements in energy density (560 J/kg with a power density of 280 W/kg and an efficiency of 27%) can be achieved using equi-biaxial stretching, a mechanical loading configuration that maximizes the capacitance changes. We demonstrate the capacitance of dielectric elastomers subjected to equi-biaxial stretches is proportional to the fourth power of the stretch. Quantification of the individual energy contributions indicates that attaining higher conversion efficiencies is limited by viscous losses within the acrylic elastomer, suggesting that still higher conversion efficiencies with other elastomers should be attainable with our novel mechanical loading design.

Wrinkle patterns in compressed thin sheets are ubiquitous in nature and technology, from the furrows on our foreheads to crinkly plant leaves, from ripples on plastic-wrapped objects to the protein film on milk. The current understanding of an elementary descriptor of wrinkles-their wavelength-is restricted to deformations that are parallel, spatially uniform, and nearly planar. However, most naturally occurring wrinkles do not satisfy these stipulations. Here we present a scheme that quantitatively explains the wrinkle wavelength beyond such idealized situations. We propose a local law that incorporates both mechanical and geometrical effects on the spatial variation of wrinkle wavelength. Our experiments on thin polymer films provide strong evidence for its validity. Understanding how wavelength depends on the properties of the sheet and the underlying liquid or elastic subphase is crucial for applications where wrinkles are used to sculpt surface topography, to measure properties of the sheet, or to infer forces applied to a film.elastic sheets | wrinkles | curved topography W rinkles emerge in response to confinement, allowing a thin sheet to avoid the high energy cost associated with compressing a fraction e Δ of its length ( Fig. 1) (1-7). The wavelength, λ, of wrinkles reflects a balance between two competing effects: the bending resistance, which favors large wavelengths, and a restoring force that favors small amplitudes of deviation from the flat, unwrinkled state. Two such restoring forces are those due to the stiffness of a solid foundation or the hydrostatic pressure of a liquid subphase (Fig. 1A). Cerda and Mahadevan (1) realized that a tension in the sheet can give rise to a qualitatively similar effect ( Fig. 1B) and thereby proposed a universal law that applies in situations where the wrinkled sheet is nearly planar and subjected to uniaxial loading:Here the bending modulus B = Et 3 =½12ð1 − Λ 2 Þ (with E the Young's modulus, t the sheet's thickness, and Λ the Poisson ratio), whereas out-of-plane deformation is resisted by an effective stiffness, K eff , which can originate from a fluid or elastic substrate, an applied tension, or both. Eq. 1 is appealing in its simplicity, but it applies only for patterns that are effectively one-dimensional. In particular, it does not apply when the stress varies spatially or when there is significant curvature along the wrinkles. Here, we study two experimental settings in which these limitations are crucial: (i) indentation of a thin polymer sheet floating on a liquid, which leads to a horn-shaped surface with negative Gaussian curvature, and (ii) a circular sheet attached to a curved liquid meniscus with positive Gaussian curvature. In both cases, wrinkle patterns live on a curved surface, show spatially varying wavelengths, and are limited in spatial extent. The extent of finite wrinkle patterns in a variety of such 2D situations has recently been addressed (6,(8)(9)(10)(11) and was found to depend largely on external forces and boundary conditions. Howeve...

A strategy to control the electrical charge is developed to achieve high energy density of soft dielectric elastomer generators for energy harvesting. The strategy is analytically shown and experimentally demonstrated to produce the highest energy density ever reported for a soft generator.

We study the indentation of a thin elastic film floating at the surface of a liquid. We focus on the onset of radial wrinkles at a threshold indentation depth and the evolution of the wrinkle pattern as indentation progresses far beyond this threshold. Comparison between experiments on thin polymer films and theoretical calculations shows that the system very quickly reaches the Far from Threshold (FT) regime, in which wrinkles lead to the relaxation of azimuthal compression. Furthermore, when the indentation depth is sufficiently large that the wrinkles cover most of the film, we recognize a novel mechanical response in which the work of indentation is transmitted almost solely to the liquid, rather than to the floating film. We attribute this unique response to a nontrivial isometry attained by the deformed film, and discuss the scaling laws and the relevance of similar isometries to other systems in which a confined sheet is subjected to weak tensile loads.PACS numbers: 46.32.+x,46.70.De,62.20.mq When an elastic sheet is subjected to external forces, it is often implicitly assumed that the work done is stored in the deformed sheet. Under purely tensile loads, the work is stored primarily by stretching energy. When the forces are purely compressive, as in uniaxial buckling, the strain is typically negligible, and the work is instead stored as bending energy [1]. Under more complicated compressive forces, such as those required to confine a sheet in a box [2], the work is stored in localized (stressfocusing) zones that involve bending and stretching. In this Letter, we report a new response exhibited by the indentation of an elastic film floating at a liquid-gas interface. We show that for sufficiently large indentations, only a negligible fraction of the work done by the indenter is stored as elastic energy -the majority is stored in the gravitational and surface energies of the liquid.Interest in the indentation of elastic objects includes a range of metrological applications. Just as one tests an object's stiffness by poking it, controlled indentation is used in the measurement of internal pressure within polymeric [3] and biological [4][5][6][7][8] capsules and to determine the modulus of thin membranes [9]. These applications motivated theoretical studies of indented spherical shells, which suggested that 'mirror-buckling ' [10] (fig. 1a) occurs in the presence of an internal pressure [8]. Mirror buckling is the simplest possible isometric (i.e. strainless) deformation of an infinitely thin shell so the work done in indenting the shell is nearly independent of the elastic moduli; instead it goes into compressing the gas within the shell [8].In contrast to shells, the indentation of elastic sheets is highly sensitive to tension. If a sheet is not under tension, indentation typically leads to the formation of a developable cone ("d-cone") [11][12][13], which is isometric everywhere except within a small region around the indenter (fig. 1b). The formation of this nearly isometric shape involves large ver...

An ultrathin polymer sheet floating on a fluid forms a periodic pattern of parallel wrinkles when subjected to uniaxial compression. The wave number of the wrinkle pattern increases sharply near the fluid meniscus where the translational symmetry of this one-dimensional corrugated profile is broken. We show that the observed multiscale morphology is controlled by a new "softness" number that quantifies the relative strength of capillary forces at the edge and the rigidity of the bulk pattern. We discover a new elastic cascade by which the wrinkling pattern in the bulk is smoothly matched to the fine structure at the edge by a discrete series of higher Fourier modes.

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