Electro-mechanically controlled assembly of reconfigurable 3D mesostructures and electronic devices based on dielectric elastomer platforms

Abstract The manufacture of 3D mesostructures is receiving rapidly increasing attention, because of the fundamental significance and practical applications across wide-ranging areas. The recently developed approach of buckling-guided assembly allows deterministic formation of complex 3D mesostructures in a broad set of functional materials, with feature sizes spanning nanoscale to centimeter-scale. Previous studies mostly exploited mechanically controlled assembly platforms using elastomer substrates, which limits the capabilities to achieve on-demand local assembly, and to reshape assembled mesostructures into distinct 3D configurations. This work introduces a set of design concepts and assembly strategies to utilize dielectric elastomer actuators as powerful platforms for the electro-mechanically controlled 3D assembly. Capabilities of sequential, local loading with desired strain distributions allow access to precisely tailored 3D mesostructures that can be reshaped into distinct geometries, as demonstrated by experimental and theoretical studies of ∼30 examples. A reconfigurable inductive–capacitive radio-frequency circuit consisting of morphable 3D capacitors serves as an application example.


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deformations. To achieve non-uniformly distributed 3D mesostructures, engineered elastomer substrates with either spatial variation of thickness/modulus or kirigami patterns were introduced as tailorable platforms that can offer desired strain distributions [58,59]. It is noteworthy that the existing studies based on buckling-guided approaches all exploit mechanical stages to apply the overall, pre-stretch deformations to the substrate, and the resulting 3D assembly follows in a global and concurrent manner at different spatial locations. A key limitation is the lack of ability to achieve on-demand local assembly with desired time sequences, and to reshape as-assembled mesostructures into distinct 3D configurations.
Here, we present a set of strategies to overcome this limitation, where highly deformable dielectric elastomers (DE) capable of sequential, local actuation serve as a platform for buckling-guided 3D assembly. Dielectric elastomers have been widely used as a type of high-performance soft actuators for applications in soft robotics, biomedical devices, optical devices and many other areas [60][61][62][63][64]. This work introduces strategic designs of electrode layouts and strain-limiting fibers [65] in DE substrates, which allows the utility of electrical actuation and electromechanically coupled deformations to achieve complex strain distributions, with capabilities of sequential, local loading and strain isolation. As validated by experimental measurements, the theoretical modeling of electro-mechanically coupled deformations, implemented with simulations of finite element analyses (FEA), can predict accurately the distributions of strain components in DE substrates. These capabilities allow access to precisely tailored 3D mesostructures during electro-mechanically controlled assembly, whose geometries can be reshaped rapidly (∼1 s) through electrical actuation. Demonstrations encompass experimental and theoretical studies of nearly 30 examples in different length scales (from micrometer to millimeter scales) and material types (e.g. metals, polymers, and cellular graphene), including structures that resemble frogs, eyeglasses, starfishes and domes and those that can be reshaped between two distinct stable geometries. A reconfigurable inductive-capacitive (LC) radio-frequency (RF) circuit enabled by an electrically controlled 3D capacitor serves as a device demonstration, which suggests prospects of applications in wireless communication. Figure 1a provides results of finite element analyses (FEA; see 'Methods' section for details) that schematically illustrate the assembly process of 3D mesostructures based on electrically controlled DE substrates. A free-standing DE membrane (VHB, 3M, thickness 1 mm) is pre-stretched (e.g. prestrain of ∼250%) to offer an enhanced actuation performance (see Supplementary 1a for the detailed manufacturing process) [66]. Then pre-designed 2D precursors (see 'Methods' section for details of the fabrication) are transferred onto the pre-stretched DE membrane, with strong bondings (four free ends of the ribbons in Supplementary Fig. 1a marked by red, available as Supplementary Data at NSR online) selectively distributed at the interface. Here, shadow masks with the patterns of the bonding sites allow accurate positioning of 2D precursors during the transfer printing process. Anti-stick powders (talcum powder) are exploited to reduce the adhesion energy at the non-bonded regions, avoiding the failure of 3D assembly due to the strong adhesion of the DE membrane (VHB 4910, 3M). It should be pointed out that the anti-stick powders may be unnecessary if the DE membrane (VHB 4910, 3M) is replaced by other dielectric elastomers (e.g. silicon rubber-Nusil, CF19-2186) with much lower adhesion energy. The applied voltages on the compliant electrodes (MG Chemicals, USA) at the top/bottom surfaces induce Maxwell forces that expand the dielectric membrane biaxially along the in-plane direction. Such actuation deformations result in inward movements of four bonding sites and trigger the compressive buckling of 2D precursors, transforming them into 3D configurations, through coordinated spatial bending/twisting deformations as well as translational/rotational motions.

Conceptual illustration of 3D assembly with DE substrates
Strain-limiting fibers can be embedded in the DE substrates to achieve non-equal biaxial in-plane expansion during the electrical actuation, which can enhance the complexity of strain distribution and enrich the diversity of accessible geometries during 3D assembly. Fibers with well-designed structural patterns and thicknesses are able to limit not only the deformation along specified linear directions, but also the deformation along desired radial directions. These fibers are typically placed on the bottom surface of DE platforms, and thereby do not affect the transfer printing process. Figure  1b presents a schematic illustration of the deformation of the composite DE substrates with strainlimiting fibers fabricated by 3D printing method, induced by the application of voltage (see Supplementary Fig. 1b for manufacturing process and 'Methods' section for preparation of fibers). Here, the 3D printing method is adopted for the rapid prototyping of strain-limiting fibers with diverse geometries. Figure 1c provides results of finite element analyses (FEA; see 'Methods' section for details) and experiments for the assembly of 3D structures in a range of different materials (cellular graphene/polyimide (PI) laminated film [21]; polyethylene terephthalate (PET) film; PI/gold (Au)/PI laminated film; see 'Methods' section for details) and length scales (ribbon width from 180 μm to 6 mm; ribbon thickness from 8 μm to 50 μm). The designs of electrode layouts and 2D precursors are provided in Supplementary Fig.  2. Here, FEA can predict accurately the electromechanical deformations in the pre-stretched DE substrate under a prescribed voltage, and the resulting post-buckling process of 2D precursor structures. This is evidenced by the good agreements of predicted 3D configurations with optical images for all of the four examples in Fig. 1c. The assembled 3D mesostructures are mechanically robust, with capabilities to endure cyclic electrical loading and unloading. Figure 1d shows the electrical resistance of the cellular graphene/PI mesostructure (in the top-left panel of Fig. 1c) wired from two of the bonding regions, during cyclic electrical loading with an amplitude of 5500 V and a frequency of ∼0.5 Hz. The relative variation of the electrical resistance is below 0.17% for 500 cycles. Figure 1e, Supplementary Fig. 3 and Supplementary Movie 1 illustrate the utility of electrically controlled, local, sequential loading enabled by the DE platform to achieve a morphable 3D mesostructure whose shape can be stabilized between two distinct geometries [51]. In this example, the 2D precursor consists of three identical ribbons, each with two creases (with a reduced width of 200 μm, as compared to 800 μm in the other regions), and a supporting ribbon at the bottom of the design, as shown in the top-left panel. Two types of electrodes (A and B) are designed to offer sequential actuation in the DE platform. Specifically, two different loading paths are exploited, denoted as (Path I: Fig. 1e). During 'Path I' loading, the supporting ribbon remains almost flat and attached to the substrate during the entire process, resulting in the formation of a 3D structure (Shape I) with three arches connected at the center. In contrast, 'Path II' loading yields a different configuration (Shape II) where the center is elevated and the supporting ribbon is evidently curved. Both shapes (I and II) are stable and can be transformed reversibly into each other, by removing and applying the electrical loading with different sequences.

Experimental and theoretical studies of electro-mechanically coupled deformations in DE substrates
To offer versatile loading combinations and sequences for 3D assembly, the pattern of electrode layouts can be tailored to achieve a variety of desired strain distributions in DE substrates, with FEA as a design platform. Note that several different approaches were developed to predict the non-linear electro-mechanical deformations of the DE platform under electrical/mechanical loadings [67][68][69].
In the current study, the FEA were carried out using commercial software (ABAQUS), in which equivalent in-plane forces perpendicular to the edge of regions covered by electrodes were applied to account for the effect of Maxwell stress [66] (see 'Methods' section for details). Quantitative measurements by tracking the displacements of deposited metal external arrays allow us to obtain the in-plane strain fields of DE substrates experimentally (see 'Methods' section for details). Figure 2a-c and Supplementary  Fig. 4 show that the distributions of circumferential and radial nominal strain (ε θ and ε R respectively) calculated based on the FEA agree quantitatively with both experimental measurements and theoretical results based on Suo's theory [66,70] (see Supplementary Note, available as Supplementary Data at NSR online), for the cases of circular and annular electrodes, even at relatively high voltages (e.g. 5500 V). It is noteworthy that both the electrically induced circumferential and radial nominal strain are almost zero within the inner circle of the annular electrode ( Fig. 2c and Supplementary Fig.  4b), as evidenced by the magnitude of electrically induced nominal strain that is less than 0.8% at 5500 V according to FEA.
Figure 2d-f and Supplementary Figs 5 and 6 provide combined experimental and numerical results of in-plane strain distribution for four representative electrode layouts, including annular electrode, circular electrode, sector electrode without any fibers, and sector electrode with strain-limiting fibers. For a 2 × 2 array of circular electrodes (Fig.  2d), the distributions of three strain components (ε 11 , ε 22 and γ 12 ) as well as the in-plane maximum principal strain (ε max ) predicted by FEA all agree well with the experimental results. Here, ε 11 and ε 22 are the two in-plane nominal normal strain components, and γ 12 represents the in-plane engineering shear strain. These results show very slight mechanical interactions of the neighboring electrodes, indicating an excellent strain isolation, in the condition that the spacing is equal to (or larger than) the electrode diameter before the electrical loading. The normal strain components (ε x ) are alternatively

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Nominal strain 11 Supplementary Fig. 6b). (f) Similar results for the case of the sector electrode with strain-limiting fibers. Details of ε 22 can be found in Supplementary Fig. 6c. The deformed strain-limiting fibers are marked by red in the optical image. Scale bars: 5 mm.
negative and positive across the line connecting the centers of the two electrodes ( Supplementary  Fig. 7). Figure 2e and

Assembly of 3D structures through the DE platform
Accurate modeling of the electro-mechanically coupled deformations in DE substrates, together with precise post-buckling analyses, allows rational designs of electrode layouts, 2D precursor patterns, bonding sites and loading magnitude to yield target 3D configurations.  Fig. 3a. Furthermore, the mesostructure in Fig. 3a can be reshaped rapidly (less than 1 s) once the voltage is applied compared with the mechanical loadings adopted in previous studies (larger than 30 s) (see Supplementary Movie 2). Here the speed of loading is limited by the relatively high viscosity of the VHB membrane.
To further improve the actuation speed and the actuation efficiency, other dielectric elastomers with lower viscosities can be exploited. The kirigami arch mesostructure in Fig. 3b shows a 2D configuration at the zero-voltage state. In this case, the strain-limiting electrode induces a uniaxial compression to the 2D precursor structure upon application of the voltage, and therefore the amplitude of the kirigami arch increases gradually with increasing voltage. The coordinates of the three mark points (A, B, C) in Fig. 3b predicted by FEA also match the experimental results well. Figure 3c presents six demonstrative examples of electrically controlled 3D assembly, including 2D precursors (with electrodes and bonding sites marked by gray and red, respectively), FEA predictions and experimental images of final 3D mesostructures. The mesostructures in the left column are assembled through the lateral buckling controlled by the voltage applied to the electrodes that do not contain any strain-limiting fibers. The second example resembles an eyeglass, which is formed by applying a voltage of 5500 V equally to the three electrodes. The assembly of the third mesostructure involves a coordinated process of tensile buckling and compressive buckling, where the curvy ribbon structure connected to the two central bonding sites undergoes tensile buckling, and the two outer ribbons experience compressive buckling. The designs in the right column are achieved by exploiting strategically designed fibers in the electrodes, and the resulting 3D geometries are unachievable using conventional elastomer substrates. Here, the fibers mainly restrict the radial expansion, such that the compressive buckling along the circumferential direction can be realized to form 3D mesostructures with a certain degree of rotational symmetry. In particular, the last mesostructure with a five-fold rotational symmetry resembles a starfish. Four additional examples of electrically controlled 3D assembly are provided in Supplementary Fig. 10. Figure 3d and Supplementary Fig. 11 show a frog-like mesostructure enabled by concurrent tensile buckling and compressive buckling during the electrically controlled 3D assembly, such that the gestures of forelegs and hindlegs can resemble those of real frogs. In the aforementioned examples, the largest electrically induced strain (nominal linear strain) of the DE platform is ∼80%, which is smaller than the mechanical strain (nominal linear strain, typically larger than 100%) achievable with the traditional silicone substrate.
Based on the DE platform, coupled electrical and mechanical loadings can be achieved easily to enrich the capability of geometrical control during the 3D assembly. For example, an equal biaxial compression followed by electrical loading can be exploited to reshape the mechanically assembled 3D mesostructures into a distinct configuration, as shown in Fig. 3e-i and Supplementary  Fig. 12a. Specifically, the mesostructure in Fig. 3f and Supplementary Movie 3 resembles an insect, and exhibits a different gesture after rapid electrical actuation (∼1 s). Figure 3g shows that a threelayer cage structure can be formed through biaxial compression during the release of pre-strain in the DE substrate. Such a three-layer cage structure can be reshaped through two individually addressable electrodes, such that the middle layer can selectively be in contact with the top layer (shape II) or the bottom layer (shape III). This reconfigurable characteristic can be potentially utilized to design reconfigurable electronic components (e.g. inductors and antennas). The mesostructure in Fig. 3h elucidates a design where the state of contact between the suspended straight ribbons at the bottom layer (in green) and arch-shaped ribbons at the top layer (in yellow) can be tuned by adopting different electro-mechanical loadings. Reversible local actuation of the 3D mesostructure is also possible by adopting designs of electrode arrays with the feature of strain isolation, which is otherwise unobtainable using the mechanically guided assembly approaches reported previously. Figure 3i and Supplementary Fig. 12b present a periodical array of a 3D ribbon network assembled through biaxial compression during the release of pre-strain in the DE substrate. Appropriate circuit designs allow the classification of nine circular electrodes into three groups (marked by different colors in the leftmost panel), such that the electrodes in each group can be addressed individually. When the voltage (∼5200 V) is applied only to the Group-A electrode in the center, the central mesostructure is flattened, while the other 3D mesostructures are almost unaffected, especially those sitting on the other electrodes. Similarly, the voltage (∼5200 V) applied only to four Group-B (or Group-C) electrodes results in the flattening of four associated mesostructures, with negligible influences on the mesostructures sitting on the other electrodes.

A reconfigurable inductive-capacitive radio-frequency (LC-RF) circuit enabled by a morphable 3D capacitor
Versatile design freedom to access to diverse 3D geometries and powerful capabilities to reshape assembled mesostructures into distinct 3D configurations pave the way for unusual electronics with functionally reconfigurable features. Figure 4 demonstrates an example of a morphable 3D capacitor that enables a reconfigurable LC-RF circuit capable of shifting the resonant frequency on demand. Figure 4a illustrates schematically the separable bi-layer construction of the 2D precursor, where the upper layer, called the 'capacitor layer', has thin copper layers (100 nm) selectively deposited on the top and bottom surfaces of the PET layer (25 μm) to form parallel-plate capacitors, and the lower layer, called the 'conducting layer', has a single copper layer fully deposited on top of the PET layer (25 μm). Partial release of the pre-strain (ε pre = 266.7%, ε m = 230%) in the DE substrate ensures a good contact between the lower and upper layers in the mechanically assembled device, and thereby all of the four capacitors are electrically conducting in the circuit ( Fig. 4b and Supplementary Fig. 13a). We introduced a cross-shaped fiber on top of the DE substrate after the mechanical assembly, such that excellent strain isolation can be realized during the electrical actuation ( Supplementary Fig. 14a). As a result, when the voltage is applied only to electrode A, the lower and upper layers are separated only in the adjacent capacitor while the other three capacitors remain electrically connected in the circuit (Fig.  4c). Similarly, the application of voltage to two (or three) electrodes leads to the formation of two capacitors connected in parallel (or a single capacitor) in the circuit. Thereby, the capacitance of the device can be reconfigured rapidly (within ∼1 s) through application of voltage to a different number of electrodes. When the above morphable capacitor is connected with inductive and resistive components in an RF circuit (see Fig. 4b and Supplementary  Fig. 13a Supplementary Fig. 13b). Scale bars: 6 mm.
corresponding to the application of voltage to 0/1/2/3 electrodes, in which S 11 and S 21 represent the reflection coefficient and the insertion loss of the input signal, respectively. According to the theory of LC resonant circuits, the resonance frequency (f) can be given by f = 1/2π √ LC , where L is the inductance and C is the capacitance. As the number of parallel capacitors in action increases, the capacitance value increases, leading to a shift of the resonance frequency to the lower band. Figure 4d demonstrates that the electrical actuation is able to substantially and continually achieve reconfigured resonant frequencies from ∼10.7 MHz to ∼21.3 MHz, while maintaining the reflection coefficient and the insertion loss relatively stable at −20.5 dB and − 0.1 dB, respectively. The results of electromagnetic simulations (see 'Methods' section for details) match the measured data very well. Figure 4e provides a further experiment to demonstrate the frequency reconfigurability, in which four identical LEDs are connected in parallel at two ends of the capacitors (see Supplementary  Fig. 13b, Supplementary Movie 4 and 'Methods' section for details). Considering that the dielectric loss and radiation loss of the demonstrative circuit is negligible, when the reflection coefficient achieves the minimum value at the resonant frequency, the circuit load (LEDs) should absorb the largest power from the source, suggesting that the four LEDs achieve the maximum brightness. A comparative experiment was carried out, in which the voltages were applied to three or none of the four electrodes. In these two conditions, the LED brightness reaches a peak clearly at distinct frequencies (∼12 MHz versus 8 MHz). It is noteworthy that when the capacitive network in Fig. 4a is loaded with LEDs (shown in Fig. 4e), parasitic effects such as additional inductive or capacitive parameters associated with LEDs lead to the offset of the resonant frequency from that of the original capacitive network. Furthermore, the uncontrollable electrical performance tolerance of the capacitors also contributes to the discrepancy between the desired and the measured frequency for achieving the maximum brightness. The design concepts introduced herein can be extended to the GHz band, and possible future applications include multi-channel 5G or post-5G wireless communications, and miniaturization of microwave systems.

CONCLUSION
In summary, the design concepts, assembly strategies and validated modeling methods presented here establish the DE substrate as a powerful platform for the electro-mechanically controlled assembly of 3D mesostructures in a range of advanced materials, with the feature sizes spanning microscale to centimeter-scale. Combined theoretical and experimental studies show that strategic designs of electrode layouts and strain-limiting fibers in DE substrates can enable sequential, local and fast loading with desired strain distributions (with a maximum nominal linear strain of ∼80%), which allows access to precisely tailored 3D mesostructures and reconfigurable mesostructures. A morphable capacitor is designed and utilized to demonstrate a wide band frequency reconfigurable LC-RF circuit, holding promise for applications in wireless communication. The electro-mechanically controlled assembly approach developed herein can also be potentially used in the areas of optical metamaterials, flexible electronics, and MEMS/NEMS.

Fabrication of 2D precursors
The 2D precursors made of PI/Au/PI films were fabricated by spin-coating (3000 rpm for 30 s) and curing (180 • C for 12 min) a layer of poly(methyl methacrylate) (PMMA, Microchem, USA) (∼100 nm) onto a silicon wafer, followed by spincoating (5000 rpm for 45 s) a layer of polyimide (PI, Sigma-Aldrich, USA) (∼8 μm) and curing (180 • C for 2 h) on the PMMA layer. Depositing thin layers of metal (∼10 nm Cr/∼200 nm Au) by electron beam evaporation, and spin-casting another layer of PI (∼8 μm) finishes the preparation of the PI/Au/PI tri-layer film. Femtosecond laser cutting (Rofin, Germany) then defines the desired patterns of the 2D precursors. Immersing the silicon wafer in acetone for 10 min dissolves the PMMA layer, allowing the retrieval of the 2D precursors from the wafer.
The 2D precursors made of cellular graphene/PI films were prepared by ablating the PI film with a CO 2 laser cutting machine (VLS2.30, USA) in scanning mode, generating cellular graphene on the top surface of the PI films [21].

Experimental visualization of strain fields of DE substrates
Strain visualization of the DE platform with tailored electrode patterns began with the sputtering of an array of copper dots (∼5 nm Ti/∼100 nm Cu, diameter = 400 μm, and pitch = 1 mm) on the surface of pre-stretched DE substrates with the aid of shadow masks. A series of optical images with different applied voltages were captured by a digital camera. The coordinate positions of the dots were processed automatically by image processing software (PhotoModeler) and the strain distributions could then be computed by MATLAB (version 2017b).

Fabrication of 3D tunable capacitors for the LC-RF devices
The 2D precursors of the tunable capacitor device were made of composite films (∼30 μm PET/∼100 nm Cu for the 'conducting layer' and ∼100 nm Cu/∼30 μm PET/∼100 nm Cu for the 'capacitor layer'). The fabrication of 3D LC-RF devices began with transferring the 2D precursors of the 'conducting layer' and 'capacitor layer' onto the DE platform, followed by selective bonding of the 2D precursors onto the DE platform. Releasing the pre-strain of DE platforms uniformly (mechanical loading process) allows transformation of 2D precursors into 3D mesostructures. Attaching the cross-shaped strain-limiting fibers onto the bottom surface of the DE platform enables tight bonding, thanks to the high viscosity of the DE membrane (VHB 4910, 3M, USA). Application of voltages to the electrodes reshapes the 3D mesostructures into new configurations (electrical loading process).
In the experiments to adjust the light intensity of LEDs, the parameters of the exploited components include: the commercial LEDs (red light, rated voltage = 1.5 volts, rated current = 5 ∼ 20 mA and rated power = 0.01 W); the external inductor (1.5 μH); the external resistance (1 ) and the signal generator (sinusoidal alternating current (AC) signal and peak-to-peak voltage = 1.5 volts, Tektronix AFG 2021, USA).

Electromagnetic measurements
Two port S-parameters were measured using a network analyzer (Agilent E5071B, USA). The capacitance value of each 3D capacitor is approximately 36.7 pF according to the measurement of the capacitance meter. The measured four resonant frequencies in Fig. 4d