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.

Keywords: 3D assembly; buckling; dielectric elastomers; reconfigurable RF circuits; reconfigurable structures.

Figure 1.

Electro-mechanically controlled deterministic assembly of 3D mesostructures in different material systems and length scales based on dielectric elastomer platforms. (a) Results of FEA that illustrate the process of electrically controlled 3D assembly based on dielectric elastomers (DE) substrates. Upon application of a high voltage to the compliant electrodes (dark gray), the 2D precursor structure (green) selectively bonded with the pre-stretched DE substrate is transformed into a deterministic 3D configuration. (b) Results of FEA that illustrate the deformation of composite DE substrates consisting of strain-limiting fibers (red lines), including the states before and after applying high voltages to the electrodes. (c) FEA and optical images of the assembled 3D mesostructures based on DE substrates, including structures in different material systems (cellular graphene/polyimide (PI) laminated film, polyethylene terephthalate (PET) film and PI/gold (Au)/PI laminated film) and length scales (ribbon width from 180 μm to 6 mm; ribbon thickness from 8 μm to 50 μm). (d) Electrical-resistance variation of the 3D structure made of cellular graphene/PI laminated film (top left in Fig. 1c) under cyclic electrical loading. (e) An example of a reconfigurable 3D mesostructure based on the electrically controlled DE substrate, with the use of two different loading paths. The 2D precursor structure, 3D FEA results and optical images are shown following the two different paths (I and II). Colors in FEA results represent the magnitude of the out-of-plane displacement of 3D mesostructures. Scale bars: 8 mm in (a); 8 mm for the top two images in (c); 0.8 mm for the bottom two images in (c) and 9 mm in (e).

Figure 2.

Theoretical and experimental studies on the distributions of strain components in DE substrates with four representative electrode layouts. (a) Experimental images of circular and annular electrodes with and without the voltage application (i.e. 0/5000 V). (b) Theoretical, FEA and experimental results of the distributions of circumferential and radial normal strain ( and , respectively) along the x direction of the circular electrode, at two different levels of applied voltages. (c) Similar results for the annular electrode at an applied voltage of 5500 V. (d) Optical images of the unactuated (0 V) and actuated (5000 V) configurations of the DE substrate with 2 2 array of circular electrodes and the distributions of strain components (normal strain and , shear strain and maximum principal strain ) determined from the experiment and FEA. Arrays of displacement markers are used for strain visualization. Colors in the contour plots denote the magnitude of strain components. (e) Optical images of the actuated (5000 V) configurations of the DE substrate with a sector electrode and the distributions of strain components (normal strain and maximum principal strain ) determined from the experiment and FEA. (Details of and can be found in Supplementary Fig. 6b). (f) Similar results for the case of the sector electrode with strain-limiting fibers. Details of can be found in Supplementary Fig. 6c. The deformed strain-limiting fibers are marked by red in the optical image. Scale bars: 5 mm.

Figure 3.

Experimental and FEA results of diverse reconfigurable 3D structures based on electro-mechanically controlled assembly. (a, b) Quantitative comparisons of FEA and experimental results for the dome-like mesostructure actuated by a circular electrode (a) and the ribbon mesostructure actuated by two rectangular electrodes with strain-limiting fibers (b). Three mark points (A, B and C) are selected to quantitatively characterize the electrically actuated deformation of 3D mesostructures at different voltages, where A-x (or A-y, A-z) represents the x (or y, z) coordinate value of point A. Dots and lines denote experimental results and FEA predictions, respectively. (c) Experimental and FEA results of six representative mesostructures achieved by electrically controlled 3D assembly. The electrodes, fibers and bonding sites are marked by gray, black and red in the schematics of the 2D precursor, made of Cu/PET (1 μm/50 μm) for the bottom-left mesostructures, and Al/PET (2.5 μm/30 μm) for the others. (d) Optical images of the frog-like mesostructure and its 2D precursor (details of the FEA results can be found in Supplementary Fig. 11). (e–h) Experimental and FEA results of four representative reconfigurable mesostructures with coupled mechanical and electrical loadings. and denote the pre-stretching strain initially applied to the DE substrate and the tensile strain after the mechanical loading process, both with respect to the undeformed configuration of the DE substrate. ‘M-load’ and ‘E-load’ represent ‘Mechanical loading’ and ‘Electrical loading’, respectively. (i) A 3D reconfigurable network mesostructure consisting of two different ribbon elements, demonstrating the excellent local strain control through the coupled electrical/mechanical loadings of the DE substrates. Three types of electrodes (A, B and C) are marked by purple, dark blue and deep yellow, respectively, in the leftmost panel. Scale bars: 10 mm in (a, b), (d, e) and (g–i); 6 mm in (c); 8 mm in (f).

Figure 4.

A reconfigurable inductive–capacitive (LC) radio-frequency (RF) circuit consisting of four morphable 3D capacitors that can be addressed individually. (a) Exploded view of the 2D precursor structures, consisting of separable bi-layers (capacitor layer on the top and conducting layer on the bottom). (b) A circuit diagram of the functional device in the planar state. The inductance and resistance components are externally connected. (Details of the equivalent circuit can be found in Supplementary Fig. 13a). (c) Optical images and FEA results showing the working principle of the device. Colors in FEA represent the magnitude of the out-of-plane displacement of the 3D mesostructure. Gray areas and the black crosses represent four different compliant electrodes (A, B, C and D) and strain-limiting fibers, respectively. The 3D mesostructure in the left column is obtained by equal biaxial mechanical loadings. The detailed fabrication process is shown in Supplementary Fig. 14b. After applying a voltage of V_A = 5200 V to electrode A, the adjacent 3D mesostructure can be transformed into a new configuration (from left to right), in which the top and bottom layers are separated from each other. (d) Measured (dash line) and simulated (solid line) S₁₁ and S₂₁ versus frequency for four states. ‘NONE’, ‘V_A’, ‘V_A + V_B’ and ‘V_A + V_B + V_C’ denote the cases of ‘no applied voltage’, ‘V_A = 5200 V’, ‘V_A = V_B = 5200 V’ and ‘V_A = V_B = V_C = 5200 V’, respectively. (e) Demonstration of the tunable capacitor device to adjust the light intensity of LEDs. Four commercial LEDs are connected in parallel with the morphable 3D capacitors. Two representative states of the LC-RF circuit are compared herein, in which all of the four capacitors are switched on or a single capacitor is on, thereby shifting the resonant frequency of the circuit considerably (a detailed equivalent circuit can be found in Supplementary Fig. 13b). Scale bars: 6 mm.