Print-and-Spray Electromechanical Metamaterials

Abstract

Many types of novel stretchable and conductive materials have been developed, but all exhibit a large increase in resistance upon stretching. In this article, the design and fabrication methods of two types of electromechanical metamaterials are presented, where the first has an invariant electrical resistance and the second has a decreasing electrical resistance upon elongation. The metamaterials can be fabricated by a few rapid and simple steps: a flexible polymer part is three-dimensional printed and sprayed with a conductive coating. Parametric optimization of the geometrical dimensions of the resistance invariant structure yielded a metamaterial with a nearly constant electrical resistance up to ∼1100% of tensile strain, whose behavior could be predicted using the finite element method. The second metamaterial had a resistance that reduced by as much as 38% over a displacement of 600 μm. The design principles of these new types of metamaterials can open new possibilities for high-performance soft robots and flexible electronics.

Introduction

The development of stretchable and electrically conductive materials has recently been an active research area for their applications to wearable devices,^1–4 soft robots,^5,6 E-skins,^7–9 and so on. The components of these devices need to endure rather extreme mechanical environments and are subject to large tensile stresses and strains while being required to maintain steady electrical properties for optimal performances.^10–12 However, conventional conductive materials, such as metals, can easily be ruptured at a few percent of strains. Also, an elongation of the material in one direction leads to a reduction in its cross-sectional area, which leads to an increase in electrical resistance and may be quite drastic in certain cases.¹³

Composite materials consisting of a soft matrix with embedded conductive materials have been studied to develop stretchable and conductive materials.^14–17 Some of these materials can withstand very large tensile strains with only a small increase in the electrical resistivity. For instance, patterning metal thin films on a polymeric substrate can be used to obtain a structure that can sustain large elongations without failure of the electrical connectivity.^18,19 Although precise micronscale patterning is possible, it is challenging to achieve larger strains without failure by using this approach as it relies on the stretching of the metal film covering the stretchable structure. Conductive hydrogels made by adding highly conductive elements in the structure of the hydrogel can reach strains exceeding 1000% due to the high stretchability of this category of material.^20,21 These materials can be used as highly stretchable strain sensors or as stretchable interconnects. However, they suffer from problems associated with unwanted electrochemical reactions and dehydration, as well as a significant increase in resistance at higher strains. Organogel-based stretchable composites were also suggested to solve some of these problems, but the increase in resistance at larger strains remains.¹⁷ For electrical components that require a constant power supply, any change in resistivity should be minimized or even entirely suppressed.²² Another approach taken is the knitting of wet-spun conductive fabrics into various patterns.²³ These structures can reach strains of a few hundred percent before any significant resistance change occurs, but they require rather complicated fabrication procedures.

Metamaterials are engineered materials with a controlled set of properties. An engineered microscopic design of the constituent elements of the metamaterials can allow overcoming the limitations within the intrinsic electrical and mechanical properties of conventional materials.^24–26 Kirigami metamaterials, in particular, are capable of sustaining very high deformations through a pattern of cuts in the materials such that stretching the structure results in geometrical reorientation of its features rather than stretching of the material.²⁷ This concept has been realized in Kirigami-patterned stretchable and conductive nanocomposites.^28,29 However, there are limitations for these structures in terms of maximum elongation, and there remains a significant increase in the resistance at higher deformations.

In this work, we discuss the design and fabrication strategies for two novel electromechanical metamaterials, where one has an invariant electrical resistance over a tensile strain of >1000%, and the other has an electrical resistance that decreases stepwise as it elongates, which the authors believe is the first structure engineered to exhibit this behavior. The microscopic structures of the metamaterials were designed to be bent or to come in contact with each other as the strain increases to manipulate the overall resistance versus strain relationship. These metamaterials can be fabricated by an extremely simple two-step process consisting of three-dimensional (3D) printing of a polymer with the desired configuration followed by the spraying and drying of a conductive coating. The metamaterial with an invariant electrical resistance was capable of reaching a failure strain of 1100% with a maximum resistance change of 1.3%, while the metamaterial with a discretely reducing electrical resistance reached a 38% reduction in resistance at a displacement of 600 μm.

Results and Discussion

The electrical resistance of conventional conductive materials increases parabolically as the materials are stretched [line (i) in Fig. 1a]. Assuming that the volume does not change upon elongation, the relationship between the change in the resistance and the elongation can be described by using $R ∕ R_{0} = {(L ∕ L_{0})}^{2}$ , where R is the resistance, R₀ is the resistance at zero elongation, L is the length, and L₀ is the initial length of the material.¹⁹ The blue area in Figure 1a illustrates the accessible region of $R ∕ R_{0}$ versus $L ∕ L_{0}$ for engineered composite materials, including crack-based sensors,³⁰ stretchable nanocomposites,³¹ or hydrogels,³² as well as Kirigami-based patterned composites.^28,29 The unreachable area by previous studies is indicated in red in Figure 1a and is the region of properties that the electromechanical metamaterials proposed in this work aim to cover. Here, we demonstrate a new strategy that can be used for two types of metamaterials: Type A [line (ii) in Fig. 1a] has nearly constant resistance over large strains, and Type B [line (iii) in Fig. 1a] has a discretely decreasing resistance as it is stretched.

FIG. 1.

(a) Resistance change of various materials versus their normalized length. The blue region corresponds to the electromechanical properties of previous works, while the red area represents the range of properties that can be accessed by using the metamaterials developed in this work. Deformation behaviors under the tensile strain of (b) conventional materials and the microscopic structures of (c) Type A and (d) Type B metamaterials developed in this work. The red circle in (c) illustrates the local bending of the structure. The red arrows in (d) show the path of the electrons. (e) A schematic diagram of the fabrication process of the metamaterials. (f) The surface SEM images of the metamaterials before and after the carbon spraying/drying step (scale bar = 500 μm). SEM, scanning electron microscope. Color images are available online.

Figure 1b–d compares the deformation behavior under tensile loading of a typical dog-bone specimen and the base units, which are repeated in the two proposed metamaterials. As in Figure 1b, the cross section of conventional materials becomes smaller as they are stretched, resulting in a higher overall electrical resistance. The microscopic component of the metamaterial with an invariant electrical resistance, labeled as Type A metamaterial, is shown in Figure 1c. This structure undergoes bending when macroscopic tensile strain is applied and does not result in noticeable stretching of the conductive component on its surface. Therefore, stretching the material has a minimal effect on the electrical properties. The second metamaterial, labeled as Type B, functions through two sets of teeth that progressively come into contact as the material is stretched, as shown in Figure 1d. The number of paths for the current increases as more pairs of teeth come into contact, and this leads to a stepwise decrease in the resistivity of the structure, which is the opposite behavior of a typical material where the resistivity would increase gradually.

The metamaterials designed in this work can readily be fabricated by a simple two-step fabrication process, as illustrated in Figure 1e. First, a nonconductive polymeric material is 3D printed with the desired shape. Both sides of the 3D-printed part are then manually spray coated with a conductive material from a distance of ∼20 cm for 10 s. The structure is ready to be used after drying at ambient conditions for 60 min. A stereolithography type 3D printer (Form2; Formlabs) with UV curable photoreactive resin (FLGPBL04; Formlabs) composed of methacrylated oligomers, methacrylated monomers, and a photoinitiator was used for 3D printing the structure. We used a carbon spray paint (838AR-340G; MG Chemicals) for the conductive coating, which is a mixture of acrylic lacquer and carbon particles. When this coating is deposited, it slightly etches the surface, which improves the adhesion and leaves the conductive when dried. The scanning electron microscope images in Figure 1f show that the as-printed surface has stripes, a pattern typically seen in 3D-printed structures. After the conductor coating process, the surface possesses some microcracks that form during the drying process. Despite the cracks, electrical paths are well connected, making the overall resistance lower after the spraying and drying process. The overall resistance can be reduced by adding more spraying/drying steps. The suggested fabrication method is a relatively simple, rapid, and low-cost procedure that does not require any complicated chemical synthesis.

Figure 2a shows three potential designs of the Type A electromechanical metamaterials evaluated in this section. Each design possesses a serpentine structure that allows for local bending or unfolding upon the overall elongation of the materials, and each design has a slight difference in the layout of the serpentine pattern. Serpentine designs are widely used in the development of interconnects,^33–36 electrodes,^37,38 and displacement sensors^39,40 for their stretchability. Here, we carry out the parametric studies to reach the maximum strain, with the lowest change in the electrical resistance. Samples were manufactured to evaluate how the electrical resistance varies with strain as a function of the most relevant geometric parameters, namely the number n of serpentine patterns in the upper portion of the structure, length a of a branch of the structure, and width w of a branch. The geometrical parameters of each design were varied within an area boundary and were optimized to induce the largest strain while minimizing the variation in resistance. Finite element method (FEM) simulations of the designs were also conducted to verify the possibility of predicting the behaviors of the structures. The details of the experimental setup and of the FEM simulations are shown in Section I of the Supplementary Data.

FIG. 2.

(a) Three designs of Type A metamaterials showing relevant geometrical parameters: n, a, and w. Arrows indicate the tensile loading directions. (b) Experimental and FEM results on γ for Types A1, A2, and A3 with different geometrical parameters. The dotted lines refer to FEM results, and the black data points correspond to when contact occurs during deformation (see the inset, scale bar = 5 mm). (c) Resistance change versus strain for Type A1 (n = 4, a = 3, w = 1) and Type A3 (n = 3, a = 2, w = 0.5) models. (d) The comparison of the tensile experiment and the FEM analysis on Type A3 (n = 3, a = 2, w = 0.5) model in deformation behavior (scale bar = 10 mm). (e) Experimental results on the electrical resistance change with strain between the dog-bone specimen and different types of Type A metamaterials with optimized geometric parameters: Type A1 (n = 3, a = 3, w = 0.5), Type A2 (n = 3, a = 3, w = 0.5), and Type A3 (n = 3, a = 2, w = 0.5). FEM, finite element method. Color images are available online.

The performance of the different configurations of the Type A metamaterials was characterized in terms of both strain and resistance, but a single evaluation parameter γ is used to be able to compare their overall performance. This parameter γ is defined to be proportional to the maximum strain before failure and inversely proportional to the maximum resistance change in a measured strain range as $γ = s t r a i n_{m a x} ∕ {(R ∕ R_{0})}_{m a x}$ . This means that a structure with a greater value of γ has a higher maximum strain and/or less variance in resistance than a structure with a lower value of γ, but not at a significant detriment to the other property. Figure 2b shows the γ values obtained experimentally and by FEM for the three Type A structures with different geometric parameters. When n was varied, w and a were fixed at 1 and 3 mm for Type A1 and A2, while Type A3 fixed a at 2 mm due to the design boundaries (Section II of the Supplementary Data). Likewise, when w was varied, n and a were fixed at 3 and 3 mm for Type A1 and A2, while Type A3 fixed a at 2 mm. It is to be noted that as the structures are stretched and start to deform, some branches of the structure may come into contact with each other, which can suddenly reduce the resistance. Instances of this occurring were highlighted by changing the marker on the plot from its original color to black in Figure 2b. More information on the different configurations of each design with all combinations of geometrical parameters can be found in Section III of the Supplementary Data.

In general, the performance of the structure increases for increasing values of a and decreases for increasing values of w. The value of n did not appear to have a significant effect on the performance of the structure but increasing it too high will cause unwanted contacts during deformation. However, the resistance remains fairly constant, while unwanted contacts cause a variation in resistance in the range of 0.5–2%, which may be significant for some applications but remains a fraction of the change in resistance found in the structures of the surveyed literature. The experimental results were validated using FEM simulations where metamaterials with the same combination of the geometrical parameters as the experiments were fabricated, and their properties were simulated. The details of all experimental and FEM results can be found in Section V of the Supplementary Data.

Good agreement was observed between the electromechanical behaviors of the experimental and FEM. Figure 2c compares two different cases where one has a contact that occurs during deformation, and the other has a large strain and little resistance variation. In both cases, there is good agreement between the results, although the strain at which contact occurs and the magnitude of its effect on the resistance are not exact. The FEM was still able to predict most of the occurrences of unwanted contacts. There is also good agreement between the deformed shapes obtained experimentally and predicted by FEM, as shown in Figure 2d, which corresponds to the sample where the maximum value of γ was found. This structure was a Type A3 (n = 3, a = 2, w = 0.5) metamaterial with a maximum resistance change of 1.3% at a failure strain of 1107%. Both the experimental results and the FEM identified the same Type A designs as being optimal in terms of γ: Type A1: (n = 3, a = 3, w = 0.5), Type A2: (n = 3, a = 3, w = 0.5), and Type A3: (n = 3, a = 2, w = 0.5). Figure 2e compares the experimental results on the resistance change versus strain behavior of a dog-bone specimen and the Type A structures with optimized geometrical parameters. The dog-bone shaped tensile specimen fabricated by the same two-step process of 3D printing and spray coating exhibits a limited maximum strain and a rapid increase in the electrical resistance. On the contrary, the Type A metamaterials with optimized geometrical parameters show a uniform electrical resistance up to the failure strain. The maximum strain and γ values were calculated as 73% and 0.24 for the dog-bone specimen, 678% and 6.5 for the Type A1 metamaterial (n = 3, a = 3, w = 0.5), 829% and 8.2 for the Type A2 metamaterial (n = 3, a = 3, w = 0.5), and 1107% and 10.9 for the Type A3 metamaterial (n = 3, a = 2, w = 0.5), respectively. For the optimized Type A3, a cyclic loading test for a strain range of 0–50% was also performed and it showed that the resistance change remains within a range of 1.5% for 1000 successive tests (Section VI of the Supplementary Data). Additional loading tests were carried out for the Type A3 specimens that were immersed in deionized water and isopropyl alcohol for 10 min. Both of the samples show negligible resistance changes within 380% of strain (Section VII of the Supplementary Data).

In Figure 3a, we compare $R ∕ R_{0}$ versus the maximum strain values for different invariant electrical resistance composite materials developed in other works^{17,28,29,41–49} and the invariant electrical resistance metamaterial presented in this work. It can be seen that the Type A3 metamaterial with optimized geometrical parameters (n = 3, a = 2, w = 0.5) presented in this work outperforms all surveyed structures, both in terms of strain and in terms of invariance of resistance. In Figure 3b–e, the implementation of the developed metamaterials as a flexible electronic interconnect is presented. The schematic diagram of the test circuit for powering an light emitting diode (LED) that is serially connected to the metamaterial is illustrated in Figure 3b. The circuit with the dog-bone specimen was first tested, as in Figure 3c. At zero strain, electricity flows through the circuit without issue, and the LED is fully illuminated. However, as the strain approaches the strain of 40%, the LED loses brightness. The LED then turned off as the specimen failed at a strain slightly exceeding 40%. Figure 3d depicts the same experiment with the Type A3 metamaterial presented in this work with optimized geometrical parameters (n = 3, a = 2, w = 0.5). The brightness of the LED remained almost constant even at strains reaching up to 1100%. To quantitatively describe the decrease of LED luminosity during tensile loading, we measured the power supplied to the LEDs in Figure 3c and d. It was found that the power supplied to the LED for Type A3 was kept almost constant until a strain of ∼600% and then decreased by 1.5% at a strain of 1100%. In comparison, the LED connected to the dog-bone-shaped specimen had a reduction in power by 4% at a strain of 40% (Section VIII of the Supplementary Data). Figure 3e demonstrates the proposed Type A1 (n = 3, a = 3, w = 0.5) electromechanical metamaterials used as a flexible circuit capable of holding an electric part and of sustaining large deformations with a constant resistance. In this experiment, an LED was placed in between the Type A1 metamaterials, and the intensity of the LED was kept constant even with the circuit being strained by 400%. These two examples demonstrate that the proposed electromechanical metamaterial with invariant electrical resistance can be used for a wide range of applications to provide constant power in scenarios where large deformations of the circuit can be predicted by strategically placing the proposed metamaterials to absorb these deformations.

FIG. 3.

(a) Electrical resistance change versus maximum strain values for various composites.^{17,28,29,41–49} (b) A schematic diagram of the experiments to demonstrate the metamaterials as flexible interconnects. The brightness change of an LED when tensile stress is applied to (c) a dog-bone specimen, (d) Type A3 (n = 3, a = 2, w = 0.5) model, and (e) an array of Type A1 (n = 3, a = 3, w = 0.5) metamaterials (scale bars for c–e: 10 mm). LED, light emitting diode. Color images are available online.

Another behavior in terms of resistance versus strain that is not possible to obtain using conventional materials is one where the resistance decreases as the strain increases [line (iii) in Fig. 1a]. The Type B metamaterial was designed to have such electromechanical behavior by adopting a design that provides more routes for electrical conductions as the metamaterial is stretched, leading to a decrease in overall resistance. The Type B metamaterial can be fabricated by the same process as the Type A metamaterial: 3D printing of the structure, followed by the coating and drying of the conductive layer.

Figure 4a shows the proposed design and structure of the Type B metamaterial. This structure consists of two blocks connected by three serpentine structures at the ends of three prongs, where two outer prongs protrude from one block and the third central prong from the other block. The serpentine structures are used to connect the two blocks and to allow relative motion between them. Comb-like structures are positioned on each side of the central prong and on the internal side of the outer prongs such that a sufficient movement of the blocks creates contact between opposing pairs of teeth. Each gap (d1–d9 in Fig. 4a) between the teeth of the combs has different distance values, such that they come into contact with nearby teeth sequentially as the overall strain increases. As the metamaterial is stretched, the number of teeth contacting with its neighboring teeth increases, as in Figure 4b, which lowers the overall resistance. The number of teeth and their gaps can be tuned to control the overall resistance versus strain profile of the metamaterial.

FIG. 4.

(a) Fabricated Type B metamaterial (scale bar = 10 mm) and its geometrical parameters. (b) FEM analysis of the Type B metamaterial with different overall displacements imposed, resulting in different numbers of teeth pairs in contact as indicated with yellow circles. Displacement of zero is set when the first contact is made. (c) Experimental results of the resistance change versus displacement of the Type B metamaterial (blue curve). The differential of the resistance change with respect to the displacement is shown with the orange line. The indicated numbers in the curve correspond to the number of teeth pairs being in contact. Color images are available online.

Figure 4c shows the experimentally measured resistance change of the Type B metamaterial with respect to the displacement of the tensile test. The structure was designed to have a discretely decreasing resistance in an elongation increment of 0.08 mm. The manufactured specimen produces a discretely decreasing pattern in the $R ∕ R_{0}$ versus displacement curve due to the sequential contacts of the teeth, as expected. Differentiating the blue $R ∕ R_{0}$ curve with respect to displacement allows for the identification of the contact points more easily, which is shown as the orange line in Figure 4c. The results show that larger drops in resistance occur when fewer pairs of teeth are already in contact, as could be predicted from basic circuit theory, and that the resistance decreases gradually between these larger drops as the area of contact between pairs of teeth increase.

The discrete change in resistance can be useful for developing high-performance flexible displacement sensors as the displacement can be measured by counting the bumps in the curve and can also be tailored to have specific changes in resistance at specific intervals by tailoring the spacing between teeth. In most displacement sensors, the measurement of the displacement strongly depends on the mechanical and electromechanical properties of the sensor, which may vary with temperature, humidity, and mechanical degradation. However, counting the displacement using the number of stepwise changes in resistance rather than its value allows the sensor to depend only on mechanical properties rather than the electromechanical properties. The reduction in resistance that occurs with an applied force and an increasing strain could also be used to automatically increase the input power to a connected element in response to the applied force.

Conclusions

In this study, two types of electromechanical metamaterials are presented with different electromechanical properties that are not found in conventional conductive materials or composites. Both are made using a similar manufacturing process. The first metamaterial is a metamaterial with invariant electrical resistance and has a failure strain of 1107% with a maximum resistance change of 1.3%. The second has a resistance that decreases stepwise with an applied strain and has a resistance 37.8% lower than its unstretched resistance at a displacement of 600 μm. The first proposed metamaterial has a performance far exceeding all surveyed materials, while the second proposed metamaterial has a property not displayed in any of the surveyed works. The properties of the metamaterials were confirmed using multiphysics FEM and would allow predicting their performance before fabrication. Both metamaterials were made using 3D-printed polymeric material, followed by spray coating of a carbon-based conductive layer. The proposed two-step manufacturing process is easy, quick, and inexpensive compared with the fabrication processes of other conductive composites. This allows the mechanical behavior of the metamaterials to be determined by the 3D shape of the structure and how it deforms with respect to an applied force, while the electrical behavior is determined by the surface-coated material. The performances of the metamaterials developed in this work can be expected for other combinations of nonconductive bodies and conductive coatings if the core part can be fabricated with geometries similar to the metamaterials.

The proposed design and fabrication strategy can be used to design high-performance, flexible interconnects and reliable displacement sensors that are insensitive to varying work environments. Due to the flexibility of the design of the metamaterials, they can be designed to be compatible with the already existing mechanical and electrical components. The proposed strategy is also scalable in that so much smaller or larger metamaterials can be fabricated by using a similar process.

Footnotes

Author Disclosure Statement

No competing financial interests exist.

Funding Information

This work was supported by the Samsung Research Fund, Sungkyunkwan University, 2018.

Supplementary Material

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Supplementary Material

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