Anisotropic, Wrinkled, and Crack-Bridging Structure for Ultrasensitive, Highly Selective Multidirectional Strain Sensors

Highlights Two functionally different anisotropic layers are rationally assembled for highly selective and stretchable multidirectional strain sensors. Concurrently excellent selectivity, sensitivity, stretchability, and linearity up to 100% strain is demonstrated for the first time in a multidirectional strain sensor. A novel stepwise crack propagation mechanism is proposed to enable high stretchability and linearity. Supplementary Information The online version contains supplementary material available at 10.1007/s40820-021-00615-5.


S1.2 Fabrication of Vertically Aligned CNT Forest
Vertically aligned CNT forests of 500 μm in height were synthesized by waterassisted chemical vapor deposition (CVD) method [S3]. The Al2O3 (40 nm)/Fe (1 nm) catalyst was sputtered on silicon wafers. The precursor gas C2H4 (75 sccm) and water (100 ppm) were fed into a CVD tube using He and H2 as carrier gases at a feeding rate of 1 L min -1 . The tube was heated to 750 °C at a rate of 100 °C min -1 and kept for 30 min before cooling down to room temperature to allow the growth of CNT forests.

S1.3 Calculation of Interaction Energies
To calculate the interaction energy between the individual CNTs, a simplified molecular structure containing three identical CNTs with a diameter of 7.2 Å and length of 32 Å were used, as shown in Fig. 3c. To calculate the interaction energy between the 1D CNT and 2D GO sheet, one CNT in the above model was replaced by a GO sheet of the same atomic weight. The interaction energy was calculated by: where , and are the energies of the whole system, CNTs without GO, GO without CNTs, respectively.
To calculate the interaction energy between the bottom CNT-GO hybrid film and the top aligned CNT array, a bilayer structure consisting of (i) a layer of seven aligned CNTs and (ii) a layer of CNT-GO random mixture with a lateral dimension of 75 × 80 Å was constructed (insets in Fig. 3d). The periodic boundary conditions were applied in the plane directions while a vacuum slab of 200 Å was built in the thickness direction to avoid interactions between the periodic images. A thin layer of CNT and GO random mixtures at a weight ratio of 1:1 was built using the Amorphous Cell module followed by energy minimization to establish an equilibrium state. The interaction energy between the two layers was calculated similarly according to Eq. S1.
As for the aligned CNTs with PDA treatment, a layer of PDA molecules was first constructed using the Amorphous Cell module with a target density of 1.54 g cm -3 according to the Swift's theoretical model [S4]. The molecular structures of dopamine monomers shown in Fig. S16 were used to construct PDA [S5]. The obtained PDA layer was attached to the bottom surface of aligned CNTs, followed by stacking with a CNT-GO hybrid layer, as shown in Fig. 3d. The interaction energy between the CNT-PDA and CNT-GO layers was calculated according to Eq. S1.

Fig. S1
Fabrication of (a) CNT-GO hybrid film and (b) CNT-PDA film. SEM images of GO sheets, randomly-distributed CNTs, CNT-GO hybrid film and vertically-grown CNT forest in inset   Assembly of a multidirectional sensor using two orthogonally-stacked bilayer sensors, units A and B. The copper wires were connected to the two edges along their respective T-directions to simultaneously detect the strain components along their respective T-directions (i.e., X-and Y-axis)  The membrane was easily peeled off after transferring the hybrid film to the substrate, indicating the adhesion between the substrate and hybrid film is much stronger than that between the membrane and hybrid film. (d) Release of pre-strain to create wrinkles. (e) Cross-sectional optical image of the wrinkled film on the substrate showing good connection between the two without gaps. Top-view SEM images of the wrinkled film on the substrate at (f) low and (g) high magnifications  The electromechanical performance of the bilayer sensor in the T-direction is influenced by the stepwise crack propagation mechanism. At a relatively small strain, the cracks initiated and propagated in the bottom CNT-GO film, leading to a sharp increase in resistance. Meanwhile, the top aligned CNT arrays remained intact with only slight sliding between the CNT bundles. A schematic of a cracked region in the bilayer film and the corresponding equivalent circuit model are shown in Fig. S10. The electrons transported between the two fragments via two parallel paths, namely, (i) tunneling through the cracks in the bottom layer; and (ii) CNT bridges connecting the two fragments in the top layer. The overall resistance of the bilayer film consists of numerous such cracked regions in series. Thus, the normalized resistance change is given by: where 0, is the initial resistance of the bilayer film, , is the tunneling resistance, , is the contact resistance between the top and bottom layers, , is the resistance of the aligned CNT bundle. It is noted that these parameters represent the resistances of a unit crack shown in Fig. S10, and is the number of such units interconnected in series to yield the overall resistance.
The tunneling resistance is dependent on the applied strain, , and given by [6]: where 0 is the initial tunneling distance without strain, = ℎ 2 2 √2 and = 4 ℎ √2 . Here, h is the Plank's constant, is the junction area, q is a constant structural parameter related to the fractal structure of the network, and is the height of the potential barrier.
The contact resistance is assumed constant independent of applied strain, namely, , = because no obvious change occurs in contact area between the top and bottom layers during stretching due to the strong interlayer adhesion [S7, S8].
The resistance of the CNT bundle is a function of applied strain: [8] , = is the intrinsic resistivity of the aligned CNT bundle, 0 is the initial length of the CNT bundle without strain, and is the cross-sectional area of the CNT bundle.
Based on the above, Eq. S2 is rewritten as: In Eq. S5, the normalized resistance change at small strains is expressed as a function of strain, ( ), which is used to fit the experimental data using four strainindependent non-dimensional coefficients, =( + 0 )/ 0, ′ , = 0 / 0, ′ , =

Fig. S10
Schematic illustration of sensing mechanism in T-direction at small strains and the corresponding equivalent circuit model With increasing strain, the cracks in the bottom layer became too large to allow tunneling. Meanwhile, the sliding between the CNT bundles generated cracks in the top aligned CNT layer, which became gradually more important in increasing the resistance. The electron transports in the top layer and the corresponding equivalent circuit model are shown in Fig. S11. Some electrons are transferred through tunneling between the disconnected CNTs, while others are transferred to the adjacent CNTs by physical contacts.
Therefore, the resistance variation caused by the crack propagation in the aligned CNT layer is given by: where ′ is the total number of initial cracks, ′ is the number of cracks under applied strains, , is the tunneling resistance through the cracks, , is the contact resistance between the adjacent CNTs.
Assuming the same type of resistance in each unit has the same magnitude, Eq. S11 can be simplified as: , + , + , It is assumed that ′ is proportional to the applied strain, , because a larger strain leads to more cracks in the film. Therefore, we can write ′ / ′ = ′ , where ′ is the failure probability [6,9].
Using the similar treatment as in Eqs. S2-S5 yields: Combining Eqs. S5 and S8, the overall normalized resistance change can be written depending on the applied strain as: where is the transition strain which separate the two regions in the relative resistance change curves and is the working range which is around 100% strain for the optimized-structure. The coefficients A to ′ are determined by fitting the experimental data for the two sensors with 50% and 85% area ratios and a constant 25% GO content according to Eq. S9, as shown in Fig. S12 and Table S2. The bilinear responses are in reasonable agreement with ( ) at small strains and ( ) at large strains. The nonlinear behavior for the former sensor with 50% area ratio and 25% GO content (Fig. S12a) is due to different crack propagation rates in two regions. An effective method to achieve good linearity across the whole working range is the reduction of the slope of ( ) by tuning the area ratio, so that the crack propagation at small and large strains are matched. Specifically, increasing the area ratio from 50% to 85% yields lower B', C', D' and k' values, suggesting moderate crack propagation through CNT bridging at large strains. Therefore, an almost linear response was achieved for the sensor with an area ratio of 85% (Fig. S12b). The above analysis highlights the possibility of tailoring the linearity of sensors by matching the crack propagation at both small and large strains via tuning the material parameters. The sensor exhibited a nonlinear response with stretchability of 75%, which is much inferior to the sensor fabricated with the pre-cracking step having a highly linear response with high stretchability of 100% (Fig. 4a).

Fig. S20 Comparison of storage modulus and loss moduli between VHB and PDMS
The PDMS (Sylgard184, Dow corning) samples were prepared by mixing the base and curing agents at a ratio of 10:1. The storage and loss moduli were measured using a Rheometer (MCR 301) at room temperature (25 °C) and a constant frequency of 1 Hz. The loss modulus of VHB was higher than its storage modulus, leading to a high tan of 1.166. In contrast, the tan of PDMS was only 0.145, indicating a less viscous behavior than VHB. The viscous nature of VHB substrates resulted in a sluggish response to the applied load, contributing to a slightly longer response time of ~500 ms of our sensor than ~ 130 ms for those using a PDMS substrate.  The tensile strain applied in the L-direction expended only for flattening the wrinkles without altering the conductive networks of the entire sensor, causing negligible resistance changes. Nonetheless, the adjacent crests arising from buckling may contact with each other, affording electron tunneling and thus providing additional conducting paths. Two different types of resistors exist in the equivalent circuit, namely, the resistance of bilayer film, Rin, and the contact resistance between the contacting crests, . The two resistors are arranged in parallel [S10]. Then, the initial resistance, 0 , is given by:

S3 Equivalent Circuit Model for Bilayer Sensor Loaded in L-direction
where , is the resistance of bilayer film, , is the contact resistance between the wrinkle crests, and are the total number of , and , within the conductive network, respectively.
When the tensile strain is applied, the wrinkles gradually flatten and the number of contacts between the crests decreased. Assuming the number of contacts between crests decreased to at a strain ε, the normalized resistance change, ∆ / 0 , is given by: To simplify the quantitative analysis, we assume the resistance of the same type is equal, namely, ,1 = ,2 = ⋯ = , and ,1 = ,2 = ⋯ = , . Then, Eq. S11 can be further simplified to: Since the value of contact resistance is much larger than that of the intrinsic resistance, i.e., , ≫ , , their sum can be approximated, , + , ≈ , . Eq. S12 is therefore simplified to: It is worth noting that ( − )/ is the reduction rate of the number of contacts, which is a probability function of the strain : where is a scale parameter and can be described by the Weibull empirical distribution function [11]. In this work, we assume it has a fixed value of 0.5 to perform the linear fitting [12].
Combining Eqs. S13 and S14 gives: For the fitting purpose, Eq. S15 is expressed as: where = , / , . The experiment data were fitted with Eq. S16, as shown in Fig. S23. The value obtained from the slope of the fitted line was 0.296, suggesting the much lower intrinsic resistance ( , ) than the contact resistance ( , ), which was responsible for the low GF in the L-direction.