Soft Nanocomposite Based Multi-point, Multi-directional Strain Mapping Sensor Using Anisotropic Electrical Impedance Tomography

The practical utilization of soft nanocomposites as a strain mapping sensor in tactile sensors and artificial skins requires robustness for various contact conditions as well as low-cost fabrication process for large three dimensional surfaces. In this work, we propose a multi-point and multi-directional strain mapping sensor based on multiwall carbon nanotube (MWCNT)-silicone elastomer nanocomposites and anisotropic electrical impedance tomography (aEIT). Based on the anisotropic resistivity of the sensor, aEIT technique can reconstruct anisotropic resistivity distributions using electrodes around the sensor boundary. This strain mapping sensor successfully estimated stretch displacements (error of 0.54 ± 0.53 mm), surface normal forces (error of 0.61 ± 0.62 N), and multi-point contact locations (error of 1.88 ± 0.95 mm in 30 mm × 30 mm area for a planar shaped sensor and error of 4.80 ± 3.05 mm in 40 mm × 110 mm area for a three dimensional contoured sensor). In addition, the direction of lateral stretch was also identified by reconstructing anisotropic distributions of electrical resistivity. Finally, a soft human-machine interface device was demonstrated as a practical application of the developed sensor.

the boundary of the conductive material 53 . Here, the electrodes are used to apply electrical currents and to measure electrical potentials. This technique has been used to demonstrate a stretchable and sensitive electronic skin covering on three dimensional contoured surfaces without any internal wiring using conductive fabric 43,44,[50][51][52] , conductive rubber [46][47][48] , and conductive liquid 45 . In these literatures, no complex array of stretchable electrodes needs to be fabricated within the entire sensing area. In addition, the EIT based sensor could provide robustness to various contact conditions since the electrodes of the sensor could be located only along the boundary so that direct physical contact does not occur between the applied forces and the electrodes 49 . However, a detailed study on the identification of multi-directional strain mapping based on EIT has not been introduced so far because conventional EIT method could compute only homogeneous resistivity distribution of the conductive medium. In addition, the conductive medium exhibiting anisotropic resistivity when strain is induced was required.
Here, we demonstrate multi-point and multi-directional strain mapping sensors based on the nanocomposite of multiwall carbon nanotube (MWCNT)-silicone elastomer using anisotropic electrical impedance tomography (aEIT). The nanocomposite exhibits an anisotropic piezoresistivity due to the morphological changes of MWCNT network along the direction of the strain 20,54,55 . The aEIT method computes the multi-dimensional resistivity distribution within the nanocomposite, thereby the strain directions and contact locations on large curved surfaces can be accurately identified without using complicated arrays of flexible and stretchable electrodes fabricated along the entire sensor surface. We characterized the surface indentation force and location estimation performances and stretch displacement and direction estimation performances of the strain mapping sensor in detail. Finally we implemented a soft, three-dimensional human-machine interface device to control a robotic hand system.

Results
Device fabrication using MWCNT-silicone elastomer nanocomposite. As shown in Fig. 1a, uniform nanocomposite of multiwall carbon nanotubes (MWCNT) and liquid silicone (Ecoflex ® ) were dispersed by using shear milling, which enabled randomly oriented distribution of MWCNTs within the nanocomposites 56 . The MWCNTs form an electrically conductive network with controllable resistance by the volume fraction of the MWCNTs within the silicone elastomer. When the composites deform due to external forces, the electron transport within the conductive network is changed, thereby modulating the electrical resistance. This nanocomposite material can be easily fabricated into various two or three dimensional shapes by employing injection molding techniques 57,58 . Figure 1b shows the procedures to fabricate soft strain sensors by injection molding. Plastic molds were first fabricated in various shapes using three dimensional printing process. MWCNT-liquid silicone nanocomposite was filled into the injection mold using air pressure, followed by thermal curing in a convection oven at 70 °C for 1 hour. Hemispherical and rectangular parallelepiped specimens were fabricated by using this process (Fig. 1c). The conductivity of the specimens depended on the volume fraction of the MWCNT due to the percolation phenomenon ( Fig. 1d) 59 . The percolation threshold was estimated from the percolation model and resistivity of the specimens with different volume fractions of MWCNTs (see Supplementary Figure 1). The specimens showed highly soft characteristics and good recovery against repeated bending and squeezing (Fig. 1e). In addition, from the scanning electron microscopic (SEM) images, we could observe that the MWCNTs were uniformly dispersed in random directions within the silicone elastomer matrix (Fig. 1f). The electrical resistance of specimens with the 2.5(1.29) wt% (vol%) showed a standard deviation of 16.7% with respect to the average. (2633 ± 439 ohm-mm) (Supplementary Figure S2).

Electro-mechanical characteristics of the MWCNT-silicone elastomer nanocomposite.
Tensile experiments were conducted to assess the piezoresistivity of the MWCNT-silicone elastomer nanocomposite. As shown in Fig. 2a, a custom-designed tensile tester was utilized to apply a tensile strain to the specimen while providing a constant current and measuring a voltage across the specimen simultaneously. Dog-bone shaped specimens were fabricated by injection molding. Dimensions and shapes of the specimen followed the JANNAF polymer testing standard 60 . Four specimens with different weight ratios of the MWCNT and elastomer were prepared (2.5 wt%, 3.5 wt%, 4.5 wt% and 5 wt%). Figure 2b shows the mechanical responses of each specimen. The graphs of the mechanical responses show typical characteristics of the elastomeric polymers. Mechanical stiffness of the composite increased from 76 kPa to 166 kPa by the increase of the weight ratio of the MWCNT in the nanocomposites (2.5 wt%, 3.5 wt%, 4.5 wt% and 5 wt%). The mechanical stiffness of 166 kPa is low enough to provide flexibility and softness for comfortable physical interaction with human users. The electrical resistances of the nanocomposites showed a linear relationship between voltage and current with 0% to 80% strains for all the specimens (Supplementary Figure S3). Figure 2c shows the electrical responses of the specimens to the applied strains. In this case, the resistance of the specimen increases with the extension in the range of 0-40% strain. The sensitivities of the specimens defined as (∆R/R 0 )/ε were estimated using linear regression for simplicity. From 0 to 40% strain, the sensitivities were 1.61, 1.12, 0.91, 0.67 for 2.5 wt%, 3.5 wt%, 4.5 wt%, 5 wt% of MWCNT within polymer matrix, respectively. To achieve relatively high sensitivity with low stiffness, weight percent of 2.5 wt% was selected to fabricate the sensing elements used in this work.
Investigating the anisotropic property in resistivity change against the external strain is necessary for the nanocomposite to achieve multi-dimensional strain sensing. For this reason, four point probe was used to measure the anisotropic resistivity distribution (Supplementary Figure S4). A linear guide stretched a square shaped specimen in y direction and four point probe contacted the surfaces of the specimen using 3 dimensional manipulator. The line of the four probes was aligned to the x axis to measure the resistivity change along y directions (ρ yy ), and y axis to measure the resistivity change along x directions (ρ xx ), respectively (Fig. 2d) 61 . The relationship between resistance measured from four point probe and resistivity components are explained in Supplementary Note 2. The changes of resistivity distribution along x and y directions are shown in Fig. 2e. In this figure, it can be seen how the strain in y direction at 12.5% and 20% caused the increase of ρ xx by 4.73% and 12.65%, as well as ρ yy by 8.58% and 24.02%, respectively. These results imply that strains induce anisotropic resistivity change. From the literatures 55,62 , long and slender MWCNT networks tend to be aligned along the direction of applied strain. This structural evolution of the MWCNT networks can induce anisotropic resistivity.
Fundamentals of anisotropic electrical impedance tomography. As mentioned above, the anisotropic electrical impedance tomography is suggested in this work to calculate the internal resistivity distribution of soft and conductive medium without fabricating stretchable electrodes within the medium. We focused on the reconstruction of anisotropic resistivity distributions to evaluate the multi-directional strain distribution by using the anisotropic piezoresistive characteristics of the nanocomposite. Figure 3a shows the schematic diagram of the anisotropic resistivity reconstruction system. MWCNT-silicone elastomer nanocomposite sensor structure was connected to the electrical interconnections at its boundary with silver paste. The interconnections were connected to the multiplexer that switched four connections (current+ , current− , voltage+ , voltage− ) controlled by a computer. As a switching sequence, adjacent method, which provides a symmetric switching sequence, was chosen to inject the electrical current all over the nanocomposites 53 . Figure 3b illustrates the method in which currents are injected through a pair of adjacent electrodes and electrical potentials are measured from the other adjacent electrodes. The current injection and voltage measurement were rotated through all adjacent electrode pairs to cover the entire domain. The anisotropic resistivity distributions were calculated from the two sets of the data which were measured in isotropic status and in strain induced anisotropic status as shown in Fig. 3c. The data in isotropic status was measured when the resistivity measured in x and y directions are the same due to the random orientation of the MWCNT fillers. After the strain is applied to the sensor, the anisotropic change of electrical resistivity is caused by the alignment of the long and slender MWCNTs 6 . The reconstruction of the anisotropic resistivity distributions was conducted by using inverse calculation (Supplementary Note 3). Three resistivity distributions are computed from the anisotropic resistivity reconstruction; two normal resistivity distributions and one shear resistivity distribution. Normal resistivity distribution is defined where the direction of the current injection and the direction of the voltage measurement are in parallel. Shear resistivity distribution is defined where the directions of the current injection and voltage measurement are perpendicular to each other. The hemispherical shaped strain sensor was used to identify contact locations and intensity from the test (Fig. 3d). From the resistivity reconstruction procedures, three resistivity distributions were computed (Fig. 3e). The normal resistivity showed increases at the locations where pinch forces were applied.
Strain sensing performances. Performances of the proposed sensor were measured by tensile test and indentation test using a square shaped (50 mm × 50 mm × 5 mm) planar sensor. Besides, tensile test was done using a custom-designed tensile testing machine (Fig. 4a). In this experiment, tensile strain was applied to the sensor from 0% to 50% by 16 intervals. Figure 4b shows the results of anisotropic resistivity distributions calculated by aEIT technique. From 0 to 50% strains, both normal resistivities in x and y directions were increased. The resistivity distribution along x direction (ρ xx ) increased by 10% in average while the resistivity distribution along y direction (ρ yy ) increased by 20% in average. This result implies that the sensor can distinguish the direction of the strain from the anisotropic resistivity distributions. Although the average value of the resistivity distribution along y direction showed an exponentially increasing curve due to the characteristic of the MWCNT-silicone elastomer nanocomposites as shown in Fig. 2c, exponential regression was used to estimate stretch displacement because the resistivity of the nanocomposite increased exponentially when stretched. The estimation error of the stretch displacement was 0.54 ± 0.53 mm and R 2 value was 0.98. (Fig. 4e).
The surface indentation test was conducted using three dimensional manipulator with a sphere shaped indenter to evaluate the strain localization performance on the square shaped planar sensor (Fig. 4c). As shown in this figure, the sensor was located on the ground and the indenter pressed the sensor along the normal direction to the surface. Indented locations on the planar surface of the sensor were from 10 mm to 40 mm, with an interval of 5 mm in the x and y directions, resulting in 49 indented locations in total. Figure 4d shows the anisotropic resistivity distributions for 9 different contact locations. The results of the surface indentation test demonstrates that the compressive strain to the surface of the sensor induces similar resistivity change along x and y directions. To show the performances of the strain sensor, stretch displacement from the tensile test was estimated from the average of the change in resistivity distributions along y directions (ρ yy ). The surface normal force in the indentation test was estimated by the average of the change in resistivity distribution along x and y directions. To evaluate the performances of surface normal force, indentation test was conducted as shown in Supplementary Figure 5. In the indentation test, the estimation error of the surface normal force was 0.61 ± 0.62 N (Fig. 4e). The minimum pressure the sensor can detect was 0.1727 N as evaluated from the limit of detection 63 (see Supplementary Figure 6). The response time of the sensor was evaluated using chirp signal shaped compression. The cutoff frequency of the sensor system including data acquisition, computation of resistivity distribution was calculated as 2.13 Hz (Supplementary Figure 7). Although the response time of the sensor was not sufficiently fast, this can be improved by using stiffer elastomers since the slow response time seems to be due to the softness and viscoelasticity of the nanocomposite. The location of compressive contact was estimated by calculating the centroids of the area of normal resistivity distributions (Supplementary Note 4). Figure 4f displays the errors between the estimated and actual contact locations for 49 individual contact points. Although the errors of the estimation tend to be larger at locations farther from the boundary electrodes (i.e. central regions of the sensor) due to the imperfection of the resistivity reconstruction model, estimation error of the contact locations was 1.88 ± 0.95 mm (37.6 ± 19.0% for 5 mm spatial resolution). Figure 4g illustrates the results of the stretching test with different orientations (θ = 0°, 45°, 90°) from the x axis to show the identification capability of stretch directions. When the sensor was stretched along the x axis (θ = 0°), the normal resistivity distribution in the x axis (ρ xx ) increased. A stretch to the y axis (θ = 90°) showed an increase of normal resistivity distribution in the y axis (ρ yy ). When the sensor was stretched by an angle of θ = 45°, shear resistivity distribution (ρ xy ) increased. These results imply that the anisotropic EIT technique can identify the stretching direction.
Demonstration of human-machine interface device. The proposed sensor has a great potential to be used as a soft human-machine interface because it can detect both contact force and location and be formed in various three dimensional shapes while covering a large area. Figure 5a represents an example of three dimensional contoured human-machine interface detecting contact pressures from five fingers. Figure 5b illustrates how the sensor could distinguish different pressure levels. When the finger applied pressure on the device surface, the electrical resistivity is locally increased at the location of pressure, as represented by the color intensity in the figure. Figure 5c shows the defined locations of five fingers chosen for the experiment. In Fig. 5d, the first five columns illustrate the distributions of resistivity change when each contact location is individually pressed. Meanwhile, the results of multi-contact tests in the last 2 columns exhibit the capability of our sensor in the detection of various multi-pressure patterns. The estimation accuracy of contact locations for the three dimensional contoured interface device was examined by the manipulator as shown in Fig. 4c. Indented locations on the device surface were from 20 mm to 60 mm with an interval of 10 mm in the x directions and from 25 mm to 125 mm with an interval of 10 mm in y directions, resulting in 60 indented locations in total (Fig. 5e). Estimation error of the locations was 4.80 ± 3.05 mm (48.0 ± 30.5% for 10 mm spatial resolution). This relatively large estimation error was caused by the discrepancy between the resistivity reconstruction model defined in two dimensions and the actual sensor shape with three dimensional surfaces. Due to this discrepancy, the contact locations on the device was projected to the two dimensional resistivity plane.
To demonstrate the potential of this human-machine interface device in the robotic applications, the signals from the device was utilized to control a robot hand (BH8-262, Barrett Technology, USA) that can bend and spread its fingers. Since this robot hand only has three fingers, the same number of control points were set in the sensor. In specific, the device was divided into three sections and each contact location was calculated (Fig. 5f). The average of the resistivity change from each section was used to control the rotation speed of each robotic finger. Besides, the spread angle calculated from the centroids of three contact points was used to control the spread angle of the robotic fingers. In detail, the robot fingers were spread if the spread angle was larger than 180 degrees and the difference of the angle was mapped to the spread speed of the robot finger (Fig. 5f,g). The control of the

Discussion
This paper presented a multi-point, multi-directional strain distribution sensor using anisotropic electrical impedance tomography (aEIT) on MWCNT-silicone elastomer nanocomposite-based three dimensional strain sensor. Critical components to this work are the fabrication of nanocomposites with strain induced anisotropic resistivity and implementation of aEIT system to calculate the multi-directional resistivity distributions. The resistivity distributions are computed from the voltage potentials measured at the electrodes on the boundary of the nanocomposites. This approach could be used to realize multi-directional strain distribution sensors with large coverage area and three dimensional contoured shapes. A remaining technical challenge is the enhancement of anisotropic piezoresistivity of nanocomposites and calculation accuracy in the aEIT system. Besides, applying the aEIT technique to other piezoresistive materials such as liquid metal or nanowires composites will represent another promising direction for the future research.

Methods
Device fabrication. Conductive polymer composite should have piezo-resistivity to be used as a strain sensor. We used multi-walled carbon nanotube (MWCNT, Hyosung, South Korea) as a conductive filler and silicone rubber (EcoFlex0030, Smooth-On, Inc, USA) as a polymer matrix. Mixing process was as follows. Firstly, MWCNT and silicone rubber were mixed by planetary centrifugal mixer (PDM-300, EXAKT, Germany) for 2 minutes. Then mixed composite was dispersed by three roll mills (80E, EXAKT, Germany) in four stages. Different mixing ratios of MWCNT and silicone rubber was used (2.5 wt%, 3.5 wt%, 4.5 wt% and 5 wt%). Since the sensitivity of the piezo-resistivity mainly depends on the volume fraction of the MWCNT and polymer matrix, the volume fraction showing the highest sensitivity was chosen. Acrylonitrile butadiene styrene (ABS) based plastic molds were fabricated to various shapes using three dimensional printing machine (Dimension elite, Stratasys, USA). The plastic molds had tiny air gaps for ventilation. Surfaces of the plastic molds were covered by release agent (ER200, Mann release technologies, USA). In injection molding process, liquid dispenser (AD3000C, Iwashita Engineering, Japan) provided compressed air to pressed MWCNT-silicone elastomer composite. After the composite filled the plastic mold, an oven (OF-02, Jeiotech, South Korea) cured the composite. To attach electrodes to the composite, electrical wires were fixed using silver paste (ELCOAT, CANS, Japan) to provide stable electrical contact condition.
Device characterization. The surface morphology of MWCNT-silicone rubber was characterized by field emission scanning electron microscopy (FE-SEM, Sirion, FEI, USA) operating at an acceleration voltage of 10 kV. To prepare the sample for SEM imaging, specimens were fabricated to have minimum thickness. After the specimen is located on the carbon tape, thin (~10 nm) platinum layer was sputtered. For the measurement of current-voltage (I-V) characteristics, silver paste was applied to the opposite sides of MWCNT-silicone rubber in order to reduce the contact resistance. The I-V curves were obtained by semiconductor parameter analyzer (4155A, HP, USA). To characterize anisotropic resistivity, 4 point probe (4-point meter, Dasol engineering, South Korea) was used. In order to measure the mechanical responses of the nanocomposites, a custom-designed tensile machine containing a computer-controlled linear guided actuator and a force sensor was utilized. In order to acquire the data and to control the aEIT system, data acquisition system (cDAQ 9174, National Instruments, USA) was operated with a sampling frequency of 30 kHz. The resistance of the specimen was measured simultaneously using constant current source and voltage meter from the each end. A differential voltage to current converter circuit was implemented to provide electrical currents to the sensor using operational amplifiers (OPA 177, Texas instruments, USA). The voltage difference was measured by a differential amplifier (INA 128, Texas instruments, USA).