A Route toward Ultrasensitive Layered Carbon Based Piezoresistive

Research Article Cite This: ACS Appl. Mater. Interfaces 2017, 9, 43133−43142

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A Route toward Ultrasensitive Layered Carbon Based Piezoresistive Sensors through Hierarchical Contact Design Xiaoshuang Duan,† Jiangjiang Luo,† Yanbo Yao, and Tao Liu* College of Chemistry, Chemical Engineering and Materials Science, Soochow University, Soochow, No. 199 Renai Road, Soochow 215000, P. R. China ABSTRACT: Ultrahigh sensitive piezoresistive sensors at small deformation are highly desired in many applications. Here, we propose a hierarchical contact design concept and implement it through a direct laser writing technique for fabricating layered carbon piezoresistive sensors with ultrahigh sensitivity. Sensors with unprecedented gauge factors (∼5000−10 000) at small deformation (ε < 0.1%) were successfully fabricated and demonstrated for their use in sensing both static and high-frequency (20−30 kHz) dynamic mechanical loads. A simple basic structure unit (BSU) contact network model was developed for understanding the importance of the BSU/BSU contact strength and network fractal dimension in dictating the piezoresistive sensitivity of the layered carbon piezoresistive sensors with designed hierarchical contact structures. The hierarchical contact design concept and the contact network model proposed in our work could open a general route for developing ultrasensitive piezoresistive sensors based on granular matter and composite materials. KEYWORDS: piezoresistive sensor, gauge factor, direct laser writing, layered carbon, hierarchical contact

1. INTRODUCTION The change of material electrical resistance in response to mechanical stress or strain was recognized a long time ago by Lord Kelvin.1 This phenomenon is now known as the piezoresistive effect, and it has been widely utilized in developing various piezoresistive sensors for sensing human motions, displacement and level, velocity and acceleration, force and strain, pressure, etc.2 One of the key characteristics for a piezoresistive sensor is its sensitivity, which is typically measured through gauge factor (GF), defined as the relative resistance change per unit strain ε − GF = (ΔR/R)/ε. Significant progress has been made in the past several decades in enhancing the sensitivity of various piezoresistive materials. With bulk siliconthe working horse in current sensing technology as a comparison baseline, we highlight in Figure 1 the works reported in the literature with GFs ≥ 100 at small deformation (ε < 0.5%). According to these previous findings, one can identify two different approaches that have been taken in the past for achieving ultrahigh GFs. The first approach is through discovering new materials that have inherent electronic band structures that are very sensitive to stress/strain variations. This includes the most prominent piezoresistive materialbulk silicon, which has GFs in the range of 40−200,2 and other types of semiconductive carbon materials.3,4 With down-sizing the material to the microscale and even nanoscale, the same approach has led to the discovery of some novel piezoresistive nanomaterials with extremely high GFs, such as thin films of single crystalline CdS (GF ∼ 2970)5 and p-GaN (GF ∼ 260),6 individual silicon nanowires (GF ∼ 6000),7 and carbon nanotubes (GF ∼ 200−2900).8−11 Another approach to © 2017 American Chemical Society

achieve high GFs is based upon creating a heterogeneous network structure formed by physical contacts of the basic structural unit (BSU) as in granular matter or composite materials. This approach relies on the stress/strain induced breakage/formation of the physical contacts between BSUs and/or the related electron tunneling resistance variation to achieve high GFs. The BSUs being explored include different types of metallic nanoparticles,12−19 nanographenes,20−25 and metal−carbon nanotube hybrid particles,26−28 which respectively impart GFs in the range of 100−460, 110−507, and 155− 220. Because of the availability of a wide range of BSUs in terms of composition, size, and shape, the approach of creating heterogeneously structured granular matter and composite materials is more versatile and potentially has general applicability for developing ultrasensitive piezoresistive sensors at small deformations. To fully exploit the potential of this approach, the key is to have a generally applicable method for rationally designing the physical contacts between BSUs and an efficient method to implement such a design. Herein, we report our work on developing ultrasensitive layered carbon based piezoresistive sensors guided by a hierarchical contact design concept. With this new design concept and a direct laser writing implementation technique, we are able to achieve a piezoresistive sensor with a record high GF of ∼5700−10 000 at small deformation (ε < 0.1%). Prototypical sensors with extremely high sensitivity and fast dynamic response were Received: September 24, 2017 Accepted: November 20, 2017 Published: November 20, 2017 43133

DOI: 10.1021/acsami.7b14495 ACS Appl. Mater. Interfaces 2017, 9, 43133−43142

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ACS Applied Materials & Interfaces

Figure 1. Highlights of the ultrasensitive piezoresistive sensors reported in the literature (open symbols) and this work (filled symbols) categorized according to material composition. M1−M8:12−19 aggregation/assembly of metallic nanoparticles; S1−S4:8−11 individual carbon nanotube sensors; G1−G6:20−25 aggregation/assembly of nanographene; SM1 and SM2:26,27 aggregation/assembly of metal−carbon nanotube hybrid particles; C1 and C2:3,4 carbon material sensors other than carbon nanotubes and graphene; nSC1−nSC3: nanosized various semiconductor sensors;5−7 CCAS1−3, LLAS1−2, and DDLS1: layered carbon sensors with designed hierarchical contact structures respectively representing circle−circle contact area sensor (CCAS), line−line contact area sensor (LLAS), and dot−dot contact line sensor (DDLS). The symbols listed on the top of Figure 2 (right triangle, upper right triangle (filled and unfilled), and square) respectively represent ∂GF/∂ε > 0, ∂GF/∂ε < 0, and ∂GF/∂ε = 0 of the strain dependence behavior of GFs.

Table 1. Geometric Parameters for the Piezoresistive Sensors with Designed Hierarchical Contacts

2. EXPERIMENTAL SECTION

fabricated and demonstrated for their use in pressure sensing and ultrasound sonication process monitoring. Moreover, with extension of a phenomenological model for the breakage of a BSU/BSU contact network previously developed by Kraus,29 we arrived at a simple formula that can be used for explaining the unique piezoresistive behavior of the layered carbon sensor with designed hierarchical contacts. Detailed fitting and analysis based on this formula reveal that the sensor sensitivity is closely related to the fractal dimension of the network formed by the layered carbon BSUs and the characteristic strain for BSU contact breakage.

2.1. Design and Fabrication of Layered Carbon Sensors with Hierarchical Contacts. With a line and a dot as the primary basic geometric units (BGUs), four different patterns with increasing levels of hierarchical contacts were designed for making four different types of sensors with designed hierarchical contact structures. They were respectively plain line sensor (PLS), dot−dot contact line sensor (DDLS), line−line contact area sensor (LLAS), and circle−circle contact area sensor (CCAS). Table 1 lists the corresponding sensor patterns and the related design parameters. As shown in Table 1, a PLS sensor is simply formed by a line BGU. A DDLS sensor is formed by serially connected dot BGUs. By parallel arranging multiple line BGUs and forming line-to-line interconnections between neighboring BGUs, a square LLAS sensor is formed. A square CCAS sensor is 43134


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ACS Applied Materials & Interfaces formed by first creating a secondary BGU, which is a circle formed by connecting the neighboring dot primary BGUs. These circle-shaped secondary BGUs are then interconnected side-by-side in both horizontal and vertical directions to finally give a CCAS sensor. In all of the above designed piezoresistive sensors, the lowest level of contacts is that formed by layered carbons, which are the basic structure units of our sensor with designed hierarchical contact structure and were fabricated by using a recently developed direct laser writing technique.30 The laser processing equipment utilized is a laser engraving and cutting machine (SCE4030, Wuhan Sunic Photoelectricity Equipment Manufacture Co., Ltd.) equipped with a pulsed CO2 laser with a wavelength of 10.64 μm and operated at 20 kHz. Commercial polyimide films (PI, DuPont Kapton HN, thickness of 125 μm) cut into a strip shape of size 25 mm × 6 mm × 125 μm were used in the direct laser writing process for sensor preparation. Upon irradiation by the CO2 laser at appropriate processing conditions, the irradiated region of the PI film can be readily converted into a porous network structure formed through physical contacts of layered carbons. By controlling the laser scanning mode appropriately, the PLS, DDLS, LLAS, and CCAS sensors were fabricated. The laser processing parameters are listed in Table 2. The finally achieved PLS

two methods in evaluating piezoresistive materials can be found in ref 31. In the two-probe test configuration, two copper wires were glued to the two ends of the line sensor (PLS and DDLS) by using conductive silver adhesive as the electrical contacts. During electrical testing, a predefined current I was passed through the two electrical contacts and the corresponding V was recorded. The two-probe resistance was then calculated according to R = V/I. In the vdP test configuration, four copper wires were respectively attached to the four corners of the square-shaped LLAS and CCAS by using conductive silver adhesive. By referring to the length direction of the PI strip positioned vertically and labeling the four corners as A (upper-left), B (upper-right), C (lower-right), and D (lower-left), three resistance values were measured for the LLAS and CCAS sensors in a vdP test. One is RAB(CD) = VCD/IAB with the current IAB passing through A and B contacts and the voltage drop VCD measured across C and D contacts. The second is RAD(BC) = VBC/IAD with the current IAD passing through A and D contacts and the voltage drop VBC measured across B and C contacts. The last is RAC(BD) = VBD/IAC with the current IAC passing through A and C contacts and the voltage drop VBD measured across B and D contacts. The I−V behavior for all sensors in different test configurations was examined by a Keithley 2182A nanovoltmeter and Keithley 6221 current source at room temperature with the current value set in a range from 1 μA to 100 mA. All sensors showed linear Ohmic behavior. A coupled electrical−mechanical test was applied to evaluate the piezoresistive behavior of the prepared sensors at 30 °C. In this measurement, a Q800 dynamic mechanical analyzer (TA instruments) was used to apply a cyclic tensile deformation to the test sample through either a force or displacement controlled mode. Given the small deformation being investigated in our current study (ε < 0.1%), the force control mode is preferred for minimizing sample clamping artifacts, such as sample slipping and misalignment induced strain measurement errors. With the force controlled mode, the tensile strain experienced by the sensor (PI strip film) was accordingly calculated by dividing the experimentally recorded stress by the PI tensile modulus (2734 ± 73 MPa). While the sensor was subjected to mechanical tensile deformation (0−2.5 N at a fixed rate of 2.5 N/min), its electrical resistance (R2P in two-probe and RAB(CD), RAD(BC), and RAC(BD) in vdP test configuration) was simultaneously measured by a Keithley 3706A system switch/multimeter equipped with a 3721 dual 1 × 20 multiplexer card at a sampling rate of 1/s. The channel switching time for the multiplexer card is 5.7 ms.

Table 2. Direct Laser Writing Parameters for Fabricating Layered Carbon Piezoresistive Sensors with Varied Levels of Hierarchical Contacts pattern

power (W)

line scanning speed (mm/s)

hole drilling residence time (s)

PLS DDLS LLAS CCAS

3.75 0.8 0.8 0.8

100 15 15−20 15

N/A 0.025 N/A 0.013−0.025

and DDLS sensors were symmetrically arranged on the PI strip with their long axis parallel to the length direction of the PI film. The square-shaped LLAS and CCAS sensors were similarly symmetrically arranged in the center of the PI strip. 2.2. Structural Characterization of the Layered Carbon Sensors with Designed Hierarchical Contacts. The morphologies of the direct laser writing generated porous layered carbon structures were observed and imaged by using optical microscopy (MP41, Guangzhou Mingmei Optoelectronic Technology Co., Ltd.) and scanning electron microscopy (SEM, Hitachi SU8010) with an acceleration voltage set at 5 kV. Before SEM imaging, the sample mounted on a metal stub was sputter-coated with gold at 10 mA for 40 s. The direct laser writing generated layered carbon features on a PI strip were immersed in ethanol and then subjected to mild sonication by a bath sonicator (KQ100DE, Kun Shan Ultrasonic Instruments Co., Ltd.) to obtain a dilute suspension of the BSUsisolated layered carbons, for investigating their size information. This obtained suspension was dropped onto 325-mesh copper grids and single crystalline Si wafers, respectively, and dried at room temperature to prepare the samples for transmission electron microscopy (TEM) and atomic force microscopy (AFM) imaging. Transmission electron microscopy (TEM, Hitachi HT7700, 120 kV) and atomic force microscopy (AFM, Bruker Dimension Icon) imaging were performed. The layered carbon structures achieved by direct laser writing were characterized by Raman scattering spectroscopy, the spectra of which were collected by a confocal Raman microscope in backscattering geometry with a 785 nm excitation laser (LabRam HR800, 50× objective). 2.3. Piezoresistive Performance Evaluation of the Layered Carbon Sensors with Designed Hierarchical Contacts. Given their line-shape, a two-probe test configuration was naturally adopted for preparing the electrical contacts of the line sensors (PLS and DDLS) for evaluating their piezoresistive performance. For the area sensors (LLAS and CCAS), because of their squared-shape and thin film characteristics, a van der Pauw (vdP) four-probe test configuration was used for the same purpose. A detailed discussion comparing these

3. RESULTS AND DISCUSSION The center of our hierarchical contact design concept is to create some primary basic geometric units, such as a line or a dot, to manipulate the sensitivity of the piezoresistive sensors through wisely tailoring the interconnections between the BGUs. The microstructure of the BGUs, like conventional granular matter or composite-based piezoresistive sensors, is a heterogeneous network formed by aggregation/assembly of BSUs through physical contacts. The hierarchical contacts can then be built through engineering the BGU/BGU interconnections. Within this BGU/BGU interconnected region, the BSU/BSU contacts are weaker and have smaller coordination numbers than those in the bulk region of the BGUs. As such, the BSU/BSU contacts within the BGU/BGU interconnected region are more prone to connection/disconnection under mechanical deformation, and therefore, this imparts the sensors with high sensitivity. To test this concept, we adopted a previously developed direct laser writing technique,30 which can be used to conveniently create different types of BGUs as well as to engineer their interconnections for the formation of hierarchical contacts as desired. The BSUs created by this technique are layered carbons, which are formed through an in situ carbonization process upon rapid laser heating of polyimide film. Figure 2a shows the characteristic D-band at 1297 cm−1 43135


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Figure 2. Structural characterization of the layered carbon and the corresponding piezoresistive sensors with designed hierarchical contacts created by the direct laser writing method. (a) Raman spectrum; (b) AFM images of the isolated layer carbons and a representative horizontal section-scan curve for height determination; (c) SEM images of the aggregated/assembled porous network structure (left) and TEM images of a few representative isolated layer carbons; (d), (e), (f), and (g) SEM and optical images, respectively, for plain line sensor (PLS), line−line contact area sensor (LLAS), dot−dot contact line sensor (DDLS), and circle−circle contact area sensor (CCAS).

and G-band at 1586 cm−1 of carbonaceous materials. The Dband to G-band intensity ratio was estimated to be 5.2, which suggests the presence of abundant defects and defective structures in the layered carbons generated by the direct laser writing techniques. The thickness and lateral dimension of the layered carbon BSUs were estimated by AFM (Figure 2b) and TEM (Figure 2c) imaging analysis, and are respectively 6.0 ± 3.6 nm and a few hundred nanometers. The BSUs and their aggregated/assembled porous network structure created by this process are also clearly shown in Figure 2c. A variety of BGUs can be generated by direct laser writing with controlling the laser beam scanning modes. In the present study, we focused on two different BGUs, one is a line feature (width of ∼140−

180 μm) and another is a dot feature (diameter of ∼200−230 μm). With these two different BGUs, we fabricated a series of piezoresistive sensors with different levels of hierarchical contact structures. Each sensor was written on a strip of polyimide film (length × width × thickness = 25 mm × 6 mm × 125 μm). Figure 2d shows a plain line sensor (PLS) that involves the least level of hierarchical contact structure. By forming parallel line-to-line and serial dot-to-dot interconnections, the line−line contact area sensor (LLAS, 3 mm × 3 mm, Figure 2e) and dot−dot contact line sensor (DDLS, Figure 2f) with an intermediate level of hierarchical contact structure were prepared. The sensor with the highest level of hierarchical contact structure in this study was built upon the dot BGUs. As 43136


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Figure 3. (a) Comparison of the relative resistance change with respect to stress for plain line sensor (PLS), dot−dot contact line sensor (DDLS), line−line contact area sensor (LLAS), and circle−circle contact area sensor (CCAS). The experimentally determined relative resistance change with respect to strain for one selected cycle of the sensor PLS (b), DDLS (c), LLAS (d), and CCAS (e) and the corresponding contact model fitting results with eq 2 (solid lines). The fitting parameters are m = 0.53, εc = 0.10; m = 0.53, εc = 0.014; m = 0.21, εc = 0.0014; m = 0.19, εc = 0.000029, respectively, for PLS, DDLS, LLAS, and CCAS.

tests was in general greater than the GFs derived from the subsequent cycles. With exclusion of the first cycle test results, Figure 3a compares the relative resistance change with respect to the externally applied cyclic uniaxial stress for all four different types of sensors (PLS, DDLS, LLAS, and CCAS). Given the cycle-to-cycle variations, it is apparent in Figure 3a that the sensors with increasingly higher levels of hierarchical contact structure show correspondingly increased stress sensitivity (PLS < DDLS < LLAS < CCAS). By fitting the linear region of the data set at small values of stress, we can estimate the stress coefficients of the relative resistance for PLS, DDLS, LLAS, and CCAS. They are respectively 0.0012 ± 0.000013, 0.017 ± 0.0015, 0.45 ± 0.034, and 2.10 ± 0.26 MPa−1. With the experimentally determined modulus of polyimide film (2734 ± 73 MPa), the corresponding gauge factor averaged over multiple cyclic tests, GFavg, can be accordingly determined, and it is 3.24 ± 0.04, 46.6 ± 4.2, 1234.5 ± 9.4, and 5732.2 ± 70.4, respectively, for the PLS, DDLS, LLAS, and CCAS sensors. Clearly, a remarkable 3 orders of magnitude increase in the stress/strain sensitivity has been achieved simply by introducing a hierarchical contact structure in designing the sensor from PLS to CCAS. This evidently highlights the efficacy of the concept of our hierarchical contact design in guiding a rational route for developing ultrahigh sensitive piezoresistive sensors. One notes in Figure 3a that for the sensors with high-level hierarchical contact structures (LLAS and CCAS), the stress/ strain sensitivity decreases with increasing stress/strain. This is in drastic contrast to the behavior of the ultrasensitive crack sensors formed through metallic nanoparticle aggregation/ assembly.15−19 In these previous works, the sensitivity instead increased with the applied strain/stress. Hu et al.32 summarized the three different working mechanisms that dictate the piezoresistive behavior of a particulate-filled heterogeneous material: (1) breakage of the BSU/BSU contacts; (2) tunneling resistance among the neighboring BSUs; and (3) intrinsic piezoresistivity of the BSUs. In most practical cases, such as

shown in Figure 2g, by interconnecting the dot BGUs, a circle of diameter 500 μm was formed first, which works as a secondary BGU. These circular secondary BGUs were then side-by-side interconnected in both horizontal and vertical directions to finally form a circle−circle contact area sensor (CCAS, 3 mm × 3 mm). The sensor design parameters and the laser processing conditions are listed in Tables 1 and 2. As mentioned previously, the ability to tailor the BSU/BSU contacts in the BGU/BGU interconnection region such that they are weaker than those within the BGUs is critical for the hierarchical contact design concept. With the direct laser writing technique, this can be achieved readily. In the process of direct laser writing, the line-to-line and dot-to-dot interconnection region experienced laser-induced carbonization twice, which should deliver BSU/BSU contacts with a smaller packing density and weaker strength as compared to those in their parent BGUs. As such, the BSU/BSU contacts are more prone to breakage upon external stress/strain variations, and therefore, this would lead to higher sensitivity for the piezoresistive sensors with hierarchical contact structures. The coupled electrical−mechanical test results, shown as follows, indeed confirmed this hypothesis. Three different resistances (RAB(CD), R AD(BC) , and R AC(BD) ) were measured in a vdP test configuration for the LLAS and CCAS sensors, which showed different sensitivities with respect to the applied uniaxial stress/ strain. Here, we solely focus on the most sensitive one for evaluating the piezoresistive behaviors of the sensors, which is RAD(BC) for the LLAS sensor and RAC(BD) for the CCAS sensor. More detailed studies on the anisotropic piezoresistive behavior of the sensors with designed hierarchical contact structures will be presented somewhere else. The typical resistance for an asprepared PLS and DDLS sensor fabricated in this study is respectively ∼1.8−2 and ∼2.3−4 kΩ. The typical RAD(BC) resistance for the as-prepared LLAS is ∼200−500 Ω and RAC(BD) is 1−4 Ω for the as-prepared CCAS sensor. It should also be mentioned that for all sensors, the sensor sensitivity derived from the first cycle (GF1) during the multiple cyclic 43137


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ACS Applied Materials & Interfaces vapor growth carbon fiber (VGCF)/epoxy piezoresistive materials,33 direct laser writing generated graphitic nanoplatelets,30 and various crack sensors,15−19 mechanism (3) plays a much more minor role as compared to (1) and (2). When mechanism (2) is working, one typically observes a resistance increase with the applied strain/stress, like crack sensors, which is not the case for our sensors. Therefore, this leaves (1) as the principal working mechanism dominating the stress/strain dependent sensitivity observed in our sensors, which can be qualitatively understood based on their hierarchical contact structural design, which is further explained as follows. At small strain/stress, the relatively weak BSU/BSU contacts within the line-to-line or dot-to-dot interconnection region are disconnected first to cause a significant increase of the sensor resistance, therefore leading to a higher sensitivity. Upon the breakage of the weak BSU/BSU contacts, the surviving contacts have much greater contact strength and they are less prone to disconnection. As such, the sensitivity of the sensor gradually decreases with further increasing the strain/stress. This unique nonlinear dependence of the sensitivity on stress/strain is largely attributed to the nonuniformly distributed BSU/BSU contact strength, which has been lacking in polymer nanocomposite based piezoresistive materials, e.g., VGCF/epoxy.33 As a consequence, the piezoresistive sensitivity of a polymer nanocomposite shows no dependence on the stress/strain, even when mechanism (1) is working. In addition, the granular packing nature of the BSUs in our sensor makes the load transfer mechanism(s) between the BSUs much more different compared to that of the polymer nanocomposite based piezoresistive materials. The former relies on the highly nonuniformly distributed force chains,34 and the latter depends on the polymer matrix induced shear-lag effect.35 Such drastically different load transfer mechanisms are also believed to be responsible for the different piezoresistive behaviors of our sensors as compared to those of piezoresistive polymer nanocomposites. There are a variety of microscopic and simple-to-use models concerned with the electrical transport behavior of particulatefilled heterogeneous materials, such as a modified power-law based percolation theory recently formulated by Mutlay et al.,36 which can nicely capture the influence of the filler geometry and its aggregation states on the material electrical conductivity and its temperature dependence. Nevertheless, there has been a lack of such a microscopic model(s) regarding the piezoresistivity of particulate-filled heterogeneous materials. Herein, we attempted a phenomenological model originally proposed by Kraus29 and later elaborated by Heinrich et al.37 to describe the agglomeration−deagglomeration mechanism in a filler network to facilitate our understanding of the piezoresistive behavior of our sensors with the designed hierarchical contact structures. According to this model, the strain (ε)-dependent BSU/BSU contact number N is given by

involving strain in the denominator of eq 1 implies a broad distribution of the BSU/BSU contact strength, which sets the foundation for its applicability in describing the piezoresistive behavior of our sensors with designed hierarchical contact structures. Taking a first order approximation, we consider the resistance R of the network formed by BSU contacts to be inversely proportional to N. Then, the relative resistance for the network at strain ε can be written as ⎛ ε ⎞ 2m R =1+⎜ ⎟ R0 ⎝ εc ⎠

Equation 2 suggests that for a given fractal network with specific dimension m, the smaller the εc, the higher its GF. A smaller value of εc implies a weaker contact or smaller contact strength. Upon converting the stress to strain by using the experimentally determined modulus of polyimide film, eq 2 was applied to fit the strain-relative resistance data for the PLS, DDLS, LLAS, and CCAS sensors presented in Figure 3a. In Figure 3b−e, we respectively show the experimental and eq 2 fitted results of the strain-relative resistance for a selected cycle of the PLS, DDLS, LLAS, and CCAS sensors. Apparently, eq 2 indeed provides a nice fit for all sensors. The experimentally observed sensitivity decrease with strain/stress for the sensors with high levels of hierarchical contact structure (LLAS and CCAS) has been nicely captured by eq 2. To further verify the applicability of eq 2 in describing the piezoresistive behavior of the sensors with designed hierarchical contact structures and to establish the relationship between the sensor sensitivity and the network structural parameters (m and εc), we fabricated multiple PLS, DDLS, LLAS, and CCAS sensors with varied designed parameters (Table 1) and evaluated their piezoresistive performance. Equation 2 again provided a nice fit for the strain-relative resistance of all sensors. Figure 4a,b respectively summarizes the sensor sensitivity

Figure 4. Relationship between GFavg (GF over multiple cyclic tests with the exclusion of the first cycle result) and (a) the characteristic strain εc; (b) the fractal dimension parameter m for multiple PLS, DDLS, LLAS, and CCAS sensors. The solid lines are the fitting results according to (a) GFavg = 0.025εc−1.68 and (b) GFavg = 22 342 exp(−10.5m).

N0

N= 1+

dependence on the fitting parameters m and εc. As shown in Figure 4a, one can see that the sensor sensitivity evaluated by GFavg (gauge factor averaged over multiple cyclic tests) increases with decreasing the characteristic strain εc; and the relationship can be roughly approximated by a power-law relation GFavg = 0.025εc−1.68. The increase of the sensor sensitivity with decreasing εc is understandable, because the smaller the εc, the weaker the BSU/BSU contacts. As such, it is easier for the BSU/BSU contact to break at small deformation,

2m

() ε εc

(2)

(1)

where N0 is the BSU/BSU contact number at zero strain; m is related to the fractal dimension of the network formed through the BSU/BSU contact; and εc is the characteristic strain related to the contact strength. The smaller the εc, the weaker the BSU/BSU contact. The appearance of the power-law term 43138


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for the subsequent cycles to contribute to the piezoresistivity of the sensors. A similar instability phenomenon has been identified previously in the work by Hu et al.33 for VGCF/ epoxy polymeric composite-based piezoresistive materials. These authors recognized the important role of the bonding effect of the polymer matrix in stabilizing the BSU contact network. In our future work, we will attempt the same approach to infuse different polymers into the porous structure of our sensors to overcome the instability issues. If the instability of such BSU/BSU contacts was eliminated or minimized through a polymer bonding effect, we would expect even higher GFs for the direct laser writing generated layered carbon sensors with designed hierarchical contacts. The direct laser writing generated layered carbon sensors have the high-performance polyimide film as their naturally born supporting substrate. This, along with their extremely high sensitivity facilitated through hierarchical contact design, makes these types of novel piezoresistive sensors highly compatible with the current strain gauge technology and allows them to find a broad range of new applications. Here, we demonstrate two applications: one is for pressure sensing and another is for ultrasound sonication process monitoring. The top three images of Figure 6a respectively illustrate the sensor design, pictures of the prototypical pressure sensor, and the pressure testing schemes. As shown by the design and prototypical picture, the pressure sensor is composed of a sensing element and a cantilever-like steel frame, onto which the sensing element was glued. Two pressure sensors were prepared for comparison. One has a CCAS sensor and another has a commercial metal foil strain gauge (MFSG) as the sensing elements. These two sensors were tested simultaneously under a pneumatically applied pressure of 0.125 MPa. The relative resistance change under multiple cycles of pressure application was recorded, and the results are shown in the bottom of Figure 6a. At the same 0.125 MPa pressure, the resistance of the metal foil strain gauge increased by ∼0.1% whereas it increased by 500% for the CCAS sensor. Considering the typical GF of ∼2.0 for a metal foil strain gauge, we can roughly estimate the GF of the CCAS sensing element used for making the pressure sensor, which is ∼10 000. This value is far superior to current bulk silicon technology and even better than the GFs of an individual silicon nanowire (∼6000) and carbon nanotube (∼3000). The direct laser writing generated layered carbon sensor with designed hierarchical contact structure can not only be used for sensing static mechanical loads, it also has a very fast dynamic response. This was demonstrated by a CCAS sensor applied for real time monitoring of the ultrasound sonication process. The top two images of Figure 6b schematically show the application of a CCAS sensor in monitoring a bath-sonication and a probe-sonication process, respectively. In such a testing scheme, the CCAS sensor was glued onto the bottom of a plastic dish, which floated in the sonication medium (water). By turning on the sonicator transducer, the resistance change of the sensor was recorded by an oscilloscope. The results are shown in the bottom of Figure 6b. In both the bath- and probe-sonication case, the sinusoidal ultrasound wave signals in the time domain were evidently captured by the CCAS sensor, though with the former case, a much smaller oscillation amplitude was observed. This suggests a lower power output for the bath sonication than that for the probe-sonication process. Upon fast Fourier transformation analysis of the time domain data recorded by the CCAS sensor, we can obtain the power spectra of the ultrasound in the

therefore leading to high sensitivity. In addition to the sensitivity dependence on εc, there is also a strong correlation existing between the fractal dimension parameter m and GFavg. As shown in Figure 4b, a clear increasing trend of GF with decreasing m can be observed, which can be roughly fitted by an exponential function GFavg = 22 342 exp(−10.5m). The reduced fractal dimension suggests an increase of free space in the layered carbon porous network. As mentioned previously, the BGU/BGU interconnected region in the sensors with designed hierarchical contact structure experienced the laser writing process twice, which would result in harsher heating/ carbonization conditions and therefore lead to higher porosity. Given this argument, we believe that the trend observed in Figure 4b is a result mainly due to the introduction of hierarchical contact structures through the formation of BGU/ BGU interconnection regions. Certainly, the porosity increase in the BGU/BGU interconnection region in turn reduces the hierarchical contact strength, therefore leading to enhanced sensor sensitivity. It is worth mentioning that by simply increasing the porosity without introducing the designed hierarchical contact structures, the best GF achieved in the previously reported direct laser writing generated piezoresistive sensors was ∼100,30 which is far less than the GFs of the LLAS and CCAS sensors reported in our work. This indeed suggests that the ultrahigh sensitivity of our sensors is due to the presence of the hierarchical contact structures and not simply a consequence of porosity increase. As mentioned earlier, the GFs for all sensors presented thus far have excluded the results derived from the first cycle (GF1) during the multiple cyclic tests because GF1 was consistently and significantly higher than the GFs derived from the subsequent cycles. Figure 5 plots GF1 against GFavgthe

Figure 5. Correlations between the gauge factors obtained in the first cycle test (GF1) and GFavgthe averaged GF over multiple cyclic tests excluding the first cycle result. The solid line is a fitting result according to GFavg = 0.49GF10.97.

averaged GF over multiple cyclic tests with the exclusion of the first cycle result, where one can identify a strong correlation existing between GF1 and GFavg. This correlation could be approximated by a power-law relation, GFavg = 0.49GF10.97. That a training process is required for the direct laser writing generated layered carbon piezoresistive sensors to reach stability implies that such sensors have some weak and unrecoverable BSU/BSU contacts. These contacts were disconnected during the first cycle test and cannot recover 43139


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Figure 6. Application demonstration of the circle−circle contact area sensor (CCAS) in (a) pressure sensing and (b) monitoring the ultrasound sonication process. Top images in (a) from left to right: sensor design, prototypical pressure sensors with CCAS and metal foil strain gauge (MFSG) glued onto a cantilever-like steel frame, and pressure testing scheme. Bottom picture in (a) relative resistance change of CCAS and MFSG under cyclic 0.125 MPa pressure. Top images in (b) from left to right: scheme of using CCAS for monitoring bath-sonication and probe-sonication process. Bottom pictures in (b) from left to right: real time response of the CCAS sensor to ultrasound in bath- and probe-sonication process. The insets are the corresponding power spectra in the frequency domain.

■

frequency domain for both the bath and probe-sonication process. The insets of Figure 6b show the results, which revealed 20.07 and 33.45 kHz ultrasound, respectively, generated by the probe and bath sonicators.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Jiangjiang Luo: 0000-0001-5887-4278 Yanbo Yao: 0000-0002-8619-6475 Tao Liu: 0000-0003-0267-4925

4. CONCLUSIONS In brief, a new hierarchical contact design concept was proposed and implemented through the direct laser writing technique for fabricating layered carbon piezoresistive sensors with ultrahigh sensitivity. The prototypical sensors with unprecedented high sensitivity at small deformation (GF ∼ 5000−10 000) were successfully fabricated and demonstrated for their use in sensing both static and high-frequency dynamic mechanical loads. A simple basic structure unit (BSU) contact network model was developed and used for understanding the importance of the BSU/BSU contact strength and network fractal dimension in dictating the piezoresistive sensitivity of the layered carbon piezoresistive sensors with designed hierarchical contact structures. It is believed that the hierarchical contact design concept proposed in our work could open a general route for developing ultrasensitive piezoresistive sensors based on granular matter and composite materials, which are suitable for many different applications.

Author Contributions †

X.D. and J.L. contributed equally.

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge the financial support provided by the N a t i o n a l N a t u r a l Sc i e n c e F o u n d a t i o n o f C h i n a (NSFC51673140) and startup funds provided by Soochow University (Q410900116). The support from the State and Local Joint Engineering Laboratory for Novel Functional 43140


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Polymeric Materials and the Priority Academic Program Development (PAPD) of Jiangsu Higher Education Institutions is also acknowledged.

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ABBREVIATIONS GF, gauge factor; BSU, basic structural unit; GBU, basic geometric units; PLS, plain line sensor; LLAS, line−line contact area sensor; DDLS, dot−dot contact line sensor; CCAS, circle−circle contact area sensor; PI, polyimide; OM, optical microscopy; SEM, scanning electron microscopy; TEM, transmission electron microscopy; AFM, atom force microscopy; vdP, van der Pauw

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A Route toward Ultrasensitive Layered Carbon Based Piezoresistive

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