Inkjet-Printed Flexible Strain-Gauge Sensor on Polymer Substrate: Topographical Analysis of Sensitivity

Inkjet-printed strain gauges on flexible substrates have recently been investigated for biomedical motion detection as well as the monitoring of structural deformation. This study performed a topographical analysis of an inkjet-printed strain gauge constructed using silver conductive ink on a PET (polyethylene terephthalate) substrate. Serpentine strain-gauge sensors of various thicknesses and widths were fabricated using inkjet printing and oven sintering. The fabricated gauge sensors were attached to curved surfaces, and gauge factors ranging from 2.047 to 3.098 were recorded. We found that the cross-sectional area of the printed strain gauge was proportional to the gauge factor. The correlation was mathematically modelled as y = 0.4167ln(x) + 1.3837, for which the coefficient of determination (R2) was 0.8383.


Introduction
For decades, strain-gauge sensors have been employed to measure forces applied to target objects. A strain gauge is constructed from a conductive substance with a wavy pattern, which is attached to the object under investigation. Deformations induced by applied forces result in variations in the resistance [1,2].
Additive manufacturing using techniques such as inkjet [3], screen [4], aerosol [5], gravure [6,7] and shadow-mask [8] printing have been attracting increasing interest because it is environmentally friendly and material-saving compared with conventional photolithography or chemical vapour deposition. This approach also allows direct printing of the strain gauge onto the surface of the target object without a gluing process, thereby avoiding force decoupling between the substrate and glued strain-gauge material [9].
A full Wheatstone bridge with a single-symmetry structure was suggested for compensating for surrounding temperature variations when performing structural health monitoring outdoors [15]. A parametric design and fabrication process were investigated for developing analytical models and optimized process parameters for a sandwich-layerstructure strain gauge with an insulation layer [16].
How the set-in effect, nonlinear responses and hysteresis influence the signals produced by printed strain gauges has also been investigated [17]. Moreover, a comparison study was carried out between screen-printed strain-gauge sensor with carbon and inkjetprinted sensors with Ag nanoparticles (AgNPs) [18]. The microstructure, gauge factor and long-term repeatability were analyzed. However, none of these studies performed a topographical analysis of inkjet-printed strain gauges constructed using Ag on a polyethylene terephthalate (PET) substrate.
This study used inkjet printing to fabricate serpentine strain-gauge patterns with various thicknesses and widths of the conductive material. The initial resistances, thickness profiles and cross-sectional areas were identified after sintering the printed patterns, and strains were calculated under bending. The correlation between the gauge factor and topography was investigated using both theoretical and experimental approaches.

Fabrication
A drop-on-demand (DOD) inkjet printer (DMP-2831, Fujifilm Dimatix, Santa Clara, CA, USA) was used to produce the strain-gauge pattern on the substrate. A 10 pL cartridge with 16 nozzles (DMC-11610, Fujifilm Dimatix, Santa Clara, CA, USA) was filled with Ag conductive inks. To ensure stable ink deposition, three nozzles were selected for Ag ink ejection. The nozzle aperture was 21.5 µm. The diameter of a single droplet on the substrate was approximately 51.4 µm, as shown in Figure 1a. Thus, the drop spacing for producing a serpentine pattern was determined as 30 µm to ensure the formation of a continuous line. The finalized pattern design is depicted in Figure 1b. The width, pitch and height of the standard pattern were 140 µm, 700 µm and 7 mm, respectively. The plate with the substrate was placed inside the inkjet printer and heated at 50 • C during the ink deposition, in order to form a stable pattern by the rapid evaporation of the solution. After the printing process, the deposited strain-gauge pattern was sintered in a conventional convection oven (OF-22GW, JEIO Tech, Daejeon, Korea) at 150 • C for 15 min to ensure high conductivity.
long-term repeatability were analyzed. However, none of these studies performed a top graphical analysis of inkjet-printed strain gauges constructed using Ag on a polyethylen terephthalate (PET) substrate.
This study used inkjet printing to fabricate serpentine strain-gauge patterns with va ious thicknesses and widths of the conductive material. The initial resistances, thickne profiles and cross-sectional areas were identified after sintering the printed patterns, an strains were calculated under bending. The correlation between the gauge factor and t pography was investigated using both theoretical and experimental approaches.

Fabrication
A drop-on-demand (DOD) inkjet printer (DMP-2831, Fujifilm Dimatix, Santa Clar CA, USA) was used to produce the strain-gauge pattern on the substrate. A 10 pL ca tridge with 16 nozzles (DMC-11610, Fujifilm Dimatix, Santa Clara, CA, USA) was fille with Ag conductive inks. To ensure stable ink deposition, three nozzles were selected f Ag ink ejection. The nozzle aperture was 21.5 μm. The diameter of a single droplet on th substrate was approximately 51.4 μm, as shown in Figure 1a. Thus, the drop spacing f producing a serpentine pattern was determined as 30 μm to ensure the formation of continuous line. The finalized pattern design is depicted in Figure 1b. The width, pit and height of the standard pattern were 140 μm, 700 μm and 7 mm, respectively. The pla with the substrate was placed inside the inkjet printer and heated at 50 °C during the in deposition, in order to form a stable pattern by the rapid evaporation of the solution. Aft the printing process, the deposited strain-gauge pattern was sintered in a convention convection oven (OF-22GW, JEIO Tech, Daejeon, Korea) at 150 °C for 15 min to ensu high conductivity.

Characteristics
The electrical characteristics of each printed strain gauge were evaluated by r sistance measurements using a source meter (2400, Keithley, Solon, OH, USA). The sen tivity of the strain gauge was quantified as the gauge factor ( ), which was defined as th ratio of the electrical resistance change induced by the applied strain, as in Equation (1

Characteristics
The electrical characteristics of each printed strain gauge were evaluated by resistance measurements using a source meter (2400, Keithley, Solon, OH, USA). The sensitivity of the strain gauge was quantified as the gauge factor (G f ), which was defined as the ratio of the electrical resistance change induced by the applied strain, as in Equation (1). A specified strain was applied to the printed strain-gauge pattern by bending it. Five fan-shaped pillars with various curved surfaces were manufactured using a commercial three-dimensional (3D) printer, as shown in Figure 2. Then, the printed strain-gauge pattern was attached to each curved surface to measure the electrical resistance under bending. The strain on the printed pattern induced by bending was calculated using Equation (2) [19] where G f , ε, c, ρ, ∆R, R 0 are the gauge factor, the strain, half the substrate thickness, the bending curvature, the change in resistance and the initial resistance, respectively.
A specified strain was applied to the printed strain-gauge pattern by bending it. F shaped pillars with various curved surfaces were manufactured using a commercia dimensional (3D) printer, as shown in Figure 2. Then, the printed strain-gauge was attached to each curved surface to measure the electrical resistance under be The strain on the printed pattern induced by bending was calculated using Equa [19] = (∆ / )/ = / where , , , , Δ , are the gauge factor, the strain, half the substrate thickn bending curvature, the change in resistance and the initial resistance, respectively For the topographical analysis of the printed strain-gauge sensor, specimen prepared using two approaches: stacked and expanded. For the stacked approa serpentine pattern was overprinted on the same position of the substrate, and thre of specimens were fabricated: single layer, three layers and five layers. For the exp approach, thin, normal-width and double-width patterns were produced using tw and seven droplets, respectively. In all cases, the drop spacing was fixed at 30 μ interferometer (Nanoscan NS-E1000, Nanosystems, Daejeon, Korea) was used to m and evaluate the mean width and mean thickness of the printed strain-gauge patt

Statistical Analysis
Minitab (version 20.1.3, Minitab, State College, PA, USA) was employed for sta analysis. The Anderson-Darling test was used to determine the normality of data tical significance was indicated by p < 0.05. Seven specimens were prepared for eac graphical condition, and it was confirmed statistically that they conformed to a distribution. Figure 3a illustrates the printed strain-gauge pattern on the PET substrate. T tern was 7.76 mm in width and 13 mm in length. Seven samples were prepared f topographical condition. The initial resistances of the printed strain-gauge patter sintering are depicted in Figure 3b. The resistance steadily decreased as the num stacked layers or the width increased. The mean and standard deviation (SD) va the resistance for each topographical condition are summarized in Table 1. The ma percentage coefficient of variability, calculated as SD/mean × 100 (%CV), was 3.8% seven-droplet pattern. The minimum %CV was 1.6% for the two-droplet pattern. A values were less than 5%, demonstrating the excellent reliability of the experimen taset. In addition, normality was verified in the Anderson-Darling test for all data presented in Table 1 (p > 0.05). For the topographical analysis of the printed strain-gauge sensor, specimens were prepared using two approaches: stacked and expanded. For the stacked approach, the serpentine pattern was overprinted on the same position of the substrate, and three kinds of specimens were fabricated: single layer, three layers and five layers. For the expanded approach, thin, normal-width and double-width patterns were produced using two, four and seven droplets, respectively. In all cases, the drop spacing was fixed at 30 µm. An interferometer (Nanoscan NS-E1000, Nanosystems, Daejeon, Korea) was used to measure and evaluate the mean width and mean thickness of the printed strain-gauge patterns.

Statistical Analysis
Minitab (version 20.1.3, Minitab, State College, PA, USA) was employed for statistical analysis. The Anderson-Darling test was used to determine the normality of data. Statistical significance was indicated by p < 0.05. Seven specimens were prepared for each topographical condition, and it was confirmed statistically that they conformed to a normal distribution. Figure 3a illustrates the printed strain-gauge pattern on the PET substrate. The pattern was 7.76 mm in width and 13 mm in length. Seven samples were prepared for each topographical condition. The initial resistances of the printed strain-gauge patterns after sintering are depicted in Figure 3b. The resistance steadily decreased as the number of stacked layers or the width increased. The mean and standard deviation (SD) values of the resistance for each topographical condition are summarized in Table 1. The maximum percentage coefficient of variability, calculated as SD/mean × 100 (%CV), was 3.8% for the seven-droplet pattern. The minimum %CV was 1.6% for the two-droplet pattern. All %CV values were less than 5%, demonstrating the excellent reliability of the experimental dataset. In addition, normality was verified in the Anderson-Darling test for all datasets, as presented in Table 1 (p > 0.05). Figure 4b illustrates the cross-sectional profiles of the printed strain-gauge patterns as a function of the numbers of droplets. The widths of the two-, four-and seven-droplet patterns with a fixed drop spacing of 30 μm were 144.87 μm, 176.19 μm and 264.29 μm, respectively. The width was not much smaller for two droplets than for four droplets, because the droplet could spread on the hydrophilic substrate to result in a compressed peak value of the width for the two-droplet pattern. In addition, the coffee-ring stain was clearly observed over the width of the seven-droplet pattern.      Figure 4 shows the cross-sectional profiles of the printed strain-gauge patterns. Figure 4a indicates that the thickness of the printed pattern was proportional to the number of stacked layers, and that the evenness of the pattern deteriorated for the five-layer pattern. It is assumed that the amount of evaporation was greater in the edge area of the deposited ink than in the central area, and that the resulting unbalanced evaporation forced the solute to move to the side area, producing a so-called coffee-ring effect [20,21]. The thickness of the coffee-ring stain superposed in the following printed layers. The peaks for single-, three-and five-layer patterns were 0.11934 µm, 0.32591 µm and 1.0 µm, respectively.

Results and Discussion
Appl. Sci. 2022, 12, x FOR PEER REVIEW 4 of 10 Figure 4 shows the cross-sectional profiles of the printed strain-gauge patterns. Figure 4a indicates that the thickness of the printed pattern was proportional to the number of stacked layers, and that the evenness of the pattern deteriorated for the five-layer pattern. It is assumed that the amount of evaporation was greater in the edge area of the deposited ink than in the central area, and that the resulting unbalanced evaporation forced the solute to move to the side area, producing a so-called coffee-ring effect [20,21]. The thickness of the coffee-ring stain superposed in the following printed layers. The peaks for single-, three-and five-layer patterns were 0.11934 μm, 0.32591 μm and 1.0 μm, respectively. Figure 4b illustrates the cross-sectional profiles of the printed strain-gauge patterns as a function of the numbers of droplets. The widths of the two-, four-and seven-droplet patterns with a fixed drop spacing of 30 μm were 144.87 μm, 176.19 μm and 264.29 μm, respectively. The width was not much smaller for two droplets than for four droplets, because the droplet could spread on the hydrophilic substrate to result in a compressed peak value of the width for the two-droplet pattern. In addition, the coffee-ring stain was clearly observed over the width of the seven-droplet pattern.     Figure 4b illustrates the cross-sectional profiles of the printed strain-gauge patterns as a function of the numbers of droplets. The widths of the two-, four-and seven-droplet patterns with a fixed drop spacing of 30 µm were 144.87 µm, 176.19 µm and 264.29 µm, respectively. The width was not much smaller for two droplets than for four droplets, because the droplet could spread on the hydrophilic substrate to result in a compressed peak value of the width for the two-droplet pattern. In addition, the coffee-ring stain was clearly observed over the width of the seven-droplet pattern. Figures 5 and 6 show interferometer images of printed strain-gauge patterns as functions of the number of stacked layers and the width, respectively. The size of the measured window was 1.1789 mm on the x-axis and 0.8846 mm on the y-axis for all images. In Figure 5, it is observed that the thickness of the printed pattern varied, and that the threelayer pattern was wider than the single-layer one. Figure 6 shows the distinct coffee-ring effect as the pattern widened. The mean widths and mean thicknesses of the strain-gauge patterns are summarized in Table 2.  Figures 5 and 6 show interferometer images of printed strain-gauge patterns as functions of the number of stacked layers and the width, respectively. The size of the measured window was 1.1789 mm on the x-axis and 0.8846 mm on the y-axis for all images. In Figure  5, it is observed that the thickness of the printed pattern varied, and that the three-layer pattern was wider than the single-layer one. Figure 6 shows the distinct coffee-ring effect as the pattern widened. The mean widths and mean thicknesses of the strain-gauge patterns are summarized in Table 2.   The influence of the topography of the printed serpentine pattern on the sensitivity was investigated. The stacked-layer specimens were subjected to tensile stress in a bending test. The strains calculated using Equation (2) varied from 0.625‰ to 2.5‰. It was  The influence of the topography of the printed serpentine pattern on the sensitivity was investigated. The stacked-layer specimens were subjected to tensile stress in a bending test. The strains calculated using Equation (2) varied from 0.625‰ to 2.5‰. It was observed that the gauge factor increased from 2.471 to 3.098 as more layers were stacked, as shown in Figure 7. It was particularly interesting that the gauge factor also increased with the number of droplets, corresponding to an increased width. The gauge factor varied from 2.047 for two droplets to 2.589 for seven droplets, as shown in Figure 8.     The cross-sectional areas of the printed strain gauges and corresponding sensitivity factors are summarized in Table 2. Figure 9 shows that the gauge factor was proportional to the cross-sectional area of the printed strain-gauge pattern. The correlation was mathematically modelled as y = 0.4167ln(x) + 1.3837, where x is the area in microns squared and y is the gauge factor. The coefficient of determination (R 2 ) was 0.8383.   The correlation between the geometrical variation in the conductive pattern and the gauge factor was mathematically derived based on some assumptions: (1) the geometrical deformation occurred in the linear elastic region and (2) the conductive pattern was isotropic. The resistance of the pattern with the initial geometry was calculated as The geometries were expressed using the following initial conditions and variations: where ρ e is the specific electrical resistance, L, A, H and W are the length, cross-sectional area, height and width, respectively, and dL, dA, dH and dW are their corresponding variations. Then, the variation of resistance can be calculated as The strains within the cross section are Poisson's ratio yields where ε L , ε w , ε H and ν are the longitudinal strain, transverse strains for width and height, and Poisson's ratio, respectively. Substituting Equation (8) into (7) gives Since (ε w + ε H + ε W ε H ) 1, Equation (10) can be rearranged as Combining Equations (1), (9) and (11) gives Equation (12) indicates that the gauge factor can be determined from the longitudinal strain and Poisson's ratio of the conductive pattern. To compare the gauge factors measured experimentally, we used a strain of 2.5‰ and Poisson's ratio for bulk Ag of 0.37. This yielded a gauge factor of 1.742, which was lower than the measured range from 2.047 to 3.089, as indicated in Table 2. We could speculate that this discrepancy in gauge factor is attributed to the porosity of sintered printed Ag layer. In [22], the porosity of material influences tensile mechanical properties, e.g., elastic modulus, ultimate strength, and elongation. Then, the porosity could affect the gauge factor as well as Poisson's ratio of sintered Ag layer in Equations (9) and (12). Moreover, the anisotropy of the sintered Ag layer, which was characterized by different lateral and longitudinal deformations, could markedly reduce the electrical conductivity [23,24]. In further study, we will investigate the correlation between porosity and gauge factor in microstructure investigation.

Conclusions
In this study, we performed a topographical analysis of inkjet-printed strain gauges produced using Ag on a PET substrate. Serpentine strain-gauge sensor patterns were fabricated using DOD inkjet printing, and the deposited patterns were sintered in a conventional convection oven at 150 • C for 15 min to ensure high conductivity. For the parametric investigation, the strain-gauge patterns were printed with variations in thickness, from 58.42 nm to 404.3 nm, and in width, for 151.59 µm to 209.39 µm. To calculate the gauge factor, the fabricated strain-gauge sensor was attached to curved surfaces for bending tests. The obtained gauge factors ranged from 2.047 to 3.098, and were proportional to the cross-sectional area of the printed strain-gauge pattern. The correlation was mathematically modelled as y = 0.4167ln(x) + 1.3837, with an R 2 of 0.8383.
The analysis results indicated that the gauge factor of the inkjet-printed strain-gauge sensor can be modified by controlling the cross-sectional area of the gauge pattern without changing its serpentine shape. This represents a highly useful feature for an inkjet-printed strain-gauge sensor with a controllable gauge factor.