Reliability Assessment and Multiphysics Simulation of Additively Printed Wearable Humidity Sensor With Supercapacitive Material for Astronaut in Extreme Condition

Because of its simplicity and versatility, additive manufacturing, such as three-dimensional printing, is spreading to a wide range of industries. In the case of circuit board printing, additive manufacturing is being used. The additive technology on the printing circuit is called additive printing, which includes aerosol jet printing (AJP), direct write printing, ink jet printing (IJP), and so on. Additive printing has great benefits such as adaptability, portability, and compactness. Flexible printed circuit boards (FPCB) may be manufactured by subtractive plate-and-etch or additive print processes. In the production of the FPCB, the use of additive technologies eliminates the need for labor-intensive equipment such as masks and etching baths for removing photoresist and metallization. Software-based design and manufacturing enable production flexibility and a reduction in the amount of time required for tool upgrades and design evolution. In addition, additive printing techniques are applicable to a variety of substrates and structures. Direct-surface polymers are utilized in apparel, vehicles, and polymers. This versatility across a broad range of applications facilitates the development of novel applications such as biosensors, thermistors, transistors, and humidity sensors, among others.

Several prior research have focused on the development of additively printed humidity sensors as a consequence of their extensive applicability in a variety of applications. Numerous sensor types are resistive sensors since they are affordable and do not need dielectric ink, whereas capacitive sensors are more costly but offer a broader variety of uses and higher dependability. Silver ink is extensively used for conductive traces despite its poor water permeability owing to its simplicity of manufacture. As advanced printing techniques, direct ink write (DIW) printing is relatively unusual.

Capacitance is proportional to dielectric constant multiplied by area divided by distance [1], as demonstrated by the fact that capacitance fluctuates with relative humidity for capacitive materials. Since the dielectric constant of water is significantly greater than that of dielectric materials, the hygroscopic dielectric of a humidity sensor may be altered by water absorption. Increased humidity causes the hygroscopic dielectric to absorb more water, resulting in a rise in dielectric constant and capacitance.

The capacitive material should provide moderate hysteresis and a high correlation with humidity for reliable humidity monitoring. Significant for the reduced hysteresis is the capacitive material's property. In order for the capacitive material to transport moisture, it has to have a high-water diffusivity and a high porosity. As the traces of additively printed sensors with a single layer are directly exposed to the air, they may be susceptible to stresses and delamination from the sensor's substrate. It is suggested that multilayer traces might make the traces more resistant to delamination brought on by deformation. In addition, the fabrication of complex printed humidity sensors, such as bio data acquisition (DAQ) boards for wearable devices, necessitates multilayer printing. In order for sensors to be incorporated on a tiny FPCB, the printed humidity sensor would need to have several vias, connectors, and dielectrics, requiring a multilayer printing process. Consequently, there is a growing requirement for the development of a robust additive printing technique. If exposed to flex-stresses, the printed humidity sensor may be degraded. However, the level of the damage is dependent on a number of factors, such as the print process parameters, the sintering temperature of the print's post-treatment, and the thickness of the substrate. This would need a reliability test for the printed humidity sensor.

In this study, a multilayered additively printed humidity sensor is developed. Accordingly, the humidity sensors are printed with one, two, and three layers. As the number of printed layers increases, the layer's thickness may rise, and porosity may decrease. The thickness and porosity might be related to the sensor sensitivity to humidity change because if the sensor is thicker and porosity is decreased, absorption rate of water is decreased. Furthermore, maximum capacitance changes with respect to the number of printed layers are complicated. In pure capacitor, if thickness is decreased, the maximum capacitance of the capacitor is increased. However, the capacitive material in this research is complex material to formulate pseudocapacitance and partial double layers on inside of the layers. Figure 1 shows the diagram of physics of the humidity sensor. Pure capacitance is the capacitance on the capacitor's double layer, while equivalent series resistance (ESR) is the current flow from electrode, dielectric, or undesired contacts. Here, leakage current is electron self-discharge on open circuit. It is anticipated that the capacitance material will undergo chemical interactions, causing pseudocapacitance that resembles the behavior of batteries. In the conclusion above all, if the thickness is increased, pure capacitance will be decreased but partial capacitance will be increased. In the case of porosity, if the porosity is increased, ESR could be increased so that the capacitance will be lost but the water absorption will be increased so that the pseudocapacitance will be increased. After all, the relationship between the number of layers and capacitance would be complicated.

In this regard, this study characterized the printed humidity sensor to understand such a phenomenon correctly. The sensors' capacitance fluctuation in response to temperature and humidity was measured. In order to determine the optimal printing process, the nonlinearity of the sensor was determined. This research used cyclic voltammetry (CV) to acquire data on voltage against current in order to understand the chemical behavior of the sensor. The humidity sensor's capacitance is temperature-dependent, enabling it to experience dimension changes as a consequence of thermal expansion/contraction and chemical reactions on the capacitance material. According to prior studies, an increase in temperature accelerates ionic diffusion, resulting in an increase in diffusion capacitance [2]; in addition to the potential on the double layer, the total potential also increases. Consequently, CV measurements may provide insight into the chemical response of the humidity sensor.

Due to Fick's diffusion, relaxation, and chemical reactions, the sensor's water diffusion and electrochemical reaction occur. Figure 2 depicts a change in capacitance caused by water transport and electrochemical reactions in proportion to relative humidity. First, Fick's diffusion (an ideal example of penetrant transport corresponding to free diffusion) has a very high diffusion rate because of a significant concentration difference. Then, relaxation follows. After the dielectric is saturated, diffusion will halt; in theory, capacitance will stay unaltered (slightly changed in reality). Due to the increased temperature, the diffusivity is high, but the overall diffusion rate is low due to the tiny concentration change. Once relaxation time diminishes, the following electrochemical process will begin: As water reaches the interface between the dielectric and electrodes, an electrochemical reaction (hydroxide of BaTiO₃) occurs, and capacitance rises owing to the capacitance of the partial electrical double layer due to polarity of water [3].

Finally, this study developed a multiphysics simulation model to further understand the chemical behavior characteristics of the humidity sensors in time series with respect to different temperature, humidity variation, and thickness of the layers. The comparison study among the simulation and experimental data was done.

There are a variety of additive printing methods, including IJP, AJP, screen printing, and DIW. IJP is a printing technique that employs droplets of ink to print on a substrate. The AJP is a technique for printing using a jet of ink particles in aerosol form. Screen printing is a technique for printing on substrate with a stencil and mesh. DIW is a printing technique that deposits ink directly to the substrate using an ink jet driven by a smart pump. The DIW method has the advantage of being compatible with a variety of ink types. DIW, for instance, may be manufactured with different ink viscosity, particle size, temperature, and substrate kinds. In addition, the DIW method is ideal for intricate patterns with several layers and different ink types.

Figure 3 shows additive printer with DIW method by nScrypt and smart pump for jet of ink and the printed humidity sensor which consist of positive temperature coefficient carbon paste semidielectric ink [4], polyimide dielectric ink, and barium titanate (BaTiO₃, BTO) dielectric ink for capacitive material, and silver paste ink for conductive traces.

Figure 4 depicts a DAQ system consisting of a data logger, a humidity sensor, a humidifying and thermal chamber, a potentiostat for measuring CV, and LabVIEW-based DAQ software. The DAQ measured the capacitance in relation to changes in temperature and humidity during the experiments. There are two methods for measuring capacitance, one for measuring low capacitance and one for measuring high capacitance. If the capacitor's capacitance is greater than 1 nF, its capacitance is determined by the current flowing time, which is determined by measuring the voltage change over time until it reaches 63% of the reference voltage. On the other hand, the capacitance of the capacitor less than 1 nF is computed by comparing it to the microcontroller unit's stray capacitance (25 pF).

Owing to its high porosity, cost-effective carbon capacitive material is anticipated to absorb significant quantities of water. Nevertheless, the semidielectric feature of the material may lower capacitance resulting from current leakage. In addition, large porosity produces unforeseen contact between the electrodes, which may result in a low impedance and a reduction in the sensor's precision. As a result, the carbon humidity sensors were printed with many layers to avoid unforeseen contact surfaces and to increase their resistance to flexure. Moreover, carbon material is very temperature sensitive. In order for it to be precise, adjustment of capacitance change due to temperature fluctuation would be required, as well as simultaneous calibration with temperature and humidity.

Figure 5 illustrates the capacitance of the carbon sensor in relation to relative humidity at 25 °C and 60 °C. As illustrated in the figure, the capacitance of the sensor fluctuates dramatically with the change in relative humidity, demonstrating that the sensor is able to detect changes in humidity properly. Under addition, the capacitance values of the sensors in the same relative humidity and the same temperature are statistically equal, while that of the sensors are statistically different in the same relative humidity and the different temperature condition. The sensor might be dependent on temperature due to capacitance changes which arise from chemical reactions, which might be more dominant in high temperature. Because of such dependency on temperature, calibration between capacitance and humidity requires compensation of humidity value in different temperature scenarios. Figure 6 depicts the probability distribution of capacitance in relation to relative humidity and temperature. It has been shown that the datasets of the test measurements are normally distributed, and that the values of the printed samples consistently lie within the range of the mean capacitance. It is expected that the probability distribution would be helpful for quality control of sensors in various scenarios such as massive manufacturing. The graph can offer insights to assess whether the fabricated sensor in the same process recipe has similar characteristics and capacitance values in the same environmental conditions. The reactance in proportion to frequency is seen in Fig. 7. The reactance fluctuates in proportion to the frequency shift, while the reactance at the same frequency stays constant. The dominant mechanism of capacitance change is dielectric permittivity change due to humidity change as well as change of it due to chemical reactions such as adsorption of water on electrode and ionic conductivity change due to water absorption into dielectric because water molecule's polarity can displace the mobile ions via hydrogen bonding. If the temperature changes, ionic conductivity can be accelerated. The other possible reason is that water can intercalate between the dielectric layer which could cause hydrolysis reactions and dielectric structure changes, where temperature change directly effects on intercalation rate due to kinetic energy of macule change and hydrolysis reaction rates. The various chemical reactions might change the sensor behavior and performance such as sensitivity and hysteresis. For long-term, it might be able to cause sensor performance degradation due to dielectric material degradation.

Returning to reactance measurements, measuring reactance and frequency shift can offer some insights on chemical reactions. For example, if the permittivity changes due to water absorption are dominant, reactance change would be minimal, while if chemical reactions are dominant, reactance change would be significant when temperature is changed because the higher temperature change chemical reaction rate and change electrical energy stored in the reactive component in dielectric. Figure 7 shows that the reactance change is large in different temperature which is comparable to confirmation of chemical reactions via CV measurement. Figure 8 depicts the impedance of the sensor in respect to temperature and humidity. The impedance seems to be connected with change in temperature, indicating that humidity sensors are sensitive to the temperature that may occur from a chemical reaction. Consequently, it may be important to measure CV to appreciate the chemical behavior of the sensor. Observations reveal that certain sensors have weak impedance that is close to zero, suggesting that the sensor has unanticipated contact between the electrodes, which might lead to current flow inside the capacitive material. In order to avoid the sensor's poor impedance characteristics, it may be necessary to use a multilayer printing method.

Figure 9 displays the results of CV measurements indicating that chemical reactions occur at low scan rates (dotted-solid line). If a high scan rate is seen, it is impossible to monitor chemical reactions because the CV is being measured too quickly for there to be sufficient time to witness the chemical reaction. On a high scan rate, the measurement interval is just 60 s, whereas it is 600 s on a low scan rate.

Because the period of the tests is sufficient for chemical reactions to occur in the relative humidity sensors, empirical capacitance measurements give proof of chemical processes. To prevent these disadvantages, it may be desirable to decrease the length of time the sensor is exposed to humidity, or it may be advantageous to remove humidity regularly using a heater.

Polyimide is another great potential material with excellent dielectric properties and the capacity to absorb water. Polyimide's moderate rate of water absorption and low sensitivity of capacitance fluctuation to humidity are disadvantages. Figure 10 depicts the capacitance fluctuation in respect to relative humidity. Nonlinearity is 1.3% and R² is 98.7% across the range of 55–100% relative humidity; however, it is ineffective over the range of 20–55% relative humidity owing to its poor water absorption capacity. Despite the sensor's limited operational range, its linearity is exceptionally good. Printing using polyimide is the most economical approach for making humidity sensors. Therefore, it may be used in some extreme settings (i.e., sensing in very high relative humidity area).

For the construction of supercapacitors, a dielectric material was developed which was based on BTO (BaTiO₃) ceramic. The supercapacitive material is very capacitance-capable in the same area as ordinary capacitance-capable material. The BTO dielectric has a high capacitance sensitivity to humidity and a high porosity, which might have both advantages and disadvantages. The first advantage of high sensitivity is that it may increase the accuracy of the sensor. Due to its high capacitance, the sensor might also be made more compact. Finally, a sensor with a high porosity may effectively absorb water. However, the high sensitivity may result in an excessive amount of nonlinearity, making calibration challenging. In addition, substantial porosity might lead to unforeseen contact between electrodes, necessitating multilayer printing.

Figure 11 depicts the capacitance variation of various layered samples made with the same printing process parameters as a result of changes in relative humidity. There have been multiple measurements of each variable. Figures indicate that in the low humidity range, capacitance increases linearly with respect to humidity, that in the 40–60% area, capacitance does not appear to change significantly, which may be a relaxation area due to saturation of water in the capacitive material, and that in the high humidity area, the capacitance variation rate is very high, which may be due to an electrochemical reaction that may result from self-ionization of water or intercalation. Single-layer sensors seem to have the largest hysteresis in areas of very high humidity; however in areas of low humidity, they show superior linearity relative to multilayered samples. Because the datasets are very nonlinear, data transformation is necessary.

Figure 12 shows capacitance variation of BTO-dielectric sensor versus humidity at different frequency of AC measurement. As shown on the graph, the capacitance value is increased as the AC frequency decreases. In addition, sensor sensitivity and characteristics with respect to the different frequency are changed as well. Figure 13 shows capacitance variation versus temperature (20% RH and 40% RH) which shows that the BTO sensor has limited dependence to the temperature.

For the linear regression model, the Box–Cox power transformation test for data transformation has been performed. Box–Cox test is used to determine the value of in $logy$ if $λ=0$ otherwise $(yλ−1)/λ$⁠. As seen in Fig. 14, λ is close to zero, indicating that the dataset could be logarithmically converted. The linear regression model was able to determine the sensor's nonlinearity after log-transforming the data. Figure 15 depicts the sequential outcomes of the humidity sensor regression model. Even after data linearization, it has a significant degree of nonlinearity, which seems to be the result of a curve discrepancy between the low and high humidity regions. Consequently, the data and model must be separated into these two domains. Figure 16 shows the results of a regression model split by relative humidity ranges of 25–60% and 60–80% for sensors with one, two, and three layers. As seen in the pictures, the separated model predicts humidity with great accuracy based on capacitance. Table 1 displays the mean nonlinearity values derived from the regression model using multiple-layered samples. The sensor with a single layer has the lowest nonlinearity, as seen in the table. However, a single-layer sensor cannot be described as the best since it has the largest hysteresis (shown in Fig. 11), which makes calibration difficult.

where subscript $i=s$ for electrode with capacitive material and $i=e$ for aqueous electrolytes, $Ji$= electric current flux (A/m² s⁻¹), $Øi$ = electric potential (V), $ci$ = concentration (kmol/m³), $Di$ = mass diffusivity (m² s⁻¹), t⁺ = transference number in medium, $1+(d(ln f±)/d(ln c))$ = activity term in equation to compute diffusional conductivity (⁠$KD$⁠), $f±$= activity coefficient, diffusional conductivity $KD=(2RTk/F)(1−t+)(1+(d(ln f±)/d(ln c)))$⁠, $io$ = exchange current constant (consistent units), $a1$ = reaction rate exponents 1, $a2$ = reaction rate exponents 2, $a3$ = reaction rate exponents 3, $aa$⁠, $ac$ = transfer coefficients, $U$ = equilibrium potential (V), $F$ = Faraday constant, $R$ = universal gas constant, and $T$ = temperature (K).

Figure 17 demonstrates the multiphysics of capacitive material. Between the electrode and dielectric layer, surface electrons may be charged. As a consequence of the creation of an electrical double layer, the charge might supply the ideal capacitance. Due to the difference in dielectric constants between the electrode and the dielectric, an extra double layer might be formed on the stern layer. Moreover, the dielectric might get moisture from the surrounding air. In addition, the polarity of the water molecule enables it to transport the electron into the dielectric (charge transfer), which may lead to an increase in capacitance. In addition, the intercalation of the water molecule into the structure of the dielectric may also improve capacitance. Further, there may be water adsorption in the interphase. Due to the difference in dielectric constants between water and dielectric material, water may be capable of forming a second double layer. The material properties are listed in Table 2. The ideal dielectric constant is determined by combining the fraction equation with the experimental value of the BTO dielectric and water, as indicated in the table. However, the real dielectric constants will change in response with the fluctuation in capacitance owing to the complicated facts indicated in the preceding sentence. Therefore, simulation is required for a more comprehensive understanding. The simulation parameters are shown in Table 3.

Figure 18 displays simulation results of the water concentration in capacitive material as the surrounding environment's relative humidity changes from 0% to 100% over time. As seen in the graphs, the highest concentration occurs 30 s after 100% relative humidity. The change in water concentration throughout the length is substantially bigger for a 50-μm thickness than for 80-μm and 110-μm thicknesses, which have similar values. Moreover, the temperature of humid air had little influence on the patterns.

Figure 19 depicts the electric potential and water content, as well as the sensor's length. As seen in the diagram, the largest potential (5 V) resides at the material's surface and diminishes toward the ground.

Figure 20 depicts the simulated capacitance fluctuation with regard to supply air humidity and its comparison to experiments. The simulation reveals a trend in the diffusion and relaxation of water diffusion. The fluctuation in capacitance is comparable to test data. On the graph, the hysteresis effect with 50 μm is significant which is comparable to hysteresis of one layer sensor, while thicker layer such as 80 μm and 110 μm has low hysteresis which are matched to trend of low hysteresis in two layers and three layers sensors.

In this paper, capacitive inks are used to construct multilayer capacitive humidity sensors. According to the findings of the CV measurement, the capacitance of the humidity sensor exhibits the characteristics of a chemical reaction driven by voltage. The findings demonstrate that the capacitor has both the optimal capacitance and pseudocapacitance. The pseudocapacitance is based on temperature, which may explain why the humidity sensor is similarly dependent on temperature. The carbon sensor has relatively large dependency on temperature change, whereas sensors with supercapacitive (BTO-dielectric sensor) have less dependency on it. It might be due to sensitivity of the sensors. In detail, from perspective of sensitivity, capacitance change of BTO-dielectric sensor is most sensitive with respect to humidity change, while carbon sensor and polyimide sensor are less sensitive. For example, the capacitance of carbon sensor is changed from 130 μF to 150 μF within range of 25–90% RH, while that of BTO sensor is increased from 10 pF to 20 μF. In this regard, BTO sensor's capacitance change which arises from temperature is very limited. The BTO sensor's reliability on ambient temperature change is excellent, though the BTO sensor has the largest hysteresis and nonlinearity as compared to the others. To overcome hysteresis problem on the sensor, multilayered printing was helpful. As per experimental data, multilayered sensor has less hysteresis. In addition to this, multilayer printing prevents the ESR issue which is owing to the direct contacts between the electrodes because multilayer can decrease porosity of the printed layers. To address nonlinearity issues on the BTO sensor, data processing and multipoint calibration were needed. In this study, the capacitance of the sensor is found to be linearly linked to humidity after log-transforming the datasets. Additionally, developed calibration models, which were separated between low and high ambient humidity areas, were highly precise. So, multilayered BTO sensor with developed calibration technique has highest reliability due to low hysteresis and high accuracy of sensing capability as well as no ESR issue.

Finally, a simulation study was conducted to comprehend in depth the behavior of water diffusion in the material. The results show that the sensor is not fully saturated at the moment of environmental humidity went to 100% RH because the diffusion behavior is not fast and makes delay of saturation. As viewpoint of even saturation with a direction to length, thinner layer would be helpful such as 50 μm layer, though 80 μm and 110 μm layers are not much different. For example, concentration change in 50 μm layer is much larger than 80 μm layer, while that in 80 μm layer is not much larger than that of 110 μm layer. The final graph also shows that capacitance change in 80 μm layer is largest. In these regards, it should be noted that the optimal number of layers of dielectric has to be chosen for best performance.

• NASA (National Aeronautics and Space Administration) at the NSF-CAVE3 Electronics Research Center at Auburn University (Funder ID: 10.13039/100007579).

The authors attest that all data for this study are included in the paper.