Analysis on Resistance Changes in Liquid Metal Printed Wires under Strain for Stretchable

To overcome these limitations, this thesis analyzes, experimentally verifies and applies to stretchable electronics the relationship between strain and electrical resistance changes in the diagonal and circular arc-shaped wires of liquid metal. As a first step in the analyses, the resistance changes in diagonal floating metal wires under load were formulated with the assumption that the floating metal wires had no volume change under loading. In addition, the resistance changes in circular arc-shaped floating metal wires under load were also formulated by considering the circular arcs as series of diagonal lines.

Introduction

However, the lack of the physical understanding of the complex trajectories under stress led to no precise validation of whether the resistance changes in the eGaIn applications were theoretically reasonable. Estimation of the resistance changes in the sensors under voltage is important because the resistance change means the sensitivity, which is the main performance of the sensors. The issues of the eGaIn voltage sensors and heaters have a common point that analyzes of the resistance changes in complicated eGaIn circuits under voltage are needed.

Figure 1.2 Recent studies on stretchable electronics [3-14]

Formulation of resistance estimation models

Assumptions for simplifying Pouillet’s law

It was evident that estimation errors resulted because the deformation of the semicircular eGaIn wires under voltage affected the resistance changes in the eGaIn sensors. The diagonal wire in the eGaIn heater occupies 99.8% of the total length of the eGaIn wire to dominate the resistance change in the eGaIn heater under load. First, there is an increased difference in the maximum and average temperature of the diagonal heater under load (Table 4.3).

Figure 2.2 Tensile directional eGaIn wires with and without strain

Relationships between resistance and uniaxial strain

Verification of the estimation models

Setup for tensile tests

Method for applying the estimation models

Tensile test results

To verify the resistance estimation models for diagonal and circular arc eGaIn wires, samples were fabricated to have eGaIn wires patterned by diagonal lines of verticalities between 0 and 4 and circular arcs of start angles and end angles between 0° and 90° (Figure 3.10). The results of the tensile tests showed that the estimated and measured resistance changes were extremely similar in all samples, and the differences between both resistance values ​​were less than 0.05 in terms of a root mean square error (RMSE) as shown in Figures 3.12 and 3.13. However, the small errors in the estimation were not avoidable due to the inconsistent introduction of copper wires.

As a result, it contributed to the denial of the basic assumption that the lengths of the static parts of the eGaIn wires shown in Figure 3.8 are the same as their design dimensions and each sample had a distortion in its value of the variable α in the equation. (3.1). In addition, the randomness in the RMSEs of Figures 3.12 and 3.13 supports the view that the copper wire insertion was the main cause of the errors when considering that the copper wire insertion was not related to any parameter such as the length or shape of the eGaIn wire pattern . in the samples. Although, copper wire insertion errors are expected to be reduced by increasing the proportion of patterned eGaIn wire to the entire eGaIn wire, so that the effects of copper wire insertion uncertainty are reduced.

This was due to the increased volume in the microchannel occupied by eGaIn wire, while eGaIn had no volume change. The maximum hysteresis occurred in the sample with an arc with an initial angle of 30° and a final angle of 90°, and electrical noise in this sample appeared to be the main cause of the hysteresis, as shown in Figure 3.16. However, the estimation errors are still small regardless of the hysteresis, and the strain rate, the main reason for hysteresis, is not included in estimation models.

In Chapter 3, the obtained estimation models are verified to provide an accurate estimation of resistance changes in diagonal and circular arc-shaped eGaIn wires in a strain range of 0~150%.

Figure 3.11 Samples under 150% strain

Applications

Estimation on resistance changes in an eGaIn-based strain sensor

In other words, the tensile test result supports the claim that the estimation error is significantly reduced when the resistance change under tension is estimated considering the semicircular eGaIn wires. In practice, excluding the semicircular wires when estimating the resistance changes in the eGaIn sensor containing the semicircular wires means that the entire deformable wire in the eGaIn sensor is considered the linear wire. However, the difference in resistance change in the linear and semicircular eGaIn wires under tension clearly exists, as shown in Table 4.1: the resistance values ​​of the linear eGaIn wires are 1.25 times, 1.51 times and 1.64 times that of the semi-circular eGaIn wires at 30%, 90% and 150% tension respectively.

It can be concluded that these differences, which grow as more strain is applied, increase the estimation error when estimating the resistance change without considering the semicircular eGaIn wires. Thus, the estimation model for the circular arc-shaped eGaIn wires is expected to help the accurate estimation of resistance changes in eGaIn-based electronics that contain semicircular wires and target ultra-stretchability under load.

Figure 4.2 The measured and estimated resistance changes in the eGaIn sensor under strain

If the temperature of the eGaIn heater has no change under voltage, the variables relevant to temperature in equation (4.3), that is, the convection heat transfer coefficient and the temperature difference, become constant. Then the only variable variable on the right side of equation (4.3) is the height of the eGaIn heater. Therefore, the wire of the eGaIn heater must be designed to have a resistance change similar to that presented by equation (4.7).

Between the diagonal line and the circular arc, the diagonal line was used for the pattern of the eGaIn heater because the deformation of diagonal patterns is the same throughout the wire, unlike circular arc patterns whose deformation is partially different (Figure 4.5). In the tensile test results, it is noteworthy that the estimation error of the diagonal patterned eGaIn heater was extremely small. The saturated maximum and mean temperatures for the two heaters depending on load are shown in figure 4.15.

Unfortunately, it is inevitable that the diagonal pattern heater will have temperature variations under strain, as suggested by the existence of the extreme gap, which means the result of a difference between the actual and desired resistance variation. The difference in maximum and average temperatures is important because it plays a role as an indicator of non-uniformity in heating. Another issue is that the thermal expansion of the elastomer matrix has not been investigated.

Achieving temperature variation of less than 3% in a strain range of 0~100% just by patterning the eGaIn wire is a significant achievement when compared to other stretch heaters.

Figure 4.4 A cross-section of an eGaIn heater during heating

As a first step in choosing eGaIn wiring patterns to minimize resistance changes under load, the "resistance width" is defined as the difference between the maximum and minimum values ​​of resistance in a specific load range. The resistance width becomes larger when a wider load range is aimed for by adjusting the length ratio as shown in Figure 4.22, and in this thesis the resistance widths are targeted to be less than 5%. The fabricated samples were stretched within the respective targeted strain range in the same manner as mentioned before except for a strain rate of 0.5 mm/s, and the measured resistance changes in the two samples were compared with the resistance changes estimated by the estimation model for a circular arc-shaped eGaIn wire .

As shown in Figure 4.24, the estimated and measured resistance changes were remarkably similar to each other in both samples with estimation errors less than 0.003. These errors can be small because the resistance changes themselves were small and the length of the arc-patterned eGaIn wires in the samples were long, occupying about 97% of the total wire length, which results in reducing the insertion effects of copper wire. . Even if the estimation errors were very small, the measured resistance changes were 0.5% p and 0.7% p greater than the estimated resistance changes in both samples (Table 4.7).

They hypothesized that hysteresis has little effect on the errors due to the ten times slower strain rate than that of the samples mentioned above. As a result, we could propose eGaIn wires with resistance changes of less than 5% in the strain range of 0~50%, and eGaIn patterning is proven useful for eGaIn-based applications that do not require resistance changes under strain. Although the eGaIn wires proposed in this dissertation have relatively large resistance changes at low loads compared to other studies (Figure 1. The resistance estimation models can be applied to other studies in which the wires were placed in the tensile direction to further reduce changes in the resistance of their wires.

The reduction in resistance changes by eGaIn patterning is fundamentally the result of conversion of wire deformation that makes resistance changes into wire rotation that makes no resistance change, therefore much smaller resistance changes are expected when using the resistance estimation models for patterning of eGaIn-based blends that in other studies.

Figure 4.21 A resistance change in combined two arcs with an arc 45°&90° of 3.61

Conclusion and open issues

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