# A High Compressibility Pressure--Sensitive Structure Based on CB@PU Yarn Network
## 3 Results and Discussion
### Pressure-Sensing Mechanism
The weight gain of the CB@PU network after 100 immersion cycles was 1.15 g. The mass of CB was proportionally calculated to be 0.191 g. It was considered that the CB of each load was of the same mass, so the CB content per cycle was 0.00191 g. The BP2000 carbon black had a density of 144 g/L, i.e., the CB volume per load was 0.0132 mL. The CB volume fraction at different immersion cycles thus could be calculated. According to Equation (2), the relationship between the electrical resistivity of compressive layer with a thickness of 0.29 mm and the carbon black content was obtained, as shown in Figure 4:3  
Figure 4:4  
where R is the sensor resistance, \(\sigma\) represents the sensor resistivity, l represents the height of sensor, S reveals cross-sectional area of sensor. The solid line in Figure 9 is the curve of the resistivity of the compressed layer as a function of carbon black content according to percolation theory (Equation (1)). The relevant parameters of the fitting were as follows: \(\sigma_{0}\) = 936,375 \(\Omega\)-cm, \(\varphi_{\mathrm{c}}\) = 6.626%, t = 2.8, R\({}^{2}\) = 0.990, R\({}^{2}\) is the fitting correlation coefficient. The critical exponent of the compressed layer was in reasonable agreement with both the experimental and theoretical predictions. It could be seen that the experimental data shows a good fit with Equation (1), which provides a basis for the mechanism of this sensor. It is worth noting that the current flows from top to bottom through the compressed layer vertically instead of flowing along the yarn, which means that the change of resistance of the yarn can be reflected only at the intersections of overlapping yams. What's more, the maximum length change of the single yarn in network was 20.6% and the corresponding resistance change rate was less than  
Figure 4:5 Percolation equation fit to the experimental data (conductivity data from Figure 8). 27%. Therefore, in the compression process, the change of single yarn resistance had an effect just at intersections and would have little impact on the whole network. For the uncompressed layer, the yarns are not subjected to external force directly and will not deform. The distance between the CB conductive layers is too large to form a conductive path or quantum tunneling. The current is mainly conducting along the conductive yarn, as revealed in Figure 7c, so the uncompressed layer has a high electrical resistance. Since the yarns in the network are evenly distributed, the length of yarn per unit space is approximately equal, so the resistance value of the uncompressed layer is determined by its height. During the compression, the uncompressed layer of the sensor gradually transforms into the compressed layer and the total resistance of the sensor decreases sharply during the press-down process. The sensor (with 100 immersion cycles) was subjected to different pressures and produced different strains. As illustrated in Figure 10, the upper and lower sides of CB@PU network sample were covered with 24 \(\times\) 24 \(\times\) 0.1 mm copper sheets. The copper wires were bonded with silver paste in order to remove contact resistance and obtain a stable output signal. A small copper slice was inserted at the junction of uncompressed layer and compressed layer to test the resistance of the two parts, respectively. Table 1 shows the resistance values of the two parts under different compressions. It could be seen that compressed layer resistance was much smaller than uncompressed layer resistance which approximated the resistance of the entire sensor. Therefore, the entire sensor could be regarded as a uniform resistance, ignoring the compressed layer resistance. Its resistance was only determined by the height of the uncompressed layer. To understand this resistivity behavior, a model was constructed to describe it. The resistance value of the sensor with different deformations were calculated through the resistance value formula.