# A High Compressibility Pressure--Sensitive Structure Based on CB@PU Yarn Network
## 3 Results and Discussion
### Piezoresistive Characteristics of CB@PU Network Pressure Sensors  
At a constant voltage, the electrical signal of the CB@PU elastic network was recorded as a function of deformation. The theoretical relationship between resistance change rate and deformation was expressed as Equation (5), \(\varnothing=\mathrm{GF_{0}}\cdot\mathrm{x}+\ \varnothing_{c}\), \(\mathrm{GF_{0}}=-\frac{1}{x_{0}}\). The resistance decreased after pressure applied to the surface of the copper sheet. The measured value was calculated and the actual function of deformation vs. resistance change rate was plotted. Figure 11a-c show the sensitivity of CB@PU network sensors fabricated with different PU yarns (12 tex, 34 tex, 73 tex with 100 immersion cycles) to the applied strain. The data are fitted according to Equation (5) to get the corresponding curve. The corresponding coefficients are listed in Table 2. The data shows that the change rate of resistance varies linearly with the amount of compression. The gauge factor (GF), which is usually defined as the ratio of the relative change (\(\Delta\mathrm{R/R_{0}}\)) and strain, was measured. The linearly dependent coefficients \(\mathrm{R_{2}}\) of the three samples are all greater than 0.99, so GF and \(\mathrm{GF_{0}}\) can be considered as approximately equal. It could be seen that the experimental data were highly fitting with Equation (5). These data revealed that the sensitivity of compressive strain was constant throughout the strain process, which verified the correctness of the sensing mechanism. Furthermore, the stable structure of the sensor enabled to accurate prediction of the deformation via changing sensor resistivity. In addition, since the distribution of PU yarns in the network structure was controllable, the distribution and winding method of yarns could be designed according to different requirements. This structural characteristic will be further explored in future research. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**PU Yarn Linear Density (tex)**} & \multicolumn{3}{c}{**Parameters**} \\ \cline{2-4}  & **GF (1/cm)** & \(\varphi_{c}\) & \(\mathbf{R^{2}}\) \\ \hline
12 & \(-0.8842\) & \(-4.5025\) & 0.9934 \\
34 & \(-0.9207\) & \(-5.7600\) & 0.9921 \\
73 & \(-0.8689\) & \(-6.5401\) & 0.9901 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Fitting parameters of Figure 11.  
Figure 12 shows the sensitivity of CB@PU network sensors fabricated with different PU varns (12 tex,34 tex,73 tex with 100 immersion cycles) to the applied pressure. The sensitivity of the pressure sensor was defined as \(\mathrm{S}=(R_{0}-R_{\mathrm{P}}/R_{\mathrm{P}})/\Delta\mathrm{P}\), where \(\Delta\mathrm{P}\) is the change of applied pressure, and \(R_{0}\) and \(R_{\mathrm{P}}\) represent the sensor resistance after no pressure and applied pressure, respectively. The points in Figure 12 were divided into four regions according to the sensitivity difference. They were the micro-pressure region (purple region, 0-140 Pa), low- pressure region (yellow region, 140-1.07 kPa), the medium-pressure region (pink region, 1.07-17.1 kPa) and the high-pressure region (blue region, 17.1-20 kPa). It could be seen that from the low-pressure to the high-pressure region, the sensitivity of the sensors decreased gradually. This trend was attributed to two factors. Firstly, when the PU network deformed, the elastic potential energy accumulated and required more pressure for further deformation. Secondly, the increase of the strain caused the resistance rate to decrease  
Figure 11: Change of resistance variation rate with strain under PU yarn density of 12 tex, 34 tex and 73 tex (with 100 immersing cycles). Fitting formula of (**a**): \(\varnothing=-0.8842\mathrm{x}-4.5025\); Fitting formula of (**b**): \(\varnothing=-0.9207\mathrm{x}-5.7600\); Fitting formula of (c): \(\varnothing=-0.8689\mathrm{x}-6.5401\). Figure 12: Pressure sensors with different yarn linear density respond to increasing pressures. linearly.