# A High Compressibility Pressure--Sensitive Structure Based on CB@PU Yarn Network
## 3 Results and Discussion
### Pressure-Sensing Mechanism
Electrons could move along these channels to form a current. Since such contacts are so dense that a plurality of conductive channels act simultaneously, the carbon black forms a spatial network chain structure in the compressed layer. The phenomenon is regarded as percolation transition [26; 27]. As shown in Figure 7d, the current flows straightly from top to bottom of the compressed layer through spatial network chain structure instead of flowing along the conductive yarn (Figure 7c), and the resistance drops sharply. The percolation theory is the main conductive mechanism of the compressed layer and will be demonstrated later. There is also a quantum tunneling effect [28; 29; 30; 31; 32] in the compressed  
Figure 6: A single CB@PU yarn corresponds to a gradual increase in the relative resistance of the strain. layer. As the pressure increases, the distance between carbon black particles decreases gradually. When particles are close enough but not in contact, due to the volatility of microscopic particles, some electrons will penetrate the energy barrier between adjacent carbon blacks, and then there will be a quantum tunneling effect. Figure 7b illustrated this effect. In order to verify the tunnel mechanism, we tested current-voltage behavior of samples with immersion cycles of 10 times and 20 times at 5.2 kPa and 20 kPa, respectively. Theoretically, there must be a quantum tunneling effect between the carbon black particles in the network structure and tunneling mechanism could lead to non-ohmic behavior. However, linear I-V relationships were observed which didn't match the theory. For this mismatch, we suspect that it was because even though the number of immersion cycles was small, the concentration of carbon black was still high, so it was likely that the effect of quantum tunneling was obscured by the percolation effect. In subsequent experiments, we will improve the experimental setup and explore this further. In order to prove the main theoretical mechanism of the compressed layer--the percolation theory, the resistance of the 0.29 mm thick compression layer at different immersing cycles was measured, as illustrated in Figure 8.  
Figure 4:0 Electrical resistance change of CB@PU yarn with increasing immersing cycles. Figure 4:1 (**a**) Illustration of percolation transition and (**b**) quantum tunnel; (**c**) Transfer path of current in uncompressed layer and (**d**) in compressed layer. Obviously, as the number of immersion cycles increased, the resistance exhibited an exponential change. This trend is consistent with the exponential function form of the classical percolation theory formula. According to the classical percolation theory, the volume resistivity of the conductive composite and the volume fraction of the conductive filler satisfy Equation (1). Figure 4:2  
where \(\sigma\) is the resistivity of the composite, \(\varphi\) represents the volume fraction of the CB in the composite, \(\varphi_{\mathrm{c}}\) reveals the critical volume fraction (volume fraction at percolation), \(\sigma_{0}\) and t are fitted constants. Theoretical predictions of the critical exponent, t, range from 1.6 to 2.0 [33; 34] while experimental values between 1.3 and 3.1 have been reported [33]. The relevant experimental data were measured and integrated in order to be matched with the classical percolation theory formula for further demonstration of the percolation effect in the CB@PU network. Firstly, the volume fraction of CB in the CB@PU network at different immersing cycles were calculated. The calculation method was as follows: the solid matter loaded on the yarn network, including CNC, CS, CB, NR, and their mass ratio was equal to their mass ratio in the suspension. CB/CNC/CS/NR = 0.49/0.49/0.64/1.33.