## 3 Results and Discussion
Here, the second phase of filler can affect the resistivity of printed electrodes. The resistivity of Ag NP/G composite electrodes decreased from 2.8 \(\times\) 10\({}^{-7}\) to 1.7 \(\times\) 10\({}^{-7}\)\(\Omega\cdot\)m (10% of the conductivity of bulk silver), which is approximately 61% of the resistivity of pure Ag NP electrodes. During sintering process, diffusion between silver was much easier than carbon-carbon or carbon-silver due to their same crystal structure, atoms, and less activation energy [37]. Therefore, with the same dimensions, electrodes with silver fillers have a better conductivity than those with carbon. For example, the printed pure Ag NP electrodes had a lower resistivity (2.8 \(\times\) 10\({}^{-7}\)\(\Omega\cdot\)m) than Ag NP/AC composite electrodes (3.2 \(\times\) 10\({}^{-7}\)\(\Omega\cdot\)m). The results also show that the dimension of the fillers can influent their resistivity. It was found that a small amount of CNTs have the same effect in reducing resistivity as adding 6% Ag NWs in the ink. The resistivity of Ag NP/CNT composite electrodes is 2.0 \(\times\) 10\({}^{-7}\)\(\Omega\cdot\)m, which is close to that of Ag NP/Ag NW electrodes (2.1 \(\times\) 10\({}^{-7}\)\(\Omega\cdot\)m). However, they are higher than Ag NP/G composite electrodes with 2D fillers (1.7 \(\times\) 10\({}^{-7}\)\(\Omega\cdot\)m). These composite electrodes reach the same level of resistivity, 1.0 \(\times\) 10\({}^{-7}\)\(\Omega\cdot\)m, of Ag NP ink with a silver concentration of 50 wt.% [38]. The overall resistance of an electrical network comes from the bulk resistance of fillers, constriction resistance and tunneling resistance. The constriction resistance comes from the spots where there is direct contact between the conductive fillers and it increases with the number of contact points. The tunneling resistance comes from the spots where there is no direct connection between conductive fillers and, therefore, electrons need to overcome barrier energy to transfer through those spots [39]. When the concentration of filler is below the percolation threshold, the tunneling resistance will be a dominating factor compared with constriction resistance. To understand the contribution of the second phase fillers in the electrodes, SEM analysis (see Figure 5) was performed. Figure 5a shows the formation of bounds between particles, indicating the sintering of Ag NPs creates more interconnections for electron paths. However, the higher porosity results in a high tunnel resistance in the system. In Ag NP/CNT and Ag NP/Ag NW composite electrode systems, as schematically shown in Figure 5c,d, CNTs and Ag NWs can serve as bridges to connect Ag NPs. This bridging effects helping the development of more electrical paths and as a result convert the tunnel resistance into a lower contact resistance. As for 2D filler, as illustrated in Figure 5e, large graphene sheets can connect more Ag NPs because of their large surface area [40], resulting in more contact points and significantly decreased tunnel resistance, contributing to better conductivity. However, 0D material (AC) cannot bridge Ag NPs (see Figure 5b) which result in a high tunneling resistance. Meanwhile, due to a high bulk resistance of AC caused by many pore structures and destructed sp2 hybridization [41], Ag NP/AC composite electrodes displayed the highest resistivity. To verify the results, composite electrodes with 6 wt.% silver microflakes (average width of 600 nm) were sintered under the same laser parameters, and the results show that the composite electrodes exhibit the lowest resistivity of 1.1 \(\times\) 10\({}^{-7}\)\(\Omega\cdot\)m (Figure 4). Figure 3: Schematic of laser sintering of PVP capped Ag NPs. The flexibility of these as-printed and sintered composite electrodes was characterized. The rate of change of resistance in the electrodes is calculated using K = \((\mathrm{R}-\mathrm{R}_{0})/\mathrm{R}_{0}\), where R is the resistance of the electrodes after bending, and R\({}_{0}\) is that before bending.