# Conductivity Enhancement of Graphene and Graphene Derivatives by Silver Nanoparticles
## 3 Results and Discussion
There is a very similar linear increase with a slope of 0.19 between 13 and 30% (_w_/_w_), and then the conductivity increases radically with a slope close to 10. This behavior could be explained by assuming the existence of two different pathways for the electrons through the hybrid surface. The first slope in both hybrids, which is close to 0.2 for both hybrids, indicates the formation of pathways with mild conductivity that could be reasonably attributed to the intercalation of AgNPs between the graphene nanosheets and the formation of graphene-Ag-graphene interconnections with lower resistance than graphene-graphene in the pure graphene substrates. The second slope, which is observed only in the FLG/AgNPs hybrid and indicates much more effective electron mobility, could be attributed to the formation of new pathways that were formed only by rows of aggregated AgNPs. The fact that the second slope is not observed in the hybrid _f_-rGO/AgNPs indicates that AgNPs are much better dispersed in _f_-rGO than FLG nanosheets. Finally, it is concluded that AgNPs increase the conductivity of both graphene substrates without the assistance of an annealing process. In the recent literature, graphene-based inks produced from liquid exfoliation of graphite in various solvents or solvent/surfactant systems showed sheet resistance values between 20 and \(2\times 10^{3}\)\(\Omega\) sq\({}^{-1}\) but only after annealing at several temperatures between 100 and 950 \({}^{\circ}\)C [28]. [PERSON] et al. showed that graphene ink in carboxymethylcellulose \begin{table}
\begin{tabular}{c c c c c c c} \hline  & **Ag** & **Rs** & \(\sigma\) & **Ag** & **Rs** & \(\sigma\) \\  & **\% w/w** & **(\(\Omega\) sq\({}^{-1}\))** & **(S m\({}^{-1}\)) 10\({}^{3}\)** & **\% w/w** & **(\(\Omega\) sq\({}^{-1}\))** & **(S m\({}^{-1}\)) 10\({}^{3}\)** \\ \hline _f_-rGO & 0 & 10 & 10 & FLG & 0 & 45 & 3.5 \\ \hline _f_-rGO/AgNP\({}_{1}\) & 15 & 8.8 & 11.4 & FLG/AgNP\({}_{1}\) & 13 & 15 & 6.7 \\ \hline _f_-rGO/AgNP\({}_{2}\) & 18 & 8.1 & 12.3 & FLG/AgNP\({}_{2}\) & 26 & 10 & 8.3 \\ \hline _f_-rGO/AgNP\({}_{3}\) & 30 & 7 & 14.3 & FLG/AgNP\({}_{3}\) & 29 & 9 & 9.3 \\ \hline _f_-rGO/AgNP\({}_{4}\) & 49 & 5.4 & 18.5 & FLG/AgNP\({}_{4}\) & 44 & 2.2 & 37.9 \\ \hline _f_-rGO/AgNP\({}_{5}\) & 57 & 5 & 20 & FLG/AgNP\({}_{5}\) & 57 & 0.6 & 167 \\ \hline \end{tabular}
\end{table} 
Table 1: The R\({}_{8}\) and \(\sigma\) values of _f_-rGO/AgNPs and FLG/AgNPs hybrids. Figure 7: Electrical conductivity of _f_-rGO/AgNPs and FLG/AgNPs hybrids versus Ag% (_w_/_w_). sodium saltwater solution can reach a sheet resistance of 2 \(\Omega\) sq\({}^{-1}\) after annealing at 100 \({}^{\circ}\)C [29]. As regards conductive inks based on hybrids of graphene nanosheets and Ag nanoparticles, several reports have shown the contribution of Ag nanoparticles to electrical conductivity. As an example, [PERSON] et al. used a graphene/Ag nanoparticle hybrid as ink for inkjet printing, achieving a low resistivity of 20 \(\Omega\) sq\({}^{-1}\) after annealing at 400 \({}^{\circ}\)C with an Ag percentage of 30% \(w/w\)[30]. [PERSON] et al. recently presented a water-based graphene/AgNPs hybrid ink with sheet resistance of about 9 k\(\Omega\) sq\({}^{-1}\), which, however, decreased remarkably after six inkjet printing cycles [31]. They also observed that one hour of annealing at 100 \({}^{\circ}\)C can increase the conductivity by about 60%. The combination of a high concentration of Ag nanoparticles with an annealing process in the graphene/Ag hybrid nanostructures promotes a sintering procedure between Ag nanoparticles that leads to the formation of better conductive silver networks and therefore remarkably reduces the resistance of the hybrid. In addition, a high-temperature treatment of graphene hybrid ink-printed patterns often removes organic additives and solvents that are insulators and improves the final conductivity. However, annealing is often a forbidding or unfavorable process, especially with sensitive printing substrates such as paper and polymer films.