# Cellulose and Vanadium Plasmonic Sensor to Measure Ni\({}^{2+}\) Ions
## 3 Results and Discussion
### Sensitivity and Binding Affinity  
Sensitivity in the SPR performance mainly depends on the increase in the resonance angle with the change in the refractive of the sensing medium. For a better sensor, sensitivity should be as high as possible. With the help of Figure 5a, the sensitivity of the proposed sensor could be determined. A maximum sensitivity of 0.068\({}^{\circ}\) ppb\({}^{-1}\) was obtained at the lower range of Ni(II) ion concentrations, from 0-10 ppb. Table 3 shows that this proposed sensor outperforms the best sensitivity and detection limit reported so far. An appreciable enhancement in the sensitivity and limit of detection was obtained because of the self-assembly method, which provided a much better distribution of V-CNCs-CTA for improved analyte-binding property. The inclusion of CNCs-CTA provided a larger active surface area in V film, thus allowing the interaction of van der Waals and hydrogen bonds between hydroxyl groups and oxygen atoms.  
Binding affinity measurement was another parameter used to evaluate the strength of the binding interaction between a single Ni(II) ion to its binding partner, V/CNCs-CTA sensing film. Figure 5b shows the increment in resonance angle plotted against Ni(II) ion concentration, which was nonlinearly fitted in Origin 9 with the help of the following Sips equation [61]:  
\[\theta=\frac{\theta_{\text{max}}KC^{n}}{1+KC^{n}} \tag{1}\]  
where \(K\) is the binding affinity constant, \(C\) is the concentration of the Ni(II) ion, \(\theta\) is the resonance angle at maximum binding sites, \(n\) is the heterogeneity factor of the system, which varies from 0 and 1. The system heterogeneity means that the adsorbent  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Ni(II) Ion**} & \multicolumn{3}{c}{**Au Film**} & \multicolumn{3}{c}{**V-CTA-CNC Layer**} \\ \hline \multirow{2}{*}{**Concentration**} & \multicolumn{2}{c}{**Refractive Index**} & \multicolumn{2}{c}{**Refractive Index**} & \multirow{2}{*}{**Thickness**} & \multicolumn{2}{c}{**Refractive Index**} & \multirow{2}{*}{**Thickness**} \\ \cline{2-2} \cline{6-9}  & **npb** & **k** & **n** & **k** & & **(nm)** & **n** & **k** & **(nm)** \\ \hline
0 & 1.3330 & 0 & 0.17501 & 3.6796 & 47 & 1.340 & 0.176 & 7.30 \\
2 & 1.3332 & 0.001 & 0.17501 & 3.7126 & 47 & 1.349 & 0.148 & 7.33 \\
4 & 1.3338 or the adsorbate, or both are heterogeneous. When \(n=1\), this model converts to the Langmuir model, which implies homogenous adsorption, and if it is greater than 1, the system is said to heterogeneous. The higher the value of \(n\), the more heterogenous is the system [62; 63]. However, in some cases, when the value of \(n\) is greater than 1, this model may be identified as describing a cooperative interaction with adsorbates at one site of the adsorbent influencing different binding sites on the same adsorbent [64]. Evaluation of the experimental fitting yielded an \(n\) of 2.04, thus indicating the cooperative manifestations of the adsorptive Ni(II) ions on the heterogeneous surface of Au/MPA/V-CNCs-CTA thin film. Furthermore, the \(K\) value reported in this study had a higher affinity constant of 0.0310 ppb\({}^{-1}\) (1.819 \(\times\) 10\({}^{6}\) M\({}^{-1}\)) compared to other existing SPR sensors [65; 66] (see Table 3).  
Figure 4: _Cont._  
Figure 4: Fitting experimental data to theoretical data for Au/MPA/V-CNCs–CTA thin film when detecting (**a**) DW and (**b**) 2 ppb; (**c**) 4 ppb; (**d**) 6 ppb; (**e**) 8 ppb; (**f**) 10 ppb; (**g**) 20 ppb; (**h**) 50 ppb of Ni(II) ion solution.  
Figure 5: Plot of resonance angle increment with Ni(II) ion concentration for (**a**) sensitivity and (**b**) binding affinity measurements.