## 3 Results and Discussion
### Characterization of the POF-MIP Sensor for Furfural (2-FAL) Detection in Fresh Transformer Oil
The final relationship (5) is similar to the Hill equation which is widely used for the response of biosensors [27]. The parameters of the Langmuir Equation (5), obtained by the commercially available Software OriginPro 8.5 by Origin Lab Corp. (Northampton, MA, USA) are reported for the two sensor considered in Table 2. The program returns the reciprocal of \(K_{\mathrm{f}}\), _i.e._, the dissociation constant \(K_{\mathrm{d}}\). The fitting to the experimental values is presented in Figure 3.  
Notice that in both cases \(h\) is not significantly different from 1, considering the high error associated. The value of \(K_{\mathrm{d}}\), the dissociation constant, is about 0.02 ppm in both the considered examples, which is sufficiently low to make it possible the detection at low concentration level. \(K_{\mathrm{d}}\) is similar for the two considered sensors, as expected because the same imprinted polymer is used. The corresponding affinity constant \(K_{\mathrm{f}}\) is \(5\times 10^{6}\) mol\({}^{-1}\) L. It is more than two orders of magnitude higher than those previously determined for other small molecules, such as TNT and nicotine, with the corresponding MIP of the same composition [19, 24] which have been found to be near \(10^{4}\) mol\({}^{-1}\) L. This is certainly due in part to the different molecular structure of the site, but probably most importantly to the fact that in the system here considered the sample medium is oil, instead of water as in the previously investigated cases. Notice that according to Equation (5) the concentration for which \(\Delta\lambda_{\mathrm{ex}}\) = \(\Delta\lambda_{\mathrm{lim}}\)/2 corresponds to the dissociation constant \(K_{\mathrm{d}}\), _i.e._, to the reciprocal of the affinity constant \(K_{\mathrm{f}}\). The maximum value of the signal (\(\Delta\lambda_{\mathrm{lim}}\)) is significantly different in the two sensors. This is obtained when \(\left(K_{\mathrm{f}}c\right)^{h}\) is much higher than 1, _i.e._, c is much higher than \(K_{\mathrm{d}}\), or much lower than \(K_{\mathrm{f}}\). In that situation:  
\[A+\overline{P}\leftrightarrows\overline{AP} \tag{1}\]0 \begin{table}
\begin{tabular}{c c c c c} \hline
**POF-MIP Sensor** & \(\Delta\lambda_{\mathrm{lim}}\) (**nm**) & \(K_{\mathrm{d}}\) (**ppm**) & \(h\) & **Adj R-Square** \\ \hline P1 & 0.92 (5) & 0.024 (5) & 1.6 (3) & 0.9677 \\ P2 & 1.58 (0.09) & 0.020 (3) & 1.3 (3) & 0.9506 \\ \hline \end{tabular}
\end{table} 
Table 2: Parameters of the Hill equation for two different POF-MIP sensors for 2-FAL. Standard samples were prepared in fresh transformer oil. The two sensors here examined have a similar linearity range of the standardization curve, only up to about 30 ppb. However \(\Delta\lambda_{\mathrm{lim}}\) is higher for P2 than for P1 indicating a different concentration of sites in the polymer, and/or a different sensitivity of the detection method, as seen from Equations (5) and (6). Evidently the plasmon resonance is different in each individual sensor, due for example to differences in the thickness of the gold layer or of the fiber cladding. Such irreproducibility could be particularly relevant since each sensor is built up by hand, so a certain degree of irreproducibility must be expected. The standardization curve should be a straight line for c much lower than \(K_{\mathrm{f}}\). The regression lines at these conditions are here reported:  
\[\Delta\lambda\ = 27(5)\cdot c_{2-FAL}\ +0.03\ (3)\quad R^{2}\ = 0.9449\quad\text{ for P1}\]  
\[\Delta\lambda\ = 28\ (7)\cdot c_{2-FAL}+0.08\ (13)\quad R^{2}\ = 0.9367\quad\text{for P2}\]  
The lower detection limits determined from the \"almost linear\" part of the standardization curve at lower concentrations is about 0.002 ppm for P1 and 0.009 ppm for P2. The lower detection limits are evaluated from twice the standard deviation of the solution at zero concentration (blank sample).