## 4 Results and Discussion
### Static Fluorescence in Binary and Ternary Systems  
#### 4.2.1 Binary Systems  
As observed for NR dissolved in alkanes [28], for alkan-1-ols, we also experienced a substantial overlap between the absorption and emission bands. Figure 6 displays the fluorescence emission spectra of NR in H\(-\)(CH\({}_{2}\))\({}_{n}-\)OH (n = 1-8) at various concentrations, recorded at 25 \({}^{\circ}\)C (\(\lambda_{ex}\) = 540 nm). It should be noted that, to avoid saturation of the fluorescence signal, the measurements were performed on more dilute NR solutions [0.2, 16] uM. The area under the emission band, \(I^{em}\), and maximum wavelength, \(\lambda_{max}^{em}\), were extracted from each spectrum and plotted as a function of dye concentration, \(C_{D}\), in Figure 7a,b.  
In Figure 7a it is apparent that \(I^{em}(C_{D})\) increases non-linearly. This may be due, on the one hand, to the attenuation of the light flux through an absorbing solution and, on the other hand, to the difference between the area illuminated by the exciting light and the working area from which the fluorescence is collected. This latter effect is purely instrumental, so it produces a systematic change in all measurements. On the contrary, attenuation depends on the ability to absorb, which is connected to the polarity of the medium. Theoretical studies [34] have established that, due to attenuation, the fluorescence intensity, \(F\), can be quantitatively determined using the following equation:  
\[F=F_{0}^{ex}\Phi_{f}\cdot\left(1-10^{-\epsilon\ell C_{D}}\right) \tag{27}\]  
where \(F_{0}^{ex}\) is the exciting light intensity, \(\Phi_{f}\) is the fluorescence quantum efficiency, \(\epsilon\) is the molar extinction coefficient, \(\ell\) is the cell pathlength.  
Figure 6: Fluorescence emission spectra of NR in (**a**) Methanol, (**b**) Ethan-1 ol, (**c**) Propan-1 ol, (**d**) Butan-1 ol, (**e**) Pentan-1 ol, (**f**) Hexan-1 ol, (**g**) Heptan-1 ol, and (**h**) Octan-1 ol. The concentrations of the dilutions are in the range of 0.262–16 uM.  
Accordingly, we analyzed the experimental results in terms of nonlinear models:  
\[I^{em}=\Gamma\Big{(}1-10^{-b\Delta C_{D}}\Big{)} \tag{28}\]  
where adjustable parameters \(\Gamma\) and \(b\) were computed by a Levenberg-Marquardt procedure. The curves displayed in Figure 7a with an average correlation coefficient of \(R^{2}=0.98\) indicate that Equation (28) is a good model for experimental results. Figure 7b reveals that \(\lambda_{max}^{em}\) remains practically constant, at \(0<C_{D}\leq 10\) uM, in all analyzed samples. Figure 7b shows that \(\lambda_{max}^{em}\) varies slightly with max dye concentration, while it shifts markedly to shorter wavelength with an increase in the number of carbon atoms in the alkanol. In order to relate these macro-effects to the molecular properties of the system, \(\Gamma\) and \(b\) were plotted as a function of \(n\), as can be seen in Figure 8. As one can see, both parameters are strongly related to the number \(n\), albeit in the opposite way. In particular, \(\Gamma\) tends to decrease with \(n\), while \(b\) increases. The solvent hydrophobicity grows when going from methanol to octanol, reducing the NR's ability to stabilize the excited state. Accordingly, the number of NR molecules in the excited state decreases (\(\Gamma\) reduction) and, at the same time, the average absorption coefficient increases (\(b\) growth).  
Figure 7: (**a**) Area under the emission band as a function of NR molar concentration. Although the concentration is low, the fluorescence exhibits a non-linear trend. (**b**) The wavelength of the maximum emission as a function of NR molar concentration.