## 4 Results and Discussion  
### Absorption in Binary and Ternary Systems  
#### 4.1.1 Binary Systems  
Figure 1 shows NR absorption spectra recorded in H\(-\)(CH\({}_{2}\))\({}_{n}\)\(-\)OH (\(n\) = 1-8) solutions at different dye concentrations. The complexity of the spectra is related to alkan-lols-dye and dye-dye interactions, which trigger multiple transitions in the orbitals of the dye molecule. We focus our attention on absorption peaks in the 400-700 nm wavelength range corresponding to \(\pi\rightarrow\pi^{*}\) transitions of the electron density delocalized over the whole molecule [27]. A careful inspection of the absorption spectra reveals that with an increasing NR concentration, no new band arises. On the contrary, in alkanes [28], with the same number of carbon atoms, NR was found to exhibit two sharp absorption peaks centered at 485 and 510 nm [29]. This different spectroscopic response suggests a direct involvement of the solvent in the electron transition process. Although increasing the NR concentration does not produce a new band, the absorption spectrum becomes broad, and the absorbance values, with a variation in concentrations, deviate from [PERSON]'s law. This aspect is well represented in Figure 2a, where the curves \(\overline{A}(x_{D})\) are markedly non-linear. In the literature, it is stressed that the absorption spectrum of NR in methanol follows [PERSON]'s law [30]; however, the authors analyze the absorption spectra of NR at much lower molar concentrations than those used in this study. Here, it is underlined that the deviation from [PERSON]'s law may be attributed to the formation of dimers. Therefore, Equation (20) is used to calculate the equilibrium constant by the procedure employed in the \"Theoretical Aspects\" section. The results shown in Figure 2a fit the experimental data with a correlation coefficient of \(R^{2}\) = 0.98-0.99. Figure 2b displays the calculated constants as a function of the number of carbon atoms in the alkan-lol, \(n\). As one can see, the function \(K(n)\) increases up to \(n\) = 3, then decreases. Furthermore, the curve is quite symmetrical, and by a trial-and-error procedure, the best fit to the data turned out to be:  
\[K\cdot 10^{-4}=8.76 exp\left[-\left(\frac{n-3.34}{3.06}\right)^{2}\right] \tag{21}\]  
It is well known that alkan-lol molecules produce both a direct solvent field effect and an indirect geometry effect [31]. The equilibrium constants are the juxtaposition of these two effects, and the maximum in Figure 2b indicates that the alcohol hydrophilicity plays an important role in the association process. Furthermore, it is interesting to note that for \(n\) = 0 and Equation (21) gives \(K\) = 2.7 \(\times\) 10\({}^{4}\), which agrees with the values in water determined with a chemometric method [32]. Figure 1: Absorption 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 0.785–160 uM. The chemical structure of NR, i.e., 9-(diethylamino)-5H-benzo[\(\alpha\)]phenoxazine-5-one (scheme (A\({}_{1}\)) in Figure 3), consists of a rigid aromatic group and an exocyclic diethylamine group. The diethylamino group is free to rotate around the single N\(-\)C bond so that the NR molecule can assume a conformation suitable for delocalizing the lone pair of electrons from the nitrogen atom in the aromatic moiety. Due to the high electron density, plane-by-plane stacking would cause a strong repulsion between the aromatic electrons, resulting in an unstable configuration. On the contrary, a head-to-tail arrangement can be stabilized by the alkan-1 ol molecules. Moreover, as the hydrocarbon chain of an alkanol gets larger, the compound begins to look more like an alkane, the steric hindrance increases, and the attraction between the solvent molecules becomes significant. Under these conditions, the dimer is less stable, and the equilibrium constant is reduced.