## 5 Conclusions  
Considering the outstanding role of the partitioning of hydrophobic solutes between water and nonpolar solvents in terms of energy cost and applicable processes, this study tries to give experimental inputs regarding the partitioning of Nile Red in different solvents. By varying the length of \(n\)-alkanes, differently hydrophilic environments have been created where the NR dye is soluble. In non-aqueous solutions, the integral absorbance of the individual measures shows a deviation from [PERSON]'s law. However, the experimental functions show very slight curvature, making data-fitting difficult. Based on the idea that dye-solvent and dye-dye interactions determine two molecular states with specific contributions to the absorption band, the procedure converges rapidly because it identifies fixed points on the experimental curve. The NR dimerization equilibrium constant, \(K\), in the first eight \(n\)-alkanols was calculated. The equilibrium constant plotted as a function of \(n\) shows a Gaussian trend centered around \(n=3\), indicating that the hydrophilicity extent of the medium assists the NR molecules in the aggregation process. Indeed, the chemical structure of the NR molecule includes a basic di-amino nitrogen atom and an acidic quinone-oxygen atom, which result in a charge-separating conformer (_twisted intramolecular transfer_). This conformer is more stabilized by short-chain alkanols due to their greater ability to create H-bonds. On the contrary, the longer-chain alkanols tend to form micelles due to the hydrophobic effect, thus increasing the steric hindrance and reducing the ability to form H-bonds. The spectra of NR in all \(n\)-alkanols investigated show a red shift at the absorption peak at 550 nm as the NR concentration increases. This shift is studied by analyzing the contribution to infinite dilution and the initial increase for each \(n\)-alkanol. \(\lambda_{max}^{\infty}\) decreases exponentially with \(n\), i.e., the hydrophobic \(n\)-alkanols interact with NR molecules by reducing the red shift. The term \(\lambda_{xx}\), due to the finite concentration of dye, decreases linearly with \(n^{2}\). Hence, the hydrophobicity of alkanol significantly reduces the red shift of the NR absorption band. The role of the medium hydrophilicity on the NR spectroscopic response was further investigated by adding constant volumes of pure water to the single NR-alkanol binary systems. In order to quantify the hydrophilicity, the parameter \(R\), defined as the ratio of water molecules to alkanol molecules, is introduced. The integral absorbance measured, relative to the condition of the binary system without water, decreases significantly. Furthermore, the average percentage increase undergoes a significantly greater increase if the alkanol is hydrophilic; on the contrary, the increase is very mild if the alkanol is hydrophobic. Fitting the area below the emission band allowed for the determination of the \(\Gamma\) and \(b\) parameters. They are related to the quantum yield and the molar extinction coefficient of NR molecules. The \(\Gamma\) parameter is found to decrease with \(n\), while \(b\) increases. This suggests that long-chain alkanols poorly stabilize the excited state of NR and reduce fluorescence. The introduction of water to the binary system NR-alkanol causes a decrease in fluorescence.  
Conceptualization, L.A. and A.M.; methodology, L.A., A.M., G.C. and F.L.; software, L.A.; validation, L.A., A.M. and F.L.; formal analysis, L.A.; investigation, A.M. and G.C.; data curation, L.A. and A.M.; writing--original draft preparation, L.A. and A.M; writing--review and editing, L.A; visualization, A.M.; G.C.; supervision, L.A.; project administration, L.A.; funding acquisition, L.A. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
**Acknowledgments:** CSGI (Centre for Colloid and Surface Science) is acknowledged.  
**Conflicts of Interest:** The authors declare no conflict of interest.