## 4 Results and Discussion
### Absorption in Binary and Ternary Systems
#### 4.1.2. Ternary Systems  
In order to modulate the hydrophilicity of the solvent, suitable NR-Alkanol-water ternary systems were prepared by adding fixed volumes of ultrapure water to 1 mL of NR-alkanol binary solution. The hydrophilicity of the medium was measured by parameter \(R\), defined as:  
\[R=\frac{N_{W}}{N_{A}} \tag{24}\]  
where \(N_{W}\) and \(N_{A}\) are water and alcohol moles, respectively. Indeed, \(R\) = 0 identifies the starting binary system which was taken as a reference for the relative integral absorbances, \(\overline{A}/\overline{A}_{0}\). As one can see in Figure 5, for all alkanols \(\overline{A}/\overline{A}_{0}\)< 1, the addition of water reduces the integral absorbance.  
Figure 5: (**a**) Normalized integral absorbance as a function of the hydrophilicity index, in ternary systems NR–H–(CH\({}_{2}\))\({}_{n}\)–OH–water (the \(n\) value is read directly on each line). (**b**) Average percentage increase of NR red shift in ternary systems NR–H–(CH\({}_{2}\))\({}_{n}\)–OH–water (the \(n\) value is read directly on each line).  
In order to show such reduction is not the only result of the dilution of the chromophore, we make use of the absorbance definition to write:  
\[\frac{\overline{A_{t}}}{\overline{A_{0}}}=\frac{\epsilon_{t}}{\epsilon_{0}}\frac {C_{t}}{C_{0}}\;\approx\;\frac{\epsilon_{t}}{\epsilon_{0}}\frac{1}{1+R\frac{ \overline{V_{W}}}{\overline{V_{A}}}} \tag{25}\]  
where \(C_{0}\) and \(C_{t}\) are the NR concentrations in the binary and ternary systems, and \(\epsilon_{0}\) and \(\epsilon_{t}\) are the average molar extinction coefficients in the binary and ternary systems, respectively. In Equation (25), the fact that the dye concentration is very low was made use of. If the reduction were due only to the dilution, being \(\epsilon_{0}=\epsilon_{t}\), Equation (25) would imply \(\overline{A_{0}}/\overline{A_{t}}=1+R\frac{\overline{V_{W}}}{\overline{V_{A}}}\), i.e., a linear plot of \(\overline{A_{0}}/\overline{A_{t}}\) vs. \(R\). On the contrary, experimental data exhibit marked curvature, as can be seen in Figure 5a. The interaction of NR in the hydrophilic environment was further investigated by monitoring the mean percentage increase of \(\lambda_{max}\), compared to the binary system, i.e.,  
\[\Delta(\%)=\left[\frac{\lambda_{max}(\textit{ternary system})-\lambda_{max}( \textit{binary system})}{\lambda_{max}(\textit{binary system})}\right]\cdot 100 \tag{26}\]  
Experimental results displayed in Figure 5b clarify that \(\Delta(\%)\) increases by adding water. Thus, an increase in the solvent hydrophilicity corresponds to an increase in the red shift.  
This increase is greater in short-chain alkanols and indeed reaches 3% in methanol, but remains almost zero in heptan-1 ol and octan-1 ol. In short-chain \(n\)-alkanols, the hydrophobic attraction is practically absent; the interaction with the water molecules stabilizes the excited state of NR. For long-chain \(n\)-alkanols, the attraction between the individual molecules is greater than the attraction with the water molecules, resulting in a marked hydrophobic effect and a reduced stabilizing effect on the excited state of NR.