# Prediction of Solvatochromic Polarity Parameters for Aqueous Mixed-Solvent Systems
## 2 Models and Methods
### Predictive Model
\[CF^{\rm{HBD}}=2.766\alpha-0.0115,\ \left(\rm{R}^{2}\ =\ 0.89\right) \tag{7}\]Figure 2: Plot of Kamlet-Taft dipolarity/polarizability (KT-\(\pi^{\star}\)) and electronic transition (\(E_{\rm T}^{0}\), kcal-mol\({}^{-1}\)) of three indicators as (**a**) Reichardt indicator, (**b**) phenol blue indicator and (**c**) Nile red indicator in (**\(\blacktriangle\)**) pure nonpolar solvent, (**\(\bullet\)**) pure hydrogen bond acceptor (HBA) solvent and pure polar hydrogen bond donor (HBD) solvent. Symbols of HBD solvents are given in Table 1. Solid line shows a linear relationship (reference homomorphism line) of KT-\(\pi^{\star}\) values and \(E_{\rm T}\) values of pure nonpolar solvents and pure HBA solvents. The deviation of \(E_{\rm T}\) values of pure HBD solvents from the linear line is due to HBD contribution. Data are given in detail in our previous work [20]. Figure 4 shows a flow chart developed in this work for predicting \(E_{\rm T}\) values of aqueous mixtures that is divided into five steps. In step 1, pure properties of electronic transition energy (\(E_{\rm T,\dot{\imath}}^{0}\)) and gas-phase dipole moment (\(\mu_{2}\)) of components 1 and 2 are compiled from the literature. In step 2, solvent characteristics of component 2 (cosolvent) are determined to check HBD ability by considering their molecular structures and KT-acidity. For example, HBD cosolvents are able to donate a proton so that their KT-acidity values are relatively high (Table 1). On the other hand, HBA cosolvents lack proton donor groups and, thus, the \(CF^{\rm HBD}\) value of HBA cosolvent is equal to unity. In step 3, \(CF^{\rm HBD}\) values of HBD cosolvent are calculated by either Figure 2 or Equation (7). In steps 4 and 5, the predictive model (Equation (2)) was used to estimate the \(E_{\rm T}\) values of aqueous mixtures and was validated, respectively. To validate the predictive model in step 5, nine aqueous mixtures of HBA cosolvents and nine aqueous mixtures of HBD cosolvents (Table 2) were used and discussed in Table 1. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Entry** & **HBD Solvents** & **KT-\(\alpha\)** & \multicolumn{4}{c}{**Actual \(CF^{\rm HBD}\) (\(\star\)) b**} & \multicolumn{2}{c}{**Calculated \(CF^{\rm HBD}\) (\(\star\)) c**} \\ \hline
**(Symbol)** & **(Abbreviation)** & **(-)** & **Ind. 1** & **Ind. 2** & **Ind. 3** & **Avg** & **(Equation (7))** \\ \hline
1 & Methanol (MeOH) & 1.00 & 3.65 & 2.32 & 2.34 & 2.77 & 2.75 \\
2 & Ethanol (EtOH) & 0.89 & 3.05 & 2.21 & 2.21 & 2.49 & 2.45 \\
3 & 1-Propanol (PrOH) & 0.84 & 2.79 & 1.96 & 2.51 & 2.42 & 2.31 \\
4 & 2-Propanol (iPrOH) & 0.76 & 2.44 & 1.72 & 2.17 & 2.11 & 2.09 \\
5 & 1-Butanol (BuOH) & 0.84 & 2.65 & 2.04 & 3.04 & 2.58 & 2.31 \\
6 & 1-Butanol (T-BuOH) & - & 2.65 & - & - & 2.65 & - \\
7 & Ethylene glycol (ETG) & 0.90 & 3.01 & - & 1.59 & 2.30 & 2.48 \\
8 & Acetic acid (AcOH) & 1.12 & 4.34 & 1.83 & 2.78 & 2.98 & 3.09 \\
9 & Formamide (FA) & 0.63 & 2.09 & 1.27 & 1.32 & 1.56 & 1.73 \\ \hline \hline \end{tabular}  
* Indicators: Ind. 1 = 2,6-diphenyl-4-(2,4,6-triphenyl-1-pyridinio) phenolate indicator: Ind. 2 = phenol blue and Ind. 3 = Nile red. b Actual \(CF^{\rm HBD}\) values are evaluated from Figure 2. c Calculated \(CF^{\rm HBD}\) values are obtained from Equation (7).  
\end{table} 
Table 1: Pure properties of hydrogen bond donor (HBD) at 25 \({}^{\circ}\)C showing Kamlet-Taft acidity (KT-\(\alpha\)) [27, 28] and HBD contribution factor (\(CF^{\rm HBD}\)) evaluated from three indicators (Ind.) a.  
Figure 3: Relationship of HBD contribution factor (\(CF^{\rm HBD}\)) with Kamlet-Taft acidity (KT-\(\alpha\)) of hydrogen bond donor (HBD) cosolvents at 25 \({}^{\circ}\)C. The \(CF^{\rm HBD}\) and KT-\(\alpha\) data are given in Table 1. Dashed line represents Equation (7). Symbols of HBD solvents are given in Table 1.  
Section 3. Table 2 tabulates the \(E_{\text{T,i^{\prime}}}^{0}\)\(\mu_{2}\)[29], Hunter basicity (\(\beta^{H}\)) of component 2 [30; 31] and \(CF^{HBD}\) values of solvents used in the predictions.