*3.1. Phase Equilibria of Binary [DBNH][OAc] and Water System*

Mixtures of [DBNH][OAc] and water at different ratios were analyzed by DSC. For each different sample, the corresponding liquidus temperature and/or glass transition (or eutectic temperature) were extracted from DSC curves obtained, and these were then plotted in a phase diagram as shown in Figure S1. The compositions of [DBNH][OAc] and water mixture samples analyzed are provided in Table S1.

The binary phase equilibria between [DBNH][OAc] and water are shown in Figure 5. The phase diagram was constructed based on temperature transition data obtained for the ionic liquid–water mixtures (water content was varied over a range between 0.49 wt.% and 100 wt.%). As can be seen from Figure 5, the black dot highlights glass transition or eutectic temperature, which is at −73 ◦C and the red dots relate to the liquidus temperatures. For the mixtures of [DBNH][OAc]–H2O, where water content was less than 54.3 wt.%, only four temperatures were obtained by DSC, due to the ionic liquid glass-formation that occurs with such compositions. Consequently, the ionic liquid liquidus curve was plotted by extrapolation.

**Figure 5.** Phase equilibria between [DBNH][OAc] and water with solid forms. Five different crystallization behaviors in the [DBNH][OAc] and water mixtures.

Results from the DSC study show that the [DBNH][OAc]–H2O mixtures can be divided into five regions based on their different crystallization behaviors. These regions are shown in Figure 5 and relate to the following characteristics:


The phase equilibrium obtained results show that the appropriate temperature range and composition range for freeze crystallization of aqueous [DBNH][OAc] solution are in Region 5. Aqueous [DBNH][OAc] solutions from this region with freezing points above −10 ◦C can be feasibly concentrated by freeze crystallization.

Calculated freezing points of an ideal aqueous solution (γ = 1) based on Equation (2) and experimentally obtained freezing points for an aqueous [DBNH][OAc] solution for the same range of dissolved solute were compared, as shown in Figure 6.

**Figure 6.** Freezing point depressions of ideal aqueous solutions calculated by simplified activity coefficient equation and aqueous [DBNH][OAc] solutions obtained by differential scanning calorimetry (DSC).

Water activity coefficients for aqueous [DBNH][OAc] solutions from Region 5 of the phase diagram, as calculated by Equations (1) and (2), are presented in Figure 7. It is apparent that aqueous ionic liquid solutions are non-ideal and [DBNH][OAc]–H2O has an attractive interaction, as γ<sup>L</sup> < 1. The freezing point depression data obtained by DSC were used as a basis for the thermodynamic modeling. When the two heat capacity change terms of undercooled water in Equation (2) are considered, this results in a lower level of non-ideality for the studied binary solution in higher concentrations when compared to the model based on Equation (1), where the specific heat capacity change terms are ignored. Furthermore, it is worth noting that Equation (3) was also used to calculate specific heat capacity change at −38.28 ◦C, even though Equation (3) is only considered to be valid over a temperature range between 0 and −35 ◦C according to Sippola and Taskinen [22].

**Figure 7.** Activity coefficient of water as a function of solute mole fraction.
