3.2.3. Partial Molar Volumes

The partial molar volumes of the studied DESs and water in their binary mixtures, *V*<sup>1</sup> and *V*2, were calculated from the Equations (16) and (17), using the parameters of Redlich Kister equation (Tables S6–S9) and the molar volumes of the pure components, *V<sup>o</sup>* <sup>1</sup> and *<sup>V</sup><sup>o</sup>* 2

$$\overline{V}\_1 = V\_1^o + \left(\mathbf{x}\_1 - \mathbf{1}\right)^2 \sum\_{i=0}^j A\_i \left(2\mathbf{x}\_1 - \mathbf{1}\right)^i + 2\mathbf{x}\_1 \left(1 - \mathbf{x}\_1\right)^2 \sum\_{i=0}^j A\_i i \left(2\mathbf{x}\_1 - \mathbf{1}\right)^{i-1} \tag{16}$$

$$\overline{V}\_2 = V\_2^o + \mathbf{x}\_1^2 \sum\_{i=0}^j A\_i (2\mathbf{x}\_1 - 1)^i - 2\mathbf{x}\_1^2 (1 - \mathbf{x}\_1) \sum\_{i=0}^j A\_i i (2\mathbf{x}\_1 - 1)^{i-1} \tag{17}$$

The obtained values of the partial molar volumes together with the molar volumes of pure components are presented in Table S11 in Supplementary Material. As can be seen, at all studied temperatures, the molar volumes of the interacting compounds in the pure state were higher than their corresponding values in the mixture, indicating the reduction in volume upon adding a deep eutectic solvent to water. Figure 6 shows the excess partial molar volumes of the components at 298.15 K. These properties were calculated from definition as: *V<sup>E</sup> <sup>i</sup>* = *Vi* − *<sup>V</sup><sup>o</sup> <sup>i</sup>* and their values are negative over the whole composition range. In general, the negative *<sup>V</sup><sup>E</sup>* <sup>1</sup> and *<sup>V</sup><sup>E</sup>* <sup>2</sup> values indicate the presence of significant solute–solvent interactions between unlike molecules, whereas the positive *VE* <sup>1</sup> and *<sup>V</sup><sup>E</sup>* <sup>2</sup> values indicate the presence of solute–solute or solvent–solvent interactions between like molecules in the mixture [54]. In the present work, the negative excess partial molar volumes of the components indicate that the DES—water interactions are stronger than the DES—DES or the water–water interactions, what is consistent with the conclusions from excess molar volumes.

**Figure 6.** Dependence of the excess partial molar volume *<sup>V</sup><sup>E</sup>* <sup>1</sup> of - DES1, • DES2, DES3, DES4, and water *<sup>V</sup><sup>E</sup>* <sup>2</sup> in DES1, - DES2, DES3, ♦ DES4 on molar fraction of deep eutectic solvent at 298.15 K.

Since the partial molar properties at infinite dilution provide useful information about the interactions between components of a mixture that are independent on composition, their values for DES and water were calculated.

The partial molar volumes at infinite dilution of DES were obtained by setting *x*<sup>1</sup> = 0 in Equation (18) as

$$\overline{V}\_1^{\infty} = V\_1^o + \sum\_{i=0}^j A\_i(-1)^i \tag{18}$$

Similarly, setting *x*<sup>1</sup> = 1 in Equation (19) allowed to estimate the partial molar volumes at infinite dilution of water

$$
\overline{V}\_2^{\infty} = V\_2^o + \sum\_{i=0}^j A\_i \tag{19}
$$

Table 4 presents the obtained values of partial molar volumes at infinite dilutions of DES and water in their binary systems.

**Table 4.** Partial molar volumes at infinite dilution of DES and water in their binary mixtures at *T* = (293.15 to 313.15) K and at atmospheric pressure (0.1 MPa).


As can be seen, both the partial molar volumes and the excess partial molar volumes at infinite dilution increase with the increasing temperature. Such results seem to indicate that the weakening of hydrogen bond interactions between DES and water molecules with increase in temperature is the most important factor controlling the properties of the systems and it dominates over the packing effect. Moreover, the excess partial molar volumes at infinite dilution of DES change in the order TBAB:MAE (DES 3) < TBAB:BAE (DES 4) < TBAC:AP (DES 2) < TBAB:AP (DES 1) confirming the conclusions obtained on the basis of excess molar volumes. The dependence of excess partial molar volumes at infinite dilution of water on the DES: TBAB:BAE (DES 4) ≤ TBAB:MAE (DES 3) < TBAC:AP (DES 2) < TBAB:AP (DES 1) is similar and only the reordering of DES4 and DES3 takes place. However, taking into an account the uncertainty of partial molar volume at infinite dilution, it can be said, that the *<sup>V</sup>E*<sup>∞</sup> <sup>2</sup> for systems (DES4+water) and (DES3+water) are practically equal.
