*3.3. Excess Isentropic Compressibility*

The isentropic compressibilities of aqueous solutions of DESs were estimated using experimental values of densities and sound velocities by the Laplace equation

$$\kappa\_{\rm S} = -\frac{1}{V\_m} \left( \frac{\partial V\_m}{\partial P} \right)\_{\rm S} = \frac{1}{\mathbf{u}^2 \cdot \mathbf{\boldsymbol{\rho}}} \tag{20}$$

providing the link between thermodynamics and acoustics.

Then, according to the approach developed by Benson et al. [55], the excess isentropic compressibility was calculated as

$$\kappa\_S^E = \kappa\_S - \sum\_i \Phi\_i \kappa\_{S,i} - T \sum\_i \Phi\_i V\_i a\_{p,i}^2 / \mathbb{C}\_{p,i} + T \sum\_i \mathbf{x}\_i V\_i (\sum\_i \Phi\_i a\_{p,i})^2 / \sum\_i \mathbf{x}\_i \mathbb{C}\_{p,i} \tag{21}$$

Tables S1–S4 in Supplementary Material present the experimental values of sound velocity and the calculated values of excess isentropic compressibility for aqueous solutions of DESs made of tetrabutylammonium bromide and 3-amino-1-propanol or 2- (methylamino)ethanol or 2-(butylamino)ethanol and for the aqueous solutions of DES built of tetrabutylammonium chloride and 3-amino-1-propanol over the entire range of compositions at temperatures ranging from 293.15 K to 313.15 K. Figure 7a shows the plots of *κ<sup>E</sup> <sup>S</sup>* against mole fraction of DES for the all studied mixtures at 298.15 K and Figure 7b depicts the temperature dependence of excess isentropic compressibility for the system (TBAB:AP +water) as an example. It is evident that the curves are remarkably asymmetric, with their minima shifted towards a rich mole fraction of water, even more than the excess molar volume curves are.

**Figure 7.** Dependence of the excess isentropic compressibility of aqueous solutions of DESs on molar fraction of deep eutectic solvent: (**a**) at 298.15 K for - DES1; • DES2; DES3; DES4; (**b**) for DES1 at 298.15 K (-); 298.15 K (•); 303.15 K (); 308.15 K (); 313.15 K (); —, Equation (6).

In these figures, it can be also seen that the values of *κ<sup>E</sup> <sup>S</sup>* are negative for all systems over the entire range of the mole fraction as well as the temperature range. This indicates that the mixtures might be less compressible than the corresponding ideal mixtures due to a closer approach and stronger interactions between the unlike molecules of the mixtures. The negative values of excess isentropic compressibility for the binary systems follow the order: TBAB:MAE (DES 3) < TBAB:BAE (DES 4) ≈ TBAC:AP (DES 2) ≈ TBAB:AP (DES 1). Thus, the behavior of the excess isentropic compressibility seems to be consistent with the obtained values of the excess molar volume, which suggests that the interactions and the packing effect dominate in aqueous solutions of TBAB:MAE and do not practically depend on the anion of the salt in DES.

Moreover, as can be seen in Figure 7b, the values of *κ<sup>E</sup> <sup>S</sup>* become less negative with increasing temperature for all systems at a fixed composition. It is due to the reduction of interactions between unlike molecules, what has already been suggested by volumetric properties. Indeed, the increase in temperature also increases the thermal motion of the molecules and enlargement of interstices. However, the decrease in hydrogen bonding is greater and, in the result, the excess molar compressibility of all aqueous solutions of DES decreases with increasing temperature.

#### *3.4. Deviations in Refractive Index*

From refractive indices the deviations in refractive index, Δ*nD*, were calculated using the equation

$$
\Delta n\_D = n\_D - \sum\_{i=1}^{n} \Phi\_i n\_{Di} \tag{22}
$$

where *nD* and *nDi* are the refractive index of a mixture and a pure component *i*, respectively and Φ*<sup>i</sup>* denotes the volume fraction of a pure component *i*.

Tables S1–S4 in Supplementary Material present the experimental values of refractive index and calculated values of the deviations in refractive index for aqueous solutions of DESs over the entire range of compositions at temperatures ranging from 293.15 K to 313.15 K. Figure 8a shows the plots of Δ*nD* against mole fraction of DES for the all studied mixtures at 298.15 K and Figure 8b depicts the temperature dependence of deviations in refractive index for the system (TBAB:AP +water) as an example.

**Figure 8.** Dependence of the deviations in refractive of aqueous solutions of DESs on molar fraction of deep eutectic solvent: (**a**) 298. 15 K for - DES1; • DES2; DES3; DES4; (**b**) for DES1 at 298.15 K (-); 298.15 K (•); 303.15 K (); 308.15 K (); 313.15 K (); —, Equation (6).

As can be seen from Figure 8, the values of deviations in refractive index are positive over the whole composition range of binary mixtures and their dependences on mole fraction of DES are asymmetrical.

It is known that deviations of refractive index are negatively correlated with excess molar volumes [56]. If excess molar volume is negative, then there will be less free volume available than in an ideal mixture and the photons will interact more strongly with the components of the solution. As a result, light will travel with a weaker velocity in the mixture and its refractive index will be higher than in an ideal solution. Thus, positive deviations of refractive index will be observed.

This phenomenon occurs in all systems investigated in the present study and it is the strongest for TBAB:MAE (DES 3). Therefore, the obtained deviations of refractive index confirm the conclusion regarding the strongest interactions between this deep eutectic solvent and water molecules compared to other DESs studied. Moreover, as the values Δ*nD* increase with decreasing temperature, they indicate an increase in the number of hydrogen bonds at lower temperatures, which corresponds with the results of densitometric and acoustic research.
