*3.5. Deviations in Viscosity and Excess Gibbs Energy of Activation for Viscous Flow*

Based on the viscosities of the mixtures, the viscosity deviations Δ*η* were obtained according to the equation

$$
\Delta \eta = \eta - \exp(\mathbf{x}\_1 l n \eta\_1 + \mathbf{x}\_2 l n \eta\_2) \tag{23}
$$

which uses the viscosity of the ideal mixture as suggested by Arrhenius.

The excess Gibbs energy of activation for viscous flow Δ*GE*, was calculated using the equation

$$
\Delta G^{E} = RT[\ln(\eta V\_m) - (\mathbf{x}\_1 \ln(\eta\_1 V\_1) + \mathbf{x}\_2 \ln(\eta\_2 V\_2))]\tag{24}
$$

where *R* is the gas constant and *T* is the absolute temperature. The symbols *η*1, *η*2, *V*1, and *V*<sup>2</sup> represent viscosity of DES, viscosity of water, molar volume of DES, and molar volume of water, respectively.

Tables S1–S4 in Supplementary Material present the experimental values of viscosity, calculated values of the viscosity deviations and the excess Gibbs energy of activation for viscous flow for aqueous solutions of DESs over the entire range of compositions at temperatures ranging from 293.15 K to 313.15 K. Figure 9a,b show the plots of Δ*η* and Δ*G<sup>E</sup>* against mole fraction of DES for the all studied mixtures at 298.15 K. Figure 9c,d depict the temperature dependence of viscosity deviations and the temperature dependence of the excess Gibbs energy of activation for viscous flow for the system (TBAB:BAE +water) as an example.

**Figure 9.** Dependence of the deviations in viscosity and the excess Gibbs energy of activation of aqueous solutions of DESs on molar fraction of deep eutectic solvent: (**a**,**b**) at 298.15 K for - DES1; • DES2; DES3; DES4; (**c**,**d**) for DES1 at 298.15 K (-); 298.15 K (•); 303.15 K (); 308.15 K (); 313.15 K (); —, Equation (6).

It is clearly visible that the viscosity deviations of all mixtures are positive in the whole range of composition. It is known that the viscosity of a mixture is related to the liquid structure [57]. Therefore, the viscosity deviation depends on molecular interactions as well as on the size and shape of the molecules forming the solution. The positive viscosity deviations are observed in mixtures with strong specific interactions like hydrogen bonding interactions, whereas the interstitial accommodation of one component with the other within the mixture leads to negative Δ*η* values [58]. For our DES systems, the predominant effect is the hydrogen bonding, that leads to positive Δ*η* values.

The order of viscosity deviations is the same as for the viscosity of the studied systems and is as follows: TBAB:AP (DES 1) > TBAC:AP (DES 2) > TBAB:BAE (DES 4) > TBAB:MAE (DES 3). It is different from those obtained for excess molar volume or excess compressibility. Thus, it can concluded that the values of viscosity deviations are determined not only by the interactions between unlike molecules, but also by other effects as shape of the molecules.

Estimation of the results obtained and presented in Figure 9 confirm the temperature dependence of the viscosity deviations in the studied systems because the values of Δ*η* become less positive with increasing temperature. This is due to the weakening of the interactions between the molecules present in the solution, which seem to dominate over the penetration phenomenon that obviously increases with temperature.

The positive values of excess Gibbs energy of activation presented in Figure 9a,b once again approve the dominance of specific interactions—i.e., hydrogen bonding between DES and water molecules occurring in the studied systems—which become weaker as temperature increases [58].

## *3.6. Correlations of Excess Properties*

Similarly, as in a case of excess molar volumes, in order to correlate the calculated excess thermal expansions, excess isentropic compressibilities, deviations in refractive index, deviations in viscosity, and excess Gibbs energy of activation for viscous flow with the composition, the Redlich–Kister polynomial equation was applied [34]

$$Y^E = \mathfrak{x}\_1 \mathfrak{x}\_2 \sum\_{i=0}^2 A\_i (\mathfrak{x}\_1 - \mathfrak{x}\_2)^i \tag{25}$$

where the *Ai* values are adjustable parameters. They were determined using the least squares method and their values are listed in Tables S6–S9 along with root mean square deviations of fit (RMSD). In order to obtain RMSD close to the experimental uncertainty, a different degree of the polynomial equation was chosen depending on the property and DES. For almost all systems, excess molar volumes, deviations in refractive index, and excess Gibbs energy of activation for viscous flow with composition were correlated using free-parameter Redlich–Kister polynomial equation. For viscosity deviations and excess isentropic compressibilities, a better fit was obtained for four-parameter and for five-parameter Redlich–Kister polynomial equation, respectively. In case of excess thermal expansions four-parameter for DES1 and DES 2 and five-parameter Redlich–Kister polynomial for DES3 and DES5 were chosen.

In Figures 2, 5 and 7–9, the dashed lines represent the correlated values according to the Redlich–Kister equation. As it can be seen, the calculated values agree very well with the experimental data. Thus, the Redlich–Kister equation perfectly represents the data over the experimental temperature range for the novel DES + water binary systems studied in this work.

#### **4. Conclusions**

The presented novel DESs built of tetrabutylammonium chloride and 3-amino-1-propanol or tetrabutylammonium bromide and 3-amino-1-propanol or 2-(methylamino)ethanol or 2- (butylamino)ethanol were found to be attractive in their properties, mostly for further evaluation and optimization during development of inexpensive eco-solvents or other

valuable material. Most important physicochemical properties have been demonstrated in details such as density, speed of sound, refractive index, and viscosity which were measured for their aqueous solutions over the entire range of compositions at atmospheric pressure and T = (293.15 − 313.15). The chosen Jouyban–Acree model was successfully used to correlate the experimental physical properties with respect to the concentration, and the results showed that this mathematical equation is an accurate correlation for the prediction of aqueous DES properties.

Excess molar volumes, excess isentropic compressibilities, deviations in viscosity, and deviations in refractive indices were calculated to study nonideal behavior of binary mixtures and they were correlated by the Redlich–Kister equation with temperature-dependent parameters. Excess molar volumes and excess compressiblities were negative and deviations in viscosity and deviations in refractive index were positive over the entire range of composition and temperature, suggesting strong intermolecular interactions among unlike molecules. Moreover, the temperature dependences of the excess molar volumes and compressibilities indicate that, in the studied systems, hydrogen bonding prevails over the packing effect (non-specific interactions).

The dominance of specific interactions in the aqueous solutions of the DESs also was confirmed by the Prigogine–Flory–Patterson (PFP) theory, which was applied to excess molar volumes.

The calculated negative values of the excess partial molar volumes of DESs and water demonstrated sufficient DES—water interactions which are stronger than the DES—DES or the water–water ones will probably facilitate the efficient utilization of DES.

In terms of the suitability of the water mixtures of the studied DES for the effective separation of carbon dioxide from gas streams at relatively low pressure, the obtained values of the excess properties allow us to assume that the best absorbent would be TBAB: AP, and the worst of TBAB:MAE.

**Supplementary Materials:** The following supporting information can be found online: Table S1: Densities *ρ*, excess molar volumes *VE*, isobaric thermal expansion coefficients *αp*, excess thermal expansion Δ*αp*, speeds of sound u, excess isentropic compressibilities *κ<sup>E</sup> <sup>S</sup>* , viscosities *η*, viscosity deviations Δ*η*, excess Gibbs free energy of activation of viscous flow Δ*GE*, refractive indices *nD*, refractive index deviations Δ*nD* as functions of mole fraction, *x*<sup>1</sup> of DES for TBAB:AP (DES1) + water mixtures at the temperatures (293.15 to 303.15) K and atmospheric pressure; Table S2: Densities *ρ*, excess molar volumes *VE*, isobaric thermal expansion coefficients *αp*, excess thermal expansion Δ*αp*, speeds of sound u, excess isentropic compressibilities *κ<sup>E</sup> <sup>S</sup>* , viscosities *η*, viscosity deviations Δ*η*, excess Gibbs free energy of activation of viscous flow Δ*GE*, refractive indices *nD*, refractive index deviations Δ*nD* as functions of mole fraction, *x*<sup>1</sup> of DES for TBAC:AP (DES2) + water mixtures at the temperatures (293.15 to 303.15) K and atmospheric pressure; Table S3:Densities *ρ*, excess molar volumes *VE*, isobaric thermal expansion coefficients *αp*, excess thermal expansion Δ*αp*, speed of sounds u, excess isentropic compressibilities *κ<sup>E</sup> <sup>S</sup>* , viscosities *η*, viscosity deviations Δ*η*, excess Gibbs free energy of activation of viscous flow Δ*GE*, refractive indices *nD*, refractive index deviations Δ*nD* as functions of mole fraction, *x*<sup>1</sup> of DES for TBAB:MAE (DES3) + water mixtures at the temperatures (293.15 to 303.15) K and atmospheric pressure; Table S4: Densities *ρ*, excess molar volumes *VE*, isobaric thermal expansion coefficients *αp*, excess thermal expansion Δ*αp*, speed of sound u, excess isentropic compressibilities *κ<sup>E</sup> <sup>S</sup>* , viscosities *η*, viscosity deviations Δ*η*, excess Gibbs free energy of activation of viscous flow Δ*GE*, refractive indices *nD*, refractive index deviations Δ*nD* as functions of mole fraction, *x*<sup>1</sup> of DES for TBAB:BAE (DES4) + water mixtures at the temperatures (293.15 to 303.15) K and atmospheric pressure; Table S5: Parameters of the JAM equation, together with RMSD and ARD% for density, speed of sound, viscosity and refractive index of DES (1) + water (2) systems at different temperatures; Table S6: Parameters *Ai* of Equation (6) and the corresponding RSMD f for TBAB:AP (DES1) + water mixtures at the temperatures (293.15 to 303.15) K and atmospheric pressure; Table S7. Parameters *Ai* of Equation (6) and the corresponding RSMD for TBAC:AP (DES2) + water mixtures at the temperatures (293.15 to 303.15) K and atmospheric pressure; Table S8: Parameters *Ai* of Equation (6) and the corresponding RSMD for TBAB:MAE (DES3) + water mixtures at the temperatures (293.15 to 303.15) K and atmospheric pressure; Table S9: Parameters *Ai* of Equation (6) and the corresponding RSMD for TBAB:BAE (DES4) + water mixtures at the temperatures (293.15 to

303.15) K and atmospheric pressure; Table S10: Isobaric thermal expansion coefficient (*αp*), isochoric molar heat capacity (CP), Flory theory parameters: characteristic volume (V\*), reduce volume (V), ˜ characteristic pressure (P\*), and ratio of molecular surface to volume ratio (S1/S2) of DES to water; Table S11: Partial molar volumes of DESs and water in their binary mixtures at T = (293.15 to 313.15) K and at atmospheric pressure (0.1 MPa).

**Author Contributions:** Conceptualization, D.W. and B.N.; Methodology, D.W., B.N. and J.Ł.; Investigation, B.N. and M.J.; Data curation, D.W. and B.N.; Writing—original draft preparation, D.W. and B.N.; Writing—review and editing, J.Ł. and M.J.; Supervision, D.W. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author. The data are not publicly available due to the lack of requirements of Gdansk University of Technology and Medical University of Gdansk.

**Conflicts of Interest:** The authors declare no conflict of interest.
