2.3.4. Isobaric Heat Capacity

A Mettler Toledo Star One differential scanning calorimeter (DSC), STAR-1 System (Mettler Toledo, Greifensee, Switzerland), was used to measure specific heat capacities of novel DESs. The DSC instrument was calibrated by the indium standard prior to sample measurements. During the measurement, an inert atmosphere was created under a nitrogen flow of 60 mL min<sup>−</sup>1. The sapphire method for cp determination was used [30]. A 'baseline' or blank measurement was performed for heating rate 10 K min−1. All of the results obtained were blank curve corrected and performed twice. The test material and the reference were placed into individual aluminium crucibles which were then sealed with pierced lids. The data from the DSC were recorded and then analyzed to obtain the *Cp* from the data.

#### **3. Results and Discussion**

#### *3.1. Physical Properties of Binary Mixtures*

The experimental values of density, speed of sound, viscosity, and refractive indices for aqueous solutions of DESs consisting 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 are reported in Tables S1–S4. Moreover, in Figure 1 the physical properties are plotted as a function of the DES molar fraction at 298.15 K for all systems studied. As it can be observed, depending on the properties, its dependence on the deep eutectic solvent content varies. Moreover, all trends are nonlinear, indicating deviation from the ideal course.

**Figure 1.** The dependence of the physical properties of aqueous solutions of DESs on molar fraction of deep eutectic solvent at 298.15K: (**a**) density; (**b**) speed of sound; (**c**) viscosity; (**d**) refractive index. -DES1; • DES2; DES3; DES4; —, Equation (1).

Taking into account the density, its values decrease in the whole range of DES concentrations only for aqueous TBAB:BAE (DES4) solutions for which a negative deviation from ideal behavior is observed. For the other systems, the density increases with increasing DES

concentration at low deep eutectic solvent content, reaches its maximum value at certain molar fraction of DES, and afterwards begins to decrease. The composition of the solution with the highest density depends on both the amino alcohol and the salt.

The dependence of the sound velocity and viscosity of aqueous DES solutions on the molar fraction of DES also shows a maximum. However, in the case of viscosity, unlike the speed of sound and the density, it occurs at high DES content. The refractive index increases monotonically in the whole range of DES concentrations for all systems.

When the temperature dependence is considered, one can observe that all properties decrease with the increase of temperature as the result of thermal expansion.

The experimental values of of density, speed of sound, viscosity, and refractive indices of binary mixtures were correlated by using of Jouyban–Acree model [29,31–33]. This mathematical model uses the physicochemical properties of the individual solvents as input data and a number of curve-fitting parameters represent the effects of solvent–solvent interactions in the solution

$$
\ln y = \mathbf{x}\_1 \ln y\_1 + \mathbf{x}\_2 \ln y\_2 + \frac{\mathbf{x}\_1 \mathbf{x}\_2}{T} \sum\_{i=0}^{i=n} f\_i (\mathbf{x}\_1 - \mathbf{x}\_2)^2 \tag{1}
$$

The *y*, *y*1, and *y*<sup>2</sup> are the physical properties of the mixture, deep eutectic solvent and water, at specific temperature. The *x*<sup>1</sup> and *x*<sup>2</sup> are mole fractions of DES and water, respectively. The *Ji* terms are coefficients of the model computed by using a zero-intercept regression analysis

$$
\ln y - \mathbf{x}\_1 \ln y\_1 - \mathbf{x}\_2 \ln y\_2 = \frac{\mathbf{x}\_1 \mathbf{x}\_2}{T} \sum\_{i=0}^{i=n} f\_i (\mathbf{x}\_1 - \mathbf{x}\_2)^2 \tag{2}
$$

Root mean square deviation of fit (RMSD) and the average deviation (ARD %) were calculated according to the following equations

$$RMSD = \left[\frac{\sum \left(Y\_{exp} - Y\_{pred}\right)^2}{n - k}\right]^{1/2} \tag{3}$$

$$ARD\ \% = \frac{100}{n} \sum \frac{\left| y\_{exp} - y\_{pred} \right|}{y\_{pred}} \tag{4}$$

where *n* is the number of experimental data, *k* is the number of parameters of model and *Y* is equal to *lny*.

Parameters *Ji* of Equation (1), root mean square deviation of fit (RMSD) and the corresponding average relative deviation (ARD %) for the systems studied at *T* = (293.15 to 313.15) K are presented in Table S5 (Supplementary Materials).

Moreover, the values of density, speed of sound, viscosity, and refractive index obtained by JAM are depicted as the smoothed solid lines in Figure 1. As can be seen, the Jouyban–Acree model correlates the experimental physical properties satisfactorily, especially for density and refractive index, for which average relative deviations are the same order as the experimental uncertainty. Thus, the JAM can be considered a reliable model for predicting the densities and refractive indices as well as it can be used for estimation of the speeds of sound and viscosity of aqueous DES solutions, for which, however, higher ARD % are observed.
