*2.3. Density (ρ), Thermal Expansion Coefficient (αp), Standard Entropy (S*◦*) and Lattice Potential Energy (Upot) Measurement*

The density of ammonium-based PILs was studied at temperatures ranging from 293.15 to 363.15 K. The plots of the experimental density of the PILs are shown in Figure 3 while the experimental data and the plots with standard errors are available in Table S1 and Figure S13, respectively, in the Supplementary Material. As illustrated in Figure 3, the densities for all six ammonium-based PILs decreased linearly with temperature. Experimental data also indicates that the density of the PILs deceases as the alkyl chain of the anion increases for both [EHA] and [BEHA] PILs. The results are in accordance with published results in literature for PILs with diethylammonium and dibutylammonium cations with

the density values ranging approximately from 0.82 g.cm−<sup>3</sup> to 0.94 g.cm−<sup>3</sup> [50]. A similar observation was also found by other researchers when the densities of their tetrabutylammonium ionic liquids were analyzed over a temperature range of 283.4 to 333.4 K [51]. As temperature increases, the volume of ionic liquids increases, and the density of the ionic liquids decreases accordingly. At higher temperatures, the intermolecular forces between the constituent ions weaken, and this increases the mobility of the ions which in turn increases the volume of these ions [37,52,53]. Further analysis also revealed that [EHA][C5] has the highest density values compared to the rest of the ammonium-based PILs. The small size of [EHA] cation compared to [BEHA] cation affects local packing of the PIL structure and thus contributes to the increase in the density values of [EHA][C5] [37,54]. Comparable observations using PIL with ethylammonium cation were also found by several researchers, in which an increasing trending packing efficiency was proportional with the decreasing of molecular weight [51,55]. Notably, the increased alkyl chain length in both cation and anion of the PIL has promoted the steric hindrance and asymmetric nature in the PIL structure as bigger and bulkier PILs result in a lower density value for the PILs [40,41]. This trend can be observed in [BEHA][C6] and [BEHA][C7] as they exhibit the lowest density values.

**Figure 3.** Density (*ρ*) values of (**a**) [EHA][C5], [EHA][C6], [EHA][C7], and (**b**) [BEHA][C5], [BEHA][C6], [BEHA][C7] as a function of temperature.

The thermal expansion coefficient can provide information about the intermolecular interaction in the PILs, and it can be calculated from the experimental values of density, *ρ* by using Equation (1). The calculated data is tabulated in Table 2. Thermal expansion coefficients, *α<sup>p</sup>* for the ammonium-based PILs can be defined as [37,53,56]:

$$\alpha\_p = -1/\rho. \text{ (\(\delta\rho/\delta T\) = -\(A\_2\)/(A\_1 + A\_2T)}\tag{1}$$

The calculated values in Table 2 show that the thermal expansion coefficients vary only slightly with the increase of C-numbers in the structure of the PILs. PILs with [BEHA] cation has higher *α<sup>p</sup>* than that of PILs with [EHA] cation. This indicates that the thermal expansion coefficient does not only depend on the cation symmetry but is also related to the length of the alkyl substituent [57]. Meanwhile, the behavior of the thermal expansion coefficient is almost similar for all PILs with common cations. Sarkar et al. have also reported a similar variation trend of the thermal expansion coefficient for diethylammonium-based PILs [19]. To conclude, the thermal expansion coefficient can be considered as temperature independent as it shows similar results over the temperature range studied.


**Table 2.** Thermal expansion coefficients (*αp*) of the PILs calculated using Equation (1).

The volume occupied by one mole of a compound at a given temperature and pressure is denoted as molar volume, Vm. The molar volume was calculated by using an empirical equation as shown in Equation (2) and utilizing the experimental densities [41,58–61]:

$$\mathbf{V\_m} = \mathbf{M} / (\rho. \ \mathbf{N\_A}) \tag{2}$$

where Vm is the molar volume, M is the molar mass of the ammonium-based PILs, *ρ* is the density of PILs at 303.15 K and NA is Avogadro's number.

The calculated molar volume for all ammonium-based PILs are tabulated in Table 3. From the calculated value, the molar volume, Vm, is proportional to the anion alkyl chain length as well as the size of the cation. The molar volume increases with the alkyl chain length of the anion and this behavior is caused by the addition of the CH2 group in the anion of the PILs. Besides that, PILs with [BEHA] cation exhibit a larger molar volume value compared to PILs with [EHA] cation. This could be explained by the difference in the size of the cations. Similar findings have been observed in other studies [19,37].

**Table 3.** Molar volume, Vm; standard entropy, S◦; lattice potential energy, Upot at 303.15 K.


Entropy is the measurement of the randomness of molecules, and generally, entropy increases with molar volume [19]. The relationship between molar volume (Vm) and standard entropy (S◦) for the ammonium-based PILs in this work can be explored by using the following standard equation that is available in the literature [62]:

$$\mathbf{S}^{\odot} = 1246.5 \text{ V}\_{\text{m}} + 29.5 \tag{3}$$

The results presented in Table 3 clearly indicate that the standard entropy increased with the molar volume value for all ammonium-based PILs. The increasing number of carbon atoms in the alkyl chain of carboxylate anion has resulted in the increment of the S◦ of the ammonium-based PILs. From the calculated values obtained, [BEHA]-based PILs depicted the highest standard entropy due to their larger size compared to [EHA]-based PILs, which causes the least interaction between cation and anion [41]. In this work, the standard entropy of [EHA] and [BEHA] PILs increases in the sequence of [C5] < [C6] < [C7].

In addition, to predict the relative stabilities of ILs, Glasser [62] has also developed a method for calculating lattice potential energies (Upot) of ILs by using Equation (4):

$$\mathbf{U}\_{\rm pot} = \left[ \gamma \left( \rho / \mathbf{M} \right)^{1/3} \right] + \delta \tag{4}$$

where <sup>γ</sup> and <sup>δ</sup> are fitting coefficients with values of 1981.9 kJ·mol−<sup>1</sup> and 103.8 kJ·mol−1, respectively.

The lattice potential energy of the studied PILs was calculated at 303.15 K. The main factor contributing to lattice potential energy is electrostatic or columbic interaction. However, lattice potential energy is inversely related to the volume of ions [19,52,54]. As can be seen in Table 3, lattice potential energy decreases with the addition of the carbon chain length of the carboxylate groups. The addition of methylene group in the alkyl chain of both cation and anion increases the entropy, and consequently reduces packing efficiency in the PILs [63]. As a result, lattice potential energy will decrease with the increase in the alkyl chain length of the PILs.
