A New Compartmentalized Scale (PN) for Measuring Polarity Applied to Novel Ether-Functionalized Amino Acid Ionic Liquids

Functionalized and environmentally friendly ionic liquids are required in many fields, but convenient methods for measuring their polarity are lacking. Two novel ether-functionalized amino acid ionic liquids, 1-(2-methoxyethyl)-3-methylimidazolium alanine ([C1OC2mim][Ala]) and 1-(2-ethoxyethyl)-3-methylimidazolium alanine ([C2OC2mim][Ala]), were synthesized by a neutralization method and their structures confirmed by NMR spectroscopy. Density, surface tension, and refractive index were determined using the standard addition method. The strength of intermolecular interactions within these ionic liquids was examined in terms of standard entropy, lattice energy, and association enthalpy. A new polarity scale, PN, is now proposed, which divides polarity into two compartments: the surface and the body of the liquid. Surface tension is predicted via an improved Lorentz-Lorenz equation, and molar surface entropy is used to determine the polarity of the surface. This new PN scale is based on easily measured physicochemical parameters, is validated against alternative polarity scales, and is applicable to both ionic and molecular liquids.


Introduction
The green chemistry concept is a widely accepted focus of modern chemical research, including the design of new materials. Ionic liquids (ILs) have emerged as useful green reaction media due to their many unique features, such as low vapor pressure and high thermal stability [1,2]. They play important roles in many fields, including energy storage [3], catalysis [4], pharmaceuticals, and medicine [5,6]. However, the relatively high viscosity of ILs is a barrier to further practical applications. Inserting ether groups into the cations of ILs has been shown to substantially reduce their viscosity without lowering thermal stability, while also reducing their toxicity [7][8][9][10]. Ether-functionalized ILs (EFILs) have demonstrated remarkable performance in many fields. For example, they dissolve lignocellulosic biomasses [7], reduce viscosity and provide coordination sites for lithium ions in Li/Li-ion batteries [8], and enhance CO 2 selectivity during CO 2 capture [11]. However, traditional ILs containing anions such as Cl − , [BF 4 ] − , and [PF 6 ] − are environmentally hazardous. The development of environmentally friendly, task-specific ILs based on renewable bioresources (such as amino acids and fatty acids) is an environmental necessity. Ohno and Fukumoto were the first to prepare amino acid ILs (AAILs), using 20 different amino acids as the anion; these AAILs demonstrated lower toxicity [12,13]. AAILs have now been utilized in enantioselective separation [14], extraction separation [15], and CO 2 capture [11]. ILs with imidazolium-based cations exhibit low toxicity. Meanwhile, the shorter the alkyl chain on the imidazole ring, the lower the toxicity [16,17]. Thus, imidazolium ILs have proved more attractive than ILs based on ammonium, phosphonium, and pyridinium cations. The

Strength of [C n OC 2 mim][Ala](n = 1, 2) Intermolecular Interactions
The density of ILs increases gradually as temperature rises. At higher temperatures, the mobility of constituent ions improves and the unit volume increases [31]. The thermal expansion coefficient (α) is defined as where V is molar volume. Molar volume is defined as The molecular volume V m is defined as where N is the Avogadro constant, V is molar volume, and M is molar mass. At 298. 15 (Table S4). The difference between these indicates that the contribution of methylene (-CH 2 -) to V m is 0.0271 nm 3 . This is close to the average contribution methylene makes to the V m of several other ILs listed in Table S5 (0.0278 nm 3 ).
U POT reflects the strength of intermolecular interactions and can be used to measure the stability of ILs [32,33]. U POT is 443 kJ·mol −1 for [C 1 OC 2 mim][Ala] and 435 kJ·mol −1 for [C 2 OC 2 mim][Ala], implying that methylene's average contribution to U POT is −8 kJ·mol −1 . U POT is inversely related to molar volume. Addition of a methylene group will reduce the ionic or molecular packing efficiency, decreasing the strength of the interactions.
To some extent, standard entropy reflects the degree of disorder of molecular arrangements [33] (Table S5). This indicates that ILs with longer aliphatic chains are more disordered. Standard entropy increases as molecular volume increases. S θ 298 of ILs is usually greater than 200 J·K −1 ·mol −1 , compared with the more molecularly ordered conventional inorganic salts such as NaCl (72.1 J·K −1 ·mol −1 ) and KCl (82.6 J·K −1 ·mol −1 ) [34]. This may explain why ILs are molten below 373 K. The association enthalpy (∆ A H m 0 ) also reflects the strength of intermolecular interactions: the higher the ∆ A H m 0 , the stronger the gaseous state interactions. ∆ A H m 0 of ILs in the gaseous phase can be calculated based on the thermodynamic cycle shown in Scheme 1 [29]. Vaporization enthalpy (Δl g Hm 0 ) is a key parameter for calculating ΔAHm 0 . It is estimated from Equation (6): where gs is the molar surface Gibbs energy; γ is surface tension; V is molar volume; N is the Avogadro constant; Δl g Hm 0 is vaporization enthalpy; R is the gas constant; T is temperature; and a and b are the empirical constants −1.519 kJ·mol −1 and 0.09991, respectively [29]. The estimated vaporization enthalpy is 164.  Table S5. Again, addition of methylene reduces packing efficiency and increases the degree of molecular disorder. Thus, for ILs with the same anions, the absolute value of ΔAHm 0 decreases as the length of the imidazole ring alkyl side chains increases. For ILs with the same cations, ΔAHm 0 decreases with increasing anion volume.

Prediction of Surface Tension Based on Molar Surface Gibbs Energy
The parameter gs used to estimate vaporization enthalpy was developed in our previous work by modifying Li's model [35]. The definition of gs is consistent with the concept presented by Myers [36]. Thus, gs is a true thermodynamic function that integrates volumetric and surface properties.
Plotting gs against T for [CnOC2mim][Ala](n = 1,2) yields straight lines ( Figure 2) such that their relationship can be expressed as  Table 2. Vaporization enthalpy (∆ l g H m 0 ) is a key parameter for calculating ∆ A H m 0 . It is estimated from Equation (6): where g s is the molar surface Gibbs energy; γ is surface tension; V is molar volume; N is the Avogadro constant; ∆ l g H m 0 is vaporization enthalpy; R is the gas constant; T is temperature; and a and b are the empirical constants −1.519 kJ·mol −1 and 0.09991, respectively [29].
The estimated vaporization enthalpy is 164.  Table S5. Again, addition of methylene reduces packing efficiency and increases the degree of molecular disorder. Thus, for ILs with the same anions, the absolute value of ∆ A H m 0 decreases as the length of the imidazole ring alkyl side chains increases. For ILs with the same cations, ∆ A H m 0 decreases with increasing anion volume.

Prediction of Surface Tension Based on Molar Surface Gibbs Energy
The parameter g s used to estimate vaporization enthalpy was developed in our previous work by modifying Li's model [35]. The definition of g s is consistent with the concept presented by Myers [36]. Thus, g s is a true thermodynamic function that integrates volumetric and surface properties.
Plotting g s against T for [C n OC 2 mim][Ala](n = 1, 2) yields straight lines ( Figure 2) such that their relationship can be expressed as Vaporization enthalpy (Δl g Hm 0 ) is a key parameter for calculating ΔAHm 0 . It is estimated from Equation (6): where gs is the molar surface Gibbs energy; γ is surface tension; V is molar volume; N is the Avogadro constant; Δl g Hm 0 is vaporization enthalpy; R is the gas constant; T is temperature; and a and b are the empirical constants −1.519 kJ·mol −1 and 0.09991, respectively [29].
The estimated vaporization enthalpy is 164.  Table S5. Again, addition of methylene reduces packing efficiency and increases the degree of molecular disorder. Thus, for ILs with the same anions, the absolute value of ΔAHm 0 decreases as the length of the imidazole ring alkyl side chains increases. For ILs with the same cations, ΔAHm 0 decreases with increasing anion volume.

Prediction of Surface Tension Based on Molar Surface Gibbs Energy
The parameter gs used to estimate vaporization enthalpy was developed in our previous work by modifying Li's model [35]. The definition of gs is consistent with the concept presented by Myers [36]. Thus, gs is a true thermodynamic function that integrates volumetric and surface properties.
Plotting gs against T for [CnOC2mim][Ala](n = 1,2) yields straight lines ( Figure 2) such that their relationship can be expressed as  Table 2.   Figure 2 and substituted into Equation (8) to give the estimated molar surface Gibbs energy, g s(est) . Values of g s , G 0 , G 1 , and g s(est) are listed in Table 2. Table 2. Molar surface Gibbs energy (g s ), G 0 , G 1 , and estimated molar surface Gibbs energy (g s(est) ) for [C n OC 2 mim][Ala](n = 1, 2). The Lorentz-Lorenz equation expresses the relationship between n D and the mean molecular polarizability (α p ) [37]: where R m is molar refraction, α p is mean molecular polarizability, and n D is refractive index. This has been combined with g s to give an improved Lorentz-Lorenz equation [38] that can predict surface tension, γ (est) : The R m , α p , and γ (est) for [C n OC 2 mim][Ala](n = 1, 2) are listed in Table 3. Plotting estimated surface tension values against their corresponding experimental values produces a straight line (Figure 3). A similar plot for other ionic and molecular liquids also illustrates a linear relationship (Table S6, Figure 4), showing that this method is applicable for the surface tension prediction of both types of liquid. The Lorentz-Lorenz equation expresses the relationship between nD and the mean molecular polarizability (αp) [37]: where Rm is molar refraction, αp is mean molecular polarizability, and nD is refractive index. This has been combined with gs to give an improved Lorentz-Lorenz equation [38] that can predict surface tension, γ(est): The Rm, αp, and γ(est) for [CnOC2mim][Ala](n = 1,2) are listed in Table 3. Plotting estimated surface tension values against their corresponding experimental values produces a straight line (Figure 3). A similar plot for other ionic and molecular liquids also illustrates a linear relationship (Table S6, Figure 4), showing that this method is applicable for the surface tension prediction of both types of liquid.    Table  S6). γ(est) = 1.0009γ(exp) − 0.03643; r 2 = 0.999; sd = 0.10.   Figure 4. Plot of surface tension γ (est) against γ (exp) for various ionic and molecular liquids (see Table S6). γ (est) = 1.0009γ (exp) − 0.03643; r 2 = 0.999; sd = 0.10.
For ILs sharing the same anions (Table 1 and Table S6), n D decreases as the length of the alkyl chain in the cations increases. Refractive index correlates with dipole moment [39,40], which increases with higher molecular packing density [41]. Thus, a larger dipole moment results in a higher refractive index. The n D is larger in [C 1 OC 2 mim][Ala] than [C 2 OC 2 mim][Ala], so the packing density of the former is higher, which is consistent with the density trend of the two ILs.
As polarizability increases, Coulomb interactions are reduced and ion mobility rises [42]. The α p of [C 1 OC 2 mim][Ala] is lower than [C 2 OC 2 mim][Ala], so its Coulomb interactions are stronger. This finding is similar to the pattern observed for U POT and ∆ A H m 0 .

Molar Surface Entropy: Polarity Contribution from Surface Liquid
For most liquids, surface tension declines as temperature increases, as shown by the Eötvös equation: where T c is critical temperature and k is the Eötvös equation parameter, which is associated with polarity. For some organic liquids with weak polarity, k is nearly 2.2 × 10 −7 J·mol −2/3 ·K −1 , while for some with strong polarity, such as molten NaCl, it is nearly 0.4 × 10 −7 J·mol −2/3 ·K −1 [35,43]. However, the physical significance of k is not clear. Multiplying both sides of the Eötvös equation by N 1/3 [35] gives which fits the fundamental thermodynamic concept: C 1 denotes the molar surface entropy and is given by C 1 = −( ∂g s ∂T ) p . The relationship between molar surface entropy (defined here as s [29]) and k is expressed as Entropy is directly linked to the number of microstates [44]. Higher entropy means molecules can be arranged in more ways, while the total energy remains constant. Thus, the physical significance of s is clear-it reflects the polarity of a liquid's surface (higher s, lower surface polarity). The value of s is 17.   (Table 4) imply that, for ILs with the same number of alkyl side chain carbons, the position of the ether group also affects s, presumably because it affects packing efficiency on the liquid surface.

A New Model for Predicting Polarity
Experimental methods for measuring polarity, such as E T (30), are time consuming and laborious. Here, we present a predictive model that establishes a relationship between polarity and the easily determined physicochemical properties of density, surface tension, and refractive index.
Our previous work [28], based on Hildebrand and Scott's theory [47], proposed δ µ as a polarity scale. δ µ is the solubility parameter derived from the contribution of the average permanent dipole moment: where V is the molar volume and ∆ g l H 0 mµ is the contribution of the average permanent dipole moment to ∆ g l H 0 m , such that (16) where ∆ g l H 0 mn is the contribution of the induced dipole moment to ∆ g l H 0 m and can be calculated from the Lawson-Ingham equation [48]: where C is the empirical constant 1.297 kJ·cm −3 . In Equation (15) However, there is an obvious drawback to δ µ : it has a dimension (J 1/2 ·cm −3/2 ), while some polarity scales, such as the dielectric constant, are non-dimensional. Furthermore, the contribution of the induced dipole moment was neglected. Therefore, δ µ was improved as follows and designated as P [45]: where δ n is the solubility parameter from the contribution of the induced dipole moment. Comparison of ∆ g l H 0 mµ and ∆ g l H 0 mn shows that (1−x)RT/V and xRT/V can be omitted and Equation (18) can be expressed as The effects of average permanent dipole moment and induced dipole moment are both considered within P, which is dimensionless, with a large value indicating high polarity. [ This study divided polarity into two compartments: the contribution from the body of a liquid, and the contribution from the surface. Cohesive energy density can demonstrate the strength of intermolecular interactions within the body [48]. δ µ 2 is the cohesive energy density from the average permanent dipole moment and δ n 2 is from the induced dipole moment. Consequently, P 2 can describe the polarity of the body of a liquid: Molar surface entropy (s) was proven above to reflect the polarity of a liquid surface. Combining s and P 2 , a new polarity scale, P N , is now proposed: This compartmentalized scale is a novel method to evaluate polarity, with a large P N indicating weak polarity. Based on literature data [50][51][52][53][54][55] , which is the same polarity trend observed using δ µ and P. As discussed above, ILs with longer alkyl chains exhibit higher standard entropy and lower molecular packing efficiency. The observed higher polarity of [C 1 OC 2 mim][Ala] may be due to its stronger intermolecular interactions and more ordered molecular arrangement. This fact can be explained as follows: a polar molecule has a permanent electric dipole moment, and a molecule may be polar if it has low symmetry [44]. ILs have asymmetric structures, and an orderly arrangement of ILs will maintain this structure. In this situation, their permanent electric dipole moments will not counteract each other, and polarity will be enhanced. The P N of various etherfunctionalized ILs are listed in Table 5. For ILs with the same anion, P N declines as the length of the imidazole ring alkyl side chain increases. This trend supports the contention that the strength of intermolecular interactions and the degree of disorder of molecular arrangements influence polarity. 19.64 [39] The P N scale can be validated by comparison with other polarity scales (Table 6). FTIR spectroscopy probes [56] and E T N [57] show that the polarity of [C 2 mim]BF 4 is larger than [C 4 mim]BF 4 . The P N scale gives the same qualitative result. Wu [58]. Again, P N gives the same result. Furthermore, when P N is applied to molecular liquids, the estimated polarity is broadly, and inversely, consistent with the dielectric constant ε [59] (Table 7). The correlation between P N and the inverse ε −1 ( Figure 5) is r 2 = 0.94, demonstrating that P N is also suitable for molecular liquids. Furthermore, when PN is applied to molecular liquids, the estimated po broadly, and inversely, consistent with the dielectric constant ε [59] (Table 7). T lation between PN and the inverse ε −1 ( Figure 5) is r 2 = 0.94, demonstrating that P suitable for molecular liquids.  ET (30) is one of the most popular polarity scales for evaluating ILs, but it is l and costly [60]. Moreover, the results vary depending on the molecular probe u However, using PN, polarity can be determined simply from density, surface tens refractive index. The dielectric constant is the traditional polarity scale for org vents. The comparison of dielectric constant and PN proves the universal applic PN. Thus, this new PN scale is demonstrated to be a viable predictive method for ev the polarity of both ionic and molecular liquids based on easily measured physic E T (30) is one of the most popular polarity scales for evaluating ILs, but it is laborious and costly [60]. Moreover, the results vary depending on the molecular probe used [61]. However, using P N , polarity can be determined simply from density, surface tension, and refractive index. The dielectric constant is the traditional polarity scale for organic solvents. The comparison of dielectric constant and P N proves the universal applicability of P N . Thus, this new P N scale is demonstrated to be a viable predictive method for evaluating the polarity of both ionic and molecular liquids based on easily measured physicochemical properties. It will find applications in many fields, particular those employing novel ionic liquids for which the evaluation of polarity is expensive and time consuming.

Materials
The sources and purity of reagents are listed in Table 8. N-Methylimidazole (AR grade) was purified by distillation, while 2-chloroethyl methyl ether and 2-chloroethyl ethyl ether (both AR grade) were used as purchased. DL-Alanine was recrystallized from water and dried in a vacuum oven [62].
Since [CnOC2mim][Ala](n = 1,2) form strong hydrogen bonds with water, it is difficult to remove all traces of water from these ILs, which affects their density, surface tension, and refractive index. Therefore, the standard addition method was used to determine these properties. Each parameter was measured in [CnOC2mim][Ala](n = 1,2) at different water contents following heating at graduated temperatures. Values were then plotted against water content, and the intercept of the regression lines yielded the parameter values in the anhydrous ILs at a given temperature.

Conclusions
[CnOC2mim][Ala](n = 1,2) were prepared and their structures confirmed by NMR. Density, surface tension, and refractive index were determined by the standard addition method. Adding methylene to the aliphatic chain of an IL increased its standard entropy. Lattice energy and association enthalpy measurements showed that molecules of  Figure S4. 13 Table S5. Molecular volume, Vm, standard molar entropy, S 0 , lattice energy, UPOT, vaporization enthalpy, ΔlgHm 0 , association enthalpy, ΔAHm 0 for some ionic liquids; Table S6. The estimated surface tension, γ(est),
Since [C n OC 2 mim][Ala](n = 1, 2) form strong hydrogen bonds with water, it is difficult to remove all traces of water from these ILs, which affects their density, surface tension, and refractive index. Therefore, the standard addition method was used to determine these properties. Each parameter was measured in [C n OC 2 mim][Ala](n = 1, 2) at different water contents following heating at graduated temperatures. Values were then plotted against water content, and the intercept of the regression lines yielded the parameter values in the anhydrous ILs at a given temperature.

Conclusions
[C n OC 2 mim][Ala](n = 1, 2) were prepared and their structures confirmed by NMR. Density, surface tension, and refractive index were determined by the standard addition method. Adding methylene to the aliphatic chain of an IL increased its standard entropy. Lattice energy and association enthalpy measurements showed that molecules of [C 1 OC 2 mim][Ala] were more compacted, and their intermolecular interactions stronger, than [C 2 OC 2 mim][Ala]. An improved Lorentz-Lorenz equation predicted the surface tension of both ionic and molecular liquids. A new compartmentalized polarity scale (P N ) based on molar surface Gibbs energy and dipole moments is presented. It encompasses the polarity of both the surface and body of a liquid. [C 1 OC 2 mim][Ala] is shown to have higher polarity than [C 2 OC 2 mim][Ala] based on P N . The validity of P N is demonstrated by comparison with alternative polarity scales and published polarities of both ionic and molecular liquids.  Figure S4. 13