Abstract
The critical temperatures of two dozen deep eutectic solvents, for only some of which these have been estimated previously, were estimated from the temperature dependences of their surface tensions and densities available in the literature according to the Eötvös and the Guggenheim expressions.
1. Introduction
Deep eutectic solvents are binary mixtures of a hydrogen bond accepting component (HBA), typically quaternary ammonium or phosphonium salt, and a hydrogen bond donating component (HBD), typically polyol, at a definite molar ratio. These mixtures are liquid at room temperature and freeze at a temperature considerably below the freezing points of the components, and hence, they are eutectics. Mirza et al. [1] reported a group additivity method for the estimation of the critical temperatures (also the boiling points and densities) of deep eutectic solvents. An alternative path for the estimation of the critical temperatures is described here for deep eutectic solvents that for most of them no previous estimates were reported.
The surface tensions of liquids over a temperature range are related to their critical temperatures according to either of two relationships. One relationship, according to Eötvös [2], iswhere is the molar volume of the liquid, is its molar mass, and is its density. The other relationship, according to Guggenheim [3], is
These relationships may be inverted in order to deduce the critical temperatures from and data that are available in the literature. In order to apply these expressions, it is necessary to determine the parameters of (1) and of (2). The experimental functions and are linear over a wide temperature range:
The molar volume is therefore also linear with the temperature (because ). Therefore, extrapolation to the nominal temperature yields according to (1) and (2), respectively, .
Thus, the critical temperature according to (1) isand according to (2) is
2. The Data Employed and the Results
Table 1 presents the surface tension data and their temperature coefficients as well as the molar masses and the density coefficients of (4), and , for obtaining the molar volumes. The derived critical temperature values and for those deep eutectic solvents are also included in Table 1, for which the required data have been reported. Table 1 also shows the values of according to the group contribution estimates; the first entries are from Mirza et al. [1] and the second ones are from Mjalli et al. [4]. The following abbreviations are used for the HBA components of the solvents: ChCl = choline chloride; DEANCl = diethylethanolammonium chloride; Pr4NBr = tetrapropylammonium bromide; Bu4NCl = tetrabutylammonium chloride; MePh3PBr = methyltriphenylphosphonium bromide; BzPh3PBr = benzyltriphenylphosphonium bromide; and AllPh3PBr = allyltriphenylphosphonium bromide. The HBD components are EG = 1,2-ethanediol, Gly = glycerol, Fru = fructose, Glu = glucose, TEG = triethylene glycol, Mea = monoethanolamine, Asa = aspartic acid, Gla = glutamic acid, and Arg = arginine, and the molar ratios for the eutectics are also shown.
The resulting estimates of the critical temperatures according to the Eötvös relationship are on the average by 50% larger than the estimates according to the Guggenheim relationship. However, the estimates are nearer the values of from the group contributions according to Mirza et al. [1] than are the ones. On the whole, the values appear to be the more trustworthy.
3. Discussion
The normal boiling points of deep eutectic solvents are generally not relevant for their applications but represent the upper limit of their usage, if they do not decompose below these . Therefore, the critical temperatures , which are on the average about [1], are not the quantities that are relevant to their applications but have found use for the estimation of other properties that have not been measured as functions of the temperature [1, 4]. Still, the critical temperatures are physical properties that ought to be known; hence, the present estimates for two dozens of deep eutectic solvents of which only eight had their estimated previously make sense. The values are based on the nominal extrapolation of the experimental surface tension data to for the estimates (to obtain ) and of both these and the densities for the estimates (to obtain ), but these parameters do not have any real significance.
Previous estimates of the critical temperatures of deep eutectic solvents were conducted according to two paths. One was the use of the modified Lydersen−Joback−Reid group contribution method to obtain first values of and from them the values of , which is applicable to organic liquids for which at least is known and then extended [1, 4, 17] to the deep eutectic solvents. It was applied to twenty different deep eutectic solvents (shown as [1, 4] and [17] in Table 1 for those also studied here) as well as to noneutectic compositions of some of them. Some disagreements between the results of the application of this method are noted in Table 1. The other path was the application of the Eötvös [4, 15] and the Guggenheim [15] expressions, but in a different manner than done here. The former expression was recast in the linear form:and from the intercept and slope of its plots resulted [4]. The agreement with the values of from the group contributions is poor. Better agreement was obtained in [15] between values derived from the Eötvös and Guggenheim expressions.
Conflicts of Interest
The author declares that there are no conflicts of interest regarding the publication of this paper.