Estimation of the Critical Temperatures of Some More Deep Eutectic Solvents from Their Surface Tensions

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. +ese 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 Tc (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. +e surface tensions σ of liquids over a temperature range are related to their critical temperaturesTc according to either of two relationships. One relationship, according to Eötvös [2], is


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.ese 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 T c (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.
e surface tensions σ of liquids over a temperature range are related to their critical temperatures T c according to either of two relationships.One relationship, according to Eötvös [2], is where V � M/ρ is the molar volume of the liquid, M is its molar mass, and ρ is its density.e other relationship, according to Guggenheim [3], is ese relationships may be inverted in order to deduce the critical temperatures from σ(T) and ρ(T) data that are available in the literature.In order to apply these expressions, it is necessary to determine the parameters A of (1) and σ 0 of (2).e experimental functions σ(T) and ρ(T) are linear over a wide temperature range: e molar volume V � M/ρ is therefore also linear with the temperature (because b ≪ a).erefore, extrapolation to the nominal temperature T � 0 yields according to (1) and (2), respectively, A 0 � σ(0)V(0) 2/3 and σ 0 � σ(0).us, the critical temperature T E c according to (1) is and T G c according to (2) is

The Data Employed and the Results
Table 1 presents the surface tension data σ(T � 298.15 K) and their temperature coefficients (zσ/zT) p as well as the molar masses M and the density coefficients of (4), a and b, for obtaining the molar volumes.e derived critical temperature values T E c and T G c 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 T M c 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].e following abbreviations are used for the HBA components of the solvents: ChCl � choline chloride; DEANCl � diethylethanolammonium chloride; Pr 4 NBr � tetrapropylammonium bromide; Bu 4 NCl � tetrabutylammonium chloride; MePh 3 PBr � methyltriphenylphosphonium bromide; BzPh 3 PBr � benzyltriphenylphosphonium bromide; and AllPh 3 PBr � allyltriphenylphosphonium bromide.e 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.e resulting T E c estimates of the critical temperatures according to the Eötvös relationship are on the average by 50% larger than the T G c estimates according to the Guggenheim relationship.However, the T G c estimates are nearer the values of T M c from the group contributions according to Mirza et al. [1] than are the T E c ones.On the whole, the T G c values appear to be the more trustworthy.

Discussion
e normal boiling points T b 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 T b .erefore, the critical temperatures T c , which are on the average about 4/3(T b /K) [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 T c estimated previously make sense.e values are based on the nominal extrapolation of the experimental surface tension data to T � 0 for the T G c estimates (to obtain σ 0 ) and of both these and the densities for the T E c estimates (to obtain A 0 ), 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   [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.e other path was the application of the Eötvös [4,15] and the Guggenheim [15] expressions, but in a different manner than done here.e former expression was recast in the linear form: and from the intercept and slope of its plots T c � −A ′ /B resulted [4].e agreement with the values of T M c from the group contributions is poor.Better agreement was obtained in [15] between values derived from the Eötvös and Guggenheim expressions.

Table 1 :
e surface tension σ at 298.15 K and its temperature coefficient (zσ/zT) p ; the molar masses M and the density coefficients of ρ � a − b(t/ °C) of deep eutectic solvents; and the derived critical temperatures: T E [1,4]17]n first values of T b and from them the values of T c , which is applicable to organic liquids for which at least T b is known and then extended[1,4,17]to the deep eutectic solvents.It was applied to twenty different deep eutectic solvents (shown as T M c[1,4]and T H c