Generalized linear solvation energy model applied to solute partition coefficients in ionic liquid–supercritical carbon dioxide systems

Journal of Chromatography A, 1250 (2012) 54–62

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Generalized linear solvation energy model applied to solute partition coefficients in ionic liquid–supercritical carbon dioxide systems ˇ Josef Planeta, Pavel Karásek, Barbora Hohnová, Lenka St’avíková, Michal Roth ∗ Institute of Analytical Chemistry of the ASCR, v. v. i., Veveˇrí 97, 60200 Brno, Czech Republic

a r t i c l e

i n f o

Article history: Available online 13 April 2012 Keywords: Supercritical fluid chromatography Ionic liquid Carbon dioxide Organic solute Partition coefficient

a b s t r a c t Biphasic solvent systems composed of an ionic liquid (IL) and supercritical carbon dioxide (scCO2 ) have become frequented in synthesis, extractions and electrochemistry. In the design of related applications, information on interphase partitioning of the target organics is essential, and the infinite-dilution partition coefficients of the organic solutes in IL–scCO2 systems can conveniently be obtained by supercritical fluid chromatography. The data base of experimental partition coefficients obtained previously in this laboratory has been employed to test a generalized predictive model for the solute partition coefficients. The model is an amended version of that described before by Hiraga et al. (J. Supercrit. Fluids, in press). Because of difficulty of the problem to be modeled, the model involves several different concepts – linear solvation energy relationships, density-dependent solvent power of scCO2 , regular solution theory, and the Flory–Huggins theory of athermal solutions. The model shows a moderate success in correlating the infinite-dilution solute partition coefficients (K-factors) in individual IL–scCO2 systems at varying temperature and pressure. However, larger K-factor data sets involving multiple IL–scCO2 systems appear to be beyond reach of the model, especially when the ILs involved pertain to different cation classes. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Organic salts with melting points below 100 ◦ C, or ionic liquids (ILs), have attracted an ever increasing attention from diverse fields of science and technology [1]. A crucial point seems to have been the introduction of air- and moisture-stable ILs in 1992 [2], and the surge of interest in ILs has partly been driven by their extremely low vapor pressures [3–5] as contrasted to those of molecular (organic) solvents. Applications of ILs have become frequented, e.g., in chemical [6,7] and enzymatic [8] synthesis, extractions [9], and electrochemistry [10]. An important part of IL applications have combined the use of ILs and supercritical fluids, notably supercritical carbon dioxide (scCO2 ). It appears that most ILs can dissolve large amounts of CO2 while, in turn, ILs themselves are nearly insoluble in scCO2 . These features are highly useful for delicate extraction of thermolabile organic compounds from IL media with scCO2 [11,12], and also for application of biphasic IL–scCO2 systems in phase transfer catalysis [13,14]. Several reviews of these and other aspects of IL–scCO2 systems are available [15–18]. A qualified design of applications combining the use of an IL and scCO2 certainly requires detailed information on the

∗ Corresponding author. Tel.: +420 532290171; fax: +420 541212113. E-mail address: [email protected] (M. Roth). 0021-9673/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.chroma.2012.04.016

underlying phase behavior. Naturally, the applications often involve finite concentrations of all components in the IL-rich phase. Consequently, there are numerous studies of the phase behavior in the organic–IL–CO2 systems at finite concentrations [19–23], and some of them indicate that the phase behavior can be highly complex [24]. In the development of thermodynamic models for the organic–IL–CO2 systems, a complementary experimental information on infinite dilution partition coefficients of the organic solutes in the IL–scCO2 systems can be very useful, and the partitioning data can conveniently be obtained from retention measurements by supercritical fluid chromatography (SFC) with the IL serving as the stationary liquid and scCO2 as the carrier fluid. To determine the partitioning data, SFC retention measurements have been carried out with both wall-coated open tubular capillary columns [25–31] and packed columns [32–34]. In the past few years, predictive modeling of infinite-dilution partition coefficients has been developed along two different routes. In one of these, Machida et al. [32,33] used the Sanchez–Lacombe mean-field lattice gas equation of state [35,36] to model the equilibrium distribution of a trace amount of organic solute between both phases in an IL–scCO2 system. The other route employed linear solvation energy relationships (LSERs) that have often been applied to other IL-containing systems as well [37–41]. Since LSERs have originally been developed for incompressible media, their applications to systems with supercritical fluids are complicated because of density-dependent solvent

J. Planeta et al. / J. Chromatogr. A 1250 (2012) 54–62

power of the fluid [42]. Therefore, applications of LSERs to SFC with ILs were originally confined to retention data taken at a fixed temperature and pressure to avoid the effect of variations of the solvent power of CO2 and the effect of varying proportion of dissolved CO2 in the IL with temperature and pressure [26,28,29]. In the most recent development, Hiraga et al. [34] described a generalized model combining the LSER approach with additional terms accounting for the density-dependent solvent power of CO2 and with a regular solution theory-based term to account for the effect of dissolved CO2 on the solute activity coefficient in the stationary (IL-rich) phase. Therefore, Hiraga et al.’s model marks an important breakthrough over our previous applications of LSERs to SFC with ILs [26,28,29] through combining the LSER formalism with provisions for the density-dependent solvent power of the mobile phase and for the composition-dependent solvent properties of the stationary phase. Hiraga et al.’s model proved highly successful in correlating solute partition coefficients in a particular IL–scCO2 system at varying temperature and pressure. The purpose of the present contribution is to test an amended version of the Hiraga et al.’s model [34] on an extensive set of partition coefficient data in several IL–scCO2 systems as obtained previously in this laboratory [25–31]. 2. Description of the model The property used in the model to quantify the partitioning equilibrium is different from the molarity-based distribution constant employed in analytical chemistry. Hiraga et al. [34] used mole-fraction based K-factor, a quantity common in chemical engineering and defined by K=

ysolute xsolute

(1)

where ysolute and xsolute are the equilibrium mole fractions of the solute in the gas (mobile) and liquid (stationary) phases, respectively. Note that, contrary to the common practice in chromatography, solute concentration in the stationary phase is in the denominator in Eq. (1) so that the K-factor decreases with increasing retention of the solute. Under the conditions of linear chromatography [43], the K-factor is related to the solute retention factor k by K=

MCO2 nIL

(2)

[kVcol CO2 (1 − xCO2 )]

where MCO2 is the molar mass of CO2 , nIL is the number of moles of IL in the column, Vcol is the void volume of the column, CO2 is the density of CO2 at the temperature and mean pressure in the column, and xCO2 is the mole fraction solubility of CO2 in the IL. With some amendments to the Hiraga et al.’s original formulation, the model employed here to correlate solute K-factors in IL–scCO2 systems can be written as ln K

= (c0 + e0 E + s0 S + a0 A + b0 B + (v0 + v1 ıCO2 )V )



+ +

c1 r + c2 ln r +



c4

¯ vsolute (ısolute − ı)

  +

c3 ıCO2

c5 1 −

2

r =

 c

(4)

where  is density of CO2 at the particular temperature and pressure and c is the critical density of CO2 [45]. The regular solution part of Eq. (3) employs the Scatchard–Hildebrand solution theory [46] to express the effect of varying composition of the stationary phase (IL/CO2 proportion) on the intermolecular interactions and the solute activity coefficient. In this part, R is the molar gas constant, T is the temperature, vsolute and ısolute are the molar volume of the solute and the solubility parameter of the solute, respectively, and ı¯ is an effective solubility parameter of the IL + CO2 stationary liquid, ı¯ = IL ıIL + CO2 ıCO2

(5)

In Eq. (5), ıIL is the solubility parameter of the pure IL and IL and CO2 are the volume fractions of the IL and CO2 , respectively, in the stationary liquid, IL =

xIL vIL xIL vIL + xCO2 vCO2

CO2 =

xCO2 vCO2 xIL vIL + xCO2 vCO2

(6) (7)

where vIL and vCO2 are molar volumes of the IL and CO2 , respectively, and xIL and xCO2 are mole fractions of the two components in the stationary liquid. The definition of volume fractions by Eqs. (6) and (7) implies zero excess volume of the IL + CO2 stationary liquid. In addition to the original formulation of Hiraga et al. [34], we have amended Eq. (3) with the combinatorial entropy part to account for molecular size differences among the solute, IL and CO2 . The reason for doing so is that the size differences give rise to excess entropy as compared to that of a mixture of molecules of equal size. This part of Eq. (3) is based on the Flory–Huggins theory of athermal solutions, namely, on the expression for the infinite-dilution activity coefficient of the solute in polymer [47]. In the present application, the “polymer” has been replaced with the IL + CO2 mixture. Evaluation of the combinatorial entropy part does not need any additional input parameters beyond those already needed in

CO2 solvent power part



(3) regular solution part

RT

vsolute

E, dipolarity/polarizability S, hydrogen bond acidity (=hydrogen bond donating ability) A, hydrogen bond basicity (=hydrogen bond accepting ability) B, and the solute molecular size V proportional to the McGowan’s characteristic volume of the solute [44]. The hydrogen bond acidity term was absent from Hiraga et al.’s original formulation of Eq. (3) as their data set did not include any solute with nonzero value of the A descriptor. Following Hiraga et al., the coefficient at the V descriptor has been made a linear function of the solubility parameter of CO2 . In the part of Eq. (3) describing the effect of CO2 solvent power on ln K, ıCO2 is the solubility parameter of CO2 at the particular temperature and pressure, and r is the reduced density of CO2 ,

solute part



xIL vIL + xCO2 vCO2

55

− ln

vsolute xIL vIL + xCO2 vCO2

 combinatorial entropy part

In Eq. (3), c0 , e0 , s0 , a0 , b0 , v0 , v1 , c1 , c2 , c3 , c4 and c5 are coefficients to be determined by multidimensional linear regression whereas all other symbols are input parameters. The solute part makes use of the LSER formalism to reflect the effects on ln K of the solute properties including the excess molar refractivity

the other parts of Eq. (3). From the purely statistical viewpoint, inclusion of the combinatorial entropy part should improve the correlation as it provides an additional explanatory variable that is not correlated with the other variables. It follows from the above overview that most input parameters are pure component properties, with the only binary property

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Table 1 Solutes included with individual IL–scCO2 systems. Solute/ionic liquid Acetophenone Aniline Anisole Azulene Benzoic acid Benzothiazole p-Cresol Dibenzothiophene N,N-Dimethylaniline 1-Hexanol Indole N-Methylaniline Naphthalene Phenol 1-Phenylethanol 2-Phenylethanol Pyrene Thianaphthene

[bmim][PF6 ]

× ×

[bmim][BF4 ]

[hmim][Tf2 N]

[bmim][MeSO4 ]

[bmim][TfO]

[thtdp][Cl]

× × × ×

× × × ×

× × ×

×

×

×

× × ×

× × × × × × × × × × × × ×

× × × × ×

×

×

× × × × × ×

×

× ×

×

× × × ×

× ×

being the mole fraction solubility of CO2 in the particular IL at the particular temperature and pressure. 3. Review of experimental and auxiliary data forming the training sets 3.1. Chromatographic retention data SFC retention data used to obtain the source K-factor values came from our previous studies involving several ILs, namely, 1-n-butyl-3-methylimidazolium hexafluorophosphate ([bmim][PF6 ]) [25], 1-n-butyl-3-methylimidazolium tetrafluoroborate ([bmim][BF4 ]) [26], 1-n-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([hmim][Tf2 N]) [27], 1-n-butyl3-methylimidazolium methyl sulfate ([bmim][MeSO4 ]) [29,30], trifluoromethanesulfonate 1-n-butyl-3-methylimidazolium ([bmim][TfO]) [31] and trihexyltetradecylphosphonium chloride ([thtdp][Cl]) [28]. Solute retention factors were measured within an overall range 313.2–353.2 K in temperature and 7.3–23.2 MPa in pressure. Only a subset of the previous data has been used in the present work as the molecular descriptors employed [48] were not available for all the solutes studied. Table 1 shows a brief overview of what solutes were included with a particular IL–scCO2 system. In the previous papers on SFC measurements with the individual ILs [25–31], retention data were mostly reported as relative retention factors but, for the present purpose, they were converted to K-factors via Eq. (2). Altogether, in the source data set there were 516 K-factor values for imidazolium ILs and additional 118 K-factor values for [thtdp][Cl]. Together with auxiliary input parameters to be discussed below, the K-factor values are compiled in the electronic supplementary file. As the data set involves several IL–scCO2 systems and a variety of solutes of different volatilities and polarities, it should provide for a stringent and representative test of the model. 3.2. Input parameters The diverse input parameters for the correlation in Eq. (3) were obtained from multiple sources. Solute molecular descriptors E, S, A, B and V were those reported by Abraham et al. [48] (note that different symbols for the descriptors were used in the original source, namely, R2 , 2 H , ˛2 H , ˇ2 H and Vx , respectively). Density, molar volume and solubility parameter of CO2 were calculated from the Span–Wagner equation of state [45] using the software package developed by Wagner and Overhoff [49]. When calculating the cohesive energy needed to obtain ıCO2 , the internal energy

× × × × ×

× × ×

of CO2 in the ideal-gas state was taken at the particular temperature and the pressure of 10−6 Pa. Molar volume of the solute was estimated from the modified Rackett equation [50] employing the critical data obtained either from the compilation by Poling et al. [51] or from the NIST Chemistry WebBook data base [52]. In calculating the solute solubility parameter, the cohesion energy was estimated from the Antoine vapor pressure equation with the constants taken either from the compilation by Dykyj and Repáˇs [53] or from the NIST Chemistry WebBook [52]. In the solutes that are solids at the particular temperature, both vsolute and ısolute refer to subcooled liquid state. The solubility parameters of individual ILs were estimated using the procedure employed by Hiraga et al. [34]. First, the estimations of the critical properties and acentric factors reported by Valderrama and Rojas [54] were used to estimate the enthalpies of vaporization of the ILs from the Pitzer correlation as reported by Poling et al. [55]. The vaporization enthalpies were converted to the cohesive energies of ILs (Uc = Hv − RT), and these were used together with the respective molar volumes to obtain the solubility parameters of ILs. For the sake of consistency in ıIL estimations, the molar volumes of ILs were obtained from the densities calculated with the correlation of Valderrama and Rojas [54]. However, the molar volumes vIL to be used in the combinatorial entropy part of Eq. (3) and in Eqs. (5)–(7) were obtained by interpolation of authentic experimental data on the densities of the individual ILs, namely, [bmim][PF6 ] [56], [bmim][BF4 ] [57], [hmim][Tf2 N] [58], [bmim][MeSO4 ] [59], [bmim][TfO] [60] and [thtdp][Cl] [61]. The mole fraction solubilities of CO2 in ILs were interpolated from the literature data on phase equilibria in the respective IL–CO2 systems with [bmim][PF6 ] [62], [bmim][BF4 ] [63], [hmim][Tf2 N] [64], [bmim][MeSO4 ] [65], [bmim][TfO] [62] and [thtdp][Cl] [66]. These sources of CO2 solubility data in the individual ILs were also employed in converting the retention factors to K-factors via Eq. (2) together with the respective experimental data on k, nIL and Vcol and with the calculated densities of CO2 [45,49]. Numerical values of all the input parameters appearing in Eq. (3) are compiled in the electronic supplementary file together with the K-factor values.

4. Results and discussion Testing of Eq. (3) in reproduction of experimental K-factor data proceeded in the order of increasing complexity of the training set, i.e., from individual single IL data sets through the set involving all imidazolium-based ILs to the most complex set containing also the phosphonium IL ([thtdp][Cl]).

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Table 2 Coefficients of Eq. (3), their standard errors and other statistical characteristics determined by linear regression of K-factor data sets in individual IL–scCO2 systems. Ionic liquid

[bmim][PF6 ]

[bmim][BF4 ]

[hmim][Tf2 N]

[bmim][MeSO4 ]

[bmim][TfO]

[thtdp][Cl]

Number of data points (N) c0 Standard error in c0 e0 Standard error in e0 s0 Standard error in s0 a0 Standard error in a0 b0 Standard error in b0

35 −2.841 1.3 −1.759 0.55 −0.5562 0.46 0 0 2.726 1.5 0 0 0.2129 0.14 0.7976 2.3 −1.551 3.3 −2.341 13 −0.5949 0.11 2.538 4.6

176 −1.601 1.1 −2.252 0.34 −2.309 0.46 −4.964 0.28 −1.946 0.33 4.045 1.3 0.0955 0.10 −7.594 1.6 15.23 2.4 48.44 8.6 −0.1332 0.053 −2.017 1.4

54 −0.2778 0.68 −1.135 0.52 1.596 0.36 0 0 0 0 −4.053 1.4 0.1926 0.10 −0.1387 1.7 −0.4074 2.7 2.621 11 −0.5756 0.057 1.891 1.3

85 7.609 4.0 −3.288 0.35 −0.5960 0.40 −6.806 0.49 −3.429 0.49 0.9921 2.9 0.2585 0.26 −21.26 5.4 31.92 6.0 93.40 17 0.2630 0.61 3.025 2.4

166 2.914 1.1 −2.077 0.22 −1.631 0.30 −6.258 0.27 −1.371 0.26 −1.931 1.3 0.4594 0.11 −9.148 1.9 13.14 2.8 40.85 10 0.1312 0.081 3.056 1.4

118 2.256 1.7 −2.700 0.34 1.703 0.41 −5.246 0.83 −4.653 0.47 0.3144 1.7 0.1960 0.14 −7.559 3.1 9.733 4.4 23.76 16 −0.6881 0.12 −0.7342 0.79

v0 Standard error in v0

v1 Standard error in v1 c1 Standard error in c1 c2 Standard error in c2 c3 Standard error in c3 c4 Standard error in c4 c5 Standard error in c5 RSS/N Mean of [(Kcalc − Kexp )/Kexp ]2 Square root of the mean of [(Kcalc − Kexp )/Kexp ]2 Median of [(Kcalc − Kexp )/Kexp ]2 Square root of the median of [(Kcalc − Kexp )/Kexp ]2

0.01055 0.01283 0.1133 0.002113 0.04597

0.1226 0.1766 0.4203 0.05438 0.2332

0.01141 0.01144 0.1070 0.004855 0.06968

0.1089 0.1729 0.4158 0.03240 0.1800

0.1094 0.1948 0.4414 0.04381 0.2093

0.1091 0.1296 0.3600 0.03545 0.1883

4.1. Single IL–scCO2 systems Table 2 shows the coefficients c0 , e0 , s0 , a0 , b0 , v0 , v1 , c1 , c2 , c3 , c4 and c5 together with their standard errors and other characteristics of the K-factor data fits via Eq. (3) for the individual single IL data sets. As the quantity modeled by Eq. (3) is the logarithm of the Kfactor, it may be more sensitive to the equation coefficients than the K-factor itself. Therefore, in order to retain precision in the ln K values calculated from Eq. (3), we used more significant digits (4) in the individual coefficients than actually implied by the respective standard errors. Below, the results are discussed separately for the individual ILs. 4.1.1. [bmim][PF6 ] The study with [bmim][PF6 ] [25] was the first in our series of SFC measurements with ILs, and the source set of K-factors for the present correlation includes only 35 data points covering only four relatively nonpolar solutes (anisole, azulene, naphthalene and pyrene). Therefore, given the fact that in Eq. (3) there are 12 coefficients to be fitted, the resultant correlation is fairly strong and the parity plot of calculated versus experimental K-factors (Fig. 1) shows relatively little scattering around the perfect-fit line. Zero values of the a0 and v0 coefficients (see Table 2) result from the particular combination of solute properties in the selection; azulene is the only solute with nonzero value of the A descriptor, and the V descriptor values are the same for the isomeric solutes azulene and naphthalene. Because of high degree of similarity among the four solutes and relatively low number of data points, the signs and relative magnitudes of the fitted coefficients with [bmim][PF6 ] differ from those with the other ILs. 4.1.2. [bmim][BF4 ] With 176 K-factor values of 13 solutes (1-hexanol, 2-phenylethanol, aniline, anisole, azulene, benzoic acid, indole, N,N-dimethylaniline, naphthalene, N-methylaniline, p-cresol,

Fig. 1. Calculated versus experimental K-factors in [bmim][PF6 ]–scCO2 system. () Anisole; (×) azulene; (+) naphthalene; () pyrene.

phenol and pyrene), the source set for the correlation with [bmim][BF4 ] [26] is the most extensive among all ILs included in this study. Unlike the [bmim][PF6 ] data, the [bmim][BF4 ] set involved strongly H-bonding solutes adding to the complexity of intermolecular interactions operating within the set. Because of that and because of larger number of data points, the data set with [bmim][BF4 ] provides a much more stringent test of Eq. (3) as compared to the [bmim][PF6 ] set and the parity plot in Fig. 2 shows larger scattering as compared to the [bmim][PF6 ] plot (see also Table 2). The largest deviations of the calculated from the experimental values were observed in indole. As regards the fitted coefficients in Table 2, note that the coefficients a0 and b0 at the

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Fig. 2. Calculated versus experimental K-factors in [bmim][BF4 ]–scCO2 system. () 1-Hexanol; (䊉) 2-phenylethanol; () aniline; () anisole; () azulene; () benzoic acid; () indole; () N,N-dimethylaniline; (♦) naphthalene; () N-methylaniline; (+) p-cresol; (×) phenol; (*) pyrene.

solute hydrogen bonding acidity and basicity descriptors, respectively, are negative as the solute H-bonding interactions with the IL + CO2 stationary phase tend to increase retention and to make ln K (and K) lower. In most other ILs in Table 2, a0 and b0 are also negative. In turn, the coefficients c1 , c2 and c3 at the properties of pure CO2 combine in such a way as to reflect decreasing retention and increasing ln K with the rising density of CO2 . 4.1.3. [hmim][Tf2 N] The purpose of the SFC measurements with [hmim][Tf2 N] [27] was related to potential application of ILs in deep desulfurization of oil refinery streams. Except for naphthalene, therefore, all other solutes were sulfur-containing aromatics. The source data set for the present correlation with [hmim][Tf2 N] included 54 K-factor values of 4 solutes (benzothiazole, dibenzothiophene, naphthalene and thianaphthene). Therefore, for the same reasons as with [bmim][PF6 ], the resultant correlation is again rather strong with relatively small deviations of the calculated from the experimental K-factors (Fig. 3). As all solutes have zero hydrogen bonding acidity descriptors, the a0 coefficient is zero (see Table 2). Coefficient b0 is also zero because of the particular distribution of the B descriptor values among the four solutes in the set (the descriptor values are included in the electronic supplementary file). Consequently, because of low number and mutual similarity of the solutes included, the sign distributions in resultant coefficients for the [hmim][Tf2 N] and [bmim][PF6 ] data sets differ from those with the other ILs, and the values of residual sum of squares per one data point, RSS/N, are by about an order of magnitude lower as compared to the data sets for the other ILs with more varied solute selections (see Table 2). 4.1.4. [bmim][MeSO4 ] Source data set for the correlation with [bmim][MeSO4 ] [29,30] included 85 K-factor values of 14 solutes (1-hexanol, 1phenylethanol, 2-phenylethanol, acetophenone, aniline, anisole, azulene, benzothiazole, dibenzothiophene, N,N-dimethylaniline, naphthalene, N-methylaniline, pyrene and thianaphthene). As seen from Fig. 4, the largest deviations of the calculated from the experimental values appeared in N-methylaniline and, somewhat surprisingly, also in less polar solutes dibenzothiophene and

Fig. 3. Calculated versus experimental K-factors in [hmim][Tf2 N]–scCO2 system. () Benzothiazole; (×) dibenzothiophene; (+) naphthalene; () thianaphthene.

pyrene. The sign distribution in the resultant coefficients of the [bmim][MeSO4 ] fit resembles that of the [bmim][BF4 ] fit except for the coefficients c0 , c4 and c5 . 4.1.5. [bmim][TfO] With 166 K-factor values of 17 solutes (1-hexanol, 1-phenylethanol, 2-phenylethanol, acetophenone, aniline, anisole, azulene, benzothiazole, dibenzothiophene, indole, N,N-dimethylaniline, naphthalene, N-methylaniline, p-cresol, phenol, pyrene and thianaphthene), the source data set for the correlation with [bmim][TfO] [31] is the second largest after that with [bmim][BF4 ]. In this set, the largest deviations of the calculated from the experimental values appeared in p-cresol, indole and dibenzothiophene (see Fig. 5). The sign distribution in the resultant coefficients of the [bmim][TfO] fit is similar to that of the [bmim][MeSO4 ] fit except for the coefficient v0 .

Fig. 4. Calculated versus experimental K-factors in [bmim][MeSO4 ]–scCO2 system. () 1-Hexanol; (䊉) 1-phenylethanol; () 2-phenylethanol; () acetophenone; () aniline; () anisole; () azulene; () benzothiazole; (♦) dibenzothiophene; () N,Ndimethylaniline; (+) naphthalene; (×) N-methylaniline; (hatched ) pyrene; (*) thianaphthene.

J. Planeta et al. / J. Chromatogr. A 1250 (2012) 54–62

Fig. 5. Calculated versus experimental K-factors in [bmim][TfO]–scCO2 system. () 1-Hexanol; (䊉) 1-phenylethanol; () 2-phenylethanol; () acetophenone; () aniline; () anisole; () azulene; () benzothiazole; (♦) dibenzothiophene; () indole; (hatched ) N,N-dimethylaniline; (+) naphthalene; (×) N-methylaniline; (hatched ) p-cresol; (vertically hatched ♦) phenol; (hatched ) pyrene; (*) thianaphthene.

4.1.6. [thtdp][Cl] Source data set for this only non-imidazolium IL [28] in this study contained 118 K-factor values of 11 solutes (1-hexanol, 2-phenylethanol, aniline, anisole, azulene, dibenzothiophene, N,N-dimethylaniline, naphthalene, N-methylaniline, pyrene and thianaphthene). Fig. 6 indicates that the largest deviations of the calculated from the experimental values appeared in 1-hexanol and pyrene. In the previous studies with [bmim][MeSO4 ] [29] and with [bmim][TfO] [31], we compared the coefficients of simple LSER relationships for relative retention factors at a fixed temperature and pressure, and the comparison showed distinct difference between the LSER coefficients for [thtdp][Cl] and those of imidazolium ILs. In the present correlation of the K-factors, however, it is impossible to identify any distinctive feature of the LSER coefficients (e0 through v1 in Table 2) for [thtdp][Cl] against the coefficients for the imidazolium ILs. This finding just indicates that, in addition to the solute part, the CO2 solvent power part of Eq. (3) also makes significant contributions to interpretation of solute K-factors at varying densities of CO2 as illustrated in the following section.

59

Fig. 6. Calculated versus experimental K-factors in [thtdp][Cl]–scCO2 system. () 1-Hexanol; (䊉) 2-phenylethanol; () aniline; (×) anisole; () azulene; () dibenzothiophene; () N,N-dimethylaniline; () naphthalene; (+) N-methylaniline; () pyrene; (*) thianaphthene.

4.1.7. Illustration of contributions to ln K by individual terms of Eq. (3) As an example, Fig. 7 shows the contributions of individual terms of Eq. (3) to the calculated values of ln K for 1-hexanol in [bmim][TfO]–scCO2 system at 333.2 K for several different pressures within the range of the source experimental data [31]. The contributions are expressed as percentages of the resultant value of ln K at the particular temperature and pressure, and they differ in signs, magnitudes and the rates of change with pressure. In the particular system, the solute part of Eq. (3) (the terms with coefficients c0 through v1 ) only makes a moderate contribution to the resultant K-factor value. The terms with coefficients c1 and c2 , related to the solvent power of CO2 , show rather steep rates of change with pressure whereas the rate is less pronounced in the term with c3 coefficient. The terms with coefficients c4 and c5 , measuring the effect of the changing composition of the IL + CO2 stationary phase on the intermolecular interactions and combinatorial entropy, respectively, appear to be of minor significance. In

Fig. 7. Percentage contributions of the individual additive terms in Eq. (3) to the calculated values of ln K of 1-hexanol in [bmim][TfO]–scCO2 system at 333.2 K and pressure of 8.7, 10, 10.9, 12.1, 13.3 and 16.7 MPa [31].

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Table 3 Coefficients of Eq. (3), their standard errors and other statistical characteristics determined by linear regression of K-factor data set involving multiple imidazolium IL–scCO2 systems (IL = [bmim][PF6 ], [bmim][BF4 ], [hmim][Tf2 N], [bmim][MeSO4 ] and [bmim][TfO]). Function fitted

Eq. (3)

Eq. (3) without the combinatorial entropy part

Number of data points (N) c0 ± standard error in c0 e0 ± standard error in e0 s0 ± standard error in s0 a0 ± standard error in a0 b0 ± standard error in b0 v0 ± standard error in v0 v1 ± standard error in v1 c1 ± standard error in c1 c2 ± standard error in c2 c3 ± standard error in c3 c4 ± standard error in c4 c5 ± standard error in c5

516 3.148 ± 0.69 −2.113 ± 0.17 −1.186 ± 0.22 −5.702 ± 0.15 −1.230 ± 0.19 −3.634 ± 0.62 0.5914 ± 0.060 −11.92 ± 1.1 17.48 ± 1.5 63.58 ± 5.2 0.08663 ± 0.021 6.141 ± 0.48

516 −0.1782 ± 0.73 −2.710 ± 0.18 −1.237 ± 0.26 −5.870 ± 0.17 −1.898 ± 0.22 1.140 ± 0.57 0.2811 ± 0.063 −9.405 ± 1.2 16.97 ± 1.8 54.83 ± 5.9 0.1479 ± 0.023 –

RSS/N

0.1865

0.2471

Mean of [(Kcalc − Kexp )/Kexp ]2 Square root of the mean of [(Kcalc − Kexp )/Kexp ]2 Median of [(Kcalc − Kexp )/Kexp ]2 Square root of the median of [(Kcalc − Kexp )/Kexp ]2

0.3449

0.5860

0.5873

0.7655

0.06333

0.08945

0.2517

0.2991

the other solutes and IL–scCO2 systems, the relative weights of the individual contributions to ln K are similar to those shown in Fig. 7. 4.2. Multiple imidazolium IL–scCO2 systems After fitting the data sets from the individual IL–scCO2 systems, Eq. (3) was tested on a larger data set including the combined K-factor values from all imidazolium IL–scCO2 systems (516 data points). Table 3 contains the resultant coefficients and other characteristics of the K-factor data fit via Eq. (3) together with the fit performed without the combinatorial entropy term (no c5 coefficient). Comparison of the statistical characteristics of the residuals in Table 3 indicates that inclusion of the combinatorial entropy term in Eq. (3) was helpful in improving the fit as the residual sum of squares per data point decreased by 24.5%. However, as illustrated by Fig. 8, even with inclusion of the combinatorial entropy term the deviations of the calculated from the experimental values exceed markedly those in the individual IL–scCO2 systems (Figs. 1–6). So, from the viewpoint of balance between the model’s demand for input data on one side and dependability of the model’s predictions on the other, a simultaneous application to a set of K-factor data for a variety of solutes in several IL–scCO2 systems appears to stretch the model’s capabilities to the very limit even if the ILs belong to a single class of cations (imidazoliums) and, in fact, most of them have the same cation ([bmim]). Therefore, inclusion into Eq. (3) of the combinatorial entropy term, although somewhat helpful in reconciling solute K-factors in different IL–scCO2 systems into a single fit (see the data in Table 3), is not sufficient to provide for an “ab initio”, reliable estimation of solute K-factor for real use in engineering design of applications of IL–scCO2 systems. 4.3. Imidazolium + phosphonium IL–scCO2 systems Table 4 shows the results of application of Eq. (3) to the largest data set including the K-factors from all imidazolium IL–scCO2 systems as well as those from the [thtdp][Cl]–scCO2 system (634 data points). Again, it follows from comparison of the statistical

Fig. 8. Simultaneous application of Eq. (3) to solute K-factor data from imidazolium IL–scCO2 systems. () [bmim][PF6 ]; (+) [bmim][BF4 ]; () [hmim][Tf2 N]; () [bmim][MeSO4 ]; (×) [bmim][TfO]. The calculated K-factors were obtained from Eq. (3) with coefficients from Table 3 (with the combinatorial entropy term).

characteristics of the fits with and without the combinatorial entropy term in Eq. (3) that inclusion of the term is helpful in improving the fits. Nevertheless, as documented by Fig. 9, even with inclusion of the combinatorial entropy term the overall fit is rather poor, with the data from the [thtdp][Cl]–scCO2 system being effectively “pushed out” to the outskirts of the calculated-versusexperimental data cluster of the imidazolium IL–scCO2 systems, reflecting largely the different characters of the IL–solute intermolecular interactions that the [bmim] and [thtdp] cations can participate in. Apparently, therefore, extensive data files involving more than a single family of IL cations are beyond reach of the model described Table 4 Coefficients of Eq. (3), their standard errors and other statistical characteristics determined by linear regression of K-factor data set involving imidazolium and phosphonium IL–scCO2 systems (IL = [bmim][PF6 ], [bmim][BF4 ], [hmim][Tf2 N], [bmim][MeSO4 ], [bmim][TfO] and [thtdp][Cl]). Function fitted

Eq. (3)

Number of data points (N) c0 ± standard error in c0 e0 ± standard error in e0 s0 ± standard error in s0 a0 ± standard error in a0 b0 ± standard error in b0 v0 ± standard error in v0 v1 ± standard error in v1 c1 ± standard error in c1 c2 ± standard error in c2 c3 ± standard error in c3 c4 ± standard error in c4 c5 ± standard error in c5

634 634 2.094 ± 0.84 −1.492 ± 0.99 −2.176 ± 0.20 −2.272 ± 0.25 −0.5072 ± 0.29 −0.3869 ± 0.35 −5.645 ± 0.20 −4.960 ± 0.24 −1.838 ± 0.25 −2.178 ± 0.29 −3.519 ± 0.66 −0.01274 ± 0.75 0.5210 ± 0.072 0.2475 ± 0.085 −10.59 ± 1.4 −4.073 ± 1.6 16.36 ± 1.9 7.845 ± 2.3 61.29 ± 6.8 26.88 ± 7.8 −0.02892 ± 0.026 −−0.1869 ± 0.029 3.705 ± 0.22 –

RSS/N Mean of [(Kcalc − Kexp )/Kexp ]2 Square root of the mean of [(Kcalc − Kexp )/Kexp ]2 Median of [(Kcalc − Kexp )/Kexp ]2 Square root of the median of [(Kcalc − Kexp )/Kexp ]2

Eq. (3) without the combinatorial entropy part

0.3806 1.889 1.375

0.5554 3.505 1.872

0.1012 0.3181

0.1699 0.4122

J. Planeta et al. / J. Chromatogr. A 1250 (2012) 54–62

Fig. 9. Simultaneous application of Eq. (3) to solute K-factor data from all IL–scCO2 systems included. () [bmim][PF6 ]; (+) [bmim][BF4 ]; () [hmim][Tf2 N]; () [bmim][MeSO4 ]; (×) [bmim][TfO]; (♦) [thtdp][Cl]. The calculated K-factors were obtained from Eq. (3) with coefficients from Table 4 (with the combinatorial entropy term).

61

Fig. 10. Test of the model with independent data [33] at 333 K. () [bmim][PF6 ], PhCH2 OH, 12 MPa; (䊉) [bmim][PF6 ], PhCH2 OH, 16 MPa; (hatched ) [bmim][PF6 ], PhCH2 OH, 20 MPa; () [bmim][BF4 ], PhCH2 OH, 12 MPa; () [bmim][BF4 ], PhCH2 OH, 16 MPa; (hatched ) [bmim][BF4 ], PhCH2 OH, 20 MPa; () [bmim][BF4 ], PhOH, 16 MPa; () [bmim][BF4 ], PhCOCH3 , 16 MPa; (♦) [bmim][BF4 ], PhCl, 16 MPa; () [bmim][PF6 ], PhOH, 16 MPa; () [bmim][PF6 ], PhCOCH3 , 16 MPa; () [bmim][PF6 ], PhCl, 16 MPa.

by Eq. (3) as the implied uncertainties in the K-factor predictions are clearly too high to be useful in the process design, even if used only as an initial guess. 4.4. Test of the model with independent data Independent K-factor data to test the predictive ability of the present model were calculated from the weight-fraction-based partition coefficients reported by Machida et al. [33], and included K-factors of acetophenone, benzyl alcohol, chlorobenzene and phenol in [bmim][PF6 ]–scCO2 and [bmim][BF4 ]–scCO2 systems at 333 K. With both ILs, the K-factors of acetophenone, chlorobenzene and phenol referred to 16 MPa pressure whereas the K-factors of benzyl alcohol were measured at 12, 16 and 20 MPa. The pure component data needed in Eq. (3) for benzyl alcohol and chlorobenzene were calculated as described in Section 3.2, and the other two solutes and both ILs were already included in the data base for the present study (although in different solute–IL combinations). Fig. 10 shows the comparison of the experimental K-factor data [33] with the values calculated from Eq. (3) using the coefficients c0 , e0 , s0 , a0 , b0 , v0 , v1 , c1 , c2 , c3 , c4 and c5 obtained from the fit involving all imidazolium IL–scCO2 systems (Table 3). All data points appear in the lower triangle of the parity plot, i.e., Eq. (3) with the present parameters tends to underestimate the K-factor data of Machida et al. [33]. The cause of this particular result is not known. Overall, given the complexity of the systems modeled, the result shown in Fig. 10 is probably adequate to the use of a linear model described by Eq. (3) and based largely on pure component data as the input parameters (except for the CO2 solubility in the particular IL). Naturally, the situation improves with decreasing generality of the problem, i.e., when the comparison of the model predictions with independent data only involves a single IL–scCO2 system. In Fig. 11, experimental K-factor data from the [bmim][BF4 ]–scCO2 system [33] are compared with the values calculated from Eq. (3) using the coefficients c0 , e0 , s0 , a0 , b0 , v0 , v1 , c1 , c2 , c3 , c4 and c5 obtained from the fit involving only the [bmim][BF4 ]–scCO2 system (Table 2). The predictions in Fig. 11 are considerably better as compared to those based on a wider selection of IL–scCO2 systems (Fig. 10).

Fig. 11. Constrained test of the model with independent data [33] at 333 K ([bmim][BF4 ]–scCO2 system only). () PhCH2 OH, 12 MPa; () PhCH2 OH, 16 MPa; (hatched ) PhCH2 OH, 20 MPa; () PhOH, 16 MPa; () PhCOCH3 , 16 MPa; (♦) PhCl, 16 MPa.

5. Conclusion In general, the outcome of this study confirms the conclusions voiced previously by Hiraga et al. [34]. The present results indicate that extensive K-factor files involving data on more than a single family of IL cations are difficult to model by Eq. (3). Amendment of the Hiraga et al.’s original model with the combinatorial entropy term, although somewhat helpful in improving the correlations through providing an additional explanatory variable, does not seem to open the way to a predictive and dependable tool to predict infinite dilution K-factors of organic solutes in multiple

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families of IL–scCO2 systems in a wide range of temperature and pressure. The inclusion among the input parameters of the binary property, the mole fraction solubility of CO2 in the particular IL, detracts somewhat from the predictive power of the model. However, our preliminary testing of model versions using only pure component properties as input data gave very poor results, particularly in the data sets involving multiple IL–scCO2 systems. Therefore, we have finally followed the approach of Hiraga et al. [34] as it did not appear feasible to describe the large variations in the IL solvent properties on absorption of CO2 without resorting to xCO2 as an input parameter. Contrary to the applications involving multiple IL–scCO2 systems, the model described by Eq. (3) appears to be relatively useful in correlating solute K-factor data sets in single IL–scCO2 systems at varying temperature and pressure. Acknowledgments We thank the Czech Science Foundation (Projects P206/11/0138, P503/11/P523 and P106/12/0522) and the Academy of Sciences of the Czech Republic (Institutional Research Plan No. AV0Z40310501) for financial support of this work. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.chroma. 2012.04.016. References [1] N.V. Plechkova, K.R. Seddon, Chem. Soc. Rev. 37 (2008) 123. [2] J.S. Wilkes, M.J. Zaworotko, J. Chem. Soc. Chem. Commun. (1992) 965. [3] M.J. Earle, J.M.S.S. Esperanc¸a, M.A. Gilea, J.N.C. Lopes, L.P.N. Rebelo, J.W. Magee, K.R. Seddon, J.A. Widegren, Nature 439 (2006) 831. [4] J.P. Armstrong, C. Hurst, R.G. Jones, P. Licence, K.R.J. Lovelock, C.J. Satterley, I.J. Villar-Garcia, Phys. Chem. Chem. Phys. 9 (2007) 982. [5] J.M.S.S. Esperanc¸a, J.N.C. Lopes, M. Tariq, L.M.N.B.F. Santos, J.W. Magee, L.P.N. Rebelo, J. Chem. Eng. Data 55 (2010) 3. [6] P. Wasserscheid, T. Welton (Eds.), Ionic Liquids in Synthesis, 2nd ed., WileyVCH, Weinheim, 2008. [7] J.P. Hallett, T. Welton, Chem. Rev. 111 (2011) 3508. [8] P. Lozano, Green Chem. 12 (2010) 555. [9] C.F. Poole, S.K. Poole, J. Chromatogr. A 1217 (2010) 2268. [10] P. Hapiot, C. Lagrost, Chem. Rev. 108 (2008) 2238. [11] L.A. Blanchard, D. Hancu, E.J. Beckman, J.F. Brennecke, Nature 399 (1999) 28. [12] L.A. Blanchard, J.F. Brennecke, Ind. Eng. Chem. Res. 40 (2001) 287. [13] R.A. Brown, P. Pollet, E. McKoon, C.A. Eckert, C.L. Liotta, P.G. Jessop, J. Am. Chem. Soc. 123 (2001) 1254. [14] F. Liu, M.B. Abrams, R.T. Baker, W. Tumas, Chem. Commun. (2001) 433. [15] S.V. Dzyuba, R.A. Bartsch, Angew. Chem. Int. Ed. 42 (2003) 148. [16] S. Keskin, D. Kayrak-Talay, U. Akman, Ö. Hortac¸su, J. Supercrit. Fluids 43 (2007) 150. [17] M. Roth, J. Chromatogr. A 1216 (2009) 1861. [18] F. Jutz, J.-M. Andanson, A. Baiker, Chem. Rev. 111 (2011) 322. [19] A.M. Scurto, S.N.V.K. Aki, J.F. Brennecke, J. Am. Chem. Soc. 124 (2002) 10276. [20] V. Najdanovic-Visak, A. Serbanovic, J.M.S.S. Esperanc¸a, H.J.R. Guedes, L.P.N. Rebelo, M. Nunes da Ponte, ChemPhysChem 4 (2003) 520. [21] E. Kühne, C.J. Peters, J. van Spronsen, G.-J. Witkamp, Green Chem. 8 (2006) 287. [22] D. Fu, X. Sun, Y. Qiu, X. Jiang, S. Zhao, Fluid Phase Equilibr. 251 (2007) 114.

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