Phase Separation in Solutions of Room Temperature Ionic ... - CiteSeerX

Z. Phys. Chem. 220 (2006) 1417–1437 / DOI 10.1524/zpch.2006.220.10.1417  by Oldenbourg Wissenschaftsverlag, München

Phase Separation in Solutions of Room Temperature Ionic Liquids in Hydrocarbons By D. Saracsan, C. Rybarsch, and W. Schröer ∗ Institut für Anorganische und Physikalische Chemie, Fachbereich Biologie-Chemie, Universität Bremen, D-28359 Bremen, Germany (Received July 5, 2006; accepted August 15, 2006)

Ionic Liquids / Corresponding State / Phase Diagrams / Critical Phenomena The room temperature ionic liquids (RTIL) trihexyl-tetradecyl phosphonium chloride (P 666 14 Cl) and the bromide (P 666 14 Br) are soluble in hydrocarbons. The investigated solutions in heptane, octane, nonane and decane show liquid–liquid phase separation with an upper critical solution point at ambient temperatures at molar fractions near 0.03 of the salt. Phase diagrams are reported and analysed presuming Ising criticality. The critical temperatures and the critical densities increase with the chain length of the hydrocarbons, where the figures corresponding to the bromides are above that of the chlorides. Scaled by the critical data the phase diagrams show corresponding state behaviour. In accordance with the prediction of the restricted primitive model (RPM), which is a model fluid of equal sized, charged hard spheres in a dielectric continuum, the critical points are located at low temperature and low concentration, when the corresponding state variables of this model are used. However, the critical temperature Tc* and the critical density ρc* are well below the figures of the RPM prediction. Comparison is made with the phase diagrams of alcohol solutions of imidazolium ionic liquids and with simulation results of the RPM.

1. Introduction Ionic liquids (IL) are salts that are already liquid at ambient temperatures. Because of their potential for industrial applications ILs enjoy high attention [1–3]. The properties of ILs are determined by a complicated interplay of Coulomb interactions and specific properties of the ions, which in general are organic entities with structures that are similar to that of ionic detergents. Understanding of the macroscopic properties of ILs from their microscopic structure provides a formidable challenge for theory and experiments. * Corresponding author. E-mail: [email protected]

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While typical inorganic salts as NaCl melt at high temperatures, in the region of 1000 K, the melting points of organic salts are much lower; mostly in the region above the boiling point of water. Organic salts with melting points below 100 ◦ C have been termed ionic liquids, while ILs that are fluid already at room temperature are called room temperature ionic liquids (RTIL). RTILs with melting points as low as 200 K [4] are known. In spite the low melting temperatures, the vapour pressure is very low, in fact too small to be measurable till now. At high temperatures, the liquid range is limited by the chemical stability of the ILs. The boiling temperatures at normal pressure and the critical temperatures would be above the decomposition temperatures [5], which typically are above 600 K. The need for investigations of basic physical properties of the pure ILs and of their solutions has been emphasized repeatedly [1–3]. In particular, phase diagrams and other thermodynamic properties of mixtures form the basic background for separation processes. Phase diagrams for solutions in alcohols have been reported for ILs with anions PF 6 − [6, 7], BF 4 − [8–11], N(SO 2 CF 3 )2 − [11–13]. The typical cations investigated so fare are derivatives of the imidazolium or the pyridine cations. Here we report phase diagrams of phosphonium halides in hydrocarbons. Physical properties of the ILs with phosphonium ions have been given in [14, 15]. By our knowledge phase diagrams for solutions of phosphonium ILs have not been reported before. It is a particular fascinating aspect of this research that the investigated systems are ionic solutions in the non-polar hydrocarbons. The only phase diagram reported of an ionic solution in a hydrocarbon was that of tributyl heptyl ammonium dodecyl sulfat in cyclohexane [16].

2. Theoretical background The Ising model is a very simple lattice model, which takes into account nextneighbour interactions only. The model considers occupancy of the lattice by two kinds of particles (spins). The interactions are described by one interaction parameter only, which assumes a positive value for unlike neighbours and vice versa a negative one for particles of the same kind. Irrespective of the simplicity of the model, which contradicts chemical intuition, it has been shown by experiments that the critical properties of the liquid–gas phase transitions and of the liquid–liquid phase transitions [17, 18] of non-ionic fluids are in accordance with the properties of the Ising model in three dimensions (3d). Note, all classical analytical theories as the van der Waals theory or the theory of regular solutions are mean-field theories, which cannot describe the critical behaviour correctly. It has been proven by theory, that all phase-transitions of fluids, which are driven by short-range interactions belong to the 3d-Ising universality class. Short-range interactions are defined as interactions following an r −n power law with n > 4.97. However, the phase transitions in ionic systems

RTIL–hydrocarbon solutions

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may be determined by long-range Coulomb interactions, which vary as r −1 , so that the question of the nature of the critical point in ionic systems is a scientific topic of fundamental importance [19–21]. In fact, there are theoretical predictions of mean field behaviour for intermolecular potentials of infinite range. Although mean-field critical behaviour was reported for demixing ionic solutions [22–24], it appears now that phase transitions of solutions driven by Coulomb interactions also belong to the Ising universality class. Evidence comes from experimental investigations [25–27] on the liquid–liquid phase transition of ionic solutions, but also from simulations of the simplest model for an ionic fluid, the restricted primitive model (RPM). The RPM considers charged hard spheres of equal size in a dielectric continuum with the dielectric constant ε [28–32]. According to the correspondence principle [17] the properties of the liquid–gas phase transition of this model are expected to apply also for the liquid–liquid phase transition, where the dielectric constant is identified with that of the solvent. Simulations of the RPM and of generalizations, which allow different sizes and charges [33, 34] of the ions, consistently yield Ising critical behaviour also. Presuming Ising criticality, the temperature dependence of a concentration variable X at coexistence can be represented by a power series [17, 18] in τ = |T − Tc|/Tc , termed Wegner expansion, which is of the form X± Xm = ± B * τ β 1 + B 1* τ ∆ + B 2* τ 2∆ + . . . , Xc Xc where Xm = 1 + A * τ + C * τ 2β + D * τ 1−α 1 + D 1* τ ∆ + . . . . Xc

(1)

(2)

By X we denote a variable for the composition that will be discussed below. The plus refers to the region X > X m and vice versa; X m is the so called diameter, defined by the average X m = (X + + X − )/2 of the compositions X + and X − of the coexisting phases. Equations (1) and (2) are written in the form appropriate for a corresponding state analysis, where the temperatures and the compositions are related to the crititical data. The coefficients A * , B * etc. are dimensionless, specific to the system, but become identical, when the principle of corresponding states applies. For the Ising model the exponents assume the universal values β = 0.325, α = 0.11, and ∆ = 0.51, where β is the leading exponent for the phase diagram, α is the exponent of the specific heat, and ∆ is the crossover exponent, describing the crossover from Ising to classical mean-field behaviour. In mean-field theories β = 1/2 and α = 0. The rectilinear diameter rule of Cailletet-Mathias, which assumes a linear temperature dependence of the diameter, is a consequence of mean-field theory. By definition, there is no crossover exponent ∆ in mean-field models. At large separation from the critical point other specific contributions become important and universality looses importance.

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The temperature dependence of the diameter has been a matter of controversy for some time [35, 36]. For a long time it was accepted that the 1 − α-term is the leading term near the critical point, while the 2β-term was regarded as a consequence of a non-appropriate choice of the concentration variable. Recent work, however, advocates the number density as the appropriate variable [37] and suggests the 2β-term as the leading part [38–40]. However, partial cancellation of the 2β- and the 1 − α terms may cause apparent linear temperature dependence of the diameter. Thus, deviations from the linear temperature dependence are often small and not observable in many cases [39]. Therefore, it is difficult to determine uniquely the various coefficients of Eq. (2) by a numerical analysis, even of the best experimental data. Notably, simulations of the RPM have not reached the accuracy to show the non-analytical contributions to the diameter. The exponents in Eqs. (1) and (2) are universal, while the coefficients are specific to the system. This is also true for similar expansions, which concern other properties, e.g. the susceptibility. The coefficients in the different expansions are not independent, because certain products of the coefficients have universal values. There are rather strict conditions on size and sign of the terms in the various expansions. The corrections to scaling, given in Eqs. (1) and (2), suffice in the region τ < 10 −2 [5]. In general, a crossover theory [41] should be applied, when analyzing data in a wider temperature region. Analysing phase diagrams using the Eqs. (1) and (2) or the more advanced theories requires precise knowledge of the data of the critical point and measurements with mK-accuracy. Most phase diagrams reported in the literature are obtained by the so called visual method, where the temperature of the cloud point for samples of different composition is measured [6–8, 11–13]. Commonly, this method is not accurate enough to allow for a data analysis by Eqs. (1) and (2). However, the purpose of this work is localizing the phase diagrams in order to provide the ground for accurate measurements of the critical properties. Therefore, the visual method is also used in this work, thus allowing applying a simpler approach for the data evaluation, which is given in what follows. In the engineering literature usually classical expansions are applied for estimation and fitting excess functions, which implies mean-field exponents for the critical properties, e.g. for the shape of the coexistence curve [42]. Because this approach ignores the fundamental fact, that the liquid–liquid phase transition belongs to the Ising universality class, we have proposed a method, which is simpler than Eqs. (1) and (2), but takes care of the non-classical nature of the phase diagrams [10]. The simplified scaling laws applied in the analysis are X ± − X m = ±B(Tc − T )1/3 ,

(3)

where X m = X c + A(Tc − T ) .

(4)


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In variance to Eqs. (1) and (2) the temperature and the composition are not scaled by their critical values, which is appropriate for a first data analysis. The resulting cubic equation for T can be solved exactly. However, the resulting solutions are too messy to be applied in a fitting procedure. In many cases the slope of the diameter is not very large and an expansion of |X − X m | 3 in first order of A suffices. The resulting function T(X), which will be used as fitting function, is T = Tc −

|X − X c | 3 . B 3 ± 3A(X − X c)2

(5)

The positive and negative sign correspond to the range X > X c and X < X c respectively. The parameters of the fit are the critical data Tc , X c , the width B of the coexistence curve and the slope A of the diameter. By such fit the non-classical shape of the phase diagrams is taken into account in a reasonable approximation. The approximation of β = 1/3 is near to the Ising value β = 0.325. Note, straight forward fits by an analytic power series not only imply classical exponents, but often also lead to erroneous descriptions e.g. by showing spurious maxima. In mean-field theory, the equations corresponding to Eqs. (3) and (4) are quadratic equations with a simple exact solution. On experimental grounds, many choices for the composition variable X can be thought of e.g. the mole fraction x, the mass fraction w or the volume fraction ϕ. The mass fraction is most directly related to the experiment. From the physical point of view w it is not appropriate, because the masses are irrelevant for the thermodynamics of fluids. All possible choices for the variables have been tried in the analysis. The volume fraction yields the most symmetrical phase diagram. The thermodynamic analysis of Anisimov et al. [37] removes the arbitrariness of the composition variable. According to Landau theory, the free energy density is the appropriate thermodynamic potential for analyzing phase transitions. In this thermodynamic potential the variable is the density and the corresponding field is the chemical potential. Therefore, the number density of one of the components is the proper thermodynamic variable to be used, when investigating liquid–liquid phase transitions that are well separated from a liquid–gas transition. The application of the partial density as variable, however, requires the knowledge of the density as function of temperature and concentration. In good approximation, the densities can be estimated by assuming additivity of the molar volumes, thus ignoring the excess volumes [43]. In this approximation the reduced ion number density ρ * of the ILs, which is the corresponding state variable of the RPM, is estimated from the mole fraction x IL of the IL and the molar volumes VIL and VS of the IL and of the solvent. ρ* =

2x IL σ 3 NA x IL VIL + (1 − x IL )VS

(6)

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NA is the Avogadro number. By σ we denote the separation of the centres of the distributed charges of the ions at contact, which in the RPM is identical with the ion diameter. The reduced temperature in the RPM model is defined by the ratio of the thermal energy kT to the Coulomb energy of the ions with the charges q at contact in a continuum with the dielectric constant ε. T* =

kTεσ q2

(7)

The RPM, which is a model for the liquid–gas phase transition in a dielectric continuum with the dielectric constant ε, is adopted for the liquid–liquid phase transition by using the dielectric constant of the solvent in Eq. (7). With this setting the RPM has been used successfully as guide for classifying the liquid–liquid phase transition as driven by Coulomb interactions [44, 45]. Reasonable agreement with critical data predicted by the RPM is regarded as an indicator for a phase transition driven by Coulomb interactions. We report the data in terms of the mole fraction and analyse the data also in terms of the RPM variables, given in Eqs. (6) and (7), compare the results with that of other ionic systems and with the predictions of the RPM.

3. Experimental The ionic liquids P 666 14 Cl (trihexyl-tetradecyl phosphonium chloride) and P 666 14 Br (trihexyl-tetradecyl phosphonium bromide) were purchased from Merck, and Strem Chemicals, respectively. Standard NMR and MS analysis did not show impurities. The solvents were chosen of highest quality. Traces of water were removed from the solvents by adding P 2 O 5 in a round-bottomed flask. “Pump and freeze” technique at a vacuum line was used to remove the gases and volatile compounds from the solvents and from the ILs. In a glove box under argon atmosphere the ILs were placed with a syringe into a glass sample cell and then dried for thirty hours at 60 ◦ C under vacuum of 6 × 10 −3 bar. A Teflon tap (Normag) attached to the sample cell enabled connecting and removing the sample cell from the vacuum line, thus allowing weighing the sample during the drying process, and also when adding the solvent. The solvent was condensed via the vacuum line into the sample cell that was cooled with liquid nitrogen. The concentrations were determined by weight with an accuracy of 10−4 g. In this manner a set of concentrations is prepared with the identical sample of the IL by adding or removing solvent from the sample by distillation via the vacuum line. This method avoids uncontrollable traces of impurities and variations of the composition that can cause deformations of the separation curves, when different samples are investigated. Mixtures with the mass-fractions of 0.03 to 0.27 were prepared in that way. The cloud points were determined visually by repeated cooling the homogeneous mixture in a thermostat with glass window filled with water. The tem-


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perature was controlled with an accuracy of 0.01 ◦ C using a Quartz thermometer (Hereus QUAT200). The temperature range investigated reached from 16 ◦ C to 90 ◦ C. Clearly, the accuracy of the visual method is limited by the subjectivity of the experimentalist. The visual method is appropriate to get an overview for providing the ground for the preparation of samples of critical composition.

4. Results 4.1 Phase diagrams with the mole fraction as variable In Fig. 1 we show the phase diagrams for the solutions of the ionic liquid (a) P 666 14 Cl (trihexyl-tetradecyl phosphonium chloride) and (b) P 666 14 Cl in the hydrocarbons heptane, octane, nonane, and decane. The corresponding data are given in Table 1. We show in Fig. 1 the separation temperatures as function of the mole fraction of the Ils, which is determined exactly from the weight of the samples. All solutions have an upper critical solution point. The curves shown in Fig. 1 are the results of the fits using Eq. (5). In Table 2 we give the resulting parameters. Within the accuracy of the measurements, the quality of the fits is perfect. Figure 1 also shows the critical data resulting from the fit. The critical temperatures and the critical mol fractions increase with the chain length of the solvent. The bromides separate at higher temperature than the chlorides. Those trends can be seen more clearly in Fig. 2, where we show (a) the variation of the critical temperatures and (b) of the critical mol fractions as function of the chain length of the solvent. The critical temperatures of the solutions of the bromide and of the chloride increase almost parallel in a linear fashion with the chain length of the alkanes. A similar trend is observed for the critical mole fraction. Qualitatively those trends can already be seen in the plots of the phase diagrams Fig. 1. The trends of the width and the asymmetry of the separation curves cannot be judged by bare inspection but require a numerical analysis of the data. The width of the phase diagrams, described by the parameter B and the slope A of the diameter given in Table 2 are shown in Fig. 3. We see clearly an increase of B with the size of the solvent, which is not much different for the two salts. The diameter slope also shows a tendency to increase with the solvent size. The phase diagrams of the bromide solutions are slightly more symmetrical than the chloride solutions. The next step is investigating the corresponding state behaviour of the phase diagrams. In Fig. 4 we show the reduced temperature (Tc − T )/Tc as function of the reduced mole fraction (x − x c )/x c for the solutions of both ILs. The agreement is perfect for the solutions of a certain IL. It is still rather good, when we compare the solutions of both ILs. The curves for the bromide solutions (open symbols) appear slightly more symmetrical. The parameters B * and A * characterising the shape of the phase diagrams in the corresponding

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Fig. 1. Phase diagrams of the solutions of the ILs P 666 14 Cl (a, filled symbols) and P 666 14 Br (b, open symbols) in the hydrocarbons heptane ( , ), octane ( , ), nonane ( , ), and decane ( , ) with the mole fraction as composition variable. The curves are the fits by Eq. (5). The critical points ( ) result from the fit.

state representation are given in Table 2. The clear variation of B and A with the size of the solvent is removed, when using corresponding state variables. No clear trends for B * and A * can be seen in the table. The plots would not give additional information and, therefore, are not shown.

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Table 1. Data of the liquid–liquid phase diagrams for the solutions of the ILs P 666 14 Cl and P 666 14 Br in alkanes. The composition is given in mol percent. P 666 14 Cl heptane

octane

nonane

decane

T [K]

100 x

T [K]

100 x

T [K]

100 x

T [K]

100 x

289.37 292.14 294.10 294.67 295.13 295.18 295.18 295.13 295.02 294.85 294.36 292.95 288.63

0.785 0.968 1.204 1.371 1.666 1.870 2.044 2.202 2.418 2.774 3.343 4.250 5.950

292.96 297.70 299.05 299.82 300.17 300.22 300.21 300.12 299.86 299.75 299.49 298.59 296.87 293.75

0.894 1.206 1.423 1.693 1.997 2.365 2.573 2.859 3.286 3.619 3.967 4.813 5.688 7.226

296.03 302.22 303.41 304.95 305.59 305.92 306.06 306.12 305.96 305.92 305.73 305.29 303.95 301.91

0.815 1.174 1.291 1.536 1.982 2.072 2.325 2.665 2.845 3.095 3.644 4.245 5.299 6.357

305.48 310.33 312.06 312.92 312.95 313.09 313.05 313.02 312.90 312.73 311.68 310.42 308.37

1.019 1.398 1.779 2.373 2.726 2.846 3.012 3.224 3.612 4.212 5.196 6.228 7.392

P 666 14 Br heptane

octane

nonane

decane

T [K]

100 x

T [K]

100 x

T [K]

100 x

T [K]

100 x

325.40 331.41 335.57 338.43 339.85 340.76 341.31 341.46 341.62 341.70 341.64 341.60 341.50 341.25 340.50 338.46 331.62

0.567 0.703 0.857 1.006 1.207 1.376 1.579 1.703 1.861 2.000 2.150 2.373 2.715 3.095 3.675 4.577 6.242

333.65 339.68 341.76 343.75 344.35 344.73 344.85 344.97 345.02 345.02 344.99 344.71 344.06 342.50 338.55

0.777 1.005 1.203 1.500 1.690 1.871 2.005 2.102 2.310 2.541 2.931 3.397 4.124 5.152 6.476

337.93 342.25 346.27 348.15 349.60 350.87 351.19 351.58 351.61 351.61 351.38 351.07 350.18 347.57 343.85

0.794 0.929 1.156 1.352 1.565 1.829 2.038 2.391 2.624 3.274 3.831 4.434 5.179 6.464 7.747

353.76 356.17 357.13 357.63 357.95 358.25 358.29 358.29 358.32 358.23 358.09 357.93 357.35 356.39 354.75

1.195 1.468 1.697 1.831 2.027 2.249 2.430 2.592 2.860 3.238 3.635 4.042 4.763 5.323 6.218

4.2 Phase diagrams in terms of the RPM variables The RPM model has proved to be a useful guide in the search for phase transitions driven by Coulomb forces: If the phase transition is driven by Coulomb interactions, it can be expected that the critical point is located in the region

P 666 14 Cl/heptane P 666 14 Cl/octane P 666 14 Cl/nonane P 666 14 Cl/decane P 666 14 Br/heptane P 666 14 Br/octane P 666 14 Br/nonane P 666 14 Br/decane

systems

100x c 2.26 ± 0.03 2.70 ± 0.03 3.00 ± 0.04 3.22 ± 0.03 2.46 ± 0.03 2.81 ± 0.03 3.26 ± 0.02 3.47 ± 0.03

Tc [K] 295.13 ± 0.05 300.17 ± 0.05 305.99 ± 0.07 312.98 ± 0.04 341.73 ± 0.08 345.03 ± 0.06 351.66 ± 0.06 358.29 ± 0.03

1.16 ± 0.02 1.40 ± 0.02 1.51 ± 0.02 1.65 ± 0.01 1.12 ± 0.01 1.34 ± 0.01 1.52 ± 0.01 1.69 ± 0.01

100B [K −1/3 ] 0.15 ± 0.01 0.19 ± 0.01 0.17 ± 0.01 0.21 ± 0.01 0.09 ± 0.01 0.13 ± 0.01 0.13 ± 0.01 0.21 ± 0.01

100A

3.40 ± 0.05 3.46 ± 0.04 3.38 ± 0.05 3.49 ± 0.03 3.18 ± 0.03 3.33 ± 0.03 3.30 ± 0.02 3.46 ± 0.03

B*

19.76 ± 0.80 21.47 ± 0.72 16.91 ± 1.04 20.74 ± 0.75 12.84 ± 0.43 16.17 ± 0.58 14.47 ± 0.42 21.75 ± 1.03

A*

Table 2. Parameters characterising the phase diagrams obtained by fitting the data using Eq. (5). The parameters B * and A * are the parameters in the corresponding state representation shown in Fig. 4.

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predicted by the RPM model, if the appropriate RPM variables, defined in Eqs. (6) and (7) are used. Here we will carry out a detailed comparison of experimental phase diagrams with that obtained from simulations for this model. The first step is to transform the variables. For estimating the partial densities we need the mass densities of the ILs and of the alkanes. The mass densities d (in g/cm 3 ) of the Ils are taken from the figures given in Ref. [14], fitted


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Fig. 2. a Critical temperature and b critical mole fraction (×10) of the solutions of P 666 14 Cl ( ) and P 666 14 Br ( ) in hydrocarbons as function of the chain length of the alkanes.

by a linear relation yielding: d = 0.8969 − 5.65 × 10 −4 (T − 273.15) for P 666 14 Cl and d = 0.9710 − 6.61 × 10 −4 (T − 273.15) for P 666 14 Br. The mass densities of the alkanes are taken from Ref. [46], and also fitted by a linear relation yielding

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Fig. 3. Width (a) and slope of the diameter (b) of the phase diagrams for solutions of P 666 14 Cl ( ) and P 666 14 Br ( ) in hydrocarbons as function of the chain length of the alkanes. The mole fraction of the salt is the variable for the composition.

d = 0.7017 − 8.00 × 10 −4 (T − 273.15) for heptane, d = 0.7195 − 8.46 × 10 −4 (T − 273.15) for octane, d = 0.7336 − 8.01 × 10 −4 (T − 273.15) for nonane, and d = 0.7454 − 7.70 × 10 −4 (T − 273.15) for decane. The separation σ is estimated by interpolating results of an X-ray investigation [47] of crystals of symmetric phosphonium and ammonium salts of


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Fig. 4. Corresponding state representation of the phase diagrams with the molar fraction as variable. The symbols are the same as that used in Fig. 1.

comparable size. The charge separation in tetra dodecyl ammonium bromide is 4.74 Å, while the separation in the corresponding chloride is 4.63 Å. The charge separation in tetradecyl phosphonium bromide is 4.86 Å; we take this value for the distance in our bromide and 4.75 Å for the chloride. For calculating the RPM-temperatures we use the dielectric permittivities, given in Ref. [48], which again are fitted by a linear relation yielding ε = 2.348 − 0.00146 T for heptane, ε = 2.345 − 0.00136 T for octane, ε = 2.359 − 0.00134 T for nonane, and ε = 2.360 − 0.00126 T for decane. The parameters obtained from the data analysis in terms of the RPM variables are given in Table 3. The table includes also the results of fitting the simulation data for the RPM [32] by Eq. (5). We pause to show the phase diagrams in the RPM variables but discuss the parameters obtained from the fit. In Fig. 5 we show (a) the critical temperature and (b) the critical density as function of the dielectric permittivity and compare with the fit-results to the RPM simulation data. We include also the data, obtained in our lab by the visual method for solutions of 1-hexyl 3-methyl imidazolium tetrafluoro borate (C6 mimBF 4 ) in al-

P 666 14 Cl/heptane P 666 14 Cl/octane P 666 14 Cl/nonane P 666 14 Cl/decane P 666 14 Br/heptane P 666 14 Br/octane P 666 14 Br/nonane P 666 14 Br/decane RPM

systems 0.0163 0.0167 0.0172 0.0177 0.0186 0.0190 0.0195 0.0201 0.0506 ± 0.0003

Tc* 100B 25.21 ± 0.32 26.81 ± 0.27 26.35 ± 0.32 26.31 ± 0.17 24.92 ± 0.21 26.54 ± 0.20 27.34 ± 0.16 27.87 ± 0.19 52.38 ± 1.20

100ρc* 1.85 ± 0.03 1.97 ± 0.02 1.97 ± 0.02 1.94 ± 0.02 1.99 ± 0.02 2.06 ± 0.02 2.17 ± 0.01 2.13 ± 0.02 6.96 ± 0.25

2364 ± 100 2612 ± 95 2076 ± 124 2396 ± 81 1579 ± 52 1957 ± 74 1775 ± 50 2495 ± 122 803 ± 44

100A

3.46 ± 0.04 3.48 ± 0.04 3.44 ± 0.04 3.53 ± 0.02 3.31 ± 0.03 3.43 ± 0.03 3.40 ± 0.02 3.55 ± 0.02 2.78 ± 0.06

B*

20.84 ± 0.89 22.18 ± 0.81 18.03 ± 1.08 21.83 ± 0.75 14.73 ± 0.49 18.06 ± 0.69 16.01 ± 0.46 23.54 ± 1.15 5.84 ± 0.32

A*

Table 3. Parameters characterising the phase diagrams represented in RPM-variables (see Eqs. (6) and (7)), obtained by fitting with Eq. (5). The parameters B * and A * are the parameters in the corresponding state representation shown in Fig. 6.

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cohols and water. The separation distance σ in C 6 mimBF 4 of 4.73 Å was estimated from the shortest distance 3.79 Å, obtained from an X-ray investigation of C1 mimCl [8, 49], replacing the van der Waals radius of the chloride anion of 1.81 Å by the radius estimated for the BF 4 cation by adding the B–F bond length of 1.4 Å [50] and the van der Waals radius of the fluorine 1.35 Å [51].


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Fig. 5. Critical temperatures Tc* (a) and critical densities ρc* (b) in the RPM variables for the solutions of P 666 14 Cl and P 666 14 Br ( ) in hydrocarbons and C 6 mimBF 4 ( ) in alcohols including water as function of the dielectric permittivity at the critical temperature. The dashed lines are the critical data of the RPM, obtained by fitting simulation results using Eq. (5).

The striking finding is the linear relation of the RPM critical temperature for the different solutions with the dielectric permittivity of the solvent. This relation was reported before [8], based on measurements on solutions in alcohols of Cn mimBF 4 and Cn mimPF 6 ILs. The RPM critical temperatures of the solutions of P 666 14 Cl and P 666 14 Br in alkanes are located on the same line as

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Fig. 6. Corresponding state phase diagram in RPM variables for the systems phosphonium halogenide/alkane ( ), C 6 mimBF 4 /alcohol ( ) and the RPM ( ). The curve is the fit to simulation data of the RPM.

that of the alcohol solutions of C6 mimBF 4 . In the scale oft this representation the critical temperatures of the alkane solutions are not to distinguish. They are much below the figure predicted by the RPM, while the figures of the alcohol solutions, which include n-hexanol, n-pentanol, n-butanol, isomers and water, are above the RPM prediction. The RPM critical density, shown in Fig. 5b also increases with the dielectric permittivity of the solvent. For the BF 4 − ILs one might assume a fairly linear relation. The RPM-critical density estimated for the alkanes, however, is much lower. With the exception of the water solution all densities are below the RPM prediction. There is clearly some uncertainty about the definition of σ and its estimate. This is particular relevant for the density, where an uncertainty of 20% changes the figure of ρ c* by a factor of two. The general trend of an increasing RPM critical density with the dielectric constant of the solvent may nevertheless be stated. We now turn to a corresponding state representation of the phase diagrams in the RPM variables. The nice feature of this representation is that it is independent of the choice of σ. The RPM-corresponding state diagram is shown in Fig. 6. The figure includes the RPM phase diagram extracted from simulation data [32]. The simulation data concern lower temperatures than the measure-


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Fig. 7. a Widths B * and b slope of the diameter A * of the corresponding state phase diagrams in RPM variables for the phosphonium halogenide/alkan ( ) and C 6 mimBF 4 / alcohol ( ) mixtures. The dotted lines are the figures of the RPM, obtained from the fit to simulation data.

ments. In fact there are no simulations in the near-critical temperature region, where the experiments are carried out. Thus, the agreement of the fit to the simulation data with the experiments is quite striking. Below the critical concentration, the agreement is very good for the data for the alkane/phosphonium halides solutions, while for the C n mimBF 4 /alcohol solutions deviations are no-

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ticeable. At high concentrations, where all experiments agree quite well, we see clear deviations between the simulation of the model fluid and the experiments. The width and the asymmetry of the experimental curves are larger than that predicted by the RPM. In order to elucidate this deviation in more detail we show in Fig. 7(a) the widths B * and (b) the diameter slopes A * of the RPM corresponding state diagram Fig. 6. The data are given in Table 3. With the exception of the water solutions the width of the experimental curves is about 50% larger than in the RPM model fluid. The asymmetry is also larger for the real solutions in particular for the phosphonium halogenide/alkane solutions.

5. Discussion Considering the huge number of papers concerned with ionic liquids there is little work on phase diagrams and phase equilibrium. In view of the large number of ILs, which can be prepared, it appears important to elucidate general trends and basic properties. For this purpose it is helpful to compare with properties predicted for generic models. Basic thermodynamic properties e.g. the low vapour pressure are consequences of the Coulomb interactions. Simulations attribute 80% of the interaction energy to the Coulomb interactions [52]. Therefore we have taken the RPM, which considers charged hard spheres of equal size in a dielectric continuum, as a first reference model. In this work we have reported phase diagrams for the solutions of an alkyl phosphonium chloride (P 666 14 Cl) and the bromide (P 666 14 Br) in hydrocarbons. For evaluating the data we have used a novel fit function, which presumes Ising criticality but neglects the non-analytical contributions to the diameter. The fit function applied here is appropriate in view of the limited accuracy of the phase diagrams, which can be achieved by the visual method. The critical temperatures, critical molar fractions, amplitudes of the phase diagram, and slopes of the diameter, which are obtained as fit parameters, allow for an excellent representation of the data. All solutions have an upper critical solution point. The critical temperatures and the critical molar fractions increase almost linearly with the chain length of the solvent. The bromides separate at higher temperature than the chlorides. The critical temperatures of the solutions of the bromide and of the chloride increase almost parallel in a linear fashion with the chain length of the alkanes. The width of the phase diagrams, which is much the same for the two salts, also increases with the size of the solvent. This is also true for the slope of the diameter. At present, there is no explanation available for the trends observed. In thermodynamics corresponding states analysis applies reduced variables that are given by differences to the critical point, reduced by the critical data. The analysis reveals corresponding state behaviour for all solutions investi-


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gated. All phase diagrams map on one master curve although differences are noticeable. The common thermodynamic corresponding states analysis has to be distinguished from the statistical mechanical approach. In statistical mechanics the condition for corresponding states is based on the functional form of the intermolecular potential. It is required that the intermolecular potentials of the systems are determined by a two parameter potential of the same form, which implies that the potential is given by an energy parameter E and a rangefunction ϕ(σ/r). All thermodynamic functions can then be written in terms of a reduced temperature T * = kT/E and a reduced number density ρ * = ρσ 3 . If the potentials are of the same form, the critical points and other thermodynamic properties of different systems are invariant in respect to the particular values of E and σ, when reduced variables are used. In case that the RPM would sufficiently model the properties of solutions of Ils, then the critical data and other properties should agree, when the reduced variables defined in Eqs. (6) and (7) are used, independent of the particle size and of the dielectric constant of the solvent. This is not the case. Clearly, the ILs are anything else than charged hard spheres in a dielectric continuum. Therefore, it is remarkable that in solvents of low dielectric constant the critical data are in the region predicted by theory and simulations for the RPM. It was already emphasized by Guggenheim [53], that deviations from the corresponding state behaviour point towards special properties that need to be elucidated. In the RPM variables the critical temperature and the critical density of the phosphonium halogenide/hydrocarbon solutions are below the figures predicted for the RPM. Including the alcohol solutions of the C 6 mimBF 4 into the consideration we find that the reduced critical temperatures increase linearly with the dielectric constant of the solvent. A similar trend is also observed for the critical density. The correlations, which include water, alcohols, and hydrocarbons as solvents, indicate a continuous change from phase transitions determined by Coulomb interactions to those driven by solvophobic forces. The dielectric constant appears as a relevant parameter determining this crossover. First simulations of mixtures of charged hard spheres with hard spheres [54, 55] and also with dipolar hard spheres [55] seem to show the trend of the reduced critical temperature found in our experiments. A theoretical explanation, however, is not available. The conditions for corresponding state behaviour of the phase diagrams, which can be derived by statistical mechanics, are less restrictive than that for the location of the critical point. Considering the Landau expansion [17, 41] of the free energy density, phase diagrams can be expected to show corresponding state behaviour, if the ratio of the coefficients of the quadratic and of the quadric term of the order parameter is the same in the systems to be compared. It is remarkable that the corresponding state phase diagram of the RPM is in reasonable agreement with the phase diagrams of the solutions of the phosphonium salts in hydrocarbons and also with that of the alcohol solutions of some

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imidazolium salts. Again deviations call for explanation and form clear targets for theory and simulations.

Acknowledgement The University of Bremen is acknowledged for supporting this work. We appreciate the help of J. Köser and G. Steinke. Discussions with M. A. Anisimov, J. Calliol and J. de Pablo are also acknowledged.

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