Solvation of Halogens in Fluorous Phases ... - ACS Publications

J. Phys. Chem. B 2008, 112, 6653–6664

6653

Solvation of Halogens in Fluorous Phases. Experimental and Simulation Data for F2, Cl2, and Br2 in Several Fluorinated Liquids A. Podgorsek,† S. Stavber,† M. Zupan,† J. Iskra,† A. A. H. Padua,‡ and M. F. Costa Gomes*,‡ Laboratory of Organic and Bioorganic Chemistry, Department of Physical and Organic Chemistry, “Jozef Stefan” Institute, JamoVa 39, 1000 Ljubljana, SloVenia, and Laboratoire de Thermodynamique des Solutions et des Polyme`res, UniVersite´ Blaise Pascal, Clermont-Ferrand/C.N.R.S., 24 aVenue des Landais, 63177 Aubie`re, France ReceiVed: December 27, 2007; ReVised Manuscript ReceiVed: February 11, 2008

The solubility of halogen gases;fluorine, chlorine and bromine;has been determined experimentally in several fluorinated solvents between 283 and 323 K at atmospheric pressure. The solubility of chlorine was studied in perfluorooctane, perfluorohexane, perfluorohexylethane, perfluoromethylcyclohexane, perfluoro1,3-dimethylcyclohexane, perfluoro-2-butyltetrahydrofuran, and perfluoroperhydrophenanthrene and was found to be on the order of 10-2 in mole fraction. The solubility of fluorine in the studied fluorinated solvents at 298 K is 1 order of magnitude lower than the solubility of chlorine. The solubility of bromine was studied as a function of temperature in perfluorooctane, and it was found to be higher than that of chlorine but of the same order of magnitude. The experimental studies were complemented by molecular simulation calculations. The molecular force fields used for the halogen gases and for the fluorinated solvents were taken, when possible, from the literature. An intermolecular potential model had to be developed for perfluoro-2butyltetrahydrofuran, with a functional form of the Lennard-Jones plus point charges type. The solubility of the three gases was calculated by molecular simulation using Widom test-particle insertion. Dissimilar interaction parameters of 0.89 and 0.75 in the Lennard-Jones well depths between the solute and the solvent had to be introduced to reach agreement with the experimental results for chlorine and fluorine solubilities, respectively. The structure of the solutions was studied by analysis of solute-solvent radial distribution functions. It was found that the preferential solvation sites for the halogen gases are the terminal CF3 groups of the different fluorinated solvents. 1. Introduction Halogens are basic reagents for the synthesis of halogenated organic compounds. These chemicals are among the most important molecules in organic chemistry per se, and they are synthetic intermediates in the various reactions ranging from nucleophilic substitution to Heck, Suzuki, and other crosscoupling reactions.1 In addition, halogenated organics are important constituents in industry, material science, biochemistry, and medicine. Molecular halogens are, however, difficult to handle because they are hazardous, toxic, and corrosive reagents whose high reactivity and highly exothermic reactions cause difficulties in performing halogenations in a selective manner. Fluorous solvents would be the ideal candidates as solvents for reactions of halogenation because of their inertness and inflammability.2,3 Fully and partially fluorinated molecules, that constitute fluorous phases, have distinctive physical and chemical properties that make them immiscible with most organic solvents and water.4,5 This property leads to the identification of “fluorophilic” molecules, that is, chemicals that are soluble in fluorous phases. These species can be obtained by the introduction of perfluoroalky groups into organic molecules making them soluble in fully or partially fluorinated solvents. The development of fluorous chemistry as an important part of “green chemistry“ uses this feature to enable the use of fluorous * Corresponding author. E-mail: [email protected] † “Jozef Stefan” Institute. ‡ Universite ´ Blaise Pascal/C.N.R.S.

Figure 1. Diffusion-controlled uptake of molecular chlorine in “phasevanishing” chlorination of alkenes.

solvents as recyclable alternatives to volatile organic solvents.6 It is possible to design cleaner reaction and separation processes by recycling the fluorinated reaction component in biphasic3 or triphasic processes.2,7 The “phase vanishing” method represents a special case of triphasic reaction, where the fluorous solvent acts as a bulk membrane for slow diffusion-controlled transport of the dihalogen from its bulk phase (that will vanish in the course of the reaction) to the reaction phase 8–10 as depicted in Figure 1.9 This reaction setup is useful when dealing with very reactive reagents, like halogens, because the reagent is introduced into the reaction phase molecule-by-molecule, instead of drop-by-drop, and because of that there is no buildup of local high concentrations that leads to local high temperatures and consequently to the loss of selectivity.9,11 The procedure described, and represented schematically in Figure 1, was also tried with other solvents immiscible with the reaction phase, like water and acetonitrile.8 In these cases, the complete transport

10.1021/jp7121104 CCC: $40.75  2008 American Chemical Society Published on Web 05/08/2008

6654 J. Phys. Chem. B, Vol. 112, No. 21, 2008 of the molecular halogen was not observed, thus confirming the unique properties of fluorous solvents and their adequacy to this type of triphasic reaction schemes. Better insight into the molecular mechanisms responsible for the properties of the fluorous phases, like the solubility and diffusivity, is necessary to generalize their use. In this work, we have decided to study the solubility of halogen gases in several fluorinated solvents, both experimentally and by molecular simulation in order to understand the molecular mechanisms behind the macroscopic behavior observed. To the best of our knowledge, no data on the solubility of halogen gases in fluorinated liquids are reported, except for the early work of Gjaldbaek and Hildebrand,12 who measured the solubility of chlorine in perfluoroheptane between 273 and 298 K at atmospheric pressure. Recently, the solubility of molecular chlorine in perfluorooctane, perfluorohexane, and perfluoro-2butyltetrahydrofuran at room temperature and close to the atmospheric pressure was measured9 because these data were necessary to carry out the triphasic reaction described above. The lack of experimental values on the solubility of halogen gases is explained by the extreme difficulty of these experimental studies. These very reactive, explosive, and corrosive chemicals prevent the use of the most common apparatus for the measurement of gas solubility, namely those based on physical methods. Solubility measurements also provide us important information about properties and structure of solutions through determination of the thermodynamic quantities, such as free energies, enthalpy, and entropy, that provide us macroscopic information about the energetic and structural contributions to solvation.13 The same solutions can also be studied using molecular simulation techniques with accurate force fields describing both the solutes and the solvents. The free energy routes of statistical mechanics enable calculation of solubilities in an extended range of thermodynamic conditions, which in comparison to the experimental results, validate the molecular interaction models used in the simulation. As a result, access to microscopic details of the structure of the solution is available, which are otherwise not easily observable. This work presents how the combination of two approaches, experimental and molecular simulation calculations, can contribute to a better understanding of the solvation of halogen gases in fluorous solvents in molecular terms and to a more accurate prediction of the behavior of these solutions. 2. Experimental Section 2.1. Materials. Measurements were performed using fluorinated liquids: perfluorohexane (C6F14, 3 M FC-72, LOT NO: 40029, 3 M Belgium N.V.), perfluorooctane (C8F18, 3 M FC77, LOT NO: 40008, 3 M Belgium N.V.), perfluorohexylethane (C6F13C2H5, 100% pure from PharmPur GmbH, Germany), perfluoromethylcyclohexane (C7F14, 97.4% pure from PharmPur GmbH, Germany), perfluoro-1,3-dimethylcyclohexane (C8F16, 99.2% pure from PharmPur GmbH, Germany), perfluoro-2butyltetrahydrofuran (C8F16O, 3 M FC-75, LOT NO: 2316, 3 M Belgium N.V.), perfluoroperhydrophenanthrene, C14F24 (>93% pure from PharmPur GmbH, Germany). All of the liquids were used as supplied by the manufacturers. The halogen gases used in the solubility measurements were fluorine (F2, purity 98-99%, Solvay), chlorine (Cl2, purity >99.8%, Merck) and bromine (Br2, purity 99.5%, Merck). 2.2. Solubility Measurements. Gas solubilities were determined using a chemical method,14 previously described in detail by Gjaldbaek and Hildebrand,12 between 283 and 323 K and at a pressure close to the atmospheric (fluorine solubility was

Podgorsek et al.

Figure 2. Apparatus for the determination of chlorine and fluorine solubility. EC is the equilibrium cell, T is the water thermostat and P is the pressure regulator.

studied only at 298 K). Slightly different experimental procedures had to be used to assess the solubility of the different halogen gases. The experimental setup used for the measurements of chlorine and fluorine solubility is represented schematically in Figure 2. Initially, the fluorous solvent was degassed by repeating melting and freezing cycles while vacuum pumping noncondensable gases. Up to three cycles were necessary. The degassed solvent was then thermostated at selected temperatures (the temperature was held constant to within (0.1 K). The gas, fluorine or chlorine, was bubbled slowly through the degassed liquid for about half an hour at atmospheric pressure, which was maintained with a pressure regulator (a beaker filled with water). The optimum equilibration time of 30 min was found by bubbling the gas during different time periods (up to 120 min) while checking the gas solubility. During equilibration, the solvent was stirred to promote the dissolution process. After equilibrium was reached, the concentration of halogen in the solution was determined by iodometric titration. Samples of the gas-saturated solution were transferred into an aqueous solution of potassium iodide, and then the amount of dissolved gas was determined by titration of formed iodine with an aqueous solution of sodium thiosulfate. The solubility of bromine was determined using a different experimental arrangement, which is represented in Figure 3. An intermediary reservoir maintained at temperature T2 > T1 was filled with gaseous Br2 in order to avoid condensation of gaseous bromine in the equilibrium cell. Initially, the whole apparatus was connected to the vacuum line. The vacuum then was closed, and bromine was allowed to evaporate from reservoir LB in Figure 3 to fill the bulb GB. The reservoir GB was then brought in contact with the degassed fluorinated liquid (closing valve V1 and opening V3) at temperature T2 during about 24 h (T3 > T2). The concentration of bromine in the saturated solution at temperature T2 was determined, as before, by iodometric titration. The equilibrium pressure during the solubility measurement was calculated by a mass balance taking into account the vapor pressure of both the pure solvent and pure liquid bromine at temperature T2. 2.3. Vapor Pressure Measurements. The knowledge of the vapor pressure of the pure solvents is necessary for the calculation of the mole fraction solubility at a particular partial pressure of the gas (for example, 1 bar). Whenever possible, the vapor pressures were taken from literature. For some of the solvents, however, vapor pressure measurements had to be made in the same temperature range where the solubility was measured. An apparatus based on the static method, that has been described previously,15 was used. It consists mainly of a glass sample cell, a thermostatic air bath, and a temperature and pressure measurement systems. First, the fluorous solvent is

Solvation of Halogens in Fluorous Phases

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Figure 3. Apparatus for the determination of gaseous bromine solubility. EC is the equilibrium cell; T1 and T2 are water thermostats maintained at temperatures t1 and t2, respectively; T3 is the water jacket maintained at temperature t3; LB is the liquid bromine reservoir; GB is the gaseous bromine reservoir, and VP is the vacuum pump.

degassed as before through successive melting/freezing cycles while vacuum pumping noncondensable gases. Then it is introduced in the measuring cell and allowed to equilibrate, at constant temperature, with its own vapor by forced liquid circulation. Values of the vapor pressure were recorded at different constant temperatures between 288 and 320 K. 2.4. Density Measurements. The molar volumes of the different fluorinated liquids used were taken, when possible, from literature. When the molar volumes of the fluorous solvents were not known, they were calculated from densities measured in the present work. Densities were measured using a U-shaped vibrating-tube densimeter (Anton Paar, model DMA 512) operating in a static mode. The temperature was maintained constant to within (0.01 K by means of a recirculation bath equipped with a PID temperature controller (Julabo FP40-HP). For measuring the temperature, a 100 Ω platinum resistance thermometer (precision 0.02 K, accuracy 0.04 K) was used. Its calibration was performed against a 100 Ω platinum resistance Hart Scientific model 1502A. The measured period of vibration (τ) of a U tube is related to the density (F) according to: F ) Aτ2 + B where A and B are parameters that are function of temperature. They were determined in the range between 283 and 343 K using air, tridistilled water, and aqueous solutions of NaCl (molarities of 1 and 3 M),16 with well-known densities. These latter two fluids were chosen in order to cover a range of densities corresponding to the density of the liquids studied. Measurements were performed with a step of 10 K (or 5 K), and at least three independent values were obtained at each temperature. The precision of the density measurement is on the order of 5 × 10-4 g cm-3; the results are expected to be accurate to 10-3 g cm-3. 2.5. Data Reduction. Solubility data are expressed in mole fraction of dissolved gas x2. The amount of gas, n2, dissolved in n1 mole of fluorous solvent was determined, for the three gaseous solutes studied, by iodometric titration, as explained above. The amount of pure solvent was determined gravimetrically. The mole fraction solubility thus calculated is expressed, in the case of fluorine or chlorine, at a total pressure equal to atmospheric:

ptot ) p1 + p2 ) 101.326 kPa

(1)

p1 and p2 being the partial pressure of the solvent and of the gaseous solute, respectively. The partial pressure of the solvent,

p1, is calculated using the vapor pressure of the pure fluorinated liquid, admitting that the solution obeys Raoult’s law. The partial pressure of the gas will then be calculated by subtracting p1 from the atmospheric pressure. In the case of fluorine and chlorine as solutes, this value is directly used to calculate the Henry’s law constant

KH ) lim

x2 f 0

f2 φ2 p2 ≈ x2 x2

(2)

where f2 is the fugacity of the dissolved gas and φ2 its fugacity coefficient. The fugacity coefficient φ2 can be calculated by:17

(

φ2 ) exp

B22 ptot + y21δ12 RT

)

(3)

where B22 is the second virial coefficient for the pure solute and δ12 ) 2B12 - B11 - B22. B11 is the second virial coefficient for the pure solvent and B12 is the solute-solvent cross-second virial coefficient (taken here as the average of the pure component’s values). The second virial coefficients were obtained from the compilation of Dymond and Smith.18 The mole fraction solubilities, at a partial pressure of solute gas equal to 1 bar, were calculated from the values of the Henry’s law constants. In the case of bromine as a gaseous solute, the mole fraction solubility is calculated in a slightly different way. First, the amount of degassed solvent introduced in the equilibration cell (EC in Figure 3) is determined gravimetrically. The amount of gas dissolved in the solvent is measured by iodometric titration, as for the other solutes. The determination of partial pressure of the gas at equilibrium, p2, requires the knowledge of the amount of bromine initially present in the experimental setup

n2,tot )

p*2(t1)VGB Z2(t2, p*2(t1))RT

(4)

where p*2(t1) is the vapor pressure of Br2 at the temperature t1 (see Figure 3), VGB is the calibrated volume of the gaseous bromine reservoir (GB in Figure 3), and Z2 is the compressibility factor calculated for bromine at the temperature t2 and at the same pressure p*2(t1). This total amount of bromine equals the amount of gaseous solute that will saturate the liquid solvent, n2 (determined by titration), plus the amount of gas that will

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fill the total volume of the experimental apparatus delimited by valves V1 and V4 excluding the volume occupied by the liquid solution, n2,Vtot-V1* (the volume occupied by the liquid solution is considered here as being equal to that of the pure solvent, V*1)

n2,tot ) n2 + n2,Vtot-V1*

(5)

At equilibrium, the partial pressure of the gaseous solute can then be calculated iteratively by

p2 )

Z2(ptot, t2)n2,Vtot-V *1RT

(6)

(Vtot - V *1)

where Z2 is the compressibility factor for the gas calculated at temperature t2 and at the equilibrium pressure ptot, assuming, as for the other two solutes, the validity of Raoult’s law for the solvent. 2.6. Thermodynamic Functions. Henry’s law constants can be exactly converted to the Gibbs energy of solvation, corresponding to the change in partial molar Gibbs energy when the solute is transferred, at constant temperature, from the pure ideal gas state at the standard pressure to infinitely dilute state in solution.13 The partial molar differences in enthalpy (eq 7) (standard enthalpy of solvation ∆solvH) and entropy (eq 8) (standard entropy of solvation ∆solvS) between the two states can be obtained by calculating the corresponding partial derivatives of the Gibbs energy with respect to the temperature.

(

)

( ( )) ( ( ))

KH ∂ ∆solvG ∂ ) -RT2 ln 0 ∂T T p ∂T p KH ∂ ∂ RT ln 0 ∆solv S ) - (∆solvG)p ) ∂T ∂T p p

∆solvH ) -T2

)

∆solvH - ∆solvG T

(7) p

(8)

These thermodynamic quantities are in direct correlation with solvent-solute interactions because they correspond to the transfer of the solute from the ideal gas state, where there are no intermolecular interactions, to the infinite dilute solution, where only solute-solvent interactions are present.13 Enthalpic and entropic contributions to the Gibbs energy of solvation enable deeper insight into the mechanisms of dissolution. The enthalpic part reflects the strength of the interaction between the solvent and the solute, and the entropic term is in relation to the organization of the solvent molecules around the solute and thus to the structure of the solution. As the enthalpy and the entropy of solvation are derivatives of the solubility with respect to temperature, significant errors can be associated to their quantification. Because of this, we are interested in the present work on the sign of these thermodynamic properties and in their relative values to assess the importance of each of the two terms to the Gibbs energy of solvation. 2.7. Experimental Results. The vapor pressures of pure solvents were taken from the literature for perfluorooctane,19 perfluorohexane,20 perfluorohexylethane,15 perfluoromethylcyclohexane,21 perfluoro-1,3-dimethylcyclohexane,21 and perfluoroperhydrophenanthrene15 and were measured in the present work for perfluoro-2-butyltetrahydrofuran. The values obtained were adjusted to an Antoine equation:

ln(p ⁄ kPa) ) 16.189 - 4141.377 ⁄ [(T ⁄ K) - 12.703] (9) The molar volumes of the fluorinated liquids studied as solvents are necessary to calculate the mole fraction solubility

and were taken from the literature when available.15,19–21 For perfluoro-2-butyltetrahydrofuran, these values were not available, and so we have measured the density as a function of temperature:

F ⁄ kgm-3 ) -2.8772(T ⁄ K) + 2623.2

(10)

The mole fraction solubility (referred to a partial pressure of gas equal to atmospheric) of chlorine in seven fluorinated liquids is listed in Table 1 for temperatures between 283 and 323 K. These experimental values were used to calculate the Henry’s law constants that were fitted, as a function of temperature, to an empirical equation of the type

( )

ln

KH p0

n

)

∑ Ai(T ⁄ K)-i

(11)

i)0

where p0 equals 1 bar. The coefficients Ai obtained in the fit for solubility of chlorine are listed in Table 2. The thermodynamic properties of solvation could then be assessed, their values also being listed in Table 1 together with an estimation of the error bars associated with them. It is observed that, for all of the liquids, the solubility of chlorine is on the order of 10-2 in mole fraction and that it decreases with increasing temperature in the range covered in this study. These results are in agreement with those obtained in the earlier work of Gjaldbaek and Hildebrand for the solubility of chlorine in perfluoroheptane.12 The values of the solubility as a function of temperature are depicted in Figure 4. It is noticeable that the highest solubility observed is for perfluorohexylethane and the lowest values are for perfluoromethylcyclohexane. The variation of the solubility with temperature is also more important for perfluorohexylethane than for the other liquids, which leads to more negative values for ∆solvH, indicating that solvation is more exothermic for this solvent than for the other six liquids studied. It is also noteworthy that the entropy of solvation is more negative in the case of C6F13C2H5, indicating that the larger solubility observed is determined mainly by favorable solute-solvent interactions (enthalpic contribution to the Gibbs energy of solvation). For the other six liquids, the effects are more complex. As can be observed in Table 1, perfluoro-1,3-dimethylcyclohexane and perfluoro-2-butyl-tetrahydrofuran also dissolve chlorine with negative enthalpies of solvation, close to those for perfluorohexylethane, but the solubility is lower because of large negative entropic contributions. For some cases, the enthalpy of solvation seems to vary differently with temperature. Although the present results are not sufficiently precise to analyze these effects quantitatively, they can eventually indicate slightly different mechanisms of solvation that deserve to be investigated further. Because of the extreme difficulty for measuring the solubility of fluorine, we have decided to study its solubility at only one temperature, 298 K, and for five liquid fluorinated solvents. The mole fraction solubilities, corrected for a partial pressure of gas equal to 1 bar, are listed in Table 3. The solubility of fluorine in the different liquids is much lower, almost 1 order of magnitude lower than for chlorine. For this gas, the highest solubility is observed for perfluorophenanthren and the lowest value is, by far (1 order of magnitude lower), for perfluoro-2-butyltetrahydrofuran. This very low solubility value has been confirmed by repeating several times the experimental measurements. The vapor pressure of bromine, necessary for the determination of its solubility using the experimental method described, was taken from the literature.22 The solubility of gaseous bromine was measured in perfluorooctane as a function of

Solvation of Halogens in Fluorous Phases

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TABLE 1: Experimental Solubility of Chlorine in Different Fluorous Solvents between 283 and 323 Ka T/K

KH/bar

x2/10-2

% dev

∆solvG /kJmol-1

∆solvH /kJmol-1

283.2 293.3 303.3 313.2 323.2

14.1 15.6 18.2 20.8 24.0

7.11 6.42 5.48 4.81 4.17

1.0 1.0 0.8 0.8 0.4

Perfluorooctane, C8F18 6.23 ( 0.02 6.70 ( 0.02 7.32 ( 0.02 7.90 ( 0.02 8.54 ( 0.01

-7.60 ( 0.01 -9.10 ( 0.02 -10.48 ( 0.02 -11.77 ( 0.02 -13.00 ( 0.02

-48.8 ( 0.1 -53.9 ( 0.1 -58.7 ( 0.1 -62.8 ( 0.1 -66.6 ( 0.1

283.3 293.2 303.2 313.3

16.3 17.4 19.3 21.9

6.13 5.74 5.17 4.57

1.9 0.8 0.6 1.7

Perfluorohexane, C6F14 6.57 ( 0.04 6.97 ( 0.02 7.47 ( 0.02 8.04 ( 0.04

-3.48 ( 0.03 -6.16 ( 0.04 -8.68( 0.04 -11.07 ( 0.04

-35.5 ( 0.2 -44.8 ( 0.1 -53.3 ( 0.1 -61.0 ( 0.2

283.2 303.2 313.3

6.79 12.4 17.6

14.7 8.05 5.69

Perfluorohexylethane, C6F13C2H5 1.1 4.51 ( 0.02 1.1 6.35 ( 0.03 4.5 7.47 ( 0.11

-17.74 ( 0.01 -25.43 ( 0.01 -28.94 ( 0.01

-78.6 ( 0.1 -104.8 ( 0.1 -116.2 ( 0.4

293.2 303.3 313.2

18.3 23.8 27.2

5.46 4.20 3.68

Perfluoromethylcyclohexane, C7F14 1.1 7.09 ( 0.03 2.6 8.00 ( 0.07 2.1 8.61 ( 0.05

-23.83 ( 0.01 -14.74 ( 0.01 -6.41 ( 0.02

-105.4 ( 0.1 -75.0 ( 0.2 -47.9 ( 0.2

283.2 293.2 303.2 313.3 323.3

13.8 17.1 20.3 24.6 37.2

7.26 5.86 4.92 4.06 2.69

Perfluoro-1,3-dimethylcyclohexane, C8F16 2.4 6.17 ( 0.02 -6.96 ( 0.07 0.7 6.91 ( 0.02 -12.88 ( 0.08 1.7 7.39 ( 0.08 -18.41 ( 0.09 3.4 8.34 ( 0.10 -23.63 ( 0.09 2.4 9.72 ( 0.10 -28.48 ( 0.10

-46.4 ( 0.3 -67.5 ( 0.4 -85.8 ( 0.6 -102.1 ( 0.7 -118.2 ( 0.4

283.2 293.3 303.2 313.2 323.4

14.2 15.3 21.3 26.4 31.9

7.03 6.52 4.70 3.79 3.14

Perfluoro-2-butyltetrahydrofuran, C8F16O 0.7 6.25 ( 0.06 -11.23 ( 0.08 1.1 6.65 ( 0.02 -14.02 ( 0.08 3.1 7.70 ( 0.04 -16.57( 0.09 4.1 8.52 ( 0.08 -19.00 ( 0.11 1.1 9.31 ( 0.06 -21.29 ( 0.11

-61.8 ( 0.5 -70.5 ( 0.3 -80.1 ( 0.5 -87.8 ( 0.6 -94.6 ( 0.6

283.3 293.2 303.2 313.3 323.2

11.2 13.8 19.0 23.3 26.0

8.92 7.26 5.27 4.30 3.58

Perfluoroperhydrophenathrene, C14F24b 2.7 5.69 ( 0.06 0.7 6.39 ( 0.02 4.0 7.42 ( 0.10 2.9 8.19 ( 0.07 3.6 8.75 ( 0.10

∆solvS/Jmol-1K-1

-21.09 ( 0.06 -18.78 ( 0.07 -16.60 ( 0.08 -14.54 ( 0.09 -12.64 ( 0.09

-94.5 ( 0.4 -85.9 ( 0.3 -79.2 ( 0.6 -72.6 ( 0.5 -66.2 ( 0.6

a x2 is the mole fraction solubility corrected for a partial pressure of gas 1 bar; % dev is the relative standard deviation of the experimental results. The thermodynamic properties of solvation are calculated from the experimental data. Relative errors of determination of thermodynamic properties were less than 1.3% in all cases. b The mole fraction solubilities were calculated assuming that there is no contribution of the vapor pressure of perfluoroperhydrophenanthrene to the total pressure.

temperature between 293 and 313 K. The results are reported in Table 4 and represented in Figure 5. As can be observed, the experimental results present a significant dispersion due to the fact that the solute is a liquid a room temperature with a melting point of 265.90 K23 and a normal boiling point of 332 K. Bromine is more soluble than chlorine in perfluorooctane, but this difference can not be determined quantitatively in light of the dispersion of the data. From the derivative with respect to temperature of the Henry’s law constants calculated from the experimental solubilities, an average value of -(79.2 ( 25) kJ/ mol for the enthalpy of solvation was obtained. In spite of the large error bar associated with this value for the enthalpy of solvation, the large negative value obtained when compared with the one for chlorine is surely a sign of the importance of the solute-solvent interactions for the solubility of bromine in perfluorooctane. 3. Molecular Simulation. To gain insight into the structure and interactions in solution at the molecular level, the solubility of chlorine, bromine, and fluorine in the same fluorous solvents was also studied by computer simulation. Configurations of the pure solvents were generated by molecular dynamics, and the residual chemical potential of the solute at infinite dilution µres 2

TABLE 2: Coefficients of Equation 11 and Average Absolute Deviation (AAD) for the Correlation of the Experimental Data for the Henry’s Law Constants of Chlorine in the Fluorinated Solventsa A0 × 10-1

A2 × 10-5

AAD(%)

1.511

Perfluorooctane, C8F18 -6.150 7.415

0.25

2.108

Perfluorohexane, C6F14 -9.945 13.493

0.06

3.422

Perfluorohexylethane, C6F13C2H5 -16.163 19.866

0.01

Perfluoromethylcyclohexane, C7F14 29.935 -48.086

0.05

4.245

Perfluoro-1,3-dimethylcyclohexane, C8F16 -21.705 29.548

1.18

2.461

Perfluoro-2-butyltetrahydrofuran, C8F16O -11.090 13.790

1.25

Perfluoroperhydrophenanthrene, C14F24 5.692 -11.656

1.08

-4.326

-0.317 a

A1 × 10-3

The AAD of the Henry’s law constants from appropriate smoothing functions is a measure of the precision of the experimental data.

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Figure 4. Mole fraction chlorine solubilities in fluorous solvents as a function of temperature. b perfluorooctane (C8F18), O perfluorohexane (C6F14), 2 perfluorohexylethane (C6F13C2H5), 3 perfluoromethylcyclohexane (C7F14), 9 perfluoro-1,3-dimethylcyclohexane (C8F16), 0 perfluoro-2-butyltetrahydrofuran (C8F16O), and ( perfluoroperhydrophenanthrene (C12F24).

TABLE 3: Experimental Solubility of Fluorine in Fluorous Solvents at 298 Ka x2/10-3

% dev

874.5

Perfluorooctane, C8F18 1.14

2.1

682.9

Perfluorohexane, C6F14 1.46

2.7

KH/bar

565.9

Perfluoro-1,3-dimethylcyclohexane, C8F16 1.77 4.1

U)

TABLE 4: Experimental Solubility of Bromine in Perfluorooctane between 283 and 303 Ka

∑

Vijkl,n [1 - (-1)n cos(nφijkl)] + 2 n)1

∑ ∑ ijkl

nonbonded

∑ ij

T/K

KH/bar

x2/10-2

% dev

293.3 293.2 303.2 303.2 308.3 313.3

2.23 4.96 21.1 4.70 16.4 26.6

44.9 20.2 4.74 21.3 6.08 3.76

5.5 6.0 4.2 3.6 5.0 4.2

a x2 is corrected for a partial pressure of gas 1 bar; % dev is the relative standard deviation of the experimental results.

was calculated using the test particle insertion method.24 The residual chemical potential is the difference between the chemical potential of the solute in solution and in pure ideal gas state at the same temperature and density and is related to the standard Gibbs energy of solvation through eq 12, where F1 is a density of the infinitely dilute solution.13

p0

angles kr,ij kθ,ijk rij - r0,ij)2 + ( (θijk - θ0,ijk)2 + 2 2 ijk torsions 4

a x2 is corrected for a partial pressure of gas of 1 bar; % dev is the relative standard deviation of the experimental results.

RTF1

∑ ij

Perfluoroperhydrophenanthrene, C14F24 3.93 2.6

( ) ∆solvG0 ) µres 2 T, p + RT ln

field contains in general four kinds of potential energy: stretching of covalent bonds, bending of valence angles, torsion around dihedral angles, and nonbonded interactions.13 Nonbonded interactions are active between atoms of the same molecule separated by more than three bonds and between atoms of different molecules. The potential energy associated with bonds and angles is described by harmonic terms, dihedral torsion energy is represented by series of cosines, and nonbonded interactions are given by the Lennard-Jones potential and by Coulomb interactions between partial point charges placed on the atoms. The functional form is given in eq 13 bonds

Perfluoro-2-butilytetrahydrofuran, C8F16O 2022.5 0.49 1.0 254.7

Figure 5. Henry’s law constants for bromine in perfluorooctane as a function of temperature. The fitting served to the calculation of an average value of the enthalpy of solvation of bromine in perfluorooctane.

(12)

3.1. Intermolecular Potential Models. The fluorous solvents were represented by flexible force fields in which all atoms are considered explicitly. Parameters for the solvent molecules were taken from the OPLS-All Atom force field, which describes each atom as an interacting site. The functional form of this force

{ [( ) ( ) ] 4εij

σij rij

12

-

σij rij

6

+

qiqj e2 rij 4πε0

}

(13)

Parameters of the force field for perfluoroalkanes25 and for semifluorinated alkanes26 were available in the literature. Some terms in the force field necessary to simulate perfluoro-2-butyltetrahydrofuran were missing and had to be calculated in the present work. These are the electrostatic charges on the atoms of the perfluorotetrahydrofuran ring and the torsion energy profile associated with the conformations of the perfluoroalkyl side chain with respect to the ring. Without a specific parametrization of these terms, both interactions and conformations of these molecules could not be represented accurately in the simulations. The procedure for calculation of the electrostatic charges and the torsion energy profiles is identical to the one reported in a previous publication.26 Electrostatic charges are assigned to the different atoms by the ChelpG procedure, using electron densities calculated ab initio at the MP2/cc-pVTZ(-f) level. This procedure adjusts the point charges placed on the atoms so as to reproduce the electrostatic field around the molecule generated by the ab initio electron density. In order to obtain a representative set of charges, we performed calculations for different conformers corresponding to energy minima, and average values of the charges were assigned to the atoms. These are intended to be fixed values, transferable between molecules of the same family. Thus, for example, charges on fluorine atoms could be considered all equal to -0.12 without making very large modifications

Solvation of Halogens in Fluorous Phases

J. Phys. Chem. B, Vol. 112, No. 21, 2008 6659

TABLE 5: Parameters of the OPLS-AA Force Field Developed Specifically for Perfluorotetrahydrofuran and for Perfluoro-2-alkyltetrahydrofurans atom type

q/e

atom type

q/e

O1

-0.28

C2,5

Perfluorotetrahydrofuran +0.37 C3,4

+0.25

C2 C3 C4

Perfluoro-2-alkyltetrahydrofurans +0.04 C5 +0.45 C6 +0.16

+0.47 +0.37

-0.12

F

Dihedral angle V1/kJ mol-1 V2/kJ mol-1 V3/kJ mol-1 V4/kJ mol-1 C5-O1-C2-F C5-O1-C2-C3 C5-O1-C2-C6 O1-C2-C6-F O1-C2-C6-C7

-5.104 -5.104

21.439 -0.527 -0.527

10.416

4.985

1.766 1.766 5.05 -1.606

-4.170

to the ab initio charges (within about (0.05e at most). The set of charges developed specifically for perfluorotetrahydrofurans, that concerns the atoms of the ring and also the first carbon atom of a perfluoroalkyl side chain connected to C2, is collected in Table 5. Atoms beyond the first carbon of the side chain are represented by the already available parameters for linear perfluoroalkanes.25 It should be noted that the partial charges on the perfluorotetrahydrofuran ring are distributed simmetrically (the charges on the C2 and C3 atoms are equal to those on C5 and C4, respectively), whereas with a perfluoroalkyl side chain connected to C2 this symmetry is broken.

Torsion energy profiles are obtained by performing a series of single-point energy calculations at the same level of theory and using the same basis sets as for the charge distribution calculations. The dihedral angle of interest is thus scanned every 10°, and then the coefficients of the cosine series representing torsions are fitted to the ab initio energies using the method described in the literature.26 For the perfluoro-2-alkyltetrahydrofuran of interest, five new dihedral angles, not yet available in the literature, were parametrized. These are related to the conformations of the perfluoroalkyl side chain around the C2-O1 and the C6-C2 bonds and are listed in Table 5. The molecules of halogen gases were represented by rigid two-center Lennard-Jones models with point charges assigned to the atomic sites plus one charge placed at the center of the bond, in order to reproduce the quadrupole moment of the molecules. The parameters were retrieved from an extensive study27 in which intermolecular potential models for halogen molecules were adjusted to reproduce the vapor-liquid equilibrium properties of the pure substances (coexisting densities and enthalpies of vaporization). The interactions between gaseous solute and the solvents are represented by the LennardJones potential and by the Coulomb interactions. Parameters in unlike interaction terms were first assumed to obey the usual geometric combining rules assumed in OPLS-AA for LennardJones parameters, σij and ij (eq )

σij ) √σiiσjj

and

εij ) √εiiεjj

(14)

3.2. Simulation Procedure. The molecular simulations were carried out using the molecular dynamics package DL_POLY.28

TABLE 6: Simulated Solubilities of Chlorine in Fluorous Solventsa

a

F/molL-1

µ/kJmol-1

KH/bar

283 293 303 313 323

Perfluorooctane C8F18 4.096 ( 0.037 4.039 ( 0.036 3.990 ( 0.039 3.912 ( 0.039 3.864 ( 0.049

-7.56 ( 0.95 -7.34 ( 0.76 -6.94 ( 0.73 -6.77 ( 0.61 -6.52 ( 0.61

kij ) 1 3.9 ( 1.6 4.8 ( 1.5 6.4 ( 1.8 7.5 ( 1.8 9.2 ( 2.1

0.26 ( 0.10 0.21 ( 0.06 0.16 ( 0.05 0.13 ( 0.03 0.11 ( 0.03

283 293 303 313

Perfluorohexane C6F14 5.076 ( 0.058 4.990 ( 0.060 4.896 ( 0.060 4.829 ( 0.059

-7.81 ( 0.83 -7.54 ( 0.70 -7.26 ( 0.59 -6.93 ( 0.53

kij ) 1 4.3 ( 1.5 5.5 ( 1.6 6.9 ( 1.6 8.8 ( 1.8

Perfluorohexylethane C6F13C2H5 283 4.554 ( 0.041 303 4.445 ( 0.041 313 4.387 ( 0.046

-8.14 ( 1.24 -7.40 ( 0.91 -7.10 ( 0.80

Perfluoromethylcyclohexane, C7F14 293 5.201 ( 0.052 303 5.132 ( 0.045 313 5.084 ( 0.055

T/K

x2

µ/kJmol-1

KH/bar

x2

-4.70 ( 0.86 -4.55 ( 0.69 -4.20 ( 0.67 -4.09 ( 0.57 -3.90 ( 0.58

kij ) 0.89 13 ( 5 15 ( 4 19 ( 5 21 ( 5 24 ( 5

0.08 ( 0.03 0.07 ( 0.02 0.05 ( 0.01 0.05 ( 0.01 0.04 ( 0.01

0.23 ( 0.08 0.18 ( 0.05 0.15 ( 0.03 0.11 ( 0.02

-5.07 ( 0.77 -4.86 ( 0.64 -4.65 ( 0.55 -4.39 ( 0.50

kij ) 0.89 14 ( 5 17 ( 4 20 ( 4 23 ( 4

0.07 ( 0.02 0.06 ( 0.02 0.05 ( 0.01 0.04 ( 0.01

kij ) 1 3.4 ( 1.8 5.9 ( 2.1 7.5 ( 2.3

0.30 ( 0.16 0.17 ( 0.06 0.13 ( 0.04

-6.26 ( 1.19 -5.63 ( 0.89 -5.32 ( 0.75

kij ) 0.90 8(4 12 ( 4 15 ( 4

0.13 ( 0.07 0.08 ( 0.03 0.07 ( 0.02

-7.70 ( 1.02 -7.44 ( 0.90 -7.02 ( 0.79

kij ) 1 5.4 ( 2.3 6.8 ( 2.4 8.9 ( 2.7

0.19 ( 0.08 0.15 ( 0.05 0.11 ( 0.03

-4.76 ( 0.96 -4.56 ( 0.83 -4.17 ( 0.75

kij ) 0.89 18 ( 7 21 ( 7 27 ( 8

0.06 ( 0.02 0.05 ( 0.02 0.04 ( 0.01

Perfluorodimethylcyclohexane, C8F16 283 4.746 ( 0.038 293 4.681 ( 0.039 303 4.644 ( 0.039 313 4.562 ( 0.048 323 4.513 ( 0.050

-7.83 ( 1.44 -7.51 ( 1.15 -7.09 ( 1.04 -7.05 ( 0.85 -6.60 ( 0.81

kij ) 1 4.0 ( 2.4 5.2 ( 2.5 7.0 ( 2.9 7.9 ( 2.6 10.4 ( 3.1

0.25 ( 0.15 0.19 ( 0.09 0.14 ( 0.06 0.13 ( 0.04 0.10 ( 0.03

-4.83 ( 1.25 -4.50 ( 1.07 -4.14 ( 0.96 -4.18 ( 0.80 -3.74 ( 0.80

kij ) 0.89 14 ( 8 18 ( 8 23 ( 9 24 ( 7 30 ( 9

0.07 ( 0.04 0.06 ( 0.02 0.04 ( 0.02 0.04 ( 0.01 0.03 ( 0.01

Perfluorobutyltetrahydrofuran, C8F16O 283 4.467 ( 0.034 293 4.392 ( 0.037 303 4.333 ( 0.037 313 4.562 ( 0.048 323 4.513 ( 0.050

-8.17 ( 1.46 -7.79 ( 1.18 -7.56 ( 1.05 -7.22 ( 0.96 -7.01 ( 0.85

kij ) 1 3.3 ( 2.0 4.4 ( 2.1 5.4 ( 2.3 7.4 ( 2.7 8.9 ( 2.8

0.31 ( 0.19 0.23 ( 0.11 0.18 ( 0.08 0.14 ( 0.05 0.11 ( 0.04

-5.01 ( 1.29 -4.93 ( 1.09 -4.61 ( 0.88 -4.29 ( 0.87 -4.15 ( 0.77

kij ) 0.89 12 ( 7 14 ( 6 18 ( 6 23 ( 8 26 ( 7

0.08 ( 0.04 0.07 ( 0.03 0.06 ( 0.02 0.04 ( 0.02 0.04 ( 0.01

kij are the values of the dissimilar interaction parameter affecting the Lennard-Jones well depth in the solute-solvent interactions between chlorine and the fluorinated solvents.

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TABLE 7: Simulated Solubilities of Fluorine in Fluorous Solvents at 298 Ka T /K 298

F /molL-1 Perfluorooctane C8F18 4.005 ( 0.036

µ /kJmol-1

KH /bar

x2/10-3

µ /kJmol-1

KH /bar

x2/10-3

2.08 ( 0.27

kij ) 1 230 ( 25

4.35 ( 0.48

5.35 ( 0.30

kij ) 0.65 860 ( 102

1.16 ( 0.14

4.23 ( 0.29

kij ) 0.70 700 ( 83

1.43 ( 0.17 1.72 ( 0.28 0.49 ( 0.08

1.63 ( 0.27

kij ) 1 236 ( 26

Perfluorodimethylcyclohexane, C8F16 298 4.675 ( 0.044

2.62 ( 0.40

kij ) 1 334 ( 54

3.00 ( 0.48

4.00 ( 0.41

kij ) 0.87 582 ( 96

Perfluorobutyltetrahydrofuran, C8F16O 298 4.365 ( 0.040

2.35 ( 0.37

kij ) 1 279 ( 42

3.58 ( 0.54

7.30 ( 0.41

kij ) 0.50 2059 ( 338

Perfluorohexane C6F14 298 4.940 ( 0.056

4.23 ( 0.46

a kij are the values of the dissimilar interaction parameter affecting the Lennard-Jones well depth in the solute-solvent interactions between fluorine and the fluorinated solvents.

Figure 6. Simulated and experimental solubilities of chlorine in perfluorooctane, 1 experimental values, b simulated values at kij ) 1, O simulated values at kij ) 0.89.

Solvents were simulated in periodic cubic boxes containing 200 molecules. The Lennard-Jones nonbonded interactions were considered explicitly up to a cutoff radius of 15 Å and corrected for truncation. All types of bonds were represented as flexible, except for C-H bonds that were constrained to remain rigid. The simulations were performed with a time step of 1 fs. Starting from low-density initial configurations, the systems were allowed to relax internal modes for a small number of time steps in the NVE ensemble, after which equilibration continued in the NpT ensemble to bring the system to its equilibrium density (Nose´-Hoover thermostat and barostat). This took about 200 ps. Production runs of 100 ps were then performed at constant NpT from which 1000 configurations were stored at regular intervals. The residual chemical potential of the halogen solutes was calculated using the test-particle insertion method, by attempting up to 85 000 insertions of the solute molecules at random positions and orientations in each of the previously stored configurations of the solvents (as a thumb rule, one insertion is attempted per Å3 of solvent). An explicit cutoff radius of 12 Å was considered and long-range corrections applied. Because the volume of the system fluctuates, the residual chemical potential was calculated from eq 1529 where uTP is the interaction energy of the test particle with a configuration of solvent molecules.

µres 2 ) -kBT ln

〈Ve-uTP ⁄kT 〉NPT 〈V 〉NPT

(15)

Then the Henry’s law constants were calculated using eq 16 2

KH ) RTF1eµres ⁄RT

(16)

3.3. Simulation Results. The values of simulated solubilities of chlorine and fluorine in the fluorous solvents are given in

Figure 7. Simulated mole fraction solubilities of fluorine in fluorous solvents at kij ) 0.75. Error bars on the simulated solubilities are of (0.4 in mole fraction; b simulated and O experimental solubility in perfluorooctane, 1 simulated and 3 experimental solubility in perfluorohexane, 9 simulated and O experimental solubility in perfluoro-1,3dimethylcyclohexane, ( simulated and ] experimental solubility in perfluoro-2-butyltetrahydrofuran.

Tables 6 and 7, respectively. Comparison with the experimental results shows that the simulated values are systematically higher but are of the correct order of magnitude. The temperature dependence of the solubility is predicted correctly. Higher simulated values indicate that interactions in the real system fluorous solvent-halogen gas are weaker than predicted by the molecular models using the geometric combining rule, eq 14. This is a recurring observation when perfluorinated liquids are involved, and similar results were already obtained in studies of second virial coefficients and thermodynamic properties of mixtures of alkanes and perfluoroalkanes,30,31 as well as in various studies of the solubility of different gases in fluorous solvents (O2,15,32–35 CO2,36 N2O,37 CO,15 Xe,17,38 CF4,39 CH439). It becomes evident that interactions in such systems cannot be described by simple geometric rules. To reproduce experimental data, an unlike interaction parameter kij was introduced in the combining rule for the Lennard-Jones well depths, as in eq 17. In the present work, this unlike interaction parameter affects all interaction pairs between atoms in the solute and atoms in the solvent. At the best, values for kij should be temperatureand composition-independent and transferable to other analogue systems. Although empirical, these unlike interaction parameters tell us something important about the nature of the interactions.

εij ) kij√εiiεjj

(17)

The optimized values for the binary energy interaction parameters between molecules of fluorous solvents and chlorine are given in Table 6. Almost perfect agreement with experimental solubilities (deviations lying within the mutual experi-

Solvation of Halogens in Fluorous Phases

J. Phys. Chem. B, Vol. 112, No. 21, 2008 6661

TABLE 8: Simulated Solubilities of Fluorine in Fluorous Solvents with kij ) 0.75 T/K

µ/kJmol-1

KH/bar

x/10-3

283 293 298 303 313 323

4.43 ( 0.34 4.43 ( 0.29 4.45 ( 0.29 4.53 ( 0.32 4.47 ( 0.29 4.49 ( 0.34

633 ( 92 606 ( 71 598 ( 70 607 ( 76 567 ( 63 552 ( 69

Perfluoroctane, C8F18 1.58 ( 0.23 15.19 1.65 ( 0.19 15.62 1.67 ( 0.20 15.85 1.65 ( 0.21 16.15 1.76 ( 0.20 16.51 1.81 ( 0.23 16.96

1.81 2.22 2.41 2.60 2.95 3.29

-47.3 -45.7 -45.1 -44.7 -43.3 -42.3

283 293 298 303 313

3.89 ( 0.35 3.89 ( 0.30 3.89 ( 0.29 3.87 ( 0.30 3.90 ( 0.28

624 ( 94 600 ( 74 588 ( 68 573 ( 68 562 ( 61

Perfluorohexane, C6F14 1.60 ( 0.24 15.15 1.67 ( 0.21 15.59 1.70 ( 0.20 15.81 1.75 ( 0.21 16.01 1.78 ( 0.19 16.49

3.28 2.83 2.62 2.41 2.02

-42.0 -43.6 -44.3 -44.9 -46.2

283 293 298 303 313 323

4.79 ( 0.42 5.00 ( 0.40 5.18 ( 0.42 5.19 ( 0.37 5.00 ( 0.39 5.18 ( 0.40

855 ( 152 888 ( 146 937 ( 158 918 ( 135 811 ( 122 834 ( 123

Perfluoro-1,3-dimethylcyclohexane, C8F16 1.17 ( 0.21 15.89 1.13 ( 0.18 16.55 1.07 ( 0.18 16.96 1.09 ( 0.16 17.20 1.23 ( 0.18 17.44 1.20 ( 0.18 18.07

-4.60 -1.45 + 0.04 + 1.49 + 4.24 + 6.83

-72.4 -61.4 -56.8 -51.8 -42.2 - 34.8

283 293 298 303 313 323

4.97 ( 0.37 4.88 ( 0.37 4.95 ( 0.38 4.94 ( 0.32 5.04 ( 0.36 5.00 ( 0.34

869 ( 137 793 ( 119 797 ( 123 776 ( 100 774 ( 108 731 ( 92

Perfluoro-2-butyltetrahydrofuran, C8F16O 1.15 ( 0.18 15.93 1.26 ( 0.19 16.27 1.25 ( 0.19 16.56 1.29 ( 0.17 16.77 1.29 ( 0.18 17.32 1.37 ( 0.17 17.72

4.40 3.56 3.16 2.77 2.03 1.34

-40.7 -43.4 -45.0 -46.2 -48.8 -50.7

TABLE 9: Coefficients in Equation 11 Used to Fit the Simulated Henry’s Law Constants as a Function of Temperature (Calculated with kij ) 0.75) for Fluorine in the Fluorinated Solvents A0

A1 × 10-3

A2 × 10-5

AAD (%)

3.137

Perfluorooctane, C8F18 1.656 -2.036

0.15

7.837

Perfluorohexane, C6F14 -1.186 2.235

0.05

Perfluoro-1,3-dimethylcyclohexane, C8F16 -10.900 10.547 -15.708

0.43

Perfluoro-2-butyl-tetrahydrofuran, C8F16O -2.450 4.216

0.19

10.1510

mental and simulation errors) were obtained with a value of kij ) 0.91 for system chlorine-perfluorohexylethane and kij ) 0.89 for the interactions of chlorine and other studied fluorous solvents (Figure 6). On the contrary, for the system fluorine-fluorous solvent, we did not obtain a general value for kij. The optimized values of kij for each combination of solvent-fluorine are listed in Table 7. Solubility of fluorine measured only at one temperature is small, and the results have a somewhat lower reliability. Nevertheless, we tried to obtain a general value for kij as in the case for chlorine, and we got the overall value of kij ) 0.75. This value was used to predict the solubility of fluorine in fluorous solvents in the temperature range from 283 to 323 K and the associated thermodynamic quantities of solvation (Table 8). The coefficients of eq 11 in the case of F2 were derived from the simulation results, which in our opinion is the most reliable way to represent the solubility of this gas in the different fluorinated liquids (Table 9). The simulated values for the solubility of fluorine show a slight increase with temperature, although this may not be considered a significant variation if error bars are taken into

∆solvG /kJmol-1

∆solvH /kJmol-1

∆solvS /Jmol-1K-1

account. The Gibbs energy of solvation has positive values and increases with temperature, the values being higher than those for chlorine and bromine, which is in accordance with the lower solubility of fluorine. The enthalpy of solvation of fluorine in perfluorooctane and perfluorohexane is positive, relatively small, and almost independent of temperature. Stronger temperature dependence of enthalpy of solvation is shown for solubility of fluorine in perfluoro-1,3-dimethylcyclohexane. It can be concluded from all aforementioned observations that for solubility of fluorine in fluorinated liquids solute-solvent interactions are less important (enthalpy) and the major contribution to the Gibbs energy of solvation is entropic. We attempted to calculate the solubility of bromine in the fluorous liquids using the same procedure as for F2 and Cl2. The results of the residual chemical potential that were obtained are exaggeratingly low (of the order of -10 kJ mol-1 or even more negative), leading to mole fraction solubilities that are unreasonably high. This discrepancy could not be corrected by the introduction of an unlike interaction parameter as for the other two gases. We looked for an explanation to these abnormal results in the potential model for Br2 published by Vrabec et al.27 But we could not identify a reason because it is clear that there is nothing particular about the case of bromine when compared to the other two halogen gases considered here. Errors due to temperature extrapolation are unlikely because the source data for Br2, to which the potential was adjusted, lie closer to the temperature range of the present study than those for F2, which are at much lower temperatures (vapor-liquid equilibrium data range from 80 to 150 K for F2, from 260 to 400 K for Cl2, and from 320 to 560 K for Br2). The test-particle insertion yielded comparable statistics for Br2 as for the other two solutes. If insertion probability had been poorly sampled because of the larger size of Br2, then the values of the

6662 J. Phys. Chem. B, Vol. 112, No. 21, 2008

Podgorsek et al.

Figure 8. Solute-solvent radial distribution functions between sites in chlorine and in the fluorinated solvents at 303 K. C(2,7)F2 are the carbon atoms adjacent to the terminal CF3 groups in perfluorooctane. C(3,6)F2 are the carbon atoms separated by two C-C bonds from the terminal CF3 group in perfluorooctane. C(5)F2 indicates the C5 carbon atom in the perfluoro-1,3-dimethylcyclohexane. Idem for C(4) in the perfluoro-2-butyltetrahydrofuran ring.

chemical potential would have been too high, due to the contribution of repulsive interactions and not too low as is this case. To obtain further details about the structure of the solutions of halogen gases in fluorinated liquids, we examined the solute-solvent radial distribution functions of these systems. The radial distribution functions were obtained by molecular dynamics simulation of a system consisting of 200 solvent molecules and 10 solute molecules. Our previous experience with similar systems32,36,34,37,40,41 showed that this is a good compromise between statistics and the accurate representation of a diluted solution. Using just one solute molecule would require much longer simulations, and it is verified that the solute-solvent radial distribution functions are virtually unchanged when 10 solute molecules are used. Equilibrations of 600 ps in the NpT ensemble were performed under pressure of 15 bar to reach the liquid densities, and then acquisition runs lasted 200 ps. The higher pressure is required to prevent evaporation of the solute molecules. Representative examples of site-site radial distribution functions are plotted in Figure 8 for the case of Cl2, while the other two solutes have very similar behavior. Radial distribution functions of F2, Cl2, and Br2 in perfluorooctane and perfluorohexane show that the halogen molecules are the nearest to the terminal CF3 groups. The first peak in the solute-solvent radial distribution functions is at a smaller distance and has a slightly higher intensity for CF3 groups than for the CF2 groups adjacent to the terminal carbons, and these in turn have higher intensity peaks than the CF2 groups near the middle of the fluorinated molecule (Figure 8a). In the case of interaction of halogen gases with perfluorohexylethane, the same preference for the terminal atoms was observed (Figure 8b) and, as expected given the smaller size of the H atoms, the solute molecule is able to approach more closely to the hydrogenated carbons than to the fluorinated ones. However, the similar intensity of the first peaks indicates that the halogen gases are solvated equally well by the hydrogenated and fluorinated parts of

the solvent. Radial distribution functions of chlorine in perfluoromethylcyclohexane and perfluoro-1,3-dimethylcyclohexane again show that the most solvent accessible atoms are the CF3 groups, whereas there is not a strong first peak with the C atom of the ring furthest from the CF3 groups (Figure 8c). Solute-solvent radial distribution functions of Cl2 with perfluoro-2-butyltetrahydrofuran show that there is no special correlation between Cl atmos and either the O atom or the C4 carbon of the perfluorotetrahydrofuran ring, and again the strongest spatial correlation is with the terminal CF3 group of the perfluoroalkyl chain (Figure 8d). The overall structural picture is that the three halogen gases behave in very similar ways. No pronounced effects were observed with respect to the different sites in the solvent molecules, and therefore no specific solute-solvent interaction sites were discerned. 4. Conclusions The aim of this work was to determine experimentally the solubility of halogen gases (chlorine, fluorine and bromine) in several fluorous solvents, and also the temperature dependence of solubility. This study had two main purposes: first, to obtain accurate data about solubility of halogen gases in fluorinated liquids and, second, to provide a better understanding of the solubility processes and of the structure of the solutions. The latter was attained by using a combination of experimental measurements and molecular simulation techniques. From experimental data, thermodynamic properties of solvation could be calculated, which provided us with information about solute-solvent interactions. Molecular simulation tools allowed the prediction of solubilities outside the experimentally measured temperature range and provided detailed microscopic-level insight, otherwise not easily observable. Solubilities of Cl2, F2, and Br2 in perfluorooctane, perfluorohexane, perfluorohexylethane, perfluoromethylcyclohexane, perfluoro-1,3-dimethylcyclohexane, perfluoro-2-butyltetrahydrofuran, and perfluorophenanthrene were measured from 283

Solvation of Halogens in Fluorous Phases to 323 K following a chemical method at pressures close to atmospheric, except for fluorine for which the solubility was measured only at 298 K. The original experimental data obtained in this work constitutes surely the larger body of values available in the literature concerning the solubility and the interactions between halogens and fluorous phases. Molecular simulations with atomistic force fields describing both the solute and the solvent were carried out using molecular dynamics. Some parameters of the force field describing perfluorotetrahydrofurans had to be calculated because they were not available in the literature. These include electrostatic charge distributions and torsion energy profiles that are important to represent interactions and conformations of this fluorinated solvent, respectively. Solubility was determined using Widom’s method of inserting halogen molecule in previously stored configurations of solvent. The structure of the solutions was analyzed through solute-solvent radial distribution functions. It was observed experimentally and by molecular simulation that fluorine is approximately 1 order of magnitude less soluble than the other two halogen gases that exhibit mole-fraction solubilities of the order of 10-2. Solubilities calculated from simulation using geometric combining rules for the unlike interaction parameters were systematically higher than the experimental ones, which is a consequence of weak halogenfluorous solvent interactions. However, the correct order of magnitude and temperature dependence of solubility were predicted. To reproduce experimental results, we introduced a binary energy interaction parameter kij into the Lennard-Jones well depths describing the interaction between the halogen gases and the fluorous solvents. The general values of the unlike interaction parameter is kij ) 0.89 for chlorine-fluorous liquids and kij ) 0.75 was obtained for fluorine-fluorous solvents. Experimental and simulation values of solubilities of chlorine and bromine decrease with temperature, which indicates an exothermic solvation process in the temperature range studied. Both enthalpy and entropy of solvation show significant variation with temperature meaning both enthalpy and entropy contribution are important. In case of fluorine where solubility was measured experimentally only at 298 K, molecular simulation was used to predict the temperature dependence of solubility. Results show that there is no significant dependence of temperature. From thermodynamic solvation properties, it can be concluded that energetic interactions between molecules fluorine and fluorous solvents are less important and the predominant effect is entropic. Solute-solvent radial distribution functions were calculated to investigate structural features in the solutions studied, and no significant difference in structure of solution of fluorine, chlorine, and bromine in the same fluorinated liquid was found. There are also no specific interaction sites between the halogens and solvent molecules. This means that the interactions are dominated by dispersive forces and not by electrostatic interactions between the quadrupole of the solutes and the charge distributions in the solvents, even in the cases where there are nonfluorinated functional groups (as in the semifluorinated alkane and the perfluorinated tetrahydrofuran) that could give rise to electrostatic effects. In general, the preferential solvation sites for the halogen gases are the easily accessible terminal CF3 groups. Acknowledgment. We are grateful to Dr. D.H. Menz from Pharpur GmbH for supplying the fluorinated solvents and to Dr. P. Husson for her help with the density measurements. Traveling between Slovenia and France was supported by a scholarship for scientific project from French Government

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