18566
J. Phys. Chem. B 2006, 110, 18566-18572
Interactions of Nitrous Oxide with Fluorinated Liquids Margardia F. Costa Gomes,* Johnny Deschamps, and Agı´lio A. H. Pa´ dua* Laboratoire de Themodynamique des Solutions et des Polyme´ res, UniVersite´ Blaise Pascal Clermont-Ferrand/ CNRs, France ReceiVed: May 16, 2006; In Final Form: July 8, 2006
The interactions of nitrous oxide with fluorinated liquids are investigated by reporting original experimental results on gas solubility and interpreting them using molecular simulation. Nitrous oxide is highly soluble in the three fluorinated liquids studiedsperfluorooctane, 1-bromoperfluorooctane (perfluorooctylbromide), and perfluorohexylethaneswith mole fraction solubilities on the order of 0.03 under ambient conditions. An intermolecular potential model was developed for nitrous oxide, with a functional form of the Lennard-Jones plus point charges type, adjusted to the experimental multipole moments and to vapor-liquid equilibrium properties. The solubility of nitrous oxide in perfluorocarbon liquids was calculated by molecular simulation methods, and a dissimilar interaction parameter of 0.92 in the Lennard-Jones well-depths between solute and solvent had to be introduced to reach agreement with the experimental results, similar to what is found for hydrocarbon-fluorocarbon interactions. The structure of the solutions was studied by analysis of solutesolvent radial distribution functions, showing that, although electrostatic interactions are not predominant, a small orientational effect is still present between the dipole of nitrous oxide and those of the substituted fluorinated liquids.
Introduction Fluorous phases can play an important role in the search for cleaner technologies and cleaner synthetic paths. The dependence on temperature of the partial miscibility of fluorous liquids with hydrocarbons leads to the test of these compounds as alternatives to more conventional reaction media. One example is their use in biphasic homogeneous catalysis,1 a process that presents the advantage of allowing the easy recovery of the reaction products or catalysts with a considerable reduction of undesired waste. The peculiar physicochemical properties of fluorinated organic liquids have determined their many other applications, for example, as effective surfactants in supercritical solvents2 or in several biomedical uses.3 To explore the possibilities of further uses of these liquids, the understanding of the properties of their mixtures with other substances is of great importance. We have been studying the microscopic properties of solutions containing fluorinated organic species4-8 with the objective of relating them to macroscopic properties. The strategy followed consisted of the assessment of the thermodynamic properties of solvation (Gibbs energy, enthalpy, and entropy) through precise measurements, namely, the solubility of small (gaseous) solutes in liquids as a function of temperature. Because the solutes studied are gases under atmospheric conditions and have a low solubility in liquids, these experiments provide important information about the solute-solvent interactions, through the enthalpy of solvation, and about the structure of the solution, which is related to the entropy of solvation.9 These properties of solvation, particularly the Gibbs energy, are also accessible by models of statistical thermodynamics and can be directly calculated by molecular simulation, provided that realistic intermolecular force fields are available both for the solvent and for the solute. The * Corresponding author. E-mail:
[email protected] (M.F.C.G.);
[email protected] (A.A.H.P.).
link between the macroscopic properties and the microscopic interactions can then be established, and the molecular mechanisms of solvation can be easily investigated by molecular simulation.10 In this work, the solubility of nitrous oxide, N2O, was studied, both experimentally and by molecular simulation, in three fluorinated liquids, all with a carbon skeleton with eight carbon atoms: one totally fluorinated, one with one terminal fluorine atom substituted by bromine, and one semifluorinated hydrocarbon with six consecutive fluorinated carbons and two hydrogenated carbons. N2O is a widely available gas that is largely used in medicine as an anaesthetic gas, with an analgesic effect, and for surgical purposes.11 It is also used in the food industry as a mixing and foaming agent.12 Nitrous oxide is one of the major greenhouse gases closely associated with anthropogenic activities, as it is produced in soils mainly by the bacterial processes of nitrification and denitrification after the application of nitrogen fertilizers.13 From the molecular point of view, nitrous oxide is an interesting species since, although it is still a gas at room temperature and a simple molecule, it exhibits both a quadrupole and a small dipole. After studying the solvation of carbon dioxide7,8,14 and of carbon monoxide14 in several fluorinated liquids and concluding that specific electrostatic interactions play a minor role in the solvation of these molecules, we decided that the study of a gas exhibiting a larger dipole moment seemed to be a logical choice to investigate the relative importance of the polarity in the solvation process. In the present study, the solvents are not strictly perfluorocarbons, but contain functional groups that introduce some polarity. In this paper, we present a new intermolecular potential for nitrous oxide suitable for the calculation of fluid-phase properties, since the sole N2O model that has been reported in the literature15 was derived solely from crystal lattice data. Experimental measurements of the solubility of nitrous oxide in the
10.1021/jp062995z CCC: $33.50 © 2006 American Chemical Society Published on Web 08/31/2006
Interaction of N2O with Fluorinated Liquids
J. Phys. Chem. B, Vol. 110, No. 37, 2006 18567
TABLE 1: Parameters of the Nitrous Oxide Molecular Model rN1-N2 ) 1.128 Å
rN2-O ) 1.184 Å
site
σ/Å
/kJ mol-1
q/e
N1 N2 O
3.15 3.15 3.03
0.470 0.470 0.650
-0.2497 +0.5159 -0.2662
three fluorinated liquids as a function of temperature are presented, and the thermodynamic properties of solvation are calculated from these data. The new intermolecular potential for the solute allowed the calculation of the Gibbs energy of solvation of nitrous oxide in the three liquids by molecular simulation following an appropriate free energy route. Molecular simulation was used to study the solvation process and the microscopic structure of the solutions. Intermolecular Potential Model for Nitrous Oxide. The geometry and the multipole moments of N2O are known experimentally, so this information was used in the present model. The N-N and N-O distances at equilibrium were taken from the literature,16 and their values are rN1-N2 ) 1.128 Å and rN2-O ) 1.184 Å. Nitrous oxide is a linear molecule. Three point charges were placed at the atomic sites, and their values were adjusted to reproduce the experimental dipole and quadrupole moments, which are µ ) 0.161 D and Q ) -3.29 D Å, respectively.16 The molecular axis is oriented with the positive direction from the O to the N, and, in this frame, the dipole moment is positive. The partial charges thus obtained are listed in Table 1. The repulsion-dispersion interactions were represented by three Lennard-Jones sites located at the atomic positions. Dissimilar interactions are calculated using geometric combining rules for both molecular diameters, σ, and well-depths, . The Lennard-Jones parameters were derived from thermodynamic data such as coexisting liquid and vapor densities, vapor pressure, and enthalpy of vaporization. The vapor-liquid coexistence curve for the N2O model was calculated using the Gibbs ensemble Monte Carlo method,17 implemented in our own computer program. The simulated systems consisted of two cubic boxes with periodic boundary conditions, each of them containing between 256 and 500 molecules in the initial configuration, depending on the temperature. Larger systems are required at temperatures that are closer to the gas-liquid critical point to limit the statistical uncertainties in the densities caused by the large fluctuations. The total density was chosen in a manner to obtain sufficient amounts of substance in both the liquid and vapor boxes once equilibration was attained. Interactions were cut off beyond 10 Å, and long-range corrections were applied (tail corrections for the Lennard-Jones interactions and the Ewald summation for electrostatic terms, with a reciprocal space cutoff equivalent to three box lengths). Production runs consisted of 100 000 Monte Carlo cycles, each cycle being composed of attempted displacement and rotation moves of molecules within a box (N such moves per cycle, with N being the total number of molecules), attempted volumechange moves of the two boxes (four times per cycle), and attempted molecule transfers between boxes (one every four translation/rotation moves). The phase diagram obtained from simulation is shown in Figure 1, together with experimental coexisting densities.18 The error bars on the simulated values were estimated by the block-average procedure.19 The final, adjusted values of the Lennard-Jones diameters and well-depths, which are listed in Table 1, provide agreement with the
Figure 1. Densities of coexisting liquid and vapor nitrous oxide. A comparison of the simulation and experimental results is shown. Open squares are experimental liquid densities, open circles are experimental vapor densities, and closed symbols are simulation results.
Figure 2. Clausius-Clapeyron plot of the vapor pressure of nitrous oxide obtained by molecular simulation. The symbols are the simulation results, and the line is the best fit straight line.
experimental phase envelope that lies within the statistical uncertainties of the simulated densities. A Clausius-Clapeyron plot of the vapor pressure obtained from simulation is shown in Figure 2, from which the enthalpy of vaporization was calculated, ∆Hvap ) 15.6 ( 0.5 kJ mol-1. This result can be compared with the experimental datum20 ∆Hvap ) 16.55 kJ mol-1 at the normal boiling point of 184.65 K. The deviation of 1 kJ mol-1 is acceptable considering the large statistical uncertainties that are found for simulated pressure and the fact that the simulations cover a wide temperature range. The enthalpy of vaporization was also calculated at the normal boiling point from the energy differences obtained in simulations of the gas and liquid phases. The calculated value, ∆Hvap ) 16.4 ( 0.1 kJ mol-1, agrees perfectly with experiment. Hence, the proposed model reproduces the experimental molecular geometry, multipole moments, liquid-vapor coexisting densities, vapor pressure, and enthalpy of vaporization of nitrous oxide. Cardini et al.15 reported an intermolecular potential model for N2O, obtained from a fit to crystal lattice data. Although this is a model of the “Lennard-Jones plus point charges” type, it contains a number of features that, beside the fact that it was adjusted to solid-state data, make it less appropriate in our opinion for the calculation of thermodynamic properties in fluid phases. First, the central N2 atoms do not interact with each other through Lennard-Jones potentials, and different σ and parameters are attributed to each pair of atoms. This lack of an
18568 J. Phys. Chem. B, Vol. 110, No. 37, 2006
Costa Gomes et al.
implicit combining rule for dissimilar interactions makes the model cumbersome to apply to mixtures of nitrous oxide with other substances. Second, the electrostatic charges proposed by the authors (qN1 ) -0.3665e, qN2 ) 0.6858e, qO) -0.3193e) lead to a dipole moment (µ ) -0.166 D) that has a direction opposite to the dipole in the present model and that in the highlevel ab initio calculations of Coriani et al.16 Our own ab initio calculations at the MP2/cc-pVTZ(-f) level led to a positive dipole moment. Third, the quadrupole moment of the Cardini model is -4.4 D Å, whereas the experimental (and that of the present model) is -3.29 D/AA, because the charges in the Cardini model are significantly higher than those proposed here. We could not find information in the Cardini paper on the geometries (N-N and N-O distances) that we suppose were matched to the experimental crystal-structure data. Solubility of Nitrous Oxide in Fluorinated Liquids The solubility of nitrous oxide was studied in three fluorinated liquids: perfluorooctane, C8F18, 1-bromoperfluorooctane (or perfluorooctylbromide), C8F17Br, and perfluorohexylethane, C6F13C2H5, both experimentally and by molecular simulation. Experimental. All the fluorinated liquids used were obtained from PharmPur GmbH, Germany. In molar terms, perfluorooctane is 99.4% pure, 1-promoperfluoroocatane is 98.1% pure, and perfluorohexylethane is 100.0% pure. Purity analyses were described in a previous publication.21 Nitrous oxide was supplied by Linde Gas, France, with a purity of 99.5%. Solubility was measured by means of an orthobaric saturation technique, described in previous publications,6,21 in which a known quantity of degassed solvent is put in contact with a presaturated solute gas at a constant temperature and pressure. The quantity of gas dissolved in the liquid is determined from the displacement of a cylinder inside a piston of accurately known diameter. Gas solubilities can be expressed as an Ostwald coefficient, which is related to experimental measured quantities:
VV VL
L2,1 )
(1)
where VV is the volume of gas dissolved and VL is the total volume of the liquid solution after equilibrium is reached. The mole fraction of component 2 (taken here to be the gaseous solute) in the liquid solution can be directly related to L2,1 by
x2 )
L2,1p2VL Z12RT
(2)
where p2 is the partial pressure of the solute, VL is the molar volume of the liquid solution (which can be considered to be, in the conditions of this study, equal to the orthobaric molar volume of the pure solvent, V/1), and Z12 is the compressibility factor of the vapor phase in equilibrium with the solution, calculated here at the level of the second virial coefficient. The solubility can also be expressed in terms of the Henry’s law constant, which can be defined as22
KH(T, p) ) lim
x2f0
() f2 x2
(3)
where f2 ) φ2p2 is the fugacity of component 2 in the solution, with φ2 being the fugacity coefficient, calculated in the usual way.22 The Henry’s law constant can then be related to the
TABLE 2: Experimental Data for the Solubility of Nitrous Oxide in Perfluorooctane, in 1-Bromoperfluorooctane, and in Perfluorohexylethane between 288 and 313 K Expressed as Ostwald Coefficients, Henry’s Law Constants, and Mole Fraction Solubilities at a Solute Partial Pressure of 105 Pa. T/K
p/kPa
289.15 292.92 297.28 303.00 307.34 307.47 311.67
96.30 95.40 95.10 102.5 95.20 95.80 96.40
289.44 292.97 297.47 302.75 307.42 311.55
96.3 95.0 96.1 94.8 100 95.0
289.39 292.68 297.04 303.11 307.57 311.93
95.6 96.1 97.1 96.1 95.5 95.7
L2,1
KH/MPa
102x2
3.29 3.48 3.77 3.97 4.23 4.30 4.42
3.02 2.86 2.64 2.51 2.36 2.32 2.22
2.92 3.08 3.26 3.47 3.67 3.82
3.47 3.29 3.11 2.92 2.76 2.65
2.70 2.84 3.13 3.31 3.58 3.72
3.75 3.57 3.24 3.06 2.83 2.72
C8F18 2.92 2.78 2.59 2.49 2.36 2.32 2.27 C8F17Br 3.29 3.14 3.00 2.85 2.71 2.62 C6F13C2H5 3.96 3.80 3.47 3.33 3.10 3.01
experimentally determined Ostwald coefficient by
KH(T, psat 1 ))
RTZ12φ2
(4)
V/1L2,1
where the molar volume of the solution is approximated by the orthobaric molar volume of the pure solvent and the pressure dependence of KH, L1,2, and V∞2 is considered negligible. When expressed as a mole fraction, the solubility is normally given at a constant value of the partial pressure of the gas (for example, at p2 ) 105 Pa). It is nevertheless necessary to determine the mole fractions in the vapor phase in equilibrium with the liquid solution, yi, to calculate the product φ2Z12 (normally close to unity). This quantity is obtained iteratively, making use of the phase equilibrium condition for component 1, the liquid solvent:
φ1y1p ) γ1x1f1°
(5)
where φ1 is the fugacity coefficient of component 1, γ1 is its activity coefficient (considered to be unity in the thermodynamic conditions of this work), p is the equilibrium pressure, f1°is the standard-state fugacity, and x1 and y1 are the mole fractions in the liquid solution and in the gaseous phase in equilibrium with it, respectively. Equation 5 can be rewritten as23
y1 ) (1 - x2)
( )( ) [
]
psat φsat V10(p - psat 1 1 1 ) exp p φ1° RT
(6)
The fugacity coefficient and the standard-state fugacity of component 1 are calculated in the usual way.22 The measurements of the solubility of nitrous oxide in the three fluorinated liquids are reported in Table 2. The direct experimental values of solubility expressed as Ostwald coefficients are listed together with the equilibrium pressures and temperatures. From these values, the Henry’s law constants could be calculated as well as the mole fraction solubilities at a constant partial pressure of the gaseous solute. Nitrous oxide is highly soluble in the three fluorinated liquids: roughly 1 order of magnitude more soluble than oxygen and even about 10%
Interaction of N2O with Fluorinated Liquids
J. Phys. Chem. B, Vol. 110, No. 37, 2006 18569
TABLE 3: Vapor Pressure and Liquid Density of the Pure Solventsa vapor pressure
A
B
C
C8F18 C8F17Br C6F13C2H5
18.921 15.330 12.914
5892.0 4001.2 3600.0
36.717 -42.571 20.000
a
liquid density
d0
d1
C8F18 C8F17Br C6F13C2H5
2523.2 2639.7 2185.5
2.6027 2.4701 2.1434
Coefficients of eqs 7 and 8.
TABLE 4: Coefficients for Eq 9 and Average Absolute Deviation (AAD) for the Correlation of Henry’s Law Constants C8F18 C8F17Br C6F13C2H5
A0
A1/103
A2/105
AAD
-5.4364 0.4428 -7.4165
5.2718 1.5543 6.4531
-9.7038 -3.9697 -11.633
0.6% 0.2% 0.9%
more soluble than CO2.14 The high solubilities of N2O and CO2 are expected to reflect similar types of interaction with the fluorinated liquids, since these two gases have similar molecular sizes, shapes, and even electrostatic moments. The order of solubility in the three solvents is identical in N2O and CO2, and different from that of O2, which is more soluble in perfluorooctane and has similar solubilities in the two other liquids.14 The vapor pressures of the pure solvents were taken from the literature14,24,25 and are expressed by Antoine’s equation,
ln(psat/kPa) ) A -
B T/K + C
(7)
with coefficients listed in Table 3. Second virial coefficients were obtained from the compilation of Dymond and Smith26 for the case of nitrous oxide and were estimated using Tsonopoulos’ equation27 for the vapor phases of the different solvents (when necessary, the critical constants were estimated by Amboise’s group contribution method). The cross virial coefficients were considered to be the arithmetic mean of the values for the pure components. The orthobaric liquid density for the three liquids was taken from the literature14 and can be calculated with a precision of ( 0.02% in the temperature range of the present work from the fitting equation
F/(kg m-3) ) d0 - d1 (T/K)
(8)
using the coefficients listed in Table 3. The experimental results for the Henry’s law constant were adjusted to a power series in 1/T: 2
AiT-i ∑ i)0
ln(KH/MPa) )
(9)
The coefficients Ai as well as the average absolute deviations (AADs) obtained are listed in Table 4, where the AADs are included to characterize the precision of the data. The solubility results of nitrous oxide in the three fluorinated liquids, expressed as Henry’s law constants, are precise to within 1%. No values were found in the literature for comparison but, from the analysis of the data and after a careful study of the sources and order of
Figure 3. Henry’s law constants for nitrous oxide in the fluorinated liquids: b, perfluorooctane; 9, 1-bromoperfluorooctane; 2, perfluorohexylethane.
magnitude of the systematic errors during the measurements, it is believed that the present values are accurate to within a few percent. As can be seen in Figure 3, nitrous oxide is less soluble in perfluorooctane than in the other two fluorinated liquids in the temperature range studied. This observation cannot be explained by considerations of free volume in the solvents, since it is in perfluorooctane and in perfluorohexylethane that the cavities naturally existing in the liquid phase are larger and more easily formed.28 It is expected that the interactions of nitrous oxide with the solvents are the determinant factor for the order of solubilities. The solubility in the three solvents decreases and the Henry’s law constant increases with increasing temperature. The variation in solubility with temperature is similar in the three liquid solvents. Gas solubility, expressed as a Henry’s law constant, is in direct relation with the Gibbs energy of solvation, which is the variation of the Gibbs energy when the solute is transferred from the ideal gas state into an infinitely dilute solution at constant pressure and temperature. From the behavior with temperature of KH, the enthalpy of solvation and the entropy of solvation can be derived. The values for these properties, which are difficult to obtain directly from calorimetric or volumetric measurements, can provide insight into the molecular interactions (namely, the solute-solvent interactions) responsible for the macroscopic behavior of these solutions.10 It is then expected that the values of these properties will clarify the behavior of the solubility of nitrous oxide in the three solvents. The values for the different thermodynamic properties of solvation were calculated6,29 and are collected in Table 5. The solvation of nitrous oxide in the three solvents is an exothermic process and the values of the enthalpy of solvation increase slightly with temperature. The entropy of solvation is negative and comparable in the three cases. A parallel between the values of nitrous oxide solubility and the thermodynamic properties of solvation is not easy to establish. The solvation process seems to be more exothermic in perfluorohexylethane and hence compatible with a larger solubility. The lower solubility in perfluorooctane could be due to an unfavorable entropic term that counterbalances the more negative enthalpy of solvation relative to that obtained for 1-bromoperfluorooctane. Molecular Simulation. Atomic-level insight on the energetic and structural features of solutions of nitrous oxide in the fluorinated liquids can be attained using molecular simulation to represent the systems studied. Nitrous oxide was modeled by the intermolecular potential developed in this work, whereas the fluorinated liquids were represented by all-atom models
18570 J. Phys. Chem. B, Vol. 110, No. 37, 2006
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TABLE 5: Partial Molar Thermodynamic Properties of Solvation for Nitrous Oxide in Perfluorooctane, 1-Bromoperfluorooctane, and Perfluorohexylethanea T/K
∆solvG2/kJ mol-1
288 293 298 303 308 313
8.28 8.63 8.96 9.28 9.58 9.87
288 293 298 303 308 313
8.01 8.31 8.62 8.91 9.20 9.44
288 293 298 303 308 313
7.79 8.15 8.49 8.82 9.12 9.41
∆solvH2/kJ mol-1 C8F18 -11.9 -11.2 -10.4 -9.48 -8.51 -7.46 C8F17Br -9.87 -9.58 -9.25 -8.89 -8.49 -8.04 C6F13C2H5 -13.2 -12.3 -11.3 -10.3 -9.11 -7.87
∆solvS2/J mol-1K-1 -70 -68 -65 -62 -59 -55 -62 -61 -60 -59 -57 -56 -73 -70 -66 -63 -59 -55
a The values are calculated at several temperatures between 288 and 313 K and are relative to the ideal gas state at 105 Pa.
within the OPLS-AA force field.30 Specific parameters were considered for perfluoroalkanes,31 bromine-substituted perfluoroalkanes,32 and hydrocarbon-perfluorocarbon diblocks.32 Geometric combining rules were adopted for both molecular diameters (σ) and well-depths () in the Lennard-Jones function, as specified in OPLS-AA.30 The solvents were simulated using the DL_POLY33 molecular dynamics program, using cubic boxes with periodic boundaries containing 256 molecules. The cut off distance for the interactions between atomic sites was taken to be 15 Å. Long-range tail corrections were applied beyond the cutoff to the Lennard-Jones interactions, and, for electrostatic terms, the Ewald summation was used (with a reciprocal-space cutoff equivalent to three box-lengths), even if all molecules in the system are neutral. After equilibration, production runs of 500 ps with a time step of 2 fs were performed, from which configuration snapshots were saved every 250 time steps. The solubility of nitrous oxide in these solvents was calculated using the Widom test-particle insertion method.34 Insertions of a solute molecule at random positions and orientations were attempted in each of the configuration snapshots of the liquid solvent previously stored. As a guideline, one insertion was attempted per cubic angstrom of the solvent box, meaning that around 105 insertions were tried in each of the saved configurations. For a small solute molecule such as N2O in the solvents studied here, the test-particle insertion procedure yields a good sampling of its chemical potential. The statistical uncertainty reported here is the standard deviation of the test-particle insertions, since these are uncorrelated events. As can be observed in Figure 4, simulation reproduces the order of magnitude of the experimental mole fraction solubilities. The average deviations are on the order of +40%, with the simulation systematically overestimating the experimental solubility. Differences are more marked for perfluorooctane as solvent. The behavior of solubility with temperature is correctly predicted by simulation, meaning that the enthalpy of solvation is obtained with the right sign and order of magnitude. The relative solubility of nitrous oxide in the three fluorinated solvents is not correctly predicted by simulation. Experimentally, the solute is less soluble in perfluorooctane and its solubility is
Figure 4. Comparison of the mole fraction solubility determined experimentally (lines) and calculated by molecular simulation (symbols and respective error bars): O, full line, perfluorooctane; 0, dashed line, 1-bromoperfluorooctane; 4, dashed-dotted line, perfluorohexylethane. Filled symbols correspond to solubility calculated using a dissimilar interaction parameter kij ) 0.92 in the Lennard-Jones ij.
similar in the other two liquids. This order is not reproduced by the simulations, but this is a severe test to the models and to the calculation methods because the solubilities in the three solvents are similar within the statistical error bars of the simulated results. The agreement between simulation and experiment can be improved if a dissimilar interaction parameter is introduced. Such an interaction parameter was applied to all the solutesolvent site pairs, but only in the Lennard-Jones well-depths:
ij ) kij(iijj)1/2
(10)
A value of kij ) 0.92 yields much better quantitative agreement with the experiment, as shown in Figure 4 at 288, 298, and 313 K, and the temperature dependence of the calculated results matches the experimental trend very well. However, there is no change in the relative order of solubility in the three solvents from that originally obtained using simulation without the binary interaction parameter. As can be seen in Figure 4, the difference in solubility observed experimentally between the three solvents (around 20%) is not larger than the statistical error bars of the simulated values. Like in the present case, several researchers have resorted to dissimilar interaction parameters to explain properties of mixtures of several species with fluorinated liquids.35-38 Nonideality in hydrocarbon-fluorocarbon mixtures has been a recurrent subject in the physical chemistry of fluids. In general, these mixtures show positive deviations from ideality connected to weaker than expected interactions between hydrocarbons and fluorocarbons. This behavior can be observed in the liquid phase through excess thermodynamic properties,39 and also in the gas state through the cross second virial coefficients.35 A number of recent studies have dealt with this nonideality using molecular simulation36 or models based on molecular theory.37,38 For hydrocarbon-fluorocarbon interactions, for example, the value for kij, if defined in the same way as here, is, in general, very close to 0.92. The situation that has been most studied is that in which the alkane and the perfluoroalkane have similar molecular sizes and, as a consequence, are in the same physical state. This has been done from methanes up to hexanes in the two series.36,37 Since in the present systems containing N2O and longer fluorocarbons there is a strong size asymmetry, it was not clear to us if the same value of the dissimilar interaction parameter would hold. We investigated two cases in which there is an asymmetry in size: either a small, gaseous hydrocarbon solute interacts with a longer perfluorocarbon that is liquid or,
Interaction of N2O with Fluorinated Liquids
J. Phys. Chem. B, Vol. 110, No. 37, 2006 18571
TABLE 6: Values of the Dissimilar Interaction Parameter Affecting the Lennard-Jones Well-Depth in the Solute-Solvent Interactions between Alkanes and Perfluoroalkanes solvent C6H14 C8H18 C8H18 C7F16 a
solute CF4 CF4 CF4 CH4
T/K
x2/10-3(exp)
kij
298.15 293.00 298.00 300.00
2.35a
0.912 0.940 0.933 0.918
2.02b 1.99b 8.17c
Reference 40. b Reference 41. c Reference 42.
vice-versa, a gaseous fluorocarbon interacts with a liquid hydrocarbon that has a longer molecule. The same methodology previously explained was adopted here: computer simulations using molecular dynamics and the OPLS-AA force field for alkanes30 and perfluoroalkanes,31 followed by test-particle insertion to calculate chemical potentials. The gases chosen were methane and perfluoromethane with the liquid solvents hexane, octane, and perfluoroheptane, for which experimental data could be found in the literature and therefore no new measurements were required. In Table 6 are reported the values of the dissimilar interaction parameter, kij, that provide the best fit to the experimental solubilities of CF4 in hexane and in octane, and CH4 in perfluoroheptane. The individual values lie between 0.912 and 0.940, with an average of kij ) 0.926. As can be concluded, essentially the same value for the dissimilar interaction parameter was obtained for the size-asymmetric mixtures, as had been obtained in the other studies reported in the literature for mixtures of compounds with similar sizes. In our own work5 a value of kij ) 0.83 occurred for xenon in perfluorohexane using simulation, and a value of kij ) 0.92 was obtained using the SAFT-VR equation. There is still not a fundamental physicochemical explanation for this recurring need of a dissimilar interaction parameter, systematically with values around 0.9, in the interactions between nonpolar or weakly polar compounds and fluorinated hydrocarbons. Rossky et al.36 also suggested the use of the WaldmanHagler mixing rules43 for hydrocarbon-fluorocarbon interactions:
σij )
(
)
σii6 + σjj6 2
1/6
, ij ) 2
(
σii3σjj3
)
σii6 + σjj6
xiijj
(11)
For nitrous oxide in the three fluorinated liquids studied here, these mixing rules did not lead to good results: the average deviation between the calculated and experimental solubilities over the temperature range considered is +33%, with large deviations observed for perfluorooctane (between +60 and +70%), intermediate deviations for 1-bromoperfluorooctane (between +15 and +24%) and small deviations for perfluorohexylethane (between -1 and +9%). Lennard-Jones σ parameters calculated by the Waldman-Hagler combining rules are very close to those obtained from a geometric mean for all solute-solvent atom pairs (differences are less than 1%, in general) except when hydrogen atoms are present. For pairs of solute atoms with hydrogen from the solvent, the WaldmanHagler combining rule gives dissimilar σ values, which are between 2.7 and 3.8% larger than the geometric rule. LennardJones parameters calculated by the Waldman-Hagler combining rule are, in general, between 3.3 and 8% larger than those given by a geometric combining rule affected by kij ) 0.92, except once again for hydrogen, for which the deviations are between -7.2 and -13.1%. For the atom pairs considered here, Waldman-Hagler combining rules yield dissimilar parameters
Figure 5. Solute-solvent RDFs between sites in N2O and the solvents, at 298 K. N1 and O are the terminal atoms of nitrous oxide, C3F is a terminal carbon in a fluorinated solvent, C2F is a nonterminal carbon, C3H is a methylenic carbon, and C2H is an ethylenic carbon.
that are not that different from geometric means, except for the cases in which hydrogen is present. The use of the WaldmanHagler combining rule does not seem to be appropriate for the present systems since the results are not convincing. Picking a combining rule empirically is not essentially different from applying a dissimilar interaction parameter to simple geometric means. As in our previous study on the interactions of carbon dioxide with fluorinated liquids,7 we tried to investigate the contribution of electrostatic terms to the properties of solvation. As for CO2, it was found that removing the electrostatic charges from the N2O model did not significantly reduce the calculated solubility. In all three solvents, this effect amounted to a reduction of about 5% in the solubility expressed in mole fraction. Hence, no specific solute-solvent interactions are found in these systems, and electrostatic forces cannot explain the high solubility of N2O in fluorinated liquids. Solute-solvent radial distribution functions (RDFs) were obtained to investigate structural features in the solutions of nitrous oxide in the fluorinated liquids. Simulations were carried out with 16 molecules of N2O and 240 molecules of solvent for 500 ps after the necessary equilibration periods, maintaining a pressure of 10 bar to keep the system condensed. The effect of that pressure on the static structural properties of the solution when compared to the state at 1 bar at higher dilution should be negligible. Nitrous oxide is not an associating molecule, and, as expected, no segregation between species was observed; the solution remained homogeneous. Site-site pairs were selected to give a structural picture of the solutions, and are shown in Figure 5. The plots show RDFs between the terminal atoms of N2O and the selected atoms of the solvents. We feel that the central atom of N2O conveys less valuable information than the terminal ones, which can tell us about the orientation of the solute. The top plot in Figure 5 refers to perfluorooctane. The almost perfect superposition of RDFs between N1 and O with both terminal (C3F) and nonterminal (C2F) carbon atoms of the
18572 J. Phys. Chem. B, Vol. 110, No. 37, 2006 solvent means that there is no orientational bias of the solute with respect to the solvent molecules, as expected. In the middle plot, which concerns 1-bromoperfluorooctane, the RDFs are not as coincident, but they are nevertheless close. It is observed that the peak of the N1-C3F pair is slightly higher than that of the O-C3F pair, whereas the order is reversed for the brominated extremity of the solvent molecule. The same feature is present for perfluorohexylethane, in the bottom plot. It appears that the oxygen atom of the solute has a slightly enhanced correlation with the positively charged part of the solvent molecule (either the Br atom or the ethyl group) and that the terminal nitrogen atom has a slight preference for the negatively charged part of the solvent (the perfluorinated chain). This is logical given the orientation of the dipole moment of N2O, with the oxygen atom carrying a more negative charge than the terminal nitrogen. and being also more distant from the central, positively charged nitrogen. This is a small but observable effect in the present RDFs. In 1-bromoperfluorooctane and in perfluorohexylethane, the first peaks in the solute-solvent RDFs have the same height for both extremities of the solvent molecule, showing that the solute is not solvated preferentially by these solvent sites. In the middle plot of Figure 5, a shoulder is observed after the main peak in the RDFs between the solute atoms and the bromine atom of the solvent. This probably corresponds to distances to bromine atoms belonging to solvent molecules that are not the closest neighbors from the solute. A less pronounced shoulder after the first peak is also present for perfluorohexylethane in the bottom plot. Conclusion In this work, a set of original experimental results is reported on the solubility of nitrous oxide in three fluorinated liquids. Nitrous oxide is highly soluble in all three solvents when compared to other gases, for example, carbon dioxide or oxygen. N2O is more soluble in 1-bromoperfluorooctane and in perfluorohexylethane than in perfluorooctane. This order of solubility is not that expected from free-volume considerations, since it is in perfluorooctane and in perfluorohexylethane that the naturally existing cavities are larger and more easily formed.28,14 The thermodynamic properties of solvation show that the enthalpic term is more favorable for perfluorohexylethane, followed by perfluorooctane. The lower solubility of the latter being explained by an unfavorable entropic contribution. Simulation results yielded an order of solubility that does not match experiment, and calculations overestimated the experimental mole fraction solubility by up to 40%. A dissimilar interaction parameter was introduced in the Lennard-Jones welldepths between solute and solvent atoms, and a value of kij ) 0.92 brought quantitative agreement between the calculations and the experimental results. This has been observed in a number of studies reported in the literature concerning interactions of different nonpolar species with fluorinated molecules. The order between the three solvents was, however, not corrected, but the calculated solubilities in the three solvents lie within the mutual statistical uncertainties. It was shown that electrostatic terms do not contribute significantly to the solute-solvent interactions. Solute-solvent RDFs gave a picture in which the solute is not solvated preferentially by a particular solvent site. There is, however, a small but noticeable orientational effect determined by the dipole moment of N2O and the polarity of the substituted fluorinated solvents. Acknowledgment. The authors are grateful to D. H. Menz from Pharmpur GmbH for supplying the fluorinated solvents.
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