J. Phys. Chem. 1996, 100, 7435-7439
7435
Molecular Modeling Approach for Contrasting the Interaction of Ethane and Hexafluoroethane with Carbon Dioxide Anthony Cece, Sharon H. Jureller, Judith L. Kerschner,* and Karl F. Moschner UnileVer Research U.S., 45 RiVer Road, Edgewater, New Jersey 07020 ReceiVed: December 7, 1995; In Final Form: February 16, 1996X
Interactions between carbon dioxide and ethane or hexafluoroethane were examined using ab initio calculations which were performed at the restricted Hartree-Fock level of theory using the STO-3G and 6-31G* basis sets. Computations at the 6-31G* level have identified key differences between the interaction of hydrocarbons and fluorocarbons with carbon dioxide. The interaction of the fluorocarbon with carbon dioxide is predominantly electrostatic in nature, with the positively charged CO2 carbon atom having a strong attraction to the negatively charged fluorine atoms of the fluorocarbon, resulting in a favorable interaction energy of 0.75-0.8 kcal/mol for each CO2 molecule in the first solvent shell. The interaction of CO2 with hydrocarbons is minimal due to the neutral nature of the hydrocarbon molecule. Calculations on CO2/hydrocarbon systems show a clustering of CO2 molecules away from the hydrocarbon, whereas the calculations on the CO2/fluorocarbon systems indicate that the CO2 molecules orient around the C2F6 by sandwiching the positively charged CO2 carbon between two negatively charged fluorine atoms. These molecular modeling computations have brought to light differences between the interaction of hydrocarbons and fluorocarbons with carbon dioxide which may help to explain the different solubilities of these types of molecules in supercritical carbon dioxide.
Introduction Carbon dioxide is an extremely nonpolar solvent characterized by a low polarizability per volume, a low Hildebrand1 solubility parameter (5.5-6.0 (cal/cm3)0.5), and a low dielectric constant. Due to these properties, only volatile or relatively nonpolar compounds are soluble in CO2. One class of compounds, perfluorinated compounds, are known to exhibit negative dipolarity/polarizability parameters and have the lowest known solubility parameter of any fluid (4-5 (cal/cm3)0.5).2 These compounds have been shown to have especially high solubility in carbon dioxide. This unusual solubility may simply be due to the similar dielectric constants and solubility parameters of carbon dioxide and perfluorinated compounds, or another more specific interaction between these molecules may be influencing the high solubility of fluorocarbons in CO2. “CO2-philic” molecules,3 like perfluorinated alkanes, have been utilized for the synthesis of high molecular weight polymers in supercritical carbon dioxide2-4 for the design of metal chelating compounds for use in supercritical CO25 and for the synthesis of surfactants that form micelles, emulsions, and microemulsions in CO2.6-8 Recently, DeSimone and coworkers have synthesized high molar mass fluoropolymers (MW > 500 000) in supercritical carbon dioxide, and these polymers remain soluble in the reaction medium,4 whereas the corresponding high molecular weight hydrocarbon polymers have no solubility in carbon dioxide. This example effectively demonstrates the different solubilities of hydrocarbons and fluorocarbons in CO2 and confirms the high “CO2-philicity” of fluorinated molecules. Besides fluorocarbons, the other known “CO2-philic” molecules are silicone polymers and to a lesser extent poly(propylene glycol)s. A better understanding of the specific interactions between carbon dioxide and these “CO2philic” molecules may be beneficial to identifying other molecules that may have high solubility in the carbon dioxide medium. X
Abstract published in AdVance ACS Abstracts, April 1, 1996.
S0022-3654(95)03627-6 CCC: $12.00
Yee et al. have performed an IR analysis of the interactions of perfluorinated alcohol compounds with carbon dioxide by monitoring the solvatochromic shifts of the solute vibrational bands which indicate a change in the dielectric constant of the solvent.10 The magnitude of these shifts directly correlates with the chemical interaction of the solute with the solvent through a semiempirical relationship of the KBM model.11 These results, along with a comparison of solubilities of hydrocarbon alcohols and perfluorinated alcohols in supercritical carbon dioxide and supercritical ethane, indicate that there is no specific attractive interaction between the fluorinated compound and CO2. The fluorinated alcohol was found to have a much higher solubility in both carbon dioxide and ethane than the nonfluorinated alcohol, and this was attributed to a reduction in the hydrogen-bonding energy of the fluorinated alcohol and not necessarily to any specific interaction of the fluorine atoms and the carbon dioxide. The authors conclude that the exceptional solubility of perfluorinated analogs can be described by several mechanisms. Primarily, the substitution of the fluorinated methyl or ethyl groups can alter the chemical/physical properties of the new compound, such as by reducing the hydrogenbonding energies and/or creating new local dipoles within the molecule. Second, the repulsive properties of the fluorine atoms impart steric constraints which reduce the solute/solute attractive interactions.10 Molecular modeling has become a useful tool for understanding the interaction of different molecules under controlled conditions, and a number of different types of computer simulations have been used to understand the solvent/solvent and solvent/solute interactions in supercritical carbon dioxide. Recently, molecular modeling calculations using MINDO/3, a semiempirical method, have been utilized to study the interaction of carbon dioxide with naphthalene, and evidence for the formation of a charge transfer complex was found.12 Monte Carlo simulations have also been utilized to quantify the “structure” of the carbon dioxide molecules in condensed fluid phases,13 and through ab initio calculations, the solubility of © 1996 American Chemical Society
7436 J. Phys. Chem., Vol. 100, No. 18, 1996 various organic compounds was found to depend on the total variance of the electrostatic potential on the molecular surface and on the molecular volume.14 In an effort to pursue further the possible specific interactions between fluorinated compounds and carbon dioxide, ab initio calculations were performed comparing the interactions of two simple systems, ethane/carbon dioxide and hexafluoroethane/ carbon dioxide. The total energy of interaction for each system was calculated while increasing the number of carbon dioxide molecules (from one to four) surrounding the fluorocarbon and hydrocarbon. The results of the computations were compared to show the energy differences between the fluorocarbon/carbon dioxide system and the hydrocarbon/carbon dioxide system. Computational Methods Ab initio calculations were carried out using Spartan V3.115 running on a Silicon Graphics (SGI) Indigo2 with an R4400 150 MHz processor, an SGI Indy R4400 150 MHz server, and an SGI 4xR4400 150 MHz Challenge L server. Computations were performed initially at the restricted Hartree-Fock level of theory using the STO-3G and 6-31G* basis sets. In all cases full geometry optimizations were performed at the STO-3G level followed by optimization at the 6-31G* level, and natural, Mulliken, and mapped electrostatic and potential (MEP) charges were computed. Computations on a single R4400 processor took 1 day to 2 weeks for the ethane/carbon dioxide systems and 4 days to 7 weeks for the fluorocarbon/carbon dioxide system. Calculations were carried out using ethane as a model hydrocarbon and hexafluorethane as a model fluorocarbon to keep the problem as simple as possible and to minimize computational costs. Interactions between carbon dioxide and the hydrocarbon or fluorocarbon were investigated by placing the first carbon dioxide molecule approximately 3.0-3.5 Å from the hydrocarbon or fluorocarbon and performing a full geometry optimization. On the basis of the orientation of the first CO2 molecule with respect to the hydrocarbon or fluorocarbon, a second CO2 was introduced, and the geometry was again optimized. The same procedure was followed in placing the third and fourth CO2 molecules to build up the systems. Interactions between CO2 and the fluorocarbon or hydrocarbon were determined as the difference between the energy of the complex and the sum of the energies of the individual components of the system. Single-point calculations were also performed at the 6-31G* level on the separate CO2 and fluorocarbon or hydrocarbon components extracted from the geometry-optimized complexes. This was done to determine if any of the observed energy differences were due to CO2/ CO2 interactions or solvent-induced changes in the solute molecule. Results and Discussion The high-level ab initio calculations performed on the model ethane/CO2 and hexafluoroethane/CO2 systems have shown distinct differences between the interactions of hydrocarbons and fluorocarbons with carbon dioxide. With the addition of an increasing number of carbon dioxide molecules (solvent molecules), the interaction between the fluorocarbon and carbon dioxide is strong enough to overcome any solvent/solvent interactions. However, identical calculations indicate that the solvent/solvent interactions predominate in the hydrocarbon/ CO2 system. The initial calculations focused on a full geometry optimization of the ethane/CO2 system, and Table 1 lists the energies of these 6-31G* geometry optimized complexes in hartrees (1
Cece et al. TABLE 1: Energies (hartrees) of CO2/Hydrocarbon Interactions no. of CO2’s
energy (E) of complex
∑E of components
E of CO2’s from complexa
E of C2H6 from complex
1 2 3 4
-266.8634 -454.4981 -642.1358 -829.7722
-266.8629 -454.4971 -642.1313 -829.7655
-187.6342 -375.2683 -562.9062 -750.5422
-79.2287 -79.2287 -79.2287 -79.2287
a
For an isolated CO2, E ) -187.6342 hartrees.
TABLE 2: Interaction Energies for Ethane/CO2 Systems no. of CO2’s
Ei-total (kcal/mol)
Ei-CO2 (kcal/mol)
Ei-CO2-ethane (kcal/mol)
1 2 3 4
-0.3 -0.6 -2.9 -4.2
0.0 0.0 -2.3 -3.5
-0.3 -0.6 -0.6 -0.7
hartree ) 627.5 kcal mol-1). The first column of values is the energy of the optimized geometry of the complex formed by the interaction of ethane with the appropriate number of carbon dioxide molecules. The second column contains the sum of the energies of the individual components which make up the complex. The difference between these two columns represents the total energy of interaction and is shown in Table 2 for each of the ethane/carbon dioxide systems. The third column of values in Table 1 is the single-point energy of the CO2 molecules calculated using the geometries obtained from the corresponding complexes. The difference between this value and the sum of the energies of individual 6-31G* optimized CO2 molecules (-187.6342 hartrees for each CO2) represents the energy of interaction of the carbon dioxide molecules with one another, and this difference is shown in the second column of Table 2. Finally the fourth column of values in Table 1 shows the energy from a single-point calculation of the ethane molecule extracted from the optimized geometries for each complex. The fact that the energy of the ethane molecule in each case is almost identical to that of a 6-31G* optimized molecule of ethane (-79.2288 hartrees) indicates that the carbon dioxide molecules do not induce changes in the ethane molecule. Table 2 highlights the total energy of interaction for each of the ethane/carbon dioxide systems, the CO2/CO2 interaction energy, and the CO2/ethane interaction energy for each system. Column 1 (Ei-total) is the total energy of interaction for the system and is computed as the difference between the optimized energy of the complex and the sum of the optimized energies of the individual components which make up the complex. Column 2 contains the energy of interaction between the CO2 molecules in the system (Ei-CO2) and is computed as the difference between the energy of the cluster of CO2 molecules in the complex (Table 1, column 3) and the energy of an optimized CO2 molecule (-187.6342 hartrees) multiplied by the number of CO2 molecules in the complex. The final column in Table 2 is the interaction energy between the ethane molecule and the CO2 molecules in the system (Ei-CO2-ethane). This value is computed as the difference between column 1 and column 2 of Table 2. The results of these calculations show that there is little interaction between the hydrocarbon and the carbon dioxide molecules. Actually, the interaction of carbon dioxide molecules with one another is strong enough to cause significant geometry changes in the location of the CO2 molecules around the hydrocarbon. Thus, once the third and fourth CO2 molecules are added, these solvent molecules begin to migrate toward one another to form a cluster independent of the hydrocarbon, as shown in Figure 1. This is confirmed by the calculations listed in the second and third columns of Table 2, which show a large
Interactions between CO2 and Ethane or Hexafluoroethane
J. Phys. Chem., Vol. 100, No. 18, 1996 7437
Figure 1. 6-31G* optimized geometries for ethane/CO2 systems.
TABLE 3: Energies (hartrees) of CO2/Fluorocarbon Interactions no. of CO2’s 1 2 3 4 a
energy (E) of complex
∑E of components
-860.0199 -860.0187 -1047.6553 -1047.6528 -1235.2907 -1235.2870 -1422.9261 -1422.9212
E of C2F6 E of CO2’s from complexa from complex -187.63417 -375.26836 -562.9026 -750.5368
-672.3845 -672.3844 -672.3844 -672.3844
For an isolated CO2, E ) -187.6342 hartrees.
increase in the CO2/CO2 interaction energies with the addition of the third and fourth CO2 molecules compared to the CO2/ ethane interaction energies. These results indicate that solvent/ solvent interactions predominate over the solvent/solute interactions, therefore likely producing lower solvation of the ethane in the carbon dioxide due to the nonrandom mixing of the solute and solvent. Computations performed on the system of hexafluoroethane and carbon dioxide reveal a different interaction. Carbon dioxide shows a very favorable interaction with the fluorocarbon which agrees with the observed solubility of fluorocarbons in supercritical CO2. Table 3 contains the energies of the 6-31G* geometry optimized complexes of hexafluoroethane and carbon dioxide. The data columns in Table 3 are analogous to those of Table1 for the ethane/carbon dioxide system. The first conclusion which can be drawn from looking at this data is that the C2F6 molecule, like the ethane molecule, does not seem to undergo any significant changes in the presence of CO2, as is evidenced by the consistent energies of C2F6 in each of the complexes (last column). The energy of a 6-31G* optimized hexafluoroethane molecule is -672.3845 hartrees, which is very close to the energy of C2F6 in each of the complexes (Table 3, column 4). The results listed in Table 4 provide further insight into the nature of the CO2/fluorocarbon interaction. Column 1 contains the total energy of interaction, which is the difference between the total energy of the system and the sum of the energies of the components. Column 2 lists the CO2/CO2 contribution to the total interaction energy and is determined in a fashion identical with that for the hydrocarbon system. Finally the third column lists the CO2/fluorocarbon contribution to the total energy of interaction (column 1 minus column 2). A compari-
Figure 2. 6-31G* optimized geometries for hexafluoroethane/CO2 systems.
TABLE 4: Interaction Energies for Hexafluoroethane/CO2 Systems no. of CO2’s
Ei-total (kcal/mol)
Ei-CO2 (kcal/mol)
Ei-CO2-C2F6 (kcal/mol)
1 2 3 4
-0.8 -1.6 -2.3 -3.1
0.0 0.0 -0.1 -0.1
-0.8 -1.6 -2.3 -3.0
son the CO2/CO2 interaction energies with the CO2/C2F6 interaction energies in Table 4 shows that unlike the ethane system, there is very little solvent/solvent interaction even after all four CO2 molecules are added to the system. Instead, the interaction energy between the CO2 and the fluorocarbon is quite significant and continues to increase with the addition of more CO2 solvent molecules. A further comparison of the total energy of interaction for the fluorocarbon/CO2 system and the hydrocarbon/CO2 system reveals a dramatic difference between the two systems, and this is further displayed in a comparison of Figures 1 and 2. Unlike the configuration of CO2 molecules around ethane, the CO2 molecules orient around the C2F6 by sandwiching the positively charged CO2 carbon between two negatively charged fluorine atoms. The carbon dioxide molecules are slightly tilted to allow one of the oxygen atoms to interact with the positively charged carbon backbone of the fluorocarbon, as shown in Figure 2. This is not possible with ethane, as the ethane molecule is essentially neutral and there is no apparent electrostatic interaction between carbon dioxide and ethane. Figure 3 shows the electrostatic charges for the CO2/hydrocarbon and CO2/ fluorocarbon systems and for the individual components. This type of charge distribution is consistent with experimental results comparing the Lewis acidity of carbon dioxide and ethane reported by O’Shea et al.16 Additional CO2 molecules orient themselves around hexafluoroethane while distancing themselves from one another as much as possible, accounting for the lack of CO2/CO2 interaction energy (Table 4, column 2). All of the favorable interaction energy stems from the CO2/C2F6 interaction, which averages to 0.77 kcal/mol for each CO2 placed around hexafluoroethane
7438 J. Phys. Chem., Vol. 100, No. 18, 1996
Cece et al.
Figure 3. Atom-centered charges derived from mapped electrostatic potentials for 6-31G* optimized geometries.
Figure 5. Interatomic distances for the 6-31G* optimized geometries.
Figure 4. Interaction energies for ethane and hexafluoroethane as a function of the number of CO2 molecules.
for the systems of one to four CO2 molecules investigated (Table 4, column 3). Figure 4 graphically displays a comparison of the interaction energy for ethane and hexafluoroethane with CO2 as a function of the number of carbon dioxide molecules surrounding the molecule and confirms further the different interactions between the two solute molecules and the solvent. Further insight into the nature of the interaction of ethane and hexafluoroethane with CO2 can be provided by a comparison of the interatomic distances between the molecules, as shown in Figure 5. While both the fluorine atoms and the hydrogen atoms are at an average distance of 3.2 Å from the CO2 carbon and oxygen, respectively, the larger atomic radius of the fluorine atom results in complex formation with the CO2 carbon sandwiched between two fluorine atoms. On the other hand, the small atomic radius of the hydrogen leads to at best only a marginal through-space interaction between the ethane and the carbon dioxide. These interactions are represented more accurately by the space-filling models in Figures 1 and 2. Computations of larger systems using the method described in this report would require extensive computing time and resources. A full geometry optimization at the 6-31G* level on the system of hexafluoroethane with four CO2 molecules took 6 weeks to complete running on an SGI R4400 150 MHz processor. The difficulty in performing geometry optimizations on larger systems is due to the increased number of basis functions as well as the increase in the degrees of freedom. As with the explicit treatment of any solvent, problems arise in convergence due to slight movement in the solvent molecules, which results in a very shallow potential well. However,
examination of the configuration of four carbon dioxide molecules around hexafluoroethane shows that several more CO2 molecules could easily fit around the fluorocarbon to form the first solvation shell. Taking this into consideration, it is easy to see how this significant interaction energy translates into increased solubility of the fluorocarbon in supercritical CO2. While these theoretical results indicate that a specific CO2/ fluorocarbon interaction does exist, it does not preclude the possibility that more nonspecific forces also contribute to the CO2-philicity of these molecules. Conclusions Computations at the 6-31G* level have identified key differences between the interaction of hydrocarbons and fluorocarbons with carbon dioxide. The interaction is predominantly electrostatic in nature, with the positively charged CO2 carbon atom having a strong attraction to the negatively charged fluorine atoms of the fluorocarbon, resulting in a favorable interaction energy of 0.75-0.8 kcal/mol for each CO2 molecule in the first solvent shell. These theoretical modeling calculations do indicate that a specific CO2/fluorocarbon interaction does exist, contrary to the experimental findings reported by Yee et al., but it is possible that the specific interaction described in this study is not strong enough to influence the bending mode of the carbon dioxide studied by Yee. This is especially true since it is the carbon of the CO2 that directly interacts with the fluorine atoms. The interaction of CO2 with hydrocarbons is minimal due to the neutral nature of the hydrocarbon molecule. Calculations on CO2/hydrocarbon systems actually show a clustering of CO2 molecules away from the hydrocarbon. While low molecular weight gases such as ethane and hexafluoroethane are both miscible in carbon dioxide, these molecular modeling computations have brought to light differences in the interaction of hydrocarbons and fluorocarbons with carbon dioxide which may
Interactions between CO2 and Ethane or Hexafluoroethane help to explain the different solubilities of higher molecular weight analogs of these types of molecules in supercritical carbon dioxide. References and Notes (1) Hildebrand, J. H.; Scott, R. L. Regular Solutions; Prentice Hall: Englewood Cliffs, NJ, 1962. (2) Stofesky, D.; Reid, M.; Enick, R. M. In Proceedings 2nd International Symposium on Supercritical Fluids; M. A. McHugh, Ed.; Johns Hopkins University: Baltimore, MD, 1991; p 341. (3) DeSimone, J. M.; Maury, E. E; Combes, J. R.; Menceloglu, Y. Z. Polym. Prepr. Am. Chem. Soc. DiV. Polym. Mater. Sci. Eng. 1993, 68, 41. (4) (a) DeSimone, J. M.; Guan, Z.; Elsbernd, C. S. Science 1992, 257, 945. (b) Guan, Z.; Combes, J. R; Menceloglu, Y. Z.; DeSimone, J. M. Macromolecules 1993, 26, 2663. (5) Laintz, K. E.; Yonker, C. R.; Smith, R. D.; Wai, C. M. J. Supercrit. Fluids 1991, 4, 194. (6) Consani, K. A.; Smith, R. D. J. Supercrit. Fluids 1990, 3, 51. (7) (a) Hoefling, T. A.; Enick, R. M.; Beckman, E. J. J. Phys. Chem.
J. Phys. Chem., Vol. 100, No. 18, 1996 7439 1991, 95, 7127. (b) Newman, D. A.; Hoefling, T. A.; Beitle, R. R.; Beckman, E. J.; Enick, R. M. J. Supercrit. Fluids 1993, 6, 205. (8) Harrison, K.; Goveas, J.; Johnston, K. P.; O’Rear, E. A. Langmuir 1994, 10, 3536. (9) (a) DeSimone, J. M.; Maury, E. E.; Menceloglu, Y. Z.; McClain, J. B.; Romack,T. J.; Combes, J. R. Science 1994, 265, 356. (b) Guan, Z.; DeSimone, J. M. Macromolecules 1994, 27, 5527. (10) Yee, G. G; Fulton, J. L.; Smith, R. D. J. Phys. Chem. 1992, 96, 6172. (11) (a) Kirkwood, J. G. J. Chem. Phys. 1934, 2, 351. (b) Bauer, E.; Magat, M. J. Phys. Radium 1938, 9, 319. (12) Battersby, P.; Dean, J. R.; Hitchen, S. M.; Tomlinson, T. W. J. Comput. Chem. 1994, 15, 580. (13) Terzis, A. F.; Samulski, E. T. Chem. Phys. Lett. in press. (14) Politzer, P.; Murray, J. S.; Lane, P.; Brink, T. J. Phys. Chem. 1993, 97, 729. (15) Spartan V3.1 Wavefunction Inc., 1804 Von Karman Ave., Irvine, CA, 92715. (16) O’Shea, K.; Kirmse, K.; Fox, M. A.; Johnston, K. P. J. Phys. Chem. 1991, 95, 7863.
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