Spectroscopic Interpretation of Silver Ion Complexation with Propylene

Center for Facilitated Transport Membranes, Korea Institute of Science and Technology, P.O. Box 131,. Cheongryang, Seoul 130-650, South Korea, and ...
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J. Phys. Chem. B 2002, 106, 2786-2790

Spectroscopic Interpretation of Silver Ion Complexation with Propylene in Silver Polymer Electrolytes Jong Hak Kim,†,‡ Byoung Ryul Min,‡ Chang Kon Kim,†,§ Jongok Won,† and Yong Soo Kang†,* Center for Facilitated Transport Membranes, Korea Institute of Science and Technology, P.O. Box 131, Cheongryang, Seoul 130-650, South Korea, and Department of Chemical Engineering, Yonsei UniVersity, Seoul 120-749, South Korea ReceiVed: February 7, 2001; In Final Form: October 30, 2001

Propylene solubility is almost 2-fold higher in 1:1 poly(2-ethyl-2-oxazoline) (POZ):AgBF4 or poly(vinyl pyrrolidone) (PVP):AgBF4 than in 1:1 POZ:AgCF3SO3 or 1:1 PVP:AgCF3SO3, according to our previous work. It is confirmed in this paper that the CdC stretching band of propylene coordinated with silver cations in 1:1 PVP:AgBF4 is about 2-fold more intense than that in 1:1 PVP:AgCF3SO3. This difference in solubility is investigated here in terms of the differences in the interactions of silver cations with the different anions of the dissolved salts and hence with the carbonyl oxygen atoms of POZ. The strength of interaction between silver cations and carbonyl oxygen, as characterized by the band shift of the complexed CdO bands, arises in the order AgBF4 > AgCF3SO3 > AgNO3, whereas the interaction between the cation and anion, as determined by Raman spectroscopy of ion pairing behavior, shows the order AgBF4 < AgCF3SO3 < AgNO3. In addition, these measured differences between the ionic interactions are in agreement with theoretical ab initio calculations of the complexation and bond dissociation energies. It is concluded that AgBF4 polymer electrolytes, with their strong silver cation/carbonyl oxygen and weak silver cation/anion interactions, exhibit more favorable silver cation complexation of propylene molecules, resulting in higher propylene solubility. Interestingly, we also found that when propylene is introduced into silver polymer electrolytes propylene molecules compete with carbonyl oxygen for coordination with silver cations.

Introduction Solid polymer electrolytes (SPE) are complexes of solventfree polymer with metal salts, which are formed by dissolving such salts in high molecular weight polar polymer hosts. SPEs have received considerable attention over the past decades because of their potential for use in applications such as solidstate batteries, fuel cells, chemical sensors, etc.1-3 Research has particularly been directed toward understanding the complex chemistry and ion transport properties of these materials.4,5 Recently, SPE containing silver ions have been of special interest, owing to their possible use in applications such as facilitated transport membranes for olefin/paraffin separations.6-10 It is well-known that silver ions can reversibly react with olefin molecules to form silver-olefin complexes. Silver ions dissolved in a polymer matrix have thus been used as carriers in facilitated transport membranes for olefin/paraffin separation.6-10 In recent papers, we have described the facilitated transport of propylene through silver polymer electrolyte membranes that are made from AgBF4 or AgCF3SO3 dissolved in poly(2-ethyl-2-oxazoline) (POZ) or in poly(N-vinyl pyrrolidone) (PVP).6,10 It was found in this work that: (1) POZ:AgBF4 polymer electrolyte membranes with a 1:1 mole ratio of [CdO]: [Ag] show better separation properties than 1:1 POZ:AgCF3SO3; (2) the former exhibit almost 2-fold higher propylene * To whom correspondence should be addressed. Tel: +82-2-958-5362; Fax: +82-2-958-6869. E-mail: [email protected]. † Center for Facilitated Transport Membranes, Korea Institute of Science and Technology. ‡ Department of Chemical Engineering, Yonsei University. § Current address: Department of Chemistry, Inha University, Inchon, South Korea.

solubility than the latter; (3) the differences between the polymeric matrixes of POZ and PVP have little effect on membrane performance; and (4) propylene solubility in 1:1 POZ:AgBF4 membranes is almost 25-fold higher than in pure POZ membranes. In this study, the variation in the solubility of propylene in polymer electrolytes containing AgBF4, AgCF3SO3, and AgNO3 is investigated spectroscopically. In particular, the effect on the complexation of propylene with silver cations of the differences in the interactions of the silver cations with their respective anions, and hence with the carbonyl oxygen atoms of the polymer matrixes, will be emphasized. Complexation energies and bond dissociation energies calculated by the ab initio method are also reported to support the observed differences in the ionic interactions. Experimental Section Poly(2-ethyl-2-oxazoline) (POZ) (Mw ) 5 × 105) and all silver salts, including silver tetrafluoroborate (AgBF4), silver triflate (AgCF3SO3), and silver nitrate (AgNO3), were purchased from Aldrich Chemical Co. Poly(N-vinyl pyrrolidone) (PVP) (Mw ) 1 × 106) was supplied by Polyscience Inc. All chemicals were used without further purification. Depending on the desired mole ratio of [CdO]:[Ag], predetermined amounts of POZ and silver salts were dissolved in methanol to make up solutions of 10 wt % The solutions were then cast on a Teflon-glass plate and dried in an N2 environment. The films were further dried in a vacuum oven for 2 days at room temperature. IR measurements were performed on a 6030 Mattson Galaxy Series FT-IR spectrometer; 250-250 scans were signal-averaged at a

10.1021/jp010481o CCC: $22.00 © 2002 American Chemical Society Published on Web 02/14/2002

Silver Ion Complexation with Propylene

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Figure 1. The solubility of propylene in silver polymer electrolytes at 25 °C vs propylene pressure.10

Figure 2. FT-IR spectra of pure POZ and POZ:AgNO3 complexes with varying [CdO]:[Ag] mole ratios.

resolution of 1 cm-1. Raman spectra were collected for POZ: silver salt films at RT using Perkin-Elmer System 2000 NIR FT-Raman at a resolution of 1 cm-1. This experimental apparatus included a neodymium-doped yttrium aluminum garnet (Nd:YAG) laser operating at 1064 nm. Spectroscopic characterization was performed using a pressure cell equipped with CaF2 windows.

TABLE 1: Position of the Carbonyl Band in Pure POZ and in POZ Complexesa system pure POZ POZ:AgBF4 POZ:AgCF3SO3 POZ:AgNO3

FT-IR cm-1

1641 1595 cm-1 1601 cm-1 1605 cm-1

FT-Raman 1641 cm-1 1607 cm-1 1612 cm-1 1619 cm-1

Complexes with AgBF4, AgCF3SO3, and AgNO3 ([CdO]:[Ag] ) 1:1 mole ratio), as determined by IR and Raman spectroscopy. a

Theoretical Calculations Electronic energies were calculated by full optimization, without any geometrical constraint, of Becke’s three parameter hybrid functional,11 using the Lee, Yang, and Parr correlation functional12 with the 6-31+G(d) basis set,13 except for the use of Effective Core Potential (ECP) basis sets of type LANL2DZ14 for the transition metal element, Ag. In the calculations we used 6D-Cartesian functions for d-orbitals in order to obtain more accurate results for energies. The nature of all stationary species was verified by the vibrational frequencies.15 Gibbs free energy changes (∆G) were calculated from the electronic energy change (∆E) corrected for zero-point vibration energies (∆Ezpe), thermal energies (∆ET), and applied entropies (∆S) at 298 K, as given by eq 1.16 The Gaussian 98 program package17 was used throughout in this work.

∆G ) (∆E + ∆Ezpe + ∆ET) - T ∆S ) ∆H - T ∆S (1) Results and Discussion Propylene Solubility. Figure 1 shows the variation of the solubility of propylene in silver polymer electrolyte films at 25 °C with the pressure of propylene.10 The mole ratio of carbonyl oxygen to silver ions was fixed at 1:1. It is apparent that the solubility of propylene in the AgBF4 electrolyte is much higher than in the AgCF3SO3 electrolyte, and that the effect of the differences between the polymers POZ and PVP on the solubility is marginal. The former is approximately 2-fold higher than the latter. Polymer electrolytes containing AgNO3 exhibit very poor propylene solubility. For example, AgBF4 in poly(ethylene oxide) (PEO) absorbs 8.5 g of propylene per 100 g of polymer electrolyte whereas AgNO3 in PEO absorbs only 0.52 g.18 This dependence of the solubility of propylene in silver polymer electrolytes on the anion type will be interpreted here in terms of the interactions of the silver ion with the anion, with the carbonyl oxygen atoms of the polymers, and with the double bond of propylene.

The Interaction between the Silver Cation and Carbonyl Oxygen. It has been reported that silver salts such as AgBF4 and AgCF3SO3 coordinate to a different extent with the carbonyl oxygen atoms of POZ.19 The IR spectra of carbonyl stretching in POZ:AgNO3 complexes in the range 1800-1300 cm-1 are presented in Figure 2. The free CdO stretching band of uncomplexed POZ appears at 1641 cm-1; the intensity of this band diminishes, and a new band at 1605 cm-1 appears and grows, with increasing silver salt content. This new band is thought to be associated with the coordination interaction between silver ions and carbonyl oxygen. The shift of the free CdO band to a lower wavenumber originates from the loosening of the CdO double bond by this coordination. Therefore, the strength of the coordination interaction between silver cations and the POZ matrix can be estimated in terms of the magnitude of this band shift. The positions of the carbonyl band in pure POZ and in its complexes ([CdO]:[Ag] ) 1:1 mole ratio) with AgBF4, AgCF3SO3, and AgNO3, as detected by IR and Raman spectroscopy in the 1750 to 1500 cm-1 range, are shown in Table 1. The extent of band shift toward a lower wavenumber region occurs in the following sequence: AgBF4 > AgCF3SO3 > AgNO3. Therefore, it is concluded that the strength of interaction between silver cations and carbonyl oxygen has the above order. The Interaction between Silver Cations and Anions. The strength of the interaction between silver cations and their respective anions may dictate the identity of the ionic constituents: the possibilities include free ions, ion pairs, and higher order aggregates. For instance, free ions are more likely to be formed on dissolution of the salts in the polymer solvents when the cation/anion interaction is weak. Therefore, assessing the strength of these interactions is important for the characterization of the ionic constituents, and consequently for developing an understanding of the interaction between silver ions and olefin

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Kim et al.

Figure 3. FT-Raman spectra for the NO3- stretching mode of POZ: AgNO3 complexes for varying [CdO]:[Ag] mole ratios.

molecules. The Raman spectra of POZ complexes with AgNO3 were recorded from 7:1 to 1:1 mole ratios of [CdO]:[Ag]. Figure 3 shows the Raman spectra of the ν1 symmetric stretching vibration of the NO3- anion for POZ:AgNO3. Only a single band at 1034 cm-1 for mole ratios from 7:1 to 2:1 POZ:AgNO3 is seen, which is associated with the presence of the free NO3anion.20 However, when the salt concentration is increased to [CdO]:[Ag])1:1, the main band shifts to a higher wavenumber (1040 cm-1). This shift is thought to be associated with ion pair formation. The Raman spectra of POZ:AgBF4 complexes in the region where medium intensity bands arise from the ν1 symmetric stretching mode of the BF4- anion were also recorded.20 The position of the band at 765 cm-1, which is attributed to the free BF4- anion, remains invariant with increasing silver salt concentration. Therefore, it can be concluded that the presence of ion pairs is unlikely and that free ions are the dominant ionic constituent in POZ:AgBF4 for mole ratios up to 1:1. The Raman spectra of the ν1 symmetric stretching vibration of the SO3- anion in POZ:AgCF3SO3 were also measured. According to previous assignments, the 1031 cm-1 band originates from the free SO3- anion.19-21 A single band at 1031 cm-1 was evident for concentrations up to 2:1, and for higher concentrations the main band shifted slightly to a higher wavenumber region (1034 cm-1), demonstrating the presence of ion pairs. This suggests that, since ion pairs are more likely to be formed in 1:1 POZ:AgCF3SO3 than in 1:1 POZ:AgBF4, the silver cation/anion interaction is stronger in the former than in the latter. In summary, free ions are dominant for concentrations up to 1:1 POZ:AgBF4, whereas ion pairs start to form at concentrations above 2:1 in POZ:AgCF3SO3 and POZ:AgNO3. This result demonstrates that the silver cation/ anion interaction is weaker in POZ:AgBF4 relative to such interactions in POZ:AgCF3SO3 and POZ:AgNO3. Papke et al.20 carried out research on the complexes of PEO with Li salts using Raman spectroscopy and reported that the ion pair vibrational mode appeared at a higher wavenumber than the free ion mode owing to the stronger cation/anion interaction within the ion pair. To identify the ionic species in POZ complexes with AgCF3SO3 and AgNO3, the stretching bands of the SO3- and NO3- anions were deconvoluted into contributions from free ions and ion pairs, as shown in Figure 4. In polymer electrolytes containing AgCF3SO3, the bands of the SO3- stretching mode assigned to free ion, ion pair, and ion aggregates appear at 1032, 1038, and 1048 cm-1, respectively.19 The bands of NO3- ionic species at 1034, 1040, and 1045 cm-1 are attributed to free ion, ion pair, and ion aggregates,

Figure 4. The deconvoluted curves for the free ion and ion pair contributions in POZ complexes with AgCF3SO3 and AgNO3 (1:1 mole ratio).

respectively. Figure 4 demonstrates that 1:1 POZ:AgCF3SO3 has a much higher concentration of free ions than 1:1 POZ: AgNO3. The deconvoluted peaks confirm that the silver cation/ anion interaction is stronger in POZ:AgNO3 than in POZ: AgCF3SO3 or POZ:AgBF4. Therefore, the strength of interaction between the silver cations and their anions occurs in the order AgNO3 > AgCF3SO3 > AgBF4, which is consistent with the lattice energies of the salts.22 Comparison between Spectroscopic and Theoretical Results. The complexation between silver salts and polymer containing carbonyl groups can be written as follows when the mole ratio of [CdO]:[Ag] is 1:1.

The complexation energy, ∆EC (or ∆GC), is the energy difference in eq 2, which was calculated by density functional theory at B3LYP level. The bond dissociation energy, ∆EBD (or ∆GBD), represented by eq 3, was also calculated and is summarized in Table 2.

A large negative value of ∆EC (or ∆GC) represents a strong interaction between silver cations and the carbonyl oxygen atoms of the polymer matrix. On the other hand, a large positive value of ∆EBD (or ∆GBD) represents a strong interaction between silver cations and their anions. Therefore, it is expected that the POZ: AgBF4 complex, with both the highest negativity of ∆EC (or ∆GC) and the lowest positivity of ∆EBD (or ∆GBD), will exhibit strong silver cation/polymer and weak silver cation/anion

Silver Ion Complexation with Propylene

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TABLE 2: Complexation Energies and Heterolytic Bond Dissociation Energies at B3LYPa Level for POZ:Ag Salt Complexes at 298 K complexation energyb

bond dissociation energyc

POZ complexes

∆EC (kcal/mol)

∆GC (kcal/mol)

∆EBD (kcal/mol)

∆GBD (kcal/mol)

AgBF4 AgClO4 AgCF3SO3 AgNO3

-27.00 -26.83 -26.39 -25.14

-16.66 -15.44 -15.68 -13.57

98.99 102.88 103.77 116.40

89.16 92.16 94.11 106.16

a Calculations were carried out using the general basis set method, i.e., 6 - 31 + G(d) for the 1st and 2nd row elements and the LANL2DZ basis set for Ag. b The complexation energy is the energy difference between separated POZ+AgX and [POZ-AgX] complexes. c The bond dissociation energy is the energy difference between [POZ-AgX] and [POZ-Ag]+ + X-.

Figure 5. FT-IR spectra of PVP:Ag salt complexes with and without propylene sorption ([CdO]:[Ag])1:1 mole ratio). The solid and the dotted lines represent the data with and without propylene, respectively. The inserted figures indicate the deconvoluted curves for the contributions of the carbonyl bond of PVP coordinated with silver ion and of the double bond of propylene complexed with silver ion. (a) PVP:AgBF4 (b) PVP:AgCF3SO3 (c) PVP:AgNO3.

interactions. This calculation is consistent with the experimental spectroscopy study. The Interaction between Silver Cations and Propylene. The interaction between silver cations and propylene was investigated by IR spectroscopy as shown in Figure 5. Since the bands of the double bond of propylene, which is complexed with silver ion in POZ electrolytes, overlapped with carbonyl bands in POZ:silver salt complexes at around 1586 cm-1, PVP complexes were used instead. (The differences between the polymeric matrixes of POZ and PVP do not have a significant effect on propylene complexation with the silver ion.6,10) When 1:1 PVP:AgBF4 electrolyte was exposed to 40 psig of propylene for 1 h and subsequently purged with N2, the main CdO band shifted from 1630 cm-1 to a higher wavenumber of 1640 cm-1 and a new shoulder band appeared at 1586 cm-1. This new shoulder peak represents the coordination of the CdC stretching vibration of propylene with silver ions (ν1 and ν2 of CdC in free propylene are 1665 and 1640 cm-1, respectively). The shift to higher wavenumber of CdO bond stretching from 1630 to 1640 cm-1 after propylene sorption indicates that the interaction between silver ions and carbonyl oxygen is weakened by the coordination of propylene to silver ions. This strongly suggests that propylene molecules compete with the carbonyl groups of PVP for the coordination sites of silver ions. In the case of the PVP:AgCF3SO3 electrolyte, the shoulder peak also appeared

with medium intensity at 1586 cm-1 after propylene sorption. On the other hand, for PVP:AgNO3 the variation in these bands from prior to propylene sorption to after propylene sorption was minimal, implying that no specific complexation of propylene with silver ions occurs. For quantitative analysis of the intensity of complexation of propylene and silver ions, the FT-IR spectra of PVP:Ag salt complexes absorbing propylene were deconvoluted into the contributions from CdO stretching in PVP and from the CdC stretching of coordinated propylene. The absorbance area of the coordinated CdC vibration peak in PVP: AgBF4 is 6.20 and that in PVP:AgCF3SO3 is 3.27 (a.u.). This suggests that the intensity of complexation of propylene and silver ions in PVP:AgBF4 is around 2-fold higher than that in PVP:AgCF3SO3. This spectroscopic result is consistent with the gravitationally measured propylene solubility shown in Figure 1.10 According to this spectroscopic result, we expect that the solubility of propylene in AgNO3 electrolytes will be very low. In previous research,10 we proposed the importance of the bond length of the bond between silver ions and their closest anion atom for the solubility of propylene in silver polymer electrolytes. The bond length of the bond between silver ions and their closest anion atom is influenced by the relative strength of the interactions of silver ions with the anions and the polymer matrix as well as by steric effects. The longer the bond length, the weaker the interaction of silver ions with anions and the stronger the interaction with the polymer matrix. Therefore, since the POZ:AgNO3 complex has weak silver cation/polymer and strong silver cation/anion interactions according to IR and Raman spectroscopy, it is expected to exhibit short bond lengths in the bonds between silver cations and the closest anion atoms, resulting in lower solubility of propylene in silver nitrate polymer electrolytes. Conclusions IR and Raman spectroscopy were used to characterize the relative strengths of the interactions of silver ions with anions, such as BF4-, CF3SO3-, and NO3-, and their polymer hosts POZ and PVP. In addition, the intensity of complexation of silver ions and propylene was observed using IR, and was interpreted in terms of the interactions of silver cations with carbonyl oxygen and of the cations with the anions. The experimental conclusions as to the relative intensity of such interactions were supported by the complexation and bond dissociation energies that were calculated by density functional theory at B3LYP level. We concluded that the observed higher solubility of propylene in POZ:AgBF4 than in POZ:AgCF4SO3 or POZ:AgNO3 may be predominantly resulting from strong silver cation/carbonyl oxygen and weak cation/anion interactions. Acknowledgment. The authors gratefully acknowledge financial support from the Ministry of Science and Technology of Korea through the Creative Research Initiatives Program. References and Notes (1) Wright, P. V. Br. Polym. J. 1975, 7, 319. (2) Killis, A.; LeNest, J. F.; Gandini, A.; Cheradame, H.; Cohen, J. P. Solid State Ionics 1984, 14, 231. (3) Vallee, A.; Besner, S.; Prud′homme, J. Electrochim. Acta 1992, 37, 1579. (4) Schantz, S.; Torrel, L. M.; Stevens, J. R. J. Chem. Phys. 1991, 94, 6862. (5) Edman, L.; Doeff, M. M.; Ferry, A.; Kerr, J.; Jonghe, L. C. De. J. Phys. Chem. B 2000, 104, 3476. (6) Yoon, Y.; Won, J.; Kang, Y. S. Macromolecules 2000, 33, 3185.

2790 J. Phys. Chem. B, Vol. 106, No. 10, 2002 (7) Hong, S. U.; Jin, J. H.; Won, J.; Kang, Y. S. AdV. Mater. 2000, 12, 968. (8) Kim, J. H.; Min, B. R.; Kim, C. K.; Won, J.; Kang, Y. S. Macromolecules 2001, 34, 6052. (9) Pinnau, I.; Toy, L. G.; Casillas, C. U.S. Patent 5, 670, 051, 1997. (10) Hong, S. U.; Kim, C. K.; Kang, Y. S. Macromolecules 2000, 33, 7918. (11) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (12) (a) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. 1988, B37, 785. (b) Miehlich, B.; Savin, A.; Stoll, H.; Preuss, H. Chem. Phys. Lett. 1989, 157, 200. (13) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab initio Molecular Orbital Theory; John Wiley & Sons: New York, 1986; Chapter 4. (14) (a) Hay, P. J.; Wadt, W. R. J. Chem. Phys. 1985, 82, 270. (b) Wadt, W. R.; Hay, P. J. J. Chem. Phys. 1985, 82, 284. (c) Hay, P. J.; Wadt, W. R. J. Chem. Phys. 1985, 82, 299. (15) (a) Pople, J. A.; Krishnan, R.; Schlegel, H. B.; Binkley, J. S. Int J. Quantum Chem. 1979, S13, 225. (b) Pople, J. A.; Schlegel, H. B.; Krishnan, R.; DeFree, D. J.; Binkley, J. S.; Frisch, M. J.; Whiteside, R. A.; Haut, R. F.; Hehre, W. J. Int J. Quantum Chem. 1979, S15, 269. (16) Foresman, J. B.; Frisch, Æ. Exploring Chemistry with Electronic Structure Methods, 2nd ed.; Gaussian Inc.; Pittsburgh, 1996; p 166.

Kim et al. (17) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A., Jr.; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Gonzalez, C.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Andres, J. L.; Gonzalez, C.; Head Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian 98, revision A.6; Gaussian, Inc.: Pittsburgh, PA, 1998. (18) Sunderrajan, S.; Freeman, B. S.; Hall, C. K. Ind. Eng. Chem. Res. 1999, 38, 4051. (19) Jin, J. H.; Hong, S. U.; Won, J.; Kang, Y. S. Macromolecules 2000, 33, 4932. (20) Papke, B. L.; Ratner, M. A.; Shriver, D. F. J. Electrochem. Soc. 1982, 129, 1434. (21) Schantz, S.; Torell, L. M.; Stevens, J. R. J. Chem. Phys. 1991, 94, 6862. (22) Kim, C. K.; Won, J.; Kim, H. S.; Kang, Y. S.; Li, H. G.; Kim, C. K. J. Comput. Chem. 2001, 22 (8), 827.