Conductivity Dependence of PEG Content in an Anhydrous Proton

Chem. Mater. , 2005, 17 (3), pp 661–669. DOI: 10.1021/cm0486969. Publication Date (Web): January 13, 2005. Copyright © 2005 American Chemical Socie...
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Chem. Mater. 2005, 17, 661-669

661

Conductivity Dependence of PEG Content in an Anhydrous Proton Conducting Sol-Gel Electrolyte Braja D. Ghosh, Kyle F. Lott, and Jason E. Ritchie* Department of Chemistry and Biochemistry, The UniVersity of Mississippi, UniVersity, Mississippi 38677 ReceiVed August 7, 2004. ReVised Manuscript ReceiVed NoVember 19, 2004

Proton conducting electrolytes composed of mixtures of a MePEGnSO3H acid and a sol-gel based MePEGn polymer have been prepared. These solutions display anhydrous proton conductivity reaching a maximum value of 1.38 × 10-5 S/cm at 55 °C with a 1.32 M mixture of MePEG16SO3H dissolved in the MePEG12 polymer. The molar equivalent conductivity of the MePEGnSO3H acid is correlated with the volume fraction of PEG present in the mixture. This result indicates that conductivity in these solutions of acid and polymer is a function of the PEG content strongly suggesting the presence of a Grotthus mechanism of conductivity. In addition, we show the lack of a dependence of ionic and equivalent conductivity on the size of the MePEGnSO3H acid, indicating little to no contribution to conductivity from the vehicle mechanism.

Introduction Proton conducting polymer electrolytes have important electrochemical applications in devices such as fuel cells and electrochromic displays. Nafion (a sulfonated fluoropolymer) is the most widely used proton exchange membrane because of its mechanical properties, its chemical stability, and its high proton conductivity when hydrated. However, Nafion membranes require hydration, which limits its maximum operating temperature to around 100 °C. At these relatively low temperatures, the tolerance of the electrocatalyst against CO poisoning is low. Thus, a new electrolyte material is needed that can operate at high temperatures and low relative humidities. Our groups’ goal is to gain a fundamental understanding of the mechanism of proton conductivity in our MePEG polymer.1 Understanding how molecules and ions travel through polymeric electrolytes is a fundamental question of great significance.2-4 Ethylene oxide based materials are known to conduct Li+ through segmental motions of the ethylene oxide units2 which are dependent on the glass transition temperature (Tg) of the material. Similarly, there are two general mechanisms for proton conductivity: the vehicle mechanism (which relies on the physical transport of a vehicle to move protons) and the Grotthus mechanism (which involves the proton being handed off from one hydrogen bonding site to another).3 The Grotthus mechanism of H+ conductivity is similar to Li+ conductivity in these materials that rely on ethylene oxide segmental motions and the rate of polymer reorganization. The vehicle mechanism of H+ conductivity is governed by the rate of physical diffusion of the vehicle. * Corresponding author. E-mail: [email protected].

(1) (2) (3) (4)

Ritchie, J. E.; Crisp, J. A. Anal. Chim. Acta 2003, 496, 65-71. Ratner, M. A.; Shriver, D. F. Chem. ReV. 1988, 88, 109-124. Kreuer, K. D. Chem. Mater. 1996, 8, 610-641. Paddison, S. J.; Paul, R.; Zawodzinski, T. A., Jr. J. Chem. Phys. 2001, 115, 7753-7761.

Several recent reports have highlighted thermally stable polymeric materials with high proton conductivities.5-15 In addition, our group has shown an interesting concentration dependence of the ionic conductivity in a mixture of MePEG7SO3H acid (5b) and our MePEG polymer (4b) that seems to indicate a change in the mechanism of conductivity as a function of added acid concentration.1 Our hypothesis is that the H+ transport is accomplished primarily through a Grotthus mechanism. In addition, we hypothesize that H+ transport is dependent on the volume fraction of poly(ethylene glycol) (PEG) present and that the Grotthus mechanism will dominate at high PEG volume fractions. The materials used in this paper are based on low molecular weight PEGs, which are typically viscous liquids or soft, waxy solids that are known for their ability to dissolve and conduct small cations. The proton conducting electrolytes described in this paper are amorphous and incorporate siloxane groups. The ability of PEG-based polymers to both provide coordination sites for small cations and rapidly reorganize their polymer segments makes this system (5) Schuster, M. F. H.; Meyer, W. H.; Schuster, M.; Kreuer, K. D. Chem. Mater. 2004, 16, 329-337. (6) Depre, L.; Ingram, M.; Poinsignon, C.; Popall, M. Electrochim. Acta 2000, 45, 1377-1383. (7) Zukowska, G.; Chojnacka, N.; Wieczorek, W. Chem. Mater. 2000, 12, 3578-3582. (8) Ericson, H.; Svanberg, C.; Brodin, A.; Grillone, A. M.; Panero, S.; Scrosati, B.; Jacobsson, P. Electrochim. Acta 2000, 45, 1409-1414. (9) Miyatake, K.; Iyotani, H.; Yamamoto, K.; Tsuchida, E. Macromolecules 1996, 29, 6969-6971. (10) Miyatake, K.; Fukushima, K.; Takeoka, S.; Tsuchida, E. Chem. Mater. 1999, 11, 1171-1173. (11) Tanaka, R.; Yamamoto, H.; Shono, A.; Kubo, K.; Sakurai, M. Electrochim. Acta 2000, 45, 1385-1389. (12) Tsuruhara, K.; Rikukawa, M.; Sanui, K.; Ogata, N.; Nagasaki, Y.; Kato, M. Electrochim. Acta 2000, 45, 1391-1394. (13) Kawahara, M.; Morita, J.; Rikukawa, M.; Sanui, K.; Ogata, N. Electrochim. Acta 2000, 45, 1395-1398. (14) Bermudez, V. D. Z.; Armand, M.; Poinsignon, C.; Abello, L.; Sanchez, J. Y. Electrochim. Acta 1992, 37, 1603-1609. (15) Herz, H. G.; Kreuer, K. D.; Maier, J.; Scharfenberger, G.; Schuster, M. F. H.; Meyer, W. H. Electrochim. Acta 2003, 48, 2165-2171.

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attractive because of the likelihood of relatively fast Grotthus conductivity under anhydrous conditions. Furthermore, Murray and co-workers have reported that the attachment of oligomeric PEG “tails” to normally crystalline organic materials is a general route to amorphous materials.16-19 Dunn and Kaner have reported that the mixing of poly(ethylene oxide) into a silica sol-gel imparts plasticity to the resulting hybrid material.20 Moreover, proton conductors based on PEGs have been described.14,21,22 Several research groups are examining Li+ conductivity in PEG-based materials. West, Hooper, and Lyons are studying lithium ion conductivity in polysiloxane comb polymers with PEG “bristles” that are structurally similar to our MePEGn polymer.23 Shriver and co-workers have prepared Li+ conducting polymers containing trifluoromethylsulfonamide anions and PEG side chains bound to a polysiloxane, and they report that the flexible polymer structure results in a high concentration of charge carriers and good ionic conductivity.24 In addition, Shriver’s group has also examined Li+ conduction in mixtures of PEG and inert fillers such as SiO2 and Al2O3 and found that the filler has little influence on ionic conductivity.25 Angell and coworkers have prepared poly[(ethylene glycol)oxalate], a new Li+ conducting polymer, which they report has a higher dielectric constant than PEO.26 This work is exciting because our system is a member of the relatively rare class of polymeric materials that display H+ conductivity in the absence of water or plasticizing solvent. Experimental Section Tri(ethylene glycol) monomethyl ether (CH3(OCH2CH2)3OH, Aldrich), poly(ethylene glycol) monomethyl ether (CH3(OCH2CH2)nOH ) MePEGnOH, n ) 7.24, 12.0, 16.3; Mn ) 350, 550, 750; Aldrich) were dried at 60 °C under vacuum (∼10 mTorr) for 24 h. For clarity, this paper will refer to tri(ethylene glycol) monomethyl ether as MePEG3, the Mn ) 350 poly(ethylene glycol) monomethyl ether as MePEG7, the Mn ) 550 material as MePEG12, and the Mn ) 750 material as MePEG16. Triethoxysilane (Aldrich), sodium hydride (Aldrich), sodium sulfite (Fisher), phosphorus tribromide (Aldrich), and anhydrous pyridine (Acros) were used as received. Tetrahydrofuran was dried by distillation from Na/ benzophenone under N2. (16) Ritchie, J. E.; Murray, R. W. J. Phys. Chem. B 2001, 105, 1152311528. (17) Dickinson, E.; Masui, H.; Williams, M. E.; Murray, R. W. J. Phys. Chem. B 1999, 103, 11028-11035. (18) Ritchie, J. E.; Murray, R. W. J. Am. Chem. Soc. 2000, 122, 29642965. (19) Williams, M. E.; Masui, H.; Long, J. W.; Malik, J.; Murray, R. W. J. Am. Chem. Soc. 1997, 119, 1997-2005. (20) Wu, P.-W.; Holm, S.; Duong, A.; Dunn, B.; Kaner, R. Chem. Mater. 1997, 8, 1004-1011. (21) Pedone, D.; Armand, M.; Deroo, D. Solid State Ionics 1988, 28-30, 1729-1732. (22) Qiao, J.; Yoshimoto, N.; Ishikawa, M.; Morita, M. Chem. Mater. 2003, 15, 2005-2010. (23) Zhang, Z.; Sherlock, D.; West, R.; West, R.; Amine, K.; Lyons, L. J. Macromolecules 2003, 36, 9176-9180. (24) Siska, D. P.; Shriver, D. F. Chem. Mater. 2001, 13, 4698-4700. (25) Johansson, P.; Ratner, M. A.; Shriver, D. F. J. Phys. Chem. B 2001, 105, 9016-9021. (26) Xu, W.; Belieres, J.-P.; Angell, C. A. Chem. Mater. 2001, 13, 575580.

Ghosh et al. The densities of dry polymer and acid samples were measured gravimetrically by drawing the neat liquid into a tared 2 mL micropipet which was weighed using an ATI Cahn C-33 microbalance. Concentrations of neat MePEGnSO3H acids (5) were calculated by dividing the density (g/mL) of the neat acid by its molecular weight (MW; g/mol), yielding mol/mL (reported in mol/L) (eq 1). Concentrations of mixtures of the MePEGnSO3H acid and MePEGn polymer were calculated by (1) converting the mass of the MePEG polymer to volume (using its density), (2) converting the mass of the MePEG acid to volume, and (3) converting the mass of the MePEG acid to moles and dividing by the total volume of the acid + polymer. This approach specifically assumes that the volumes are additive (Table S-1 in Supporting Information). concnsample )

density (g/cm3) mol ) 3 MW (g/mol) cm

(1)

Electrochemical measurements were made with a PAR 283 potentiostat equipped with a Perkin-Elmer 5210 lock-in amplifier for ac-impedance measurements using PowerSine software. The construction and use of the electrodes have been described previously.1,27 Variable temperature measurements were made with electrodes in a jacketed cell connected to a circulator.27 Gel permeation chromatography (GPC) measurements were made with a Polymer Laboratories ELS 2100 evaporative light scattering detector and two 30 cm PL Mixed-D analytical columns. Polystyrene molecular weight standards (PL-EasiCal PS-2, MW range 580-400K) were used to calibrate the instrument prior to running unknown samples. NMR measurements were made with either a Bruker AC-300 or a Bruker DRX-500. Synthesis of Poly(ethylene glycol) Allyl Methyl Ether (MePEG3OCH2CHCH2) (2a). This material was prepared analogously to a method described by Hooper et al.28,29 and Siska and Shriver.24 Here, NaH (4.60 g, 192 mmol) and THF (35 mL) were added to an air-free round-bottom flask. Dry tri(ethylene glycol) methyl ether (MePEG3OH, 30.00 g, 182.9 mmol) was dissolved in ∼20 mL of dry THF and added dropwise to the NaH/THF slurry. The mixture was stirred at room temperature (RT), under argon, for 30 min to complete the deprotonation. Allyl bromide (22.57 g, 187 mmol) was dissolved in 10 mL of THF and added dropwise to the reaction mixture (a white precipitate of NaBr appeared upon addition). The reaction was stirred at RT for 5 h, followed by the addition of ∼5 mL of wet acetone to quench any unreacted NaH. The NaBr precipitate was removed by filtration, and the filtrate was extracted with 50 mL of 0.5 M NaCl and 3 × 75 mL of CHCl3. The organic fraction was dried (Na2SO4) and concentrated by rotary evaporation, yielding a clear and colorless liquid (2a) (33.25 g, 163.0 mmol, 89.1%). NMR (1H, in CDCl3), δ (ppm) 3.35 (s, 3H), 3.51-3.70 (m, 12H), 3.99 (m, 2H), 5.20 (dd, 2H), 5.88 (m, 1H). NMR (13C, in CDCl3), δ (ppm) 58.43, 68.94, 70.01-70.12, 71.44, 71.44, 116.32, 134.37. Synthesis of Poly(ethylene glycol) Allyl Methyl Ether (MePEG7OCH2CHCH2) (2b) was prepared similarly to (2a) with the following amounts: NaH (2.07 g, 86.3 mmol), MePEG7OH (28.67 g, 81.90 mmol), and allyl bromide (10.14 g, 83.80 mmol). Yield: 33.34 g (85.49 mmol, 104% yield). The 1H and 13C NMR spectra of the product have a complete absence of the -CH2OH and -CH2Br proton resonances and -CH2OH and -CH2Br carbon (27) Wooster, T. T.; Longmire, M. L.; Zhang, H.; Watanabe, M.; Murray, R. W. Anal. Chem. 1992, 64, 1132-1140. (28) Hooper, R.; Lyons, L. J.; Moline, D. A.; West, R. Organometallics 1999, 18, 3249-3251. (29) Hooper, R.; Lyons, L. J.; Mapes, M. K.; Schumacher, D.; Moline, D. A.; West, R. Macromolecules 2001, 34, 931-936.

Proton ConductiVity in Sol-Gel Electrolyte resonances from the starting materials, indicating a complete conversion to the product. We conclude the excess yield is due to adsorption of water by the highly hydroscopic product. NMR (1H, in CDCl3), δ (ppm) 3.19 (s, 3H), 3.34-3.49 (m, 28H), 3.84 (m, 2H), 5.05 (dd, 2H), 5.73 (m, 1H). NMR (13C, in CDCl3), δ (ppm) 58.52, 68.91, 70.00-70.11 (several peaks), 71.41, 71.68, 116.55, 134.28. Synthesis of Poly(ethylene glycol) Allyl Methyl Ether (MePEG12OCH2CHCH2) (2c). This material was prepared similarly to (2a) with the following amounts: NaH (1.51 g, 62.9 mmol), MePEG550OH (33.22 g, 60.4 mmol), and allyl bromide (7.46 g, 61.7 mmol). Yield: 36.53 g (61.9 mmol, 102%). NMR (1H, in CDCl3), δ (ppm) 3.34 (s, 3H), 3.5-3.62 (m, 48H), 3.98 (m, 2H), 5.22 (dd, 2H), 5.89 (m, 1H). NMR (13C, in CDCl3), δ (ppm) 58.51, 68.89, 69.99-70.09, 71.39, 71.67, 116.55, 134.26. Synthesis of Polymer Precursor MePEG3Si(OEt)3 (3a). The hydrosilation catalyst PtO2 (∼2 mg) was added to an air-free Schlenk tube. Triethoxysilane (SiH(OEt)3, 1.70 g, 10.36 mmol) and (2a) (2.04 g, 10.0 mmol) were also added to the Schlenk tube, which was then heated to 70 °C in oil bath under argon. NMR analysis after 6 h showed the complete disappearance of the alkene protons with a slight excess of SiH(OEt)3, indicating completion of the reaction. The reaction mixture was heated under vacuum (∼50 mTorr) at 50 °C for 30 min to remove excess SiH(OEt)3. The PtO2 catalyst was removed by inert atmosphere filtration with activated charcoal in THF. Two successive filtrations were needed to completely remove the highly colored PtO2. The THF solvent was removed by rotary evaporation, yielding a clear and colorless viscous liquid (3a) (2.60 g, 7.06 mmol, 70.7%). NMR (1H, in CDCl3), δ (ppm) 0.64 (m, 2H), 1.19 (m, 9H), 1.67 (m, 2H), 3.35 (s, 3H), 3.38 (m, 2H), 3.52-3.68 (m, 12H), 3.77 (m, 6H). Synthesis of Polymer Precursor MePEG7Si(OEt)3 (3b). This material was prepared similarly to (3a) with the following amounts: PtO2 (∼2 mg), triethoxysilane (1.70 g, 10.4 mmol), and (2b) (3.80 g, 9.74 mmol). Yield: 3.31 g (60.2%). NMR (1H, in CDCl3), δ (ppm) 0.59 (m, 2H), 1.20 (m, 9H), 1.65 (m, 2H), 3.35 (s, 3H), 3.39 (m, 2H), 3.50-3.63 (m. 28H), 3.80 (m, 6H). Synthesis of Polymer Precursor MePEG12Si(OEt)3 (3c). This material was prepared similarly to (3a) with the following amounts: (2c) (6.00 g, 10.1 mmol), triethoxysilane (1.70 g, 10.36 mmol), and PtO2 (∼2 mg). Yield: 4.96 g (6.58 mmol, 65.8% yield). NMR (1H, in CDCl3), δ (ppm) 0.58 (m, 2H), 1.19 (m, 9H), 1.57 (m, 2H), 3.35 (s, 3H), 3.37 (m, 2H), 3.50-3.63 (m, 48H), 3.80 (m, 6H). Preparation of Sol-Gel Polymer (MePEG3SiO3)n (4a). To the MePEG3Si(OEt)3 polymer precursor (3a) was added an excess of acidic water (pH ∼3, one drop of concentrated HCl in 100 mL of water). The solution was mixed well and allowed to hydrolyze for 12 h at room temperature. The solution was then concentrated on a rotovap and placed in a vacuum oven at 60 °C for 48 h. The resulting gel was a clear and colorless viscous liquid. NMR analysis showed that the ethoxy peaks had disappeared. GPC analysis of the dried polymer showed two peaks with Mw values of 10 004 Da (Mn ) 8512, polydispersity index (PDI) ) 1.1753) and 2001 Da (Mn ) 1394, PDI ) 1.4354). NMR (1H, in CDCl3), δ (ppm) 0.63 (broad, 2H), 1.68 (broad, 2H), 3.35 (s, 3H), 3.42 (broad, 2H), 3.53.72 (m, 12H). Preparation of Sol-Gel Polymer (MePEG7SiO3)n (4b). This material was prepared similarly to (4a). GPC analysis of the dried polymer showed two peaks with Mw values of 3952 Da (Mn ) 3434, PDI ) 1.1508) and 602 Da (Mn ) 471, PDI ) 1.2781). NMR (1H, in CDCl3), δ (ppm) 0.65 (broad, 2H), 1.68 (broad, 2H), 3.35(s, 3H), 3.42 (broad, 2H), 3.49-3.68 (m, 28H).

Chem. Mater., Vol. 17, No. 3, 2005 663 Preparation of Sol-Gel Polymer (MePEG12SiO3)n (4c). This material was prepared similarly to (4a). GPC analysis of the dried polymer showed one peak with a Mw value of 926 g/mol (Mn ) 617, PDI ) 1.5008). NMR (1H, in CDCl3), δ (ppm) 0.64 (broad, 2H), 1.57 (broad, 2H), 3.35 (s, 3H), 3.42 (broad, 2H), 3.5-3.76 (m, 48H). Synthesis of MePEG7SO3H Acid (5b). This acid was prepared as previously reported.1,16,18,30 Synthesis of MePEG12SO3H Acid (5c). This material was prepared similarly to (5b) with the following amounts: (i) Synthesis of MePEG12Cl. MePEG12OH (87.01 g, 158.2 mmol) and SOCl2 (36.65 g, 308.2 mmol) and were used. Yield: MePEG12Cl (46.06 g, 81.09 mmol, 57.3%). NMR (1H, in CDCl3), δ (ppm) 3.34 (s,3H), 3.59 (m, 2H), 3.60-3.69 (m, 48H), 3.72 (t, 2H). NMR (13C, in CDCl3), δ (ppm) 41.80, 57.41, 69.14-69.26 (several peaks), 70.02, 70.65. (ii) Synthesis of MePEG12SO3H (5c). MePEG12Cl (5.05 g, 8.89 mmol) and sodium sulfite (Na2SO3, 2.04 g, 16.2 mmol) were used. Yield: MePEG12SO3H (6.80 g, 6.19 mmol, 70.0%). NMR (1H, in CDCl3), δ (ppm) 3.15 (t, 2H), 3.34 (s,3H), 3.59-3.69 (m, 48H), 3.88 (t, 2H). The acidity of (5c) was assayed at 99%, by titrating a H2O/EtOH solution of the acid with NBu4+OH- (TBAOH) to pH 7, and ratioing the integrals of the CH3 peaks on the TBA+ cation and the MePEG12SO3- anion.1 The MePEG12SO3H acid has a density of 1.15 g/mL, which when divided by the molecular weight (MW) of 614 g/mol gives a neat concentration of 1.87 M. Synthesis of MePEG16SO3H Acid (5d). (i) Synthesis of MePEG16Br. In an air-free round-bottom flask, PBr3 (11.40 g, 42.10 mmol) was slowly added to a solution of poly(ethylene glycol) monomethyl ether (Mn ) 750, MePEG16OH, 37.40 g, 49.90 mmol) in 50 mL of diethyl ether. The reaction was stirred overnight at RT and then poured over 100 g of ice. The mixture was then extracted with 100 mL of diethyl ether, and 2 × 100 mL dichloromethane. After drying with Na2SO4 and concentration by rotary evaporation, 25.86 g of the clear and colorless MePEG16Br (31.80 mmol, 64% yield) was recovered. NMR (1H, in CDCl3), δ (ppm) 3.34 (s, 3H), 3.56 (m, 2H), 3.60 (m, 65H), 3.71 (t, 2H). NMR (13C, in CDCl3), δ (ppm) 29.00, 58.89, 70.06-70.49 (several peaks), 71.05, 71.77. (ii) Synthesis of MePEG16SO3H. A modification of the procedure from (5b) was used with the following amounts of materials: MePEG16Br (10.29 g, 12.41 mmol) and sodium sulfite (Na2SO3, 3.12 g, 24.7 mmol). Yield: MePEG16SO3H acid (6.40 g, 7.86 mmol, 63.4%). NMR (1H, in CDCl3), δ (ppm) 3.22 (t, 2H), 3.35 (s,3H), 3.50-3.70 (m, 65H), 3.88 (t, 2H). The acidity of (5d) was measured at 101%. Neat MePEG16SO3H has a density 1.17 g/mL, which when divided by the MW of 814 g/mol gives a neat concentration of 1.44 M.

Results and Discussion Synthesis. The MePEG polymer precursors (3) synthesized for this study were prepared from a PtO2-catalyzed31 hydrosilation reaction between triethoxysilane and various length poly(ethylene glycol) allyl methyl ethers (2) (Scheme 1). This approach is similar to methods used by Hooper et al.,28,29 Zhang et al.,23 Allcock et al.,32 and Siska and Shriver24 to prepare lithium conducting polymers. This hydrosilation reaction occurred relatively quickly with good yields at (30) Ito, K.; Ohno, H. Solid State Ionics 1995, 79, 300-305. (31) Salourault, N.; Mignon, G.; Wagner, A.; Mioskowski, C. Org. Lett. 2002, 4, 2117-2119. (32) Allcock, H. R.; O’Conner, S. J. M.; Olmeijer, D. L.; Napierala, M. E.; Cameron, C. G. Macromolecules 1996, 29, 7544-7552.

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Ghosh et al.

Scheme 1

Scheme 2

70 °C. This reaction was followed by 1H NMR, monitoring the alkene and silane protons. An excess of the volatile triethoxysilane was used which was then evaporated from the reaction after complete conversion of the alkene. The MePEG polymer precursor (3) was hydrolyzed and condensed to form the corresponding MePEGn polymer (4). We have prepared MePEGn polymers with PEG chain lengths of 3 repeat units (4a), 7 repeat units (4b), and 12 repeat units (4c). These various chain lengths allow the control of volume fraction of PEG in the resulting polymer. The molecular weights of the MePEG polymers (4) were measured by GPC against polystyrene molecular weight standards. We have found that polystyrene MW standards tend to underestimate the number-average molecular weight (Mn) of short-chain methyl poly(ethylene) glycols. For example, poly(ethylene) glycol methyl ether (Mn ) 750 according to the manufacturer) has a GPC determined Mn of 412 g/mol, an underestimation of 45%. In tests of four different PEG methyl ethers (Mn values of 350, 550, 750, and 2000), we found underestimations of 37, 42, 45, and 31%, respectively, with an average underestimation of 39%. The GPC-measured molecular weights of our polymers indicate that the smallest MePEG polymer precursor (3a) forms the largest Mw polymer, and the largest MePEG polymer precursor (3c) forms the smallest Mw polymer. The MePEG3 polymer (4a) forms a polymer with a Mw of 10 004 g/mol, which corresponds to 38.9 monomer units (which does not take into account the underestimation of MePEG molecular weights). The MePEG7 and MePEG12 polymers (4b and 4c) form polymers with Mw values of 3952 g/mol (8.9 monomer units) and 926 g/mol (1.4 monomer units). This apparently small degree of polymerization in the MePEG12 polymer (4c) is likely higher than the value calculated from calibration with polystyrene standards. Furthermore, the 1H and 13C NMR spectra are similar to our other MePEG polymers and consistent with complete polymerization (i.e., no -OH groups are visible, and the peaks near the siloxane backbone are broad and inhomogeneous).

Proton and 13C NMR measurements of the polymers show distinct and sharp peaks for the PEG protons and carbons similar to the MePEGn alcohol starting materials. The carbon atoms and protons on the alkyl section near the siloxane backbone are very broad and inhomogeneous.1 This likely indicates that the PEG units of the polymer are well solvated and reside in a homogeneous environment, while the siloxane section of the polymer may be poorly solvated, or reside in a inhomogeneous chemical environment. We have prepared MePEGnSO3H acids with 7 PEG repeat units (MePEG7SO3H, 5b), 12 repeat units (MePEG12SO3H, 5c), and 16 repeat units (MePEG16SO3H, 5d) which are miscible with the MePEGn polymers. These chain lengths are designed to allow us to control the mobility of the MePEGnSO3- ions by changing their physical size and to test the hypothesis that our proton conductivity is primarily through the Grotthus mechanism. The MePEGnSO3H acids (5) were prepared by halogenation of the MePEGnOH alcohol starting material (Scheme 2), followed by reaction with sodium sulfite (Na2SO3) in ethanol and water to form sulfonic acid functionalized MePEGnSO3H acid (5). MePEGnBr was more reactive toward the sodium sulfite, completing the sulfonization in less than 12 h, versus 36 h or more for MePEGnCl. In addition, chlorination with thionyl chloride tended to produce a MePEGnCl product with a yellow tint, while MePEGnBr is completely clear and colorless. The yellowish contaminant in the MePEGnCl product is likely due to a small amount of a highly colored oxidation product of pyridine. No specific contaminant (i.e., pyridine) is visible in NMR spectra. Ionic Conductivity. Ionic conductivity measurements were performed on anhydrous samples of polymers and acids that had been dried on the electrode under vacuum at 50 °C for at least 6 h. Conductivities were measured by ac impedance on an electrode consisting of two Pt electrodes.1 Figure 1 shows the activation of ionic conductivity (σ) for three different sized MePEGnSO3H acids (5b, n ) 7; 5c, n ) 12; 5d, n ) 16) dissolved in the small MePEG3 polymer (4a). Results are shown at a low concentration (0.26 M) and at a high concentration (1.32 M). As expected, the higher concentrations of the acids produce larger ionic conductivities. However, the relationship between the conductivity and acid size reverses from high to low concentration. For

Proton ConductiVity in Sol-Gel Electrolyte

Figure 1. Activation of ionic conductivity (σ) of MePEGnSO3H acids (5ac) dissolved in the small MePEG3 polymer (4a) at high (1.32 M; closed symbols b, 1, 9) and low concentrations (0.26 M; open symbols O, 3, 0). Acids shown: MePEG7SO3H (5b, b, O); MePEG12SO3H (5c, 1, 3); MePEG16SO3H (5d, 9, 0). Lines are VTF fits.

example, MePEG16SO3H (5d), the largest MePEG acid, has the largest ionic conductivity of the three MePEG acids at high concentration (1.32 M), and the smallest ionic conductivity of the three MePEG acids at low concentration (0.26 M). We attribute this conductivity dependence to the MePEGnSO3H acid adding fluidity to the polymer and acid mixture. This relationship has been noted by Murray and co-workers in their hybrid redox polyether melts.19 Murray found that Co(bipy)3 cations with longer attached MePEG tails had faster physical diffusion rates despite larger sizes. This increase in Dphys was attributed to the longer MePEG tails acting as solvent in the melt and increasing the fluidity. Accordingly, we have measured zero-shear-rate viscosities (η0) for 1.32 M solutions of the three MePEGnSO3H acids (5b, n ) 7; 5c, n ) 12; 5d, n ) 16) dissolved in the small MePEG3 polymer (4a) (the same samples found in Figure 1). We found that a 1.32 M solution of the large MePEG16SO3H acid (5d) displayed the smallest viscosity of 6.67 cP, the MePEG12SO3H acid (5c) displayed an intermediate viscosity of 10.1 cP, and the small MePEG7SO3H acid (5b) displayed the largest viscosity of 85 400 cP. This trend is in agreement with the observed conductivity data such that the largest fluidity (i.e., smallest viscosity) of the large MePEG16SO3H acid (5d) displayed the largest conductivity. In addition, the smallest fluidity (i.e., largest viscosity) corresponded to the smallest conductivity observed with the small MePEG7SO3H acid (5b). The addition of a high concentration of MePEG16SO3H acid (5d) to the MePEGn polymer results in a mixture with a weight fraction of MePEG16SO3H acid between 91.4% and 92.1% depending on the polymer (Table S-1). With this large weight fraction, more PEG units are available to act as solvent in the mixture which is likely the source of the increase in fluidity. Accordingly, the high concentration of MePEG16SO3H acid in the MePEG polymer has a large volume fraction of PEG (Table S-1) (vida infra). This increased fluidity in the mixture of MePEG16SO3H acid (5d) and MePEG3 polymer (4a) allows for both an increased rate of physical diffusion of the MePEG16SO3H acid and an increased rate of motion of the segmental units of the polymer. This may result in a higher mobility of both the H+ and MePEG16SO3- charge carriers, resulting in a

Chem. Mater., Vol. 17, No. 3, 2005 665

Figure 2. Activation of ionic conductivity (σ) of the large MePEG16SO3H acid (5d) dissolved in three MePEG polymers (4a-c) at high (1.32 M; closed symbols b, 1, 9) and low concentrations (0.26 M; open symbols O, 3, 0). Polymers shown: MePEG3 polymer (4a, b, O); MePEG7 polymer (4b, 1, 3); MePEG12 polymer (4c, 9, 0). Lines are VTF fits.

larger overall ionic conductivity and a larger contribution from the vehicle mechanism of conductivity. However, at the low concentration (0.26 M), the MePEGnSO3H acids (5) are present at much lower weight fractions (Table S-1). With low acid weight fractions, it is expected that the fluidity of the mixture will be dominated by the high weight fraction MePEG3 polymer. Figure 1 shows that the trend of ionic conductivity vs MePEGnSO3H acid size is reversed from high to low concentration, yielding a trend where conductivity decreases with increased size of the acid. It is possible that this result indicates that the mobility of the MePEGnSO3- anion is important to the overall ionic conductivity at this low concentration, which in turn may indicate that H+ conductivity from the vehicle mechanism may be important. The higher ionic conductivity with the small MePEG7SO3H acid (5b) may indicate that this acid has a larger physical diffusion coefficient (Dphys) than the larger acids, as expected from the Stokes-Einstein equation (eq 2). Dphys )

kT 6πηRH

(Stokes-Einstein equation)

(2)

Here, Dphys is proportional to fluidity (η-1) and inversely proportional to the hydrodynamic radius (RH) of the diffusing species. Thus, the mobility of a larger solute is expected to be slower than a smaller solute. Figure 2 shows the activation of ionic conductivity for the large MePEG16SO3H acid (5d) dissolved in three MePEG polymers (4a-c) with different lengths of PEG chains. The activation behavior is shown at low (0.26 M; open symbols) and high (1.32 M; solid symbols) concentrations of the large MePEG16SO3H acid (5d) in the polymers. At low concentrations (0.26 M) of the MePEG acid (5d), the conductivity appears dependent on the length of the PEG chains in the MePEG polymer (4a-c) (open symbols, Figure 2). This increase in conductivity with larger MePEG polymers is likely due to an increase in the volume fraction of PEG units in mixtures containing the larger MePEG polymer (vida infra). That is, in the MePEG12 polymer a greater fraction of the polymer consists of the solvating PEG unit, and less of the alkyl siloxane unit that is not likely to participate in conduction.25 Using this volume fraction argument, we would predict that low concentrations of MePEGnSO3H acid (where most of the mixture is composed

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Ghosh et al. Table 1. Concentrations of Neat Samples

species

density (g/mL)

MW (g/mol)

concn (mol/L)

molar vol (L/mol)

Vf,PEG

MePEGnOH (tri(ethylene glycol) methyl ether) n ) 3 MePEGnOH (poly(ethylene glycol) methyl ether, Mn ) 350), n ) 7.22 MePEGnOH (poly(ethylene glycol) methyl ether, Mn ) 550), n ) 11.8 MePEGnOH (poly(ethylene glycol) methyl ether, Mn ) 750), n ) 16.3 [MePEG3(CH2)3SiO3]x, 4a [MePEG7(CH2)3SiO3]x, 4b [MePEG12(CH2)3SiO3]x, 4c MePEG7SO3H, 5b MePEG12SO3H, 5c MePEG16SO3H, 5d

1.026 1.094 1.069 1.105 1.241 1.157 1.133 1.237 1.15 1.17

164.2 350 550 750 257 443 643 414 614 814

6.25 3.13 1.94 1.47 4.83 2.61 1.76 2.99 1.87 1.44

0.160 0.319 0.514 0.680 0.207 0.383 0.568 0.334 0.535 0.694

1.00 1.00 1.00 1.00 0.773 0.833 0.905 0.955 0.961 0.979

of the MePEG polymer) in the small MePEG3 polymer (4a) would have a lower conductivity than the same concentration of the same acid in the larger MePEG12 polymer (4c). This relationship is seen in the 0.26 M data (open symbols) in Figure 2. Moreover, we can state that the mobility of the charge carriers is higher in the MePEGn polymers with longer PEG chains, according to the Nernst-Einstein equation (eq 3). σion )

F2 2 [z D C + z-2D-C-] RT + + + (Nernst-Einstein equation) (3)

Volume Fraction Contributions. Our hypothesis is that the conductivity in these materials occurs primarily through the Grotthus mechanism in the PEG region of the material and is dependent on the volume fraction of PEG. We have developed the following equation to calculate the volume fraction of PEG in MePEGnSO3H acids and MePEGn polymers. Vf,PEG )

MVMePEG MVsample

(volume fraction of PEG)

(4)

Here, Vf,PEG is the volume fraction that is occupied by the PEG segmental units; MVMePEG is the molar volume (concentration-1) of the corresponding MePEGnOH starting material, CH3(OCH2CH2)nOH; and MVsample is the molar volume of the MePEGnSO3H acid (5) or the MePEG polymer (4) that is calculated from the density and molecular weight. For example, the density of MePEG7OH is 1.094 g/mL. When this density is divided by the molecular weight of 350 g/mol, a concentration of 3.13 M is obtained. The inverse of this concentration gives a molar volume of 0.319 L/mol (MVMePEG). The density of the MePEG polymer (4b) is 1.157 g/mL (synthesized from MePEG7) and the molar mass of one unit of this polymer is 443 g/mol, giving a monomer concentration of 2.61 M and a molar volume of 0.383 L/mol (MVsample). Using eq 4, the volume fraction (Vf,PEG) of PEG in (4b) is 0.833 (Table 1). That is, 83.3% of this polymer is composed of PEG (by volume). The volume fraction of PEG in a mixture of MePEGnSO3H acid and MePEGn polymer can be calculated using a method analogous to the molar volume approach used in eq 4. Vf,PEG,mixture )

VMePEG,acid + VMePEG,poly Vacid + Vpoly

(5)

Equation 5 calculates the volume fraction using the absolute volumes of the polymer and acid (Vpoly and Vacid) and the volumes of the PEG in the MePEGnSO3H acid and MePEG polymer (VMePEG,acid and VMePEG,poly). Absolute volumes are used to allow for mixtures with different MePEG chain lengths in the acid and polymer. Mixtures of polymer and acid are prepared gravimetrically, so mass divided by density can easily be substituted for the volumes Vpoly and Vacid. The volume of the MePEG fractions can be calculated from the number of moles of MePEG (calculated as described below) multiplied by the MePEG’s molar volume, yielding Vf,PEG,mixture )

nacid(MVMePEG,acid) + npoly(MVMePEG,poly) (6) macid mpoly + dacid dpoly

Here, macid, dacid, mpoly, and dpoly are the mass and density of the MePEGnSO3H acid (5) and the MePEG polymer (4). In addition, nMePEG,acid and nMePEG,poly are the number of moles of the MePEGnSO3H acid (5) and the MePEG polymer (4), calculated from the MW of the acid or the MW of the monomer unit of the polymer. The values of MVMePEG,acid and MVMePEG,poly (as above) are the molar volumes of the MePEG chains attached to the MePEGnSO3H acid (5) and the MePEG polymer (4) (Table 1). Figure 2 shows that the properties of the acid and polymer mixtures are apparently controlled by the volume fraction of PEG present in these mixtures. In the low concentration (0.26 M) mixtures of MePEG16SO3H (5d) in the three MePEG polymers (4a, 4b, and 4c) the volume fractions of PEG are 0.809, 0.860, and 0.954, respectively (open symbols in Figure 2). This relatively large difference in the volume fractions of PEG in the low concentration samples is reflected in a relatively large difference in conductivities for the three MePEGn polymers (i.e., a stronger dependence on the length of the MePEG chain on the polymer). Likewise, the volume fractions of PEG in the high concentration (1.32 M) mixtures of MePEG16SO3H (5d) in the three MePEG polymers (4a, 4b, and 4c) are 0.961, 0.966, and 0.975 (solid symbols in Figure 2). This relatively small difference in volume fraction of PEG is reflected in a relatively small difference in the conductivities for the three MePEGn polymers (Table 2). Here, the VTF fits of the small MePEG polymers (4a,b) are essentially overlapping and the largest MePEG12 polymer (4c) has only a slightly larger ionic conductivity. Figure 3 shows the activation of ionic conductivity for the smallest MePEG acid (5b) dissolved in three MePEG polymers (4a, 4b, 4c) with different length PEG chains. This

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Chem. Mater., Vol. 17, No. 3, 2005 667

Figure 3. Activation of ionic conductivity (σ) of the small MePEG7SO3H acid (5b) dissolved in three MePEG polymers (4a-c) at high (1.32 M; closed symbols b, 1, 9) and low concentrations (0.26 M; open symbols O, 3, 0). Polymers shown: MePEG3 polymer (4a, b, O); MePEG7 polymer (4b, 1, 3); MePEG12 polymer (4c, 9, 0). Lines are VTF fits.

figure shows a behavior similar to that of Figure 2 at low concentrations, and a stronger dependence of the MePEGn polymer’s (4) PEG chain length at high concentration. The larger the MePEGn polymer, the higher is the conductivity (i.e., 4c > 4b > 4a). The MePEG7SO3H acid (5b) used in Figure 3 is significantly smaller (i.e., fewer PEG units) than the MePEG16SO3H acid (5d) used in Figure 2. As a consequence, the weight fraction of the small MePEG7SO3H acid (5b) in the polymer will not be as large as the larger MePEG16SO3H acid (5d). With smaller weight fractions, the volume occupied by the acid is smaller, which yields a smaller volume fraction of PEG in the mixture. For example, the volume fractions of PEG in the 1.32 M mixtures of the small MePEG7SO3H acids (5b) in the MePEGn polymers (4a, 4b, and 4c) are 0.853, 0.887, and 0.951, respectively (a 10.3% difference between highest and lowest), while the volume fractions of PEG in the same concentration mixtures of MePEG16SO3H acids (5d) in the same polymers are 0.961, 0.966, and 0.975 (a 1.4% difference). This leads to the larger observed dependence on ionic conductivity (Table 2). Figure 4 shows the dependence of ionic conductivity (σ) and molar equivalent conductivity (Λ) vs the number of repeating PEG units in MePEGnSO3H acids (5b, 5c, 5d) dissolved in three MePEG polymers (4a, 4b, 4c). This plot shows that low concentration (0.26 M) mixtures of the MePEG acids in the large MePEG12 polymer (4c) have higher conductivities than mixtures of MePEGnSO3H acids in the small MePEG3 polymer (4a). This dependence is similar to data presented in Figure 2. As described above, this dependence is likely due to the increase in the volume fraction of PEG units in a MePEG polymer with long PEG chains. The molar equivalent conductivity (Λ) plot in Figure 4 shows that the equivalent conductivity is larger in the high concentration point for each matching low (0.26 M) and high (1.32 M) concentration data point. Thus, the mobility of one or both of the ions has increased in the high concentration samples. One possibility for this behavior is that the increase in volume fraction of PEG in the high concentration samples (Table 2) leads to an increase in the mobility of the H+ cation. Furthermore, low concentrations (0.26 M) of the MePEGnSO3H acids in the MePEGn polymers have no dependence on the size of the MePEGnSO3H acid and a very

Figure 4. Dependence of ionic conductivity (σ) and molar equivalent conductivity (Λ) on number of PEG units in the MePEGnSO3H acid (5bd) at high (1.32 M; closed symbols b, 1, 9) and low concentrations (0.26 M; open symbols O, 3, 0). Conductivities are for mixtures of MePEGnSO3H in MePEG3 polymer (4a, b, O), MePEG7 polymer (4b, 1, 3), and MePEG12 polymer (4c, 9, 0). All data points are at 55 °C. Lines simply connect the points.

Figure 5. Dependence of ionic conductivity (σ) and molar equivalent conductivity (Λ) on number of PEG units in the MePEGn polymer (4a-c) at high (1.32 M; closed symbols b, 1, 9) and low concentrations (0.26 M; open symbols O, 3, 0). Conductivities are for mixtures of MePEGn polymers (4a-c) with MePEG7SO3H (5b, b, O), MePEG12SO3H (5c, 1, 3), and MePEG16SO3H (5d, 9, 0). All data points are at 55 °C. Lines simply connect the points.

small slope that is not significantly different from zero.33 This suggests that, at low MePEGnSO3H acid concentrations, the mobility of the acid is not playing an important role in ionic conductivity. That is, the vehicle mechanism of H+ conductivity is likely not important here. Figure 5 shows the dependence of ionic conductivity (σ) and molar equivalent conductivity (Λ) vs the number of repeating PEG units in the MePEG polymer (4a-c) for low and high concentration mixtures (0.26 and 1.32 M) of the (33) Determined using GraphPad Prism, GraphPad Software Inc.

668 Chem. Mater., Vol. 17, No. 3, 2005

MePEG polymer and MePEGnSO3H acid (5b-d). At low concentrations (0.26 M) of MePEGnSO3H acids, the ionic conductivity and equivalent conductivity data essentially overlap for the three MePEG polymers (4). The three low concentration lines have small slopes, indicating some dependence on the length of the PEG chain in the MePEG polymer. This is likely an effect of the change in the volume fraction of PEG in these mixtures. For example, 0.26 M mixtures of MePEG7SO3H (open circles, Figure 5) in the MePEG polymers (4a, 4b, and 4c) give volume fractions of PEG of 0.788, 0.843, and 0.949, respectively. Here, we predicted that the increase in Vf,PEG would lead to an increase in the molar equivalent conductivity in this series (which it does). Furthermore, the Vf,PEG values for the low concentration series of three MePEGnSO3H acids (5b, 5c, and 5d) in the MePEG3 polymer are 0.788, 0.799, and 0.809. This is a much smaller increase in the Vf,PEG, and we would predict a much smaller increase in equivalent conductivity (here the three data points fall almost on top of each other). At high concentrations, Figure 5 shows a dependence of conductivity on the number of repeating PEG units in the MePEGn polymer (4a-c), especially with the large MePEG16SO3H acid (5d). Here, the conductivities and equivalent conductivities for the large acid (5d) are much higher than for the other mixtures and increase with increasing PEG length in the MePEG polymer (4). This trend is also seen in dramatically larger conductivities for the large MePEG acid in Figure 4. Furthermore, the equivalent conductivity (Λ) in Figure 5 shows, similarly to Figure 4, that for each matching low (0.26 M) and high (1.32 M) concentration data point, the equivalent conductivity is larger in the high concentration point. This again suggests that the MePEGnSO3H acid serves to add fluidity to the mixture, which increases the rate of ionic motion. This increase in fluidity is apparently occurring through an increase in the volume fraction of PEG in the high concentration MePEGnSO3H acid samples. This demonstrates the overall dependence of this system on the volume fraction of PEG and how this controls the mobility of ions in these polymers. Figure 5 shows how the volume fraction of PEG controls the conductivity in these systems. Here, each mixture of MePEGn polymer and MePEGnSO3H acid has conductivities and molar equivalent conductivities that increase as the PEG chain length on the polymer increases. For each set of three points consisting of a high (1.32 M) or low (0.26 M) concentration of MePEGnSO3H acid in three MePEG polymers, the weight fraction of the MePEGnSO3H acid is essentially constant in the three MePEG polymers (Table S-1). For example, for the three data points at the 0.26 M concentration of 5b in 4a, 4b, and 4c the weight percentages of the MePEG7SO3H acid are 8.7%, 9.3%, and 9.5%, respectively. This indicates that the increase in conductivity (σion) as a function of the MePEG polymer’s PEG chain length is likely due to the increase in volume fraction of PEG (0.728, 0.804, and 0.880 for 5b in 4a, 4b, and 4c; Table S-1). The highest volume fractions of 0.955, 0.962, and 0.969 are reached in the samples containing a high concentration

Ghosh et al.

Figure 6. Dependence of molar equivalent conductivity (Λ) versus inverse of volume fraction of PEG (1/Vf,PEG,mixture) in mixtures of MePEGnSO3H acids (5b, 5c, 5d) with MePEGn polymers (4a, 4b, 4c) at 55 °C. The results of 34 experiments at four different MePEGnSO3H acid concentrations (0.26, 0.43, 1.05, and 1.32 M) are presented.

of MePEG16SO3H acid dissolved in 4a, 4b, and 4c. These mixtures with a large volume fraction of PEG also show the highest conductivities. Figure 6 shows the log of equivalent conductivity (Λ) versus the inverse of volume fraction of PEG for a series of mixtures of the MePEGnSO3H acids (5b-d) with the MePEGn polymers (4a-c) at 55 °C. Here, the results of experiments with four different concentrations of MePEGnSO3H acids (0.26, 0.43, 1.05, and 1.32 M) are presented. According to free-volume theory, diffusivity is exponentially related to the inverse of free volume.17,34 This type of plot has been used to determine the role of free volume in ion transport.17 The equivalent conductivity (Λ) is linearly related to the diffusion coefficient of the ions through the NernstEinstein equation (eq 3), and a plot of log Λ vs 1/Vf should show a linear dependence if the ion mobility is a function of the volume fraction of PEG. In Figure 6 the largest equivalent conductivities are obtained for mixtures with the largest volume fraction of PEG. In addition, higher concentrations of the MePEGnSO3H acid generally give mixtures with higher volume fractions of PEG. The 34 data points in Figure 6 include all the 1.32 and 0.26 M data presented thus far, plus several data points from intermediate concentrations of 0.43 and 1.05 M. The data in Figure 6 can be fit by a linear regression to give a line with a slope of -5.37 ( 0.55. While the correlation coefficient is somewhat small (r2 ) 0.751) and the scatter in the data appears large, an analysis of the residuals and a runs test indicate that the scatter is random, and that the regression line is not significantly nonlinear.33 In addition, the P value of the slope is less than 0.0001, indicating a highly significant result. Thus, we conclude that the volume fraction of PEG in the mixtures is a good indicator of the overall ionic mobility in mixtures of our MePEGnSO3H acid and MePEGn polymers. Mechanism of H+ Conductivity. Our hypothesis is that H+ transport is dependent on the volume fraction of PEG present in the mixtures and that we primarily have a Grotthus mechanism of proton conductivity. We have discussed how the low concentration data of Figure 1 may suggest the presence of the vehicle mechanism of conductivity. However, Figure 4 shows much more clearly the lack of a dependence (34) Cohen, M. H.; Turnbull, D. J. Chem. Phys. 1959, 31, 1164-1169.

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Table 2. Electrochemical Properties of Acid/Polymer Solutions

solution 4a + 5b 4a + 5c 4a + 5d 4b + 5b 4b + 5c 4b + 5d 4c + 5b 4c + 5c 4c + 5d

[acid] (mol/L)

Vf,PEG,mixture

σion (µS cm-1), 55 °C

0.26 1.32 0.26 1.32 0.26 1.32 0.26 1.32 0.26 1.32 0.26 1.32 0.26 1.32 0.26 1.32 0.26 1.32

0.788 0.853 0.799 0.907 0.809 0.961 0.843 0.887 0.851 0.923 0.860 0.966 0.949 0.951 0.951 0.959 0.954 0.975

0.102 2.51 0.063 2.69 0.033 13.2 0.468 4.47 0.562 5.01 0.426 10.5 0.851 6.31 0.741 3.39 0.708 13.8

Λ (mS cm2 mol-1), 55 °C 0.392 1.90 0.243 2.04 0.127 10.0 1.80 3.39 2.16 3.79 1.64 7.95 3.27 4.78 2.85 2.57 2.72 10.4

of the equivalent conductivity on the size of the MePEGnSO3anion. This result strongly suggests that, at low MePEGnSO3H acid concentrations, the mobility of the acid is not related to ionic conductivity, and that the low concentration trend in Figure 1 is due to some other factor. That is, the vehicle mechanism of H+ conductivity is apparently not important at low concentrations. More importantly, this system has shown an overall dependence on the free volume of the mixtures as measured by the volume fraction of PEG. This dependence is evident

in the data presented in Figure 5. Here, a dependence of conductivity on the number of repeating PEG units in the MePEG polymer (4a-c) is noted. The increase in the number of repeating PEG units causes an increase in the volume fraction of PEG in the mixture. From Figure 6, the volume fraction of PEG is linearly correlated with the equivalent conductivity (i.e., ionic mobility). We conclude that the volume fraction of PEG in the mixtures is in control of ionic mobility in our acid/polymer mixtures. This volume fraction of PEG result is important, because the Grotthus mechanism of H+ conductivity in this system would be controlled by the rearrangement of ethylene oxide segments. Thus, the importance of the amount of PEG strongly suggests that the Grotthus mechanism is primarily responsible for conductivity in this system. Acknowledgment. This research was supported in part by the National Science Foundation through the EPSCoR program (EPS-0132618). The authors thank Ms. Ambika Ramsundar (UM SRIU program) for her assistance in making GPC measurements. J.E.R. thanks Mr. Shawn McConaughy and Dr. Charles McCormick (USM Polymer Science) for assistance in making viscosity measurements. Supporting Information Available: Table S-1 detailing the calculation of volume fractions of PEG in mixtures of the acid and polymer (PDF). This material is available free of charge via the Internet at http://pubs.acs.org CM0486969