ARTICLE pubs.acs.org/JPCB
Star-Shaped MePEGn Polymers as Hþ Conducting Electrolytes Chengjun Sun and Jason E. Ritchie* Department of Chemistry and Biochemistry, The University of Mississippi, University, Mississippi 38677, United States
bS Supporting Information ABSTRACT: Proton conducting electrolytes composed of a mixture of MePEG7SO3H acid and a four-armed, PEG-based, star molecule were prepared. Four MePEGn (n = 3, 7, 12) arms were attached to a pentaerythritol or tetrakis(dimethylsilyl) orthosilicate core to form the star molecules. We have examined the structure of these star electrolytes to observe how the structure of an electrolyte affects the observed ionic conductivity. In terms of structural parameters, these star electrolytes showed large volume fractions of PEG, high fluidities, and large fractional free volumes, all of which predict larger ionic conductivities. Through a comparison of the conductivity and structural parameters in a variety of different star electrolytes, we have shown that each of these three structural parameters are important and can strongly affect the observed ionic conductivity. Walden plots indicated a large extent of ion-pairing in our star electrolytes and that MePEG7SO3H acid was a weak acid in our star electrolytes.
1. INTRODUCTION Proton conducting polymer electrolytes are important materials due to their potential applications in fuel cells and electrochromic displays. In our previous publications, we have explored how the structure of a polymer electrolyte affects its ion transport properties. Specifically, we have shown how the fractional free volume (FFV), volume fraction of PEG (Vf,PEG), and the viscosity (η) of a polymer electrolyte affect the observed Hþ conductivity.13 In this paper, we have prepared four-armed, polyether “star-shaped” macromolecules composed of MePEGn (n = 3, 7, 12) “arms” attached to pentaerythritol or tetrakis(dimethylsilyl) orthosilicate “star-shaped” core. These star molecules are composed primarily of the MePEGn arms, which, give large volume fractions of PEG because each macromolecule contains four large MePEGn arms.4,5 In our studies of the structural effects of polymer electrolytes, we have adopted the general strategy of trying to independently vary these different structural parameters (FFV, Vf,PEG, and η), in order to observe how each parameter affects ion transport in the electrolyte. Based on the observation that branched polymers give lower viscosities than linear polymers of the same molecular weight,6 we expect that our star molecules will produce lower viscosities than our previously studied MePEGn polymer.2,3 This should allow us to make a comparison on the effects of viscosity on ionic transport in these different polymers. In addition, we expect that our star molecules will give larger ionic conductivities because of both their large volume fractions of PEG and their low viscosities. In general, branched macromolecules tend to be more fluid than linear macromolecules. That is, given the same total chain length, a linear macromolecule will experience a greater “pervaded volume” than does a branched macromolecule.6 Massively branched dendrimers show even smaller pervaded volumes.5 With a smaller pervaded volume, the branched macromolecule has a smaller hydrodynamic volume, which allows for higher r 2011 American Chemical Society
segment densities, and produces a lower viscosity. Several groups have studied the ionic conductivity of dendrimer-based polymer electrolytes. For example, Shriver has studied Liþ transport in branched poly(amidoamine), poly(ethylenimine), and poly(propyleneimine)-based dendrimers and shown that they exhibit large ionic conductivities.7 PEG-based electrolytes have long been popular for Liþ polymer electrolyte applications. For example, West and co-workers have developed Liþ conducting siloxane/oligoether compounds containing MePEGn side chains.811 In addition, Creager and DesMarteau have developed Liþ conducting electrolytes from PEG oligomers covalently attached to TFSI counterions.12 Several papers have focused on the ionic conductivity of branched macromolecules containing PEG units. For example, Baker has developed a four-armed polyether star compound in which MePEG2 arms were attached to a pentaerythritol core.13 Baker compared their electrolyte’s Liþ conductivity with PEGDME 500 (a linear polymer of nearly the same molecular weight) and found that their branched compound showed similar conductivities at room temperature but higher conductivities at low temperature. However, when a tetra-substituted carbon core replaced the pentaerythritol core, the chain flexibility was reduced which subsequently decreased the observed Liþ conductivity.7 We have shown that PEG-based polymers can also be used as anhydrous Hþ conducting electrolytes, in the complete absence of water. We believe that the Lewis basic oxygen atoms in PEG coordinate to the Lewis acidic Hþ ions, with the PEG units of the polymer effectively acting as solvents for Hþ.13,14 Furthermore, we believe that Hþ ion transport occurs through a rearrangement of the PEG segments in the polymer.15,16 Received: November 24, 2010 Revised: May 18, 2011 Published: May 18, 2011 8381
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The Journal of Physical Chemistry B Scheme 1. Synthesis of the Star (MePEGn)4C Molecules
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Scheme 2. Synthesis of the Star (MePEGn)4Si5 Molecules
We have developed PEG-containing, solgel based polymer electrolytes into which we dissolve our MePEG7SOnH acid (n = 3, 7, 12, 16) acids to form Hþ conducting electrolytes.1,14 In this paper, we show how the length of MePEG “arms” and different cores in our four-armed polyether star molecules affect structural parameters (FFV, Vf,PEG, and η). In addition, we will show how these structural effects subsequently affect Hþ ion conductivity.
2. EXPERIMENTAL SECTION Nomenclature. The star molecules containing the pentaerythritol (carbon) core were named after the number and size of the MePEG arms with the core carbon atom represented. For example, Star (MePEG3)4C, Star (MePEG7)4C, and Star (MePEG12)4C denote star molecules containing four MePEG3, MePEG7 or MePEG12 arms (Scheme 1) attached to pentaerythritol core. The star molecules containing the tetrakis(dimethylsilyl) orthosilicate (silicon) core were named after the number and size of the MePEG arms with the five core silicon atoms represented. For example, Star (MePEG3)4Si5, Star (MePEG7)4Si5, and Star (MePEG12)4Si5 denote star molecules containing four MePEG3, MePEG7, or MePEG12 arms attached to a tetrakis(dimethylsilyl) orthosilicate core (Scheme 2). Materials. Pentaerythritol tetrabromide (Aldrich), and Tetrakis (dimethylsilyl) orthosilicate (Gelest) were used as received. Polyethylene glycol monomethyl ether (MePEGn, n = 3.0, 7.24, 12; Mn = 164, 350, 550; Aldrich) was dried at 60 °C under vacuum for 12 h. The monomethyl triethylene glycol (MePEG3OH) is a monodisperse molecule, while the MePEG7OH and MePEG12OH are polydisperse polymers. Sodium hydride (Aldrich) was received as a slurry in mineral oil, and was washed with toluene and filtered in an inert atmosphere drybox prior to use. Tetrahydrofuran was dried and purified by passing through alumina using a Contour Glass solvent delivery system. Synthesis. The MePEG7SO3H acid was prepared as previously described.13,14 Star (MePEGn)4C molecules were synthesized according to a method developed by Baker and co-workers (Scheme 1).13 Synthesis of Star (MePEG3)4C. NaH (0.445 g, 18.5 mmol) and THF (5 mL) were added to an air-free round-bottom flask. MePEG3OH (2.600 g, 15.8 mmol) was dissolved in 5 mL of THF and added dropwise to the NaH/THF slurry. The mixture was stirred at room temperature for 30 min to complete the deprotonation. Pentaerythritol tetrabromide, C(CH2Br)4 (1.550 g, 4.00 mmol), was dissolved in 10 mL of THF and added dropwise
to the deprotonated MePEG3O solution. The mixture was refluxed for 72 h, at which time 13C NMR showed a total disappearance of the CH2OH (∼61 ppm) group from the MePEG3OH starting material, indicating the completion of the reaction. The NaBr precipitate was removed by filtration, and the filtrate was then extracted with 50 mL of 0.5 M NaCl and 3 75 mL of toluene. The organic fraction was then dried (Na2SO4), and concentrated by rotary evaporation, yielding a brown liquid (0.88 g, 1.2 mmol, 31%). NMR (1H, in CDCl3, δ ppm), 3.36(s, 12H), 3.40(m, 8H), 3.53.62 (m, 48H). NMR (13C, CDCl3, δ ppm) 35.49, 47.93, 59.17, 70.0871.12 (several peaks), 72.12. Synthesis of Star (MePEG7)4C. This molecule was synthesized similarly to the above-described Star (MePEG3)4C with the following amounts: NaH (0.436 g, 18.2 mmol), MePEG7OH (5.590 g, 16.0 mmol), and C(CH2Br)4 (1.550 g, 4.0 mmol). Yield: 2.01 g, 1.4 mmol, 34%. NMR (1H, in CDCl3, δ ppm), 3.35 (s, 12H), 3.39 (m, 8H), 3.53.62 (m, 112H). NMR (13C, CDCl3, δ ppm) 35.45, 44.47, 59.15, 70.0571.10 (several peaks), 72.08. Synthesis of Star (MePEG12)4C. This molecule was synthesized similarly to the above-described Star (MePEG3)4C with the following amounts: NaH (0.450 g, 18.8 mmol), MePEG12OH (8.780 g, 16.0 mmol), and C(CH2Br)4 (1.550 g, 4.0 mmol). Yield: 1.55 g, 0.7 mmol, 17%. NMR (1H, in CDCl3, δ ppm), 3.30 (s, 12H), 3.49 (m, 8H), 3.53.62 (m, 192H). NMR (13C, CDCl3, δ ppm) 35.37, 44.36, 59.08, 69.8570.98 (several peaks), 71.94. The synthesis of the Star (MePEGn)4Si5 molecules is shown in Scheme 2. The MePEG allyl methyl ether (MePEGnOCH2CHCH2) was prepared as previously described.1,2 Synthesis of Star (MePEG3)4Si5. Tetrakis(dimethylsilyl) orthosilicate, Si(O(CH3)2SiH)4 (1.642 g, 5.0 mmol) and MePEG3OCH2CHCH2 (4.082 g, 20.0 mmol) were added to an airfree Schlenk tube in an inert atmosphere drybox. Karstedt’s catalyst (∼60 μL) was added to the Schlenk tube. The reaction mixture was then heated to 70 °C in oil bath under argon for 6 h, at which time 1H NMR showed the complete disappearance of both the alkene protons and the silane peak (∼4.7 ppm), indicating 8382
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Table 1. Vf,PEG and FFV of Star Molecules Vw,PEG a compounds
3. RESULTS AND DISCUSSION MV d
Vw b
(cm3/mol) (cm3/mol) Vf,PEGc (cm3/mol) FFV e
MePEG7SO3H acid
175
216
0.81
314
0.35
Star (MePEG3)4C
305
404
0.76
532
0.24
Star (MePEG3)4Si5
305
689
0.44
1082
0.36
MePEG3 polymer f
76
143
0.53
219
0.35
Star (MePEG7)4C
715
813
0.88
1177
0.31
Star (MePEG7)4Si5
715
1099
0.65
1747
0.37
Star (MePEG12)4C Star (MePEG12)4Si5
1155 1155
1254 1540
0.92 0.75
1853 2442
0.32 0.37
a van der Waals volume of the PEG portion of the species. b Total van der Waals volume of the whole species. c Volume fraction of PEG calculated from eq 1. d Molar volume calculated from density measurement (vide infra). e Overall fractional free volume calculated from eq 3. f From ref 3.
completion of the reaction. The Karstedt’s catalyst was then removed by filtration with activated charcoal in THF in the drybox.1,2 The THF was then removed by rotary evaporation, yielding a clear and colorless viscous liquid (4.68 g, 4.1 mmol, 82% yield). NMR (1H, in CDCl3, δ ppm), 0.040.14 (m, 24H), 0.88 (m, 8H), 1.57 (m, 8H), 3.35 (s, 12H), 3.39 (m, 8H), 3.513.64 (m, 48H). NMR (13C, CDCl3, δ ppm) 14.10, 17.73, 23.42, 59.17, 70.1570.76 (several peaks), 72.10. Synthesis of Star (MePEG7)4Si5. This molecule was synthesized similarly to the above-described Star (MePEG3)4Si5 with the following amounts: Si(O(CH3)2SiH)4 (0.821 g, 2.5 mmol) and MePEG7OCH2CHCH2 (3.904 g, 10.0 mmol). Yield: 3.06 g, 1.6 mmol, 65%. NMR (1H, in CDCl3, δ ppm), 0.040.14 (m, 24H), 0.88 (m, 8H), 1.57 (m, 8H), 3.35 (s, 12H), 3.39 (m, 8H), 3.523.62 (m, 112H). Synthesis of Star (MePEG12)4Si5. This molecule was synthesized similarly to the above-described Star (MePEG3)4Si5 with the following amounts: Si(O(CH3)2SiH)4 (0.848 g, 2.6 mmol) and MePEG12OCH2CHCH2 (6.080 g, 10.3 mmol). Yield: 4.77 g, 1.77 mmol, 69%. NMR (1H, in CDCl3, δ ppm), 0.06 0.16 (m, 24H), 0.51 (m, 8H), 1.68 (m, 8H), 3.36 (s, 12H), 3.543.62 (m, 200H). Characterization. The densities of the polymer electrolyte samples were measured gravimetrically by drawing the sample into a tared 2 μL micropipet,1 followed by weighing using an ATI Cahn C-33 microbalance. The average of three measurements were taken for each sample. Viscosity measurements were performed using a Brookfield DV-3 Ultra programmable rheometer with cone and plate geometry (Cone CPE-40 or CPE-52). Viscosity measurements were only made after the copolymer sample was dried at 60 °C under vacuum for 12 h.2,3,17 AC-impedance conductivity measurements were made using a PAR 283 potentiostat with a Perkin-Elmer 5210 lock-in amplifier using PowerSine software.1 Conductivity measurements were only made after the samples had dried at 55 °C to a constant conductivity (i.e., the conductivity reaches a constant plateau, typically 1824 h).1,2,15,16 NMR spectra were recorded on either Bruker AC-300 or Bruker DRX-500. The high (1.32M) and low (0.26M) MePEG7SO3H acid concentrations were originally chosen to mirror Hþ/PEG ratios of 1:8 and 1:64, respectively.1,18 We have kept these ratios in our subsequent papers to allow easy comparison of ionic conductivity results.
Synthesis. The Star (MePEGn)4C molecules were prepared by reacting MePEGnOH with Pentaerythritol bromide using a molar ratio of 4:1. These Star (MePEGn)4C molecules were colorless to light yellow liquids, with the exception of Star (MePEG3)4C, which was a brown liquid. The pentaerythritol bromide starting material showed a single sharp peak (3.57 ppm) in 1H NMR and two peaks (34.4 and 43.1 ppm) in 13C NMR spectra. Once the pentaerythritol core was incorporated into the Star (MePEGn)4C molecules, the NMR peaks of pentaerythritol slightly shifted to 3.46 ppm in 1H NMR and 35.4 ppm in 13C NMR spectra. This complete shift in the NMR resonances of the pentaerythritol protons was indicative of the completion of the reaction. The hydrogen atoms of the PEG units gave sharp peaks, similar to the MePEGnOH starting material. We believe that this indicates that the PEG units are well solvated and reside in a homogeneous environment.17 This also likely indicates that the PEG units have the potential for high segmental mobility which bodes well for potential Hþ conductivity. Star (MePEGn)4Si5 molecules were prepared by reacting MePEGallyl (MePEGnOCH2CHCH2) with tetrakis(dimethylsilyl) orthosilicate at a molar ratio of 4:1. Star (MePEGn)4Si5 molecules also show sharp 1H NMR resonances for the PEG hydrogens. However, the methyl groups attached to the tetrakis(dimethylsilyl) orthosilicate core showed very broad 1H NMR resonances. This result is similar to what our group has previous found in the NMR spectra of our MePEGn polymers.1,14,17 This shows that the siloxane cores of the Star (MePEGn)4Si5 molecules are poorly solvated and/or reside in an inhomogeneous environment and are thus not likely to play an important part in the Hþ conductivity. Volume Fraction of PEG (Vf,PEG). We have shown in previous publications that the volume fraction of PEG (Vf,PEG) is important in predicting the mobility of Hþ ions in our MePEGn electrolytes.13 The Vf,PEG is the fraction of the volume of the polymer that is occupied by PEG units. This measurement was originally developed by Murray to analyze the electrochemical properties of their redox molten salts.19 In this paper, the volume fraction of PEG (Vf,PEG) in our star MePEGn polymers is computed using the estimated van der Waals volumes using the functional group contribution method,4,5 according to eq 1
Vf , PEG ¼
Vw, PEG Vw
ð1Þ
Here Vw,PEG is the computed van der Waals volume of only the PEG units in the molecule or segment of the copolymer. Likewise, Vw is the computed van der Waals volume of the whole molecule or segment of the copolymer. Both Vw,PEG and Vw are computed using the functional group contribution method.4,5 Table 1 shows the results of the calculation of the volume fraction of PEG (Vf,PEG) of the Star (MePEGn)4C and Star (MePEGn)4Si5 molecules. Note that the calculated value of Vw,PEG is the same for all of the star molecules that have the same MePEGn side arms. For example, both the Star (MePEG3)4C and Star (MePEG3)4Si5 showed the same value of Vw,PEG, because the calculation of Vw,PEG only counts the van der Waals volume of the PEG units, which are identical in these two molecules. While the Vw,PEG values are similar, the total van der Waals volume (Vw) is different for each molecule. Most of the star molecules showed large Vf,PEG values (i.e., > 0.65), as we had expected. The Star 8383
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(MePEG12)4C, which contains the smallest core, and the longest MePEG12 arms, showed the largest Vf,PEG (0.92). The overall Vf,PEG of Star (MePEGn)4C molecules increases when the length of the PEG arms are increased from MePEG3 (Vf,PEG = 0.76) to MePEG7 (Vf,PEG = 0.88) to MePEG12 (Vf,PEG = 0.92). The Vf,PEG of the Star (MePEGn)4Si5 molecules also increase similarly: MePEG3 (Vf,PEG = 0.44) to MePEG7 (Vf,PEG = 0.65) to MePEG12 (Vf,PEG = 0.75). In the Star (MePEGn)4Si5 molecules, the tetrakis(dimethylsilyl) orthosilicate core is significantly larger than the Pentaerythritol core of the Star (MePEGn)4C molecules. This increased core size in the Star (MePEGn)4Si5 molecules serves to dilute the Vf,PEG and Vw in these molecules compared with the Star (MePEGn)4C molecules. When the core size is held constant, the Vw,PEG values increase as the number of PEG units increases. Here, we find, as expected, that the star molecules with longer MePEGn arms result in larger volume fractions of PEG. The difference in Vf,PEG between the Star (MePEGn)4Si5 molecules and the Star (MePEGn)4C molecules becomes smaller as the length of MePEGn arms grow. The Star (MePEG3)4C has a Vf,PEG value 73% greater than the corresponding Star (MePEG3)4Si5. The Star (MePEG7)4C has a Vf,PEG 35% greater than Star (MePEG7)4Si5, and Star (MePEG12)4C is 23% greater than the Star (MePEG12)4Si5. Here, the dilution effect of the larger silicon-based core becomes less important as the overall volume of the longer MePEGn arms increases. Fractional Free Volume. The fractional free volume (FFV) in a polymer is the relative fraction of space taken up by the polymer that is not directly occupied by the molecule. That is, the free volume of a polymer is the difference between the actual observed space (i.e., the molar volume, measured through a density measurement) and the estimated van der Waals volume of the polymer (see eq 2 below). Free volume theory specifies that the frequency or rearrangement of the polymer segments is a function of free volume.20,21 We have previously shown that conductivity in our polymer is dependent on the rearrangement of PEG units, such that, in order to move ions from one binding site to another the polymer must physically rearrange.1,1416 In general, we expect that the Hþ conductivity of our PEG-based polymers will increase as the fractional free volume of our copolymers grows.22 We first calculate the free volume (FV) by subtracting the estimated the van der Waals volume (Vw, from a functional group contribution method) from the observed molar volume (MV, from a density measurement), according to eq 2.25 FV ¼ MV V W
ð2Þ
The molar volume of a polymer is the actual, observed volume of one mole of molecules. As we have described previously, the free volume (FV) is a scalar value that depends on the absolute size.2,3 The FFV is independent of the absolute size of the molecule and describes the fraction of unoccupied space (essentially the concentration of free volume) in the polymer, according to eq 3.5 FFV ¼ FV=MV
ð3Þ
We have previously noted that the FFV of our MePEGn polymers depend on the length of the MePEGn units in the polymer.2,3,19 The calculated values of FFV for the various star molecules used in this report are shown in Table 1. In general, star molecules, with the same core, showed increasing FFV with longer MePEGn arms. Specifically, the Star (MePEG3)4C, Star
Figure 1. Arrhenius plot of fluidity (η1) in star molecules: Star (MePEG3)4C (b), Star (MePEG3)4Si5 (O), Star (MePEG7)4C (1), Star (MePEG7)4Si5 (Δ), Star (MePEG12)4C (9), Star (MePEG12)4Si5 (0); Star (MePEGn)4C (closed symbols b,1,9), Star (MePEGn)4Si5 (open symbols O,Δ,0).
(MePEG7)4C, and Star (MePEG12)4C showed FFVs of 0.24, 0.31, and 0.32, respectively. Similarly, the Star (MePEGn)4Si5 molecules showed a smaller proportional increase in the FFV from 0.36 for (MePEG3)4Si5 to 0.37 for the largest (MePEG12)4Si5. The carbon and silicon-based cores used to construct the star molecules also have a strong effect on the measured FFVs (Table 1). Here, the short MePEG3-armed Star (MePEG3)4Si5 molecule showed a larger FFV (0.36) than the long MePEG12armed Star (MePEG12)4C (0.32). Here, the four dimethyl silyl groups of the tetrakis(dimethylsilyl) orthosilicate core of the Star (MePEGn)4Si5 molecules, contributes a significant amount of flexibility, and FFV, to the polymer. In comparison, the four methylene (CH2) groups in the Pentaerythritol core in the Star (MePEGn)4C molecules, are significantly smaller, and more prone to crystallization than the four dimethyl silyl groups in the Star (MePEGn)4Si5 molecules. Thus, the pentaerythritol cores of the Star (MePEGn)4C molecules, contribute a much smaller amount of flexibility and FFV to the overall macromolecule. The effect of the two different cores on the fractional free volume (FFV) becomes progressively smaller as the length of the MePEGn arms increase. Specifically, the Star (MePEG3)4C, Star (MePEG7)4C, and Star (MePEG12)4C show smaller FFVs than the corresponding Star (MePEGn)4Si5 molecules by 33%, 16%, and 14%, respectively (Table 1). That is, as the number of PEG units increases, the volume fraction of the molecule’s cores become smaller and, thus, the effect of the different cores on the FFV decreases. Viscosity of the Star Molecules. The viscosity of a polymer is a good predictor of the overall rate of reorganization in the polymer electrolyte. We have predicted that the PEG-based star molecules will show much lower viscosities than our previously studied MePEGn polymers because of their highly branched structures.2,3 We have measured the viscosities (η) of the various star molecules at several temperatures and plotted the results in Figure 1 as Arrhenius plots of fluidity (fluidity = η1).2,3,19,23,24 As we expected, the star molecules showed lower viscosities (higher fluidities) than our previously studied MePEGn polymers.3 Typically, the viscosity of a polymer increases as the molecular weight increases, and as the FFV decreases. Our Star (MePEGn)4Si5 8384
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Figure 2. Dependence of viscosity on molecular weight of star molecules at 55 °C (note: this is a loglog plot).
molecules show both larger FFVs (favoring larger fluidities) and larger molecular weights (favoring smaller fluidities) than the Star (MePEGn)4C molecules. Figure 1 compares the fluidity of the different star molecules with the two different cores. In each case, the Star (MePEGn)4C molecules give larger fluidities than the corresponding Star (MePEGn)4Si5 molecules (despite their favorable FFV). While the difference in the molecular weights between the two cores was a constant 425 g/mol, the percentage difference, in molecular weight, decreases as the number of PEG units increases. That is, the difference in the molecular weight of the core remains constant, as the length of the arms increases. For comparison, the small MePEG3-armed Star (MePEG3)4C has a much smaller molecular weight (37%) than the corresponding Star (MePEG3)4Si5, and, consequently, showed a much larger fluidity (Figure 1, VTF parameters listed in Table S1). In addition, the long-armed Star (MePEG12)4C and Star (MePEG12)4Si5 molecules have a much smaller difference in molecular weight (16%), and consequently, show a smaller change in viscosity than Star (MePEG3)4Si5 (Figure 1). While the fractional free volumes (FFV) of our star molecules increased as the length of MePEGn arms increased, both the Star (MePEGn)4C and Star (MePEGn)4Si5 showed smaller fluidities with the increase of the length of the MePEGn arms of the star molecules (Figure 1). Thus, it appears that the effect of molecular weights on viscosity was more important than the effect of FFV in the star molecules. The MarkHouwink equation describes the relationship between molecular weight and viscosity (eq 4) ½η ¼ KðMw ÞR
ð4Þ
Here, Mw is the weight-average molecular weight, [η] is the intrinsic viscosity, which is the ratio of specific viscosity to concentration in the limit of infinite dilution, and R and K are empirical parameters obtained from the slope and intercept of the power law plot.2527 In viscosity measurements of pure polymer samples, logarithmic plots of the zero-shear viscosity versus molecular weight typically show two linear regions, with different slopes, that intersect at a certain molecular weight (MC).25 At this value of MC, the polymer’s chains are long enough to entangle. Therefore, the molecular weight dependence of the viscosity can be described by eq 5 η ¼ K 0 ðMw Þβ
ð5Þ
In eq 5, the exponent β is equal to 3.4 when above the entanglement molecular weight (MC), and 1 < β < 2.5 when
Figure 3. Arrhenius plot of ionic conductivity (σ) of MePEG7SO3H acid dissolved in the Star (MePEGn)4Si5 molecules: Star (MePEG3)4Si5 (b,O); Star (MePEG7)4Si5 (1,Δ); Star (MePEG12)4Si5 (9,0) at high (1.32 M; closed symbols b,1,9) and low MePEG7SO3H acid concentrations (0.26 M; open symbols O,Δ,0).
Figure 4. Arrhenius plot of ionic conductivity (σ) of MePEG7SO3H acid dissolved in the Star (MePEGn)4C molecules: Star (MePEG3)4C (b,O); Star (MePEG7)4C (1,Δ); Star (MePEG12)4C (9,0) at high (1.32 M; closed symbols b,1,9) and low MePEG7SO3H acid concentrations (0.26 M; open symbols O,Δ,0).
below the entanglement molecular weight.26,27 We have plotted the dependence of viscosity on the molecular weight of the different star molecules at 55 °C according to eq 5 (Figure 2, VTF parameters listed in Table S1). Here, the correlation coefficient (R = 0.963) and P value (0.01) of the power law plot indicate a significant correlation of the two parameters. The slope of this power law plot (β = 1.554) is between 1 and 2.5, indicating that the molecular weights of our various star molecules are all smaller than the entanglement molecular weight (MC). That is, the overall sizes of even our long MePEG12-armed star molecules are not long enough to become entangled. Ionic Conductivity. We have measured how the ionic conductivity is affected by the length of the MePEGn arms in our Star Molecules. Specifically, we have measured the ionic conductivity 8385
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Table 2. Volume Fraction of PEG (Vf,PEG) and FFV of the Star Electrolytes with MePEG7SO3H [MePEG7SO3H acid] (M) a
electrolytes
viscosity Vf,PEG,mixb
FFVmixc
(cP) d
Star (MePEG3)4C þ MePEG7SO3H
0.26 1.32
0.76 0.78
0.25 0.29
6.3 13.7
Star (MePEG3)4Si5 þ
0.26
0.49
0.36
21.8
MePEG7SO3H
1.32
0.56
0.36
33.5
MePEG3 polymer þ
0.26
0.56
0.35
MePEG7SO3H e
1.32
0.65
0.35
Star (MePEG7)4C þ
0.26
0.87
0.31
14.0
MePEG7SO3H
1.32
0.85
0.33
26.8
Star (MePEG7)4Si5 þ MePEG7SO3H
0.26 1.32
0.67 0.70
0.37 0.37
22.1 29.3
MePEG7 polymer þ
0.26
0.74
0.37
149 e
1.32
0.76
0.36
111 e
0.26
0.91
0.33
31.8
1.32
0.87
0.34
32.1
0.26
0.76
0.37
36.9
MePEG7SO3H
1.32
0.77
0.36
38.0
MePEG12 polymer þ MePEG7SO3H e
0.26 1.32
0.81 0.81
0.37 0.36
75.8 e 83.1 e
MePEG7SO3H
e
Star (MePEG12)4C þ MePEG7SO3H Star (MePEG12)4Si5 þ
a
Concentration of the added MePEG7SO3H acid in the electrolyte mixture. b Volume fraction of PEG in the mixture of star molecule þ MePEG7SO3H acid. c Fractional free volume in the mixture of star molecule þ MePEG7SO3H acid. d Viscosity in the mixture of star molecule þ MePEG7SO3H acid at 55 °C. e From refs 1 and 2.
of high and low concentrations of the MePEG7SO3H acid dissolved in the Star (MePEGn)4Si5 molecules (Figure 3, VTF parameters listed in Table S2) and the Star (MePEGn)4C molecules (Figure 4, VTF parameters listed in Table S2). The ionic conductivity data are presented as Arrhenius plots and have been fit by the VogelTammannFulcher (VTF) eq 628,29 B 1=2 σ ¼ AT exp ð6Þ TC In eq 6, A is the pre-exponential factor and is related to the concentration of charge carriers, B is the pseudoactivation energy (with units of K), T is temperature, and C is the ideal glass transition temperature. Electrolytes formed from the Star (MePEGn)4Si5 molecules and the MePEG7SO3H acid (called star electrolytes from here forward) showed an increase in conductivity, with the increase in the length of the MePEGn arms, at both high and low acid concentrations (Figure 3). The Star (MePEG12)4Si5 electrolyte with the high acid concentration showed the largest ionic conductivity (1.91 105 S/cm at 55 °C). Interestingly, the Star (MePEG3)4Si5 electrolyte showed the lowest ionic conductivity even at a high concentration of acid, despite the fact that the differences in FFV among the different Star (MePEGn)4Si5 molecules were very small (less than 0.01). The fact that there are differences in ionic conductivity in this series of electrolytes shows that the FFV is not the only factor controlling the ionic conductivity. Thus, we focused on comparing the effects of Vf,PEG and viscosity on the ionic conductivity. Of the three different arm-length Star (MePEGn)4Si5 molecules, the long-armed Star (MePEG12)4Si5 showed the largest
Vf,PEG (0.76; Table 1), as expected, and the largest ionic conductivity (Figure 3). The short-armed Star (MePEG3)4Si5 had the smallest Vf,PEG (0.44) and, consequently, the lowest conductivity. As expected, the medium-armed Star (MePEG7)4Si5 fell between the short and long-armed Star (MePEGn)4Si5 electrolytes. Interestingly, the difference in Vf,PEG between the Star (MePEG7)4Si5 and short-armed Star (MePEG3)4Si5 was 32%, whereas the difference in Vf,PEG between the Star (MePEG7)4Si5 and longarmed Star (MePEG12)4Si5 was only 13%. Consequently, the ionic conductivity of the Star (MePEG7)4Si5 electrolyte is much closer to the long-armed Star (MePEG12)4Si5 than to the short-armed Star (MePEG3)4Si5. Recall that our viscosity results showed that the viscosity of the Star (MePEGn)4Si5 molecules increased as the size of the MePEGn arms increased. The results in Figure 3 showed that the ionic conductivity is increasing as the length of the MePEGn arms increases, in spite of an increasing viscosity. Because of this, and the similarity in the FFVs of these materials, we believe this result shows that the effect of Vf,PEG is more important than viscosity to ionic conductivity in Star (MePEGn)4Si5 electrolytes. Figure 4 shows the effect of MePEGn chain length on the ionic conductivity of the small-core, Star (MePEGn)4C electrolytes. While the Star (MePEG3)4C electrolyte showed the lowest ionic conductivity of all of the Star (MePEG3)4C electrolyte at the low acid concentration (Figure 4), it showed, to our surprise, the highest conductivity at high acid concentration (reaching 2.82 105 S/cm at 55 °C). In order to reach the low acid concentration, only a small amount of MePEG7SO3H acid is added to the electrolytes. With only a small amount added, the MePEG7SO3H acid does not significantly increase the FFV of the electrolyte mixture. From Table 1, we see that the FFV of Star (MePEG3)4C molecule is 0.24, and that value increases to only 0.25 in the low acid concentration electrolyte formed from this star molecule (Table 2). However, in order to reach the high acid concentrations, a large amount of MePEG7SO3H acid is added to the electrolytes, which can add a substantial amount of FFV to the electrolyte mixture. In the case of the high acid concentration Star (MePEG3)4C electrolyte, the FFV (0.29, Table 2) increases substantially from the parent Star (MePEG3)4C molecule (0.24; Table 1). Although the Star (MePEG3)4C molecule showed the highest fluidity in Figure 1, it has a small FFV, which appears to contribute to its low conductivity at the low acid concentration. The ionic conductivity of Star (MePEG7)4C electrolytes and Star (MePEG12)4C electrolytes are also shown in Figure 4. Here, the long-armed Star (MePEG12)4C only showed a slightly larger Vf,PEG and FFV than the medium-armed Star (MePEG7)4C (Table 2). However, the Star (MePEG7)4C electrolytes showed higher conductivities than the Star (MePEG12)4C electrolytes at both high and low acid concentrations. The Star (MePEG7)4C did show a higher fluidity than the Star (MePEG12)4C (Figure 1). This seems to indicate that in the absence of strong variation in the Vf,PEG and the FFV, the viscosity can play an important in predicting the ionic conductivity in these materials. Figure 5 shows a comparison of how the different cores affect the ionic conductivity in the resulting star electrolytes with short MePEG3 arms. Both high and low acid concentrations of the Star (MePEG3)4C electrolyte have higher conductivities than the Star (MePEG3)4Si5 electrolytes (Figure 5, VTF parameters listed in Table S2), in spite of the fact that, the Star (MePEG3)4Si5 molecule shows a 33% larger FFV (Table 1) than the Star (MePEG3)4C. However, the Star (MePEG3)4C shows a higher 8386
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Figure 5. Arrhenius plot of ionic conductivity (σ) of MePEG7SO3H acid dissolved in star molecules with short MePEG3 arms, Star (MePEG3)4C (1,Δ) and Star (MePEG3)4Si5 (9,0) at high (1.32 M; closed symbols 1,9) and low MePEG7SO3H acid concentrations (0.26 M; open symbols Δ,0).
fluidity, and much larger Vf,PEG, than the Star (MePEG3)4Si5 molecule. Here, it appears that the much larger Vf,PEG and higher fluidity were the critical reasons that the Star (MePEG3)4C electrolyte showed higher conductivity. The experimental results were different when we compared the two different cores with the longer MePEG12 arms (Figure 6, VTF parameters listed in Table S2). The Star (MePEG12)4Si5 electrolytes showed a higher ionic conductivity, at both low and high acid concentrations, than the corresponding Star (MePEG12)4C electrolytes. While the Star (MePEG12)4C electrolytes showed larger Vf,PEG (0.91 and 0.87; Table 2) than the Star (MePEG12)4Si5 electrolytes (0.76 and 0.77; Table 2), the Star (MePEG12)4Si5 electrolytes have larger FFV (0.37 and 0.36; Table 2) than the Star (MePEG12)4C electrolytes (0.33 and 0.34; Table 2). Importantly, the FFV is the only factor driving the difference in this comparison. The difference in fluidity between the small core Star (MePEG12)4C and the large-core Star (MePEG12)4Si5, is not nearly as great as the difference between the two different cores with the short-MePEG3 arms (Figure 1). In addition, the relative difference in Vf,PEG is also not nearly as great between the two cores with the long-MePEG12 arms. Thus, it appears that the fluidity and Vf,PEG are as not important as the FFV is in determining the ionic conductivity in these samples. Correlation between Conductivity and Viscosity. We have examined the relationship between conductivity and viscosity in our Star electrolytes. Walden’s rule (eq 7) shows the relationship between conductivity and viscosity in an ideal solution where there are no ionion interactions. Λη ¼ constant
ðWalden0 s ruleÞ
ð7Þ
Here Λ is the molar equivalent conductivity and η is the viscosity. Unfortunately, most ionic liquids and polymer electrolytes (with ionion interactions) do not obey the Walden’s rule. To analyze these ionic liquids and polymer electrolytes, Angell has developed the fractional Walden rule (eq 8).6,30,31 ΛηR ¼ constant
ð8Þ
Here R is the ratio of activation energies for conductance and viscous flow and is a constant between zero and one. An R of 1 indicates ideal behavior, where viscous friction is the only force
Figure 6. Arrhenius plot of ionic conductivity (σ) of MePEG7SO3H acid dissolved in Star molecules with long MePEG12 arms, Star (MePEG12)4C (1,Δ) and Star (MePEG12)4Si5 (9,0) at high (1.32 M; closed symbols 1,9) and low MePEG7SO3H acid concentrations (0.26 M; open symbols Δ,0).
Figure 7. Walden plot of the log of molar equivalent conductivity (Λ) versus the log of fluidity (η1) for MePEG7SO3H acid dissolved in Star (MePEG3)4C and Star (MePEG3)4Si5 electrolytes: Star (MePEG3)4C (b,O); Star (MePEG7)4C (1,Δ); Star (MePEG12)4C (9,0) at high (1.32 M; closed symbols b,1,9) and low MePEG7SO3H acid concentrations (0.26 M; open symbols O,Δ,0).
impeding the motion of ions. The slope of the Walden plot (R) effectively describes the extent of ion-pairing in the sample. Here, the ion-pairing results in an additional impedance to the motion of ions, and yields R values of less than 1. In addition, the presence of ion-pairing increases the overall activation barrier to conductivity, and correspondingly, the ionic conductivity increases more slowly with temperature than fluidity does. In the Walden plot, the y intercept can also provide details about the properties of the solution.32 The “ideal” Walden line is simply a diagonal line (y = x) with a slope equal to one, and an intercept of zero. Data lying below the ideal Walden line, that is, data with a y intercept of less than zero, indicates subionic behavior. There has been a lot of work done exploring the relationship between the conductivity and viscosity.30,3239 8387
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Table 3. Walden Plot Slopes (r) of the Star Electrolytes [MePEG7 electrolytes Star (MePEG3)4C þ MePEG7SO3H Star (MePEG3)4Si5 þ MePEG7SO3H Star (MePEG7)4C þ MePEG7SO3H Star (MePEG7)4Si5 þ MePEG7SO3H Star (MePEG12)4C þ MePEG7SO3H Star (MePEG12)4Si5 þ MePEG7SO3H
SO3H acid] (M) a
Rb
0.26
0.59
1.32
0.59
0.26
0.65
1.32
0.43
0.26
0.54
1.32
0.16
0.26 1.32
0.50 0.30
0.26
0.56
1.32
0.22
0.26
0.61
1.32
0.37
a
Concentration of the added MePEG7SO3H acid in the electrolyte mixture. b Alpha value from the Walden rule (eq 8, data taken from slope of Figure 7).
For example, Ward has studied the correlation between ionic conductivity and viscosity of lithium triflate doped poly(vinylidene fluoride).35 They found Λη decreases with increasing concentration and implied that the amount of ionic association (i.e., ion pairing) increased with increasing salt concentration. Walden plots of our star electrolytes were constructed at low (0.26 M) and high (1.32 M) MePEG7SO3H acid concentrations. Figure 7 shows the correlation between molar equivalent conductivity (Λ) and fluidity (η1) of MePEG7SO3H acid dissolved in the Star (MePEGn)4C molecules. The Star (MePEGn)4Si5 electrolytes gave similar results (not shown). In Figure 7, log Λ is linearly correlated with log fluidity in all of the star electrolytes, as predicted by the Walden relationship. However, all of the data were far below the ideal Walden line, indicating subionic behavior. We believe that this result indicates that our MePEG7SO3H acid is behaving as a weak acid in our polymer electrolytes, and is not completely ionized (i.e., the fraction of mobile Hþ ions is significantly less than 1). This is important that the PEG-based polymers are able to allow some dissociation of the MePEG7SO3H acid (which would be a strong acid in aqueous solution). This indicates that the ether groups are able to act as basic sites, and are able to coordinate to the mobile Hþ cations. We are currently measuring the Ka of the MePEG7SO3H acid in PEG polymers and plan to report this result in an upcoming manuscript. We have previously prepared MePEG7 polymers containing ptoluenesulfonic acid, and determined the degree of acid dissociation in these electrolyes.18 We found that p-toluenesulfonic acid has a much smaller degree of acid dissociation that the MePEG7SO3H acid does in the MePEG7 polymer. However, this subionic result, could also indicate that our MePEG7SO3H acid is disassociated, but is experiencing strong ionpairing between the Hþ cations and the MePEG7SO3 anions in our electrolytes. Table 3 shows the Walden plot slopes (R) of our MePEGn-based star electrolytes. Here, all the slopes of our star electrolytes were less than 0.7, indicating a substantial amount of ionpairing in our Star electrolytes. Moreover, most of the Star electrolytes showed smaller R values at high acid concentration than at low acid concentration. For example, the Star (MePEG7)4C electrolyte showed a slopes of 0.54 at low acid concentration, which decreased dramatically to 0.16 high acid concentration (Table 3). This result is
similar to what has been observed by Ward and co-workers.35 That is, as the ionic concentration increases, the strength of the ion-pairing interaction also increases. In Figure 7, all of the Star electrolytes show linear slopes, that is, the R value is not changing with temperature. This temperature independence suggests that any existing ion-pairing did not vary with temperature. This result likely points to the fact that our acid is incompletely disassociated rather than ion-pairing, as you would expect that ion-paring would be temperature dependent.33
4. CONCLUSION In this paper, we have prepared PEG-based star-shaped macromolecules based on two different “cores” with four MePEGn arms in order to study how the structure of a polymer electrolyte affects it is ionic conductivity. Here, we are examining the viscosity, volume fraction of PEG (Vf,PEG), and FFV as structural parameters. As we expected, the star compounds showed Vf,PEG, higher fluidities, and in some cases larger FFV than our previously studied MePEGn polymers. Through a comparison of the conductivity in a variety of different star electrolytes, we have shown that under different circumstances, each of these three structural parameters are important and can strongly affect the observed ionic conductivity. We also found that the viscosity increased with MePEGn chain length and was linearly proportional to the molecular weight of the star molecule. The Star (MePEG3)4C electrolyte reached a maximum ionic conductivity of 2.82 105 S/cm with high acid concentration (1.32 M) at 55 °C. Graphs of the star molecules on a Walden plot gave results that were far below the ideal Walden line and the slopes (R) of less than 0.7, indicating a large extent of ion-pairing, and, or small populations of free Hþ cations in our star electrolytes. We now believe that MePEG7SO3H acid is behaving as a weak acid in our star compounds. ’ ASSOCIATED CONTENT
bS
Supporting Information. Additional tables of data. This material is available free of charge via the Internet at http:// pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT This research is supported in part by the National Science Foundation (CHE-0616728 and EPS-0903787) and the National Oceanographic and Atmospheric Administration through the NURP/NIUST program (NA16RU1496). ’ REFERENCES (1) Ghosh, B. D.; Lott, K. F.; Ritchie, J. E. Chem. Mater. 2005, 17, 661–669. (2) Ghosh, B. D.; Ritchie, J. E. Chem. Mater. 2010, 22, 1483–1491. (3) Sun, C.; Ritchie, J. E. J. Electrochem. Soc. 2010, 157, B1549– B1555. (4) Bondi, A. J. Phys. Chem. 1964, 68, 441–451. (5) Krevelen, D. W. V. Properties of polymers, 3rd ed. ed.; Elesevier Science Publishers B.V.: Amsterdam, 1990. (6) Videa, M.; Angell, C. A. J. Phys.Chem. B 1999, 103, 4185–4190. 8388
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