Volume Fraction of Ether Is a Significant Factor in Controlling Conductivity in Proton Conducting Polyether Based Polymer Sol-Gel Electrolytes

Article abstract of DOI:10.1021/jp5072082

We have synthesized several copolymers of methyl polyethylene glycol siloxane (MePEG₇SiO₃)_m and methyl polypropylene glycol siloxane (MePPG_nSiO₃)_m as hydrogen ion (H⁺) conducting polymer electrolytes. These copolymers were prepared by a sol-gel polymerization of mixtures of the MePEG and MePPG monomers. We synthesized these H⁺ conducting polymer electrolytes in order to study the relationship between observed ionic conductivity and structural properties such as viscosity, fractional free volume, and volume fraction of ether. We found that viscosity increased as the fraction of the smaller comonomer increased. For the MePPG₂/MePPG₃ copolymer, an increase in fractional free volume increased the fluidity. The heterogeneous copolymers (PEG/PPG copolymers) obeyed the Doolittle equation, while the homogeneous (PEG/PEG and PPG/PPG) copolymers did not. The increase of FFV did not, however, correspond to an increase in conductivity, as would have been predicted by the Forsythe equation. The conductivity data did correspond to a modified Forsythe equation substituting Volume Fraction of Ether (V_f,ether) for FFV. We conclude that the proton conductivity of MePEG copolymers is more dependent on the volume fraction of ether than on the fractional free volume. (Chemical Equation Presented).

Full text of DOI:10.1021/jp5072082

Article
pubs.acs.org/JPCB
Volume Fraction of Ether Is a Significant Factor in Controlling
Conductivity in Proton Conducting Polyether Based Polymer Sol−Gel
Electrolytes
Benjamin Yancey, Jonathan Jones, and Jason E. Ritchie*
Department of Chemistry and Biochemistry, The University of Mississippi, 222 Coulter Hall, University, Mississippi 38677, United
States
S
* Supporting Information
ABSTRACT: We have synthesized several copolymers of methyl poly-
ethylene glycol siloxane (MePEG7SiO3)m and methyl polypropylene glycol
siloxane (MePPGnSiO3)m as hydrogen ion (H+) conducting polymer
electrolytes. These copolymers were prepared by a sol−gel polymerization
of mixtures of the MePEG and MePPG monomers. We synthesized these H+
conducting polymer electrolytes in order to study the relationship between
observed ionic conductivity and structural properties such as viscosity,
fractional free volume, and volume fraction of ether. We found that viscosity
increased as the fraction of the smaller comonomer increased. For the
MePPG2/MePPG3 copolymer, an increase in fractional free volume increased
the fluidity. The heterogeneous copolymers (PEG/PPG copolymers) obeyed the Doolittle equation, while the homogeneous
(PEG/PEG and PPG/PPG) copolymers did not. The increase of FFV did not, however, correspond to an increase in
conductivity, as would have been predicted by the Forsythe equation. The conductivity data did correspond to a modified
Forsythe equation substituting Volume Fraction of Ether (Vf,ether) for FFV. We conclude that the proton conductivity of MePEG
copolymers is more dependent on the volume fraction of ether than on the fractional free volume.
small cations in the absence of water. Neither PEG nor PPG
have the mechanical stability required to serve as a fuel cell
membrane. However, attachment of PEG or PPG groups to an
inorganic matrix can form a hybrid organic/inorganic material
combining the mechanical properties of the inorganic portion
with the anhydrous conductivity of PEG and PPG.5−12
Siloxanes are easy to functionalize, and are chemically and
mechanically stable, due to their chemical similarities to
silica.13−15 Both PEG and PPG can be coupled to siloxanes
by hydrosilylation reactions to form the inorganic/organic
hybrid.5,16−22 Siloxane polymers are easily made from the acid
catalyzed, sol−gel condensation of chlorosilanes or alkoxysi-
lanes. Polymers formed by this condensation can exhibit the
advantages of both the organic and inorganic portions, making
them useful as polymer electrolytes.
We are interested in how the structure of the polymer
electrolyte affects the ionic conductivity. In terms of studying
the structure, we look to intrinsic properties of the polymer
including viscosity, ionic conductivity, fractional free volume,
and volume fraction of the ionically conductive ether
component (i.e., either the PEG or PPG units).
INTRODUCTION
■
Proton exchange membrane fuel cells (PEMFCs) use a
polymer electrolyte to both physically separate the anode
from the cathode and conduct hydrogen ions (H+) between the
electrodes. Polymer electrolytes have the advantage of being
easy to chemically modify, and have properties that support ion
mobility as well as mechanical durability.1−3 Currently, Nafion,
a sulfonated perfluorinated polymer, is the most widely used
proton conducting polymer electrolyte. Nafion has the
necessary chemical stability, mechanical properties, and ionic
conductivity when hydrated for use in a PEM fuel cell. The
major disadvantages of Nafion are its cost, poor hydrophobicity,
and hydration dependent conductivity. Alternatively, mem-
branes based on polybenzimidazole (PBI) and phosphoric acid
have also been developed with an eye toward higher
temperatures without the same water management require-
ments of Nafion.
The hydration dependent ionic conductivity in Nafion limits
the operational temperature to below 80 °C.4 The platinum
catalytic anode in a PEMFC has a low resistance to CO
poisoning (which is commonly present in H2 fuel streams
produced from reforming of fossil fuels). These disadvantages
necessitate the development of new anhydrous polymer
electrolytes for PEM fuel cells, for which the U.S. Department
of Energy has set an operational goal of 0.1 S/cm conductivity
at 120 °C and 50% relative humidity.
Free volume theory is used to statistically evaluate glassy or
amorphous polymer systems.23 The free volume (vf) is defined
as the virtual volume of the molecule (the total volume
Received: July 18, 2014
Polyethylene glycol (PEG) and poly(ethylene oxide) (PEO),
and the related polymer polypropylene glycol (PPG), conduct
Revised: October 14, 2014
Published: October 14, 2014
© 2014 American Chemical Society
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indirectly occupied through random molecular motions, vm)
minus the hard sphere volume (van der Waals volume, vw) of
the molecule.23−25 Free volume is a scalar quantity that is
dependent on the sample size of the material but can be
expressed as the sample size independent: molar free volume
(Vf, eq 1).
When calculating the free volume of a polymer, the molar
volume (Vm, eq 2) is first calculated using the density and
molecular weight of the molecule, and then, the molar van der
Waals volume (Vw) is calculated using the group contribution
method developed by Bondi.24,26,27 Further, the fractional free
volume (FFV, eq 3) is very useful in describing transport
behavior in these systems, and is expressed as the ratio of molar
free volume (Vf) to total molar volume (Vm). Fractional free
volume is independent of sample geometry and volume and is
useful for comparing the free volume of different materi-
als.24,26,27
Fractional Walden’s Rule:
Ληα = constant
(6b)
Doolittle developed an empirical equation (eq 7) to describe
the relationship between free volume and viscosity.29,33
Doolittle’s relationship demonstrates that a smaller fractional
free volume results in a smaller fluidity. In eq 7, A and q are
material specific constants where A represents the fluidity
extrapolated to zero free volume and q is a measure of the
liquid’s intermolecular forces. In addition, Vm and Vf are the
total molar volume and molar free volume, respectively. The
ratio Vm/Vf is equivalent to the inverse fractional free volume
(FFV−1), and substitution results in eq 7a.
Doolittle’s Equation:
⎡
⎤
Vm
1
η
= A exp −q
⎢
⎥
⎦
V
⎣
(7)
f
V = Vm − Vw
(1)
f
⎡ −q ⎤
1
η
= A exp
⎢
⎥
⎦
MW
d
⎣
FFV
(7a)
Vm =
(2)
Cohen and Turnbull combined the Stokes−Einstein
equation (eq 4) with the Doolittle equation (eq 7), resulting
in the Cohen−Turnbull equation (eq 8). In this equation, A
incorporates all of the constants in eq 4 and γ is the same as q
in the Doolittle equation.25 The Cohen−Turnbull equation
illustrates that, as the fractional free volume increases, the
diffusion coefficient will also increase. Forsythe combined the
Nernst−Einstein equation (eq 5) with the Cohen−Turnbull
equation (eq 8), resulting in the Forsythe equation (eq 9).34
The Forsythe equation shows that, when the fractional free
volume is increased, the ionic conductivity (σ) should increase
as well.
V
Vm
(Vm − Vw)
f
FFV =
=
Vm
(3)
In free volume theory, the transport properties of a material
(e.g., viscosity - η, conductivity - σ, and diffusion coefficient -
D) are dependent on the free volume.28,29 For example,
diffusion through a material is described as translation through
openings in the free volume in a particle’s vicinity.25 Free
volume, in this description, is a measure of the concentration of
void space in a material.
The Stokes−Einstein equation (eq 4) predicts that an
increase in fluidity (fluidity = η−1) will result in an increase in
the diffusion coefficient (D). The Nernst−Einstein equation
(eq 5) predicts that an increase in the diffusion coefficient of
either ion results in a proportional increase in the ionic
conductivity.30 Equations 4 and 5 together indicate that an
increase in the fluidity will cause an increase in the ionic
conductivity.
Cohen−Turnbull Equation:
⎡
⎤
γ
D = A exp −
⎢
⎥
⎦
⎣
(8)
(9)
FFV
Forsythe Equation:
2
2
⎛
⎞
⎡
⎤
ACF Z
−γ
FFV
σ =
exp
⎜
⎝
⎟
⎠
⎢
⎣
⎥
⎦
Stokes−Einstein Equation:
RT
kT
D
=
phys
6πηRH
(4)
EXPERIMENTAL SECTION
Materials. Polyethylene glycol monomethyl ether
■
Nernst−Einstein Equation:
(CH3(OCH2CH2)nOH = MePEGnOH, Mn = 350, n = 7.24;
Aldrich) and polypropylene glycol monomethyl ether
(CH3(OCH(CH3)−CH2)nOH = MePPGnOH, Mn = 148.2,
206.3, n = 2, 3; Aldrich) were dried at 60 °C under a vacuum
for approximately 24 h prior to use. This paper will refer to
poly(ethylene glycol) monomethyl ether Mn = 350 as
MePEG7OH, tri(propylene glycol) monomethyl ether Mn =
206.3 as MePPG3OH, and di(propylene glycol) monomethyl
ether Mn = 148.2 as MePPG2OH. Copolymers of MePEG7 and
MePPG3 will be referred to as MePEG7/MePPG3, MePEG7
and MePPG2 copolymers as MePEG7/MePPG2, and MePPG3
and MePPG2 copolymers as MePPG3/MePPG2.
Triethoxysilane (Aldrich), allyl bromide (Acros), Karstedt’s
catalyst (platinum(0)-1,3-divinyl-1,1,3,3-tetramethyldisiloxane
complex solution in xylene, Pt ∼2%; Aldrich), and sodium
sulfite (Fisher) were all used as received. Amberlite IRA-
400(Cl) anion exchange resin (Aldrich) and Amberlite IR-
F2
RT
2
2
σION
=
[z+ D C + z− D−C−]
+
+
(5)
Walden’s rule (eq 6a) defines the relationship between
fluidity and conductivity. In this equation, Λ is the molar
equivalent conductivity and η is the viscosity. This rule
generally holds true for ideal solutions in which there are no
ion−ion interactions. However, in real electrolyte solutions, the
fractional Walden rule (eq 6b) is a better descriptor of real
physical observations.31,32 In eq 6b, α is a constant between 0
and 1, with α = 1 representing ideal behavior (eq 6a); that is,
viscosity is the only force impeding ionic mobility. Where 0 < α
< 1, other forces are present that impede ionic mobility.
Walden’s Rule:
Λη = constant
(6a)
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120H cation exchange resin (Aldrich) were used as received.
Phosphorus tribromide (99%; Aldrich) was prepared as a 1.98
M solution in dry diethyl ether using 55.91 g of phosphorus
tribromide dissolved into 85.0 mL of dry diethyl ether. Sodium
hydride (Aldrich) was rinsed thoroughly with hexanes and
filtered prior to use to remove any mineral oil. Dry
tetrahydrofuran (THF) and diethyl ether (Et2O) were obtained
from Fisher as Optima grade and dried using a PPT Glass
Contour Solvent Purification System, under argon, immediately
prior to use, and kept under an inert atmosphere.
Scheme 1. Synthesis of MePEG/MePPG Polymer
Methods. The density and concentrations of the polymer
samples were measured gravimetrically, as has been previously
described.35 The concentrations of the MePEG7SO3H acid/
MePEGn copolymer mixtures were calculated by converting the
mass of both the acid and the polymer to volume using their
respective densities. Then, the mass of acid was converted to
moles by using the acid’s molecular weight and was divided by
the total volume of the acid plus polymer (this method
specifically assumes that the volumes are additive).
The viscosities of the polymer samples were measured using
a Brookfield DV-III Ultra Programmable Rheometer. The CPE-
40 spindle was used and the viscosities measured under a flow
of dry nitrogen at three different rotational speeds which were
averaged. The rotational speeds were selected to keep the
torque in a range of 10−100%. The samples were dried at 50
°C under a vacuum prior to measurement.
Gel permeation chromatography (GPC) measurements were
performed using two 30 cm PL Mixed-D analytical columns
with a Polymer Laboratories ELS-2100 evaporative light
scattering detector. Polystyrene molecular weight standards
(PL-EasiCal PS-2, MW range 580−480 000) were used to
calibrate the MW range prior to running unknown samples.
THF was then allowed to elute through the column for 30 min
to remove any remaining samples and to equilibrate the system.
Unknown samples were made by dissolving 2−3 mg of sample
in 1 g of THF.
Synthesis of Tri(propylene glycol) Allyl Methyl Ether
(MePPG3OCH2CHCH2) (2b). MePPG3 allyl (2b; Scheme 1)
was synthesized analogously to the method used to prepare 2a.
Briefly, NaH (4.87 g, 202.9 mmol) was slurried with THF in an
air-free round-bottom flask. MePPG3OH (20.91 g, 101.5
mmol) was dissolved in THF and added dropwise to the
NaH/THF slurry. Allyl bromide (19.63 g, 162.2 mmol) was
dissolved in THF and added dropwise to the reaction mixture.
A clear viscous liquid (2b) was recovered (18.11 g, 73.6 mmol,
72.5% yield). NMR (1H, in CDCl3), δ (ppm): 1.1 (s, 9H),
3.27−3.41 (m, 9H), 3.99 (d, 2H), 5.12 (dd, 2H), 5.83 (m, 1H).
NMR (13C, in CDCl3), δ (ppm): 17.02, 56.60, 58.98, 70.02,
72.89−75.85, 116.10, 135.45.
Synthesis of Di(propylene glycol) Allyl Methyl Ether
(MePPG2OCH2CHCH2) (2c). MePPG2 allyl (2c; Scheme 1)
was synthesized according to the method used to prepare 2b
using the following amounts: NaH (6.10g, 254.1 mmol),
MePPG2OH (25.13 g, 169.6 mmol), and allyl bromide (40.00
g, 330.6 mmol). A clear viscous liquid (2c) was recovered
(22.34 g, 118.7 mmol, 70.0% yield). NMR (1H, in CDCl3), δ
(ppm): 1.16 (s, 6H), 3.34−3.62 (m, 6H), 4.07 (d, 2H), 5.21
(dd, 2H), 5.91 (m, 1H). NMR (13C, in CDCl3), δ (ppm):
17.35, 56.88, 59.25, 70.26, 73.19−76.05, 116.50, 135.48.
MePEG7 Monomers: MePEG7OCH2CH2CH2Si(OEt)3 (3a)
was prepared as previously described.5,16,17
AC-impedance measurements were performed using a PAR
283 potentiostat equipped with a PerkinElmer 5210 lock-in
amplifier.16 Conductivity is determined from a Nyquist plot by
the diameter of the high frequency semicircle.36
NMR measurements were made with either a Bruker AC-300
or Bruker DRX-500 instrument.
Strong acid ion exchange columns were prepared by placing
50 mL (95 mequiv) of Amberlite IR-120H ion-exchange resin
(1.9 mequiv/mL) in a chromatography column with a porous
frit. Hydrochloric acid (1 M, 300 mL, 300 mequiv) was allowed
to flow through the column to exchange all of the cation sites to
H+. Deionized water was then allowed to flow through the
column until the pH of the column was near neutral pH
(∼6.0−8.0). A strong base exchange column was similarly
prepared with 50 mL (70 mequiv) of Amberlite IRA-400(Cl)
strongly basic ion-exchange resin (1.4 mequiv/mL), followed
by charging with sodium hydroxide (1 M, 225 mL, 225
mequiv), and rinsing with deionized water to a near neutral pH.
Synthesis. Scheme 1 describes the synthesis of MePEG and
MePPG polymers (4a−c) from MePEG7OH and MePPGnOH
(1a−c). Samples with the “a” designation were prepared from
the MePEG7OH as a starting material, while samples with the
“b” and “c” designations were prepared from MePPG3OH and
MePPG2OH, respectively. Table S1 (Supporting Information)
summarizes preparation of the sol−gel copolymers.
Synthesis of MePPG3 Monomer (MePPG3OCH2CH2CH2Si-
(OEt)3) (3b). The MePPG3 monomer was prepared analogously
to 3a using the following amounts: triethoxysilane (14.50 g,
88.4 mmol), 2b (18.11 g, 73.6 mmol), and Karstedt’s catalyst
(∼80 μL). A clear viscous liquid (3b) was recovered (28.30 g,
69.0 mmol, 93.8% yield). NMR (1H, in CDCl3), δ (ppm): 0.57
(m, 2H), 1.07 (m, 9H), 1.17 (m, 9H), 1.58 (m, 2H), 3.29−3.54
(m, 9H), 3.80 (m, 6H).
Synthesis of MePPG2 Monomer (MePPG2OCH2CH2CH2Si-
(OEt)3) (3c). MePPG2 monomer (3c) was prepared in the same
manner as 3a using the following amounts: triethoxysilane
(30.60 g, 186.6 mmol), 2c (22.34 g, 169.6 mmol), and
Karstedt’s catalyst (∼80 μL). A clear viscous liquid (3c) was
recovered (31.16 g, 88.5 mmol, 52.2% yield). NMR (1H, in
CDCl3), δ (ppm): 0.56 (m, 2H), 1.07 (m, 6H), 1.16 (m, 9H),
1.60 (m, 2H), 3.25−3.54 (m. 6H), 3.76 (m, 6H).
Synthesis of MePEG7 Polymer (MePEG7OCH2CH2CH2SiO1.5)
(4a). The MePEG7 polymer (4a) was prepared as previously
described.5,16,17
MePEG7 Allyl: (MePEG7OCH2CHCH2) (2a) was prepared as
previously described.5,16,17
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Table 1. Fractional Free Volumes for PEG−PPG Copolymers and MePEG7SO3H Acid
a
b
c
d
e
polymers and copolymers
MePEG7 polymer
MW (g/mol)
D (g/mL)
molar volume (Vm)
van der Waals volume (Vw)
FFV
Vf,ether
443
299
241
407
371
335
393
342
292
285
270
256
414
1.169
1.109
1.141
1.151
1.137
1.148
1.159
1.156
1.136
1.104
1.116
1.123
1.212
379
270
211
354
326
292
339
296
257
258
242
228
342
262
183
147
242
222
203
234
205
176
174
165
156
267
0.309
0.321
0.304
0.314
0.317
0.305
0.310
0.308
0.315
0.325
0.318
0.314
0.330
0.789
0.697
0.622
0.772
0.751
0.727
0.763
0.729
0.685
0.681
0.663
0.644
0.973
MePPG3 polymer
MePPG2 polymer
f
MePEG7/MePPG3 copolymer
75:25
50:50
25:75
75:25
50:50
25:75
75:25
50:50
25:75
MePEG7/MePPG2 copolymer
MePPG3/MePPG2 copolymer
MePEG7SO3H
a
The effective MW for copolymers represents the MW of one “repeat unit” of the polymer. One repeat unit of MePEG7 polymer is defined as
b
c
MePEG7OCH2CH2CH2SiO3/2. Vm for polymers and copolymers represents the weighted Vm calculated using the effective MW. Vw for polymers
d
and copolymers represents the weighted Vw calculated by the Bondi group contribution method. Fractional free volume (FFV) is calculated
according to eq 3. The calculation of the volume fraction of ether (Vf,ether) has been reported.17,20,37 The 75:25 ratio indicates that this copolymer is
e
f
75% mole fraction MePEG7 polymer and 25% mole fraction MePPG3 polymer (Table S1, Supporting Information).
Synthesis of Sol−Gel Polymer (MePPG3OCH2CH2CH2SiO3/2)
(4b). The MePPG3 polymer (4b) was prepared analogously to
4a using the following amounts: 3b (4.11 g, 10.0 mmol). The
resulting gel 4b was a clear viscous liquid.
Synthesis of Sol−Gel Polymer (MePPG2OCH2CH2CH2SiO3/2)
(4c). The MePPG2 polymer (4c) was prepared in the same
manner as the MePEG7 polymer (4a) using the following: 3c
(4.38 g, 12.43 mmol). The resulting gel 4c was a clear viscous
liquid.
∼100 mTorr for 30 min. The resulting product was a clear and
colorless viscous liquid. The integration of the 1H NMR
trimethylsilyl peak at δ = 0.10 ppm was ratioed to the −OCH3
peak of the MePEG group, showing the presence of 5.7%
uncondensed Si−OH groups in this polymer.
RESULTS AND DISCUSSION
■
Fractional Free Volume (FFV). We have previously
described how to determine the Vw and FFV of a
copolymer.20,24,26,27 The FFV data for our MePEG and
MePPG polymers and their copolymers are shown in Table
1. The FFV values are based on the van der Waals volume as
calculated by the Bondi group contribution method. These
values are average values taken from many different sample
types and generally have a small amount of error associated
with them. However, due to the magnitude of the values, this
error is much smaller than the differences in the values
presented in Table 1. The density is also used in the calculation
of FFV which was measured using a micro balance in triplicate.
The error associated with these measurements is also
insignificant to the tabulated values of FFV.
Synthesis of Sol−Gel Copolymers. The sol−gel copolymers
were polymerized in the same way as the MePEG7 polymer
(4a). Here, the two comonomers were mixed together and an
excess (6 equiv) of slightly acidic water (pH ∼ 3, one drop of
conc. HCl in 100 mL of distilled water) was added. The
millimoles and mole fractions of the comonomers are
summarized in Table S1 (Supporting Information). The
solution was mixed well and allowed to hydrolyze at room
temperature for 12−24 h. The excess water and ethanol were
removed by rotary evaporation, and the resulting gel was placed
in a vacuum oven at 60 °C for 24 h. Table S1 (Supporting
Information) shows the GPC results for these copolymers.
Synthesis of MePEG7SO3H Acid (MePEG7(CH2)3SO3H) was
prepared as previously described.16,17,20−22,35,37
End Group Analysis. End group analysis was performed on
all of the prepared copolymers to test for uncondensed Si−OH
from the sol−gel condensation to form the polymers. Test
samples were mixed with chlorotrimethylsilane, (CH3)3Si−Cl,
with which the uncondensed −OH groups reacted with to label
each residual OH group with a trimethylsilyl group. We then
measured the labeled samples by NMR and ratioed the
integrated peak areas of the trimethylsilyl groups and the
terminal MePEG methyl groups to quantitate the amount of
unreacted −OH groups per polymer unit.
In general, the MePPG3 polymer has greater FFV than the
MePEG7 polymer, and the copolymerization of MePPG3 with
the MePEG7 polymer leads to copolymers with greater FFV as
compared to the MePEG7 polymer. While the differences in
FFV seen in Table 1 appear to be small, we have found that
these small differences in FFV can have a large effect on the
ionic conductivity.20−22,37
We have also described how to calculate the volume fraction
of PEG (Vf,PEG) of a copolymer.17,20,37 Note that we have
previously called this term the volume fraction of PEG;
however, we are also using polypropylene glycol in this paper;
thus, we are switching our notation to the volume fraction of
ether (Vf,ether).5,16,17 The mass and density both were used to
calculate the Vf,ether of these polymers. The error associated with
the density measurements, as stated above, is not significant.
The masses were measured on a standard analytical balance
whose mass is accurate to 0.001 g; this is less than 0.01% of
the masses of the samples measured and is also not significant.
The Vf,ether data is also summarized in Table 1. Of note in
these data is that several polymers have similar FFVs but very
In one experiment, MePEG7 polymer (0.035 g, 0.079 mmol)
was dissolved in 20 mL of toluene in an argon purged flask.
Then, a large excess of chlorotrimethylsilane (0.5 mL, 4 mmol)
was added. The reaction mixture was stirred for 6 h. Afterwards,
2.0 g of K2CO3 was added to quench any unreacted HCl and
then stirred for 1 h. The solution was filtered, and the toluene
and unreacted chlorotrimethylsilane (BP = 57 °C) was
removed by rotary evaporation followed by evacuation to
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Table 2. Ether Volume Fractions for PEG−PPG Copolymer Electrolyte Mixtures with 0.26 and 1.32 M MePEG7SO3H Acid
a
b
polymer
MePEG7 polymer electrolyte
[MePEG7SO3H] (mol/L)
Vf,ether,mix
FFVmix
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
0.26
1.32
0.26
1.32
0.26
1.32
0.452
0.455
0.446
0.454
0.441
0.453
0.450
0.454
0.449
0.454
0.448
0.454
0.450
0.454
0.448
0.454
0.445
0.454
0.445
0.454
0.444
0.454
0.443
0.454
0.309
0.316
0.322
0.324
0.306
0.314
0.315
0.320
0.318
0.322
0.307
0.315
0.312
0.318
0.310
0.317
0.316
0.320
0.325
0.326
0.319
0.322
0.316
0.320
MePPG3 polymer electrolyte
MePPG2 polymer electrolyte
MePEG7/MePPG3 copolymer electrolyte
75:25
50:50
25:75
75:25
50:50
25:75
75:25
50:50
25:75
MePEG7/MePPG2 copolymer electrolyte
MePPG3/MePPG2 copolymer electrolyte
a
b
Vf,ether,mix for copolymer electrolytes is the weighted Vf,ether,mix of the monomeric units and the MePEGSO3H acid. FFVmix for copolymer
electrolytes is the weighted FFVmix of the monomeric units and the MePEGSO3H acid.
Table 3. GPC Data for Copolymers with Weight Average Molecular Weight (Mw), Polydispersity Index (PDI), and Number of
Monomers with the Percent Uncondensed Si−OH
c
d
“high” MW peak
“low” MW peak
a
b
a
b
e
polymers and copolymers
MePEG7 polymer
Mw (Da)
PDI
no. of monomers
Mw (Da)
PDI
1.31
no. of monomers
1.23
% Si−OH
3813
2652
3163
5017
4140
2794
4165
4166
3332
2191
2485
3813
1.37
2.43
8.01
1.53
1.51
4.70
1.46
1.61
1.52
4.57
2.98
3.06
8.61
8.86
13.1
12.3
11.2
8.33
10.6
12.2
11.4
7.69
9.20
14.4
546
1.00
2.30
1.78
1.44
4.74
4.96
1.19
1.19
5.07
1.07
1.96
1.19
MePPG3 polymer
MePPG2 polymer
MePEG7/MePPG3 copolymer
75:25
50:50
25:75
75:25
50:50
25:75
75:25
50:50
25:75
550
577
1.55
1.50
1.35
1.55
MePEG7/MePPG2 copolymer
527
539
450
1.60
1.26
1.52
1.34
1.58
1.54
MePPG3/MePPG2 copolymer
a
b
c
PDI = Mw/Mn. No. of monomers is calculated by dividing Mw by the weighted monomer molecular weight. “High” MW peak is the peak
d
observed with the highest Mw when more than one peak is present. “Low” MW peak is the peak observed with the lowest Mw when more than one
peak is present. % uncondensed Si−OH is equal to H NMR −OTMS divided by 3 Si−OH per monomer times 9 protons per TMS.
e
1
different Vf,ether. For instance, the MePEG7 polymer, the
MePPG2 polymer, and the MePEG7/MePPG2 copolymer all
have a smaller variation in FFV (Table 1: 0.304−0.315, a 4%
variation) but have a much larger variation in the range of the
Vf,ether value (Table 1: 0.622−0.789, a 27% variation).
It appears that in this system we have small variations in FFV
but much larger variations in Vf,ether. We have probed the effect
of FFV on the transport properties by incorporating bulky
groups such as diphenyl siloxane and isobutyl siloxane.20 In this
report, we are adding free volume using PPG groups that lower
the volume fraction of conducting ethers. Thus, we are able to
make a better comparison about the relative contributions of
fractional free volume and volume fraction of ether to the
observed transport properties.
The calculation of the volume fraction of ether in a mixture
of MePEGnSO3H acid and MePEGn and MePPGn copolymers
(Vf,ether,mix) has also been described previously.17,20,37 Table 2
shows the calculated values of the FFV and the volume
fractions of ether in the copolymer/acid electrolyte mixtures. In
the 1.32 M acid containing polymer electrolytes, Vf,ether,mix is
dominated by the contributions of the added MePEG7SO3H
acid. For the low concentration 0.26 M acid containing polymer
electrolytes, Vf,ether,mix for the MePEG7 based polymers had
larger values than the shorter MePPGn based polymers. In this
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case, the lower concentration of the MePEG7SO3H acid
higher MePEG7 fractions. This more random polymerization is
also consistent with a faster polymerization and an open-ended
ladder geometry.
contributes a much smaller amount to the overall Vf,ether
.
Gel Permeation Chromatography (GPC). GPC analysis
was performed to determine the effects of cross-linking in the
polymerization of the MePEGn and MePPGn polymers and
copolymers. Evidence of cross-linking and the degree of
polymerization can be determined from GPC analysis from
the mass and polydispersity index (PDI). The GPC analysis
results for the MePEGn and MePPGn polymers and copolymers
are summarized in Table 3. The GPC data allows us to predict
the structure of our polymers based on the previous work of
Ghosh et al.35 Two peaks were observed in the GPC for many
of the copolymers that correspond to the polymer and dimer
peaks. There is only one peak observed for several of the
copolymers because the monomer and “dimer” of these
copolymers have a small Mw. The ELS detector has difficulty
detecting these low Mw components (ELS sensitivity ∝
MW2).17,20,37
For the polymers that have two peaks, there is a low
molecular weight peak that corresponds to a mixture of
monomers and dimers. For high MW peaks, the Mw, Mn, and
PDI support the formation of T8 silsesquioxane clusters
(Scheme S1, Supporting Information).35 In these high MW
peaks, the number of monomer units ranges from approx-
imately 8 to 15 for the high MW peaks. We have previously
noted that the polystyrene MW standards used to obtain the
Mw and Mn values appear to systematically underestimate the
actual molecular weight of glycol based polymers by up to
40%.16 We did not use PEG based calibration standards so that
our data would be comparable to other data for polymer
electrolytes that use polystyrene calibration standards. In the
low MW peaks, the Mw, Mn, and PDI support the formation of
T2 dimer clusters where one silicon atom is connected to one
other silicon atom with one or more Si−O−Si bonds.
End Group Analysis. End group analysis was performed to
determine if the copolymers were completely condensed, and if
the presence of the copolymer altered the degree of
polymerization. The end group analysis results are also included
in Table 3. The copolymers ranged from 1 to 5% uncondensed
Si−OH. These relatively low numbers indicate that the
condensation was nearly complete, as would be expected
from a completely condensed T8 silsesquioxane cluster. The
highest percentage of uncondensed silanols was in the
copolymers with the highest fraction of PPG. These could be
caused by size incompatibilities or differences in polymerization
rates. Both occurrences would be expected to increase the
amount of uncondensed silanols.
Viscosity. The viscosities of the copolymers were measured
to determine the relationship between fractional free volume
and viscosity for these copolymers. The viscosity data taken at
25 °C is summarized in Table S1 (Supporting Information).
The viscosity of the pure polymers decreases in the order
MePPG2 < MePPG3 < MePEG7. We also see a similar decrease
for the MePPG3/MePPG2 copolymers in the order 25%
MePPG3 < 50% MePPG3 < 75% MePPG3.
The viscosities of the MePPG3/MePPG2 copolymers follow
the same trend as their calculated FFV values. However, in the
heterocopolymers (MePEG7/MePPG3 and MePEG7/
MePPG2), the order of viscosity is 75% > 25% > 50%. This
odd arrangement seems counterintuitive, but this trend is in
fact following the calculated FFV trend.
Figure 1 shows the Doolittle plot of all the copolymers at 25
°C. The best fit line for all of the data points together (i.e., the
For both of the copolymers with the longer MePEG7 (i.e.,
the MePEG7/MePPG3 and MePEG7/MePPG2 copolymers),
the number of monomer units in the high MW peak decreased
as the mole fraction of PPG increased. This likely indicates the
presence of incomplete T8 clusters (i.e., open T7 or T6 clusters;
Scheme S1, Supporting Information). We have characterized
the formation of these incomplete clusters in a previous
publication.35 For the MePPG3/MePPG2 copolymers, the
number of monomer units increased, perhaps indicating the
presence of a ladder type structure.
We also infer from these results that the rate of polymer-
ization is greater for the MePPG polymers, and relatively slower
for the MePEG polymer. The reaction was carried out for 12−
24 h so that the sol−gel reaction would complete hydrolysis of
the ethoxy groups and reach equilibrium. The smaller MePPG2
and MePPG3 comonomers have less steric hindrance, which
likely allows the condensation reaction to proceed faster than it
does for the larger MePEG7 comonomer. It is also noteworthy
that the MePPG2 had the highest number of monomer units in
the high molecular weight peak, indicating that its polymer-
ization rate is the fastest.38 Here a faster rate of polymerization
may make a polymer more likely to adopt the ladder geometry
than the T8 silsesquioxane geometry.
For the polymers with the highest fraction of MePEG7, the
PDI was between 1.3 and 1.6, indicating a small dispersity in
the polymer’s molecular weight. The polymers with higher
fractions of PPG, especially MePPG2, had considerably higher
PDI values ranging from 2.4 to 8.0, indicating a much more
random polymerization compared to those polymers with the
Figure 1. Doolittle plot for all MePEG/MePPG copolymers. The best
fit linear line is shown for the MePPG3/MePPG2 copolymers (y =
−2.2601x + 6.138, R2 = 0.983, p-value = 0.0009) and MePEG7/
MePPGx copolymers (y = −0.3294x + 0.3625, R2 = 0.0505, p-value =
0.628817).
pure polymers, heterocopolymers, and homocopolymers
grouped together) had a poor R2 value (0.0063) and a high
p-value (0.8059), indicating that there is no correlation between
FFV and viscosity for these samples (note: the best fit for all
the data is not shown in Figure 1).
On further inspection, the linear fit of just the MePPG3/
MePPG2 homocopolymers (solid circles and solid line in Figure
1) yielded a very good R2 value (0.983) and a significant p-value
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(0.0009), indicating that there is a strong relationship for these
copolymers. Furthermore, when all of the MePEG/MePPG
heterocopolymers were grouped together (i.e., both the
MePEG7/MePPG2 copolymers and MePEG7/MePPG3 copoly-
mers; open circles in Figure 1), the correlation again showed a
much smaller slope, a poor R2 value (0.0505), and a high p-
value (0.6282). This indicates that the heterocopolymers with
heteromonomers do not follow the Doolittle equation.
There are two considerations to take into account. First,
there is a clear mismatch of monomer sizes that may affect the
viscosity, and second, there is also a great difference in the
slopes (−2.26 and −0.329 for the MePPG homopolymers and
MePEG7/MePPGx heterocopolymers) which, as mentioned
above, is the material specific constant q in eq 7a. This result
agrees with our previous results,20 where the Doolittle fit for
heterogeneous copolymers showed only a moderate R2 value
(0.5340), a low p-value (0.0020), and a shallow slope (−0.611).
Those results indicated that the FFV and viscosity were
correlated, but the moderate R2 and shallow slope suggest the
correlation is not strong, and the low p-value indicates a
significant correlation. The p-value is likely to be larger if the
slope is small, and much more likely to be small with a larger
slope; that is, it is harder for the correlation to occur randomly
if the slope is larger. If this were the case, then the p-value may
not be indicative of a correlation and the FFV and viscosity may
only be moderately correlated for that set of heterogeneous
copolymers.
9). The linear best fit shown has a small slope, a very low R2
value (0.0030), and a large p-value (0.7966). These results
clearly indicate that the Forsythe equation is not obeyed for this
set of copolymers. This is an interesting lack of correlation,
because we have previously observed a correlation between
ionic conductivity and the volume fraction of PEG in a
polymer, which we used as a proxy for free volume. This
correlation, however, existed for MePEG based polymers and
mixtures of MePEG based polymers.16,17 From our previous
studies using the volume fraction of PEG, we understand that
ionic conductivity results from the rearrangement of ether
units. For this work, the Vf,PEG concept has been extended to
include the ethers of PPG, making Vf,ether
.
In our heterocopolymers, both the MePEG and MePPG have
repeating ether units, and can thus both participate in the
overall ionic conductivity. Figure 3 shows a modified Forsythe
These taken together indicate that the structures of the
different copolymers are significantly different (as mentioned
above in the GPC and end group analysis discussion). That is,
differences in reactivity and associational forces make the
MePPG/MePPG homocopolymers have a different structure
from the MePEG/MePPG heteropolymers. Also, this difference
in structure results in a significant difference in the transport
properties of the MePEG/MePPG heterocopolymers.
Ionic Conductivity. The ionic conductivities of the
copolymers were measured to determine the relationship
between ionic conductivity and FFV for these copolymers.
Figure 2 shows a Forsythe plot correlating the molar equivalent
ionic conductivity (Λ) with the inverse of FFV for all
copolymers at 25 °C according to the Forsythe equation (eq
Figure 3. Forsythe plot with volume fraction of ether (Vf,ether) for all
MePEG7/MePPGx copolymers with the best fit linear line shown. y =
−13.1827x − 9.2248, R2 = 0.6146, p-value < 0.00001.
plot with molar equivalent conductivity (Λ) correlated with
Vf,ether (instead of FFV) for all copolymers at 25 °C. The linear
best fit shown has a much greater slope than the Forsythe
correlation with FFV shown in Figure 2. In addition, the
correlation in Figure 3 has a much greater R2 value (0.6146)
and a small p-value (<0.0001), indicating a significant result.
These values indicate that there is a correlation between the
Vf,ether and the equivalent conductivity, indicating that the
MePPGx copolymers behave similarly to our previously studied
MePEG based polymers with respect to the mechanism of ionic
conductivity.16,17,20,37 Further support for this mechanism is
derived from the Arrhenius activation plots (Figure S1,
Supporting Information) which are curved and obey the VTF
equation. It is well-known that this behavior is indicative of ion
transport that is associated with a rearrangement of the polymer
segmental units.
Walden Plot. Figure 4 is the Walden plot for the 1.32 M
polymer electrolytes. It should be noted that these samples are
far below the ideal Walden line. The ideal Walden line has a
slope of α = 1 and passes through the origin. The data was fit to
a linear best fit based on the fractional Walden rule (eq 6b)
where α is the slope of the line for this relationship. For the
1.32 M copolymer electrolytes, the α values ranged from 0.2155
Figure 2. Forsythe plot with fractional free volume for all MePEG7/
MePPGx copolymers with the best fit linear line shown. y = −1.1883x
− 2.6406, R2 = 0.0030, p-value = 0.7966.
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This work and the work by Ghosh et al. suggest that, for the
single component polymers (i.e., those with only MePPG or
MePEG), the FFV can be systematically changed, while, for
heterocopolymers, there seems to be no overall correlation
between FFV and polymer composition. Only the MePPG2/
MePPG3 homocopolymers followed the Doolittle equation,
with the heterocopolymers found to have no correlation to
viscosity.
While there was no relationship found between FFV and
ionic conductivity, there was, however, a strong correlation
between ionic conductivity and Vf,ether observed. These two
observations together provide further evidence that proton
conduction, in this polymer system, proceeds through
rearrangement of the ether units in the PEG or PPG segmental
units. The results of this experiment show that, for
heteropolymers, free volume is less of a contributor to ionic
conductivity than the volume fraction of ether present.
Figure 4. Walden plot for all 1.32 M polymer electrolytes with linear
ASSOCIATED CONTENT
* Supporting Information
Table S1 describing the preparation of the MePEG/MePPG
copolymers, Scheme S1 showing condensed and incompletely
condensed polymer cluster structures, and Figure S1 showing
an Arrhenius activation plot for all 1.32 M polymer electrolytes
with VTF best fit lines. This material is available free of charge
via the Internet at http://pubs.acs.org.
■
●
○
▼
best fit lines shown: ( ) 100% MePEG7; ( ) 100% MePPG3; (
100% MePPG2; ( ) 75% MePEG7/25% MePPG3; ( ) 50%
)
S
■
△
□
◆
MePEG7/50% MePPG3; ( ) 25% MePEG7/75% MePPG3; (
)
▲
◇
75% MePEG7/25% MePPG2; ( ) 50% MePEG7/50% MePPG2; (
25% MePEG7/75% MePPG2; ( ) 75% MePPG3/25% MePPG2; (⬢)
50% MePPG3/50% MePPG2; (⬡) 25% MePPG3/75% MePPG2.
)
△
to 0.5611. No trend was observed for the α values for any of the
copolymer series.
AUTHOR INFORMATION
Corresponding Author
*Phone: 662-915-5329. E-mail: jritchie@olemiss.edu.
Notes
■
The Walden plots shown give further evidence that the FFV
of these copolymer systems is not correlated with the ionic
conductivity. The fact that there is no correlation suggests that,
while viscosity is dependent on the FFV, the ionic conductivity
is not related to FFV. This is most likely due to the mechanism
of ionic conductivity being dependent on hydrogen bond
acceptors such as the ether oxygens in the PEG and PPG. In
addition, the low α values in the Walden plot indicate that
forces other than viscosity are impeding ion mobility (i.e.,
polymer rigidity, small dissociation constant, and/or ion
pairing).
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
■
This work was supported in part by the National Science
Foundation under award numbers CHE-0616728, EPS-
0903787, and EPS-10068S83.
The lower right region of the Walden plot that these polymer
electrolytes fall within also defines electrolytes that are not
completely ionized. Electrolytes in this region demonstrate
ionic conductivity that is considerably smaller than an ideal
electrolyte of the same viscosity. One possibility is that the low
ionic conductivity results from ion pairing, possibly indicating
incomplete dissociation of our MePEG7SO3H acid in these
anhydrous copolymers. Studies are currently underway to
measure the acidity constant of the MePEG7SO3H acid in a
model PEG system. This would allow us to have direct
evidence of the extent of dissociation in systems of this type.
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