Ionic conduction and dielectric response of poly(imidazolium acrylate) ionomers

Article abstract of DOI:10.1021/ma202784e

We use X-ray scattering to investigate morphology and dielectric spectroscopy to study ionic conduction and dielectric response of imidazolium-based single-ion conductors with two different counterions [hexafluorophosphate (PF₆^-) or bis(trifluoromethanesulfonyl)imide (F₃CSO₂NSO ₂CF₃^- = Tf₂N^-)] with different imidazolium pendant structures, particularly tail length (n-butyl vs n-dodecyl). A physical model of electrode polarization is used to separate ionic conductivity of the ionomers into number density of conducting ions and their mobility. Tf₂N^- counterions display higher ionic conductivity and mobility than PF₆^- counterions, as anticipated by ab initio calculations. Ion mobility is coupled to polymer segmental motion, as these are observed to share the same Vogel temperature. Ionomers with the n-butyl tail impart much larger static dielectric constant than those with the n-dodecyl tail. From the analysis of the static dielectric constant using Onsager theory, there is more ionic aggregation in ionomers with the n-dodecyl tails than in those with the n-butyl tails, consistent with X-ray scattering, which shows a much stronger ionic aggregate peak for the ionomers with dodecyl tails on their imidazolium side chains.

Full text of DOI:10.1021/ma202784e

Article
pubs.acs.org/Macromolecules
Ionic Conduction and Dielectric Response of Poly(imidazolium
acrylate) Ionomers
U Hyeok Choi,† Minjae Lee,‡ Sharon Wang,§ Wenjuan Liu,† Karen I. Winey,§ Harry W. Gibson,‡
and Ralph H. Colby*,†
†Department of Materials Science and Engineering, Pennsylvania State University, University Park, Pennsylvania 16802, United States
‡Department of Chemistry, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, United States
§Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
S
* Supporting Information
ABSTRACT: We use X-ray scattering to investigate morphology and dielectric
spectroscopy to study ionic conduction and dielectric response of imidazolium-based
−
single-ion conductors with two different counterions [hexafluorophosphate (PF6 ) or
−
bis(trifluoromethanesulfonyl)imide (F3CSO2NSO2CF3 = Tf2N−)] with different
imidazolium pendant structures, particularly tail length (n-butyl vs n-dodecyl). A
physical model of electrode polarization is used to separate ionic conductivity of the
ionomers into number density of conducting ions and their mobility. Tf2N−
−
counterions display higher ionic conductivity and mobility than PF6 counterions, as
anticipated by ab initio calculations. Ion mobility is coupled to polymer segmental
motion, as these are observed to share the same Vogel temperature. Ionomers with the
n-butyl tail impart much larger static dielectric constant than those with the n-dodecyl
tail. From the analysis of the static dielectric constant using Onsager theory, there is
more ionic aggregation in ionomers with the n-dodecyl tails than in those with the n-
butyl tails, consistent with X-ray scattering, which shows a much stronger ionic aggregate peak for the ionomers with dodecyl tails
on their imidazolium side chains.
ionic liquids, which carry an ionic liquid species in each of the
repeating units.22−34 The major advantages of using the
polymeric forms of ionic liquids are the enhanced stability
and improved mechanical durability resulting from polymer-
ization and the simplification that only the counterions are able
to move large distances rapidly, making polymerized ionic
liquids single-ion conductors. It is of great interest to
understand the general physical picture of structure−property
relations in polymerized ionic liquids. In this paper we focus on
the effects of varying the tail length of the pendant imidazolium
side chains and of two different popular anions as counterions.
Computer simulations have been used to investigate the
influence of different counterions and cation chain lengths in
imidazolium ionic liquids35−39 that are not polymeric. As tail
length increases, locally heterogeneous environments emerge,
consisting of polar (anion/cation pairs) and nonpolar (tail)
regions. Such a morphology has been suggested to affect
viscosity, diffusion, and ionic conductivity. The polar regions
form a variety of ionic structures, consisting of ion pairs and
aggregates formed by dipolar interactions between pairs.40
In contrast to the extensive studies on ionic liquids, little is
known about the basic mechanism of counterion transport in
1. INTRODUCTION
Ionic conduction in ion-containing polymers is of considerable
interest from both fundamental and applied points of view.
Recently, ionic liquids, which are composed entirely of large
cations and anions with weak interactions (310 kJ/mol for 1-
butyl-3-methylimidazolium cation with Tf2N− counterion at 0
K in vacuum),1 have attracted significant interest due to their
unique physical properties such as high thermal and chemical
stability, negligible vapor pressure, broad electrochemical
window (many are stable up to 5 V), and high ionic
conductivity.2−9 In particular, a number of groups have
described imidazolium salts in which the geometric packing
constraints of the planar imidazolium ring, its dangling alkyl
groups, and the delocalization of the charge over the N−C−N
moiety in the ring together reduce ion−ion interactions.6,9−11
These remarkable characteristics make it possible for ionic
liquids to be used as novel and safe electrolytes for advanced
devices such as electrochemical membranes for capacitors,
lithium batteries, fuel cells, and electromechanical transduction
devices for actuators and sensors.12−21 There is a wide chemical
composition range of ionic liquids, achieved by pairing various
organic cations with numerous anions that allows for fine
control of their physicochemical properties.
Moreover, imidazoliums and other organic ionic liquid
cations can be synthesized with vinyl groups so that they can
be easily incorporated into polymers, so-called polymerized
Received: December 26, 2011
Revised: April 4, 2012
Published: April 18, 2012
© 2012 American Chemical Society
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a
Table 1. Ab Initio Interaction Energies at 0 K in a Vacuum for 1-Butyl-3-methylimidazolium Cation with Tf2N− and PF6
−
Counterions
ion pair Epair
(kJ/mol)
triple (+) Etr+
(kJ/mol)
triple (−) Etr−
quadrupole Equad
aggregation factor
pair dipole mpair
counteranion
(kJ/mol)
(kJ/mol)
Equad/2Epair
(D)
−
PF6
320
310
417
413
440
415
732
680
1.14
1.10
15.1
14.1
Tf2N−
a
All calculations were performed using density functional theory methods with the Gaussian 03 software package. Exchange and correlation were
included using the hybrid-GGA B3LYP functional.50−52
residue was extracted with dichloromethane/water 3 times. The
combined organic layer was washed with water and then dried over
Na2SO4. The drying agent was filtered, and the filtrate solution was
concentrated. Column chromatography through a short silica gel
column with THF gave clear yellow oil (20.51 g, 86.8%).
polymerized ionic liquids. Here, we demonstrate the effect of
counterion and tail length on ion migration, aggregation,
dielectric constant, and polymer chain dynamics, which provide
better understanding of conduction in polymerized imidazo-
lium acrylate polymers. Polymerized ionic liquids are single-ion
conductors, and this allows not only a transference number
close to unity as required for advanced electrochemical devices
but also the absence of concentration polarization of cations
that is a common problem encountered in the conventional
solid polymeric electrolytes in which both cation and anion are
mobile.41
To investigate ion and polymer dynamics, the glass transition
temperatures (Tg), ionic conductivities, and dielectric constants
of these polymers were measured. The dielectric measurement
is a particularly powerful tool to investigate the motion of
molecules or substituent groups over a broad time range, 10−7−
102 s.42,43 Segmental motion of polymers and ionomers are
observed in a wide frequency range (mHz to MHz), allowing
study over wide temperature ranges.43 The macroscopic
electrode polarization at lower frequencies in dielectric
measurements can also be interpreted to determine the number
density of conducting ions and their mobility,44−46 which has
recently been utilized with great success for single-ion
conductors above Tg.34,47−49 Our studies of polymer dynamics
are complemented by morphology studies using X-ray
scattering.
−
1-Butyl-3-(10′-carboxydecyl)imidazolium PF6 (1a). A mix-
ture of N-butylimidazole (6.21 g, 50.0 mmol) and 11-bromoundeca-
noic acid (13.97 g, 50.0 mmol) in THF (60 mL) was refluxed for 4
days. After the reaction mixture was cooled to room temperature
(RT), the precipitated bromide salt was filtered and then washed with
cold THF 3 times. The residual brown solid was dissolved in deionized
water (100 mL), and KPF6 (10.12 g, 55 mmol) was added. The
mixture was stirred for 24 h at 50 °C. After decanting the upper
aqueous layer, the residual oil was washed with deionized water and
ethyl ether 3 times each. Drying in a vacuum oven gave a yellow
viscous liquid (16.58 g, 73.1%). DSC (−80 to 200 °C, heating and
cooling rate 5 K/min in N2): Tg = −42.2 °C (second cycle), no other
transition found.
1-Butyl-3-(10′-carboxydecyl)imidazolium Tf2N− (1b). A mix-
ture of N-butylimidazole (6.21 g, 50.0 mmol) and 11-bromoundeca-
noic acid (13.97 g, 50.0 mmol) in THF (120 mL) was refluxed for 4
days. After the reaction mixture was cooled to RT, the precipitated
bromide salt was filtered and washed with cold THF 3 times. The
filtered solid was dissolved in deionized water (100 mL), and LiTf2N
(15.6 g, 55 mmol) was added. The mixture was stirred for 24 h at 50
°C. After decanting the upper aqueous layer, the precipitated oil was
washed with ethyl ether 3 times. The oily product was dissolved in
ethyl acetate (EA) (100 mL) and dried over Na2SO4. After removing
the drying agent by filtration, solvent evaporation and drying in a
vacuum oven gave a yellow viscous liquid (19.4 g, 66%). DSC (−80 to
200 °C, heating and cooling rate 5 K/min in N2): Tg = −55 °C, no
other transition found.
We also compare two ionic liquid counterions:
−
−
F3CSO2NSO2CF3 (referred to as Tf2N−) and PF6 . Both
only bind weakly to imidazolium cations: Table 1 compares 0 K
energies50−52 of formation for ion pairs, positive triple ions,
negative triple ions, and quadrupoles of butylmethylimidazo-
−
1-Dodecyl-3-(10′-carboxydecyl)imidazolium PF6 (1c). A
mixture of N-dodecylimidazole (4.73 g, 20.0 mmol) and 11-
bromoundecanoic acid (5.30 g, 20.0 mmol) in MeCN (15 mL) was
refluxed for 4 days. After the reaction mixture was cooled to RT, the
MeCN was removed by a rotary evaporator. Ethyl ether (80 mL) was
added to solidify the residual bromide salt. The precipitate was filtered
and washed with ethyl ether 3 times. The colorless crystalline solid
(9.02 g, 90%) was obtained after drying in air. The bromide salt (3.55
g, 7.08 mmol) was dispersed in deionized water (200 mL), and KPF6
(2.76 g, 15 mmol) was added. The mixture was stirred for 24 h at 50
°C. After decanting the upper aqueous layer, the residual oil was
washed with deionized water and ethyl ether 3 times each. Drying in a
vacuum oven gave a light-yellow viscous liquid (3.95 g, 98% from the
bromide salt). The product solidified at RT after several days. DSC
(−80 to 200 °C, heating and cooling rate 5 K/min in N2): Tg = −20.3
°C, Tm = 44 °C (second heating scan).
lium with Tf2N− and PF6 . Tf2N− binds more weakly than
PF6 , particularly for the quadrupole energy. Since there is an
−
−
equilibrium between quadrupoles and two ion pairs, Table 1
also lists the ratio of quadrupole energy to twice the pair
energya useful gauge of the propensity to aggregate, which is
larger for PF6 than Tf2N−. This is important because it
−
indicates immediately that imidazolium−Tf2N− should aggre-
−
gate less than imidazolium−PF6 , and this directly affects the
glass transition temperature of these ionomers, with resultant
effects on ion conduction.
2. EXPERIMENTAL SECTION
Materials. 2,2′-Azobis(isobutyronitrile) (AIBN, Aldrich Chemical)
was recrystallized from chloroform below 40 °C and dried in a vacuum
oven. Acetonitrile (MeCN, Aldrich Chemical) for polymerizations was
distilled over calcium hydride. Imidazole, 1-bromodecane, N-
butylimidazole, 11-bromoundecanoic acid, and 4-hydroxybutyl acrylate
were purchased from Aldrich Chemical and used as received.
1-Dodecylimidazole. To a solution of imidazole (6.81 g, 100
mmol) in NaOH (50%) solution (8.80 g, 110 mmol), 1-
bromododecane (24.92 g, 100 mmol) and tetrahydrofuran (THF)
(30 mL) were added. The mixture was refluxed for 3 days. After the
mixture had cooled, THF was removed by a rotary evaporator. The
1-Dodecyl-3-(10′-carboxydecyl)imidazolium Tf2N− (1d).
From the previous experiment, the bromide salt (5.48 g, 11.0
mmol) was dispersed in deionized water (200 mL), and LiTf2N (4.58
g, 16 mmol) was added. The mixture was stirred for 24 h at 50 °C.
After decanting the upper aqueous layer, the residual oil was washed
with deionized water and ethyl ether 3 times each. Drying in a vacuum
oven gave a light-yellow viscous liquid (7.65 g, 99% from the bromide
salt). DSC (−80 to 200 °C, heating and cooling rate 5 K/min in N2):
Tm = 0 °C (first heating scan) Tg = −57 °C (second heating scan), no
other transition found.
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1-{ω-[1′-(4″-Acryloyloxy)butoxy]carbonyldecyl}-3-butylimi-
dazolium PF6− (2a). A solution of 1a (2.98 g, 6.56 mmol) in freshly
distilled SOCl2 (8 mL) was stirred for 24 h at RT under a N2
atmosphere. After removing the excess SOCl2 by vacuum, the residue
was washed with anhydrous ethyl ether 5 times and then dried by a N2
stream. The residue (acid chloride of 1a) was dissolved in dry MeCN
(5 mL), and 4-hydroxybutyl acrylate (1.229 g, 8.53 mmol) was added.
Into the reaction mixture, triethylamine (0.665 g, 6.56 mmol) was
slowly added in an ice bath. The reaction mixture was stirred for 24 h
at RT. After water (20 mL) was added, the product was extracted 3
times with EA, and the combined organic layer was dried over
anhydrous Na2SO4. The drying agent was removed by filtration, and
the solvent of the filtrate was removed by a rotary evaporator. The
product was rinsed with ethyl ether 5 times with vigorous stirring.
Drying in a vacuum oven at RT gave a brown viscous liquid (3.40 g,
89%). DSC (−80 to 60 °C, heating and cooling rate 5 K/min in N2):
Tg = −62 °C, no other transition found.
1-{ω-[1′-(4″-Acryloyloxy)butoxy]carbonyldecyl}-3-butylimi-
dazolium Tf2N− (2b). A solution of 1b (6.150 g, 10.4 mmol) in
freshly distilled SOCl2 (12 mL) was stirred for 24 h at RT under a N2
atmosphere. After removing the excess SOCl2 by vacuum, the residue
was washed with anhydrous ethyl ether 5 times and dried by a N2
stream. The residue (acid chloride of 1b) was dissolved in dry MeCN
(20 mL), and then 4-hydroxybutyl acrylate (1.656 g, 10.9 mmol) was
added. Into the reaction mixture, triethylamine (1.052 g, 10.4 mmol)
was slowly added in an ice bath. The reaction mixture was stirred for
24 h at RT. After water (20 mL) was added, the product was extracted
3 times with EA, and the combined organic layer was dried over
anhydrous Na2SO4. The drying agent was removed by filtration, and
the solvent of the filtrate was removed by a rotary evaporator. The
product was rinsed with ethyl ether 5 times with vigorous stirring.
Drying in a vacuum oven at RT gave a yellow viscous oil (3.16 g,
42%). DSC (−80 to 60 °C, heating and cooling rate 5 K/min in N2):
Tg = −69 °C, no other transition found.
1-{ω-[1′-(4″-Acryloyloxy)butoxy]carbonyldecyl}-3-dodecyli-
midazolium PF6− (2c). A solution of 1c (2.94 g, 5.2 mmol) in freshly
distilled SOCl2 (10 mL) was stirred for 24 h at RT under a N2
atmosphere. After removing the excess SOCl2 by vacuum, the residue
was washed with anhydrous ethyl ether 5 times and dried by a N2
stream. The residue (acid chloride of 1c) was dissolved in dry MeCN
(10 mL), and 4-hydroxybutyl acrylate (0.823 g, 5.7 mmol) was added.
Into the reaction mixture, triethylamine (0.578 g, 5.7 mmol) was
slowly added in an ice bath. The reaction mixture was stirred for 24 h
at RT. After water (20 mL) was added, the product was extracted 3
times with EA, and the combined organic layer was dried over
anhydrous Na2SO4. The drying agent was removed by filtration, and
the solvent was removed by a rotary evaporator. The product was
rinsed with ethyl ether 5 times with vigorous stirring. Drying in a
vacuum oven at RT gave a brown viscous liquid (3.33 g, 84%). DSC
(−80 to 60 °C, heating and cooling rate 5 K/min in N2): Tm = −24
°C, no other transition found.
1-{ω-[1′-(4″-Acryloyloxy)butoxy]carbonyldecyl}-3-dodecyli-
midazolium Tf2N− (2d). A solution of 1d (5.31 g, 7.5 mmol) in
freshly distilled SOCl2 (12 mL) was stirred for 24 h at RT under a N2
atmosphere. After removing the excess SOCl2 by vacuum, the residue
was washed with anhydrous ethyl ether 5 times and dried by an N2
stream. The residue (acid chloride of 1d) was dissolved in dry MeCN
(20 mL), and 4-hydroxybutyl acrylate (1.20 g, 8.3 mmol) was added.
Into the reaction mixture, triethylamine (0.839 g, 8.3 mmol) was
slowly added in an ice bath. The reaction mixture was stirred for 24 h
at RT. After water (20 mL) was added, the product was extracted 3
times with EA, and the combined organic layer was dried over
anhydrous Na2SO4. The drying agent was removed by filtration, and
the solvent was removed by a rotary evaporator. The product was
rinsed with ethyl ether 5 times with vigorous stirring. Drying in a
vacuum oven at RT gave a yellow viscous oil (4.88 g, 79%). DSC (−80
to 60 °C, heating and cooling rate 5 K/min in N2): Tg = −70 °C, no
other transition found.
mol % of the monomer) in degassed MeCN was bubbled with N2 for
30 min. The solution was stirred for 24 h at 65 °C. After removing
MeCN under vacuum, the residue was stirred with EA. Reprecipitation
of the resultant solid from acetone into EA was performed 5 times, and
the precipitated polymer was washed with deionized water twice.
Drying in a vacuum oven at 60 °C gave high-viscosity materials.
4-(Heptanoyloxy)butyl Acrylate (4). To a solution of n-
heptanoic acid (2.60 g, 20.0 mmol), 4-hydroxybutyl acrylate (1.20 g,
13.0 mmol), and N,N′-dicyclohexylcarbodiimide (2.89 g, 14.0 mmol)
in dried dichloromethane (10 mL), a solution of 4-(N,N-
dimethylamino)pyridine (1.71 g, 14.0 mmol) in dichloromethane (5
mL) was slowly added in an ice bath. The reaction mixture was stirred
for 12 h at RT. After ethyl ether (40 mL) was added, a precipitate was
removed by a short Celite column. The filtrate solution was washed
with 1 N HCl solution 3 times, concentrated NaHCO3 2 times, and
water. The organic layer was dried over anhydrous Na2SO4. The
drying agent was removed by filtration, and the solvent of the filtrate
was removed by a rotary evaporator. Drying in a vacuum oven at RT
gave colorless oil (3.01 g, 90%).
Radical Polymerization of 4. A mixture of 4 (1.28 g, 5.0 mmol)
and AIBN (0.164 g, 0.10 mmol) was bubbled with N2 for 30 min. The
mixture was stirred for 24 h at 65 °C. The polymerization mixture was
dissolved in chloroform (5 mL). Precipitation from chloroform into
methanol was performed 3 times. Drying in a vacuum oven at 60 °C
gave colorless rubbery material (0.833 g, 65% yield). No Tg or Tm in
the range of −80 to 200 °C on DSC.
Spectroscopic and Thermal Characterizations. 1H and 13C
NMR spectra were obtained on Varian Inova 400 MHz and Unity 400
MHz spectrometers (results are in Supporting Information). High-
resolution electrospray ionization time-of-flight mass spectrometry
(HR ESI TOF MS) was carried out on an Agilent 6220 Accurate Mass
TOF LC/MS spectrometer in positive ion mode. Differential scanning
calorimetry (DSC) with heating and cooling rates of 5 or 10 K/min on
∼10 mg samples was done using a TA Instruments Q2000 differential
scanning calorimeter (see Supporting Information Figure S11). The
thermal stabilities of these polymers were studied by thermogravi-
metric analysis (TGA) under N2 using a TA Instruments Q500
thermogravimetric analyzer at a heating rate of 10 K/min heating
under N2 purge.
Dielectric Spectroscopy. The dielectric measurements of the
polymers were performed by dielectric relaxation spectroscopy.
Samples were prepared for the dielectric measurement by allowing
them to flow to cover a 30 mm diameter freshly polished brass
electrode at 100 °C in vacuo. To control the sample thickness at 50
μm, silica spacers were placed on top of the sample after it flowed to
cover the electrode. Then a 15 mm diameter freshly polished brass
electrode was placed on top to make a parallel plate capacitor cell
which was squeezed to a gap of 50 μm in the instrument (with precise
thickness checked after dielectric measurements were complete). The
ionomers sandwiched between two electrodes were positioned in a
Novocontrol GmbH Concept 40 broadband dielectric spectrometer,
after being in a vacuum oven at 100 °C for 24 h. Each sample was then
annealed in the Novocontrol at 120 °C in a heated stream of nitrogen
for 1 h prior to measurements. The dielectric permittivity was
measured using a sinusoidal voltage with amplitude 0.1 V and 10−2−
107 Hz frequency range for all experiments. Data were collected in
isothermal frequency sweeps every 5 K, from 120 °C to near Tg.
X-ray Scattering. X-ray scattering was performed with a multi-
angle X-ray scattering system that generates Cu Kα X-rays, λ = 0.154
nm, from a Nonius FR 591 rotating anode operated at 40 kV and 85
mA. The bright, highly collimated beam was obtained via Osmic Max-
Flux optics and pinhole collimation in an integral vacuum system. The
scattering data were collected using a Bruker Hi-Star two-dimensional
detector with a sample-to-detector distance of 11 cm. To minimize the
exposure of the materials to moisture, previously dried samples were
inserted into 1 mm glass capillaries under vacuum at elevated
temperatures from RT to 110 °C. As the samples flowed into the
capillary under vacuum, bubbles were eliminated. The filled capillaries
were cooled to RT under vacuum. Scans were performed from RT to
120 °C, controlling the temperature in situ using a Linkam
Radical Polymerizations of Imidazolium Acrylate Mono-
mers. A solution of the imidazolium acrylate monomer and AIBN (2
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Scheme 1. Synthesis of Poly(N-alkylimidazolium acrylate)s 3a−d
Scheme 2. Synthesis of Nonionic Polymer 5
Table 2. DSC, DRS, and TGA Thermal Analysis, Total Ion Concentration p0, Refractive Index n, and Fragility m of Ionomers
a
b
b
c
sample
DSC Tg (K)
DRS Tg (K)
TGA (°C) 5% w/w loss
p0 (×1020 cm−3
)
n
m
6
C4-PF6 (3a)
C4-Tf2N (3b)
C12-PF6 (3c)
C12-Tf2N (3d)
256
230
244
226
248
222
245
221
341
382
340
12.1
10.3
9.62
8.46
1.461
1.462
1.468
1.469
105
115
83
336
88
a
b
Tg determined from dielectric spectroscopy (defined at ωa(Tg) = 10−2 rad/s). Total ion concentration and refractive index from group
contribution method based on structure.55 m determined from eq 15 using the VFT fit parameters for the segmental (α) peak frequency (open
c
symbols in Figure 8a).
temperature control stage with a step size of ∼30 K and heating and
cooling rates of 10 K/min. Adjustments were made to the set
temperature of the heating device so that the temperature of the
sample inside the glass capillary would equal the desired temperature.
The samples were equilibrated at each temperature for 10 min before
starting the X-ray data collection. The X-ray scattering profiles were
evaluated using Datasqueeze software.53 The intensities were first
corrected for primary beam intensity, and background scattering from
an empty 1 mm glass capillary was subtracted. Intensities were not
corrected for sample density. The isotropic 2-D scattering patterns
were azimuthally integrated to yield intensity versus scattering angle.
ether or water. To prevent a self-polymerization, all monomers
were stored in a freezer (<0 °C) after packing with dry N2.
The radical polymerization of the monomers was done with
2,2′-azobis(isobutyronitrile) (AIBN) in MeCN. The product
polymers were purified by precipitation from EA, which is a
good solvent for the monomers but does not dissolve the
polymers. After purification, the water contents of the polymers
1
1
were checked by H NMR spectroscopy. In the H NMR
spectra (see Supporting Information) the vinyl protons of the
monomers disappeared in the purified polymers, and the
polymers exhibited some peak broadening. The CH2 protons
that are close to the polymer backbone were broadened,
whereas the alkyl protons which are well removed from the
polymer backbone still appear as sharp signals because carbon−
carbon bond rotation is much faster in the alkyl chains which
are far from the polymer backbone and they remained sharp.
To compare the dielectric properties, nonionic polymer 5
was prepared similarly to the imidazolium ionomers as shown
in Scheme 2. After coupling heptanoic acid and 4-hydroxybutyl
acrylate to form monomer 4, the polymerization of 4 was
performed with AIBN without any solvent. The nonionic
polymer 5 was purified by several precipitations from its
chloroform solution to methanol with vigorous stirring. The
nonionic polymer 5 is a rubbery elastomer; however, it does
not show a glass transition in DSC down to −80 °C.
3. RESULTS AND DISCUSSION
A. Ionomer Synthesis. We synthesized new acrylate
monomers and polymers with ionic imidazolium units, as
depicted in Scheme 1. The quarternization reactions of 1-
alkylimidazole and ω-bromoalkanoic acids gave water-soluble
carboxy-terminated imidazolium salts. Ion exchange from the
bromide salts to hexafluorophosphate (PF6−) or bis-
(trifluoromethanesulfonyl)imide (Tf2N−) counterions was
done in water with excess KPF6 or LiTf2N. To confirm the
essentially complete removal of the bromide ions from the
imidazolium salts, a Beilstein copper/flame test54 was
performed before the next reaction. The polymerizable acrylate
unit was introduced by the esterification of the imidazolium
carboxyl salts with 4-hydroxybutyl acrylate. The imidazolium
acrylate monomers (2a−d) are soluble in acetone, MeCN,
DMF, and ethyl acetate (EA), but not soluble in either diethyl
B. Thermal Analysis. The new imidazolium pendant
homopolymers each have a single glass transition, as reported
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Figure 1. X-ray scattering intensity as a function of scattering wavevector q for (a) the imidazolium-based ionomers at room temperature and (b) C4-
PF6 (3a), (c) C4-Tf2N (3b), and (d) C12-Tf2N (3d), each at four temperatures (30, 60, 90, and 120 °C). The arrows indicate peaks that correspond
to the amorphous halo (qI), anion−anion correlations (qII), and separation between ionic aggregates (qIII). The intensity of the ionic aggregation
spacing peak (qIII) increases enormously as the tail length increases from n-butyl to n-dodecyl, which we interpret to signify that dodecyl tails favor
ion aggregation. The data were shifted on the log intensity scale for clarity.
in Table 2. The polymers do not display crystallization or
lower q and its intensity increases significantly, as the tail length
increases from n-butyl to n-dodecyl. The ionomer peak (qIII)
intensity arises from both the uniformity of the interaggregate
spacing and the electron density difference between the matrix
and the ionic aggregates.59 Both the peak positions and peak
intensities remain nearly the same with increasing temperature
as shown in Figures 1b,c,d. Morphological studies of 1-alkyl-3-
methylimidazolium PF6− or Tf2N− ionic liquids as a function of
the alkyl chain length by means of neutron scattering60 and
molecular dynamics simulation38,61 observed quite similar ion
aggregation: ionic liquids with long side chains exhibit a
bicontinuous morphology, one region consisting of polar
moieties (anion/cation pairs and aggregates) and the other
consisting of nonpolar alkyl tails.
D. Ionic Conductivity. To understand the influence of
anions and tail length on ionic conductivity, the temperature
dependence of DC conductivity shown in Figure 2 is evaluated
from a roughly 3 decade frequency range where the in-phase
part of the conductivity σ′(ω) = ε″(ω)ε0ω is independent of
frequency, as shown in Figure 3. The inset in Figure 2 shows
the strong correlation between ionic conductivity at 25 °C and
Tg for these monomers and their polymers. As expected,
monomers with lower Tg show higher ionic conductivity than
the polymers with higher Tg. There also exists a significant
effect from different anions on ionic conductivity for these
ionomers. Because of the suppression in the Tg, the larger
Tf2N− anion raises the ionic conductivity of C4-Tf2N (3b) and
C12-Tf2N (3d) by ∼100× at room temperature, compared to
the PF6− ionomers (C4-PF6 (3a) and C12-PF6 (3c)). However,
an effect from the n-dodecyl vs n-butyl tail on ionic conductivity
is more subtle; that is, ionomers with shorter tail (C4-PF6 (3a)
and C4-Tf2N (3b)) showed slightly higher ionic conductivity in
spite of having higher Tg. In order to better understand
counterion conduction, it is necessary to distinguish whether
the increase in ionic conductivity is due to a larger number
melting in the temperature range of −80 to 200 °C by DSC.
Replacing PF6 with Tf2N− consistently lowered Tg by ∼22 K.
−
The Tf2N− counterion has previously been shown to act at a
plasticizer for imidazolium ionic liquids9,18 and their
polymers.27,33,34 Since association of ion pairs allows them to
act as temporary cross-links that raise Tg, the more strongly
associating PF6 imparts higher Tg than Tf2N− for the
−
poly(imidazolium acrylate)s, as anticipated from the ab initio
results of Table 1. The length of tail also affects the Tg
determined by DSC (denoted DSC Tg): ionomers with n-
dodecyl tails exhibit slightly (∼8 K) lower DSC Tgs than those
with n-butyl tails. However, the Tg, obtained by dielectric
spectroscopy as the temperature at which the peak segmental
relaxation time was 100 s (denoted DRS Tg; listed in Table
255), shows no effect of tail length between ionomers with n-
dodecyl tails and with n-butyl tails. TGA under nitrogen at 10
K/min suggests that all four ionomers are thermally stable at
least until 300 °C.
C. X-ray Scattering. Figure 1a compares the room
temperature X-ray scattering profiles for the four imidazolium
acrylate ionomers with different side chain tail lengths and
counterions. Three distinct peaks are observed: the higher-
angle peak at qI ≈ 14 nm−1 corresponds to the amorphous halo,
the more subtle intermediate-angle peak at qII ≈ 8 nm−1 is
attributed to correlation between the anions,56,57 and the lower-
angle peak at qIII ≈ 2 nm−1 for the ionomers with n-dodecyl
tails and qIII ≈ 4 nm−1 for the ionomers with n-butyl tails
indicates the spacing between ion aggregates.58 For the
amorphous halos at qI, the peak slightly shifts to lower
wavevector as the size of anion increases from PF6− to Tf2N−. A
similar shift is also observed for the anion−anion scattering
peak at qII. However, both qI and qII peaks appear at the same
position as the tail length increases from n-butyl to n-dodecyl.
In contrast, the ionic aggregation scattering peak at qIII shifts to
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decrease in the in-phase part of the conductivity, as the
polarizing ions reduce the field experienced by the transporting
ions. The natural time scale for conduction is the time when
counterion motion becomes diffusive.
εsε0
σDC
τ ≡
σ
(1)
At low frequencies the conducting ions start to polarize at the
electrodes and fully polarize at the electrode polarization time
scale
εEPε0
σDC
τEP
≡
(2)
wherein εEP is the (considerably larger) effective permittivity
after the electrode polarization is complete (see Figure 3). The
Macdonald and Coelho model44−47,62,63 treats electrode
polarization as a simple Debye relaxation with loss tangent,
Figure 2. Temperature dependence of ionic conductivity for PF6− and
Tf2N− ionomers. Tf2N− (C4-Tf2N (3b) and C12-Tf2N (3d)) ionomers
have consistently higher conductivities than PF6 (C4-PF6 (3a) and
C12-PF6 (3c)) ionomers. Solid and dashed curves are eq 16 with all
parameters fixed (values in Tables 3 and 4): Ea and p∞ are determined
by an Arrhenius fit to simultaneously conducting ion content p (Figure
4), while μ∞, D, and T0 are determined by a VFT fit to simultaneously
conducting ion mobility μ (Figure 5). The inset shows ionic
conductivity at room temperature as a function of glass transition
−
ωτEP
tan δ =
1 + ω2τ τ
(3)
σ EP
allowing a two-parameter fit to determine the electrode
polarization time τEP and the conductivity time τσ. The
Macdonald and Coelho model then determines the number
density of simultaneously conducting ions p and their mobility
μ from τEP and τσ
■
●
▲
temperature for these four ionomers (3a ( ), 3b ( ), 3c ( ), and 3d
(
○
▽
)) and two monomers (2b ( ) and 2d ( )).
▼
2
⎛
⎞
τEP
1
p =
⎜
⎝
⎟
⎠
πlBL2
τ
(4)
σ
eL2τ
σ
μ =
4τE2PkT
(5)
wherein lB ≡ e2/(4πεsε0kT) is the Bjerrum length, L is the
spacing between electrodes, k is the Boltzmann constant, and T
is absolute temperature.
Conducting Ion Content. The temperature dependence of
the number density of simultaneously conducting ions p
calculated from eq 4 is plotted in Figure 4, and the fraction of
ions participating in conduction (p/p0 wherein p0, listed in
Figure 3. Dielectric response of imidazolium-based ionomer C4-Tf2N
(3b) to applied AC field at 273 K. The dielectric loss derivative
function εder (blue circles) shows two relaxation processes: segmental
motion (α) at ωα and ions exchanging states (α2) at ωα2. After ion
motion becomes diffusive at τσ, the α2 process not only contributes to
DC conductivity σDC, noted as the plateau region in the in-phase part
of conductivity σ′ (red squares), but also enhances the static dielectric
constant εs in the dielectric permittivity function ε′ (green triangles).
The peak of the loss tangent tanδ (orange diamonds) gives the
geometric mean of the time scales of conductivity and electrode
polarization (τEPτσ)1/2, then determining the number density of
simultaneously conducting ions p and their mobility μ.
density of simultaneously conducting ions p or to an increase in
their mobility μ.
E. Electrode Polarization Analysis. A physical model of
electrode polarization (EP) makes it possible to separate ionic
conductivity into the number density of simultaneously
conducting ions and their mobility,44−46,62,63 as has recently
been done for other single-ion conductors above
Tg.34,47−49,64,65 Electrode polarization occurs at low frequencies,
where the transporting ions have sufficient time to polarize at
the blocking electrodes during the cycle. That polarization
manifests itself in (1) an increase in the effective capacitance of
the cell (increasing the apparent dielectric constant) and (2) a
Figure 4. Temperature dependence of simultaneously conducting ion
concentration p. Solid (PF6− ionomers) and dashed (Tf2N− ionomers)
lines are Arrhenius fits to eq 6 with two fitting parameters (Ea and p∞,
listed in Table 3). The observation that ionomers with the n-dodecyl
tails have much lower p∞ than ionomers with the n-butyl tails suggests
that the n-dodecyl tails aggregate ions. The inset displays the fraction
of anions simultaneously participating in conduction (p divided by the
total anion concentration p0).
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Table 2, is the total anion number density55) is shown in the
Figure 4 inset. The temperature dependence of simultaneously
conducting ion concentration for these imidazolium-based
ionomers is well described by an Arrhenius equation
Mobility of Conducting Ions. The temperature dependence
of the mobility of the simultaneously conducting ions
determined from the EP model is displayed in Figure 5 as
⎛
⎞
⎟
⎠
Ea
RT
⎜
p = p exp −
∞
⎝
(6)
wherein p∞ and Ea, listed in Table 3, are the conducting ion
concentration as T → ∞ and the activation energy for
Table 3. Fitting Parameters (Eq 6) for the Temperature
Dependence of the Number Density of Simultaneously
Conducting Ions
conducting ion concentration
log(p0)
log(p∞)
Ea
1 −
sample
(cm−3
)
(cm−3
)
(kJ/mol)
p∞/p0
C4-PF6 (3a)
C4-Tf2N (3b)
C12-PF6 (3c)
C12-Tf2N (3d)
21.1
21.0
21.0
20.9
20.9
20.5
20.1
19.8
17.5
14.1
12.8
10.2
0.29
0.68
0.86
0.93
Figure 5. Temperature dependence of simultaneously conducting ion
mobilities for PF6− and Tf2N− ionomers, determined from (1) the EP
model (filled symbols) and (2) dividing the DC conductivity data by
the product of the elementary charge e and the Arrhenius fit to eq 6 of
simultaneously conducting ion number density p (open symbols,
referred to as extended mobility). Both mobility and extended mobility
are fit to eq 7 as solid and dashed curves. Tf2N− ionomers (C4-Tf2N
(3b) and C12-Tf2N (3d)) have consistently higher mobilities than
PF6− ionomers (C4-PF6 (3a) and C12-PF6 (3c)). The inset shows the
ionic mobilities with respect to inverse temperature normalized by T0,
indicating that ionomers with n-butyl tails have higher mobilities than
those with n-dodecyl tails.
conducting ions, respectively. The fact that for some ionomers
∞ is smaller than p0 indicates some of the counterions are too
p
strongly aggregated to participate in ionic conduction, and 1 −
p∞/p0 (listed in Table 3), tells us the fraction of counterions
that are trapped and are unable to participate in conduction.65
The observation that ionomers with n-dodecyl tails have much
higher fraction of trapped ions than ionomers with n-butyl tails
suggests that C12-PF6 (3c) and C12-Tf2N (3d) exhibit stronger
ionic aggregation than C4-PF6 (3a) and C4-Tf2N (3b),
consistent with the stronger qIII peak in X-ray scattering in
section 3C and the analysis of the static dielectric constant in
section 3F. The activation energies for the PF6− ionomers (C4-
PF6 (3a) and C12-PF6 (3c)) are higher than those for the
Tf2N− ionomers (C4-Tf2N (3b) and C12-Tf2N (3d)),
indicating a lower binding energy for the imidazolium ions
the filled symbols. Since conductivity can be measured over a
far wider temperature range, we divide the DC conductivity
data in Figure 2 by the elementary charge e and by the
Arrhenius fit to eq 6 of simultaneously conducting ion number
density p to determine an extended mobility, plotted in Figure
5 as the open symbols. Both mobility and extended mobility are
then fit to the Vogel−Fulcher−Tammann (VFT) equation,
⎛
⎞
⎟
⎠
with the larger Tf2N− ions than for the PF6 ions,31 as
−
DT
T − T
0
μ = μ exp −
⎜
∞
anticipated by the ab initio calculations presented in Table 1.
The length of tail also affects the activation energy; ionomers
with n-dodecyl tails exhibit lower activation energies of the
simultaneously conducting ions than those with n-butyl tails.
Without microphase separation, the nonpolar n-butyl tails are
included in the dielectric constant of the surroundings, but
when the n-dodecyl tails microphase separate, they no longer
lower the dielectric constant in the phase where the ions reside.
This effectively means that the dielectric constants (before ions
move) are larger for ionomers with n-dodecyl tails than for
those with n-butyl tails, lowering the effective activation energy
for ion motion.
The inset in Figure 4 indicates that the fraction of
counterions simultaneously participating in conduction (p/p0)
in these single-ion conductors is quite low, <0.1% of the total
number of counterions, except at the highest temperatures
studied. The conducting ion content evaluated from the EP
model is the number density of ions in a conducting state in
any snapshot, which sets the boundary condition for the
solution of the Poisson−Boltzmann equation. Only a small
fraction of total ions is in a conducting state at any given instant
in time, similar to observations on other single-ion conducting
ionomers with alkali metal counterions47−49 or ionic liquid
counterions.34,64,65
⎝
(7)
0
wherein μ∞ is the highest temperature limit of the mobility, T0
is the Vogel temperature, and D is the so-called strength
parameter (reciprocally related to fragility m). The ionic
mobilities of Tf2N− in C4-Tf2N (3b) and C12-Tf2N (3d) are
−
higher than those of PF6 in C4-PF6 (3a) and C12-PF6 (3c)
because the larger Tf2N− anion imparts lower Tg. To
understand the effect of tail length, the mobilities are also
plotted against T0/T (see inset of Figure 5). The data do not
merge into a single curve but instead yield two separate curves.
The ionomers with shorter tails (C4-PF6 (3a) and C4-Tf2N
(3b)) have somewhat higher mobilities than those with longer
tails (C12-PF6 (3c) and C12-Tf2N (3d)) for the same T0/T.
Similar results were reported for pure ionic liquids,11,66
whereby increasing the alkyl chain length from butyl to hexyl
to octyl increases the viscosity of ionic liquids based on 1-alkyl-
3-methylimidazolium with a Tf2N− anion. Since the VFT
temperature dependence of ion mobility reflects the coupling of
segmental motion and ion transport, the lower ion mobility in
our ionomers with C12 is likely caused by their slower
segmental motion due to their stronger ion aggregation, seen
in the X-ray data in Figure 1.
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F. Static Dielectric Constant. The static dielectric
constant εs is defined as the low-frequency plateau of ε′(ω)
before EP begins, shown in Figure 3 and calculated using eq 1
from the measured σDC and τσ obtained from fitting EP to eq
3.47,64,65 Figure 6 displays the static dielectric constant for these
wherein νpair is the number density of ion pairs and mpair is their
dipole moment. The solid and dashed lines in Figure 6 are the
Onsager predictions of eq 9 for each ionomer, assuming all ions
are in the isolated ion pair state (νpair = p0, listed in Table 2)
with the contact pair dipole from ab initio listed in Table 1.
Starting at the top of Figure 6, the Onsager prediction for the
ionomers with n-butyl tails, C4-PF6 (3a) and C4-Tf2N (3b),
agree reasonably with their measured εs. The Onsager equation
predicts that the dielectric constant decreases as temperature
increases (as 1/T) from thermal randomization. The Onsager
prediction for C4-PF6 (3a) is ∼13% above the measured
dielectric constant, presumably indicating that the dipole of the
ion pairs for imidazolium-PF6 is overestimated by ∼7% in our
ab initio calculations (Table 1). Although the ionomers with n-
dodecyl tails exhibit dielectric constants that parallel the
Onsager prediction of eq 9, C12-PF6 (3c) and C12-Tf2N (3d)
show nearly identical dielectric constants across the entire
temperature range, which are more than a factor of 2 below the
Onsager prediction of eq 9. Those ionomers with n-dodecyl
tails are still significantly more polar than the nonionic polymer
5, but many of their ions are aggregated, analogous to lithium
sulfonate−PEO ionomers.59
Figure 6. Temperature dependence of static dielectric constant εs for
imidazolium-based ionomers and a nonionic polymer. The lines are
predictions of the Onsager equation with fixed concentration and
strength of dipoles: the purple dotted line is eq 8 for nonionic polymer
5 with ∑ivimi2/(9ε0k) = 249 K as the sole fitting parameter, and the
colored solid and dashed lines are eq 9 for the four imidazolium-based
ionomers, assuming all ions exist as isolated contact pairs (νpair = p0)
with dipoles given by the ab initio estimates in Table 1 and assuming
the Kirkwood correlation factor g = 1.
Another way to view ion aggregation is that this effectively
correlates neighboring dipoles of ion pairs. Correlation of
neighboring dipoles was considered by Kirkwood70,71 and
Frohlich69 by introducing a prefactor g into eq 9, and this idea
̈
is extensively utilized.42,68,69 For example, the dielectric
constants for highly associating liquids such as acids, alcohols,
and water are underestimated by the Onsager theory.71 On the
other hand, molecules with internal hindered rotation or
restricted rotational degrees of freedom that prohibit alignment
with the field cannot fully respond to the field as expected from
their individual dipole moments, and therefore, the Onsager
model overestimates the resulting dielectric constant.72
imidazolium-based ionomers and the nonionic polymer 5 vs
inverse temperature. The nonionic polymer 5 having no
imidazolium cation nor anion exhibits εs = 8 at room
temperature. εs for the ionomers with imidazolium cation and
either PF6 or Tf2N− anion is much larger, especially for those
−
with n-butyl tails (C4-PF6 (3a) and C4-Tf2N (3b)) with εs ≈ 80
at the lowest temperatures studied. As the tail length increases
from butyl to dodecyl, εs in C12-PF6 (3c) and C12-Tf2N (3d)
significantly decreases.
⎧
⎪
9ε0kT
pairmpair
(εs − ε∞)(2εs + ε∞)
εs(ε∞ + 2)2
⎨
⎪
⎩
g =
2
ν
The temperature dependence of εs for the nonionic polymer
⎫
can be understood through the Onsager equation67−69
⎡
⎤
⎥
⎦
⎪
(εs − ε∞)(2εs + ε∞)
⎬
⎪
⎭
⎢
⎣
−
εs(ε∞ + 2)2
⎡
⎢
⎣
⎤
⎥
⎦
(εs − ε∞)(2εs + ε∞)
εs(ε∞ + 2)2
1
(10)
nonionic
=
νm 2
∑
i
i
9ε0kT
i
(8)
nonionic
If there are no specific correlations, g = 1 and the Kirkwood−
Frohlich equation reduces to the Onsager equation. For polar
̈
wherein νi is the number density of dipoles, mi is their dipole
moment, and ε∞ is the high-frequency limit of the dielectric
constant (here taken to be an approximate value of ε∞ = n2,
where n is the refractive index, listed in Table 2). The purple
dotted line in Figure 6 is fit to eq 8 with the ∑ivimi2 term as the
sole fitting parameter, showing that εs of the nonionic polymer
5 is well described by the Onsager equation. The polymerized
ionic liquids have an imidazolium cation attached to each side
liquids in which dipoles tend to orient with parallel dipole
alignments, g > 1. For example, hydrogen bonding in water
makes g = 2.9 at 0 °C, decreasing steadily as temperature is
increased, to g = 2.3 at 100 °C. When dipoles either prefer
antiparallel alignment or a significant fraction of dipoles are
unable to move in response to the field, g < 1. The g factor can
be calculated from eq 10 by assuming that all ions are in the
isolated contact pair state (vpair = p0 where p0, listed in Table 2,
is the total anion number density) with the contact pair dipole
from ab initio listed in Table 1. Our imidazolium ionomers
exhibit apparent Kirkwood correlation factors 0.8 < g < 1.1 for
ionomers with n-butyl tails and 0.2 < g < 0.4 for ionomers with
n-dodecyl tails, over the whole temperature range studied. This
can explain the strong increase in intensity of the ionic
aggregate scattering peak in the X-ray data of Figure 1, as the
tail length increases from n-butyl to n-dodecyl. Ionic
aggregation makes g ≪ 1 for the ionomers with n-dodecyl
tails while g ≅ 1 for the ionomers with n-butyl tails.
chain with the associated anion (PF6 or Tf2N−) and for such
−
ionomers the contribution of the ions to the static dielectric
constant can be analyzed49,59 by simply adding the effect of ion
pairs to eq 8:
⎡
⎢
⎣
⎤
⎥
⎦
(εs − ε∞)(2εs + ε∞)
εs(ε∞ + 2)2
ionomer
2
⎡
⎢
⎣
⎤
⎥
⎦
ν
pairmpair
(εs − ε∞)(2εs + ε∞)
=
+
εs(ε∞ + 2)2
9ε0kT
(9)
nonionic
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⎛
⎞
G. Dielectric Relaxations. In addition to ion conduction of
these ionomers, to assess the effect of anions and tail length on
polymer chain or ion dynamics, the loss peaks of dipolar
relaxation processes are evaluated. However, electrode polar-
ization and conduction can obscure the loss peaks of interest
that are due to ion motion or segmental relaxation.43 Thus, we
use the derivative formalism73 which eliminates the con-
ductivity contribution from loss spectra to elucidate relaxation
processes in the temperature range where EP and conductivity
dominate.48,49
⎡
⎤
⎡
⎤
′
′
∂εHN(ω)
∂εHN(ω)
π
= Aω−s
−
+
⎜
⎜
⎝
⎟
⎟
⎠
ε
⎢
⎣
⎥
⎦
⎢
⎣
⎥
⎦
der
2
∂ ln ω
∂ ln ω
α2
α
(12)
with
⎧
⎨
⎩
⎫
Δε
′
⎬
εHN(ω) = Real
[1 + (iω/ω )a]b
⎭
HN
wherein A and s are constants, Δε is the relaxation strength, a
and b are shape parameters, and ωHN is a characteristic
frequency related to the frequency of maximal loss ωmax
by43,74,75
∂ε′(ω)
π
ε
= −
der
(11)
2 ∂ ln ω
1/a
−1/a
⎛
⎞
⎛
⎜
⎞
⎟
aπ
abπ
2 + 2b
⎜
⎟
ωmax = ωHN sin
sin
In the derivative spectra of Figure 7, these imidazolium-based
ionomers exhibit two dielectric relaxations designated as α and
α2 in the order of decreasing frequency. The dipolar relaxations
were further explored by fitting the derivative spectra with one
power law for EP plus two Havriliak−Negami (HN) functions
for those two dielectric relaxations
⎝
⎠
⎝
⎠
(13)
2 + 2b
In each fit of the ionomer derivative spectrum at each
temperature, five of the ten parameters in eq 12 are fixed
(EP power law exponent76 s and the two sets of HN shape
parameters a and b) to values given in the Figure 7 caption, and
the relaxation strengths are constrained with Δεα + Δεα + ε∞ =
2
εs. The peak relaxation frequency ωmax and relaxation strength
Δε of the α and α2 processes are determined from this fitting,
and their temperature dependences are displayed in Figure 8. In
ionic liquids, dielectric relaxation processes from motions of
anions and cations are observed.77,78 Ionomers exhibit two
Figure 7. Dielectric loss derivative spectra fit (solid lines) to the sum
of a power law for EP and two derivative forms of the HN function for
−
ion rearrangement and polymer segmental motion of (a) PF6
ionomers (C4-PF6 (3a) and C12-PF6 (3c)) at 303 K and (b) Tf2N−
ionomers (C4-Tf2N (3b) and C12-Tf2N (3d)) at 273 K. Two
relaxation processes (α2 at lower frequency and α at higher frequency)
are observed, and individual contributions of the relaxations are shown
as dashed lines. The solid curves are five-parameter fits to eq 12 with
fixed values of the EP power law slope76 (s) and shape parameters of
Figure 8. Temperature dependence of (a) relaxation frequency
maxima ωmax and (b) relaxation strengths Δε of the α (open symbols)
the two HN functions (a and b) for (a) PF6− ionomers: s = 1.88, aα2
=
and α2 (filled symbols) processes. The solid (PF6 ionomers) and
−
1.0, bα2 = 0.5, aα = 1.0, and bα = 0.2 and for (b) Tf2N− ionomers: s =
1.91, aα2 = 0.88, bα2 = 0.55, aα = 1.0, and bα = 0.2.
dashed (Tf2N− ionomers) curves are fits of the VFT equation (eq 14)
using T0 from the mobility VFT fits in Figure 5.
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Table 4. Fitting Parameters of the VFT Temperature Dependence of the α2 and α Processes and Mobility of Simultaneously
Conducting Ions
α2 process
α process
conducting ion mobility
sample
log(ω∞) (rad/s)
D
log(ω∞) (rad/s)
D
log(μ∞) (cm2 V−1 s−1
)
D
T0 (K)
DSC Tg − T0 (K)
C4-PF6 (3a)
C4-Tf2N (3b)
C12-PF6 (3c)
C12-Tf2N (3d)
8.8
8.7
9.2
8.8
4.3
4.1
5.6
5.0
11.1
11.3
11.0
10.8
4.3
4.1
5.6
5.0
−1.0
−1.1
−0.8
−0.8
3.7
3.4
5.0
4.5
217
196
207
189
39
34
37
37
dipolar relaxations,48,49 assigned to the usual segmental motion
of the polymer (α) and a lower frequency relaxation that
increases in strength with ion content,49 (α2) attributed to ions
rearranging, for instance, exchanging states between isolated
pairs and aggregates of pairs.
Aggregated ions present a strong energetic barrier for
segmental motion that always lowers fragility.81,82 Similar
reductions in fragility with increasing side chain length have
been reported for poly(n-alkyl methacrylates)83 and poly(α-
olefins).84
The peak relaxation frequencies of the α process of glass-
forming liquids, polymers, and ionomers follow VFT temper-
ature dependence with the same Vogel temperature T0 as was
found for the mobility of simultaneously conducting ions.
The peak relaxation frequencies of the α2 processes of these
ionomers occurring at frequencies ∼2 orders of magnitude
lower than those of the α processes also follow a VFT
temperature dependence. Like the α process, Tf2N− ionomers
have faster α2 process than PF6 ionomers due to Tf2N−
−
⎛
⎞
⎟
⎠
DT
T − T
0
counterion imparting lower Tg. Ionomers with the same
counterion have almost identical α2 relaxation frequencies in
spite of having different tail length. This suggests that the α2
processes must be primarily related to rearrangements of ions
that are not strongly aggregated, consistent with literature on
dielectric spectroscopy of other single-ion conducting ion-
omers.48,49,59 In Figure 8b, the relaxation strength Δε for the α2
process is much larger than that for the α process. Additionally,
ωmax = ω exp −
⎜
∞
⎝
(14)
0
The curves in Figure 8a are fits to eq 14 using the T0 from the
mobility VFT fits in Figure 5 with strength parameter D and
high-temperature limiting frequency ω∞ listed in Table 4 for
the α and α2 processes. The α process involves segmental
motion and hence is related to the glass transition. This is why
PF6− ionomers having higher Tg exhibit slower α processes than
Tf2N− ionomers having lower Tg. Many glass-forming liquids
and nonionic polymers have ωmax of the α process ∼0.01 rad/s
at their Tg.79 Here we extrapolate the VFT fits of the α process
(eq 14 and curves in Figure 8a) to 0.01 rad/s to get the DRS Tg
listed in Table 2. There is reasonable agreement between DRS
Tg and DSC Tg for the ionomers with C12 tails but those with
C4 tails have DRS Tg ∼ 8 K lower than DSC Tg and the DRS
Tgs of the ionomers with the same anions (PF6− or Tf2N−) are
nearly identical in spite of different tail length (also evident in
Figure 8a). The ionomers with C12 tails aggregate most of their
ions so the magnitude of the α2 relaxation involving ion
rearrangement is much smaller than for the ionomers with C4
tails, and this is likely why there is a large difference in DRS and
DSC Tgs of the ionomers with C4 tails. Calorimetry sees both α
and α2 processes and is more impacted by the latter, slower
process when its magnitude is stronger (see Supporting
Information Figure S11).
Δεα has a strong temperature dependence, but Δεα has no
2
temperature dependence with Δεα ≈ 8 for all four ionomers.
The stronger α2 process involving ionic rearrangements
primarily determines the temperature dependence of εs
shown in Figure 6. Interestingly, ionomers with n-butyl tails
(C4-PF6 (3a) and C4-Tf2N (3b)) have much larger Δεα than
2
those with n-dodecyl tails (C12-PF6 (3c) and C12-Tf2N (3d)),
consistent with n-dodecyl tails promoting ion aggregation as
seen in X-ray (Figure 1). The n-butyl tails in C4-PF6 (3a) and
C4-Tf2N (3b) allow more ions to participate in conduction
(Figure 4) and rearrange in the α2 process, by not having so
many aggregated ions.
H. Temperature Dependence of Ion Conduction and
Polymer Relaxation. Conductivity is the product of charge e,
number density of carriers p, and their mobility μ for single-ion
conductors, so the temperature dependence of σDC(T) shown
in Figure 2 has already been evaluated by our Arrhenius fit of
p(T) = p∞ exp[−Ea/(RT)] in Figure 4 and our VFT fit of
extended mobility μ(T) = σDC(T)/[exp(T)] to eq 7 in Figure
5.
In polymers with polar side groups, generally an α process is
assigned to side-chain motion.80 The observation that ionomers
with n-butyl tails (C4-PF6 (3a) and C4-Tf2N (3b)) having
higher Tg show even faster α process than those with n-dodecyl
tails (C12-PF6 (3c) and C12-Tf2N (3d)) having lower Tg is
connected to their fragility m, calculated by
⎛
⎞
⎟
⎠
⎛
⎞
⎟
⎠
DT
T − T
Ea
RT
0
⎜
σDC = eμ p exp −
exp −
⎜
∞
∞
⎝
⎝
(16)
0
d log(ω)
DT
0
Predictions of eq 16 with parameters listed in Tables 3 and 4
are shown as the solid and dashed curves in Figure 2. The fact
that ωα, ωα2, μ, and σDC all share a common Vogel temperature
demonstrates strong coupling between motion of counterions
and polymer segmental dynamics. The Vogel temperature T0
lies 37 K below the DSC glass transition temperature for each
ionomer (Tg − T0 ≈ 37 K). A vital point is that the VFT fit in
Figure 5 to extended mobility data calculated from conductivity
enables this conclusion because conductivity is measured with
high precision very close to Tg. Independent VFT fits to the
m = −
=
T (ln 10)(1 − T /T )2
d(T /T)
g
g
0
g
T=T
(15)
g
wherein D and T0 are VFT fitting parameters for ωα (open
symbols in Figure 8a). The estimated fragility m values of these
imidazolium-based ionomers are given in Table 2 with error
estimates based on the extrapolation of the VFT fit to Tg,
discussed above. The 25% higher fragility of ionomers with C4
tails can be understood by the enhanced aggregation of the
ionomers with C12 tails, reflected in the X-ray data of Figure 1.
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Macromolecules
Article
significantly less precise ωα or ωα2 would not yield identical T0
to that from extended mobility, but the Vogel temperature from
extended mobility can give a good description of the
temperature dependences of ωα and ωα2 (compare curves
and data in Figure 8a).
ASSOCIATED CONTENT
* Supporting Information
NMR and high resolution mass spectral data of 1-
■
S
1
dodecylimidazole, 1a−d, 2a−d, and 4; H NMR spectra of
1a−d, 2a−d, 3b, and 4; DSC thermograms of 3a−d; frequency
dependence of loss tangent for 3a−d. This material is available
free of charge via the Internet at http://pubs.acs.org.
Barton, Nakajima, and Namikawa85−87 (BNN) suggested
that conduction and dielectric relaxation have their origins in
one diffusion process and proposed a simple empirical scaling
correlation between ionic conductivity σDC and the product of
relaxation strength Δε and frequency at the loss maximum
AUTHOR INFORMATION
Corresponding Author
*E-mail: rhc@plmsc.psu.edu.
■
ωmax
.
σDC ∝ Δεωmax
(17)
Notes
The authors declare no competing financial interest.
As shown in Figure 9, the conductivity can be successfully
scaled in accordance with eq 17, further demonstrating that
ACKNOWLEDGMENTS
■
This work was supported in part by the U.S. Army Research
Office under Grant W911NF-07-1-0452 Ionic Liquids in
Electro-Active Devices (ILEAD) MURI. The authors are
grateful to James McGrath and Timothy Long for use of
their thermal analysis equipment, James Runt for use of his
dielectric spectrometer, Terry L. Price Jr. for his help in
analytical data collection, David Salas de la Cruz for his help in
X-ray data collection, and Yossef Elabd, Friedrich Kremer,
James Runt, and Qiming Zhang for many helpful discussions.
REFERENCES
■
(1) Ab initio calculations exhibit that the ion dissociation energy at 0
K for 1-buty-3-methylimidazolium cation with Tf2N− counterion (310
kJ/mol) is much lower than that for lithium cation with Tf2N−
counterion (580 kJ/mol).
Figure 9. DC conductivity σDC against the product of relaxation
strength Δε and frequency ωmax of the α2 (filled symbols) and α (open
symbols) processes. The solid and dashed lines are fits of the BNN law
(eq 17) with slopes of unity.
(2) Welton, T. Chem. Rev. 1999, 99, 2071.
(3) Buzzeo, M. C.; Evans, R. G.; Compton, R. G. ChemPhysChem
2004, 5, 1106.
(4) Ohno, H. Electrochemical Aspects of Ionic Liquids; Wiley-
Interscience: Hoboken, NJ, 2005.
(5) Hapiot, P.; Lagrost, C. Chem. Rev. 2008, 108, 2238.
conductivity is strongly coupled with both ion motion (α2
process) and polymer segmental motion (α process).
(6) Weingartner, H. Angew. Chem., Int. Ed. 2008, 47, 654.
̈
(7) Soukup-Hein, R. J.; Warnke, M. M.; Armstrong, D. W. Annu. Rev.
Anal. Chem. 2009, 2, 145.
4. CONCLUSIONS
(8) Armand, M.; Endres, F.; MacFarlane, D. R.; Ohno, H.; Scrosati,
B. Nat. Mater. 2009, 8, 621.
(9) Green, M. D.; Long, T. E. Polym. Rev. 2009, 49, 291.
This paper correlates morphology, ion conduction, and
dielectric response of imidazolium-based single-ion conductors
with two different anions and with two different imidazolium
tail lengths. The effect of counterions is clearly observed in the
glass transition temperature and ionic conductivity; Tf2N−
ionomers with lower Tgs have higher ionic conductivities
than PF6− ionomers with higher Tgs, as anticipated by ab initio
calculations that show that the imidazolium cation is less prone
(10) Leys, J.; Wubbenhorst, M.; Menon, C. P.; Rajesh, R.; Thoen, J.;
̈
Glorieux, C.; Nockemann, P.; Thijs, B.; Binnemans, K.; Longuemart, S.
J. Chem. Phys. 2008, 128, 064509.
(11) Huddleston, J. G.; Visser, A. E.; Reichert, W. M.; Willauer, H.
D.; Broker, G. A.; Rogers, R. D. Green Chem. 2001, 3, 156.
(12) Nanjundiah, C.; McDevitt, S. F.; Koch, V. R. J. Electrochem. Soc.
1997, 144, 3392.
(13) Doyle, M.; Choi, S. K.; Proulx, G. J. Electrochem. Soc. 2000, 147,
34.
(14) Lu, W.; Fadeev, A. G.; Qi, B. H.; Smela, E.; Mattes, B. R.; Ding,
J.; Spinks, G. M.; Mazurkiewicz, J.; Zhou, D. Z.; Wallace, G. G.;
MacFarlane, D. R.; Forsyth, S. A.; Forsyth, M. Science 2002, 297, 983.
(15) Ue, M.; Takeda, M.; Toriumi, A.; Kominato, A.; Hagiwara, R.;
Ito, Y. J. Electrochem. Soc. 2003, 150, A499.
−
to aggregation with Tf2N− counterions than with PF6
counterions. The ionic conductivity is also strongly coupled
with ion motion (α2) and polymer segmental motion (α) from
the observation of a common Vogel temperature in the VFT
temperature dependence of the mobility of simultaneously
conducting ions μ, ion rearrangements (α2), and polymer
segmental motion (α).
(16) Sakaebe, H.; Matsumoto, H. Electrochem. Commun. 2003, 5, 594.
(17) Xu, W.; Angell, C. A. Science 2003, 302, 422.
(18) Fernicola, A.; Scrosati, B.; Ohno, H. Ionics 2006, 12, 95.
(19) Galinski, M.; Lewandowski, A.; Stepniak, I. Electrochim. Acta
2006, 51, 5567.
(20) Zhu, Q.; Song, Y.; Zhu, X.; Wang, X. J. Electroanal. Chem. 2007,
601, 229.
(21) Greaves, T. L.; Drummond, C. J. Chem. Rev. 2008, 108, 206.
(22) Ohno, H.; Ito, K. Chem. Lett. 1998, 751.
(23) Yoshizawa, M.; Ohno, H. Chem. Lett. 1999, 889.
The n-dodecyl tail results in strong ion aggregation over the
whole temperature range studied, as clearly seen in X-ray
scattering and dielectric constant. The n-butyl tail promotes
very little ionic aggregation, with a significantly larger dielectric
constant that agrees reasonably with the Onsager prediction.
Significant increase of the relaxation strength of the ion
rearrangement α2 for ionomers with n-butyl tails accounts for
the significantly larger static dielectric constants and higher
mobilities for the simultaneously conducting ions.
3984
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Macromolecules
Article
(24) Snedden, P.; Cooper, A. I.; Scott, K.; Winterton, N.
Macromolecules 2003, 36, 4549.
(25) Ohno, H.; Yoshizawa, M.; Ogihara, W. Electrochim. Acta 2004,
(62) Coelho, R. J. Non-Cryst. Solids 1991, 131, 1136.
(63) Coelho, R. Physics of Dielectrics for the Engineer; Elsevier: New
York, 1979.
(64) Tudryn, G. J.; Liu, W. J.; Wang, S. W.; Colby, R. H.
Macromolecules 2011, 44, 3572.
(65) Wang, S. W.; Liu, W. J.; Colby, R. H. Chem. Mater. 2011, 23,
50, 255.
(26) Washiro, S.; Yoshizawa, M.; Nakajima, H.; Ohno, H. Polymer
2004, 45, 1577.
(27) Nakajima, H.; Ohno, H. Polymer 2005, 46, 11499.
(28) Ogihara, W.; Suzuki, N.; Nakamura, N.; Ohno, H. Polym. J.
2006, 38, 117.
(29) Ogihara, W.; Washiro, S.; Nakajima, H.; Ohno, H. Electrochim.
Acta 2006, 51, 2614.
(30) Ohno, H. Macromol. Symp. 2007, 249, 551.
(31) Green, O.; Grubjesic, S.; Lee, S.; Firestone, M. A. Polym. Rev.
2009, 49, 339.
1862.
(66) Tokuda, H.; Hayamizu, K.; Ishii, K.; Susan, M. A. B. H.;
Watanabe, M. J. Phys. Chem. B 2005, 109, 6103.
(67) Onsager, L. J. Am. Chem. Soc. 1936, 58, 1486.
(68) Hill, N. E.; Vaughan, W. E.; Price, A. H.; Davies, M. Dielectric
Properties and Molecular Behaviour; Van Nostrand Reinhold Co.:
London, 1969.
(69) Frohlich, H. Theory of Dielectrics: Dielectric Constant and
̈
Dielectric Loss; Clarendon Press: London, 1949.
(70) Kirkwood, J. G. J. Chem. Phys. 1939, 7, 911.
(71) Oster, G.; Kirkwood, J. G. J. Chem. Phys. 1943, 11, 175.
(72) Izgorodina, E. I.; Forsyth, M.; MacFarlane, D. R. Phys. Chem.
Chem. Phys. 2009, 11, 2452.
(32) Xie, M.; Han, H.; Ding, L.; Shi, J. Polym. Rev. 2009, 49, 315.
(33) Chen, H.; Choi, J. H.; Salas-de La Cruz, D.; Winey, K. I.; Elabd,
Y. A. Macromolecules 2009, 42, 4809.
(34) Lee, M.; Choi, U. H.; Colby, R. H.; Gibson, H. W. Chem. Mater.
2010, 22, 5814.
(35) Wang, Y.; Voth, G. A. J. Am. Chem. Soc. 2005, 127, 12192.
(36) Wang, Y.; Voth, G. A. J. Phys. Chem. B 2006, 110, 18601.
(37) Jiang, W.; Wang, Y.; Yan, T.; Voth, G. A. J. Phys. Chem. C 2008,
112, 1132.
(73) Wubbenhorst, M.; van Turnhout, J. J. Non-Cryst. Solids 2002,
̈
305, 40.
(74) Boersma, A.; van Turnhout, J.; Wubbenhorst, M. Macromolecules
̈
1998, 31, 7453.
(75) Diaz-Calleja, R. Macromolecules 2000, 33, 8924.
(38) Lopes, J. N. A. C.; Padua, A. A. H. J. Phys. Chem. B 2006, 110,
(76) The actual EP is often slightly broader than Debye, and in the
past we have fit EP to an asymmetric broader function49 and to a
symmetric Cole−Cole function.65 These yield results for EP that are
qualitatively identical and nearly quantitatively identical to those from
Debye fitting, which is far simpler. When the asymmetric function is
3330.
(39) Margulis, C. J. Mol. Phys. 2004, 102, 829.
(40) Delsignore, M.; Maaser, H. E.; Petrucci, S. J. Phys. Chem. 1984,
88, 2405.
(41) Sun, X. G.; Kerr, J. B.; Reeder, C. L.; Liu, G.; Han, Y.
Macromolecules 2004, 37, 5133.
(42) Bottcher, C. J. F. Theory of Electric Polarization; Elsevier:
Amsterdam, 1973; Vol. 1.
(43) Kremer, F.; Schonhals, A. Broadband Dielectric Spectroscopy;
−
used with slopes of 1.91 for Tf2N− ionomers and 1.88 for PF6
ionomers on the high frequency side of EP, the conducting ion
−
content p is increased 2.1-fold (Tf2N−) and 1.7-fold (PF6 ) at all
temperatures where tan δ shows a maximum for EP and the activation
energy Ea was identical.
(77) Daguenet, C.; Dyson, P. J.; Krossing, I.; Oleinikova, A.; Slattery,
Springer-Verlag: New York, 2002.
(44) Macdonald, J. R. Phys. Rev. 1953, 92, 4.
(45) Coelho, R. Rev. Phys. Appl. 1983, 18, 137.
(46) Barsoukov, E.; Macdonald, J. R. Impedance Spectroscopy Theory,
Experiment and Applications; Wiley: New York, 2005.
(47) Klein, R. J.; Zhang, S.; Dou, S.; Jones, B. H.; Colby, R. H.; Runt,
J. J. Chem. Phys. 2006, 124, 144903.
J.; Wakai, C.; Weingaertner, H. J. Phys. Chem. B 2006, 110, 12682.
̈
(78) Nakamura, K.; Shikata, T. ChemPhysChem 2010, 11, 285.
(79) Angell, C. A. Chem. Rev. 1990, 90, 523.
(80) Yamane, M.; Hirose, Y.; Adachi, K. Macromolecules 2005, 38,
10686.
(81) Adam, G.; Gibbs, J. H. J. Chem. Phys. 1965, 43, 139.
(82) Rodenburg, B. V.; Sidebottom, D. L. J. Chem. Phys. 2006, 125,
024502.
(83) Floudas, G.; Stepanek, P. Macromolecules 1998, 31, 6951.
(84) Stukalin, E. B.; Douglas, J. F.; Freed, K. F. J. Chem. Phys. 2009,
131, 114905.
(85) Namikawa, H. J. Non-Cryst. Solids 1974, 14, 88.
(86) Namikawa, H. J. Non-Cryst. Solids 1975, 18, 173.
(87) Dyre, J. C. Phys. Rev. B 1993, 48, 12511.
(48) Fragiadakis, D.; Dou, S.; Colby, R. H.; Runt, J. Macromolecules
2008, 41, 5723.
(49) Fragiadakis, D.; Dou, S.; Colby, R. H.; Runt, J. J. Chem. Phys.
2009, 130, 064907.
(50) Becke, A. D. J. Chem. Phys. 1993, 98, 5648.
(51) Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B 1988, 37, 785.
(52) Stephens, P. J.; Devlin, F. J.; Chabalowski, C. F.; Frisch, M. J. J.
Phys. Chem. 1994, 98, 11623.
(53) Heiney, P. A. Comm. Powder Diffr. Newsl. 2005, 32, 9.
(54) Beilstein test: A copper wire was heated in a burner flame until
there was no further coloration of the flame. The wire was allowed to
cool slightly, then dipped into the monomer, and again heated in the
flame. A green flash is indicative of halide ions, whereas pure Tf2N−
−
and PF6 salts give orange or red colors.
(55) van Krevelen, D. W. Properties of Polymers; Elsevier: New York,
1990.
(56) Annapureddy, H. V. R.; Kashyap, H. K.; De Biase, P. M.;
Margulis, C. J. J. Phys. Chem. B 2010, 114, 16838.
(57) Salas-de la Cruz, D.; Green, M. D.; Ye, Y. S.; Elabd, Y. A.; Long,
T. E.; Winey, K. I. J. Polym. Sci., Part B: Polym. Phys. 2012, 50, 338.
(58) Wang, W.; Liu, W. J.; Tudryn, G. J.; Colby, R. H.; Winey, K. I.
Macromolecules 2010, 43, 4223.
(59) Wang, W.; Tudryn, G. J.; Colby, R. H.; Winey, K. I. J. Am. Chem.
Soc. 2011, 133, 10826.
(60) Russina, O.; Triolo, A.; Gontrani, L.; Caminiti, R.; Xiao, D.;
Hines, L. G.; Bartsch, R. A.; Quitevis, E. L.; Pleckhova, N.; Seddon, K.
R. J. Phys.: Condens. Matter 2009, 21, 424121.
(61) Bhargava, B. L.; Devane, R.; Klein, M. L.; Balasubramanian, S.
Soft Matter 2007, 3, 1395.
3985
dx.doi.org/10.1021/ma202784e | Macromolecules 2012, 45, 3974−3985