Polymerized ionic liquids with enhanced static dielectric constants

Article abstract of DOI:10.1021/ma301833j

Dielectric spectroscopy was used to determine the static dielectric constants (ε_s) of imidazolium acrylates and methacrylates and their ionomers, with different imidazolium pendant structures containing a combination of alkylene [(CH₂)_n, n = 5 or 10] and ethyleneoxy [(CH₂CH₂O)_n, n = 4 or 7.3 (the average of a mixture of n = 1 to 20)] units as spacers between the backbone and the imidazolium cation. All monomers and polymers exhibited two dipolar relaxations, assigned to the usual segmental motion (α) associated with the glass transition and a lower frequency relaxation (α₂), attributed to ions rearranging. From the analysis of the static dielectric constants using the Kirkwood g correlation factor, the dipoles in conventional (smaller) ionic liquids prefer antiparallel alignment (g ≈ 0.1), lowering ε_s values (≤30), because their polarizability volumes V _p strongly overlap, whereas the dipoles in the larger ionic liquid monomers display g of order unity and 50 ≤ ε_s ≤ 110. A longer spacer leads to higher static dielectric constant, owing to a significant increase of the relaxation strength of the α₂ process, which is directly reflected through an unanticipated increase of the static dielectric constant with ionic liquid molecular volume V_m. The glass transition temperature of polymerized imidazolium ionic liquids with various counterions is also shown to simply be a monotonically decreasing function of V_m. Furthermore, the ionomers consistently exhibit 1.5-2.3 times higher static dielectric constants (ε_s up to ～140 at room temperature) than the monomers from which they were synthesized, suggesting that polymerization encourages the observed synergistic dipole alignment (g > 1).

Full text of DOI:10.1021/ma301833j

Article
pubs.acs.org/Macromolecules
Polymerized Ionic Liquids with Enhanced Static Dielectric Constants
†
‡
‡
‡
†
,†
U Hyeok Choi, Anuj Mittal, Terry L. Price, Jr., Harry W. Gibson, James Runt, and Ralph H. Colby*
†Materials Science and Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
‡Department of Chemistry, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, United States
*
S Supporting Information
ABSTRACT: Dielectric spectroscopy was used to determine the static
dielectric constants (ε ) of imidazolium acrylates and methacrylates and
s
their ionomers, with different imidazolium pendant structures containing
a combination of alkylene [(CH ) , n = 5 or 10] and ethyleneoxy
2
n
[
(CH CH O) , n = 4 or 7.3 (the average of a mixture of n = 1 to 20)]
2 2 n
units as spacers between the backbone and the imidazolium cation. All
monomers and polymers exhibited two dipolar relaxations, assigned to the
usual segmental motion (α) associated with the glass transition and a
lower frequency relaxation (α ), attributed to ions rearranging. From the
2
analysis of the static dielectric constants using the Kirkwood g correlation
factor, the dipoles in conventional (smaller) ionic liquids prefer
antiparallel alignment (g ≈ 0.1), lowering ε values (≤30), because their
s
polarizability volumes V strongly overlap, whereas the dipoles in the
p
larger ionic liquid monomers display g of order unity and 50 ≤ ε ≤ 110. A
s
longer spacer leads to higher static dielectric constant, owing to a significant increase of the relaxation strength of the α process,
2
which is directly reflected through an unanticipated increase of the static dielectric constant with ionic liquid molecular volume
Vm. The glass transition temperature of polymerized imidazolium ionic liquids with various counterions is also shown to simply
be a monotonically decreasing function of V . Furthermore, the ionomers consistently exhibit 1.5−2.3 times higher static
m
dielectric constants (ε up to ∼140 at room temperature) than the monomers from which they were synthesized, suggesting that
s
polymerization encourages the observed synergistic dipole alignment (g > 1).
INTRODUCTION
direct access to molecular-level interactions and dynamics over
38
■
very wide ranges of molecular sizes and time scales.
A molecular-level understanding of dynamics in ion-containing
polymers is of considerable interest from both fundamental and
applied points of view. Recently, ionic liquids (ILs), composed
entirely of large cations and anions with weak interactions, have
attracted significant interest due to their unique physical
properties, such as high thermal and chemical stability,
negligible vapor pressure, broad electrochemical window
3
9−41
42,43
Weingar
̈
tner
and Buchner and Hefter
measured the
static dielectric constant ε for various ILs using microwave
dielectric spectroscopy. Weingartner’s 2006 review shows that
̈
most ILs have 10 < ε < 15 with a few ILs having roughly twice
s
40
s
as large static dielectric constant. Since the dielectric response is
sensitive to the square of the dipole moment of any dipolar
species present, dielectric measurements enable not only
detection of small concentrations of ion pairs, but the ability
to distinguish among the various types, for example, solvent
1
−7
(
many are stable up to 5 V), and high ionic conductivity.
These remarkable characteristics make it possible for ILs to be
used as novel and safe electrolytes for advanced devices such as
electrochemical membranes for capacitors, lithium-ion bat-
teries, fuel cells, and electromechanical transduction devices for
44
̈
separated, solvent-shared and contact ion pairs. Weingartner
41
et al. have suggested that the main relaxation mode observed
in ILs is dominated by reorientation of bulky dipolar cations,
not by dielectric relaxation involving ion pairs. A recent study
using both microwave dielectric measurements and MD
simulations suggests that the main relaxation is not only due
to cation reorientation, but also to cooperative motions
8
−17
actuators and sensors.
However, while the applications of
ILs develop, our understanding of their fundamental physical
properties is far from complete. Moreover, the physical
properties of ILs can be significantly altered by modifying the
chemical structures of the constituent ions or by incorporating
IL monomers into polymers, so-called polymerized ionic liquids
45
involving the surrounding ions. According to computer
46,47
1
8−37
simulations,
dielectric polarization results from the orienta-
(
PILs).
The properties of ILs are undoubtedly dominated by the
tional polarization caused by the molecular dipole moment and
polarizability, representing the volume response of dipoles to an
long-range Coulombic interactions among the ions. Such
interactions are difficult to probe by the usual spectroscopic
techniques (NMR, IR, etc.), which are mostly sensitive to
localized effects. In contrast, being responsive to dipolar
species, the frequency-dependent dielectric function provides
Received: September 11, 2012
Revised: December 7, 2012
Published: January 28, 2013
©
2013 American Chemical Society
1175
dx.doi.org/10.1021/ma301833j | Macromolecules 2013, 46, 1175−1186

Macromolecules
Article
external electric field. The orientational order can be quantified
using the Kirkwood g factor, which correlates the mean-
Table 1. TGA Thermal Analyses, Molecular Weights and
48
Distributions, Total Ion Concentrations p , and Refractive
0
square dipole moment of noninteracting isolated dipoles with
Indices n of PILs
49
neighboring dipoles. Krossing et al. predicted the dielectric
constants of ILs with good accuracy, using a combination of
volume-based thermodynamics and quantum chemical calcu-
lations, and other studies demonstrated a strong relationship
between the molecular volumes Vm of ILs and their
c
p
0
a
b
b
(×1020 cm−3
c
sample Td (°C) Mn,SEC (kg/mol) M /Mn
)
n
w
3
3
a
332
333
252
356
291
8.7
19
1.12
1.22
1.43
1.37
1.88
10.3
9.05
6.89
10.3
9.05
1.45
1.45
1.45
1.45
1.45
b
50,51
3c
36
40
34
fundamental physical properties such as viscosity,
ductivity, and dielectric constant.
con-
5
5
a
5
1
49,52,53
b
In contrast to the extensive studies on ILs, there have been
a
b
TGA (10 K/min, N , 5 wt % loss). Polystyrene equivalent molecular
2
few studies of static dielectric constants of PILs. Nakamura et
c
3
1
weight in NMP (0.05 M LiBr, 0.5 mL/min at 40 °C). p
group contribution method based on molecular structure.
0
5a8nd n from
al.
investigated poly[1-ethyl-3-vinylimidazolium bis-
(
trifluoromethylsulfonyl)imide (Tf N)] in the frequency
2
range from 10 mHz to 2 MHz, and reported its room
Table 2. DSC and DRS Glass Transition Temperatures of IL
Monomers (Left Three Columns) and Their PILs (Right
Three Columns)
temperature static dielectric constant to be ε ≈ 10. On the
s
other hand, we recently reported a significantly larger static
dielectric constant (ε = 65 at 25 °C) for a PIL with pendant
s
−
a
a
imidazolium cations and Tf N counterions, having much
sample DSC T (K) DRS T (K) sample DSC T (K) DRS T (K)
2
g
218
210
210
209
205
g
g
232
235
229
235
234
g
larger molecular volume than the PIL studied in ref 31. The
high static dielectric constant resulted from an additional
2
2
a
220
3a
3b
3c
5a
5b
230
b
210
223
209
202
236
228
225
229
orientational polarization (referred to subsequently as the α
relaxation), involving rearrangement of ions.
2
2c
37
4
4
a
Herein the effects of varying the spacer length between the
backbone and the imidazolium cation on the static dielectric
constant are demonstrated. We find that the static dielectric
constant increases with ionic liquid molecular volume and this
persists in the polymerized ionic liquids, with the polymer
always significantly more polarizable than its monomer.
b
a
T determined from dielectric relaxation spectroscopy (defined at
g
−2
59
ω (T ) = 10 rad/s).
α
g
270 dual light scattering and viscosity detector. N-Methylpyrrolidone
NMP), which contained 0.05 M LiBr, was the mobile phase (40 °C,
.5 mL/min) and calibration was performed with polystyrene
(
0
EXPERIMENTAL SECTION
■
standards (Varian Polymer Laboratories: 0.2−126 kg/mol). Poly-
styrene equivalent molecular weights and polydispersity indices are
listed in Table 1.
Materials. Monomer and polymer syntheses were carried out
under inert atmosphere. The solvents, acid chloride, and 2,2′-
azobis(isobutyronitrile) (AIBN) were dried by reported literature
Dielectric Relaxation Spectroscopy (DRS). The dielectric and
conductivity measurements of the monomers and polymers were
performed by dielectric relaxation spectroscopy. Samples were
prepared by allowing them to flow to cover a 30 mm diameter
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. A 15 mm diameter polished brass
electrode was then placed on top to create a parallel plate capacitor cell
which was squeezed to a gap of 50 μm in the instrument (with precise
thickness checked after the dielectric measurements were complete).
The sandwiched polymers were positioned in a Novocontrol GmbH
Concept 40 broadband dielectric spectrometer, after being in a
vacuum oven at 100 °C for 24 h. The dielectric permittivity was
54
procedures and stored in Schlenk flasks. Acetonitrile (MeCN,
Aldrich Chemical) for polymerizations was distilled over calcium
hydride. Unless stated otherwise all chemicals were purchased with
highest purity (or anhydrous) from Aldrich/Alfa Aesar and used as
received. Poly(ethylene glycol) methacrylate (PEGMA) containing
MEHQ (monomethyl ether of hydroquinone) was purchased from
Aldrich with a claimed M = 360, corresponding to an average of 6.3
n
ethyleneoxy units; this material is known to contain free poly(ethylene
glycol) and the mono- and di-methacrylate with 1 to 20 ethyleneoxy
55
55
units. Therefore, it was purified by solvent extraction as reported
1
and analyzed by H NMR (see Supporting Information, Figure S1) by
comparison of the integrals of the ethyleneoxy protons [3.5−3.8 and
−2
7
4
6
.3 (COOCH ) ppm] to those of the signals for the vinylic (5.6 and
measured using an ac voltage amplitude of 0.1 V and 10 −10 Hz
frequency range. Each sample was annealed in the Novocontrol at 120
°C in a heated stream of nitrogen for 1 h prior to measurement to
remove any moisture acquired during sample loading. Data were
collected in isothermal frequency sweeps from 120 °C to near Tg.
2
.2 ppm), COOCH and methyl (1.9 ppm) protons and found to
2
contain 6.5 (±0.2) ethyleneoxy units on average. A common
commercial ionic liquid used in this study [1-butyl-3-methylimidazo-
lium bis(trifluoromethylsulfonyl)imide] (C MIM-Tf N) was pur-
4
2
chased from EMD Chemicals and used as received.
Synthesis. 1-Butyl-3-(10′-carboxydecyl)imidazolium Tf N¯ (1a).
2
Spectroscopic and Thermal Characterization. 1H and 13
C
30
This was prepared as reported previously. A solution of N-
NMR spectra were recorded on Varian Inova and JEOL 400 and 500
MHz spectrometers. High resolution electrospray ionization time-of-
flight mass spectrometry (HR ESI TOF MS) was carried out with
dilute chloroform solutions on an Agilent 6220 Accurate Mass TOF
LC/MS spectrometer in positive ion mode. Thermal properties (listed
in Tables 1 and 2) were determined using a TA Instruments Q2000
differential scanning calorimeter (DSC) (heating rate of 5 or 10 K/
min) and a Q500 thermogravimetric analyzer (heating rate of 10 K/
min) with both instruments under N2.
Size Exclusion Chromatography (SEC). The molecular weight
estimation was conducted using a Waters gel permeation chromato-
graph (GPC) equipped with three Waters Styragel columns (7.8 × 300
mm, HR1-HR3-HR4), an RI detector (Waters 2414) and a Viscotek
butylimidazole (22.0 g, 0.177 mol) and 11-bromoundecanoic acid
(50.45 g, 0.190 mmol) in THF (400 mL) was refluxed for 4−5 days.
After cooling, the precipitated salt was filtered and washed with excess
cold THF followed by hexane. The bromide salt (51.0 g, 0.131 mol)
was dissolved in 100 mL of deionized water at 60 °C; 46 g (0.16 mol)
of LiNTf were added and the mixture, which immediately became an
2
off-white milky color, was stirred for 24−48 h. Upon decanting the
aqueous layer, the precipitated dark oil was washed with deionized
water and a large excess of ethyl ether. The viscous liquid was
dissolved in MeCN and treated with anhydrous Na SO and
2
4
evaporated. Drying in a vacuum oven gave the Tf N¯ salt, a dark
2
1
brown viscous liquid (57 g, 75%). H NMR (400 MHz, MeCN-d ): δ
3
8.43 (s, 1H), 7.40 (s, 2H), 4.13 (t, J = 10 Hz, 4H), 2.28 (t, J = 7 Hz,
1
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Scheme 1. Synthesis of Imidazolium-Based Methacrylate Monomers (2a−c) and Their Polymers (3a−c) and Acrylate
Monomers (4a,b) and Their Polymers (5a,b)
3
2
H), 1.91−1.77 (m, 4H), 1.62−1.52 (m, 2H), 1.34 (m, 14H), 0.96 (t,
× 10− mmol) as a polymerization inhibitor. Thereafter, 51 mL of
J = 7 Hz, 3H).
TEA (0.37 mol) were added to an addition funnel using a degassed
syringe followed by addition of 150 mL of dry THF and transferred to
the reaction flask. Acryloyl chloride (AC, 15 mL, 0.18 mol) dissolved
in 50 mL of THF was added dropwise to the reaction flask at 0 °C
over a period of 20 min. The mixture was stirred at 0 °C for 4 h,
brought to ambient temperature and stirred for 2 d. The reaction was
quenched by dropping the mixture into a large excess of cold water.
The compound was extracted with methylene chloride. The combined
organic layers were washed several times with deionized water,
saturated NaHCO and brine, dried using anhydrous Na SO , and
filtered. Evacuation under reduced pressure resulted in a crude pale
yellow viscous liquid. Column chromatography over neutral alumina
with ethyl acetate as eluent resulted in the pure compound (11.2 g,
60%). The monomer was stored in a Schlenk flask at 0−4 °C in a
refrigerator. H NMR (500 MHz, CDCl ; see Supporting Information,
1
-Butyl-3-(5′-carboxypentyl)imidazolium Tf N¯ (1b). This was
30
2
prepared as reported previously. The procedure above for the
analogue 1a was followed. Drying in a vacuum oven gave a pale-yellow
viscous liquid (100 g, 70%). H NMR (500 MHz, MeCN-d ): δ 0.95
1
3
(
t, J = 8 Hz, 3H), 1.40 (m, 4H), 1.65 (m, 4H), 1.97 (m, 4H), 2.32 (t, J
=
8 Hz, 2H), 4.36 (q, J = 8 Hz, 1H), 7.77 (m, 2H), 9.03 (s, 1H).
Tetra(ethylene glycol) Monomethacrylate (TEGMA). To 55 mL of
MeCN were added tetra(ethylene glycol) (TEG, 100 g, 0.512 mol)
and triethylamine (TEA, 15 mL, 0.10 mol) dissolved in MeCN (15
3
2
4
−3
mL). Butylated hydroxytoluene (BHT, 2 mg, 9 × 10 mmol) was
added as a polymerization inhibitor. Methacryloyl chloride (MAC, 5
mL, 0.05 mol) dissolved in 25 mL of MeCN was added dropwise to
the reaction flask at 0 °C over a period of 20 min. The mixture was
stirred at 0 °C for 4 h, brought to ambient temperature and stirred for
1
3
2
d. Most of the solvent was evacuated and the remaining mixture was
Figure S3): δ 6.47 (m, 1H), 6.23 (m, 1H), 5.58 (m, 1H), 4.31 (t, J = 5
13
dropped into 300 mL of cold water. The compound was extracted
using methylene chloride. The combined organic layers were washed
several times with deionized water, saturated NaHCO , and brine,
dried over anhydrous Na SO , and filtered. Evaporation of the filtrate
gave the crude product, which was purified by column chromatog-
raphy over neutral alumina (eluent: ethyl acetate, R = 0.18) to give the
pure compound (7.8 g, 60%) as a pale yellow viscous liquid. The
monomer was stored in a Schlenk flask at 0−4 °C in a refrigerator. H
NMR (500 MHz, CDCl ; see Supporting Information, Figure S2): δ
Hz, 2H), 3.52−3.79 (m, 16H), 2.48 (s, 1H). C NMR (126 MHz,
CDCl ) δ 174.83, 166.22, 131.08, 128.34, 100.13, 72.56, 70.43, 69.19,
3
+
3
63.72, 61.79, 60.44, 21.07, 14.25. HR ESI MS: m/z 248.1266 [M] ;
calcd for C H O m/z 248.1260; error 3 ppm).
2
4
11 21
6
1-[ω-Methacryloyloxy[tetraethyleneoxy]carbonylpentyl]-3-(n-
butyl)imidazolium Bis(trifluoromethylsulfonyl)imide, Imidazolium-
Based Methacrylate Monomer (2a). A one-neck 250 mL round-
bottom flask containing 3.53 g (6.80 mmol) of 1b and SOCl
68 mmol) was stirred for 24−48 h at room temperature under a
nitrogen atmosphere. After removal of the excess SOCl under
vacuum, the residue was washed with anhydrous ethyl ether and dried
under a stream of nitrogen. The flask was equipped with a rubber
septum and an oil-bubbler. Dry MeCN (40 mL) was transferred under
nitrogen flow and cooled using crushed ice. Using a degassed syringe
1.90 g (7.21 mmol) of TEGMA dissolved in 6 mL of MeCN was
added and followed by dropwise addition of 1.1 equiv of triethylamine
f
1
(5.0 mL,
2
3
6
2
.14 (s, 1H), 5.58 (s, 1H), 4.21 (t, J = 5 Hz, 2H), 3.65−3.79 (m, 14H),
.8 (s, 1H), 1.94 (s, 3H). The H NMR spectral data are the same as
2
1
56
+
reported in the literature. HR ESI MS: m/z 262.1423 [M] ; calcd for
C H O m/z 262.1416; error 2 ppm.
12
22
6
Tetra(ethylene glycol) Monoacrylate (TEGA). Into a 1L two-neck
round-bottom flask, equipped with an addition funnel and septum
adapter, were transferred TEG (360.2 g, 1.85 mol) and BHT (2 mg, 9
1
177
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Macromolecules
Article
+
(
TEA, 1.0 mL). The reaction mixture was brought to ambient
error 5.6 ppm; m/z 309.2522 (100%) [1a − Tf N] ; calcd for
2
temperature after 4 h and stirred for 2 days. Thereafter MeCN was
evacuated. After adding ethyl acetate, the solution was washed five
times with deionized water (10 mL each) until the water layer was
clear. The combined organic layer was dried (anhydrous Na SO ) and
evacuated under reduced pressure to get a dark brown viscous oil
(
C H N O m/z 309.2537; error 4.8 ppm.
18
33
2
2
1-[ω-Acryloyloxy[tetraethyleneoxy]carbonylpentyl]-3-(n-butyl)-
imidazolium Bis(trifluoromethylsulfonyl)imide, Imidazolium-Based
Acrylate Monomer (4a). The procedure was the same as mentioned
for 2a except the amounts of reagents, viz., 1b (5.2 g, 10 mmol),
2
4
SOCl (7.0 mL, 0.10 mol), TEA (1.6 mL, 11 mmol), TEGA (3.0 g, 12
mmol). A dark brown viscous oil (6.14 g, 82%) was obtained. Before
the polymerization, it was rinsed vigorously with diethyl ether twice
4.10 g, 80%). Before the polymerization, it was rinsed vigorously with
2
diethyl ether twice and dried under high vacuum. DSC (−70 to +150
1
°
(
(
C, heating and cooling rate 10 K/min., N ): T = −55 °C. H NMR
2
g
and dried under high vacuum. DSC (−70 to +150 °C, heating and
500 MHz, MeCN-d ; see Supporting Information Figure S4): δ 8.44
3
1
cooling rate 10 K/min, N ): T = −64 °C. H NMR (500 MHz,
s, 1H), 7.38 (s, 2H), 6.06 (s, 1H), 5.63 (s, 1H), 4.27 (m, 4H), 4.17−
2
g
CDCl ; see Supporting Information, Figure S7): δ 8.82 (s, 1H), 7.35
4
.09 (m, 2H), 3.71−3.53 (m, 14H), 2.32 (t, J = 7 Hz, 2H), 1.93 (s,
3
(
s, 1H), 7.31 (s, 1H), 6.40 (dd, J = 17, 1 Hz, 1H), 6.12 (dd, J = 17, 10
Hz, 1H), 5.83 (dd, J = 10, 1 Hz, 1H), 4.29 (m, 4H), 4.22 (m, 2H),
.75−3.59 (m, 14H), 2.33 (t, J = 7 Hz, 2H), 1.82 (m, 2H), 1.65 (m,
H), 1.39 (m, 6H), 0.94 (t, J = 7 Hz, 3H). HR ESI MS: m/z 772.2009
3
3
H), 1.82 (m, 2H), 1.63 (m, 2H), 1.33 (m, 6H), 0.94 (t, J = 7 Hz,
+
H). HR ESI MS: m/z 483.3101 [M − Tf N] ; calcd for C H N O
2
25 43
2
7
3
2
m/z 483.3065; error 7.4 ppm.
1
-[ω-Methacryloyloxy[tetraethyleneoxy]carbonyldecyl]-3-(n-
+
butyl)imidazolium Bis(trifluoromethylsulfonyl)imide, Imidazolium-
Based Methacrylate Monomer (2b). The procedure was the same as
mentioned for 2a except for the amounts of reagents, viz., 1a (6.70 g,
([M + Na] ; calcd for C26
H N O S F Na m/z 772.1979; error 3.9
41 3 11 2 6
ppm.
1-[ω-Acryloyloxy[tetraethyleneoxy]carbonyldecyl]-3-(n-butyl)-
imidazolium Bis(trifluoromethylsulfonyl)imide, Imidazolium-Based
Acrylate Monomer (4b). The procedure was the same as mentioned
for 2a except the amounts of reagents, viz., 1a (6.06 g, 10.3 mmol),
SOCl (8.0 mL, 0.10 mol), TEA (1.6 mL, 11 mmol), and TEGA (3.06
g, 12.3 mmol). A dark brown viscous oil (6.9 g, 80%) was obtained.
Before the polymerization, it was rinsed vigorously with diethyl ether
1
1.4 mmol), SOCl (8.2 mL, 0.11 mol), TEA (1.72 mL, 13.1 mmol),
2
and TEGMA (3.11 g, 11.88 mmol). A dark brown viscous oil (7.5 g,
6%) was obtained. Before the polymerization, it was rinsed vigorously
with diethyl ether twice and dried under high vacuum. DSC (−70 to
7
2
1
+
150 °C, heating and cooling rate 10 K/min., N ): T = −63 °C. H
2
g
NMR (500 MHz, MeCN-d ; see Supporting Information Figure S5): δ
8
4
3
twice and dried under high vacuum. DSC (−70 to +150 °C, heating
.43 (s, 1H), 7.38 (s, 2H), 6.06 (s, 1H), 5.63 (s, 1H), 4.23 (m, 4H),
.17−4.08 (m, 2H), 3.72−3.53 (m, 16H), 2.29 (t, J = 7 Hz, 2H), 1.93
1
and cooling rate 10 K/min., N ): T = −68 °C. H NMR (500 MHz,
2
g
MeCN-d ; see Supporting Information, Figure S8): δ 8.42 (s, 1H),
(
s, 3H), 1.81 (m, 4H), 1.62−1.52 (m, 2H), 1.38−1.25 (m, 12H), 0.94
3
+
7
4
.38 (s, 2H), 6.42 (m, 1H), 6.23 (m, 1H), 5.88 (m, 1H), 4.25 (m, 4H),
(
t, J = 7 Hz, 3H). HR ESI MS: m/z 856.2935 [M + Na] ; calcd for
.12 (m, 2H), 3.76−3.40 (m, 16H), 2.29 (t, J = 8 Hz, 2H), 1.82 (m,
C H N O S F Na m/z 856.2918; error 1.9 ppm.
32
53
3
11 2 6
1
-[ω-Methacryloyloxy[oligoethyleneoxy]carbonylpentyl]-3-(n-
4H), 1.62−1.53 (m, 2H), 1.37−1.26 (m, 12H), 0.94 (t, J = 7 Hz, 3H).
+
butyl)imidazolium Bis(trifluoromethylsulfonyl)imide, Imidazolium-
based Methacrylate Monomer (2c). The procedure was the same as
mentioned for 2a except for the amounts of reagents, viz., 1a (10.0 g,
1
1
HR ESI MS: m/z 842.2801 [M + Na] ; calcd for C31
m/z 842.2761; error 4.8 ppm.
H N O S F Na
51 3 11 2 6
General Procedure for Polymerization. The monomer (2a−c
or 4a−b) was transferred to a flame-dried round-bottom flask followed
by solvent, MeCN:toluene (8:2 v/v), and 2 mol % of AIBN with
respect to the monomer. The reaction mixture was degassed for 30−
60 min with bubbling nitrogen, and immersed in an oil-bath preheated
at 60−70 °C for 24 h. The polymer was precipitated in a large excess
of ethyl acetate. Drying in a vacuum oven at 60 °C for 24 h afforded
the highly viscous polymer.
6.0 mmol), SOCl (13 mL, 0.17 mol), degassed PEGMA (6.06 g,
2
6.8 mmol) in 6 mL of dry MeCN and TEA (2.4 mL, 17 mmol) in 5
mL of MeCN. A dark brown, viscous oil was obtained (3.5 g, 25%).
TGA (10 °C/min., N , 5 wt % loss) T : 252 °C; DSC (−70 to +150
2
d
1
°
(
(
C, heating and cooling rate 10 K/min., N ): T = −63 °C. H NMR
2
g
500 MHz, MeCN-d ; see Supporting Information Figure S6): δ 8.42
3
s, 1H), 7.38 (s, 2H), 6.34 (s, 1.0H), 5.63 (s, 1.0H), 4.25 (t, J = 7 Hz,
2
2
1
.0H), 4.20−4.18 (m, 6H), 3.72−3.46 (m, 25.2H), 2.33−2.27 (m,
H), 1.93−1.90 (m, 3H), 1.86−1.77 (m, 4H), 1.60−1.51 (m, 2H),
.36−1.23 (m, 14H), 0.94 (t, J = 7 Hz, 3H). Comparison of the
Tetra(ethylene glycol) Monotosylate (TEG-MT). To a solution of
TEG (200 mL, 1.04 mol) and NaOH (6.58 g, 0.164 mol) in 50 mL of
THF and 50 mL of deionized water cooled using ice was added
dropwise a solution of 20 g (0.10 mmol) of p-toluenesulfonyl chloride
in 40 mL of THF over a period of 1 h. Thereafter the mixture was
stirred overnight at 0 °C. The reaction mixture was dropped into 300 g
of crushed ice and extracted using dichloromethane (DCM). The
combined organic layers were washed several times with deionized
integrals of the ethyleneoxy signals (3.46−3.72, 4.25 ppm) to those of
the vinyl (5.63 and 6.34 ppm) protons and taking into account the
additional four COOCH protons occurring in the range 4.1−4.3 ppm,
indicated that the monomer contained on average 7.3 (±0.2)
ethyleneoxy units. HR ESI MS: m/z 1037.6628 (0.094%) [M(EO )
2
1
5
+
−
Tf N] ; calcd for C H N O m/z 1037.6731; error 9.9 ppm; m/z
water, dried using anhyd. Na SO4 and evacuated under reduced
2
52 97
2
18
2
+
9
93.6378 (0.26%) [M(EO ) − Tf N] ; calcd for C H N O m/z
pressure, resulting in a yellow viscous liquid, which upon drying in a
vacuum oven at 40 °C became brown; thus, it was redissolved in
1
4
2
50 93
2
17
+
993.6469; error 8.1 ppm; m/z 949.6110 (0.36%) [M(EO ) − Tf N] ;
13
2
calcd for C H N O m/z 949.6207; error 10 ppm; m/z 905.5875
DCM, washed with saturated NaHCO followed by water, and finally
48
89
2
16
3
+
(
0.66%) [M(EO ) − Tf N] ; calcd for C H N O m/z 905.5944;
passed over activated charcoal. The solution was dried over anhyd.
Na SO and evaporated under reduced pressure, yielding 29 g (66%
1
2
2
46 85
2
15
+
error 7.6 ppm; m/z 861.5585 (1.2%) [M(EO ) − Tf N] ; calcd for
C H N O m/z 861.5682; error 11 ppm; m/z 817.5353 (2.2%)
11
2
2
4
1
44
81
2
14
with reference to tosyl chloride) of yellow viscous liquid. H NMR
+
[
M(EO ) − Tf N] ; calcd for C H N O m/z 817.5420; error 8.1
(400 MHz, CDCl ) δ: 7.77 (d, J = 8 Hz, 2H), 7.32 (d, J = 8 Hz, 2H),
1
0
2
42 77
2
13
3
+
ppm; m/z 773.5106 (2.7%), [M(EO ) − Tf N] ; calcd for
C H N O m/z 773.5158; error 6.7 ppm; m/z 729.4834 (5.3%)
4.18−4.11 (m, 2H), 3.74−3.52 (m, 14H), 2.42 (s, 3H). The NMR
9
2
5
7
40
73
2
12
spectrum was as reported.
+
[
M(EO ) − Tf N] ; calcd for C H N O m/z 729.4896; error 8.7
1-Butyl-3-(2′-(2″-(2‴-(2⁗-hydroxyethoxy)ethoxy)ethoxy)ethyl)-
8
2
38 69
2
11
+
ppm; m/z 685.4578 (9.0%) [M(EO ) − Tf N] ; calcd for
C H N O m/z 685.4634; error 8.1 ppm; m/z 641.4324 (14%)
imidazolium Bis(trifluoromethylsulfonyl)imide (C EO IM-Tf N). A
7
2
4
4
2
solution of 20.05 g (63.29 mmol) of TEG-MT and 9.45 g (76.0
mmol) of N-butylimidazole in 120 mL of acetonitrile was refluxed for
3 days under nitrogen. Thereafter, the solvent was removed and the
residue was washed several times with diethyl ether. Drying in vacuum
overnight resulted in the tosylate salt as a yellow viscous liquid (28.4 g,
76%). In an extraction funnel the tosylate salt in 200 mL of deionized
water was washed with 100 mL of ethyl ether twice. The aqueous layer
36
65
2
10
+
[
M(EO ) − Tf N] ; calcd for C H N O m/z 641.4372; error 7.4
6
2
34 61
2
9
+
ppm; m/z 597.4063 (25%) [M(EO ) − Tf N] ; calcd for C H N O
5
2
32 57
2
8
m/z 597.4109; error 7.6 ppm; m/z 553.3807 (36%) [M(EO ) −
4
+
Tf N] , calcd for C H N O m/z 553.3847; error 7.2 ppm; m/z
2
30 53
2
7
+
5
5
09.3551 (39%) [M(EO ) − Tf N] ; calcd for C H N O m/z
3
2
28 49
2
6
+
09.3585; error 6.6 ppm; m/z 465.3286 (40%) [M(EO ) − Tf N] ;
2
2
calcd for C H N O m/z 465.3323; error 7.9 ppm; m/z 421.3037
was stirred at 60 °C with 19.8 g (69.0 mmol) of LiNTf for 48 h under
26
45
2
5
2
+
(
100%) [M(EO ) − Tf N] ; calcd for C H N O m/z 421.3061;
nitrogen. The mixture immediately developed off-white milky
1
2
24 41
2
4
1
178
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Macromolecules
Article
Figure 1. Chemical structures of two model ILs (C MIM-Tf N and C EO IM-Tf N).
4
2
4
4
2
turbidity. After the precipitate settled, the aqueous phase was decanted
and the residue was washed with deionized water, followed by washing
with saturated NaHCO3 solution. The residue was dissolved in
acetonitrile and washed with hexane. After removal of the solvent, the
residue was washed with a large excess of diethyl ether and the
longer side chains. Some properties of these novel monomers
and polymers are presented in Tables 1 and 2.
Two model ILs were also examined: the well-known
C MIM-Tf N and the larger room temperature IL 1-butyl-3-
4
2
(
2′-(2″-(2‴-(2⁗-hydroxyethoxy)ethoxy)ethoxy)ethyl)-
imidazolium bis(trifluorosulfonyl)imide (C EO IM-Tf N)
Figure 1).
B. Static Dielectric Constant. Figure 2 displays a
resulting Tf N salt was dried under high vacuum (17.9 g, 49% overall).
2
1
4
4
2
H NMR (500 MHz, MeCN-d ) δ: 8.59 (s, 1H), 7.46 (t, J = 2 Hz,
3
(
1
3
H), 7.39 (t, J = 2 Hz, 1H), 4.32−4.21 (m, 2H), 4.14 (t, J = 7 Hz, 2H),
.84−3.75 (m, 2H), 3.58 (m, 11H), 3.52−3.48 (m, 2H), 1.86−1.78
13
representative example of the frequency dependence of the
(
m, 2H), 1.38−1.29 (m, 2H), 0.94 (t, J = 6 Hz, 3H). C NMR (126
MHz, MeCN-d ) δ: 135.9, 123.2, 122.1, 121.3, 118.8, 117.4, 72.3, 70.2,
3
6
−
9.9, 68.3, 61.0, 49.6, 31.6, 19.1, 12.7. HR ESI MS: m/z 301.2135 [M
Tf N] ; calcd for C H N O m/z 301.2122; error 4.3 ppm.
2 15 29 2 4
+
RESULTS AND DISCUSSION
■
A. Monomer and Polymer Synthesis. We synthesized
imidazolium acrylates and methacrylates and their polymers,
with pendant imidazolium cations having Tf N¯ counterions
2
(
Scheme 1).
The synthesis of imidazolium-based monomers 2 and 4
involved three steps: viz., quaternization of N-butylimidazole
with an ω-bromo-n-alkanoic acid, metathesis ion exchange, and
esterification with oligoethyleneoxy (meth)acrylates. The
sequence yielded ionic monomers of type [Bu−I −R−Z−
m
Figure 2. Dielectric permittivity spectra as functions of angular
frequency ω of two model ILs (C MIM-Tf N at 223 K and C EO IM-
Tf N at 243 K), an IL acrylate monomer (4b at 253 K), and its
2
(
meth)acrylate][Tf N], namely monomers 2 and 4. The
2
4
2
4
4
spacers utilized in our study were a combination of hydro-
phobic [R = (CH ) , n = 5 or 10] and hydrophilic [Z =
polyacrylate PIL (5b at 263 K), showing electrode polarization at
lower ω and ion rearrangement/segmental motion at higher ω. The
inset shows the dielectric spectra shifted horizontally to superimpose
2
n
(
CH CH O) , n = 4 or 7.3] species; note that methacrylate 2c
2 2 n
was prepared from a commercial methacrylate made from an
3
4
in the range 10 < ε′ < 10 and hence compare the static dielectric
oligo(ethylene glycol) mixture (containing 1 to 20 ethyleneoxy
1
constants, usually defined as the value of ε′ just above the frequency at
units), so the n = 7.3 is an average determined by H NMR.
60
which electrode polarization commences (see Figure 3).
These IL monomers are liquids at room temperature and they
are soluble in MeCN, dimethylformamide, and dimethyl
sulfoxide. The IL monomers were amorphous, having low
dielectric permittivity ε′(ω) for two model ILs (C MIM-Tf N
4
2
glass transition temperatures in the range of −50 °C < T <
g
and C EO IM-Tf N), an IL acrylate monomer (4b) and its
4 4 2
−
70 °C. All monomers were dark brown viscous liquids; they
were washed with anhydrous diethyl ether just before the
polymerization to remove the inhibitor (BHT).
corresponding polyacrylate PIL (5b). The static dielectric
constant ε is defined as the low frequency plateau of ε′(ω)
s
before the onset of electrode polarization (EP). However,
ε′(ω) was not clearly observed to plateau before EP, but to
decrease gradually with increasing frequency, indicating under-
All the monomers were polymerized free radically using 2,2′-
azobis(isobutyronitrile) (AIBN) as the initiator in degassed
MeCN at 65 °C. Initial polymerizations in either this polar
solvent or nonpolar solvents resulted in insoluble gels. This
could be because of the monomer having hydrophobic and
hydrophilic groups. However, a mixture of solvents (MeCN:
toluene: 8:2 v/v) proved to be a better choice, since it resulted
in fluid homogeneous reaction mixtures. The polymers were
purified by precipitation in a large excess of ethyl acetate and
dried in a vacuum oven at 60 °C for 24 h, affording the highly
lying relaxations. To display the ε difference among the ILs, the
s
IL monomer and the PIL, the dielectric permittivity spectra in
the inset of Figure 2 were horizontally shifted. Remarkably, the
PIL exhibited higher ε than either its IL monomer or the
s
smaller ILs, which have significantly higher number densities of
dipoles. The same result was also observed for IL methacrylate
monomers and polymethacrylate PILs. This is an unexpected
result: in general, polymerization of nonionic polar monomers
lowers their static dielectric constant due to lower configura-
1
viscous polymers. Disappearance of vinyl protons in H NMR
61−64
spectroscopy confirmed complete conversion into the homo-
polymers; polymer signals were broader compared to
monomers (see Supporting Information, Figures S9−S11 for
tional entropy after polymerization.
The dielectric permittivity ε′(ω) can be decomposed into
frequency-dependent contributions such as electrode polar-
3
a−c and Figures S12 and S13 for 5a,b, respectively).
ization (EP), orientational polarizations (α and α), and a high-
2
Additionally, proton resonances were sharper for those that
were away from the polymer backbone; most pronounced for
frequency contribution ε (here taken to be an approximate
∞
2
value of ε = n , where n is the refractive index (listed in Table
∞
1
179
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Macromolecules
), since the electronic and atomic polarizations leading to ε∞
Article
1
two ILs vs inverse temperature. The neat small ILs exhibit the
lowest static dielectric constants at the temperatures studied.
are faster than our frequency range)
After polymerization, the ε of the PILs are 1.9 ± 0.4 times
s
ε′(ω) ≈ ε′ (ω) + ε′ (ω) + ε′ (ω) + ε
EP
α
α
∞
(1)
higher than that of their IL monomers.
2
C. Dielectric Relaxations. In order to identify the origin of
ε′ (ω) can be modeled by an empirical modification of the
EP
the differences in ε for IL monomers vs PILs, we have carefully
65
s
Macdonald model, while ε′ (ω) and ε′ (ω) can be modeled
66
α
2
α
8
explored dipolar relaxations in dielectric derivative spectra
3
by Havriliak−Negami (HN) functions. The static dielectric
π ∂ε′(ω)
2 ∂[ln ω]
constant ε , shown in Figures 3 and 4, is given by the sum of the
s
ε
= −
der
two HN relaxation strengths Δε and the high-frequency
(3)
2
dielectric constant ε = n
∞
elucidating the relaxation processes by removing the pure-loss
conductivity contribution which obscures the loss peaks of
εs  lim [ε′ (ω) + ε′ (ω)] + ε = Δε + Δε + ε
∞
α
α
∞
α2
α
2
65,67
ω→0
interest (ion rearrangement or segmental relaxation).
(2)
The derivative dielectric loss curves of the ILs (C MIM-Tf N
4
2
at 223 K and C EO IM-Tf N at 243 K) exhibit one relaxation
4
4
2
(
α), centered at 0.01−1 MHz as shown in Figure 5. It has been
Figure 3. Dielectric permittivity ε′(ω) of imidazolium-based IL
acrylate monomer 4b (black circles) at 253 K. ε′(ω) is decomposed
into frequency-dependent contributions from electrode polarization
Figure 5. Dielectric derivative spectra fit (solid lines) to the sum of a
power law for EP (dashed lines) and derivative forms of the HN
(
ε′ (ω): blue dashed line), ionic orientational polarization (ε′ (ω):
68
EP
α
2
green dashed line), dipolar orientational polarization (ε′ (ω): orange
α
function for the α and α processes (dashed lines) of the ILs (C MIM-
2
4
dashed line), and a high-frequency dielectric constant (ε : purple
∞
Tf N at 223 K and C EO IM-Tf N at 243 K), an acrylate IL monomer
2 4 4 2
dashed line). The dark solid line that perfectly describes the data
(
4b at 253 K) and its acrylate PIL (5b at 263 K).
(
black circles) corresponds to the sum of ε′ (ω) + ε′ (ω) + ε′ (ω) +
EP
α
2
α
ε , and the red solid line indicates the static dielectric constant ε ,
based on eq 2. Its proximity to ε′α2 is typical, as the ionic orientational
polarization dominates the static dielectric constant of liquid state
polar ionomers.
shown previously41,43,45,69−71 that imidazolium-based ILs
∞
s
exhibit the same relaxation process, located at ∼1 GHz, at
room temperature. The process has been reported to originate
41
in the reorientation of the bulky dipolar imidazolium cation
(
72
2
supported by simulation results and a H magnetic relaxation
73
study ) or in mesoscale (larger aggregate or cluster)
45
74
cooperative motions (consistent with computer simulations
75
and an optical Kerr effect study ). However, there is no
evidence for contributions of cation−anion pairs in neat ILs to
the long-time component of the dielectric signal. In contrast
76
to the ILs, an additional dipolar relaxation (α ) is observed in
2
the IL monomers and PILs at lower frequencies, attributed to
37,65
ion rearrangement
(such as, exchanging states between
isolated pairs and aggregates of pairs), in addition to the
segmental relaxation (α) involving the typical characteristics of
the glass transition dynamics at higher frequencies (see Figure
77
5
). Using FTIR spectroscopy, on several generally similar but
not identical ionomers, the isolated pairs are clearly observed.
The FTIR findings demonstrate that ion pairs and aggregates
are in fact the dominant ionic species at ambient and elevated
Figure 4. Temperature dependence of static dielectric constant for two
ILs (C MIM-Tf N and C EO IM-Tf N), IL monomers (2a, 2b, 2c,
4
2
4
4
2
4
a and 4b), and their PILs (3a, 3b, 3c, 5a and 5b).
temperatures. These ionomers also exhibit α processes and
2
65
have high static dielectric constants. Consequently, although
ion pairs presumably form, dissociate and reform, under static
conditions there is likely a substantial population of pairs in the
PILs under investigation here. Moreover, our recent linear
viscoelastic (LVE) measurements (not shown) support this
argument. We have found that the ion association/dissociation
6
0
Figure 4 displays the ε values, determined using eq 2 from
s
the relaxation strengths (Δε and Δε , obtained by fitting the
relaxations to HN functions) and the high-frequency dielectric
constant (ε , estimated from the square of refractive index n),
for the imidazolium-based PILs, their IL monomers, and the
α
2
α
∞
1
180
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Macromolecules
Article
78
lifetime obtained using a sticky Rouse model and LVE
measurements is quantitatively identical to the time scale for
the ion rearrangement from dielectric measurements. A full
report on the correspondence of the association lifetime with
EP shifts to lower frequency. This means that (1) the α2
process is a relaxation characteristic of the material and (2) the
static dielectric constant should include this α relaxation as
2
shown in Figure 3.
the α process will be detailed in a forthcoming publication.
The EP peak shifts to lower frequency with increasing
thickness (L). At low frequencies EP is complete on the
2
It is likely that the dielectric constant (ε) relevant for ion
rearrangement is that between segmental motion and ion
rearrangement (ε = 14 ± 4). For this dielectric constant range,
3
7,65,79
electrode polarization time scale
(see Figure 7)
2
ε ε
σDC
L εε
EP 0
s 0
the Bjerrum length (l ≡ e /(4πεε kT)) is 4 nm. In this
B
0
τEP
≡
=
situation, for ion rearrangement over the scale of a few
Angstroms to occur, several rearrangements of neighboring
segments must take place. Therefore, it is reasonable that the α2
process is 2 orders of magnitude slower than the α process (see
Figure 8a). On the other hand, the static dielectric constant
2L σ
(4)
D
DC
(
after ion rearrangement) is presumably the dielectric constant
relevant to using our materials in a macroscopic capacitor.
The dependence of the dielectric response on sample
thickness L was evaluated to confirm the coexistence of two
relaxation processes in the IL monomers and PILs, as shown in
Figure 6. There are three primary relaxations observed: (1) EP
Figure 7. Dielectric response of acrylate monomer 4b at 253 K. The
vertical green dashed line represents the time scale of EP (τ ), the
EP
blue dashed lines are the α and α relaxation processes with peak
2
frequencies (ωα2 and ω ) shown as the vertical blue dashed lines.
α
wherein εEP = ε L/(2L ) is the effective permittivity after EP is
s
D
complete, ε is the permittivity of vacuum, σ is the DC
0
DC
conductivity, L is the spacing between electrodes, L
≡
D
2
1/2
(
ε ε kT/(e p)) is the Debye length, k is the Boltzmann
0 s
constant, T is absolute temperature, and p is the number
density of simultaneously mobile ions that can respond to the
electric field. Equation 4 clearly shows that τEP ∼ L.
Consequently, the relaxations still ongoing at the frequencies
where EP starts, can be more clearly resolved in the thicker
sample.
The peak relaxation frequencies (ω and ω ) and strengths
α
2
α
Δε of the α and α processes can be extracted by fitting the
2
derivative loss spectra with one power law for EP plus two
Figure 6. Frequency dependence of (a) dielectric permittivity ε′(ω),
Havriliak−Negami (HN) functions for the α and α relaxations:
2
(
b) dielectric loss ε″(ω), (c) in-phase conductivity σ′(ω), (d) out-of-
phase conductivity σ″(ω), and (e) derivative loss ε (ω) for the
⎛
⎞
der
⎡
⎢
⎤
⎥
⎡
⎤
⎥
π
∂ε′ (ω)
∂ε′ (ω)
⎣ ∂ln ω ⎦
s
⎜
HN
HN
⎟
⎟
acrylate monomer 4b (L = 0.05 and 1.03 mm) and its PIL 5b (L =
4
b
5b
εder = Aω−
−
+ ⎢
with
⎜
0.05, 0.10, and 1.04 mm) with different specimen thicknesses L at 263
2 ⎣ ∂ln ω ⎦
⎝
α2
α⎠
K. The black solid lines indicate the results from fitting the derivative
spectra for sample 4b at 1.03 mm thickness in (e) to eq 5 and then
calculating ε*(ω) and σ*(ω). In part (e), the two vertical red dashed
⎧
⎫
Δε
ε′ (ω) = Real⎨
⎬
HN
a b
⎩
[1 + (iω/ωHN) ] ⎭
(5)
lines represent the time scales of EP (τ ) at the two thicknesses and
EP
the vertical green dashed line is the thickness-independent frequency
wherein A and s are constants, Δε is the relaxation strength, a
of the α relaxation (ω ).
2
α
2
and b are shape parameters, and ω
is a characteristic
HN
frequency related to the frequency of maximal loss ω
by
max
at lower frequency, (2) ion rearrangement at intermediate
38,80,81
frequency (α ), and (3) dipolar relaxation at higher frequency
2
1
/a
−1/a
(
α). As expected, the response from EP exhibited a thickness
⎛
⎜
aπ
⎞
⎛
⎜
abπ ⎞
⎟
ωmax = ωHN
sin
⎟
sin
dependence, while both ε*(ω) and σ*(ω) at intermediate and
high frequency are observed to be independent of thickness,
because these are properties of the sample, although the ion
motion relaxation is better resolved in the thicker sample,
where EP is pushed to lower frequency. Figure 6e shows that
⎝
⎠
⎝
⎠
2 + 2b
(6)
2
+ 2b
82
Such fits approximate the data quite well (Figure 5) and yield
ωmax and Δε for the α and α processes.
2
The peak relaxation frequencies ω
follow a Vogel−
83
max
the α relaxation does not shift to lower frequency and only the
Fulcher−Tammann temperature dependence (see Figure 8a).
2
1
181
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Macromolecules
Article
87
as temperature is increased to g = 2.5 at 80 °C. When dipoles
either prefer antiparallel alignment or a significant fraction of
dipoles are unable to move in response to the field, g < 1.
Figure 9 displays the temperature dependence of the
Kirkwood g factors of the two smaller ILs, the five IL
Figure 9. Temperature dependence of the Kirkwood g correlation
factor estimated from the measured static dielectric constant via eq 7.
monomers, and their PILs. The correlation factor g was
calculated from the measured ε in Figure 4 and the dipole of an
s
isolated ion pair
⎡
⎤
⎥
⎦
9
ε kT (ε − ε )(2ε + ε )
Figure 8. Temperature dependence of (a) relaxation frequency
maxima ωα2 and ω (and ionic conductivity σ in the inset) vs T /T
0
s
∞
s
∞
g =
⎢
2
2
α
DC
g
vpair
m
⎣
ε(ε + 2)
pair
s
∞
(7)
using the DRS T (Table 2) and (b) relaxation strength of the α and
g
2
α processes. The dashed horizontal line separates the weaker α
wherein νpair is the number density of ion pairs and m is their
pair
90,91
relaxation strengths from the stronger α relaxation strengths.
dipole moment. Assuming
all ions are in the isolated ion
2
pair state (νpair = p where p is the total anion number density
0
0
listed in Table 1) with the contact pair dipole from ab initio
This finding is similar to that for the conductivity vs T /T
g
37
(
mpair(Debye) = 14.1), apparent Kirkwood correlation factors
(
inset of Figure 8a), demonstrating that conductivity is also
are g > 1 for PILs, g ≅ 1 for IL monomers (except 2c with g ≈
2
range studied.
strongly coupled with the glass transition temperature. PILs
have consistently much larger relaxation strengths for the α2
process (Δε ) compared to the corresponding IL monomers
.7), and g ≪ 1 for the smaller ILs, over the entire temperature
α
2
Similar small g factors of order 0.1 were also obtained for
(
(
Figure 8b), and the relaxation strength for the α process
above the dashed line) is much larger than that for the α
47,92
2
imidazolium-based ILs in computational studies,
indicating
that dipoles in smaller ILs seem to prefer an overall antiparallel
alignment. However, the dipoles in the larger IL monomers do
not show a preference for correlation with neighboring ones.
For monomer 2c, its ethyleneoxy (CH CH O) spacer is
process. The stronger α process dominates the temperature
2
dependence of the static dielectric constant ε shown in Figure
s
84
4. For monomers Δεα2 decreases as 1/T as Onsager expects,
2
2
7.3
but Δεα2 exhibits a stronger temperature dependence for the
ionomers.
D. Kirkwood g Correlation Factor. A common way to
perhaps long enough to allow formation of separated pairs
(with larger dipole and smaller g factor). After polymerization,
the dipoles in PILs bias the orientation of surrounding dipoles
in the same direction, leading to much higher static dielectric
constants.
understand the origin of ε is that ionic species effectively
s
correlate neighboring dipoles of ion pairs. Correlation of
4
8,85
neighboring dipoles was considered by Kirkwood
and
E. Molecular Volume Dependence of Static Dielectric
Constant. We will now consider interrelations between the
glass transition temperature, static dielectric constant and
8
6
Fro
equation and this concept is extensively utilized.
̈
hlich by introducing a prefactor g into the Onsager
8
4
86−88
For
93
instance, the static dielectric constants for highly associating
liquids such as acids, alcohols and water are underestimated by
molecular volume Vm (including anion) of imidazolium-based
ILs, IL monomers and PILs, with V taken to be the molecular
m
8
5,87
the original Onsager theory.
On the other hand, molecules
volume of the repeat unit for the polymers. Figure 10
with internal hindered rotation or restricted rotational degrees
of freedom that prohibit alignment with the field cannot fully
respond to the field, and, therefore, the Onsager model
demonstrates that the T of imidazolium-based PILs with
g
various side chains decreases exponentially with increasing V .
m
94
Similar results were reported for poly(n-alkyl acrylate)s,
89
overestimates their static dielectric constant. If there are no
specific correlations, g = 1 and the Kirkwood−Frohlich
whereby longer side chains lower T . This correlation is indeed
g
̈
independent of the molecular structure of the anion, as
imidazolium salts with five different anions are included in
Figure 10.
equation reduces to the Onsager equation, as observed for
many polar liquids. For polar liquids in which dipoles tend to
orient with a slight parallel bias, g > 1; for example, hydrogen
bonding in water results in g = 2.8 at 0 °C, decreasing steadily
Another V -dependent correlation was found for the static
m
dielectric constant of ILs; that is, lower static dielectric
1
182
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Macromolecules
Article
Figure 10. Correlation between glass transition temperature T and
g
repeat unit molecular volume Vm (including the anion) for
imidazolium-based PILs with various side chains and counterions. Tg
for imidazolium-based PILs with different counterions are also added
Figure 11. Correlation between static dielectric constant and (a)
molecular volume V and (b) polarizability volume overlap parameter
−
30,32,99
m
from literature data: [hexafluorophosphate (PF )],
6
V /V at 298 K for ILs (purple and orange colors) and at 288 K for
−
30−33,99
−
33,99
p
m
[
Tf N ],
[trifluoromethylsulfonate (TfO )],
[tetrafluoro-
The solid line is a fit to guide
2
the imidazolium-based IL monomers (open symbols) and PILs (filled
−
33,99,100
−
33,99
borate (BF )],
and [Br ].
−
−
4
symbols) with PF6 or Tf N counterions. Static dielectric constants
2
the eye, using an exponential curve, with the large V limit having T =
m
g
for 1-alkyl-3-methylimidazolium (C MIM, where n is the length of the
n
−52 °C.
alkyl chain) with two different anions (PF and Tf N) are also added
6
2
3
9,40,45
from literature data.
Blue colored symbols represent monomers
and polymers with imidazolium side chains
symbols with imidazolium main chains. The deviations from linearity
30,37
and green colored
3
2
constants are observed as the alkyl chain length of the cation
for the polymers with n-dodecyl tails (S6-PF6 and S6-Tf N) are
2
4
9,95
37
increases, in the same way as in alcohols.
computer simulations,
According to
circled: the n-dodecyl tail results in strong ion aggregation. Solid
9
6,97
as the length of the alkyl chain
(polymers) and dashed (monomers) lines are only guides for the eye.
increases, locally heterogeneous environments emerge, consist-
ing of polar (anion/cation pairs) and nonpolar (alkyl chain)
regions. More recently, X-ray scattering experiments on 1-alkyl-
overlap of the polarizability volumes, which force the ion pair
dipoles to interact strongly.
Since our static dielectric constants predominantly result
98
3
-methylimidazolium-based ILs (4 ≤ C ≤ 10) by Triolo et al.
n
provided direct experimental evidence for such heterogeneous
structures: a scattering peak arises from structural inhomoge-
neities on the nanometer length scale. In ILs with longer side
chain lengths the nonpolar domains not only become larger
and more connected, but also dilute the polar (ionic) domains,
which should decrease the static dielectric constant.
from orientational polarizations (see Figure 8b), the polar-
105
izability volume V can be determined by
p
mpair2
1
Vp =
4
πε 3kT
(8)
0
When data from our IL monomers and PILs with
significantly longer side chains are included with the ILs (see
Figure 11a), it becomes clear that the static dielectric constant
using the dipole mpair from ab initio, listed in Table 3. Then, the
overlap of polarizability volume can be quantified as
mpair2
increases linearly with increasing V . This finding is consistent
m
V /V =
p
m
with the known effects of dilution on conventional electrolyte
1
2πε kTV
(9)
0
m
1
01
solutions, considering that ion aggregates formed by dipolar
interaction between pairs in ILs can form ion pairs when they
are diluted. A general scheme for the dilution of an IL by a
and Figure 11b displays the static dielectric constant ε as a
s
function of V /V .
p
m
102
In conventional (smaller) ionic liquids, polarizability volumes
molecular solvent has been proposed by Dupont.
His
of ion pairs strongly overlap (V /V ≥ 3.5): i.e., the ion pairs all
simplified two-dimensional model of imidazolium-based ILs
showed that a highly structured form for the neat IL is gradually
broken down into smaller species with increasing dilution,
forming large aggregates, triple ions, contact ion pairs, and
ultimately free ions, sequentially.
p
m
interact strongly with their neighbors. Since each system with
the same anion has the same dipole and polarizability volume,
t
h
e
o
v
e
r
l
a
p
p
a
r
a
m
e
t
e
r
V
/
V
d
e
c
r
e
a
s
e
s
w
i
t
h
i
n
c
r
e
a
s
i
n
g
V
.
p
m
m
When the dipoles overlap less (V /Vm < 3.5), the static
p
6
9,71
Hunger et al.
experimentally investigated this model by
measuring dielectric spectra of imidazolium-based ILs in
dichloromethane (DCM) over a wide composition range.
Their results indicate that the ILs retain their chemical
character to high levels of dilution in DCM; that is, their static
dielectric constants decrease with increasing dilution. At even
higher dilutions, where significant formation of distinct ion
pairs (an additional relaxation) is observed, however, the ILs
behave as conventional electrolytes. Their static dielectric
constants increase with increasing dilution. This was also
Table 3. Pair Dipoles and Polarizability Volumes for the
−
−
1-Butyl-3-methylimidazolium Cation with Tf
Counterions
N and PF
2
6
b
polarizability volume Vp
a
3
counterion
pair dipole mpair (D)
(nm at T = 298 K)
−
Tf N
14.1
15.1
1.61
1.85
2
PF6−
a
mpair calculated by ab initio at 0 K in a vacuum using density
37
103
104
confirmed in dilute solution by FTIR
and conductivity
functional theory methods with the Gaussian 03 software package.
b
measurements. This distinction can be understood through
Vp determined from eq 8 using the dipole of a contact pair at 0 K.
1
183
dx.doi.org/10.1021/ma301833j | Macromolecules 2013, 46, 1175−1186

Macromolecules
Article
dielectric constant increases with V owing to the dipoles freely
m
responding to the applied field. Therefore, Figure 11b
demonstrates that the smaller ILs, having strongly overlapping
ion pairs, exhibit low static dielectric constants because of
hindered rotation of dipoles, while less overlapping ion pairs in
our IL monomers and PILs allow for the presence of dipoles
that can rotate or align under an applied field; consequently
their static dielectric constants increase with increasing V . In
m
particular, for the PILs (having a higher g value than the IL
monomers) their static dielectric constants increase more
rapidly with increasing Vm.
F. Correlation Between Conduction and Dielectric
Relaxation. The similar temperature variation of σDC and ωmax
(
Figure 8a) in these monomers and polymers establishes that
there is strong coupling between ion transport and ion
rearrangement. Furthermore, the significantly larger relaxation
Figure 12. DC conduction rate σDC/ε0 vs the product of static
strength for the α process compared to that for the α process
2
dielectric constant ε and frequency ω of the α process. The solid
(
Figure 8b) demonstrates that there can be additional
s
α
2
2
orientational polarization that is not accounted for by the
dipolar polarizabilities of individual molecules in these
materials.
line is a fit of the BNN relation (eq 12) with B = 7 and the dashed line
indicates eq 12 with B = 1.
DC conductivity of any single-ion conductor is σDC = epμ
where e is the elementary charge, p is the number density of
charge carriers, μ = De/kT is their mobility, with D their
diffusion coefficient and kT the thermal energy, leading to the
Nernst−Einstein equation.
species can exist appreciably when the ILs are substantially
diluted by introducing nonionic parts to the cation and their
molecular volumes become larger. Consequently, both IL
monomers and PILs show an additional α process, resulting
e2Dp
2
from ion rearrangements (for example, exchanging states
between isolated pairs and aggregates of pairs) owing to their
polarizability volumes overlapping less. The PILs with shorter
side chains have very restricted motion of imidazolium cations
because the cation is attached close to the polymer backbone.
On the other hand, combining imidazolium cations with longer
nonionic parts allows ions to more readily respond to the field
because the cation is far away from the backbone. This results
in a significant increase of the relaxation strength of the α2
process in longer chain PILs, leading to a large increase in static
dielectric constant. This is presumably why polymethacrylate 3c
σDC = epμ =
kT
(10)
2
1/2
The Debye length L ≡ (ε ε kT/(e p)) is the length scale
D
0 s
over which thermal fluctuations allow ions to move. Our
dielectric methods directly determine the time scale for this ion
rearrangement, beyond which counterion motion becomes
diffusive.
ε εkT
e p
2
0 s
D = BL ω = B
ωα2
D
α2
2
(11)
where B is a nonuniversal constant of order unity. Then,
putting this diffusion coefficient into eq 10, the dc conductivity
can be written as
having the longest spacer exhibits the highest ε
among the
s
PILs.
The increases in the static dielectric constant are also
discussed in terms of the Kirkwood correlation factor g. In ILs
having high dipole density, dipoles apparently prefer to orient
surrounding dipoles in an antiparallel fashion (g ≪ 1) because
their polarizability volumes strongly overlap. As the molecular
volume of the IL monomer is increased, the same dipole
becomes increasingly diluted, allowing the ions to form more
isolated pairs, which do not interact with each other (g ≈ 1).
Although polymerization can restrict dipole motion, the
restriction presumably allows dipoles to have a preference for
parallel alignment with neighboring ones or forming solvent-
separated pairs (g > 1). This might account for the doubling of
σDC = Bε εω
0 s α2
(12)
This is a simple empirical scaling correlation between ionic
conductivity σDC and the product of dielectric constant ε and
frequency at the loss maximum ωmax, proposed by Barton,
Nakajima, and Namikawa
conduction and dielectric relaxation have their origins in one
diffusion process. As shown in Figure 12, the conductivity can
be successfully scaled in accordance with eq 12, demonstrating
that conductivity is strongly coupled with ion motion (the α2
process), with B = 7. The nonuniversal aspects of B will be
discussed in a future publication (B = 7 is not always observed).
s
106−109
(BNN) who suggested that
the static dielectric constant after polymerization.
CONCLUSIONS
■
3
For smaller imidazolium ionic liquids with V < 0.5 nm , the
m
We have compared the static dielectric constant of
imidazolium-based ILs, IL monomers, and their PILs with
different spacer lengths. The PILs are consistently much more
polar than their IL monomers, while conventional ILs having a
higher density of identical dipoles are much less polar.
Although interactions in neat ILs are undoubtedly dominated
by multiple direct cation−anion interactions, neat imidazolium-
based ILs show no strong evidence for ion pair formation. Such
dielectric constant ε ≅ 15 and the Kirkwood g ≅ 0.1 are low
s
because the polarizability volumes of these dipoles strongly
overlap. For larger imidazolium monomers and polymers with
3
V > 0.5 nm , the static dielectric constant increases with V
m
m
and the glass transition temperature decreases, as ion pairs
interact less, eventually leveling off at T
nm .
≈ −52 °C for V > 1
g
m
3
1
184
dx.doi.org/10.1021/ma301833j | Macromolecules 2013, 46, 1175−1186

Macromolecules
Article
(
27) Green, O.; Grubjesic, S.; Lee, S.; Firestone, M. A. Polym. Rev.
ASSOCIATED CONTENT
Supporting Information
H NMR spectra of PEGMA, TEGMA, TEGA, 2a−c, 4a−b,
a−c, and 5a−b COSY spectra of 3a−c, C NMR spectra of
b and 5b, DEPT NMR spectrum of 3b, and HSBC NMR
■
2
(
3
(
009, 49, 339−360.
28) Xie, M.; Han, H.; Ding, L.; Shi, J. Polym. Rev. 2009, 49, 315−
38.
29) Chen, H.; Choi, J.-H.; Salas-de la Cruz, D.; Winey, K. I.; Elabd,
*
S
1
1
3
3
3
Y. A. Macromolecules 2009, 42, 4809−4816.
(30) Lee, M.; Choi, U. H.; Colby, R. H.; Gibson, H. W. Chem. Mater.
2010, 22, 5814−5822.
spectra of 3b and 5b. This material is available free of charge via
the Internet at http://pubs.acs.org.
(
31) Nakamura, K.; Saiwaki, T.; Fukao, K. Macromolecules 2010, 43,
6092−6098.
32) Lee, M.; Choi, U. H.; Salas-de la Cruz, D.; Mittal, A.; Winey, K.
I.; Colby, R. H.; Gibson, H. W. Adv. Funct. Mater. 2011, 21, 708−717.
33) Green, M. D.; Salas-de la Cruz, D.; Ye, Y.; Layman, J. M.; Elabd,
AUTHOR INFORMATION
Notes
The authors declare no competing financial interest.
■
(
(
Y. A.; Winey, K. I.; Long, T. E. Macromol. Chem. Phys. 2011, 212,
2522−2528.
ACKNOWLEDGMENTS
■
This work was supported by the U.S. Army Research Office
under Grant No. W911NF-07-1-0452 Ionic Liquids in Electro-
Active Devices (ILEAD) MURI. RHC thanks the Leverhulme
Trust for funding his visiting professorship at Imperial College,
where much of this paper was written. We thank Mr. Mark
Flynn in Prof. Judy Riffle’s lab at Virginia Tech for carrying out
the GPC analyses.
(34) Weber, R. L.; Ye, Y.; Schmitt, A. L.; Banik, S. M.; Elabd, Y. A.;
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dx.doi.org/10.1021/ma301833j | Macromolecules 2013, 46, 1175−1186

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9
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(
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(
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̈
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dx.doi.org/10.1021/ma301833j | Macromolecules 2013, 46, 1175−1186