Effect of molecular weight on the ion transport mechanism in polymerized ionic liquids

Article abstract of DOI:10.1021/acs.macromol.6b00714

The unique properties of ionic liquids (ILs) have made them promising candidates for electrochemical applications. Polymerization of the corresponding ILs results in a new class of materials called polymerized ionic liquids (PolyILs). Though PolyILs offer the possibility to combine the high conductivity of ILs and the high mechanical strength of polymers, their conductivities are typically much lower than that of the corresponding small molecule ILs. In the present work, seven PolyILs were synthesized having degrees of polymerization ranging from 1 to 333, corresponding to molecular weights (MW) from 482 to 160 400 g/mol. Depolarized dynamic light scattering, broadband dielectric spectroscopy, rheology, and differential scanning calorimetry were employed to systematically study the influence of MW on the mechanism of ionic transport and segmental dynamics in these materials. The modified Walden plot analysis reveals that the ion conductivity transforms from being closely coupled with structural relaxation to being strongly decoupled from it as MW increases.

Full text of DOI:10.1021/acs.macromol.6b00714

Article
pubs.acs.org/Macromolecules
Effect of Molecular Weight on the Ion Transport Mechanism in
Polymerized Ionic Liquids
,
†
§
‡
†
§
†
†
Fei Fan,* Weiyu Wang, Adam P. Holt, Hongbo Feng, David Uhrig, Xinyi Lu, Tao Hong,
§
†
†,∥
†,‡,∥
Yangyang Wang, Nam-Goo Kang, Jimmy Mays, and Alexei P. Sokolov
†
‡
Department of Chemistry and Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996,
United States
§
∥
Center for Nanophase Materials Sciences and Chemical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee
7831, United States
3
*
S Supporting Information
ABSTRACT: The unique properties of ionic liquids (ILs) have made them
promising candidates for electrochemical applications. Polymerization of the
corresponding ILs results in a new class of materials called polymerized ionic
liquids (PolyILs). Though PolyILs offer the possibility to combine the high
conductivity of ILs and the high mechanical strength of polymers, their
conductivities are typically much lower than that of the corresponding small
molecule ILs. In the present work, seven PolyILs were synthesized having degrees
of polymerization ranging from 1 to 333, corresponding to molecular weights
(
MW) from 482 to 160 400 g/mol. Depolarized dynamic light scattering,
broadband dielectric spectroscopy, rheology, and differential scanning calorimetry
were employed to systematically study the influence of MW on the mechanism of ionic transport and segmental dynamics in
these materials. The modified Walden plot analysis reveals that the ion conductivity transforms from being closely coupled with
structural relaxation to being strongly decoupled from it as MW increases.
1
. INTRODUCTION
in which p is the concentration of free ions, q is the charge of
the ions, and μ is their mobility. Conductivity is the sum over
the product of p, q, and μ of all the ionic species (i). The
Einstein relation has the form
Strong interest in the development of batteries with advanced
performance is rooted in the need for efficient storage and
utilization of energy. Extensive research efforts have been
devoted to the development of polymer electrolytes for
batteries since they are safer, have better mechanical properties,
and pose fewer environmental hazards than traditional organic
qiDi
μi =
k T
(2)
B
1
,2
liquid electrolytes. Early polymer electrolytes were simply
composed of polymers and salts. However, the low ionic
in which D is the diffusivity, T is the temperature, and k is the
B
3
Boltzmann constant. By combining eqs 1 and 2, it is clear that
conductivity of an electrolyte is controlled by the free ion
concentration, the diffusivity, and the charge of the ion. For
those electrolytes with decent solubility of salts, the diffusion of
ions becomes the dominant parameter controlling conductivity.
According to the Stokes−Einstein relation for ion diffusion in a
liquid, D ∝ T/η, in which η is the viscosity. For small-molecule
conductivity of traditional polymer electrolytes at ambient
temperature has impeded their practical application. On the
other hand, ionic liquids (ILs) exhibit high ionic conductivity,
nonflammability, and high thermal stability. By incorporating
polymerizable groups, such as vinyl groups into the structure of
ILs, the resulting polymerized ionic liquids (PolyILs) are
expected to combine both the high conductivity of ILs and
good mechanical strength of polymers. Ohno and co-workers
pioneered the development of PolyILs for fast ion conductors
in 1998.
different groups to improve the conductivity and overall
performance of these materials.
challenges is that the ionic conductivity of current PolyILs is
still significantly lower than that of the corresponding ILs.
The conductivity of an electrolyte is given by the equation
4
,5
solvents, η = Gτ (Maxwell equation), where G is the glassy
s
modulus and τ is the structural relaxation time. Combination
s
of these two equations gives the relationship D ∝ T/η ∝ T/τ ;
s
6
−14
i.e., the diffusion of ions in liquid electrolytes is controlled by
Since then, many studies have been conducted by
the viscosity, η, or the structural relaxation time, τ . In the case
s
of polymer electrolytes, ion transport is generally agreed to
1
5−27
However, one of the major
28,29
depend on the local segmental (structural) dynamics,
while
viscosity is controlled by the motion of the entire chain. There
Received: April 6, 2016
Revised: May 31, 2016
σ = ∑ pq μ
i
i
i
(1)
©
XXXX American Chemical Society
A
DOI: 10.1021/acs.macromol.6b00714
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Scheme 1. Synthetic Route for Ionic Liquid with “One Repeating Unit” (IL-1)
have been several studies on the molecular weight (MW)
dependence of ion transport in traditional polymer electrolytes,
based on poly(ethylene oxide) and poly(propylene gly-
Plus, 99%) were purchased from Sigma-Aldrich and used without
further purification. Silver nitrate (Alfa Aesar), dichloromethane
(
DCM, anhydrous), diethyl ether (BDH), bis(trifluoromethane)-
sulfonimide lithium salt (LiTFSI, Aldrich, >99%), oxalyl chloride
Acros Organics), 1,3,5-pentanetricarboxylic acid (TCI, America),
3
0−32
col).
In these studies, despite the change in MW, the
(
ion transport is always strongly coupled to the segmental
31
N,N-dimethylformamide (DMF), trimethylamine (Acros Organics),
tetrahydrofuran (THF, anhydrous, Fisher), hexanes (BDH), and
deionized water (Fisher) were used as received. 2-(Dimethylamino)-
ethyl acrylate (>97%) was purchased from TCI America. RAFT chain
transfer agents 2-(dodecylthiocarbonothioylthio)-2-methylpropionic
acid N-hydroxysuccinimide ester (yellow powder) and methyl 2-
(dodecylthiocarbonothioylthio)-2-methylpropionate (yellow liquid)
were purchased from Sigma-Aldrich. 2,2′-Azobis(2-methyl-
propionitrile) (AIBN, 98%, Aldrich) was recrystallized from ethanol
twice and dried under high vacuum at room temperature before use. A
solution of the purified AIBN in DMF stock solution was made and
used for the RAFT polymerizations.
relaxation of the polymer. However, a decoupling of the ion
transport from the segmental relaxation (i.e., a difference in the
rate of ion transport and the rate of segmental relaxation,
including a difference in their temperature variations), similar
33
to the behavior in superionic conductors, has been observed
34−36
in several polymer electrolytes.
Extensive experimental studies have shown that the ion
transport in aprotic ILs is strongly coupled to their structural
relaxation or viscosity regardless of their specific chemical
3
7,38
structure.
ionic conductivity can be decoupled from structural (segmen-
On the other hand, recent analysis revealed that
39,40
Synthesis of Ionic Liquid N,N-Dimethyl-N-(2-(propionyloxy)-
ethyl)butan-1-ammonium TFSI (IL-1). Propionyl chloride (7.5 mL,
tal) relaxation in PolyILs.
These results raise several
fundamental questions: How does the increase of the chain
length affect the diffusion of ions in PolyILs? Can we design
PolyILs with strongly decoupled ion transport? The answer to
these questions could potentially open new doors for the design
of single ion conductors with high conductivities. Nakamura et
al. studied the molecular weight (viscosity average molecular
8
6 mmol, diluted in 20 mL of DCM) was dropwisely added to 2-
(dimethylamino)ethanol (6.8 mL, 68 mmol, diluted in 20 mL of
DCM) and stirred for 15 h. The mixture was concentrated under
vacuum and purified by recrystallization in THF to obtain IL-1a in a
1
white solid form with a yield of 68%. H NMR showed that the
product was quaternized. Thus, the product was added in chloroform
and neutralized by washing with ammonium hydroxide aqueous
solution (30%−33%). 1L-1b was obtained by concentrating the
chloroform phase under vacuum. Quaternization of 1L-1b was
3
weights of (2.4−480) × 10 g/mol, samples synthesized by free
radical polymerization) dependence of viscoelastic properties of
4
1
PolyILs. However, to the best of our knowledge, the effect of
MW on ion transport in PolyILs has not been explored.
This paper focuses on the analysis of MW dependence of
ionic transport in PolyILs. A series of PolyILs with low
polydispersity indices (PDIs) were synthesized by reversible
addition−fragmentation chain-transfer polymerization
performed with 1-bromobutane in anhydrous DMF for 20 h at 50
1
°
C and precipitated in diethyl ether to yield IL-1c as white solids. H
NMR (400 Hz, D O), δ (ppm): 4.52 (t, 2H), 3.69 (t, 2H), 3.37 (t,
2
2
3
H), 3.13 (s, 6H), 2.45 (q, 2H), 1.76 (m, 2H), 1.36 (m, 2H), 1.09 (t,
H), 0.94 (t, 3H). The ion exchange reaction between 1L-1c and
LiTFSI was performed in water for 3 days. A yellow precipitate formed
when silver nitrate aqueous solution was added to the upper layer,
indicating the successful ion exchange. 1L-1 was obtained as a
transparent viscous liquid. The product IL-1 was dried under vacuum
4
2
(
RAFT ). The synthesized materials have numbers of
repeating units (n) ranging from 1 to 333 and MW from 482
to 160 400 g/mol. By using differential scanning calorimetry
(
DSC), broadband dielectric spectroscopy (BDS), depolarized
with P O for 3 days and heated at 80 °C for 8 h.
2 5
Synthesis of Ionic Liquid Dimer N,N′-((Glutaroylbis(oxy))bis-
ethane-2,1-diyl))bis(N,N-dimethylbutan-1-aminium) TFSI (IL-2).
dynamic light scattering (DDLS), and rheology, we performed
a comprehensive study of PolyIL dynamics over this wide range
of MWs. Our results show that the MW influences a number of
(
Glutaryl dichloride (7 mL, 55 mmol, diluted in 20 mL of DCM)
was added to 2-dimethylaminoethanol (11.1 mL, 110 mmol, diluted in
properties, such as glass transition temperature (T ), viscosity,
g
2
2
0 mL of DCM) dropwise in an ice water bath and stirred for 16 h. IL-
a was obtained as a dark brown precipitate in DCM and washed with
conductivity, and fragility. Detailed analysis reveals that the ion
transport mechanism transforms from closely coupled to
strongly decoupled with increasing MW. Surprisingly, strong
decoupling is observed already in PolyIL with n ≈ 10. We
speculate that frustration in the packing of the polymeric cation
may contribute to the decoupling of ion transport from
segmental dynamics in these materials.
hexane. After drying under vacuum (yield: 90%) in order to neutralize
L-2a, 120 mL of DCM was added to IL-2b, and then the mixture was
1
washed with 1 N NaOH aqueous solution at 0 °C for 1.5 h. The DCM
phase (bottom) was collected and DCM was removed under vacuum.
IL-2b (dark brown liquid, 60% yield) was obtained by concentrating
the DCM phase under vacuum. This procedure was previously
4
3
reported by Kim et al. After quaternizing IL-2b with 1-bromobutane
in anhydrous THF at 80 °C for 16 h, IL-2c was precipitated out from
THF. Ion exchange reaction between IL-2c and LiTFSI was
performed in water for 2 days. IL-2 was obtained as a dark purple
viscous liquid on the bottom of the reactor. The ionic liquid product
IL-2 was dried under vacuum with P O for 3 days and heated at 80
2
. MATERIALS AND METHODS
2
.1. Synthesis and Characterization. Materials. Propionyl
chloride (98%), glutaryl dichloride (98%), 2-(dimethylamino)ethanol
≥99.5%), NaOH 1 N aqueous solution, ammonium hydroxide
NH OH 30%−33% aqueous solution, and 1-bromobutane (Reagent-
(
2
5
1
°C for 8 h. H NMR (400 MHz, DMSO), δ (ppm): 4.43 (t, 4H), 3.61
4
B
DOI: 10.1021/acs.macromol.6b00714
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Scheme 2. Synthetic Route for Sample with “Two Repeating Units” (IL-2)
Scheme 3. Synthetic Route for Sample with “Three Repeating Units” (IL-3)
(
(
t, 4H), 3.30 (t, 4H), 3.03 (s, 12H), 2.39 (t, 4H), 1.80 (m, 2H), 1.65
m, 4H), 1.31 (m, 4H), 0.94 (m, 6H).
Synthesis of Ionic Liquid Trimer N,N′-(((2-(3-(2-(Butyldimethyl-
(0.35 mmol), 380 μL of AIBN stock solution (0.0057 g, 0.035 mmol
AIBN), DMAEA (2.0 g, 13.97 mmol), and DMF(1.1 mL) were added
into a 10 mL Schlenk flask and degassed by three cycles of freeze−
pump−thaw. The flask was immersed in a 65 °C oil bath for 12 h, and
the reaction was quenched by cooling with liquid nitrogen. After
precipitated from THF into hexanes for five cycles, PolyIL-72a was
dried under high vacuum. PolyIL-72b was dissolved in DMF and
mixed with 1-bromobutane at 80 °C for 24 h. The reaction mixture
was diluted with methanol and precipitated in THF five times and
dried under high vacuum at 80 °C. LiTFSI water solution was added
dropwise to the PolyIL-72c polymer water solution in a beaker while
oscillating. The mixture was oscillated for 5 days, and PolyIL-72 was
precipitated out from the solution. PolyIL-72 was dissolved in
methanol and precipitated in water for three cycles and dried under
ammonio)ethoxy)-3-oxopropyl)pentanedioyl)bis(oxy))bis(ethane-
2
,1-diyl))bis(N,N-dimethylbutan-1-aminium) TFSI (IL-3). 2.9 mL of
oxalyl chloride was added to the mixture of 7.0 g of 1,3,5-
pentanetricarboxylic acid and 30 mL of DCM, followed by addition
of a catalytic amount of DMF. The mixture was stirred at room
temperature for 30 min and then at reflux for 8 h. The volatiles were
removed under vacuum, and the oily residue IL-3a was used directly
for the next step. IL-3a was redissolved in DCM and was added
dropwise to the mixture of N,N-dimethylaminoethanol, TEA, and
DCM at 0 °C. The reaction mixture was stirred for 30 min at this
temperature and then stirred at room temperature overnight. The
mixture was filtered, washed with water, and dried over MgSO . The
solvent was removed to afford a viscous liquid IL-3b (yield: 85%). The
quaternization with 1-bromobutane was carried out in anhydrous THF
at 80 °C for 48 h. The precipitate IL-3c was collected and dried. H
4
1
vacuum with P O for 4 days and 24 h at 80 °C. H NMR (400 Hz,
2
5
DMSO), δ (ppm): 4.01−4.51 ppm (CO CH ), 3.40−3.65 ppm
2
2
1
(CH
2
CH
2
N), 2.98−3.19 ppm (CH
2
N(CH ) ), 2.19−2.36 ppm
3 2
(
(
CHCO ), 1.59−1.76 ppm (CH CHCO ), 1.25−1.40 ppm
2
2
2
NMR (D O, 500 MHz), δ (ppm): δ 4.40−4.50 (m, 6H), 3.20−3.28
(
2
CH CH ), 0.88−1.01 ppm (CH CH ).
2
3
2
3
m, 6H), 3.00−3.08 (m, 24H), 2.37−2.45 (m, 5H), 1.60−1.70 (t, 6H),
To confirm the ion exchange percentage and composition of our
1
.70−1.75 (t, 4H), 1.20−1.27 (m, 6H), 0.80−0.88 (m, 9H). The ion
exchange reaction was performed with LiTFSI in water for 5 days. IL-3
light yellow viscous liquid) was collected as bottom layer and washed
with deionized water three times, dried under vacuum with P O for 4
final products, we employed X-ray photoelectron spectroscopy (XPS)
measurements in addition to NMR. The XPS results confirmed that
(
(1) the atomic % values found for C, O, N, S, and F using XPS are
2
5
very close to the “theoretical” values derived from counting the atoms
in their chemical structures and (2) complete quaternization and ion
exchange were achieved in all sample (a trace amount of Br (less than
0.1 at. %) in PolyIL-10 and PolyIL-109; no Br in the rest of the
samples). Detailed results are presented in the Supporting
Information. Thus, the results of XPS combined with NMR data
days, and heated at 80 °C for 16 h. To the best of our knowledge, this
is the first time that the successful synthesis of IL-3 has been reported.
Polymerized Ionic Liquids (PolyIL-n, n Represents the Average
Number of Repeating Units). RAFT polymerization was employed to
prepare narrowly distributed PolyIL-na with repeating units ≥10
44
according to Truong et al. For PolyIL-72a, 0.16 g of CTA powder
C
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demonstrate complete quaternization and ion exchange in our
samples.
(TFSI-containing polymerized ionic liquids) were calculated based on
the M of initial PolyIL-na:
n
Polymer Characterization. The molecular weights and PDIs of the
nonquaternized samples PolyIL-na were determined using size
exclusion chromatography (SEC) (Table 1). SEC measurements
M of Poly‐ILna − MW of end groups
MW of one nonquarternized repeating unit
n
n =
Table 1. Summary of Molecular Weights
MW(Poly‐ILn) = (MW of one repeating unit) × n
+
MW of end groups
PDI of
PolyIL-na
(SEC)
MW of IL,
PolyIL-n
[g/mol]
sample code
M of PolyIL-na
n
n of repeating units
(SEC) [g/mol]
MW of repeating unit in Poly‐ILna (nonquaternized)
143 g/mol
IL-1
482
948
=
IL-2
IL-3
1404
a
MW of repeating unit in Poly‐ILn (quaternized and ion
exchanged with TFSI ion) = 480.1 g/mol
PolyIL-10
PolyIL-72
PolyIL-109
PolyIL-333
1800
5100
10700
16100
48000
1.06
1.19
1.17
34900
52800
160400
2.2. Methods. Differential Scanning Calorimetry (DSC). The
a
samples were dried in a vacuum oven at room temperature and then at
Due to the limit of the instrument, the MW of PolyIL-10a is too
3
53 K for at least 1 day until DSC results showed no difference in Tg.
small to be accurately determined using SEC (the peak appeared at the
very end of the spectrum). M was estimated from roughly fitting the
peak. The MW of PolyIL-10a was also measured by MALDI-TOF
MS, and Mmost = 1790 g/mol was obtained from reading the highest
m/z value near the center of the molecular weight distribution
spectrum, indicating that this MW is present in the largest amount in
the sample.
The samples for the DSC measurements were loaded in aluminum
hermetic pans and dried in a vacuum oven at 353 K overnight before
pans being sealed. The TA Instruments Q2000 unit was used for
temperature-modulated DSC (TMDSC) measurements using the
following procedure: isothermal at 353 K for 5 min and then cooled to
n
1
93 at 3 K/min with a modulation of ±1 K/min; isothermal for 5 min
and heated back to 353 K at 3 K/min with a modulation of ±1 K/min.
The T was taken as the midpoint of the step in the heating process in
g
the reversing heat flow signals.
were performed in THF containing 5% triethylamine as eluent at 40
Depolarized Dynamic Light Scattering (DDLS). The liquid sample
IL-1 was filtered through a 0.22 μm PTFE filter twice to remove
macroscopic impurities and dust. Then the sample was transferred to a
glass vial and was kept under vacuum at 353 K for 5 days to remove
any air bubbles. For the DDLS measurement, the spectra were
recorded from 238 to 210 K. The sample temperature was controlled
by liquid nitrogen in an optical cryostat (Oxford Optistat) with
temperature stability ±0.1 K. The depolarized intensity−intensity
correlation function was measured with laser wavelength λ = 647 nm
and laser power ∼10 mW.
Rheology. Small-amplitude oscillatory shear (SAOS) measurements
were performed on an AR2000ex rheometer. Samples were dried in
the same way as described in the DSC measurements. The
experiments were performed on PolyIL-10, -72, -109, and -333 in
parallel plate geometry using 3 mm plates and on IL-1, -2, and -3 using
4 mm plates. Strain sweep measurement was done before SAOS
measurement to make sure the SAOS response was within the linear
region. Creep measurements were performed on IL-3 as well as
PolyIL-10, -72, -109, and -333 in parallel plate geometry using 8 mm
plates and on IL-1 and -2 using 20 mm plates. The temperature was
controlled by an environmental test chamber with nitrogen as the gas
source.
°
C at a flow rate of 1 mL/min using a Polymer Laboratories GPC-120
size exclusion chromatograph. The GPC-120 is equipped with
Polymer Laboratories PL-gel columns; 7.5 × 300 mm; 10 μm; 500,
1
3
5
6
0 , 10 , and 10 Å, a Precision Detector PD2040 two-angle static light
scattering detector, a Precision Detector PD2000DLS dynamic light
scattering detector, a Viscotek 220 differential viscometer, and a
Polymer Laboratories refractometer. The columns were calibrated with
narrow polydispersity polystyrene standards. The RI increment (dn/
dc) was measured with a Wyatt Technology Optilab Rex differential
refractometer in THF at 25 °C at a wavelength of 648 nm (dn/dc =
0
.075 mL/g).
Matrix-assisted laser desorption ionization time-of-flight (MALDI-
TOF) mass spectrometry measurements were performed using a
Voyager-DE Pro mass spectrometer operated in linear mode. Ions
were accelerated at a potential of 25 kV with a nitrogen laser emitting
at 337 nm. Both PolyIL-a polymer and the matrix (α-cyano-4-
hydroxycinnamic acid) were prepared at a concentration of 10 mg/mL
in THF. 40 μL of matrix solution was mixed with 10 μL of the polymer
solution. A volume of 1 μL of the mixture solution was applied to the
sample target, and the solvent was evaporated by air-drying.
The measured MWs and PDIs for all the synthesized samples are
presented in Table 1. The name abbreviation of each sample (IL and
PolyILs) is used to distinguish the synthesis method. Samples made by
RAFT are under the name PolyIL-n, and the rest of the samples are
named as IL-n. The MWs of IL-ns were obtained by calculation based
Broadband Dielectric Spectroscopy (BDS). Broadband dielectric
−2
7
measurements were performed in the frequency range of 10 −10
Hz, using a Novocontrol Concept 80 system, which includes an Alpha-
A impedance analyzer, a ZGS active sample cell interface, and a Quatro
Cryosystem temperature control unit. Samples were placed between
two gold-plated electrodes separated by a Teflon spacer. Samples were
dried in the same way as described above. Before measurements, each
on their chemical structures. M s of the initial PolyIL-na (neutral
n
“precursor” of the polymerized ionic liquids, not the final product; see
Scheme. 4) were determined by SEC. Then MWs of the final PolyIL-n
Scheme 4. Synthetic Route for Polymerized Ionic Liquids PolyIL-n
D
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sample was loaded within the spacer on the bottom electrode and
dried under vacuum at 353 K to remove bubbles. The experiments
proceeded from high to low temperatures. The samples were
equilibrated at the highest temperature (353 K) for at least 3 h until
the measurement results were reproducible, indicating that the samples
did not degrade and there was no residual solvent. The samples were
equilibrated at each temperature for 20 min before the dielectric
measurements.
Density. Densities were measured for only two representative
samples IL-1 and PolyIL-109. The density of IL-1 was measured by
placing the calibrated density floats (American Density Materials, Inc.)
in the sample. The density was selected when the density bead neither
floated on the surface nor sank to the bottom. The density of PolyIL-
IL-2 to PolyIL-72. A complete summary of T s is given in
g
Table. 2. The MW dependence of T s determined by different
g
techniques is compared in Figure 8a.
It is worth noting that the PolyIL-n series was synthesized by
RAFT; thus, the final products carry large end groups from the
RAFT CTA (structures are shown in the Supporting
Information). The end groups on both sides of the polymer
chain have a total weight comparable to the MW of one
repeating unit in our PolyILs. It is possible that the bulky end
groups restrict the segmental mobility in the sample and
elevates its T . The end group effect is expected to become
g
1
09 was obtained differently. A tiny ball made from PolyIL-109
smaller as MW increases. Unlike IL-1, -2, and -3, for PolyIL-ns
PDI ≠ 1 (a little more than unity) (for PolyIL-10, the PDI
cannot be determined by SEC), which could lead to the
observed broadening.
(
hydrophobic) was placed in a volumetric column filled with saturated
calcium bromide solution. The column was calibrated with different
density floats at different gradations. We estimated the density of IL-1
to be 1.4 g/cm , and the same 1.4 g/cm was obtained for PolyIL-109.
Thus, we assume that all our samples should have similar densities,
around 1.4 g/cm , and this value is used for all the calculations. On the
scale of a Walden plot, which typically covers more than 10 orders of
magnitude on both horizontal and vertical axes, any potential small
difference between the exact density and the estimated value 1.4 g/cm
3
3
3
.2. Depolarized Dynamic Light Scattering (DDLS).
3
The depolarized intensity−intensity correlation functions
(ICF) were measured by DDLS and are presented in Figure
3
will not cause any significant change to the plot.
3. RESULTS
3.1. Differential Scanning Calorimetry. Representative
heat flow curves from DSC measurements are presented in
Figure 1. The inset shows the heat flow curve for sample IL-1,
Figure 2. Normalized intensity−intensity correlation functions for IL-
1
measured by depolarized dynamic light scattering at different
temperatures (symbols) and corresponding KWW fits (lines) by eq 3.
2
. The ICFs were fitted by using the Kohlrausch−Williams−
Watts (KWW) stretched exponential function:
⎡
⎛
βKWW ⎞⎤
⎛
⎝
⎞
t
Figure 1. Heat flow from DSC illustrating the glass transition for all
samples. The presented data were recorded on heating. The inset
shows the glass transition, cold crystallization, and melting processes
for the sample IL-1.
⎢
⎟⎥
⎟⎥
⎠⎦
⎜
ICF = α exp −2⎜
⎟
⎠
⎢
⎜
τKWW
⎣
⎝
(3)
where α is the spatial coherence factor, βKWW is the stretching
exponent, and τKWW is the characteristic decay time. The
characteristic decay time τKWW was converted to the most
probable relaxation time τ by numerically simulating the one-
sided sine Fourier transform of the best fit KWW relaxation
with three processes: the glass transition, cold crystallization,
and melting observed with temperature increase. Only one glass
transition process is observed in the DSC scans in other
α
45
samples. T of our samples clearly increases with MW, and the
function. The temperature dependence of the structural
g
glass transition process becomes broader as MW increases from
relaxation time τ -DDLS for sample IL-1 is shown in Figure 7.
α
Table 2. Summary of T , m, and Mw
g
sample code
MW, [g/mol]
Tg-DSC, [K]
Tg-BDS, [K]
Tg-rheology, [K]
m-rheology
decoupling ε
IL-1
482
948
210.6
230.2
243
200.1
225.1
232.3
265.8
274.4
275.9
277.7
199.2
222.7
233.5
264.3
275.1
275.8
276.0
85
117
116
119
112
106
105
0.05
0.06
0.15
0.55
0.66
0.65
0.65
IL-2
IL-3
1404
PolyIL-10
PolyIL-72
PolyIL-109
PolyIL-333
5100
270.2
281.1
282.4
286.8
34900
52800
160400
E
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Figure 3. Storage and loss moduli (labeled as G′ and G″ near each curve) for samples IL-1, IL-2, and PolyIL-72. Master curves are constructed by
using the time−temperature superposition, referenced to 210.6 K for IL-1, 235.6 K for IL-2, and 288.1 K for PolyIL-72.
Optical quality of other samples was not sufficient for DDLS
measurements.
3.3. Rheology. In order to obtain the information on
structural/segmental relaxation, SAOS measurements were
performed on all the samples. Representative master curves
of samples IL-1, IL-2, and PolyIL-72, constructed by applying
the time−temperature superposition principles (tTS), are
presented in Figure 3. As demonstrated in our previous
4
0
20,41
study and other reported rheology studies,
the tTS seems
to be working well for PolyILs in the current molecular weight
2
range. The characteristic slopes G′ ∼ ω and G″ ∼ ω were
observed in the terminal region for all the samples. The IL-1,
IL-2 (Figure 3), and IL-3 show very similar relaxation behavior,
with a peak in G″ in the high ω region representing the
structural/segmental relaxation. The structural/segmental
relaxation time is defined as τ = 1/ω , where ω is the
Figure 4. Temperature dependence of viscosity values of all our
samples (symbols) and their fit by the VFT function (lines).
s
0
0
frequency at the cross point of G′ and G″ (G′ = G″) at high ω.
Sample PolyIL-72 (Figure 3) and the rest of the samples
Figure 5. The derivative spectra ε″ = (−π/2)(∂ε′/∂ ln ω)
der
49,50
(PolyIL-10, -109, and -333) clearly show the existence of
were obtained based on the Kramers−Kronig relations
in
slower relaxation modes in the low ω region, in addition to the
segmental relaxation process in the high ω region. The slower
modes should originate from the chain relaxation.
order to reveal any relaxation processes covered by the
conductivity signal. There are three major components in the
dielectric spectra: (1) a dielectric relaxation process around the
first crossover point of ε′ and ε″, which appears as a small step
in ε′ and is revealed as a pronounced peak in the derivative
spectra, (2) dc conductivity in the intermediate-frequency
region of ε″, and (3) the electrode polarization effect that
The tTS worked well for all of our samples within the
temperature range studied as demonstrated by the master plot
of tan(delta) (Figure S1 in Supporting Information). Although
our method of determining τ is accurate near T , one still
s
g
needs to be careful with the data at high temperatures. It is well-
known that chain and segmental relaxations might have
appears as the sharp increase of ε′ and ε″ in the low-
der
frequency region.
46
different temperature dependencies. The successful con-
struction might be due to the relatively narrow frequency
range measured.
According to the linear response theory, the dielectric
spectrum can be described in terms of complex electric
5
1,52
modulus M*(ω) and σ*(ω) in addition to ε*(ω).
The
The viscosity results for all of our samples are presented in
Figure 4. All data can be fitted by the Vogel−Fulcher−
Tammann (VFT) function over the entire temperature range
studied:
three quantities are related by the following equations:
M*(ω) = 1/ε*(ω) = iωε /σ*(ω)
(5)
0
All three quantities together with tan δ are plotted as a function
of f = ω/2π in Figure 6.
⎛
⎞
⎛
⎞
⎟
B
B
Contributions from conductivity and electrode polarization
were suppressed in the electric modulus spectrum. A relaxation
process (a peak in M″) is clearly observed at the crossover of
M′ and M″, which is generally ascribed to the conductivity
η = η exp⎜
⎟; τ = τ exp⎜
0
0
⎝
T − T0 ⎠
⎝T − T ⎠
(4)
0
11
The fitting parameters and resulting T s (when η = 10 Pa·
g
4
7,48
38
s
) are summarized in Table S1 (Supporting Information).
relaxation. The conductivity relaxation time is obtained using
The same equation (η substituted by τ, η substituted by τ ) is
used to fit the temperature dependence of structural/segmental
τ = 1/2πf , in which f is the crossover frequency. The
conductivity relaxation represents the start of diffusion of ions
0
0
σ
σ
σ
relaxation in Figure 7.
(dc conductivity). It is worth noting that the peak maximum
3.4. Broadband Dielectric Spectroscopy. Representative
frequency of process 1 in the ε* response is very close to f (the
σ
dielectric spectra ε′ (black), ε″ (red), and the derivative spectra
conductivity relaxation) in the M* response. This information
ε ″ (blue) for samples IL-1, IL-2, and PolyIL-72 are shown in
is helpful for the analysis of the origin of process 1. The peak
der
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Figure 5. Dielectric spectra ε′ (black), ε″ (red), and the derivative spectra ε ″ (blue) for samples IL-1, IL-2, and PolyIL-72. Three major processes
der
are marked in Figure 5a.
40
Figure 6. Dielectric spectrum of IL-1 at T = 215.6 K (solid symbols). Lines show the fit of the dielectric spectrum by HN model eq 6.
Figure 7. Temperature dependence of (i) the relaxation time τ of process 1 determined from dielectric measurement (black squares), (ii)
1
conductivity relaxation τ determined from loss modulus peak (red circles), (iii) structural/segmental relaxation time τ -rheology from rheology
σ
α
measurement (blue diamonds), and (iv) structural relaxation τ -DDLS obtained from DDLS (IL-1 only) (green pentagons).
α
maximum of tan δ shows the onset of the EP process; i.e., ions
have reached the electrodes and started accumulating on the
surface of the electrodes. As demonstrated in our previous
work, the dielectric permittivity spectrum can be fitted well
40
G
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Figure 8. (a) Molecular weight dependence of the glass transition temperatures determined by DSC, BDS, and rheology. The lines are the fits using
the Fox−Flory equation. (b) Correlation between parameter K and T . Black symbols: fit result from T -rheology; green symbols: fit result from
g∞
g
T -DSC; blue symbols: fit result from T -BDS. Open symbols are data for regular polymers from ref 57. Several representative data points are shown
g
g
with polymer names: polydimethylsiloxane (PDMS), polyisobutylene (PIB), atactic polypropylene (A-PP), syndiotactic poly(methyl methacrylate)
estimated (s-PMMA EST), syndiotactic poly(α-methylstyrene) (s-PαMS).
using the “HN model” which consists of a superposition of one
100 s and τ -rheology = 1000 s. The T s determined using
α g
different techniques (Table 2) are close to each other (ΔT < 4
K). It has been reported that the structural relaxation and
53
Havriliak−Negami (HN) function, corresponding to process
1, a dc conductivity term, and an EP term:
conductivity relaxation are in quantitative agreement in many
Δε
σ
38,54
+ Aω−
n
ε*(ω) = ε +
+ i
β
ionic liquids,
which is attributed to the coupled ion
∞
[
1 + (iωτHN)α]
ε0ω
(6)
transport mechanism in liquid electrolytes. Thus, the process 1
in IL-1 might be resulted either from the structural relaxation
or conductivity relaxation. A detailed discussion of the
relationship between ion transport and structural/segmental
relaxation will be presented in section 4.3.
Here, ε represents the value of ε′(ω) at infinite frequency, Δε
∞
is the dielectric relaxation strength, τ
is the Havriliak−
HN
Negami relaxation time, α and β are the shape parameters, σ is
the dc conductivity, n is related to the slope of EP’s high
Figure 7b shows the temperature dependencies of τ , τ , and
1
σ
frequency tail, and A is related to the amplitude of EP. The
τ -rheology of sample IL-2. τ and τ -rheology overlap with
inclusion of Aω−n is helpful for the accurate fitting of process 1,
α
σ
α
each other in the common temperature range studied.
However, τ1 is slower and shows different temperature
dependence than the relaxation time of the other two processes.
despite the fact that such a simple treatment of EP cannot
describe the EP process on its lower frequency side. ε′ and ε″
were fitted using eq 6, while the maximum of the process 1’s
peak in the derivative spectra was used to determine the initial
fitting parameters. The conductivity obtained from the fitting
procedure is essentially identical to that from the direct reading
of σ′(ω) in the dc plateau region (Figure 6). The relaxation
The difference becomes smaller upon approaching T . The
g
origin of the process 1 in IL-2 cannot be determined with the
limited data presented in current work. Since IL-2 consists of
−
2+
−
2+
several types of ions, TFSI , Cation [TFSI ], Cation , etc.,
and they are likely to have different relaxation time distribution,
process 1’s peak might consist of several relaxation processes
coming from different ion types. Despite the different
temperature dependence, all the data can be fitted well by
time τ of process 1 is related to the Havriliak−Negami
relaxation time τ and the shape parameters α and β by the
1
HN
53
following equation:
1
/α
−1/α
the VFT function (eq 3), and the resulting T s are summarized
g
⎛
τ1 = τHN⎜sin
⎝
⎞
⎛
⎞
⎟
αβπ
2 + 2β ⎠
απ
in Table. 2.
⎟
⎜sin
⎝
2 + 2β ⎠
(7)
The temperature dependencies of τ , τ , and τ -rheology of
1
σ
α
sample PolyIL-72 are presented in Figure 7c. τ and τ both
1
σ
show a sudden change from the VFT-like behavior to
Arrhenius-like behavior:
4
. DISCUSSION
4
.1. Effect of Molecular Weight on Structural/
Segmental Relaxation. Figure 7 shows the temperature
dependence of (i) the relaxation time τ of the dielectric
τ = τ exp(E /kT)
(8)
0
a
1
process 1, (ii) conductivity relaxation τ determined from the
dielectric loss modulus peak, (iii) structural/segmental
as the temperature decreases. All of our PolyILs including
PolyIL-10, -72, -109, and -333 show this crossover behavior.
The crossover from VFT-like to Arrhenius behavior of
σ
relaxation time τ -rheology from rheology measurements, and
α
(
iv) structural relaxation τ -DDLS obtained from DDLS (IL-1
conductivity at T is well-known for many materials with high
α
g
55
only).
For sample IL-1, Figure 7a demonstrates that data points
from τ , τ , τ -rheology, and τ -DDLS have similar temperature
ionic conductivity, including some protic ionic liquids. The
same behavior has been observed in several PolyILs in our
40
15,17,39,56
previous study and in studies of others,
and this
1
σ
α
α
dependence, and the values are very close to each other in the
common temperature range studied. All data can be fitted well
by the VFT function (eq 4). For clarity of presentation, only
crossover temperature marks T also in the case of PolyILs
g
studied here. The temperature dependence of τ -rheology
α
follows VFT in the entire temperature range studied and is
the fitting of τ -DDLS is presented here as an example. The
much slower than the conductivity relaxation. T -rheology is
α
g
glass transition temperature was taken when τ , τ , τ -DDLS =
therefore still determined as it is in IL-1 and IL-2 (τ -rheology
1
σ
α
α
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1000 s). Figure 7c shows that in sample PolyIL-72 the
Article
=
segmental relaxation is significantly slower than the con-
ductivity relaxation over the entire temperature range studied,
and the difference became larger as the sample is cooled toward
Tg. All fitting parameters are presented in Table S2.
4.2. Effect of Molecular Weight on Glass Transition
Temperature and Fragility m. T s determined from different
g
techniques, DSC, BDS (τ -M″ = 100 s in IL-1, -2, and -3,
σ
crossover points in τ -M″ vs 1/T in PolyIL-10, -72, -109, and
σ
-
333), and rheology, are plotted as a function of MW in Figure
8
a.
Generally, Tg increases with MW of a polymer. The
dependence of T on MW is traditionally described by the
g
58,59
Fox−Flory equation:
Tg = Tg∞ − K/M , in which T is
Figure 9. Fragility values plotted as a function of MW. Black diamonds
are fragility calculated from structural/segmental relaxation extracted
from rheology data, blue circles are fragility calculated from
temperature dependence of modulus loss maximum in BDS, and red
triangle is calculated from structural relaxation of IL measured by
n
g∞
the glass transition temperature for a chain of infinite length
and K is a characteristic parameter of the dependence between
T and M . The Fox−Flory equation was used to fit our data in
g
n
Figure 8a (lines). Many polymers have been studied based on
DDLS. Inset: fragility vs T ; all data are from rheology measurements.
g
the Fox−Flory equation. A correlation between K and T of
g∞
many polymers including our result is shown in Figure 8b. It
has been found that Tg of flexible polymers, such as
poly(dimethylsiloxane), shows a weaker dependence on MW
increase the frustration in packing and raise the fragility value.
We note that in our PolyILs the fragility seems to slightly
60,61
than stiff polymers, such as polystyrene.
According to
decrease with increase in T (inset in Figure 9), in contrast to
g
Figure 8b, despite the bulky side group and strong
intermolecular interaction, our samples still follow the trend
for traditional polymers and the corresponding K values fall in
the region of flexible polymers. Recently, it has been shown that
traditional for neutral polymers monotonous increase in
63
fragility with the increase of Tg. The situation in PolyILs
might be more complicated than in regular polymers since the
intermolecular interactions were found to affect the fragility
77
T in PolyILs decreases strongly with an increase of the volume
g
values as well. A decrease of fragility with an increase of ion
content has also been observed in polymerized ionic liquids
62
of the repeating unit (monomer + counterion). Apparently, a
dilution of ionic interactions with increase in the monomer +
counterion size diminishes the role of electrostatic interactions
in PolyILs. This may be the reason that the MW dependence of
7
8
(
P(VI/C2TFSI)) and poly(ethylene oxide) polyester copoly-
+
79
mer Li single ion conductors. We do not have a clear
explanation of this behavior, but the observed slight decrease in
fragility might be related to the higher cohesive energy in these
ion-containing polymers. It has been demonstrated theoret-
ically that an increase in cohesive energy can lead to a decrease
in fragility with the increase in Tg. However, a thorough
discussion of the relationship between fragility and chemical
structures in glass-formers is beyond the scope of the present
work.
Tg in our PolyILs is similar to the behavior usually observed in
neutral polymers.
It has been suggested that the dependence of T on MW
g
61,63
64,65
74
correlate with the fragility values.
Fragility index m,
which is another important dynamic parameter, characterizes
the steepness of the temperature dependence of structural/
segmental relaxation in the vicinity of Tg:
4
.3. Effect of Molecular Weight on Ion Transport
d log τs
m =
Mechanism. 4.3.1. Conductivity. The conductivity decreases
drastically from IL-1, to IL-2, and to IL-3 and is even smaller in
PolyILs (Figure 10a). As MW increases from PolyIL-10 to
PolyIL-333, the conductivity values exhibit little change. This
d(T /T)
g
T=Tg
(9)
The MW dependence of fragility is presented in Figure 9.
drop in conductivity reflects changes in the samples’ T s. The
g
Because of the difference in data range and probed
properties, different techniques give different fragility values.
In the following discussion we will only focus on fragility
determined from rheology, since rheology measurements were
performed on all our samples and present information on
segmental dynamics. We found that (1) the fragility jumps from
IL-1 to IL-2, (2) the fragility of IL-2, IL-3, and PolyIL-10 are
almost the same, and (3) the fragility decreases slightly from
PolyIL-10 to PolyIL-333; but this slight decrease might be
caused by the fit itself (different data range, less reliable τs
values at high temperature due to intrinsic properties of tTS). It
has been found that the values of fragility in some ionic liquids
temperature dependencies of the conductivity values of IL-1,
-2, and -3 follow the VFT-type of behavior nicely, while the
temperature dependencies of conductivity in PolyIL-10, -72,
-109, and -333 show a crossover from VFT to Arrhenius-type
behavior as the temperature decreases. Normalization of the
temperature with T -BDS helps to exclude the influence of the
g
shift in the T s (Figure 10b). This presentation reveals that
g
higher MW PolyILs exhibit higher conductivity than lower MW
samples when compared at the same T /T values. These results
g
indicate that changes in MW not only shift T of the PolyILs,
g
but they also strongly affect the conductivity mechanism.
4.3.2. Walden Plot Analysis. To analyze the changes in the
66−68
can be related to their ionicity
ions available to participate in conductivity) and anion size.
Recent theoretical and experimental studies
(i.e., the effective fraction of
ion conductivity mechanism, we employ the Walden plot
48,69
80−84
analysis.
Based on eqs 1 and 2 and the Stokes−Einstein
70−76
have related
relation D ∼ T/η, we arrive at the relation σ ∼ μ ∼ D/T ∼ 1/η.
85
polymer fragility to frustration in packing of polymer chains.
The connectivity between repeating units imposes constraints
on their movement, and thus the increase in chain length would
This explains the empirical relation proposed by Walden, that
the molar conductivity (Λ) of liquid electrolytes is inversely
proportional to its fluidity = 1/η.
I
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Figure 10. Conductivity values of our samples as a function of (a) 1000/T and (b) T -BDS/T; T -BDS is defined in section 4.2.
g
g
Λη = constant
(10)
suggesting that there might be a large amount of ion pairs in IL-
. As MW increases to IL-2, the data move to higher regime,
indicating an improvement of the ion dissociation.
1
Walden’s rule presents an ideal situation when all ions are free
dissociated) and their diffusion is controlled by the macro-
(
Sometimes, the Walden rule breaks down, and it has to be
scopic viscosity of the electrolyte. The Walden rule serves as
the basis of a very useful classification of ionic conductors. In a
typical Walden plot analysis, the molar conductivity of a given
electrolyte is plotted as a function of 1/η on a double-
logarithmic scale. The “ideal” Walden line with slope of one can
be drawn using data for a dilute aqueous solution as reference
γ
replaced by the “fractional” Walden rule Λη = constant, in
82
which 0 < γ < 1. Similar to the behavior of [BMIM][PF ], the
6
data points of IL-3 deviates toward the superionic regime
(
slope ≈ 0.83) as the temperature is decreasing toward T ,
g
indicating some weak decoupling of ion motions from viscosity
in this temperature range. Apparently, the ions in IL-3 are
diffusing slightly faster than the overall fluidity of the sample. As
MW further increases to PolyIL-ns, the data points fall far
above the ideal line, e.g., data from PolyIL-72, indicating strong
decoupling between ion transport and macroscopic viscosity
(Figure 11).
(
e.g., KCl or LiCl). Data points that are higher than the “ideal”
line in the superionic regime indicate a decoupling of the ion
transport from the macroscopic viscosity. Values that are below
the “ideal” line in the subionic regime indicate that there are
many ion pairs in the electrolyte that do not contribute to the
overall conductivity.
The Walden plot for our samples IL-1, -2, and -3 as well as
PolyIL-72 is presented in Figure 11. The calculation of the
66,82,86
Both theoretical and experimental studies have shown that
the ion transport in traditional polymer electrolytes is
controlled by the local segmental dynamics of the polymer
28,29
matrix, instead of the macroscopic viscosity.
So, it has been
suggested that viscosity should be replaced by the structural
3
1
(
segmental) relaxation time in the case of polymers.
Following this approach, the viscosity η is substituted by the
structural/segmental relaxation time τ (rheology) for the
s
analysis of the relationship between ion transport and
structural/segmental relaxation in all of our samples (Figure
1
2).
The data for [BMIM][PF ] and PPG/LiClO fall close to the
6
4
ideal line of the Walden plot, demonstrating strong coupling
between ionic transport and structural/segmental relaxation in
those systems. Data of IL-1 and IL-2 fall slightly below the ideal
line (Figure 12), suggesting that the ion transport is strongly
coupled to the structural relaxation and ions are not well
dissociated. Similar to the data of [BMIM][PF ], data of IL-3
6
show weak decoupling in the vicinity of T as their slopes are
Figure 11. Relation of molar conductivity (Λ) to fluidity (1/η) for IL-
g
1
, -2, and -3 as well as PolyIL-72. [BMIM][PF ] stands for 1-butyl-3-
slightly below one. The data points move higher on the Walden
plot as MW increases from IL-1 to IL-3 (Figure 12), indicating
an increase in decoupling and improved ion dissociation in
higher MW samples. On the other hand, all of our PolyILs data
fall above the “ideal” Walden line and exhibit a slope much
smaller than unity as the temperature is approaching their Tgs.
This implies that the decrease of ionic conductivity is weaker
than the slowing down of the segmental relaxation as the
temperature decreases. Furthermore, the rate of ion diffusion is
much faster than the rate of structural/segmental relaxation in
PolyIL-n samples over the entire studied temperature range.
The modified Walden plot analysis (Figure 12) clearly
6
3
6
methylimidazolium hexafluorophosphate. The open black star
represents the dilute LiCl aqueous solution at room temperature
and is used as the reference for ideal Walden line.
molar conductivity is detailed in the Supporting Information.
The data of dilute LiCl is used as the reference to construct the
“
ideal” line. The data of a common ionic liquid, 1-butyl-3-
3
6
methylimidazolium hexafluorophosphate ([BMIM][PF ]),
6
fall on the “ideal” line with the slope slightly less than one,
representing the general behavior of an ionic liquid. Data points
of IL-1 are lower than the ideal line (subionic regime),
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might still be able to diffuse through the loose system in that
case even when the segmental motion of the polymeric cation is
very slow in the vicinity of T . Several experimental studies and
g
theoretical work have related fragility to the packing
70−74,76
70,75
efficiency.
Sokolov et al.
found that the higher the
fragility, the stronger the decoupling (characterized by larger
decoupling exponent ε) and thus proposed that the degree of
decoupling correlates with fragility. This correlation was found
to be correct in the case of decoupling of self-diffusion from
structural relaxation in small molecules, such as o-terphenyl and
8
8,92,93
tris(naphthyl)benzene,
and in the case of decoupling of
75
chain relaxation from segmental relaxation in many polymers.
It has been demonstrated that it also works for the decoupling
of ion conductivity from structural relaxation in molten salt
88
Ca−K−NO . The increase in decoupling of ionic con-
3
Figure 12. Relationship of molar conductivity (Λ) to structural
ductivity from segmental relaxation with increase in fragility has
35
relaxation rate (1/τ ) for various electrolytes (modified Walden plots):
s
been also demonstrated for polymer electrolytes and some
3
6
including aprotic ionic liquids [BMIM][PF ] and PPG/LiClO4
40
6
PolyILs (Figure 13, black and red points). Yet it fails in room
30
(
20.4%). Because of the Maxwell relation (η = Gτ ), the behavior
s
of these electrolytes in the modified Walden plot is very similar to that
in the traditional Walden plot (Figure 11).
demonstrates that the ionic transport in PolyIL-10, -72, -109,
and -333 is decoupled from the segmental relaxation, while in
IL-1 and IL-2 the two processes are strongly coupled. The
findings for IL-1 and IL-2 are in good agreement with reported
work that the ion transport and structural dynamics are closely
87
coupled in most aprotic ILs, and the decoupling in aprotic ILs
is significantly weaker than that observed in other glass-forming
88
liquids with similar fragility. In contrast, all of our PolyILs
exhibit significant decoupling of conductivity from structural
relaxation. Surprisingly, a strong decoupling is observed already
in PolyIL with n ≈ 10, and the decoupling increases even more
in PolyIL-72 and remains rather unchanged with further
increase in MW. We cannot completely exclude the effect from
the large end groups here, especially for PolyIL-10. However,
the observed strong decoupling is consistent with earlier works
Figure 13. Decoupling exponent ε (degree of decoupling) plotted as a
function of fragility. Black squares represent data from ref 35 for
3
9,40
on PolyILs.
polymers doped with LiClO . Blue stars represent data from present
Similar to the fractional Walden rule, the relation between Λ
4
α
work, in which the samples are ILs and PolyILs with various MWs.
Red circles are data for PolyILs with different pendant groups from ref
and 1/τ typically can be characterized by a power law: Λτ =
s
s
constant. The decoupling exponent ε = 1 − α reflects the
degree of decoupling between ionic transport and polymer
segmental relaxation. It is critical to understand the specific
reason for the change in ion transport mechanism in our
samples as a function of MW. First of all, the contribution from
cation and anion in ion transport and structural relaxation is
changing with increasing of MW. Cation and anion diffuse
4
0. Orange triangle represent PPG/LiClO (20.7%) estimated using
4
data from ref 30. The green hexagon is data for RTIL [C4mim][NTf2]
from ref 88. The black line is a guide for the eyes.
89
temperature ionic liquids (RTIL) [C4mim][NTf2] in which
the ionic conductivity is strongly coupled to structural
+
−
88
more or less at the same rate (D and D are comparable) in
regular ionic liquids (both cation and anion has one charge).
relaxation, despite their high fragility (Figure 13, green
90
point). An analysis of the correlation between decoupling and
fragility of our samples and other reported samples is presented
in Figure 13. It demonstrates that the correlation of decoupling
with fragility seems to work in polymeric samples, yet it fails for
As the MW of the polymeric cation increases, the diffusivity of
cation becomes much slower than that of the anions, and the
transference number of cation becomes smaller. In the case
where the MW of polymer is very large, the transference
number of the tethered ion is close to zero. That is to say, the
ion transport is dominated by the anion in those systems.
However, in traditional polymer electrolytes such as PEO
88
IL-1, -2, -3 and RTIL [C4mim][NTf2]. Work by Sangoro et
39
al. revealed that the ion transport changed from coupled to
decoupled after polymerization of the corresponding monomer.
Our previous studies revealed that the addition of flexible tail
(beneficial for better packing) to the charged side group in
91
doped with LiTFSI, where the ion transport is strongly
coupled to the segmental relaxation, the transference number of
Li was reported to be 0.41 at 358 K.
PolyIL reduces T , fragility, and decoupling of ionic
conductivity of the system. A similar decrease in decoupling
g
+
40
Second, with the increase in MW, the connections between
repeating units in polymeric cations impose space restriction
for packing of polymer chains which may contribute to the
decoupled ion transport mechanism. Therefore, the anions
of ionic conductivity (judged from conductivity values at T s)
with an increase in the length of flexible side chains in PolyILs
g
can be observed in the data published by Colby and co-
15
workers. A recent study by Paluch and co-workers observed
K
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Macromolecules
Article
that the increase of pressure applied on the PolyILs system led
the U.S. Department of Energy, Office of Science, Basic Energy
Sciences, Materials Sciences and Engineering Division. F.F. and
A.P.H. thank the NSF Polymer Program (DMR-1408811) for
funding.
94
to a decrease in decoupling. All these results suggest that the
frustration in packing of the polymeric cation might contribute
to the strong decoupling of ion conductivity from structural
relaxation in PolyILs. As the size of the polymeric cation
increases, the packing frustration also increases, leading to the
dependence of ion transport mechanism on MW (Figure 13). It
has been suggested that intermolecular interactions can also
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ASSOCIATED CONTENT
Supporting Information
The Supporting Information is available free of charge on the
ACS Publications website at DOI: 10.1021/acs.macro-
mol.6b00714.
■
*
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2
AUTHOR INFORMATION
Corresponding Author
E-mail ffan@vols.utk.edu (F.F.).
Notes
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The authors declare no competing financial interest.
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