Dielectric Relaxation and Viscoelastic Behavior of Polymerized Ionic

Apr 26, 2012 - ... estimated using a differential scanning calorimeter (DSC) (Q200, TA Instruments, New Castle, DE) at a heating and cooling rate of 1...
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Dielectric Relaxation and Viscoelastic Behavior of Polymerized Ionic Liquids with Various Counteranions Kenji Nakamura,*,† Koji Fukao,† and Tadashi Inoue‡ †

Department of Physical Sciences, Ritsumeikan University, Kusatsu, Shiga 525-8577, Japan Department of Macromolecular Science, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan

‡

S Supporting Information *

ABSTRACT: The macro and micro dynamics of poly(1butyl-3-vinylimidazolium)-based polymerized ionic liquids with various counterions X− (PC4VIX) were investigated using rheological and dielectric relaxation techniques to extract the role of counterions in the bulk polyelectrolyte system. All PC4VIX species studied showed two dielectric relaxation modes. The faster dielectric relaxation mode, side-chain motions, arose at the determined temperature if X− was not bulky. The slower mode, ion-pair motions, showed good cooperativity with direct current conductivity irrespective of the X− species. The viscoelastic behavior of PC4VIX with small BF4− or PF6− counterions was similar to that of electrically neutral polymers, in contrast to the master curves for PC4VITFSI, which possess the large TFSI− counterion and showed additional shoulders in the glass-to-rubber transition region. The additional shoulders were due to rotational motion of the nonspherical TFSI− ions. The classical Rouse segmental motion depends only on the glass transition behavior, as is the case for electrically neutral polymers; it is independent of the X− species.

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INTRODUCTION Ionic liquids (ILs) are organic molten salts that consist of a soft cation−anion pair.1−3 Some ILs are in the liquid state at room temperature and show special properties such as nonvolatility, nonflammability, electric stability, and high electrical conductivity. Many scientists and engineers have paid special attentions to ILs and reported on their fundamental properties4,5 and potential applications.6−8 Polymerized ionic liquids (PILs) are polymers consisting of IL monomers.9−15 PILs are not liquid, but solid, and thus do not possess some of the special properties of ILs. For example, PILs show 10−2−10−3 times lower electrical conductivity than IL monomers due to their high viscosity.9 However, they retain other properties characteristic of ILs such as thermal and chemical stability.11 Most PILs are noncrystalline amorphous materials, which may be molded into films by standard thermoplastic polymer heating procedures. Utilizing this processability, some researchers have reported on the use of PILs in devices such as capacitors,16 electrochemical cells,17 gas separators,18 and macroporous films.19 In contrast to these numerous applied and synthetic studies, there are relatively few reports regarding the physicochemical features of PILs.11 PILs can be classified as polyelectrolyte species, since their repeating monomer units possess an electrolyte group. While ordinary polyelectrolytes like polystyrenesulfonate or poly(acrylic acid)are soluble in water,20 PILs bearing hydrophobic counterions, such as PF6−, are insoluble in water but soluble in some polar organic solvents.11 Physicochemical studies of polyelectrolyte systems have previously been limited to aqueous © 2012 American Chemical Society

solutions due to the hygroscopicity and high glass transition temperatures of the materials studied.20 However, the above properties of PILs lead us to use them as ideal model solid-state polyelectrolytes to better understand the bulk nature of polyelectrolyte systems. We have previously focused on macro and micro dynamics of the PIL poly(1-ethyl-3-vinylimidazolium bis(trifluoromethanesulfonylimide)) (PC2VITFSI), using rheological21 and dielectric relaxation22 (DR) techniques. PC2VITFSI showed two DR modes: the faster mode was attributed to rotational motion of the polymer side chain, while the slower mode was due to ion-pair motion between the counteranion and positively charged monomer unit. (We initially had attributed the slower mode to the segmental motion of the polymer chain from the DR results.22 This attribution has found to be incorrect from the comparison between DR and rheological spectra.21) The DR times of these modes and direct current conductivity measurements showed Arrhenius-type temperature dependence both above and below the glass transition temperatures. We thus concluded that ion transportation was achieved by the formation and dissociation of ion-pairs. Viscoelastic measurements of PC2VITFSI revealed two rubbery elastic origins: classical chain entanglement and ionic aggregates. The latter is typically observed in ionomer systems.23 The master curves of PC2VITFSI showed additional Received: January 6, 2012 Revised: March 16, 2012 Published: April 26, 2012 3850

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days and obtained as a powder via freeze-drying (83% yield). Elimination of the C4VIBr component from the product was confirmed using a 1H NMR measurement in D2O. The PC4VIX series was prepared using the counterion conversion method proposed by Mecerreyes.24,25 An aqueous solution including 1.5 equiv of salts (NaBF4, KPF6, LiTfO, or LiTFSI) was slowly titrated into aqueous PC4VIBr solution and mixed for at least 2 days at room temperature (Scheme 1). The resulting precipitation of PC4VIX was washed with water until the eluent remained clear following the addition of an aqueous solution of AgNO3. The purity of PC4VIX was confirmed using elemental analysis. Found (%): C, 30.68; H, 3.42; N, 9.82; calcd for C11H15N3O4S2F6 (%): C, 30.62; H, 3.51; N, 9.74 for PC4VITFSI (85% yield). Found (%): C, 39.99; H, 5.01; N, 9.19; calcd for C10H15N2O3S1F3 (%): C, 39.99; H, 5.04; N, 9.33 for PC4VITfO (98% yield). Found (%): C, 36.42; H, 5.13; N, 9.51; calcd for C9H15N2P1F6 (%): C, 36.49; H, 5.11; N, 9.46 for PC4VIPF6 (76% yield). Found (%): C, 44.20; H, 6.42; N, 11.60; calcd for C9H15N2B1F4 (%): C, 45.40; H, 6.36; N, 11.77 for PC4VIBF4 (85% yield). Measurements. The intrinsic viscosity ([η]) of PC4VITFSI was measured using an Ubbelohde dilution viscometer at 30 °C in MEK containing 75 mM LiTFSI and estimated as [η] = 62.4 cm3 g−1. The value of the viscosity-average molecular weight (Mv) for PC4VITFSI was estimated to be Mv = 3.4 × 105 by employing the Mark− Houwink−Sakurada equation [η] = KMva with parameters of K = 2.3 × 10−2 cm3 g−1 and a = 0.62. These parameters were determined in a polystyrene/MEK solution at 30 °C.26 Since the PC4VIX species were synthesized from PC4VIBr, all PC4VIX species had the same chain length. 1 H NMR measurements were performed at 30 °C using an NMR spectrometer (JNM-ECA-400, JEOL, Tokyo, Japan) with a proton resonance frequency of 400 MHz. The glass transition temperature (Tg) of PC4VIX species were estimated using a differential scanning calorimeter (DSC) (Q200, TA Instruments, New Castle, DE) at a heating and cooling rate of 10 K/ min. The measurement temperature ranged from −50 to 250 °C. Tg values, tabulated in Table 1, were taken from the midpoint of the total heat flow curve in the thermal transition region.

shoulders in the glass-to-rubber transition region, which was not observed in the master curves of electrically neutral polymers. These studies prove that both the macro and micro dynamics of bulk polyelectrolyte systems are strongly affected by the presence of ions and charged units. In this study, we focus on the influence of counterions on PIL dynamics to obtain a further understanding of the essential dynamics of bulk polyelectrolytes. We investigated both the viscoelastic and DR behavior of PILs poly(1-butyl-3-methylimidazolium anion) (PC4VIX, Figure 1), which consisted of a

Figure 1. Chemical structure of polymerized ionic liquid poly(1-butyl3-vinylimidazolium) with counteranion X− (PC4VIX).

polymer backbone of poly(1-butyl-3-methylimidazole) (PC4VI+) and various counteranions (X−) such as BF4−, PF 6 − , trifluoromethanesulfonate (TfO − ), and bis(trifluoromethanesulfonylimide) (TFSI−). In order to facilitate the proposed study, we prepared the PC4VIX series with the same molecular weight using the anion exchange method to eliminate the factor of polymer chain length affecting the macro polymer dynamics.

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EXPERIMENTAL SECTION

Materials. 1-Vinylimidazole was purchased from Tokyo Kasei (Tokyo) and used after distillation. 2,2′-Azobis(isobutyronitrile) (AIBN), bromobutane, sodium tetrafluoroborate (NaBF4), potassium hexaflorophosphate (KPF6), and lithium trifluoromethanesulfonate (LiTfO) were purchased from Wako Pure Chemicals (Osaka). Lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) was purchased from Kanto Chemical (Tokyo). Deuterated water (D2O) was purchased from ISOTEC Inc. (Cambridge) and used as a solvent in NMR measurements. Salts and deuterated solvents were used without further purification. Deionized water with a specific resistance of >16 MΩ cm, obtained using an Elix system (Japan Millipore, Tokyo, Japan), and was used as the pure water. Synthesis. 1-Butyl-3-vinylimidazolium bromide (C4VIBr) was prepared by refluxing 1-vinylimidazole (34.0 g, 361 mmol) and excess bromobutane (64.4 g, 470 mmol) in methanol (30 mL) at 70 °C for 3 days (Scheme 1). After complete evaporation of methanol and unreacted bromoethane from the solution, C4VIBr was dried under vacuum at 50 °C. The purity of C4VIBr was confirmed using 1H NMR measurements in D2O. PC4VIBr was synthesized via the free radical polymerization of C4VIBr (20.6 g, 89 mmol). Polymerization was initiated by AIBN (147 mg, 0.89 mmol) in a water (6 mL) solution at 60 °C for 16 h (Scheme 1). After the polymerization, PC4VIBr was dialyzed against water for 3

Table 1. Glass Transition Temperature, Tg, Rheological Reference Temperature, T0, Activation Energy for κ and τ1−1, E, and Entanglement Molar Mass, Me, for PC4VIX PC4VITFSI PC4VITfO PC4VIPF6 PC4VIBF4

Tg/°C

T0/°C

E/kJ mol−1

Me/kg mol−1

53 123 163 141

55 121 155 142

103 95 87 81

68 72 90 84

Small- and wide-angle X-ray scattering (SAXS and WAXS) measurements for PIL films were performed on the BL40B2 and BL45XU beamlines at SPring-8 at 25 °C. An X-ray wavelength of 0.9 Å was used for both SAXS and WAXS measurements. The detector used in our measurements was a combination of an X-ray image intensifier and a CCD camera. The spatial resolution of the CCD camera was 0.106 mm in both the horizontal and vertical directions. The camera lengths were 2220 and 102 mm for the SAXS and WAXS measurements, respectively. The raw scattering data were corrected

Scheme 1. Synthesis of Poly(1-butyl-3-vinylimidazolium) with Various Counterions X− (PC4VIX)

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Table 2. Density, dPIL, Volume of the Monomer Unit, vILm, Volume of the Cation and Counteranion, vcat and vani, Radius of the Cation and Counteranion, rcat and rani,a and Volume Fraction of Polymer Chains in the Bulk, fch, for PC4VIX dPIL/g cm−3

vILm/nm3

vcat/nm3

vani/nm3

rcat/nm

rani/nm

fch

1.516 1.357 1.464 1.312

0.4727 0.3676 0.3726 0.3014

0.252 0.248 0.266 0.235

0.221 0.120 0.104 0.0665

0.392 0.390 0.399 0.383

0.375 0.306 0.294 0.251

0.532 0.674 0.714 0.780

PC4VITFSI PC4VITfO PC4VIPF6 PC4VIBF4 a

Assuming a spherical shape.

method.33 The radius of each cation (rcat) and anion (rani) in PC4VIX species were evaluated by assuming a spherical shape and are tabulated in Table 2. Table 2 also includes the volume fraction (fch) of polymer chains occupied in the bulk PIL calculated using the relationship fch = vcat/vILm. The value of fch for PC4VITFSI is only 0.53 due to the large size of TFSI−, in the case where PC4VI+ polymer chains are diluted by equal portions of TFSI− solvent. Figure 2 shows WAXS diffraction spectra for PC4VIX at 25 °C. The WAXS profile does shows peaksPC4VIBF4 exhibits

for variations in the intensity of incident X-rays and background scattering. Densities (dPIL) of PC4VIX, tabulated in Table 2, were determined using a pycnometer in a water solvent at 25 °C. The van der Waals volume of PC4VIX constituent ions were estimated using a program27 built into the Winmoster software28,29 following structural energy minimization using MOPAC software30 with the PM6 semiempirical method.31 Dynamic viscoelastic measurements were performed under a nitrogen atmosphere over a temperature range of 40−260 °C using strain-controlled rheometers (ARES-G2, TA Instruments, New Castle, DE) employing parallel plate geometry with diameters of 4 and 8 mm. The angular frequency (ω) was varied from 1.00 × 10−2 to 5.00 × 102 rad s−1. The storage and loss moduli (G′ and G″), which obeyed a linear viscoelastic response, were used for analysis. Dielectric relaxation (DR) measurements were performed using two measuring systems. An LCR meter (E4980A, Agilent, Santa Clara, CA) was used for the ω range from 1.26 × 102 to 1.00 × 107 rad s−1. An impedance analyzer (Alpha-A, Novocontrol Technologies, Hundsangen, Germany) was used for the ω range from 1.58 × 10−1 to 7.94 × 106 rad s−1. Measurement temperatures ranged from −190 to 210 °C. The real and imaginary parts of the measured electric capacitance (C′ and C″, respectively) were converted to relative electric permittivity (ε′ and ε″) using the relationships ε′ = C′C0−1 and ε″ = C″C0−1, with a vacant capacitance (C0). Samples for density, rheology, DR, and X-ray measurements were prepared as follows: a PC4VIX/acetone solution was cast onto a Teflon Petri dish. After slow evaporation of the solvent, the plane films were dried under vacuum at Tg + 5 °C for at least 1 day. They were then molded using a hot press at Tg + 45 °C, with or without a 1.5 mm SUS spacer to make a plane film for density and rheology or X-ray and DR measurements, respectively. All the resulting PC4VIX films were transparent with a slight yellow tinge.

Figure 2. WAXS diffractrogram for PC4VIX at 25 °C.

two peaks, while the other species studied exhibit three peaks. Table 3 shows the Bragg spacing (and the scattering vector q) Table 3. Bragg Spacing and Scattering Vectors of the WAXS Peaks for PC4VIX

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Bragg spacing/nm (scattering vector/nm−1)

RESULTS Structural Studies of PILs. We estimate the volume of the cation monomer unit (vcat) and counteranions (vani) in PC4VIX using the density (dPIL) of PILs as follows. First, the molecular volumes of a PC4VIX monomer unit (vILm) are evaluated using the relationship vILm = Mm/(dPILNa), where Mm is the molecular weight of the PC4VIX monomer unit and Na is Avogadro’s number. The vILm values are summarized in Table 2. The van der Waals volume of ions were estimated using a computational chemical method,26−31 giving BF4−: 0.0479 nm3, PF6−: 0.0679 nm3, TfO−: 0.0822 nm3, TFSI−: 0.149 nm3, and C4VI+: 0.170 nm3. These values are similar to previously reported values also generated using a computational chemical method.32 Volume ratios of PC4VI+ or X− to PC4VIX were determined using the above van der Waals volumes. Finally, the values of vcat and vani were calculated by multiplying vILm by the volume ratios. The obtained vcat values for PC4VIX, tabulated in Table 2, are all similar. The vani values shown in Table 2 decreases in the order TFSI− > TfO− > PF6− > BF4−. vcat and vani for PC4VIX are greater than those estimated using the computational chemical method. However, the vani values of PC4VIX are similar to those in IL molecules estimated using the same

PC4VITFSI PC4VITfO PC4VIPF6 PC4VIBF4

1.50 1.50 1.22 1.50

(4.19) (4.19) (5.16) (4.19)

0.762 (8.25) 0.692 (9.08) 0.598 (10.5)

0.469 0.452 0.433 0.411

(13.4) (13.9) (14.5) (15.3)

of the WAXS peaks. According to Elabd, two WAXS peaks observed around q = 4.5 nm−1 and q = 14.0 nm−1 for their PILs can be attributed to local ordering of alkyl segments and an amorphous halo, respectively.34 We have previously proposed that the additional intermediate peak observed around q = 9.0 nm−1 for PC2VITFSI reflected the ion-pair distance (dionpair) formed between a cation and an anion.21 However, the following two findings have led us to reconsider the validity of this assignment. First, although dionpair (= rcat + rani) for PC4VITFSI and PC4VITfO are close to the Bragg spacing of the intermediate peak, this is not the case for PC4VIPF6, where dionpair (0.693 nm) is significantly different to the Bragg spacing of the intermediate peak (0.598 nm). Second, PC4VIBF4 did not show an intermediate WAXS peak at q = 9.90 nm−1 corresponding to dionpair (0.634 nm). 3852

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Figure 3. Master curves of bT−1G′, bT−1G″, and tan δ for PC4VIX at reference temperature T0, shown in Table 1.

frequency regime corresponding to the rubbery and terminal regions, due to the presence of the ionic aggregates.21 In the present PC4VIX system with Mv = 3.4 × 105, PC4VITFSI shows good superposition in bT−1G′ and bT−1G″ curves; accordingly, ionic associations23 which act to enhance the rubbery modulus (also called the ionic modulus) seem to be absent from the system. Other PC4VIX species succeeded in achieving superposition in the aTω range from the glass to the rubbery region but failed in the dynamical viscoelastic measurements in the aTω range of the terminal region (240−260 °C, not shown) due to large deformation of the sample. The deformation occurred even if the magnitude of strain was varied or the parallel plate geometry was altered. Since the magnitude of the ionic modulus is strongly affected by the applied strain, this deformation is independent of the ionic modulus. Note that we did not investigate the viscoelastic behavior of PC4VIX systems with Mv > 3.4 × 105. Therefore, there is still a possibility that PC4VIX species with high Mv can show the ionic modulus in their master curves. The presence of a clear rubbery region for all the PC4VIX species indicates that PC4VIX polymer chains are fully entangled with each other. PC4VITFSI shows two tan δ peaks and additional bT−1G′ and bT−1G″ shoulders in the glassto-rubber transition region (10−5 < aTω < 10−2 rad s−1), as is the case for PC2VITFSI.21 In contrast, PC4VITfO only shows two weak tan δ peaks and seems to lack the additional bT−1G′ and bT−1G″ shoulders in the transition region. The shapes of the master curves for PC4VIBF4 and PC4VIPF6 are quite similar to those of electrically neutral polymers.36,37 These findings suggest that the viscoelastic behavior of PILs strongly depends on the size of the counterion species. We mention this counterion-dependent viscoelastic behavior in the Discussion section. Figure 3 indicates that the shape of master curves of PC4VIX (except for PC4VITFSI) correspond with each other in the rubbery region (10−9 < aTω < 10−4 rad s−1). Only the PC4VITFSI master curve is significantly different to those of the other PC4VIX species across the whole aTω region. However, the magnitude of the rubbery modulus, GN, for PC4VITFSI still appears to be similar to the other PC4VIX species. Assuming that PC4VIX species do not include a contribution of the ionic modulus, we estimated a GN value of

The present study provided us with another candidate for the assignment of the intermediate WAXS peak observed in PILs. Since the anions used in this study were larger than most ions, electrostatic repulsion between the anions was weak, which may have allowed the anions to be positioned closely together. If this is the case, scattering peaks reflecting the spacing between the anions would arise. The distance between anions for each PC4VIX species, corresponding to 2rani, is similar to the Bragg spacing of the intermediate peak, except for PC4VITfO. Moreover, the intermediate peak reflecting 2rani for PC4VIBF4 (0.503 nm) arises at q = 12.5 nm−1, which should be masked by the broad amorphous halo around q = 15 nm−1 (Figure 2). These findings do not contradict the assumption that the intermediate peak reflects the distance between assembled counteranions. In contrast, no peaks or scattering were observed in the SAXS profile (Figure S1 in the Supporting Information), as is the case for a previous PC2VITFSI system.21 It has been found that the SAXS peak due to ion aggregates formed by ion-pairs is observed in the ionomer system.23 According to Colby, ionomers possessing organic larger counterions show broad SAXS scattering, i.e., form less aggregates.35 One may assume that the SAXS results for PILs indicate the absence of ion aggregates. However, PILs are filled by only electrolyte monomer units in contrast to ionomers; the mean spacing between ions (or aggregates if they form) should be out of the SAXS q range. Hence, SAXS measurements probably show no evidence of the ion aggregates in the PIL system. Note that rheological study discussed below strongly supports the absence of the ion aggregates in the PC4VIX. Viscoelastic Behavior. Figure 3 shows master curves of bT−1G′, bT−1G″, and tan δ (= G″/G′) on aTω for the PC4VIX species, obtained by the superposition of G′ and G″ spectra at various temperatures using time- and modulus-scale multiplicative shift factors aT and bT, respectively. Reference temperatures, T0, were selected when the bT−1G″ curve in the glass region showed a peak at aTω = 1.0 rad s−1. The obtained T0 values, tabulated in Table 1, are similar to the Tg values for each PC4VIX. In the previously studied PC2VITFSI system, the time− temperature superposition principle held for polymers with Mv ≤ 1.4 × 105 but failed for polymers with Mv ≥ 2.2 × 105 in the 3853

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polymer chains in bulk PC4VIX is dependent only on Tg and is independent of the counterion species under conditions that satisfy the time−temperature superposition principle. The fitting values of c1 and c2 in Figure 4b are 14.6 and 95.4 °C. The c1 value is similar to that of ordinary polymers (17.4), whereas the c2 value is larger (51.6 °C) due to the less fragile behavior of PC4VIX.40 Dielectric Relaxation Behavior. Figure 5a shows the temperature dependence of ε′ and ε″ (solid lines) at 1 kHz for

30 kPa for PC4VITFSI and 40 kPa for the other PC4VIX species from bT−1G′ curves. GN values for PC4VIX are about 3 times smaller than for PC2VITFSI (0.1 MPa)21 and about 6 times smaller than for polystyrene (0.2 MPa).36 The small value of GN for bulk PILs arises from the dilution of the polymer chains with counterions. The entanglement molar mass, Me, for PC4VIX species is described by the relationship36,38 Me =

dPILfch RT GN

(1)

where R is the gas constant. Obtained Me values are tabulated in Table 1; these values are much higher than that for PC2VITFSI (Me = 2.2 × 104) and increase with decreasing vani of the PC4VIX species. This indicates the crucial finding that the entanglement density of PILs depends on the counterion species, even if the bulk polymer chains consist of exactly the same chemical architecture. Figure 4a shows the relationship between log aT and temperature for the PC4VIX species. Solid lines indicate the

Figure 5. Dependence of the real and imaginary parts of electric permittivities, ε′ and ε″, and conduction-free ε″, ε″der, at 1 kHz against (a) T and (b) T − Tg for PC4VIX.

the PC4VIX series. The remarkably sharp increases of the ε″ curves in the higher temperature regime were due to the direct current conductivity of the sample. In order to remove the contribution of direct current conductivity from the ε″ curve, we calculate the conduction-free ε″, ε″der, using the relationship41,42 ε″der = −

best fit curves to the data using the Williams−Landel−Ferry (WLF) equation:39 c1(T − Tr) c 2 + T − Tr

(3)

ε″der gives the conduction-free ε″ in the frequency regime where ε′ has no electrode polarization effect. Figure 5a includes the temperature dependence of ε″der (dotted lines) at 1 kHz for the PC4VIX series in the temperature regime where ε″ is greater than ε″der. Two DR modes are observed in the ε′ and ε″ (or ε″der) curves for each PC4VIX regardless of the X− species. The first mode (i = 1) is observed at temperatures >0 °C, while the second mode (i = 2) is observed at temperatures PC4VIBF4 > PC4VITFSI. This ordering appears to have no correlation with vani. Figure 5b shows the dependence of PC4VIX ε′ and ε″der on the temperature difference, T − Tg, in the region of the i = 1 DR mode. The i = 1 mode peaks in the ε″der curve in Figure 5b appear in the order PC4VITFSI > PC4VITfO > PC4VIPF6 > PC4VIBF4, starting from high T − Tg, which corresponds to the order of vani (Table 2). This indicates that the potential energy necessary to activate the i = 1 mode increases with increasing counterion volume at temperatures below Tg. One might think that this result is unexpected, since electrostatic interactions between a cation and an anion should weaken with increasing ion volume. However, this result is supported and is explained below. Figure 6 shows the dependence of ε′, ε″, and ε″der on ω for PC4VITFSI at 60 °C as a typical example. Sharp increases in

Figure 7. Arrhenius plot of the direct current conductivity, κ0, and reciprocal of the relaxation time for the i = 1 mode, τ1−1, for PC4VIX. Dashed lines represent Tg−1 for each PC4VIX. Solid lines represent the best fit curves of eq 4 to data at temperatures below Tg.

Dashed lines represent Tg−1 for each species. After adjusting the scale of κ0 (left) and τ1−1 (right) to give the same order of magnitude, the temperature dependence of τ1−1 corresponds with that of κ0 for all the PC4VIX. Similar correlation between τ1−1 and κ0 was observed in the PC2VITFSI system, indicating that the ion transport mechanism was achieved by repetitive ion-pair formation and dissociation processes.22 The transport mechanism was controlled by the motion of side chains attached to the main polymer chains; accordingly, the DR parameters were insensitive to the glass transition behavior. Our study proves that the cooperativity between ion-pair motion and direct current conductivity is common to all imidazolium-based PILs, irrespective of the counterion species. κ0 and τ1−1 for PC2VITFSI22 showed Arrhenius-type temperature dependence, represented as ⎛ E ⎞ ⎟ τ1−1 or κ0 ∝ exp⎜ − ⎝ RT ⎠

Figure 6. Dependence of ε′, ε″, ε″der, and electric conductivity, κ, on ω for PC4VITFSI at 60 °C. Master curves of bT−1G′ and bT−1G″ for PC4VITFSI at the reference temperature of 60 °C are also included.

(4)

where E is the activation energy. As shown in the solid lines in Figure 7, κ0 and τ1−1 for the PC4VIX series are also welldescribed by eq 4 at temperatures below Tg, whereas their values are larger than those predicted by the Arrhenius lines at temperatures above Tg. E values obtained from the Arrhenius lines in Figure 7 are summarized in Table 1. The values of E for PC4VIX increase with increasing vani, which agrees with the result discussed above: that the potential energy necessary to activate the i = 1 mode increases with increasing vani at temperatures below Tg (Figure 5b). Note that we confirmed that PC2VITFSI also showed the same deviation from the

the ε″ curves in the lower frequency regime is due to the direct current conductivity of the sample. Figure 6 also includes the dependence of the electric conductivity κ (= ωε″ε0, where ε0 is the vacuum permittivity) on ω for the same sample and conditions. The ε″ curve shows a relaxation due to the i = 1 mode around ω = 8.0 × 104 rad s−1. We obtain the relaxation time, τ1, of the i = 1 DR mode from the reciprocal of the peak frequency of the ε″der curve and the direct current conductivity, 3855

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S4, which shows a relationship between ε″der and ω for the PC4VITFSI at various temperatures. The magnitude of the relaxation strength for the observed i = 1 DR mode seems to increase with increasing temperature. The same temperature dependence was also observed in other PC4VIX. These results are well explained by assuming the i = 1 DR mode to be due to the ion-pair motion. At low temperatures, two ion-pairs are expected to form a quadrupole, which has no dipole moment and does not contribute to increase of the dielectric strength.47 With increasing temperature, ion-pairs are dissociated from quadrupoles, which leads to increase of the dielectric strength. Viscoelastic Behavior Depending on Counterion Species. According to Colby34 and Weiss,48 viscoelastic behavior for ionomers markedly depends on the size of counterions. Ionomers with smaller counterions such as Na+ have higher Tg and form more ionic associates, which induce an increase of the magnitude of the rubbery modulus and the terminal relaxation time. In PC4VIX systems, Tg values (Table 1) decrease with increasing vani values (Table 2), as is the case with ionomer systems. However, the ionic modulus is thought to exhibit no effect in our PC4VIX systems because the viscoelastic behavior of PC4VIBF4, which possesses the smallest counterion in our study, is similar to that of electrically neutral polymers. As shown in the Results section, we observed a contradiction when studying the effect of counterion species on the viscoelastic behavior. Master curve data (Figure 3) suggest that the viscoelastic behavior of PC4VIX species depends on the X− species, especially in the glass-to-rubber transition region for PC4VITFSI. In contrast, the WLF profile (Figure 4) indicates that segmental motion of the PC4VIX polymer chains is independent of the X− species. It is reasonable to assume that the classical Rouse segmental motion of the PC4VIX species is dependent only on Tg, as indicated in Figure 4, and that additional shoulders observed in the transition region of PC4VITFSI are not related to Rouse segmental motion; they are derived from another origin. Our preliminary optical rheology measurements (not shown) support this argument, as the stress-optical coefficient for the additional shoulders differed from that of other modes. We have previously proposed that the additional shoulders observed in PC2VITFSI are due to the dynamics of shortscale segmental motion of a charged chain affected by neighboring TFSI−.21 However, the above discussion has led us to reconsider this proposal. Here, we propose another candidate for the origin of the additional shoulders. Since the shape of the TFSI− ion is not spherical, such as BF4− or PF6−, but closer to a cylinder or ellipsoid, the additional shoulders seen for PC4VITFSI and PC2VITFSI may instead arise as a result of the rotational motion of the TFSI− ion. This motion should be restricted by electrostatic interactions with neighboring PC4VI+ monomer units, which induce cooperativity between the rotational motion of TFSI− and the segmental motion of the matrix polymers PC4VI+. If this is the case, both modes should show WLF-type temperature dependence and have the same activation energy; i.e., the time−temperature superposition will hold across the whole aTω range even if two different dynamics are present in the system. In order to confirm the validity of the above proposal, we evaluated the local viscosity ηloc around the TFSI− ion and compared this with the dynamical viscosity. We roughly estimated the time constant τshoul (3.6 × 103 s) of the

Arrhenius line at temperatures above Tg (Figure S2 in the Supporting Information). Similar temperature-dependent conductive behavior was observed in a certain ionene polymer studied by Rietz.43 In the ionene system, κ0 values showed Arrhenius-type temperature dependence at temperatures below Tg and deviated from the Arrhenius lines at temperatures above Tg. Rietz assumed that the temperature-dependent conductive behavior in ionene systems included two processes: one related to the glass transition and the other a thermally activated hopping conduction, whose model was proposed for disordered solid electrolyte systems by Funke.44 In the PC4VIX system, high cooperativity between κ0 and τ1−1 across the entire temperature range of the experiment (Figure 7) suggests that ion transport is mainly achieved by repetitive ion-pair formation and dissociation processes even at temperatures somewhat in excess of Tg. However, styrenic imidazolium PILs with various counterions studied by Mahanthappa showed Vogel−Fulcher−Tamman (VFT) type conductive behavior at temperatures well over Tg,45 suggesting that ion conductivity in PILs is perhaps mainly controlled by counterion diffusion associated with segmental motion of the polymer at much higher temperatures. κ0 values of our PC4VIX shows the deviation from the Arrhenius line at T > Tg, which implies the presence of the VFT component. It is important to note that when the horizontal axis in Figure 7 is changed from T−1 to T−1 − Tg−1, κ0 values increase with decreasing vani for a given T−1 − Tg−1. This relationship corresponds with that seen for styrenic imidazolium PILs with various counterions, studied by Mahanthappa.45

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DISCUSSION Comparison between Viscoelastic and Dielectric Behavior. In the previous PC2VITFSI system, comparison between dielectric and viscoelastic results proved that observed slower DR mode was attributed to the ion-pair motion and the segmental DR mode was masked by the electrode polarization.21 Here, we perform the same analysis for the PC4VIX and confirm the validity of the attribution of the i = 1 DR mode. Figure 6 shows a typical example, which includes the viscoelastic master curves of bT−1G′ and bT−1G″ for PC4VITFSI at T0 = 60 °C in addition to the DR spectra at 60 °C. The relaxation time of the Kuhn monomer τ0, which corresponds to the reciprocal of the maximum peak frequency in a bT−1G″ curve around the glass region, means the shortest stress relaxation time in the Rouse model, i.e., the segmental relaxation time in terms of rheology.36 Estimated τ0 value, 1.0 s, is about 8.0 × 104 times longer than the slower DR time τ1, 13 μs, for PC4VITFSI at 60 °C. Other PC4VIX systems also show the same relationship (τ0 ≫ τ1) (Figure S3 in the Supporting Information). According to the Rouse theory, the segmental relaxation time obtained from the DR measurement is 2 times longer than that estimated by the rheological measurement.38,46 In terms of this theory, the segmental DR mode is expected to be around ω = 0.5 rad s−1, and accordingly the i = 1 DR mode does not derive from the segmental motion of polymers. The segmental DR mode is masked by the strong effect of the electrode polarization (or conductivity). The temperature dependence of the dielectric strength for i = 1 mode strongly indicates that the origin of the i = 1 DR mode is the ion-pair motion. A typical example is shown in the Figure 3856

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temperature at T < Tg to yield a value of 0.03−0.07 and markedly increases with increasing temperature at T > Tg. The deviation from the Arrhenius line for κ0 at T > Tg (Figure 7) would lie in the increase of fdis at T > Tg; i.e., translational diffusion of the additional dissociated counterions contributes to the enhancement of the electric conductivity at T > Tg. It is important to note that ion-pair relaxation times (τ1) for PILs were only able to be determined below temperatures slightly above Tg in our measurement DR frequency regime because ion-pair motion was faster than the polymer segmental motion (Figure 6). High-frequency DR measurements are necessary to precisely determine the counterion dissociation behavior at temperatures greater than Tg.

additional shoulders from the reciprocal of their peak frequency (2.8 × 10−4 rad s−1) (Figure 3) and estimate the ηloc using the Stokes−Einstein−Debye equation, assuming that τshoul reflects the rotational relaxation time of the TFSI− ion:49

τshoul =

3ηlocvani kT

(5)

where k is the Boltzmann constant. The resulting ηloc value of 2.5 × 1010 Pa s is close to the complex viscosity (= bT−1G″ω−1) at the peak frequency of the additional shoulders (8.3 × 109 Pa s), indicating the validity of the proposal. Degree of Dissociations of Counterions. We have attempted to determine the degree of dissociation, fdis, of X− from PC4VIX using the combination of Nernst−Einstein and Einstein−Smoluchowski equations:50 fdis =

n ion 2kTκτh vILm = nall qe 2λ 2

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CONCLUSION We investigated the macro and micro dynamics of polymerized ionic liquids poly(1-butyl-3-vinylimidazolium) with various counterions X− (PC4VIX) using viscoelastic and dielectric relaxation techniques to clarify the roles of counterions in a bulk polyelectrolyte system. PC4VIX species exhibited two dielectric relaxation modes irrespective of X− species. The faster mode derived from side chain motion, which was independent of the X− species and the glass transition behavior if X− was not bulky. The slower mode reflected the lifetime of an ion-pair formed between a cation monomer unit and a counteranion, which depended only on counterion size and showed high cooperativity with direct current conductivity. Counteranion dissociation constants obtained from the slower relaxation time and the electric conductivity depended only upon the glass transition temperature and marked increased at temperatures above the glass transition temperature. Direct current conductivity consists of two contributions: the one is the ion transportation due to the repetitive ion-pair formation and dissociation processes observed at temperatures above and below the glass transition temperature; the other is the translational diffusion of dissociated counterions at temperatures over the glass transition temperature. The master curves for PC4VITFSI, which contained the largest counterion, showed additional shoulders in the glass-torubber transition region. By contrast, the master curves of PC4VIX species with smaller counterions, such as BF4− or PF6−, were similar to those of electrically neutral polymers. The additional shoulders in the transition region for PC4VITFSI are distinct from the classical Rouse segmental mode and would arise from the rotational motion of the TFSI− ions. The Rouse segmental mode in PIL polymers is controlled only by the glass transition behavior, as is the case for electrically neutral polymers, and accordingly they are independent of the counterion species. The value of entanglement molar mass was dependent on the counterion species even though the polymer chains consisted of identical chemical architecture. We performed small- and wide-angle X-ray scattering (SAXS and WAXS) measurements for PC4VIX species. No peaks and scatterings were observed in the SAXS profile. An intermediate WAXS peak, which has been attributed to ion-pair distance, probably reflects the distance between counteranions.

(6)

where nion is the effective number density of ions, nall is the number density of ions in the bulk, qe is the elementary charge, and λ and τh are the hopping length and lifetime of ions. We adopt the relationship τh = τ1 because τ1 reflects the lifetime of ion-pairs. We assume λ = rcat because bulk PILs consist only of polymer chains and their counterions. Figure 8a shows the relationship between fdis and temperature for PC4VIX. In order to eliminate the glass transition effect, fdis values for PC4VIX are plotted against T − Tg in Figure 8b. The fdis values overlap each other and depend only on T − Tg irrespective of PC4VIX species. This indicates that the counterion dissociation behavior of PILs is controlled only by the glass transition behavior of the bulk PIL irrespective of counterion species. fdis increased slightly with increasing

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ASSOCIATED CONTENT

S Supporting Information *

Figure S1 with the SAXS diffractrogram for PC4VIX; Figure S2 with the Arrhenius plot of the direct current conductivity and reciprocal of the i = 1 mode relaxation time for PC2VITFSI;

Figure 8. Relationship between the degree of dissociation of counteranions, fdis, and (a) T and (b) T − Tg for PC4VIX. 3857

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(28) Senda, N. Idemitsugihou 2006, 49, 106. (29) Winmoster: Senda, N. http://winmostar.com/. (30) MOPAC2009: Stewart, J. J. P. Stewart Computational Chemistry, http://OpenMOPAC.net. (31) Stewart, J. J. P. J. Mol. Model. 2007, 13, 1173. (32) McEwen, A. B.; Ngo, H. L.; LeCompte, K.; Goldman, J. L. J. Electrochem. Soc. 1999, 146, 1687. (33) Nakamura, K.; Shikata, T. ChemPhysChem 2010, 11, 285. (34) Chen, H.; Choi, J.; Salas-de la Cruz, D.; Winey, K. I.; Elabd, Y. A. Macromolecules 2009, 42, 4809. (35) Tudryn, G. J.; Liu, W.; Wang, S.-W.; Colby, R. H. Macromolecules 2011, 44, 3572. (36) Rubinstein, M. Colby, R. H. Polymer Physics; Oxford University Press: London, 2003. (37) Colby, R. H.; Fetters, L. J.; Graessley, W. W. Macromolecules 1987, 20, 2226. (38) Doi, M. Edwards, S. F. The Theory of Polymer Dynamics, 3rd ed.; Wiley: New York, 1980. (39) Ferry, J. D.; Landel, R. F.; Williams, M. L. J. Appl. Phys. 1955, 26, 395. (40) McCrum, N. G.; Read, B. E.; Williams, G. Anelastic and Dielectric Effects in Polymeric Solids; Dover Publications, Inc.: New York, 1967. (41) Wübbenhorst, M.; van Turnhout, J. J. Non-Cryst. Solids 2002, 305, 40. (42) Steeman, P. A. M.; van Turnhout, J. Macromolecules 1994, 27, 5421. (43) Rietz, R.-R.; Meyer, W. H. Polym. Adv. Technol. 1993, 4, 164. (44) Funke, K. Prog. Solid State Chem. 1993, 22, 111. (45) Weber, R. L.; Ye, Y.; Banik, S. M.; Elabd, Y. A.; Hickner, M. A.; Mahanthappa, M. K. J. Polym. Sci., Part B 2011, 49, 1287. (46) Strobl, G. R. The Physics of Polymers: Concepts for Understanding Their Structures and Behavior, 3rd ed.; Springer: New York, 2007. (47) Fragiadakis, D.; Dou, S.; Colby, R. H.; Runt, J. Macromolecules 2008, 41, 5723. (48) Weiss, R. A.; Zhao, H. J. Rheol. 2009, 53, 191. (49) Debye, P. Polar Molecules; Chemical Catalog Co.: New York, 1929. (50) Sangoro, J. R.; Serghei, A.; Naumov, S.; Galvosas, P.; Kärger, J.; Wespe, C.; Bordusa, F.; Kremer, F. Phys. Rev. E 2008, 77, 051202.

Figure S3 with the comparison between viscoelastic master curve and dielectric spectra for PC4VIX; Figure S4 with the frequency-dependent ε″der curves for PC4VITFSI at various temperatures. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The synchrotron radiation experiments were performed at the BL40B2 and BL45XU of SPring-8 with the approval of the Japan Synchrotron Radiation Research Institute (JASRI) (Proposals 2011B1469 and 2011B1398).

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