Article pubs.acs.org/Macromolecules
Dynamic Viscoelasticity and Birefringence of Poly(ionic liquids) in the Vicinity of Glass Transition Zone Tadashi Inoue,*,† Atsushi Matsumoto,† and Kenji Nakamura‡ †
Department of Macromolecular Science, Graduate School of Science, Osaka University, 1-1 Machikaneyama-cho, Toyonaka, Osaka 560-0043, Japan ‡ DIC Corporation, 631 Sakado, Sakura, Chiba 285-8668, Japan S Supporting Information *
ABSTRACT: Dynamic viscoelasticity and birefringence of two poly(ionic liquid)s, PC4VITfO and PC4VITFSI, are investigated to clarify the molecular origin of viscoelastic response of PILs. According to a previous study, PC4VITFSI having larger counterions shows a broader viscoelastic relaxation spectra around the glass-to-rubber transition zone than PC4VITfO. The rheo-optical data were analyzed with the modified stress-optical rule: The complex modulus for PC4VITfO was separated into two components, the rubbery and the glassy component, similarly to the ordinary amorphous polymers while for PC4VITFSI system an additional component was necessary in addition to the two ordinary components for a reasonable separation. From the frequency dependence, the additional component was attributed to the sub-Rouse mode of chain which is enhanced by the counterions decreasing the interchain interactions.
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mechanism.16,17 They proposed two molecular origins for this relaxation mechanism. One is the rotational motions of ion pairs, and the other one is the local motion of the polymer chain. Rheo-otical method with the simultaneous measurement of stress and birefringence is a useful technique to characterize the molecular origin of stress because birefringence has a strong correlation with the stress.18−26 For example, the stress-optical rule, SOR, holds valid for rubbery materials.27 The proportionality coefficient, stress-optical coefficient, reflects the molecular origin of the stress. Around the glass-to-rubber transition zone, the SOR does not hold valid and alternatively the modified stress-optical rule, MSOR, holds valid.26 This is because the glassy component contributes to the stress and the birefringence in addition to the rubbery component originating from the segment orientation around the transition zone. The MSOR says that the both the stress and birefringence are composed of two components, R and G, and the ordinary proportionality holds valid for each component. Here, R and G respectively stand for the rubbery and glassy components. In this study, we utilized the rheo-optical method to clarify the molecular origin of the broader relaxation in the glass-torubber transition of polymerized ionic liquids, poly(1-butyl-3vinylimidazolium bis(trifluoromethanesulfonylimide)) (PC4VITFSI). We will show that the molecular origin of the
INTRODUCTION Ionic liquids, ILs, are molten salts formed by a soft cation and an anion. Their melting temperatures are below some arbitrary temperature, such as 100 °C.1−4 ILs have attracted many researchers’ attention because of their nonvolatility, nonflammability, and high electric conductivity. These features lead to many applications, such as powerful solvents and electrically conducting fluids (electrolytes). For practical application of ILs, solidified ILs without loss of these features may be useful. Recently, polymerized ionic liquids, PILs, have received research interest.5 PILs can be chemically described as covalently bonded IL monomers. Ohno et al. have detailed the synthesis, characterization, and conductive behavior of many PIL species.6 These systems are solid at room temperature and possess both the characteristics of ILs and polymers. PILs are easily molded by heating, similar to ordinary amorphous polymers. In addition, several reviews about PILs have recently been published. However, despite this attention there have been relatively few reports regarding the physicochemical features of PILs.7−14 PILs can be classified as a polyelectrolyte species like sodium polystyrenesulfonate, in the sense that they consist of an electrolyte monomer unit, and therefore, PILs can be regarded as model systems of molten polyelectrolytes.15 In the previous study, Nakamura et al. studied viscoelastic properties of molten PILs over a wide frequency region covering from the terminal flow to the glassy zone. They reported that viscoelastic properties of PILs are sensitive to counterions; with increasing counterion size, the modulus in the glass-to-rubber transition zone becomes broader, indicating existence of a new relaxation © 2013 American Chemical Society
Received: May 24, 2013 Revised: July 15, 2013 Published: July 30, 2013 6104
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broad relaxation spectra of PC4VITFSI can be attributed to cooperative local motions of the chain.
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EXPERIMENTAL SECTION
Sample. 1-Vinylimidazole was purchased from TCI (Tokyo) and used after distillation. 2,2′-Azobis(isobutyronitrile) (AIBN), and lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) was purchased from Wako Pure Chemicals (Osaka). Lithium trifluoromethanesulfonate (LiTfO) was purchased from TCI. 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. Figure 1 shows chemical structure of PC4VIX. Synthesis of PC4VIX was conducted following the method described by
Figure 2. Composite curves for the complex modulus and the complex strain-optical coefficient for PC4VITfO. The data taken from the tensile measurement, E*/3 and O*/3, are also included as G* and K*, respectively.
+ iE″ for PC4VITfO. In what follows, we will not distinguish G* and E*/3. Here, we used the method of reduced variables to construct the composite curves.32 The reference temperature was chosen as Tr = 80 °C. The superposition worked well including the glass-to-rubber transition zone. For a more sensitive check of time−temperature superposition for the modulus, we made the so-called van Gurp−Palmen plots,33 in which the loss angle was plotted against the logarithm of G*. Again, the superposition worked well over the whole frequency region (see Supporting Information) Also included is the composite curve for the shear complex strain-optical coefficient, K*=K′+iK″, and the tensile complex strain-optical coefficient, O*=O′+iO″. Similarly, we will not distinguish K* and O*/3. Birefringence at low frequencies is negative while it is positive at high frequencies. Similar frequency dependence of the complex strain-optical coefficient was observed for polystyrene. Figure 3 displays the composite curves for the complex modulus and the complex strain-optical coefficient for
Figure 1. Chemical structure of polymerized ionic liquid poly(1-butyl3-vinylimidazolium) with counteranion X− (PC4VIX). Nakamura et al. 1-Butyl-3-vinylimidazolium bromide (C4VIBr) was prepared by refluxing 1-vinylimidazole and excess bromobutane in methanol at 70 °C for 3 days. PC4VIBr was synthesized via the free radical polymerization of C4VIBr. Polymerization was initiated by AIBN in a water solution at 60 °C for 16 h. After the polymerization, PC4VIBr was dialyzed against water for 3 days and obtained as a powder via freeze-drying. Elimination of the C4VIBr component from the product was confirmed using a 1H NMR measurement in D2O. The PC4VITfO and PC4VITFSI were prepared using the counterion conversion method proposed by Mecerreyes.28,29 An aqueous solution including 1.5 equiv of salts (LiTfO, or LiTFSI) was slowly titrated into aqueous PC4VIBr solution and mixed for at least 2 days at room temperature. The resulting precipitation 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 and sequential X-ray fluorescence spectrometer. Found (%): C, 30.85; H, 3.4; N, 9.86; S, 26.4; Br, 0.22. Calcd for C11H15N3O4S2F6 (%): C, 30.62; H, 3.51; N, 9.74 for PC4VITFSI. Found (%): C, 39.99; H, 5.01; N, 9.19; Br, 0.1. Calcd for C10H15N2O3S1F3 (%): C, 39.99; H, 5.04; N, 9.33 for PC4VITfO. Method. The experimental apparatus for rheo-optical measurements on oscillatory tensile and shear deformation is reported elsewhere.23,26 As for the viscoelastic measurements, a small amplitude oscillatory deformation, γ(t) = γ0 sin ωt (with γ0 = 0.06) in case of shear deformation is applied on the sample in order to measure the complex shear modulus G* and the complex shear strain-optical coefficient K*. G* and K* were determined in the temperature range from 120 to 190 °C. To check the reliability of the data, G* was measured with a TA Instruments ARES-G2 system with a homemade parallel plate fixture having 4 mm diameter. Instrument compliance was carefully corrected with the method reported by McKenna et al.30,31 All measurements were performed under a nitrogen atmosphere over a temperature range of 35−260 °C.
Figure 3. Composite curves for the complex modulus and the complex strain-optical coefficient for PC4VITFSI. The data taken from the tensile measurement, E*/3 and O*/3, are also included as G* and K*, respectively.
PC4VITFSI. The reference temperature was chosen as Tr = 80 °C. Again, the superposition worked well over the whole frequency region including the glass-to-rubber transition zone. As reported in the previous study, frequency dependence of the modulus of PC4VITFSI around the glass-to-rubber transition zone is broader than the ordinary polymers such as polystyrene.16 Here, we note that a similar frequency dependence of the complex modulus is observed for polyisobutylene34 and polymethly methacrylate.35 On the
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RESULTS AND DISCUSSION Overview of Modulus and Strain-Optical Coefficient. Figure 2 shows the composite curve for the complex shear modulus, G* = G′ + iG″ and complex Young’s modulus, E*= E′ 6105
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(ω/s−1) ∼2 and decreases at high frequencies, as shown in Figure 4. As will be discussed later, the anomalous maximum of K″(ω)/G″(ω) suggests the breakdown of two component MSOR for PC4VITFSI. By solving simultaneous eqs 1 and 2, we can determine the component functions with K* and G* data.
other hand, the frequency dependence of the complex strainoptical coefficient is similar to that for PC4VITfO and polystyrene. For both the samples, the SOR holds19 valid at low frequencies, log(ω/s−1) < −3. K * = CRG*
(1)
Here, the proportionality coefficient CR is called as the stressoptical coefficient. The validity of SOR indicates that both the stress and birefringence are ordinated from the orientation of segments at low frequencies. The obtained CR is summarized in Table 1. As will be explained later, CR can be related to the
CR/1012 Pa−1
CL/1012 Pa−1
C G/ 1012 Pa−1
Δα/10−24 cm−3
PC4VITfO PC4VITFSI polystyrene
−3600 −12000 −4700
NA 180 NA
19 15 30
−1.2 −2.8 −1.6
anisotropy of polarizability of repeating units, Δα.36 Negative CR value for the two polymers indicating that Δα is negative. This negative optical anisotropy comes from the large side chains as in polystyrene. MSOR Analysis. As shown in Figures 2 and 3, SOR does not hold valid over the whole frequency region. This is because the glassy component contributes to both the modulus and the strain-optical coefficient at high frequencies. Therefore, we examine the MSOR for amorphous polymers.26 The MSOR for two components system can be written as follows. G* = G R * + GG*
(1)
K * = C R G R * + CGGG*
(2)
K *(ω) − CGG*(ω) CR − CG
(4)
GG*(ω) =
K *(ω) − CRG*(ω) CG − CR
(5)
The results are shown in Figures 5 and 6. Here, we used the method of reduced variables for each component individually.
Table 1. Optical Properties of PC4VITfO and PC4VITFSI sample
GR*(ω) =
Figure 5. Component functions for PC4VITfO.
Here, Gi* is the component function. In the rubbery zone, GR* has relaxed and there eqs 1 and 2 reduced to the ordinary SOR. CG is the stress-optical coefficient for the G component, which is defined as follows.26 CG = lim
ω→∞
K ″(ω) G″(ω)
Figure 6. Component functions for PC4VITFSI determined by two components MSOR.
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Frequency dependence of the ratio, K″(ω)/G″(ω), for PC4VITFSI is shown in Figure 4. The ratio is negative at low
The reference temperature is 80 °C for PC4VITfO and PC4VITFSI. The superposition works well for both the samples. The result for PC4VITfO is very similar to the component functions of polystyrene, indicating that the decomposition of the modulus is performed reasonably. For the case of PS, GG* is very similar to G* for oligosytrene (M ∼ 1000 g mol−1). This result indicates that GG* is related to the local motion of chain, M < 1000 g mol−1. On the other hand, the R component for PC4VITFSI is different from ordinary component functions. GR″ is negative at high frequencies and GR′ shows a maximum around log(ω/s−1) = 1. Phenomenological theory for viscoelasticity requires that GR′ should be a monotonically increasing function of ω and GR″ should be positive. Therefore, we conclude that the two components MSOR does not work for PC4VITFSI. Now, let us consider the MSOR composed of three components. The MSOR for three components can be written as follows.
Figure 4. Frequency dependence of K″(ω)/G″(ω) for PC4VITFSI.
frequencies and positive at high frequencies. The limiting value at low frequencies corresponds to CR. Following definition of CG, we determined CG = 1.5 × 10−11 Pa−1. Here, we should note that K″(ω)/G″(ω)for PS and PC4VITfO increases with increasing of frequency at high frequencies (not shown here) while the ratio for PC4VITFSI shows the maximum around log
G* = G R * + G L* + GG* 6106
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Macromolecules K * = C R G R * + C LG L* + CGGG*
Article
By using thus determined, GR*, GG*, CR, CL, and CG, we finally determined GL* through the eq 11. The result is shown in Figure 8. We note all of real part of three components is a monotonically increasing function of ω and all of imaginary part is positive.
(7)
If we solve these equations following the standard method for the two components MSOR, that is, if we calculate the righthand sides of eqs 4 and 5, then we obtain K *(ω) − CGG*(ω) C − CG = GR*(ω) + L GL*(ω) CR − CG CR − CG
(8)
K *(ω) − CRG*(ω) C − CR = GG*(ω) + L GL*(ω) CG − CR CG − CR
(9)
Equation 8 explains why the apparent R component, (K*(ω) − CGG*(ω))/(CR − CG), shown in Figure 6, shows anomalous frequency dependence. The function contains the contribution of the third unknown function, GL*. The coefficient (CL − CG)/(CR − CG) can be negative, and hence the function shows change of sign as shown in Figure 6. Alternatively, if we can find true CL, and eqs 6 and 7 are solved for GR* and GL*, the function, (K*(ω) − CLG*(ω))/ (CR−CL), includes the contribution of GR* and GG*. C − CL K *(ω) − CLG*(ω) = GR*(ω) + G GG*(ω) CR − CL CR − CL
(10)
C − CR K *(ω) − CRG*(ω) GG*(ω) = GL*(ω) + G CL − CR CL − CR
(11)
Figure 8. Three component functions determined by MSOR for PC4VITFSI. Black lines represent the DTO model with n = 15.
Viscoelastic Segment Size. Molar mass of viscoelastic segment can be calculated from the limiting modulus at high frequencies for the R component, GR′(∞), can be related with the molecular weight of viscoelastic segment size.37
MS =
As suggested in Figure 3, the third function GL* would locate between the R and G components. In other words, the difference in the relaxation time between GR* and GG* will be larger than that between GR* and GL* and therefore we anticipate that location of GR* and GG* might be separated enough to distinguish the two function in (K*(ω) − CLG*(ω))/(CR − CL). In order to examine this conjecture, we sought the correct value of CL, which gave phenomenologically reasonable (K*(ω) − CLG*(ω))/(CR − CL), which was composed of GR* at low frequencies and GG* at high frequencies. The result is shown in Figure 7, which perfectly
ρRT GR′(∞)
(12)
Here, R is the gas constant and T is temperature and ρ is density. RT/GR′(∞) in eq 12 represents the number of moles of segments per unit volume, and therefore, ρRT/GR′(∞) corresponds to the molar mass of segments. It should be noted that eq 12 is applicable irrespective of ionization state of repeating units and the obtained value corresponds to the molar mass of hypothetical segments composed of all “deionized repeating units”. MS for poly(ionic liquid)s is summarized in Table 2. Here, data for polystyrene is also included as a reference data for vinyl Table 2. Rouse Segment Size of PC4VITfO and PC4VITFSI sample
GR′(∞)/MPa
MS/Kg mol−1
MS/M0
PC4VITfO PC4VITFSI polystyrene
1.86 0.851 4.0
2.4 5.3 0.86
8.1 12 8.2
polymers. In a previous study, we showed that viscoelastic segment size is in accord with the Kuhn segment size, MK.24 Since the ratio MS/M0 is related to Flory’s characteristic ratio, the ratio MS/M0 is a good measure of main chain flexibility. Here, M0 is molar mass of deionized repeating units. MS/M0 value for the PC4VITfO is close to that for PS, indicating that the chain rigidity of the two polymers is the same. PC4VITFSI is more rigid than the others. Larger rotational hindrance of chain backbone due to larger counterion might increase the dynamic rigidity. The anisotropy of the polarizability, Δβ, for the segment can be related to the stress-optical coefficient, CR.36
Figure 7. Component functions for PC4VITFSI determined by two components MSOR. Triangle marks represent for the glassy component of PC4VITfO.
satisfies our requirement. As indicated by arrows, two relaxation maxima are observed. The slower relaxation can be assigned to the R component from the similarity with GR* in Figure 5 and the faster relaxation to the G component. According to eq 10, the faster relaxation is attributed to the glassy component, (CG − CL)GG*(ω)/(CR − CL). We note that the frequency dependence of (CG − CL)G*G (ω)/(CR − CL) is very similar to the ordinary G component, which is shown in Figure 6. To show this, we added GG* of PC4VITfO in Figure 7.
CR = 6107
2π (n ̅ 2 + 2)2 Δβ 45 nkT ̅
(13)
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determined by the global motion of chain. Thus, GL* can be attributed to the loss of the interchain cooperation brought in by reducing the interchain interaction by ionized counterions. The remaining interaction is the intrachain interaction though the chain connectivity. In a cooperative manner, the intrachain interaction expands to the size of repeating units due to the imperfect flexibility of each bond.
Here, n is the refractive index. The anisotropy of the polarizability, Δα, for the repeating unit can be related to Δα ∼ Δβ M0/MS. If all the repeating units are ionized, Δα for PC4VITfO and PC4VITFSI should agree with each other because Δα is determined by the same backbone component. However, Δα for the two polymers does not agree, suggesting that not all the repeating units are ionized. Δα for PC4VITFSI is approximately 2 times larger than PC4VITfO, suggesting that PC4VITFSI is highly ionized. The Molecular Origin of G L*. The stress-optical coefficient for the L component for PC4VITFSI is CL = 1.8 × 10−10Pa−1. This value is roughly one hundred times smaller than CR and ten times larger than CG, suggesting the molecular origin of the L component has relatively large compliance than the ordinary glassy modes. We note that the CL value is close to the stress-optical ratio for a typical ionic liquid, BminCl, CS = 1.8 × 10−10 Pa−1 at −20 °C.38 (The SOR did not hold strictly for BminCl and CS defined as K″/G″ varied with temperature, indicating that some structure changes occurred in BminCl with temperature.) The similar CL value suggests that the L component might be related to the reorientation process of ions. Figure 8 shows that frequency dependence of GL* is broad and cannot be described with a simple relaxation mode. This implies that the molecular origin of GL* is not a simple rotational motion of anions, which might be described with a Maxwellian function. Broad frequency dependence suggests that the molecular origin of GL* could be some cooperative motion of main chain cations, such as sub-Rouse motion. From such a discussion, we examine the damped torsional oscillator model, DTO model39 to describe the relaxation mechanism of the L mode. In DTO model, cooperative torsional motions of structural units are considered. According to the DTO model, the complex model can be described as 2
G′(ω) = G∞ ∑ p
G″(ω) = G∞ ∑ p
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CONCLUSION We have conducted rheo-optical measurement for poly(ionic liquid)s PC4VITfO and PC4VITFSI to clarify the molecular origin of anomalous broadening of modulus around the glassto-rubber transition zone. For PC4VITfO, the two component MSOR worked well and reasonable two component functions were obtained while for PC4VITFSI having larger asymmetric counterions three component functions were needed. These three component functions were assigned to the segmental reorientation mode, the sub-Rouse mode, and the glassy mode. Sub-Rouse mode is often observed for solutions where intrachain interaction is dominant for local motions. Appearance of the sub-Rouse mode for PC4VITFSI was attributed to the decreasing of interchain interaction due to ionized large counterions which behaves like a solvent.
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S Supporting Information *
van Gurp−Palmen plot for PC4VITfO and PC4VITFSI.. This material is available free of charge via the Internet at http:// pubs.acs.org.
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*E-mail: (T.I.)
[email protected]. Notes
ω τDTO p
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was partly supported by Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science, and Technology, Japan (No. 24350120).
ωτDTOp−1 1 + ω 2τDTO 2p−2
AUTHOR INFORMATION
Corresponding Author
2 −2
1 + ω 2τDTO 2p−2
ASSOCIATED CONTENT
(15)
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Here, τDTO is the characteristic time for the DTO model. The frequency dependence of G* by the DTO model is similar to that of the Rouse model. For the case of linear array of the damped torsional oscillator arrays, the interchain interaction is ignored and the dynamics are governed by the connectivity of the chain. If the counteranions are ionized and they work as a solvent, these assumptions are quite natural.(Note that volume fraction of counterions are approximately 0.5.) Similar frequency dependence was obtained by Verdier−Stcomayer model.40,41 In this model, the polymer is made up of N beads connected by N-1 bonds having the same bond length. Local motions of polymers are represented by the jump of beads with a probability. This probability is not affected by the interchain interaction. In Figure 8, G* by the DTO model is depicted. The prediction of the DTO model is remarkably consistent with the experimental data in low frequency side of G″ maximum. In fitting procedure, we set number of units in the DTO model as 15. If we take the repeating unit as structure unit, the number suggests that the cooperative size of GL* is M = 7000. This number is comparable to the viscoelastic segments size
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NOTE ADDED AFTER ASAP PUBLICATION This article posted ASAP on July 30, 2013. Equations 14 and 15 have been revised. The correct version posted on August 2, 2013.
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