Design of superionic polymers—New insights from Walden plot analysis

SOSI-13047; No of Pages 3 Solid State Ionics xxx (2013) xxx–xxx

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Design of superionic polymers—New insights from Walden plot analysis Yangyang Wang a,⁎, Fei Fan b, Alexander L. Agapov b, Xiang Yu a, Kunlun Hong c, Jimmy Mays a,b, Alexei P. Sokolov a,b a b c

Chemical Sciences Division, Oak Ridge National Laboratory, Oak Ridge TN 37831, USA Department of Chemistry, University of Tennessee, Knoxville, TN 37996, USA Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA

a r t i c l e

i n f o

Article history: Received 13 June 2013 Received in revised form 15 September 2013 Accepted 18 September 2013 Available online xxxx Keywords: Polymer electrolytes Decoupling Walden plot Superionic

a b s t r a c t Using a modified Walden plot analysis, we demonstrate that polyether-based solid electrolytes have intrinsic limitations for ionic transport at ambient and low temperatures, due to strongly coupled segmental and ion dynamics. On the other hand, rigid polymers can exhibit ionic conductivity that is highly decoupled from segmental relaxation, thus providing a significant advantage over traditional polyether electrolytes. Our analysis emphasizes that decoupling of ionic transport from segmental dynamics is the key for macromolecular design of “superionic” polymers. © 2013 Elsevier B.V. All rights reserved.

1. Introduction Solid polymer electrolytes have continuously attracted much attention since their introduction in the 1970s [1,2]. Use of polymer electrolytes instead of traditional liquid electrolytes significantly reduces weight, increases energy density, and improves safety of batteries. However, despite intensive studies over the past few decades, the ionic conductivity of dry polymer electrolytes remains rather low at ambient temperatures or below. A possible solution to this problem is to use heavily plasticized gel-type polymers, where several advantages offered by solid electrolytes have to be compromised. An alternative approach to the problem is to learn how to decouple ionic transport from the segmental motion of the polymer matrix [3–11]. While significant effort has been devoted to suppressing crystallization and lowering the glass transition temperature (Tg) of polyether-based electrolytes, the decoupling approach has not been given sufficient attention. Here, we analyze ionic conductivity of several polymers using a modified Walden plot. We demonstrate that decoupling of ionic conductivity from segmental relaxation can bring polymer electrolytes into the “superionic” regime. Based upon this analysis, we suggest that decoupling might be the only way for solid polymer electrolytes to reach the required level of ionic conductivity at ambient or lower temperatures. 2. Materials and methods Poly[4-(2-methoxyethoxy)methyl styrene] (PMOEOMSt, Mw = 5.8 kg/mol, Mw/Mn = 1.22) was synthesized using anionic ⁎ Corresponding author. E-mail address: [email protected] (Y. Wang).

polymerization, details are presented in [12]. Lithium perchlorate (LiClO4) and poly(propylene glycol) (PPG) of 1.0 kg/mol were purchased from Sigma-Aldrich and PPG of 4.0 kg/mol was obtained from Scientific Polymer Products. All materials were used as received. Dry polymer electrolytes were prepared by dissolving the polymers and LiClO4 in appropriate solvents and subsequently removing the solvents in a vacuum oven at elevated temperatures. We have also re-analyzed the data for polyethylene glycol (PEG) from ref. [13]. The dielectric spectra of the polymer electrolytes were measured at various temperatures in the frequency range 10− 2–107 Hz, using an Alpha Analyzer with Cryosystem (Novocontrol). The samples were placed between gold-plated electrodes with a Teflon spacer of 0.054 mm. All the measurements were performed in the linear response regime. The following function was used for fitting of the dielectric spectra: Δε1 Δε2 σ −n ε
ðωÞ ¼ ε ∞ þ h þ Aω ;
α iβ þ h
 α iβ þ 1 1 2 2 iε ω 0 1 þ iωτ HN;1 1 þ iωτHN;2

ð1Þ where ε∞ represents the value of ε'(ω) at infinite frequency, Δεj is the dielectric relaxation strength of process j (j = 1, 2), τΗΝ,j is the relaxation time, αj and βj are the shape parameters, n is related to the slope of the high frequency tail of electrode polarization (EP), A gives the amplitude of EP, and σ is the dc conductivity. The first Havriliak-Negami (HN) function accounts for the “ultra-slow” relaxation [14] (not shown in Fig. 2a) in PMOEOMSt, which is a common artifact in polymers due to the presence of impurities or bubbles. The second HN function describes the segmental relaxation. The segmental relaxation time

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τ is calculated from the HN relaxation time τHN and shape parameters α and β using the following relation:    −1=α αβπ 1=α απ sin : τ ¼ τHN sin 2 þ 2β 2 þ 2β

ð2Þ

3. Results and discussion 3.1. Limitations of polyether-based solid electrolytes It is known that ionic conductivity depends on the concentration of free ions nf and their diffusion coefficient D: σ = nfDq2/kT, where q is the charge of the ion. In classical theories, the diffusion coefficient is controlled by the solvent viscosity η or structural relaxation τ: D∝ kT/η∝ 1/τ [15]. As a result, it is expected that the ionic conductivity is inversely proportional to viscosity of the electrolyte, σ ∝ 1/η. This is the basis for the Walden rule [16]: Λη = const., where Λ = σ/nf is molar conductivity. In other words, the Walden rule is based on the assumption of strong coupling of ionic conductivity and electrolyte viscosity (structural relaxation). Indeed, the ionic transport in polyethers is typically closely coupled to the segmental (structural) relaxation of the polymer matrix [15,5]. This scenario is illustrated in the inset of Fig. 1, where the segmental relaxation time and resistivity (1/σ) of PEG-100 K with 19 wt% LiClO4 exhibit identical temperature dependence. To further analyze the relationship between ionic transport and segmental relaxation in polymer electrolytes, one can borrow the concept of the Walden plot, which has been widely used for nonpolymeric ionic conductors [17]. In the Walden plot analysis, the molar conductivity of an electrolyte is presented as a function of its fluidity (1/η). The straight line of slope one, passing through the data of a reference dilute salt aqueous solution (e.g., KCl or LiCl), is often called the “ideal” Walden line. It divides the plane into superionic conductor (above) and subionic conductor (below) regimes. In order to apply the Walden plot analysis to polymers, the fluidity must be substituted by the rate of structural (segmental) relaxation (1/τ), which is the more relevant quantity for ionic transport in polymers. Fig. 1 shows that all the five PEG- and

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-log10 [s] Fig. 1. Relation of molar conductivity (Λ) to rate of structural (segmental) relaxation (1/τ) in polyether-based polymer electrolytes. Here, dilute lithium chloride (LiCl) aqueous solution is used as the reference [23]. The straight line with slope of 1.0 is the “ideal” Walden line. The horizontal dashed line indicates the target molar conductivity required to achieve σ = 10−3 S/cm in PEG-LiTFSI. Inset: temperature dependence of segmental relaxation time (τ) (up triangles) and resistivity (1/σ) (down triangles) in PEG-100 K with 19 wt% LiClO4. The left and right y-axes of the inset span the same orders of magnitude. The PEG data are from ref. [13].

PPG-based electrolytes fall onto the “ideal” Walden line of LiCl-H2O, suggesting a universal behavior for all polyether-based polymer electrolytes. Because the ion and polymer dynamics are strongly coupled, the data exhibit a slope of 1.0, i.e., Λ∝1/τ. It is generally agreed that the desirable intrinsic ionic conductivity of dry polymer electrolytes should be greater than 10− 3 S/cm [7]. This corresponds to a molar conductivity of 0.6 Scm2/mol for PEG with 50 wt% of lithium bis(trifluoromethane) sulfonimide (LiTFSI). The “target” molar conductivity is indicated by the horizontal dashed line in Fig. 1. Because of the close relation between ionic transport and segmental dynamics in polyethers, it is easy to estimate that the target molar conductivity can be reached only when the segmental relaxation time is shorter than ~ 10− 8 s. In the case of PEG-100 K with 19 wt% LiClO4 (Fig. 1 inset), τ is 10− 8 s at approximately 80 °C. Since all the analyzed polyethers show a universal relation between ionic transport and segmental relaxation – they fall onto the “ideal” Walden line, it seems impossible for any polyether-based electrolyte to reach the required level of ionic conductivity at ambient and lower temperatures, unless the polymer is heavily plasticized.

3.2. Decoupling of ionic transport from segmental relaxation in rigid polymers In contrast to flexible polyethers, the ionic transport in rigid polymers can be strongly decoupled from the segmental dynamics [3,6,10,11,18]. Here, we use poly[4-(2-methoxyethoxy)methyl styrene] (PMOEOMSt) as an example (Fig. 2). This polymer is based on the relatively rigid polystyrene backbone, with 2-methoxyethoxy methyl as the side group to increase the solubility of lithium salts. Unlike polyethers, the ion and segmental dynamics are decoupled in PMOEOMSt. While the segmental relaxation time increases by four and a half orders of magnitude when temperature changes from 40 to 5 °C, the ionic conductivity only decreases by roughly two orders over the same temperature range (Fig. 2a). This difference is highlighted in Fig. 2b, where the resistivity (1/σ) of PMOEOMSt clearly exhibits much weaker temperature dependence than its segmental relaxation time. In this regard, the behavior of PMOEOMSt is reminiscent of the well-known superionic glasses [19], and stands in stark contrast to the behavior of conventional polyethers. It should be emphasized that while the ion transport in principle can be coupled to the motion of the methoxyethoxymethyl group, such side group motion was not experimentally observed in our dielectric measurements. The molecular mechanism for ion transport in this rigid polymer remains to be identified. Because of its strong decoupling of ionic conductivity from segmental relaxation, PMOEOMSt appears in the superionic regime of the Walden plot (Fig. 3), in the vicinity of its glass transition. However, it is in the sub-ionic regime at higher temperatures (shorter τ), due to poor solvation of the lithium ion in this polymer. Our analysis based on the electrode polarization (EP) effect [11,20] reveals that most of the ions in PMOEOMSt exist as ion pairs, i.e., the concentration of free ions is relatively low. Using the EP analysis method we have developed recently [20], we are able to take the ion association into account and calculate the true molar conductivity (ΛTrue) of free ions. The percentage of free ions in PMOEOMSt is on the order of 0.01%. After this correction, molar conductivity in PMOEOMSt (Fig. 3, red circles) stays well above the “ideal” line, showing superionic behavior similar to (AgI)0.5-(AgPO3)0.5. This behavior is clearly desirable for application as an ionic conductor at low temperatures. Compared to flexible polymers such as polyethers, more rigid polymers suffer a significant amount of frustration in chain packing [21,22]. Small ions therefore can utilize the loose packing structure of rigid polymers (enhanced free volume) and move through the polymer matrix even when the segmental dynamics are slow. This unique advantage of rigid polymers for ionic transport has been demonstrated recently for a wide variety of polymers [10,11].

Please cite this article as: Y. Wang, et al., Solid State Ionics (2013), http://dx.doi.org/10.1016/j.ssi.2013.09.026

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1000/T [K-1] Fig. 2. (a) Dielectric spectra of poly[4-(2-methoxyethoxy)methyl styrene] (PMOEOMSt) with 0.3 wt% LiClO4 at 40 and 5 °C. Here, ε″ is the imaginary part of permittivity and f is the frequency. The arrows show shift of the segmental relaxation and conductivity. (b) Temperature dependence of segmental relaxation time (circles) and resistivity (1/σ, diamonds) of PMOEOMSt. Orange curve: Vogel-Fulcher-Tammann (VFT) fit of the resistivity below Tg: (1/σ) = (1/σ0)exp[B/(T-T0)]. Black line: Arrhenius fit of the resistivity below Tg: (1/σ) = (1/σ0)exp(Ea/kBT). Pink curve: VFT fit of the segmental relaxation time: τ = τ0exp[B/(T-T0)].

4. Concluding remarks Despite the strong decoupling behavior, the conductivity of PMOEOMSt at room temperature is still quite low, due to its relatively high Tg and mediocre solvating power for lithium salts. Our recent studies [10,11] have shown it is the fragility [dlog10τ/d(Tg/T)]T = Tg rather than the glass transition temperature that controls the decoupling of ionic transport in polymers. It is therefore possible to synthesize polymers with relatively low Tg, while preserving the decoupling properties. On the other hand, the salt solvation can be further improved by incorporating chemical groups with high dielectric constant into the polymer matrix. If these two factors are adequately addressed, rigid or semi-rigid polymers should be promising candidates for realizing true superionic conductivity in solid polymer electrolytes. Acknowledgements This research was sponsored by the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory, managed

Fig. 3. Comparison of the relation between molar conductivity and rate of structural relaxation in several ionic conductors. The green hexagons stand for PEG-100 K with 19 wt% LiClO4 [13]. The filled circles represent the true molar conductivity (ΛTrue) of PMOEOMSt with 0.3 wt% LiClO4 after the correction for free-ion concentration. The “ideal” Walden line (straight line with slope of 1.0) divides the Walden plot into superionic (above the ideal line) and subionic (below the ideal line) regimes. The data for superionic conductor (AgI)0.5-(AgPO3)0.5 are from refs. [24] and [25]. It should be noted that the correction for free ions is relatively small for polyethers and is not shown here.

by UT-Battelle, LLC, for the U.S. Department of Energy. The polymer synthesis was conducted at the Center for Nanophase Materials Sciences, which is sponsored at Oak Ridge National Laboratory by the Scientific User Facilities Division, Office of Basic Energy Sciences, U.S. Department of Energy. J.M. and A.P.S. acknowledge the financial support from the Division of Materials Science and Engineering, U.S. Department of Energy, Office of Basic Energy Sciences. F.F. and A.L.A. thank the NSF Polymer Program (DMR-1104824) for funding. References [1] P.V. Wright, Br. Polym. J. 7 (1975) 319. [2] M. Armand, J.M. Chabagno, M. Duclot, in: P. Vashitshta, J.N. Mundy, G.K. Shenoy (Eds.), Fast Ion Transport in Solids: Electrodes and Electrolytes, North Holland Publishers, Amsterdam, 1979. [3] X. Wei, D.F. Shriver, Chem. Mater. 10 (1998) 2307. [4] A. Nishimoto, K. Agehara, N. Furuya, T. Watanabe, M. Watanabe, Macromolecules 32 (1999) 1541. [5] M.A. Ratner, P. Johansson, D.F. Shriver, MRS Bull. 25 (2000) 31. [6] C.T. Imrie, M.D. Ingram, Electrochim. Acta 46 (2001) 1413. [7] P.V. Wright, MRS Bull. 27 (2002) 597. [8] E.R. Leite, F.L. Souza, P.R. Bueno, S. de Lazaro, E. Longo, Chem. Mater. 17 (2005) 4561. [9] F.L. Souza, E. Longo, E.R. Leite, ChemPhysChem 9 (2008) 245. [10] A.L. Agapov, A.P. Sokolov, Macromolecules 44 (2011) 4410. [11] Y. Wang, A.L. Agapov, F. Fan, K. Hong, X. Yu, J. Mays, A.P. Sokolov, Phys. Rev. Lett. 108 (2012) 088303. [12] F. Hua, W. Yuan, P.F. Britt, J.W. Mays, K. Hong, Soft Matter 9 (2013) 8897. [13] K. Yoshida, H. Manabe, Y. Takahashi, T. Furukawa, Electrochim. Acta 57 (2011) 139. [14] R. Richert, A. Agapov, A.P. Sokolov, J. Chem. Phys. 134 (2011) 104508. [15] M.A. Ratner, D.F. Shriver, Chem. Rev. 88 (1988) 109. [16] P. Walden, Z. Physiol. Chem. 55 (1906) 207. [17] C.A. Angell, Y. Ansari, Z. Zhao, Faraday Discuss. 154 (2012) 9. [18] H. Sasabe, S. Saito, Polym. J. 3 (1972) 624. [19] M.D. Ingram, Curr. Opin. Solid State Mater. Sci. 2 (1997) 399. [20] Y. Wang, C.-N. Sun, F. Fan, J.R. Sangoro, M.B. Berman, S.G. Greenbaum, T.A. Zawodzinski, A.P. Sokolov, Phys. Rev. E. 87 (2013) 042308. [21] K. Kunal, C.G. Robertson, S. Pawlus, S.F. Hahn, A.P. Sokolov, Macromolecules 41 (2008) 7232. [22] E.B. Stukalin, J.F. Douglas, K.F. Freed, J. Chem. Phys. 131 (2009) 114905. [23] P. Vanýsek, in: W.M. Haynes (Ed.), CRC Handbook of Chemistry and Physics, CRC Press, Boca Raton, 2012. [24] J.P. Malugani, A. Wasniewski, M. Doreau, G. Robert, Mater. Res. Bull. 13 (1978) 427. [25] H. Takahashi, Y. Hiki, H. Kobayashi, J. Appl. Phys. 84 (1998) 213.

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