Electric double layer capacitors with gelled polymer electrolytes based on poly(ethylene oxide) cured with poly(propylene oxide) diamines

Electric double layer capacitors with gelled polymer electrolytes based on poly(ethylene oxide) cured with poly(propylene oxide) diamines

Available online at www.sciencedirect.com Electrochimica Acta 53 (2008) 4505–4511 Electric double layer capacitors with gelled polymer electrolytes ...

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Available online at www.sciencedirect.com

Electrochimica Acta 53 (2008) 4505–4511

Electric double layer capacitors with gelled polymer electrolytes based on poly(ethylene oxide) cured with poly(propylene oxide) diamines Chien-Ping Tien, Wuu-Jyh Liang, Ping-Lin Kuo, Hsi-Sheng Teng ∗ Department of Chemical Engineering and Center for Micro/Nano Science and Technology, National Cheng Kung University, Tainan 70101, Taiwan Received 24 September 2007; accepted 12 January 2008 Available online 19 January 2008

Abstract Using a gel electrolyte for electric double layer capacitors usually encountered a drawback of poor contact between the electrolyte and the electrode surface. A gel electrolyte consisting of poly(ethylene oxide) crosslinked with poly(propylene oxide) as a host, propylene carbonate (PC) as a plasticizer, and LiClO4 as a electrolytic salt was synthesized for double layer capacitors. Diglycidyl ether of bisphenol-A was blended with the polymer precursors to enhance the mechanical properties and increase the internal free volume. This gel electrolyte showed an ionic conductivity as high as 2 × 10−3 S cm−1 at 25 ◦ C and was electrochemically stable over a wide potential range (ca. 5 V). By sandwiching this gel-electrolyte film with two activated carbon cloth electrodes (1100 m2 g−1 in surface area), we obtained a capacitor with a specific capacitance of 86 F g−1 discharged at 0.5 mA cm−2 , while the capacitance was 82 F g−1 for a capacitor equipped with a liquid electrolyte of 1 M LiClO4 /PC. The capacitance decrease with the current density was less significant for the gel-electrolyte capacitor. We found that the less restricted ion diffusion near the electrolyte/electrode interface led to the smaller overall resistance of the gel-electrolyte capacitor. The high performance of the gel-electrolyte capacitor has demonstrated that the developed polymer network not only facilitated ion motion in the electrolyte bulk phase but also gave an intimate contact with the carbon surface. The side chains of the polymer in the amorphous phase could stretch across the boundary layer at the electrolyte/electrode interface to come into contact with the carbon surface, thus improving transport of Li+ ions by the segmental mobility in polymer. © 2008 Elsevier Ltd. All rights reserved. Keywords: Gel electrolyte; PEO-copolymer-PPO; Ionic conductivity; Electric double layer capacitor; Activated carbon electrode

1. Introduction Electric double layer capacitors (EDLCs) are a clean energy storage system, in which polarization of the electrodes in opposite directions leads to accumulation of opposite charges at the electrolyte/electrode interfaces [1,2]. Because of the physical nature in charge storage, EDLCs have a longer cycle life and higher power density compared with conventional rechargeable batteries [2]. This device principally comprises of an electrolyte solution and two porous electrodes sandwiching the solution [3–5]. Activated carbon, which has a high surface area and is chemically stable, is generally used as the electrode material [6–16]. The stability and the action potential window, which are the critical issues for EDLC operation, rely heavily on the electrolytes used [1,2]. In the present work we discussed the per-



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0013-4686/$ – see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.electacta.2008.01.021

formance of an EDLC equipped with a newly-developed gelled polymer electrolyte. The electrolyte solutions used in EDLCs can be aqueous or organic [1,2]. The organic EDLC system is more effective in energy storage from the viewpoint of its wider potential window compared with that of an aqueous system [17]. However, leakage or evaporation of the solvent from organic electrolyte solutions limits the long-term stability of the cells [18]. Solid polymer electrolytes were developed for many electronic devices to avoid the leakage problem [19]. The application of solid polymer electrolytes to EDLCs so far has been limited because of the relatively low conductivity of most solid polymer electrolytes at the ambient temperature, the poor contact at electrode/electrolyte interface, and the low solubility of salts in polymer matrices [18,20]. Gel electrolytes, which consist of a polymeric framework, organic solvent (plasticizer) and supporting electrolytic salt, show high ionic conductivity of ca. 10−3 S cm−1 at the ambient temperature and sufficient mechanical strength, while still

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retain the advantage of solid polymer electrolytes [19]. These features would render gel electrolytes applicable in the EDLC system [20–32]. However, in comparison with liquid-phase electrolytes, the gel system still has problems associated with poor electrolyte/electrode contact, which would lead to a low power density. A polymeric framework to give a satisfactory electrolyte/electrode contact is thus essential for EDLCs. Poly(ethylene oxide) (PEO)-based complexes have received much attention because of its solvation tendency toward alkali metal ions [19,33]. To reduce the crystallinity, which retards ion motion in the polymeric framework, PEO is usually modified

with other polymers [19]. In the present work, we developed for the EDLC system a gel electrolyte consisting of a crosslinked polymer network of poly(ethylene oxide)-copoly(propylene oxide), designated as P(EO-co-PO), a plasticizer of propylene carbonate (PC), and a supporting electrolytic salt of lithium perchlorate. The P(EO-co-PO) network was prepared principally from poly(ethylene glycol) diglycidyl ether (PEGDE) with poly(propylene oxide) diamines used as the curing agent. To enhance the mechanical properties, diglycidyl ether of bisphenol-A (DGEBA) was blended with the polymer precursors before curing. Electrochemical analysis showed that

Scheme 1. The schematic structure of the P(EO-co-PO) polymer network and the synthetic route of the gelled polymer electrolyte.

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an EDLC with high performance could be unsophisticatedly fabricated by sandwiching this developed gel-electrolyte film with two electrodes made of activated carbon cloth. 2. Experimental PEGDE (Kyoeisha, Japan) and DGEBA (Nan-Ya, Taiwan) with epoxy group equivalent weights of 290 and 190 g/equiv., respectively, and a curing agent, ␣,␻-diamino poly(propylene oxide) (Huntsman Jeffamine D2000, USA), with an active hydrogen equivalent weight of 514 g/equiv., were used to constitute the polymeric framework of the gel electrolyte. The preparation of this polymer was initiated by dissolving 0.1 g PEGDE, 0.1 g DGEBA and 0.45 g D2000 in 0.5 g acetone via mechanical stirring. The mixture was spread onto an aluminum plate to evaporate the solvent at the ambient temperature and subsequently cured at 120 ◦ C under vacuum for 24 h. The resulting film had a thickness of 150–200 ␮m and was flexible, transparent, and brownish. Scheme 1 shows the synthetic route and schematic structure of the crosslinked polyether network. In a N2 environment, the film was soaked in an electrolyte solution of 1 M LiClO4 /PC for 5 min to entrap the solution in the polymer network. The LiClO4 /PC content of the resulting gel electrolyte film was of ca. 50 wt.%. By sandwiching with two stainless-steel electrodes, the gel electrolyte was analyzed by a.c. impedance spectroscopy (Zahner-Elecktrik IM6e, Germany) to determine the ionic conductivity [34,35], according to −1 k = R−1 b S d

(1)

where k is the ionic conductivity, Rb the intercept at the real axis in the impedance Nyquist plot, S the geometric area of the electrolyte/electrode interface, and d the distance between the two electrodes. The conductivity measurement was conducted at 0 V with an a.c. potential amplitude of 5 mV and a frequency range of 0.1 Hz–100 kHz. Using the same cell setup the stable potential window for the gel electrolyte was analyzed by cyclic voltammetry, conducted at a potential-scan rate of 5 mV s−1 . All the electrochemical measurements were conducted at 25 ◦ C. The carbon material used for EDLCs was a polyacrylonitrilebased activated carbon cloth (Taiwan Carbon Technology AW1107, Taiwan; 1100 m2 g−1 in surface area, 700 ␮m in thickness). The electrodes for EDLCs consisted of a piece of 1 cm2 carbon cloth and a stainless-steel foil serving as the current collector. A symmetric two-electrode capacitor cell was used for the examination of the capacitive performance. The cell was assembled with two facing electrodes, sandwiching a piece of the gel-electrolyte film. Prior to the cell assembly, the carbon cloth electrodes were soaked in the 1 M LiClO4 /PC solution. Cyclic voltammetric characterization of the capacitor cell was conducted within a stable potential window at different scan rates (5–50 mV s−1 ). Galvanostatic charge–discharge was used to determine the capacitance of the electrodes. The IR drop of the capacitor was measured by charging the capacitor at 0.5 mA to the maximum potential of the window followed by a discharge at a fixed current of 0.5–50 mA. The slope of the linear relationship

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between the IR drop and discharge current was used to estimate the overall resistance of the capacitors. The a.c. impedance spectrum analyzer was employed to measure and analyze the impedance behavior of the capacitor. Similar to the conductivity measurement, this analysis was conducted at 0 V with an amplitude of 5 mV, while the frequency range was expanded to 2 mHz–100 kHz. For the purpose of comparison, cells using a liquid-phase organic solution as the electrolyte were subjected to analysis for the ionic conductivity and stable potential window of the electrolyte, as well as for the capacitive performance of the resulting EDLC. The cells were assembled in the same manner as for the gel-electrolyte cells, except that a piece of filter paper was used to replace the gel film for separating the facing electrodes. These cells were soaked in a solution of 1 M LiClO4 /PC during electrochemical measurements. 3. Results and discussion The ionic conductivity of an electrolyte is associated with the energy loss during charge/discharge of the resulting EDLCs [36]. The results of a.c. impedance analysis on the gel electrolyte (GE) and the liquid electrolyte of 1 M LiClO4 /PC (LE) are shown in Fig. 1. A previous study reported that the maximum conductivity of LiClO4 /PC at the ambient temperature occurred at a concentration close to 1 M [37]. The loci of the impedance spectra for both electrolytes exhibit inclined lines intercepting the Re(Z) axis at high frequencies. According to Eq. (1), the values of the intercepts were used to determine the ionic conductivities, which were ca. 2 × 10−3 S cm−1 for both electrolytes. The high conductivity of GE, which was similar to that of the liquid-phase LE, demonstrated the important role of the P(EO-co-PO) matrices in dissociating LiClO4 as well as facil-

Fig. 1. Nyquist impedance plots for the gel electrolyte (GE) and the liquidphase 1 M LiClO4 /PC (LE) attached to stainless-steel electrodes with frequency ranging from 0.1 Hz to 100 kHz at an applied potential of 0 V.

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itating ion motion in the gel electrolyte. The Li+ ions within the polymer network could be solvated by the ether–oxygen and amine–nitrogen atoms of P(EO-co-PO) due to their high donicity while the dissociated ClO4 − ions would form hydrogen bonding with the hydroxyl groups [19,34]. Watanabe’s group also utilized ether–oxygen atoms of methoxy-oligo(ethylene oxide) group to improve the degree of self-dissociation of lithium salts for preparation of lithium ionic liquids [38], which were incorporated with a poly (ethylene oxide-co-propylene oxide) tri-acrylate macromonomer to form their ion gels. On the other hand, the addition of PC in the present work was to reduce the complexation degree of Li+ with the oxygen and nitrogen atoms and thus to increase the segmental mobility of the polymer. Also, the PC plasticizer might have formed a local solvent channel for ion motion in the gel electrolyte [33,35]. We also subjected the above cells to stability analysis. The stable potential window determines the maximum operational potential that manages total charge or energy stored for EDLCs [2]. Fig. 2 shows the cyclic voltammograms of these cells measured at a scan rate of 5 mV s−1 . A rise in the current would correspond to the chemical transformation of the electrolytes. The voltammograms reflect that both GE and LE were stable at potentials between −2.5 and 2.5 V, by showing the absence of the faradaic current due to electrolyte transformation. To assure a stable operation for EDLCs, a potential window ranging between −2.0 and 2.0 V was used for measurements thereafter. The potential-scan cyclic voltammograms of an EDLC equipped with the gel electrolyte (GE-EDLC) are shown in Fig. 3. Because a high power density is generally required for a capacitor, the potential-scan rate employed was set to reach a value as high as at 50 mV s−1 . The low scan-rate (5 mV s−1 ) voltammogram exhibited a pair of horizontal plateaus (as for a rectangle), indicating a minor impact of the resistance for ion difFig. 3. Cyclic voltammograms of GE-EDLC and LE-EDLC measured at different potential-scan rates.

Fig. 2. Cyclic voltammograms for the gel electrolyte (GE) and the liquid-phase 1 M LiClO4 /PC (LE) attached to stainless-steel electrodes with a potential-scan rate of 5 mV s−1 .

fusion at this slow double-layer formation situation. As the scan rate increased, there was a widening of the knee of the voltammogram just after the reversal of the scan direction. This could be attributed to the gradual intrusion of the ohmic resistance for ion motion in the pores, or even in the bulk phase [39,40]. The presence of the ohmic resistance resulted in a potential gradient, and thus a capacitance decrease of electrodes at a high charge-storage rate [41,42]. The voltammograms of an EDLC equipped with the liquid electrolyte (1 M LiClO4 /PC), i.e. LE-EDLC, are also shown in Fig. 3 to compare with those of GE-EDLC. The influence of the ohmic resistance on ion motion, reflected as the distortion from a rectangular shape, was also exhibited in the voltammograms for this liquid-phase system. The potential-against-time curves of GE-EDLC and LEEDLC charged and discharged at 0.5 mA are depicted in Fig. 4, showing a standard capacitive behavior for both the capacitors. The times required for charge or discharge for the two capacitors were nearly identical at this low current density. This reflects similar ultimate charge-storage capacities. The specific capaci-

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Fig. 4. Typical potential-against-time curves of GE-EDLC (solid line) and LEEDLC (dash line) charged and discharged at 0.5 mA.

tance (C) of the electrodes discharged at different currents was calculated according to C=

2It WE

(2)

where I is the discharge current, t the discharge time, W the mass of an electrode (carbon cloth), and E the potential difference in discharge, excluding the portion of IR drop. The factor of 2 comes from the total capacitance measured from the test cells being the addition of two equivalent single-electrode capacitors in series. Single-electrode capacitance was reported in the present work. Fig. 5a shows the trend of capacitance decrease with the discharge current. The capacitance values are similar at low currents (e.g., 86 and 82 F g−1 for GE- and LE-EDLCs respectively at 0.5 mA), as expected from Fig. 4. However, GE-EDLC exhibited a larger capacitance at high currents (e.g., 59 and 46 F g−1 for GE- and LE-EDLCs respectively at 50 mA). The degree of capacitance decrease with discharge current is one of the most important issues concerned for EDLCs. Fig. 5b shows the variation of the relative capacitance (compared to the ultimate value obtained at 0.5 mA) with the discharge current. It is obvious that the capacitance decrease with current for GE-EDLC was less dramatic than for LE-EDLC. This capacitance decrease should be governed by the resistance associated with the transport of electrolytic ions, or even electrons, in the cells [43]. To explore this aspect, we calculated first the overall resistance (Rt ) of the cells on the basis of the IR drop, a sudden potential drop at the very beginning of the galvanostatic discharge. Fig. 6 shows the variation of the IR drop with the discharge current for the two capacitors. The IR drop was found to increase linearly with the current. The slope of this linear relationship corresponds to the values of Rt , which were obtained and are shown in Table 1. GE-EDLC exhibited a smaller Rt than LE-EDLC, i.e. 26  vs. 32 .

Fig. 5. Variation of the specific capacitance (a) and relative capacitance (b) with discharge current for GE-EDLC and LE-EDLC. The carbon cloth used for each electrode had an area of 1 cm2 . The relative capacitance was obtained by dividing the specific capacitance with the value obtained at 0.5 mA. The capacitors have been charged at 0.5 mA to 2 V prior to discharge.

Further analysis on the resistance components regarding the double layer formation was required, in order to understand how the ion transport in GE-EDLC was affected by the presence of polymer chains. In principle, the overall resistance of an EDLC is composed of the electrical-contact resistance of the electrode (Rc ), the resistance of ion migration in the bulk solution (Rs ), and the resistance of ion migration in the carbon micropores (Rp ) Table 1 The overall resistance (Rt ), bulk solution resistance (Rs ), electrode electricalcontact resistance (Rc ), and resistance of ion migration in carbon micropores (Rp ) of EDLCs equipped with different electrolytes Resistance ()

GE-EDLC LE-EDLC

Rt

Rs

Rc

Rp

26 32

7.1 12

10 10

9.2 9.6

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Fig. 6. Variation of IR drop with discharge current for GE-EDLC and LE-EDLC charged at 0.5 mA to 2 V. The carbon cloth used for each electrode had an area of 1 cm2 .

[14,43]. To evaluate these resistance components, we subjected the capacitors to analysis with a.c. impedance spectroscopy. The impedance spectra of the capacitors are shown as Nyquist plots in Fig. 7. In the high-frequency region of each spectrum there appears a single semicircle, which has been well recognized to characterize the contact situation between the electrolyte and carbon electrode [14,43]. The locus of the semicircle intercepts the Re(Z) axis at Rs and Rs + Rc in the Nyquist plot. The values of Rs and Rc of GE-EDLC and LE-EDLC were thus

Fig. 7. Nyquist impedance plots for GE-EDLC and LE-EDLC with frequency ranging from 2 mHz to 100 kHz at an applied potential of 0 V. The equivalent circuit for the impedance data is shown in the inset, in which Cc is the capacitance due to the contact interface, Cd the capacitance inside pores and w a Warburg diffusion element.

obtained from the impedance spectra. Following the semicircle with decreasing frequency, the plots transform to a vertical line with the presence of a transition zone. The transition reflected a significant resistance for ion motion [1,2], particularly in the carbon micropores. An equivalent circuit for the capacitor cells is shown in the inset of Fig. 7. A Warburg diffusion element is incorporated in the circuit to emphasize the resistance for ion diffusion in the micropores. Here, we gave the apparent value of the pore resistance (Rp ) by subtracting Rs and Rc from the overall resistance (Rt ) determined from the IR drop. All the values of the different resistance components for the cells are summarized in Table 1. Because the same carbon electrodes were used, the values of Rc and Rp were seen to be similar for the two different capacitors (Table 1). The difference in the overall resistance was primarily contributed by that in Rs . The smaller Rs for GE-EDLC reflects an intimate contact of the gel network with carbon cloth to facilitate the transport of ions and solvent molecules toward the pore entrance. This intimate contact ensured the supply of ions and solvent molecules into the space-confined micropores. The introduction of the PPO and bisphenol-A segments, which was designed to increase the flexibility and amorphous phase of the polymer chains, should principally account for the intimate contact of the electrolyte/electrode interface. We could use the concept of a boundary layer to explain the mechanism of Li+ ions migration in electrolyte/electrode interface for LE- and GE-EDLCs. A boundary layer is defined as that part of a moving fluid in which the fluid motion is influenced by the presence of a solid boundary [44]. In LE- and GE-EDLC, fluid electrolyte migration is influenced by solid carbon cloth electrodes and forms a boundary layer on the electrolyte/electrode interface. The side chains of P(EO-co-PO) in amorphous phase could stretch across the boundary layer to come into contact with the electrode surface in GE-EDLC. The Li+ ions for GE-EDLC in the boundary layer migrate to electrode surface not only by diffusion (with concentration gradient as the driving force) but also by the segmental mobility in P(EO-co-PO). By this mechanism, the ionic conductivity of Li+ ions in GE-EDLC could be enhanced. The side chains may as well have helped the ions polarization on the electrode to promote the specific capacitance. This can probably explain the slightly higher specific capacitance for GE-EDLC at the lowest discharge rate than for LE-EDLC. A previous study also reported that activated carbon fiber showed higher double layer capacitance in a polymeric gel than in a liquid solution [32]. The leakage currents of GE-EDLC and LE-EDLC charged at 1 mA were measured at 2 V floating as shown in Fig. 8. The current decreased with time from 1 mA to a stabilized current. These two capacitors had similar stabilized leakage currents of ca. 1.4 × 10−2 mA. The leakage current could be ascribed mainly to an electronic current that resulted from irreversible decomposition of the mobile LiClO4 /PC. It was reported that the polymer chains in the solvent-free P(EO-co-PO) matrices could be polarized in an electrical field [35]. The similarity in the leakage current for these two capacitors reflects the stability of the immobile polymer network during polarization.

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Fig. 8. Variation of leakage current with time for GE-EDLC and LE-EDLC charged at 1 mA to a floating potential of 2 V. The carbon cloth used for each electrode had an area of 1 cm2 .

4. Conclusions PEO crosslinked with PPO diamines was shown to serve as an effective polymer network for a gel electrolyte used in EDLCs. When entrapping an appropriate amount of LiClO4 /PC, this polymer network facilitated efficient transport of the electrolytic ions and solvent molecules in the bulk phase of the gel electrolyte. The strong ion-solvating tendency of the polymer network was partially responsible for the high conductivity of this gel electrolyte. The flexible feature, through the introduction of PPO and bisphenol-A, not only improved the segmental motion for ion transport but also gave an intimate electrolyte/electrode contact to sustain a sufficient ion flux between the electrolyte phase and the space-confined micropores. The overall resistance of an EDLC equipped with the gel electrolyte was low because of the efficient ion transport and the intimate contact at the electrolyte/electrode interface. By using the developed gel electrolyte the relative capacitance of an EDLC was maintained above 60% with the current density increased from 0.5 mA cm−2 to 50 mA cm−2 , whereas this value was lower than 60% for an EDLC equipped with a liquid-phase LiClO4 /PC electrolyte. Acknowledgment This research was supported by the National Science Council of Taiwan (Project NSC 96-2120-M-006-006). References [1] B.E. Conway, Electrochemical Supercapacitors, Kluwer–Plenum, New York, 1999. [2] R. K¨otz, M. Carlen, Electrochim. Acta 45 (2000) 2483.

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[3] Y. Kibi, T. Saito, M. Kurata, J. Tabuchi, A. Ochi, J. Power Sources 60 (1996) 219. [4] L. Bonnefoi, P. Simon, J.F. Fauvarque, C. Sarrazin, J.F. Sarrau, A. Dugast, J. Power Sources 80 (1999) 149. [5] D. Qu, H. Shi, J. Power Sources 74 (1998) 99. [6] K. Kinoshita, Carbon: Electrochemical and Physicochemical Properties, John Wiley & Sons, New York, 1988. [7] I. Tanahashi, A. Yoshida, A. Nishino, J. Electrochem. Soc. 137 (1990) 3052. [8] H. Shi, Electrochimica. Acta 41 (1996) 1633. [9] A. Yoshida, S. Nonaka, I. Aoki, A. Nishino, J. Power Sources 60 (1996) 213. [10] M. Ishikawa, A. Sakamoto, M. Morita, Y. Matsuda, K. Ishida, J. Power Sources 60 (1996) 233. [11] M. Endo, T. Maeda, T. Takeda, Y.J. Kim, K. Koshiba, H. Hara, M.S. Dresselhaus, J. Electrochem. Soc. 148 (2001) A910. [12] E. Frackowiak, F. B´eguin, Carbon 39 (2001) 937. [13] D. Lozano-Castell´o, D. Cazorla-Amor´os, A. Linares-Solano, S. Shiraishi, H. Kurihara, A. Oya, Carbon 41 (2003) 1765. [14] Y.R. Nian, H.S. Teng, J. Electroanal. Chem. 540 (2003) 119. [15] C.S. Li, D.Z. Wang, X.F. Wang, J. Liang, Carbon 43 (2005) 1557. [16] K. Okajima, K. Ohta, M. Sudoh, Electrochim Acta 50 (2005) 2227. [17] T. Morimoto, K. Hiratsuka, Y. Sanada, K. Kurihara, J. Power Sources 60 (1996) 239. [18] M. Ishikawa, M. Morita, M. Ihara, Y. Matsuda, J. Electrochem. Soc. 141 (1994) 1730. [19] M.M. Armand, in: J.R. MacCallum, C.A. Vincent (Eds.), Polymer Electrolyte Reviews, vol. 1, Elsevier, London, 1987 (Chapter 1). [20] M. Ishikawa, M. Ihara, M. Morita, Y. Matsuda, Electrochim. Acta 40 (1995) 2217. [21] X. Liu, T. Osaka, J. Electrochem. Soc. 143 (1996) 3982. [22] X. Liu, T. Osaka, J. Electrochem. Soc. 144 (1997) 3066. [23] Y. Matsuda, K. Inoue, H. Takeuchi, Y. Okuhama, Solid State Ionics 113–115 (1998) 103. [24] T. Osaka, X. Liu, M. Nojima, J. Power Sources 74 (1998) 122. [25] T. Osaka, X. Liu, M. Nojima, T. Momma, J. Electrochem. Soc. 146 (1999) 1724. [26] H.B. Gu, J.U. Kim, H.W. Song, G.C. Park, B.K. Park, Electrochim. Acta 45 (2000) 1533. [27] R.J. Latham, S.E. Rowlands, W.S. Schlindwein, Solid State Ionics 147 (2002) 243. [28] J.L. Qiao, N. Yoshimoto, M. Morita, J. Power Sources 105 (2002) 45. [29] J.L. Qiao, N. Yoshimoto, M. Ishikawa, M. Morita, Solid State Ionics 156 (2003) 415. [30] M. Morita, J.L. Qiao, N. Yoshimoto, M. Ishikawa, Electrochim. Acta 50 (2004) 837. [31] C.M. Yang, W.I. Cho, J.K. Lee, H.W. Rhee, B.W. Cho, Electrochem. SolidState Lett. 8 (2005) A91. [32] M. Morita, T. Kaigaishi, N. Yoshimoto, M. Egashira, T. Aida, Electrochem. Solid-State Lett. 9 (2006) A386. [33] Y. Kang, K. Cheong, K.A. Noh, C. Lee, D.Y. Seung, J. Power Sources 119–121 (2003) 432. [34] P.L. Kuo, W.J. Liang, T.Y. Chen, Polymer 44 (2003) 2957. [35] W.J. Liang, T.Y. Chen, P.L. Kuo, J. Appl. Polymer Sci. 92 (2004) 1264. [36] M. Ue, J. Electrochem. Soc. 141 (1994) 3336. [37] D. Aurbach, I. Weissman, in: D. Aurbach (Ed.), Nonaqueous Electrochemistry, Marcel Dekker, New York, 1999 (Chapter 1). [38] H. Shobukawa, H. Tokuda, Md.A.B.H. Susan, M. Watanabe, Electrochim. Acta 50 (2005) 3872. [39] R. de Levie, Electrochim. Acta 8 (1963) 751. [40] L.G. Austin, G.E. Gagnon, J. Electrochem. Soc. 120 (1973) 251. [41] C.T. Hsieh, H.S. Teng, Carbon 40 (2002) 667. [42] Y.R. Nian, H.S. Teng, J. Electrochem. Soc. 149 (2002) A1008. [43] K.P. Wang, H.S. Teng, Carbon 44 (2006) 3218. [44] W.L. McCabe, J.C. Simith, P. Harriott, Unit Operations of Chemical Engineering, 5th ed., McGraw-Hill, New York, 1993 (Chapter 3).