Solid polymer electrolytes based on polyethylene ...

Available online at www.sciencedirect.com

Solid State Ionics 179 (2008) 689 – 696 www.elsevier.com/locate/ssi

Solid polymer electrolytes based on polyethylene oxide and lithium trifluoro- methane sulfonate (PEO–LiCF3SO3): Ionic conductivity and dielectric relaxation N.K. Karan a , D.K. Pradhan a , R. Thomas a , B. Natesan b , R.S. Katiyar a,⁎ a

Department of Physics and Institute for Functional Nanomaterials, University of Puerto Rico, PO Box 23343, San Juan, PR-00931, USA b Department of Physics, National Institute of Technology, Trichy 620 015, India Received 21 August 2007; received in revised form 19 March 2008; accepted 29 April 2008

Abstract Polymer electrolytes consisting of polyethylene oxide (PEO) and LiCF3SO3 were synthesized by solution casting method as a function of EO/Li ratio. An increase in the glass transition temperature of the polymer electrolytes with increasing Li salt content suggested the coordination of the Li ions to the oxygen atoms of polymer backbone. Dielectric spectroscopic studies were performed to understand the ion transport process in polymer electrolytes. The dc conductivity showed a maximum for EO/Li ≈ 24. The ac conductivity analysis revealed the existence of nearly constant loss (NCL) contribution at lower temperatures. The dielectric loss spectra showed the presence of one relaxation for all compositions, which is associated with the motions of the Li ion coordinated polymer segments. The relaxation has been characterized by the empirical Havriliak–Negami (H–N) equation. The temperature dependence of the relaxation times and the conductivity followed the Vogel–Tamman–Fulcher (VTF) equation yielding qualitatively similar pseudoactivation energies, which suggested strong coupling between the ionic conductivity and the segmental relaxation in the polymer electrolytes. © 2008 Elsevier B.V. All rights reserved. Keywords: Polymer electrolytes; Ionic conductivity; Dielectric relaxations; VTF behavior

1. Introduction Polymer electrolytes represent a fascinating class of solid-state coordination compounds, which support ionic conductivity in a flexible, yet solid membrane. They consist of salts (e.g. LiClO4) dissolved in solid polymers (e.g. polyethylene oxide, PEO). The polymer must contain a Lewis base (usually an ether oxygen), which serves to coordinate the cations, thus promoting dissolution of the salt. Among all polymers, PEO has been studied most extensively so far because of its efficiency in coordinating metal ions, due to the optimal distance and orientation of the ether oxygen atoms in polymer chains [1]. In general, polymer electrolytes based on PEO are semicrystalline in nature except in a few particular salt concentrations (depending upon the salt) ⁎ Corresponding author. Tel.: +1 787 751 4210; fax: +1 787 764 2571. E-mail addresses: [email protected], [email protected] (R.S. Katiyar). 0167-2738/$ - see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.ssi.2008.04.034

where pure crystallinity has been reported [2]. Driven by their potential applications in devices, such as in rechargeable Li ion batteries, electrochromic displays, etc. there has been much interest in the development and understanding of the mechanism of the ion conduction in solid polymer electrolytes [3–5]. It is currently admitted that the ionic conductivity in polymer electrolytes takes place in the amorphous phase, where the ion conduction is mediated by local motion of the polymer chain segments above the glass transition temperature, Tg. For example, nuclear magnetic resonance (NMR) studies of ionic motion within the PEO: LiCF3SO3 systems, at compositions where the crystalline 3:1 complex and the amorphous phase coexisted above Tg, demonstrated that ion transport occurs in the amorphous phase [6]. However, in recent years it has been shown that ion conduction might occur in the crystalline phase of polymer electrolytes as well [2,7]. Solid polymer electrolytes differ from conventional glassy ion conductors in that the glass transition temperature (Tg) of the

690

N.K. Karan et al. / Solid State Ionics 179 (2008) 689–696

former is, in general, below room temperature whereas that of the conventional glasses is way above room temperature. Thus, polymer electrolytes are, in general, in rubbery state whereas the conventional glass conductors are in “glassy” state, at room temperature [8]. Hopping of the mobile ions between different fixed vacant sites in a frozen disordered structure gives rise to the conductivity in glassy ionic conductors. However, the situation is somewhat different than simple ion hopping in polymer electrolytes, as they are in rubbery state at room temperature and the hopping sites are not fixed in a dynamically evolving disordered structure. To incorporate this dynamically changing environment in the case of polymer electrolytes, several models, such as the dynamic bond percolation (DBP) [9], dynamically disordered hopping (DDH) [10,11] have been proposed to describe the ion transport processes characterized by two time constants: one describes the local carrier hopping and the other one characterizes the reorganization of the host. From the viewpoint of an individual hopper, this means that if the local environment at any given time does not permit a hop, that environment will evolve such that, after a certain average waiting time the hop will no longer be prohibited. In these so called polymer electrolytes, long range ionic diffusion leading to ionic conductivity only occurs in the presence of local segmental motions of the polymer host [1,3,4,9–12]. Thus, ionic conductivity in polymer electrolytes is very much coupled to the segmental motion of the host polymer—more is the segmental mobility, higher is the ionic conductivity. Since the promising candidates for the polymer electrolytes have polar atoms (for solvating cations) in their backbone, one way to investigate their segmental mobility is dielectric spectroscopy, which has been used previously to study the ion dynamics in the polymer electrolytes [13–15]. In this paper we have synthesized polymer electrolyte membranes based on PEO and LiCF3SO3 as a function of EO/Li ratio. Dielectric properties in these films were studied using broadband dielectric spectroscopy as a function of temperature. Dielectric relaxations of the polymer electrolytes have been characterized by the empirical Havriliak–Negami function and an attempt has been made to correlate the ionic conductivity to the segmental relaxation of the polymer electrolytes. 2. Experimental Solid polymer electrolyte membranes, comprised of polyethylene oxide (PEO, MW N 5 × 106) and lithium trifluoromethanesulfonate (LiCF3SO3), were prepared by solution casting method using acetonitrile as solvent inside a glove box (Mbraun Unilab 2000), which was under constant Ar flow (H2O b 0.1 ppm). Appropriate amounts of the polymer and the salt, corresponding to various EO/Li ratios were first dissolved into the solvent and stirred at room temperature for ~ 24 h. The resulting viscous slurry was then casted on a Teflon plate and dried at room temperature for ~ 24 h, to get free standing electrolyte membranes having thickness of ~ 100 μm. To remove the solvent completely from these membranes, they were further vacuum dried at ~ 55 °C for one more day. Xray diffraction (XRD) was carried out using (Siemens D5000)

CuKα radiation from 5–60° in the θ–2θ scan. Differential scanning calorimetry (DSC) measurements were done using Shimadzu DSC-50 with a low temperature measuring head and liquid nitrogen as coolant. Samples were crimped in aluminum pans inside the globe box under argon atmosphere and transferred to DSC cell for the measurements. Samples in aluminum pans were stabilized by slow cooling to –100 °C and then heated to 150 °C at a rate of 10 °C/min. The data were recorded during the heating scan. Al2O3 powder was used as a reference. The real (ε′) and imaginary (ε″) parts of complex dielectric permitivity (ε⁎) were measured with a Novocontrol GmbH Concept 40 broadband dielectric spectrometer. The membrane was sandwiched between two spring-loaded gold electrodes. The film was heated to 100 °C and then cooled to − 100 °C. Temperature control was accomplished with a Quatro Cryosystem with a stability of ± 0.1 °C. Dielectric data (ε′, ε″) were collected during cooling as a function of frequency from 10− 2 to 106 Hz using an oscillation level of 10 mV, at every 10 °C interval (after 15 min equilibration at each temperature). For conductivity data analysis, the complex conductivity, σ⁎ = σ′ + iσ″, was calculated from the complex permittivity using the following relations, rV ¼ e0 xeW; rW ¼ e0 xe V

ð1Þ

where ε0 is the permittivity of free space. The dc conductivity values were obtained by extrapolating the frequency dependent real part of the complex conductivity (σ′) to zero frequency. The errors involved in the obtained conductivity values were less than 3%. 3. Result and discussion 3.1. Composition dependence of Tg and XRD Glass transition temperature (Tg) is an important parameter for amorphous polymer electrolytes. Fig. 1a shows the variation of the glass transition temperature, as measured from DSC of the polymer salt complexes (PSC) as a function of the EO/Li ratio (DSC thermograms are shown in the inset). The Tg of PSCs increased from that of pure PEO with increasing EO/Li ratio up to EO/Li = 24. However, further increase in the salt content did not have much influence on the Tg. Though the increase of Tg with increasing amount of salt is common, there have been reports where Tg variation was not very smooth and even Tg decreased with increasing amount of salt content in the polymer electrolytes [16]. In the present case, the observation can be explained by assuming that the elevation of Tg with salt addition arises from the transient cross-linking between the Li ions and the O atoms in the polymer chains. So, in a way the elevation of Tg could be correlated to the number of the free Li ions — more is the number of the free Li ions, higher is the elevation of Tg for PSCs. Even though the samples with EO/Li b 24 contained more Li salt, the number of the free Li ions might not have increased. In effect, the ion-pairing for the samples with EO/Li b 24 kept the number of the free Li ions, which were responsible for the transient crosslinking to the polymer chains, more or less constant. Hence, for the compositions with EO/Li b 24, even though the salt content


691

Fig. 2. Temperature dependence plots of the conductivity of polymer electrolytes with various EO/Li ratios. The continuous lines show the fit of experimental data to the VTF equation, σ = σo T − 1/2 exp(−B / T − To). Inset shows the conductivity as a function of EO/Li ratio at different temperatures.

fitted to the Vogel–Tamman–Fulcher (VTF) equation [3,20] of the form: r ¼ r0 T 1=2 eEv =k ðT T0 Þ

Fig. 1. (a) Variation of the glass transition temperature (Tg), (b) XRD patterns of the polymer electrolytes with EO/Li ratios. Inset of (a) shows the DSC thermograms for various compositions.

increased, the Tg remained almost the same. Fig. 1b shows the XRD pattern of the electrolyte membranes with various EO/Li along with that of the pure polymer membrane. All of the diffraction peaks corresponding to the crystalline PEO were present in the XRD pattern of the electrolyte samples [17]. Moreover, there were no extra peaks in the XRD spectra of polymer salt complexes, which suggested that the electrolyte samples were semicrystalline in nature having PEO crystallites dispersed into the amorphous polymer salt complex matrix. 3.2. dc conductivity behavior The obtained conductivity (outlined in the Experimental section) variation of the PSCs as a function of temperature is shown in Fig. 2, where conductivity has been plotted as a function of 1000/T. It is clear from the plots that the temperature dependence of conductivity did not follow the Arrhenius behavior. The bend in the curve has been observed in ionically conducting polymers and has been explained invoking the concept of free volume [18,19]. To have better insight into the temperature dependence of σ, the conductivity data have been

ð2Þ

where σ0 is the prefactor, T is the absolute temperature, k is the Boltzmann constant, Ev is the pseudoactivation energy and T0 is the equilibrium glass transition temperature at which the “free” volume disappears or at which configuration free entropy becomes zero (i.e., molecular motions cease). The continuous lines in Fig. 2 show the results of the non-linear least square fitting of the conductivity data to Eq. (2) assuming a starting T0 value on the basis of the boundary condition (Tg-60 K) ≤T0 ≤ (Tg-40 K) as described in the literature [3,21–23].The best fitted parameters, σ0, Ev and T0 are listed in Table 1. Although free volume model was originally adopted for explaining viscoelastic properties of polymers, the reasonably good fit of σ to VTF equation over a wide range of temperature demonstrates the close coupling between the conductivity and the polymer chain segment mobility of the PSCs [24]. Inset of Fig. 2 shows the variation of conductivity at different temperatures as a function of EO/Li ratio. The conductivity increased gradually with increasing salt concentration and reached a maximum of ~1.3 × 10− 6 S/cm at room temperature for EO/Li ~ 24. Conductivity decreased with further addition of salt. In a qualitative way, the conductivity Table 1 The glass transition temperature (Tg) and the VTF fitted parameters from the temperature dependence of the conductivity and the dielectric relaxation times of the polymer electrolyte for various salt content EO/Li

Tg (K)

200 100 30 24 8

212.31 212.60 218.85 219.14 216.44

σ VTF fit

VTF fit

σ0

Ev (eV)

T0 (K)

τ0 (s)

Ev (eV)

T0 (K)

45 70 125 145 185

0.207 0.202 0.172 0.194 0.207

155.50 162.07 172.75 163.00 161.00

2.47 × 10− 10 5.00 × 10− 12 1.31 × 10− 11 3.26 × 10− 11 1.58×10−12

0.090 0.119 0.110 0.110 0.125

187 190 186 182 182

692


temperatures has been analyzed for all the samples. Fig. 3a shows the frequency dependence of the ac conductivity at various temperatures for EO/Li = 30. A general trend in the frequency dependence of the conductivity was observed at all temperatures for all samples. An almost frequency independent conductivity plateau at lower frequencies was followed by the conductivity dispersion region at the higher frequencies. A similar kind of frequency dispersion was observed for all other compositions as well. The general trend of conductivity as a function of frequency is very similar to the previous reports in the literature for ionically conducting ceramics, glasses, polymers [14,22–26]. The switchover from the frequency independent to frequency dependent region marks the onset of conductivity relaxation that gradually shifts to higher frequencies as temperature increases (Fig. 3a). The frequency independent conductivity is, in general, identified with the dc conductivity (σdc). To quantitatively describe the frequency dependence of the conductivity, σac has been fitted to the wellknown power law [27,28] rac ¼ rdc þ Af n

ð3Þ

where, σdc is the dc conductivity, A is constant (weakly temperature-dependent), f is the frequency and n is the power law exponent with 0 b n b 1. The conductivity data were fitted to the above equation (continuous lines) and are shown in Fig. 3(a) for EO/Li = 30 along with the experimental points. The conductivity showed a hump in the intermediate frequencies that moved to higher frequencies with increasing temperature due to inherent inhomogeneous nature of the samples [29]. The fitting was indeed reasonably good to the above equation for higher temperatures (region I, 313 K to 253 K). However, it should be mentioned here that the above two-term equation did not reproduce the experimental data at lower temperatures (below 253 K) satisfactorily. In this low temperature region the conductivity was best fitted by adding a third term, which was nearly linear in frequency, to the above two-term equation. Therefore, in the low temperature region (region II) the conductivity was fitted to the equation rac ¼ rdc þ Af n þ Bf

Fig. 3. (a) Frequency dependence of the conductivity at various temperatures for EO/Li = 30. The dotted and continuous lines are the fits of the experimental ac conductivity data to Eqs. (3) and (4), respectively. (b) Temperature dependence of the dielectric loss at different frequencies for EO/Li = 30. (c) Variation of the power law exponent, n with temperature for various EO/Li. Inset shows the variation of n as a function of EO/Li at different temperatures.

variation was similar to the variation of Tg with EO/Li, suggesting the decrease in the conductivity was due to the ion-pairing at higher salt concentrations. 3.3. ac conductivity behavior In order to understand the ion dynamics in the polymer electrolytes, the frequency dependence of the conductivity at various

ð4Þ

where, B is a constant. This nearly linear frequency dependent term in the conductivity leads to the frequency independent dielectric loss (ε″ = σ′/2πε0 f ). Generalized Universal Power Law (G-UPL) (Eq. (3)) has been very successful in explaining the frequency dependence of σ′ in disordered materials (ionically conducting glasses, conducting polymers etc) within the framework of the physical models [25,26] that has been proposed for explaining the conductivity mechanism in structurally disordered ionic conductors. However, Nowick et al. [30,31] have shown that the two-term equation (σ′ =σ0 +Af n) does not sufficiently reproduce the experimental results and there was a need to bring in a third term, which was almost independent of frequency. This procedure has been adopted widely in the literature and the existence of NCL is now well recognized for ionically conducting glasses, ceramics, etc [30–38]. A contribution from thermally activated ionic motion is seen in any


equivalent representation of the electrical data (σ⁎ or ε⁎ or M⁎). However, there is always present another contribution that is almost frequency independent in the ε⁎ representation and leads to the addition of the third term to the UPL function. At low temperatures the thermally activated contribution from ionic motion is moved to low frequencies outside the experimental window and the constant loss is the only contribution that remains [37]. Even though existence of “ubiquitous” NCL is now well accepted, its origin is still not completely understood and remains controversial. Jain et al. [36] proposed that the NCL arise from the motion of group of atoms in the asymmetric double well potential configurations. Recently, Ngai et al. [32,37] have pointed out that the NCL originates from the slowing down of ionic motions in the cages due to the ion–ion interactions and correlations in the short time regime. Similar studies in various glassy, ceramic and polymers with different compositions are needed in order to gain further insights about the origin of NCL phenomenon. Polymer electrolytes (with glass transition temperature well below room temperature) differ from conventional disordered systems in that their structures are not fixed (in the timescale of experiments), rather it is dynamic in nature, i.e. it evolves with time, which in no way should prohibit the manifestation of NCL behavior in the polymer electrolytes. The observation of NCL behavior in polymer electrolytes along with ion conducting glasses and ceramics points to the fact that the NCL is a universal phenomenon in the case of ionic conductors. As a support to the addition of a nearly linear frequency dependent term to the two-term equation (Eq. (4)) for describing the frequency dependence of conductivity at lower temperatures, the imaginary part of permittivity, ε″ for various frequencies has been plotted against temperature in Fig. 3b for EO/Li = 30. As can be seen from Fig. 3b, below ~ 243 K, ε″ becomes independent of frequency, which in turn supports the incorporation of the linear frequency dependent term in the above equation [34]. So, clearly there exists a cross over from NCL dominated ac conductivity at lower temperatures to ion hopping mediated ac conductivity at higher temperatures in polymer electrolytes. The combination of NCL and fractional power law describes well the dynamics of ions in the polymer electrolytes. The temperature dependence of the extracted power law exponent, n is shown in Fig. 3c for all PSCs. The n values lied in the range 0.7–0.4 over the temperature range studied. Values of n in this range are common for the polymer electrolytes reported in the literature [14,21,39]. At lower temperatures, n remains almost constant and it increases with increasing temperature for all PSCs. The inset of Fig. 3c shows the composition dependence of n at selected temperatures. At constant temperature, n decreases as salt concentration increases. This agrees well with the idea that n physically represents the strength of the ion–ion interactions and as the salt concentration increases the ion–ion interactions are expected to increase [40]. 3.4. Dielectric relaxation Fig. 4 shows the real (ε′) and imaginary (ε″) parts of permittivity as a function of frequency at 293 K for various

693

Fig. 4. Frequency dependence of ε′ and ε″ at 293 K for various EO/Li.

PSCs along with pure PEO. The real part of the permittivity, ε′ showed two relaxation processes for both pure PEO and PSCs (Fig. 4a). The appearance of these processes is more clearly seen in ε″ vs. frequency plot (Fig. 4b). The relaxation in the low frequency region is the electrode polarization phenomenon occurring as a result of an accumulation of ions near the electrodes. To further justify the point the imaginary part of the conductivity, σ″ has been plotted along with ε″ as a function of frequency at various temperatures in Fig. 5a. It has been reported that the peaking of σ″ spectra in the low frequency region manifests the electrode polarization [15]. In the present case, the low frequency relaxation is accompanied by the peaking of σ″ at the same frequency (marked by horizontal lines in Fig. 5a), which clearly suggests that the low frequency relaxation is indeed due to electrode polarization. The relaxation at the high frequency arises from the motion of the polymer chains. The addition of salt had a profound effect on the relaxation rate for this process and the relaxation could be, tentatively, attributed to the motions of the Li ion coordinated polymer chain segments [41]. In order to understand the dynamics of the relaxation process in polymer electrolytes, the experimental complex dielectric permittivity, ε⁎ (ω) data were fitted to the Havriliak–Negami function [42]: o Xn b e4ðxÞ ¼ e V jeW ¼ el þ ðel es Þ=½ð1 þ ixsÞa ð5Þ þ ðr=e0 xÞN where, the second term accounts for the conductivity, which affects the low frequency loss. The summation symbol in the first term is to indicate the occurrence of more than one relaxation process including the electrode polarization. The

694


tion and the high frequency relaxation did not follow the Arrhenius behavior. Similar type of temperature dependence of the relaxation time for the electrode polarization has been observed elsewhere for polymer electrolyte [15]. For quantitative comparison they have been fitted to the VTF function of the following form s ¼ s0 eEv =k ðT T0 Þ

ð6Þ

where, τ is relaxation time, τ0 is relaxation time pre-exponential factor, T is absolute temperature, Ev is pseudoactivation energy and T0 is the equilibrium glass transition temperature. The fitted parameters, τ0, Ev, T0 are listed in Table 1. The temperature dependences of the fitting parameters (α and β) are shown in Fig. 7 for the high frequency relaxation process. As can be seen from Fig. 7, the parameter α decreased with decreasing temperature, implying the broadening of the distribution of relaxation times as temperature decreases. The parameter β remained almost constant at 1 in the whole temperature range.

Fig. 5. (a) Frequency dependence of ε″ and σ″ at different temperatures of polymer electrolyte with EO/Li = 30. (b) HN fitting of the frequency dependence of ε″ at different temperatures of EO/Li = 30. The symbols are the experimental points and the continuous lines are fits to the H–N equation.

symbols ε∞ and εs are the limiting dielectric constants at infinitely high and low frequencies, respectively; ω is the angular frequency (ω = 2πf ); τ is the characteristic average relaxation time of the process; σ is the conductivity; εo is the vacuum permittivity and N is an exponent that characterizes the conduction process. N was found to lie in between 0.5 and 0.8 depending upon salt concentration and temperature. The exponents α and β (0 b α, β b 1) are the HN fitting parameters describing the distribution of the relaxation times. The dielectric relaxation strength, ε∞ − εs, is represented as Δε. The frequency dependence of the dielectric loss for EO/ Li = 30, at several temperatures along with the corresponding fits to Eq. (5), are shown in Fig. 5b, where the symbols represent the experimental data and the continuous lines are fitted values. The relaxations became increasingly slower with decreasing temperature. The temperature dependences of the relaxation time, for both the electrode polarization and the high frequency relaxation, obtained from the fitting are shown in Fig. 6, respectively. It is clearly seen from Fig. 6 that the temperature dependence of relaxation times for both the electrode polariza-

Fig. 6. Temperature dependence of the relaxation times: (a) the electrode polarization; (b) the dielectric relaxation of the polymer electrolytes. The continuous lines are the fits to the VTF equation.


695

the ionically conducting polymers can be expressed in terms of the mobility μ by the relationship r ¼ μnq

ð8Þ

where n and μ are, respectively, the number density and mobility of the charge carriers and q is the charge. So, a complete description of temperature dependence of conductivity should take temperature dependence of both the mobility and ion concentration into account. Since the mobility of free ions is expected to be controlled by the segmental motion of polymer matrix, it should have a VTF temperature dependence [13] μ ¼ μ0 exp ½E1 =k ðT T0 Þ

Fig. 7. Temperature dependence of the H–N fitted parameters α and β for the dielectric relaxation of the polymer electrolytes.

where, E1 is the activation energy for mobility, μ0 is the infinite temperature mobility. Moreover, the mobile ion concentration is assumed to follow an Arrhenius behavior [46], n ¼ n0 exp ½E2 =kT

3.5. Coupling between ionic conductivity and dielectric relaxation In polymer electrolytes the ion transport is assisted by segmental movement of the polymer chains and in the literature the relaxation mode responsible for ionic conduction has been correlated to α relaxation [10,43]. Several workers have noted correlation between the conductivity of PPO (polypropylene oxide) salt complexes and the characteristic frequency of the dielectric relaxation corresponding to the glass transition in pure host polymer [44,45]. The temperature-dependent response of both these quantities follows the empirical VTF equation: f ðT Þ ¼ AeðB=ðT T0 ÞÞ

ð7Þ

where, A, B and T0 are the fitting parameters and f(T) is either the characteristic frequency of the relaxation or the dc conductivity of the salt complexes. Typically, the fits to the VTF equation for the conductivity data of PSCs and the dielectric data on relaxation rate of the glass transition relaxation result in similar values for the parameter B [44,45]. Based on this similarity of B values obtained from two different aspects, it has been suggested that the relaxation corresponding to the glass transition is indeed very much coupled to the ion transport in polymer electrolytes. However, the preceding discussion focused on the relation between the relaxation processes in the pure polymer host and the conductivity of the corresponding PSCs. On the contrary, the knowledge of the relaxation rate in the PSCs would be of greater interest rather than that in pure host polymer, while correlating ionic conductivity to segmental motions. In the present case, it is seen from Table 1 that the VTF fitting parameter, B, is not comparable in a quantitative way for the conductivity measurements and for the dielectric relaxation of the polymer salt complexes. This apparent discrepancy of B value obtained from the conductivity fitting and the dielectric fitting can be accounted by considering the fact that the conductivity, σ in

ð9Þ

ð10Þ

where, E2 is the coulomb energy of cation anion pair and n0 is total ion concentration as T → ∞. So, the temperature dependence of conductivity can be expressed by combining Eqs. (9) and (10) as r ¼ μ0 n0 q exp ½E2 =kT E1 =k ðT T0 Þ

ð11Þ

Consequently, this equation does not predict a simple VTF behavior for the conductivity. Furthermore, it shows that the activation energy for the conductivity is not simply E2 but also includes an Arrhenius activation energy term E1. This might be the reason behind the apparent discrepancy between the activation energy values obtained from the temperature dependence of the conductivity fitting and the dielectric relaxation fitting. It should be pointed out here that the best fitted T0 values obtained from the dielectric relaxation fitting are approximately 20 K higher than those obtained by fitting the conductivity with a simple VTF relation (Table 1), which is in good agreement with the previous report [46]. Since the VTF dependence is characteristic for an amorphous material above the glass transition temperature, it shows that the flexibility of the polymer chains, characteristic for amorphous regions of semicrystalline polymer electrolytes, determines the ionic conductivity. This observation clearly demonstrates that the segmental motions of the polymer salt complex rather than that of the host polymer alone control the ion conduction significantly in polymer electrolytes. 4. Conclusions Polymer electrolytes consisting of polyethylene oxide (PEO) and LiCF3SO3 were synthesized by a solution casting method with different EO/Li ratio. The segmental relaxation process and its role in controlling ion transport in these solid polymer electrolytes have been investigated using dielectric spectroscopy and thermal analysis. DSC results revealed that up to EO/ Li = 24, Tg increases with increasing salt content implying the coordination of Li ions to the polymer backbone oxygens.

696


Beyond this concentration ion-pairing limits the number of free Li ions and the Tg remains almost constant. The temperature dependence of ac conductivity revealed the existence of nearly constant loss (NCL) contribution at low temperatures in polymer electrolytes and there is a crossover from NCL at low temperatures to ion hopping ac conductivity at higher temperatures. The observed dielectric relaxation in the loss (ε″) spectrum is attributed to the motion of the cation coordinated PEO chain. Compared to pure PEO, the strength and the location of the relaxation frequency showed a drastic change in the PSCs. The temperature dependence of H–N fitting parameters showed that the symmetric broadening of relaxation curves decreased with increasing temperature, whereas the asymmetric broadening and dielectric relaxation strength remained constant with temperature. The temperature dependence of conductivity and relaxation times associated with the relaxation of polymer electrolytes followed VTF behavior yielding qualitatively similar pseudoactivation energy values. These observations clearly shows that the ion transport is closely coupled to the ion coordinated segmental motions, which further suggests that the polymer segmental dynamics play a crucial role in controlling the ion transport processes in the polymer electrolytes. Acknowledgements The financial support from DOE grant (DE-FGO201ER45868) is gratefully acknowledged. One of us (N. K. Karan) is grateful to the NSF RII project for the graduate fellowship. References [1] F.M. Gray, Solid Polymer Electrolytes, VCH, New York, 1991. [2] Z. Gadjourova, Y.G. Andreev, D.P. Tunstall, P.G. Bruce, Nature 412 (2001) 520. [3] J.R. MacCallum, C.A. Vincent, Polymer Electrolyte Reviews 1, Elsevier, London, 1987. [4] J.R. MacCallum, C.A. Vincent, Polymer Electrolyte Reviews 2, Elsevier, London, 1989. [5] S.D. Druger, M.A. Ratner, A. Nitzan, Solid State Ion. 9/10 (1983) 1115. [6] C. Berthier, W. Gorecki, M. Minier, M.B. Armand, J.M. Chabango, P. Rigaud, Solid State Ion. 11 (1983) 91. [7] Z. Stoeva, I.M. Litas, E. Staunton, Y.G. Andreev, P.G. Bruce, J. Am. Chem. Soc. 125 (2003) 4619. [8] C.A. Angell, Solid State Ion. 18/19 (1986) 72. [9] S.D. Druger, A. Nitzan, M.A. Ratner, J. Chem. Phys. 79 (1983) 3133. [10] M.C. Lonergan, A. Nitzan, M.A. Ratner, D.F. Shriver, J. Chem. Phys. 103 (1995) 3253.

[11] A. Nitzan, M.A. Ratner, J. Phys. Chem. 98 (1994) 1765. [12] D.F. Shriver, Chem. Rev. 88 (1988) 109. [13] J.P. Runt, J.J. Fitzgerald (Eds.), Dielectric Spectroscopy of Polymeric Materials: Fundamentals and Applications, American Chemical Society, Washington, DC, 1997. [14] V. Di Noto, J. Phys. Chem. B 106 (2002) 11139. [15] T. Furukawa, M. Imura, H. Yuruzume, Jpn.J. Appl. Phys. 36 (1997) 1119. [16] J.S. Thokchom, C. Chen, K.M. Abraham, B. Kumar, Solid state Ion. 176 (2005) 1887. [17] C.P. Rhodes, R. Frech, Macromolecules 34 (2001) 2660. [18] M.H. Cohen, D. Turnball, J. Chem. Phys. 31 (1959) 1164. [19] G.S. Grest, M.H. Cohen, Phys. Rev. B 21 (1980) 4113. [20] H. Vogel, Z. Phys. 22 (1921) 645. [21] V. Di Noto, V. Zago, G. Pace, M. Fauri, J. Electrochem. Soc. 151 (2004) A224. [22] V. Di Noto, M. Vittadello, S. Lavina, M. Fauri, S. Biscazzo, J. Chem. Phys. B 105 (2001) 4584. [23] V. Di Noto, M.D. Longo, V. Munchow, J. Chem. Phys. B 103 (1999) 2636. [24] T. Miyamoto, K.J. Shibayama, K. J. Appl. Phys. 44 (1973) 5372. [25] B. Roling, C. Martiny, K. Funke, J. Non-Cryst. Sol. 249 (1999) 201. [26] B. Roling, J. Non-Cryst. Sol. 244 (1999) 34. [27] D.P. Almond, A.R. West, R.J. Grant, J. Solid State Commun. 44 (1982) 1277. [28] D.P. Almond, G.K. Duncan, A.R. West, Solid State Ion. 8 (1983) 159. [29] J.R. Dygas, B.M. Faraj, Z. Florjan'czyk, F. Krok, M. Marzantowicz, E.Z. Monikowska, Solid State Ion. 157 (2003) 249. [30] W.K. Lee, J.F. Liu, A.S. Nowick, Phys. Rev. Lett. 67 (1991) 1559. [31] A.S. Nowick, B.S. Lim, A.V. Vaysleyb, J. Non-Cryst. Solids 172–174 (1994) 1243. [32] C. Leon, A. Rivera, A. Varez, J. Sanz, J. Santamaria, K.L. Ngai, Phys. Rev. Lett. 86 (2001) 1279. [33] A. Rivera, J. Santamaria, C. Leon, J. Sanz, C.P.E. Varsamis, G.D. Chryssikos, K.L. Ngai, J. Non-Cryst. Solids 310 (2002) 1024. [34] A. Rivera, J. Santamaria, C. Leon, K.L. Ngai, J. Phys., Condens. Matter 15 (2003) S1633. [35] J.R. Macdonald, Phys. Rev. B 66 (2002) 064305. [36] H. Jain, X. Lu, J. Non-Cryst. Solids 196 (1996) 285. [37] K.L. Ngai, J. Chem. Phys. 110 (1999) 10576. [38] B. Natesan, N.K. Karan, R.S. Katiyar, Phys. Rev. E 74 (2006) 042801. [39] T. Winie, A.K. Arof, Ionics 12 (2006) 149. [40] A. Pan, A. Ghosh, Phys. Rev. B 62 (2000) 3190. [41] R. Bergman, A. Brodin, D. Engberg, Q. Lu, C.A. Angell, L.M. Torell, Electrochim. Acta 40 (1995) 2049. [42] S. Havriliak, S. Negami, Polymer 8 (1967) 161. [43] R.M. Fuoss, J. Am. Chem. Soc. 63 (1941) 369. [44] J.J. Fontanella, M.C. Wintersgill, M.K. Smith, J. Semancik, C.G. Andeen, J. App. Phys. 60 (1986) 2665. [45] A.L. Tipton, M.C. Lonergan, M.A. Ratner, D.F. Shriver, T.T.Y. Wong, K. Han, J. Phys. Chem. 98 (1994) 4148. [46] R.J. Klein, S. Zhang, S. Dou, B.H. Jones, R.H. Colby, J. Runt, J. Chem. Phys. 124 (2006) 144903.