Electrical conductivity relaxation in PVOH–LiClO4–Al2O3

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Electrochimica Acta 53 (2007) 1422–1426

Electrical conductivity relaxation in PVOH–LiClO4–Al2O3 W.A. Castro a,∗ , V.H. Zapata a , R.A. Vargas a , B.-E. Mellander b a

b

Departamento de F´ısica, Universidad del Valle, A.A. 25360, Cali, Colombia Physics and Engineering Physics, Chalmers University of Technology, 41296 G¨oteborg, Sweden Received 13 December 2006; received in revised form 27 May 2007; accepted 29 May 2007 Available online 5 June 2007

Abstract We report on electrical conductivity relaxation measurements of solid polymer electrolytes (SPE) based on poly(vinyl alcohol) (PVOH) ˚ were dispersed. A power law frequency dependence and LiClO4 in which nanoporous Al2 O3 particles with average pore diameter of 58 A of the real part of the electrical conductivity is observed as a function of temperature and composition. This behaviour is typical of systems in which correlated ionic motions in the SPE bulk material are responsible for ionic conductivity. This variation is well fitted to a Jonscher expression σ  (ω) = σ 0 [1 + (ω/ω0 )p ] where σ 0 is the dc conductivity, ω0 the characteristic angular frequency relaxation and p is the fractional exponent between 0 and 1. For a prototype membrane with composition 0.9PVOH − 0.1LiClO4 + 7 wt.%Al2 O3 , it was found that the temperature dependence of σ 0 and ω0 , may be described by the VTF relationship, φ = φ0 exp[−B/(T − T0 )], with approximately the same constant B and reference temperature T0 , indicating that ion mobility is coupled to the motions of the polymer chains. Moreover, p decreased with increasing temperature, from 0.68 at T = 319 K, to 0.4 at T = 437 K, indicating weaker correlation effects among mobile ions when the temperature is increased. © 2007 Elsevier Ltd. All rights reserved. Keywords: Electrical relaxation; Poly(vinyl alcohol); Composite; Ionic conductivity

1. Introduction Much current research in solid sate ionics deals with polymer electrolytes because of their technological importance as thin films in electronic, biomedical and energy-storage devices. A distinguish feature of solvent-free polymer membranes, typically based on amorphous forms of poly(ethylene oxide) (PEO), is that the ion transport includes besides ion motion, local motion of polymer segments and inter- and intrapolymer transitions between coordinating sites formed by the adjacent polyether oxygens [1]. Within such systems lithium salts LiX (e.g. LiBF4 , LiClO4 , Li(CF3SO2 )2 N) have shown better performance concerning ionic conductivity at least at high temperature. The addition of inorganic fillers (e.g., Al2 O3 nanoparticles) to lithium polymer electrolytes to improve both mechanical and electrical properties has raised great interest [2–6]. It has been reported [3] that decrease of the filler size from micron-

∗

Corresponding author. Tel.: +57 2 3394610; fax: +57 2 3393237. E-mail address: [email protected] (W.A. Castro).

0013-4686/$ – see front matter © 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.electacta.2007.05.066

scale to nanometer-scale yields a significant increase of the surface-to-volume ratio and enhanced conductivity. Mechanism of such conductivity enhancement has also been studied by using impedance spectroscopy and NMR measurements [4–6]. However, the details of the mechanisms have still been unclear. In the present work, poly(vinyl alcohol) (PVOH) was selected as a polymer matrix in view of its film-forming capacities, hydrophilic properties and possible coupling of charge transport with the motions of its hydroxyl group [7,8]. Several papers [9,10] reported anhydrous conductivity in the range of 10−8 to 10−4 S/cm for the lithium salts complexed with PVOH. This contribution therefore focus on ionic conduction behaviour of the PVOH–LiClO4 polymer electrolyte system in which nanoporous Al2 O3 particles were dispersed with the objective of looking at their influence on the dynamics of the mobile ions. We used the impedance spectroscopy technique to study the ac electrical response of the studied SPE system in order to study the correlations of structure–conductivity mechanism [11–15]. As demonstrated previously [14–16], the complete characterization of the ac electrical response may be achieved by a detailed

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study of the real part of the conductivity, including the determination of the exact bulk dc conductivity without any use of equivalent circuit analysis. 2. Experimental method We used 97% hydrolyzed PVOH (Aldrich), average MW 50,000–85,000 and LiClO4 (Aldrich), which were previously dried under vacuum at 373 K for 5 h. The appropriate quantity of PVOH was poured in deionised water at 353 K. The mixture was put on a stirrer and heated continuously up to 353 K. After 30 min at this temperature, the heater was turned off and a suitable volume of concentrated LiClO4 aqueous solution was poured in the highly viscous PVOH-aqueous solution and stirred for 5 h. Afterwards the mixture was poured into Teflon vessels, under a dry atmosphere, for evaporation of solvent and film membrane formation. We prepare nine concentrations with the weight ratio (x) of LiClO4 to PVOH (0.02 ≤ x ≤ 0.3). We obtained smooth, semitransparent to the visible light, dry to the touch and thin (between 0.05 and 0.20 mm thickness) membranes with good mechanical properties. Preparation of the composite solid polymer electrolytes (SPE) based on PVOH, LiClO4 and Al2 O3 was carried out by adding nanoporous Al2 O3 particles with average pore diame˚ to the PVOH–LiClO4 viscous solutions prepared ter of 58 A as described above and stirring continued for 5 h. The added amount was determined from the desired ratio of the inorganic fillers to PVOH–LiClO4 and varied in the range of 2–10 wt.% alumina in SPE. The aspect of membranes with alumina showed a translucent white coloration and they were stronger mechanically. The electrical properties of the SPEs were determined by admittance measurements using a two-electrode configuration ss|sample|ss (ss: stainless steel, parallel-plate cell) and a home-built temperature and atmosphere controlled cell for measurements. The electrode–electrolyte contact surface (A) and the distance between electrodes (d) were measured using a micrometer. No corrections for thermal expansion of the cell were carried out. Ambient temperature measurements were performed with a HP 4192 A Impedance Analyzer. The admittance response of the membranes was collected by sweeping the frequencies from 5 Hz to 13 MHz with a 100 mV signal. The temperature was measured using a type-K thermocouple placed as close as possible to the cell. As the water content of the membranes is an important parameter, the electrical measurements were done in a shielded cell under a controlled N2 atmosphere, after treating the sample at 383 K in vacuum for 2 h. The weight loss from apparent water content in thermally treated samples did not exceed 0.8 wt.%, as shown by thermogravimetric analysis (TGA) performed with a TA Instruments 2050 microbalance. From the admittance data, Y(ω) = Z(ω)−1 = Gp (ω) + iωCp (ω) √ (where ω = 2πν/Hz is the angular frequency, i = −1 Gp and Cp , the parallel conductance and capacitance, respectively), the real part of the electrical conductivity, σ  (ω) = (d/A)Gp (ω), was obtained. It is important to stress that σ = (d/A)Y(ω) = σ  (ω) + iσ  (ω) is the preferred quantity to represent the behavior of conducting materials [11–16].

Fig. 1. Frequency dependence of the real part of the conductivity, σ  (ω) vs. log ν(Hz), at several temperatures (from 369 to 349 K) from top to bottom for an alumina doping membrane with composition 0.9PVOH–0.1LiClO4 + 7 wt.%Al2 O3 . The continuous lines are present calculation using Eq. (1) from 5 Hz to 200 kHz.

3. Results and discussion Fig. 1 is a typical plot of isotherms of the real part of the conductivity,σ  versus log ν (Hz) for a representative polymer membrane (LiClO4 in PVOH, x = 0.1, with Al2 O3 content y = 0.07) of the studied composites. At frequencies higher than 5 Hz, σ  shows a medium-frequency plateau which corresponds to the bulk dc conductivity of the SPE material, σ 0 (T) [14–16]. As temperature T is increased the values σ 0 (T) increase. For a fixed temperature, σ  (T) increases with increasing frequency after a characteristic crossover frequency, ν0 , whose values were determined from the data analysis as discussed below, see Fig. 3. These profiles are in accordance with previous studies on other SPEs [13–15] in which an additional low frequency dispersive region is usually observed that is attributed to the electrode–sample interface polarization. It is important to point out that, because of the operational frequency of our instrumentation (from 5 Hz to 13 MHz), it was selected those frequency and temperature ranges and polymer–salt compositions in which both long range transport conductivity (non-dispersive behavior, σ 0 ) and mobile ion relaxation σ  (ω) ∼ ωp are present. The conductivity σ  caused by ionic displacements (hops) are higher at high frequencies than at low ones, because more ionic hops are seen per unit time when the experimental time window, ν−1 , is short than when it is long. Thus, σ  is found to be frequency independent in the low frequency region (ν < ν0 ) because the ion diffusion is more correlated, i.e., the ions perform correlated forward–backward motions [11–13]. This relaxation process is fast at high temperatures, but slow at low temperatures. As a consequence, the crossover frequency, ν0 , at which the conductivity attains is dc plateau is found to decrease with decreasing temperature, see Fig. 1. Conductivity spectra of ion-conducting materials, taken at a fixed temperature, are often found to increase at high frequencies according to a power law, σ  (ω) ∼ ωp , where p is a fractional exponent between 0 and 1. The parameter p has been proposed to be close to 1 for strongly correlated ion motion and equals to

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0 for completely random and independent Debye-like ion hops [11,14]. It is usual to express σ  (ω) as the empirical relation [14]:   p  ω σ  (ω) = σ0 1 + (1) ω0 where σ 0 is the dc conductivity and ω0 /2π is the characteristic crossover angular frequency, ν0 . The experimental data (symbols in Fig. 1), were fitted using the Eq. (1) as showed by solid lines in Fig. 1. The bulk dc conductivity data (σ  (0) = σ 0 ) at different temperatures were obtained from the fitting of the corresponding isothermal curve, σ  (ω), to Eq. (1), without any use of equivalent circuit analysis, as discussed in references [11–16]. The results of the nonlinear least-squares fit for the dc conductivity, σ 0, are plotted in Fig. 2 as log σ 0 versus 1000/T. In Fig. 2, it is also plotted the results for a polymer membrane with the same salt concentration (LiClO4 in PVOH, x = 0.1) without Al2 O3 . Both plots showed slightly positive deviation from a linear Arrhenius relation. The addition of Al2 O3 enhanced the dc conductivity but did not change its temperature dependence profile. This suggests that the Al2 O3 addition influences the carrier concentration of the polymeric electrolyte system but does not change the intrinsic mechanism for the ionic conduction. The conductivity data in Fig. 2 were better fitted to the Vogel–Tamman–Fulcher [17] (VTF) model, σ 0 = A exp[−Bσ /(T − T0 )], with approximately the same fitting parameters Bσ = 0.27 ± 0.03 eV and T0 = 208 K. The solid line shows the VTF fitted curve obtained by means of nonlinear least-squares methods. The dependence of the crossover frequency (ν0 ) on temperature, as calculated from the nonlinear least-squares fit of Eq. (1) to the conductivity, is plotted in Fig. 3 as log ν0 versus 1000/T. The solid curve in Fig. 3 shows the result of fitting the VTF model, ν0 = A exp[−B/(T − T0 )], to the ν0 data. B and T0 are found to be 0.25 ± 0.03 eV and 200 K, respectively, and they are comparable to those values of the dc conductivity, Bσ and T0 ,

Fig. 2. Temperature dependence of the conductivity parameter, σ 0 , obtained by fitting Eq. (1) to σ  data for (a) membrane with composition 0.9PVOH–0.1LiClO4 + 7 wt.%Al2 O3 , (b) membrane with composition 0.9PVOH–0.1LiClO4 without alumina solid lines show VTF fitted curves.

Fig. 3. Temperature dependence of the crossover frequency parameter, ν0 , obtained by fitting Eq. (1) to ␴ data for the membrane with composition 0.9PVOH–0.1LiClO4 +7 wt.%Al2 O3 , solid lines show VTF fitted curves.

thus indicating that σ 0 and ν0 are correlated with chain mobility. In other words, these observations confirm that a charge transfer mechanism based on ion migration mediated by the segmental motion of polymer host is also responsible for ionic conductivity in PVOH/LiClO4 polymer electrolytes. Further information regarding the conductivity mechanisms in the investigated system is provided by analysing the temperature dependence of the parameter p obtained from the fit of Eq. (1) to the conductivity data (σ  ). The values of p decreased with increasing temperature, from 0.68 at T = 319 K, to 0.4 at T = 437 K, indicating weaker correlation effects among lithium atoms when the temperature is increased. Indeed, as pointed out previously [14], these indications (VTF behaviour of σ 0 and p < 1) suggest that ion hopping with consequent site relaxation contributes significantly to the overall conductivity of the investigated SPE materials and that this contribution is mainly regulated by the segmental motion of the host chains. To detect possible ion association interactions in the PVOH/LiClO4 blends, the dc conductivity, σ 0 , was analyzed with respect to the LiClO4 concentration, x. Three representative isothermal curves (at T = 378, 423 and 433 K) for the PVOH–LiClO4 system are shown in Fig. 4. At low salt concentrations, x ≤ 0.1, the conductivity increases with salt content, followed by a plateau at salt content ratios of x = 0.1, 0.15 and 0.2 and then increases at x = 0.25 more than one order of magnitude. The most concentrated sample, x = 0.3, shows a significant decrease in conductivity at the three isotherms. This behaviour in salt–polymer systems is usually explained by strong cation–anion interactions [1,14] given rise to formation of a variety of ionic and aggregate forms, both charged and uncharged and associated or unassociated with polymer chains, i.e., LiClO4 , the ion pair Li+ − CIO− 4 . The effect of the ceramic filler (Al2 O3 ) on the dc conductivity (σ 0 ) of the polymer blends with salt content x = 0.1 and 0.25 is shown in Fig. 5. σ 0 is plotted at 423 and 438 K as a function of the content of Al2 O3 . Maximum effects on the conductivity enhancement were obtained for the composites

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Al2 O3 ) for x = 0.25. Since the temperature dependence of the dc conductivity of the SPE containing Al2 O3 was almost the same as that observed for the SPE without Al2 O3 (both samples showing identical VTF behaviour, see Fig. 2), then the interaction between the added Al2 O3 and the polymer matrix is probably weak. That is, any change in the bulk properties of the polymer matrix are not the cause of the dc conductivity enhancement by the ceramic addition observed for the present PVOH-based system. It may rather act as a dissociation promoter, that is, the Al2 O3 influences the carrier concentration of the SPE system but does not change its intrinsic mechanisms for the ionic conduction. 4. Conclusions Fig. 4. dc conductivity σ 0 vs. LiClO4 to PVOH weight ratio, x, at three representative isothermal curves (T = 378, 423 and 433 K, respectively) for the PVOH–LiClO4 system.

containing 5 wt.%Al2 O3 for both polymer–salt composition. At T = 438 K, σ 0 increased from 4.0 × 10−5 S/cm (without Al2 O3 ) to 2.1 × 10−4 S/cm (with Al2 O3 ) for x = 0.1, and from 5.9 × 10−4 S/cm (without Al2 O3 ) to 3.6 × 10−3 S/cm (with

We report complex ionic conductivity results of solvent-free polymer electrolytes consisting of poly(vinyl alcohol) (PVOH) and LiClO4 in which nanoporous Al2 O3 particles with average ˚ were dispersed. These PVOH-based SPE pore diameter of 58 A systems are found to displays similar characteristics of their complex conductivity spectra. The interpretation of the data was achieved by adopting the universal power law approach [11] in which correlated ionic motions in this SPE material are considered to have major influences on its electrical relaxation properties. In other words, the results indicate that both the long range transport conductivity and mobile ion relaxation process may be present in the same PVOH-based system. This report was also devoted to the study of the influences of the ion-polymer chain interactions present in the PVOH–LiClO4 –Al2 O3 polymer electrolyte system. The similar VTF behaviour observed on both the dc conductivity (σ 0 ) and the time related to the initial site relaxation time (1/ν0 ) indicate that those processes that contribute mostly to the overall conductivity of this system are mainly regulated by the segmental motions of the host chains [1]. Maximum effects on the dc conductivity enhancement were obtained for the composites containing 5 wt.%Al2 O3 without any change in its temperature dependence profile. This suggests that the Al2 O3 addition influences the carrier concentration of the polymeric electrolyte system but does not change the intrinsic mechanism for the ionic conduction. Furthermore, the use of PVOH chains allowed us to obtain SPE with the degree of chain flexibility, cation complexation and ionpair separation capabilities which are typical of other polymeric matrixes [1]. Acknowledgements The authors are grateful for the financial support the International Science Program of the Uppsala University, Sweden, and the Colombian Sciences Agency, COLCIENCIAS, have granted to this work. References

Fig. 5. dc conductivity of PVOH–LiClO4 membranes with different weight percents of Al2 O3 filler, at T = 423 and 438 K, for salt to polymer weight ratios of (a) x = 0.1 and (b) x = 0.25.

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