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Polymer concentration dependence of the dynamics in gel electrolytes
Solid State Ionics 136–137 (2000) 1147–1152 www.elsevier.com / locate / ssi
Polymer concentration dependence of the dynamics in gel electrolytes b ¨ C. Svanberg a , *, J. Adebahr a , R. Bergman a , L. Borjesson , B. Scrosati c , P. Jacobsson a a
¨ , Sweden Department of Experimental Physics, Chalmers University of Technology, SE-412 96 Goteborg b ¨ , Sweden Department of Applied Physics, Chalmers University of Technology, SE-412 96 Goteborg c Department of Chemistry, University of Rome ‘ La Sapienza’, I-00185 Rome, Italy
Abstract A polymer gel electrolyte sample with a gradually varying concentration of polymer have been examined by Raman and photon correlation spectroscopy. The gel consisted of poly(methyl methacrylate) complexed with a liquid electrolyte of lithium perchlorate salt in an ethylene carbonate and propylene carbonate solution. The mole ratio composition was determined throughout the sample by means of Raman spectroscopy, which reveal a gradual vertical decrease of the polymer concentration. The photon correlation experiments show three dynamical processes of which two are attributed to diffusive processes, related to the solvent, and one to segmental motion, due to the relaxation of the polymer matrix. As the polymer concentration is increased the fast diffusive process gets slower, while there is no or a very small effect on the segmental motion. The implications for the overall performance in applications concerning ionic conductivity is also briefly discussed. 2000 Elsevier Science B.V. All rights reserved. Keywords: Polymer gel electrolytes; Dynamics; Dynamic light scattering; Raman spectroscopy; Photon correlation
1. Introduction Intensive research is currently being performed to meet the increasing demand for better batteries in for instance electrical vehicles and portable electronics. The aim is to develop new technologies and materials suitable for high energy capacity electrochemical cells [1]. Among the promising materials are alkali salts dissolved into poly-ethers, most commonly formed by the combination of poly(ethylene oxide) (PEO) and a lithium salt [2]. Despite impressive *Corresponding author. Fax: 146-31-772-3177. E-mail address: [email protected] (C. Svanberg).
efforts the ion conduction mechanism in these systems is not completely understood, but there are convincing indications that the conductivity is intimately related to the segmental mobility of the host polymer [2–7]. More recently, a different concept for polymer electrolytes has been proposed [8,9]. The idea is to combine the mechanical properties of solids with the high conductivity of the liquid electrolytes. Successful implementation of these ideas has been achieved on a laboratory level by stabilizing a liquid solution with a polymer matrix to form gel-type membranes. Typical examples of liquid electrolytes are propylene carbonate / ethylene carbonate solutions of lithium
0167-2738 / 00 / $ – see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S0167-2738( 00 )00610-X
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C. Svanberg et al. / Solid State Ionics 136 – 137 (2000) 1147 – 1152
salts and commonly used polymers are polyacrylonitrile or poly(methyl methacrylate). These systems are promising concerning both ionic conductivity and mechanical stability [10]. Another important feature is the reproducibility of the performance of the cell during repeated charge and discharge cycles, which in most cases are related to the properties of the electrolyte–electrode interface. Gel-type polymer electrolytes have been known for some years [8,11,12], and the mechanism of their ionic conductivity is in focus for ongoing research. Recent experiments performed in our laboratory have shown a close connection between a fast diffusive motion related to the solvent and the ionic conductivity [13]. NMR studies show, however, that there is no pure liquid electrolyte domains within the gel [14]. The role of the solvent in these systems has also been examined by Raman spectroscopy [15,16], which show that there is no significant interaction between the salt and the polymer. This has led to the suggestion that the main role of PC and EC is to Coulomb screen the salt from the polymer and thereby enhance the mobility of the ions [14,17]. Clearly, more research is needed to characterize the dynamics and its relation to the ionic conductivity. The issues discussed in this paper are the relaxation processes of the polymer gel and how the relative chemical composition influence the dynamics. We present experimental data on diffusive and segmental dynamics observed using photon correlation spectroscopy and combine that information with the mole ratio composition obtained through Raman spectroscopy.
2. Experimental The sample was prepared by mixing ethylene carbonate (EC) and propylene carbonate (PC) with lithium perchlorate (LiClO 4 ) to obtain a liquid electrolyte. Poly(methyl methacrylate) (PMMA) was then added to the liquid electrolyte to form a polymer gel. The initial materials used were of battery grade i.e. a water content less than 50 ppm. The obtained sample was optically transparent, dustfree and sealed under argon atmosphere. The preparation follows the standard gel preparation procedure described in Ref. [10], with the exception that the
sample in the present study was gelated directly in a cylindrical sample cell. This procedure yields a completely homogenous liquid electrolyte before the addition of the polymer. The very low diffusion rate of the high molecular weight polymer gives a high concentration of the top of the sample from where the polymer is added and a continuously decreasing amount of polymer at lower positions. The mole ratio of PMMA:LiClO 4 :EC:PC averaged over the whole sample were 30:4.5:46.5:19 where the PMMA ratio refers to the monomeric unit. The sample was characterized by Raman scattering using a Dilor Labram spectrometer, equipped with a microscope for both sample illumination and collection of the scattered light. A HeNe laser, operating at 632.8 nm, was used for excitation of the Raman spectra. A frequency doubled Nd:YAG laser (532.0 nm) in vertical polarization and with an output power of 400 mW was used in the photon correlation spectroscopy (PCS) experiments. The temperature was regulated with an accuracy of 61 K and monitored by a thermocouple in thermal contact with the sample cell. Vertically polarized light scattered at 908 angle from the incident laser beam was collected through an optical fiber and the collected light was then divided into two equal parts by a prism and fed to two photo multiplier tubes (PMT). The procedure of two PMT and subsequent cross-correlation of the two signals efficiently eliminates artefactial correlation due to afterpulsing of each individual PMT. The intensity auto-correlation function, gVV (q,t), was calculated in the time range 10 28 –10 4 s by a correlator (ALV-5000 / FAST). In a homodyne experiment the experimentally determined correlation function is related to the intermediate scattering function according to [18,19] ]]]] S(q,t) ~ œgVV (q,t) 2 1.
(1)
The intermediate scattering function, S(q,t), is for most relaxation processes well described by a stretched exponential decay [20]
F 2S]tt D G b
S(q,t) 5 S(q,0) exp
(2)
where t is the relaxation time, 0 , b # 1 the stretching parameter and S(q,0) the relaxation strength. The
C. Svanberg et al. / Solid State Ionics 136 – 137 (2000) 1147 – 1152
average relaxation time can be calculated from kt l 5 (t /b )Gs1 /bd where G is the Gamma function.
3. Results and discussion The Raman results presented in Fig. 1 show the gradually varying chemical composition at different points in the sample. The measurement points are labeled A to E and correspond to 5 mm consecutive vertical translation in the sample starting from the top. Assigned to the Raman band at 850 cm 21 is the symmetric ring vibration of PC [21]. The band at 898 cm 21 is due to the ring breathing mode of EC and the satellite band of this mode at 907 cm 21 arises from the interaction between EC and Li 1 [22]. A summation of the areas of these peaks are used for
1149
determining the relative concentration of EC. The vibration of ClO 2 4 is seen as a single symmetric peak at 933 cm 21 that implies that there are no ion-pairs present in the gel [23]. The PMMA band at 813 cm 21 (marked with an arrow in Fig. 1) is used for determining the polymer concentration [24]. Throughout the sample the Raman spectra are indistinguishable within the experimental uncertainty within any given horizontal plane. The ratio between the area of above stated peaks are calculated at point A to E and normalized with the known average composition of the whole sample, which gives the mole ratio composition presented in Table 1. As seen in Table 1 there is no detectable changes in the mole ratio between LiClO 4 :EC:PC within the experimental error that is estimated to be less than 5%. This is in clear contrast to the rapidly decreasing mole ratio of PMMA that decreases from 65 to 7.4 corresponding to 48% down to 9.6% PMMA when going from point A to E. The mole ratio compositions presented in Table 1 also show that the only detectable change in the mole ratio at different points of the sample is the amount of polymer present. The composition of the sample was found to be stable at least over a period of several weeks. In Fig. 2a we present the normalized auto-correlation function at 293 K as obtained by PCS at points A to E in the sample. The relaxation functions presented shows a complex behavior, where at least three relaxation processes can be readily distinguished, i.e. (i) a fast decay at about 10 24 210 23 s, (ii) an intermediate broad process in the 10 24 21 s range, and (iii) a slow decay above 10 s. The most pronounced differences of the correlograms of points A to E are the shifts in the relaxation times for the fast motion. The slow process is approaching the
Table 1 Mole ratio composition normalized with the average mole ratio composition for the whole sample. The errors are estimated to less than 5%. For PMMA the mole percent is also presented
Fig. 1. Raman spectra obtained at points A to E. The arrow indicates the peak used to determine the relative amount of PMMA at the measuring point. The spectra are vertically shifted for clarity.
Point
PMMA
%[PMMA]
LiClO 4
EC
PC
A B C D E
65.0 43.3 22.8 12.7 7.41
48.1 38.2 24.6 15.4 9.57
4.5 4.5 4.5 4.5 4.5
46.5 46.5 46.5 46.5 46.5
19 19 19 19 19
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C. Svanberg et al. / Solid State Ionics 136 – 137 (2000) 1147 – 1152
Fig. 2. (a) Vertically shifted and normalized correlation functions obtained at point A to E. (b) Intermediate scattering function and the total curve fit (solid line) for the sample at point E. The three contributions to the total curve-fit (see text) is also plotted, fast diffusive (dotted line), segmental motion (dashed line) and slow diffusion (dash-dotted line).
limit of practically measurable time scales with PCS and will here only be treated in a qualitative way. The chemical composition at point D is identical to the composition in previously reported work [13]. In that study it was shown that the fast and slow processes had a single exponential decay ( b 5 1 in Eq. (2)) in the intermediate scattering function, both with an Arrhenius temperature dependence and a clear wave vector dependence for the relaxation time. These features indicate a diffusive character of both processes. In contrast, the intermediate process was shown to have a stretched exponential decay in the intermediate scattering function ( b , 1 in Eq. (2)), a non-Arrhenius temperature dependence of the average relaxation time and no detectable wave vector dependence. These features are typical for segmental relaxations of polymers [20,25–28] and the intermediate process is therefore attributed to
segmental motion of the PMMA. Since the present results are completely consistent with the previous study the same assignment of the different dynamical processes will be made here. The data were thus analyzed using two single exponential decays, b 5 1, to describe the fast and slow processes and a stretched exponential decay for the intermediate process. The stretching parameter b for the intermediate process was first kept fixed and adjusted to fulfill the relation between b and t observed in bulk PMMA [29], but in the final stage of the fitting procedure also b was used as a free parameter. In Fig. 2b the intermediate scattering function for the sample at point E is plotted together with the three contributing processes as obtained from a least square curve-fit, which yields an excellent fit to the data. Note the large difference in stretching of the different processes. In Fig. 3 we show the relaxation times obtained for the two fastest processes as a function of the concentration of PMMA. Due to the very stretched behavior of the intermediate process and the large overlap between the processes the uncertainty for the stretching exponent b and thus also the average
Fig. 3. Relaxation times for the fast diffusive (circles) and the segmental motion (squares) versus the relative mole ratio of PMMA. Error bars are shown for the segmental process while the errors are of the order of the symbols for the fast process. The dash-dotted line is the least square fit to a power-law (Eq. (3)) with t0 5 5.4 3 10 24 s, c 1 553% and a51.4. The solid line through the circles represent a fit to the VFT related expression (Eq. (4)) with t0 5 6.6 3 10 24 s, Dc 5 0.96 and c 0 564%. The dotted line and the dot-dot-dashed line are extrapolations of the VFT and the power law expressions to higher concentration.
C. Svanberg et al. / Solid State Ionics 136 – 137 (2000) 1147 – 1152
relaxation time is large (see error bars in Fig. 3). There is a pronounced increase in the relaxation time for the fast process with increasing polymer concentration. Our data are well described by a power law expression based on percolation theory [30] c 1 2 c 2a kt l 5 t0 ]] (3) c1
F
G
where c 1 is the divergence concentration and a the critical exponent. A least square curve fit to the average relaxation time yields t0 5 5.4 3 10 24 s, c 1 553% and a51.4. We note the apparent divergence of the relaxation time at approximately 53% PMMA. An alternative approach, that equally well describe the data, is to use the empirical formula
F
Dc c kt l 5 t0 exp ]] c0 2 c
G
(4)
where c 0 is the concentration where the relaxation time diverges and Dc describes the deviation from an Arrhenius behavior. The formula is based on a Vogel–Fulcher–Tammann (VFT) expression [20], which is commonly used to describe the temperature dependence for the relaxation time, while in our formula we have replaced the temperature with the inverse of the concentration. Eq. 4 describes the experimental data very well with t0 5 6.6 3 10 24 s, Dc 5 0.96 and c 0 564%, as seen in Fig. 3. The behavior of the VFT-based expression and the power law is very similar within the range of experimental data and a difference is only noticeable in extrapolations of the data, where the prediction of the divergence from the power law is slightly below that from the VFT expression. What functional form that most accurately describes the data has to await future studies over a larger concentration range. Bohnke et al. [31] studied a similar system with the difference that PC was exclusively used as a plasticizer instead of the mixture between the EC and PC used in the present work. They show that the viscosity increases with increasing polymer concentration. In addition they also show a decrease in the conductivity with increasing polymer concentration from 0% to 50%. With the assumption that the relaxation time is proportional to the inverse of the conductivity their experimental data agree qualitatively well with the present study. This provides an independent confirmation of our previously stated
1151
connection [13] between the fast diffusion and the ionic conductivity. Concerning the segmental relaxation of the polymer matrix our data suggests (see Fig. 3) a weak concentration dependence within the examined polymer concentration range, but all changes are well within experimental errors. A comparison with the above stated increase in the viscosity with increasing polymer concentration then yields that the segmental relaxation time may not exclusively determine the viscosity. One possible interpretation is that the viscosity is to a large extent determined by the amount of low viscosity solvent present in the system compared to the amount of viscous polymer. An extrapolation of a concentration independent segmental relaxation time to the one of bulk PMMA is clearly inconsistent with an attribution of this process to the a -relaxation, i.e. the structural relaxation of the polymer backbone. This is because the present experiments is performed approximately 80 K below the glass transition and hence the relaxation should be immeasurably long. This apparent problem is less troublesome considering the low concentration of polymer investigated in this study. It is likely that there will be a crossover when the PMMA concentration increases further, causing the segmental relaxation time to diverge towards the PMMA bulk value. From an extrapolation of the relaxation time data it is plausible that the onset of the increasing tseg will occur around 50–60% PMMA where tseg ¯ tfast . At higher concentrations the extrapolated values of tseg and tfast merge and it is reasonable to assume that the two processes become coupled and indistinguishable to form an effective a -process of plasticized PMMA. These ideas follow the work of Williams concerning merging of relaxations [32]. Below the merging concentration the polymer segment is fully plasticized and further increase of the solvent concentration only marginally effects the segmental relaxation.
4. Conclusion We have performed Raman and photon correlation spectroscopy experiments that reveal an intimate relation between the chemical composition and the dynamical behavior in gel electrolytes. Our study
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show that diffusion of solvent within the polymer matrix is slowed down by an increase in the polymer concentration. In contrast, the time scale of the segmental motion reveals no or alternatively a very weak concentration dependence. We therefore conclude that increasing the polymer concentration in order to increase the mechanical stability, will give a decrease in ionic conductivity as it is governed by the mobility of the solvents. Keeping this in mind our results suggest a possibility to optimize the amount of polymer in the gel to improve the overall performance in terms of mechanical stability and ionic conductivity.
Acknowledgements Financial support from the Swedish Natural Science Research Council and the Swedish Foundation for Strategic Research is gratefully acknowledged.
References [1] B. Scrosati, Nature 373 (1995) 557. [2] F.M. Gray, Polymer Electrolytes, Royal Society of Chemistry, Cambridge, 1997. [3] J.R. MacCallum, C.A. Vincent (Eds.), Polymer Electrolyte Reviews, Vol. 1, Elsevier, New York, 1987. [4] J.R. MacCallum, C.A. Vincent (Eds.), Polymer Electrolyte Reviews, Vol. 2, Elsevier, New York, 1989. [5] C. Berthier, W. Gorecki, M. Minier, M.B. Armand, J.M. Chabagno, P. Rigaud, Solid State Ionics 11 (1983) 91. [6] W. Gorecki, E. Belorizky, C. Berthier, P. Donoso, M.B. Armand, Electrochim. Acta 37 (1992) 1685. ¨ [7] R. Bergman, L. Borjesson, G. Fytas, L.M. Torell, J. NonCryst. Solids 172–174 (1994) 830. [8] K.M. Abraham, in: B. Scrosati (Ed.), Application of electroactive polymers, Chapman and Hall, London, 1993, pp. 75–112.
[9] B. Scrosati, La Chimica e l’Industria 77 (1995) 285. [10] G.B. Appetecchi, F. Croce, B. Scrosati, Electrochim. Acta 40 (1995) 991. [11] G. Feuillade, P. Perche, J. Appl. Electrochem. 5 (1975) 63. [12] G. Dautzenberg, F. Croce, S. Passerini, B. Scrosati, Chem. Mat. 6 (1994) 538. ¨ [13] C. Svanberg, J. Adebahr, H. Ericson, L. Borjesson, L.M. Torell, B. Scrosati, J. Chem. Phys. 111 (1999) 1216. [14] P.E. Stallworth, S.G. Greenbaum, F. Croce, S. Slane, M. Salomon, Electrochim. Acta 40 (1995) 2137. [15] D. Ostrovskii, A. Brodin, L.M. Torell, G.B. Appetecchi, B. Scrosati, J. Chem. Phys. 109 (1998) 7618. [16] D. Ostrovskii, L.M. Torell, G.B. Appetecchi, B. Scrosati, Solid State Ionics 106 (1998) 19. [17] S.-A. Hyodo, K. Okabayashi, Electrochim. Acta 34 (1989) 1557. [18] W. Brown (Ed.), Dynamic light scattering: the method and some applications, Clarendon Press, Oxford, 1993. [19] B.J. Berne, R. Pecora, Dynamic light scattering, WileyInterscience, New York, 1976. [20] C.A. Angell, Science 267 (1995) 1924. [21] G.J. Janz, J. Ambrose, J.W. Coutts, J.R. Downey, Spectrochim. Acta 35A (1979) 175. [22] S.-A. Hyodo, K. Okabayashi, Electrochim. Acta 34 (1989) 1551. [23] D. Battisti, G.A. Nazri, B. Klassen, R. Aroca, J. Phys. Chem. 97 (1993) 5826. [24] H.A. Willis, V.I.J. Zichy, P.J. Hendra, Polymer 7 (1969) 737. [25] G. Williams, J. Non-Cryst. Solids 131–133 (1991) 1. [26] G. Fytas, G. Meier, in: W. Brown (Ed.), Dynamic light scattering, Clarendon Press, Oxford, 1993, pp. 407–439. [27] J. Gapinski, G. Fytas, G. Floudas, J. Chem. Phys. 96 (1992) 6311. [28] G. Fytas, G. Floudas, K.L. Ngai, Macromolecules 23 (1990) 1104. [29] G.D. Patterson, P.J. Carroll, J.R. Stevens, J. Polym. Sci., Polym. Phys. Ed. 21 (1983) 613. [30] D. Stauffer, Introduction to percolation theory, Taylor and Francis, London, 1985. [31] O. Bohnke, G. Frand, M. Rezrazi, C. Rousselot, C. Truche, Solid State Ionics 66 (1993) 97. [32] G. Williams, Adv. Polymer Sci. 33 (1979) 60.
Polymer concentration dependence of the dynamics in gel electrolytes b ¨ C. Svanberg a , *, J. Adebahr a , R. Bergman a , L. Borjesson , B. Scrosati c , P. Jacobsson a a
¨ , Sweden Department of Experimental Physics, Chalmers University of Technology, SE-412 96 Goteborg b ¨ , Sweden Department of Applied Physics, Chalmers University of Technology, SE-412 96 Goteborg c Department of Chemistry, University of Rome ‘ La Sapienza’, I-00185 Rome, Italy
Abstract A polymer gel electrolyte sample with a gradually varying concentration of polymer have been examined by Raman and photon correlation spectroscopy. The gel consisted of poly(methyl methacrylate) complexed with a liquid electrolyte of lithium perchlorate salt in an ethylene carbonate and propylene carbonate solution. The mole ratio composition was determined throughout the sample by means of Raman spectroscopy, which reveal a gradual vertical decrease of the polymer concentration. The photon correlation experiments show three dynamical processes of which two are attributed to diffusive processes, related to the solvent, and one to segmental motion, due to the relaxation of the polymer matrix. As the polymer concentration is increased the fast diffusive process gets slower, while there is no or a very small effect on the segmental motion. The implications for the overall performance in applications concerning ionic conductivity is also briefly discussed. 2000 Elsevier Science B.V. All rights reserved. Keywords: Polymer gel electrolytes; Dynamics; Dynamic light scattering; Raman spectroscopy; Photon correlation
1. Introduction Intensive research is currently being performed to meet the increasing demand for better batteries in for instance electrical vehicles and portable electronics. The aim is to develop new technologies and materials suitable for high energy capacity electrochemical cells [1]. Among the promising materials are alkali salts dissolved into poly-ethers, most commonly formed by the combination of poly(ethylene oxide) (PEO) and a lithium salt [2]. Despite impressive *Corresponding author. Fax: 146-31-772-3177. E-mail address: [email protected] (C. Svanberg).
efforts the ion conduction mechanism in these systems is not completely understood, but there are convincing indications that the conductivity is intimately related to the segmental mobility of the host polymer [2–7]. More recently, a different concept for polymer electrolytes has been proposed [8,9]. The idea is to combine the mechanical properties of solids with the high conductivity of the liquid electrolytes. Successful implementation of these ideas has been achieved on a laboratory level by stabilizing a liquid solution with a polymer matrix to form gel-type membranes. Typical examples of liquid electrolytes are propylene carbonate / ethylene carbonate solutions of lithium
0167-2738 / 00 / $ – see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S0167-2738( 00 )00610-X
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C. Svanberg et al. / Solid State Ionics 136 – 137 (2000) 1147 – 1152
salts and commonly used polymers are polyacrylonitrile or poly(methyl methacrylate). These systems are promising concerning both ionic conductivity and mechanical stability [10]. Another important feature is the reproducibility of the performance of the cell during repeated charge and discharge cycles, which in most cases are related to the properties of the electrolyte–electrode interface. Gel-type polymer electrolytes have been known for some years [8,11,12], and the mechanism of their ionic conductivity is in focus for ongoing research. Recent experiments performed in our laboratory have shown a close connection between a fast diffusive motion related to the solvent and the ionic conductivity [13]. NMR studies show, however, that there is no pure liquid electrolyte domains within the gel [14]. The role of the solvent in these systems has also been examined by Raman spectroscopy [15,16], which show that there is no significant interaction between the salt and the polymer. This has led to the suggestion that the main role of PC and EC is to Coulomb screen the salt from the polymer and thereby enhance the mobility of the ions [14,17]. Clearly, more research is needed to characterize the dynamics and its relation to the ionic conductivity. The issues discussed in this paper are the relaxation processes of the polymer gel and how the relative chemical composition influence the dynamics. We present experimental data on diffusive and segmental dynamics observed using photon correlation spectroscopy and combine that information with the mole ratio composition obtained through Raman spectroscopy.
2. Experimental The sample was prepared by mixing ethylene carbonate (EC) and propylene carbonate (PC) with lithium perchlorate (LiClO 4 ) to obtain a liquid electrolyte. Poly(methyl methacrylate) (PMMA) was then added to the liquid electrolyte to form a polymer gel. The initial materials used were of battery grade i.e. a water content less than 50 ppm. The obtained sample was optically transparent, dustfree and sealed under argon atmosphere. The preparation follows the standard gel preparation procedure described in Ref. [10], with the exception that the
sample in the present study was gelated directly in a cylindrical sample cell. This procedure yields a completely homogenous liquid electrolyte before the addition of the polymer. The very low diffusion rate of the high molecular weight polymer gives a high concentration of the top of the sample from where the polymer is added and a continuously decreasing amount of polymer at lower positions. The mole ratio of PMMA:LiClO 4 :EC:PC averaged over the whole sample were 30:4.5:46.5:19 where the PMMA ratio refers to the monomeric unit. The sample was characterized by Raman scattering using a Dilor Labram spectrometer, equipped with a microscope for both sample illumination and collection of the scattered light. A HeNe laser, operating at 632.8 nm, was used for excitation of the Raman spectra. A frequency doubled Nd:YAG laser (532.0 nm) in vertical polarization and with an output power of 400 mW was used in the photon correlation spectroscopy (PCS) experiments. The temperature was regulated with an accuracy of 61 K and monitored by a thermocouple in thermal contact with the sample cell. Vertically polarized light scattered at 908 angle from the incident laser beam was collected through an optical fiber and the collected light was then divided into two equal parts by a prism and fed to two photo multiplier tubes (PMT). The procedure of two PMT and subsequent cross-correlation of the two signals efficiently eliminates artefactial correlation due to afterpulsing of each individual PMT. The intensity auto-correlation function, gVV (q,t), was calculated in the time range 10 28 –10 4 s by a correlator (ALV-5000 / FAST). In a homodyne experiment the experimentally determined correlation function is related to the intermediate scattering function according to [18,19] ]]]] S(q,t) ~ œgVV (q,t) 2 1.
(1)
The intermediate scattering function, S(q,t), is for most relaxation processes well described by a stretched exponential decay [20]
F 2S]tt D G b
S(q,t) 5 S(q,0) exp
(2)
where t is the relaxation time, 0 , b # 1 the stretching parameter and S(q,0) the relaxation strength. The
C. Svanberg et al. / Solid State Ionics 136 – 137 (2000) 1147 – 1152
average relaxation time can be calculated from kt l 5 (t /b )Gs1 /bd where G is the Gamma function.
3. Results and discussion The Raman results presented in Fig. 1 show the gradually varying chemical composition at different points in the sample. The measurement points are labeled A to E and correspond to 5 mm consecutive vertical translation in the sample starting from the top. Assigned to the Raman band at 850 cm 21 is the symmetric ring vibration of PC [21]. The band at 898 cm 21 is due to the ring breathing mode of EC and the satellite band of this mode at 907 cm 21 arises from the interaction between EC and Li 1 [22]. A summation of the areas of these peaks are used for
1149
determining the relative concentration of EC. The vibration of ClO 2 4 is seen as a single symmetric peak at 933 cm 21 that implies that there are no ion-pairs present in the gel [23]. The PMMA band at 813 cm 21 (marked with an arrow in Fig. 1) is used for determining the polymer concentration [24]. Throughout the sample the Raman spectra are indistinguishable within the experimental uncertainty within any given horizontal plane. The ratio between the area of above stated peaks are calculated at point A to E and normalized with the known average composition of the whole sample, which gives the mole ratio composition presented in Table 1. As seen in Table 1 there is no detectable changes in the mole ratio between LiClO 4 :EC:PC within the experimental error that is estimated to be less than 5%. This is in clear contrast to the rapidly decreasing mole ratio of PMMA that decreases from 65 to 7.4 corresponding to 48% down to 9.6% PMMA when going from point A to E. The mole ratio compositions presented in Table 1 also show that the only detectable change in the mole ratio at different points of the sample is the amount of polymer present. The composition of the sample was found to be stable at least over a period of several weeks. In Fig. 2a we present the normalized auto-correlation function at 293 K as obtained by PCS at points A to E in the sample. The relaxation functions presented shows a complex behavior, where at least three relaxation processes can be readily distinguished, i.e. (i) a fast decay at about 10 24 210 23 s, (ii) an intermediate broad process in the 10 24 21 s range, and (iii) a slow decay above 10 s. The most pronounced differences of the correlograms of points A to E are the shifts in the relaxation times for the fast motion. The slow process is approaching the
Table 1 Mole ratio composition normalized with the average mole ratio composition for the whole sample. The errors are estimated to less than 5%. For PMMA the mole percent is also presented
Fig. 1. Raman spectra obtained at points A to E. The arrow indicates the peak used to determine the relative amount of PMMA at the measuring point. The spectra are vertically shifted for clarity.
Point
PMMA
%[PMMA]
LiClO 4
EC
PC
A B C D E
65.0 43.3 22.8 12.7 7.41
48.1 38.2 24.6 15.4 9.57
4.5 4.5 4.5 4.5 4.5
46.5 46.5 46.5 46.5 46.5
19 19 19 19 19
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C. Svanberg et al. / Solid State Ionics 136 – 137 (2000) 1147 – 1152
Fig. 2. (a) Vertically shifted and normalized correlation functions obtained at point A to E. (b) Intermediate scattering function and the total curve fit (solid line) for the sample at point E. The three contributions to the total curve-fit (see text) is also plotted, fast diffusive (dotted line), segmental motion (dashed line) and slow diffusion (dash-dotted line).
limit of practically measurable time scales with PCS and will here only be treated in a qualitative way. The chemical composition at point D is identical to the composition in previously reported work [13]. In that study it was shown that the fast and slow processes had a single exponential decay ( b 5 1 in Eq. (2)) in the intermediate scattering function, both with an Arrhenius temperature dependence and a clear wave vector dependence for the relaxation time. These features indicate a diffusive character of both processes. In contrast, the intermediate process was shown to have a stretched exponential decay in the intermediate scattering function ( b , 1 in Eq. (2)), a non-Arrhenius temperature dependence of the average relaxation time and no detectable wave vector dependence. These features are typical for segmental relaxations of polymers [20,25–28] and the intermediate process is therefore attributed to
segmental motion of the PMMA. Since the present results are completely consistent with the previous study the same assignment of the different dynamical processes will be made here. The data were thus analyzed using two single exponential decays, b 5 1, to describe the fast and slow processes and a stretched exponential decay for the intermediate process. The stretching parameter b for the intermediate process was first kept fixed and adjusted to fulfill the relation between b and t observed in bulk PMMA [29], but in the final stage of the fitting procedure also b was used as a free parameter. In Fig. 2b the intermediate scattering function for the sample at point E is plotted together with the three contributing processes as obtained from a least square curve-fit, which yields an excellent fit to the data. Note the large difference in stretching of the different processes. In Fig. 3 we show the relaxation times obtained for the two fastest processes as a function of the concentration of PMMA. Due to the very stretched behavior of the intermediate process and the large overlap between the processes the uncertainty for the stretching exponent b and thus also the average
Fig. 3. Relaxation times for the fast diffusive (circles) and the segmental motion (squares) versus the relative mole ratio of PMMA. Error bars are shown for the segmental process while the errors are of the order of the symbols for the fast process. The dash-dotted line is the least square fit to a power-law (Eq. (3)) with t0 5 5.4 3 10 24 s, c 1 553% and a51.4. The solid line through the circles represent a fit to the VFT related expression (Eq. (4)) with t0 5 6.6 3 10 24 s, Dc 5 0.96 and c 0 564%. The dotted line and the dot-dot-dashed line are extrapolations of the VFT and the power law expressions to higher concentration.
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relaxation time is large (see error bars in Fig. 3). There is a pronounced increase in the relaxation time for the fast process with increasing polymer concentration. Our data are well described by a power law expression based on percolation theory [30] c 1 2 c 2a kt l 5 t0 ]] (3) c1
F
G
where c 1 is the divergence concentration and a the critical exponent. A least square curve fit to the average relaxation time yields t0 5 5.4 3 10 24 s, c 1 553% and a51.4. We note the apparent divergence of the relaxation time at approximately 53% PMMA. An alternative approach, that equally well describe the data, is to use the empirical formula
F
Dc c kt l 5 t0 exp ]] c0 2 c
G
(4)
where c 0 is the concentration where the relaxation time diverges and Dc describes the deviation from an Arrhenius behavior. The formula is based on a Vogel–Fulcher–Tammann (VFT) expression [20], which is commonly used to describe the temperature dependence for the relaxation time, while in our formula we have replaced the temperature with the inverse of the concentration. Eq. 4 describes the experimental data very well with t0 5 6.6 3 10 24 s, Dc 5 0.96 and c 0 564%, as seen in Fig. 3. The behavior of the VFT-based expression and the power law is very similar within the range of experimental data and a difference is only noticeable in extrapolations of the data, where the prediction of the divergence from the power law is slightly below that from the VFT expression. What functional form that most accurately describes the data has to await future studies over a larger concentration range. Bohnke et al. [31] studied a similar system with the difference that PC was exclusively used as a plasticizer instead of the mixture between the EC and PC used in the present work. They show that the viscosity increases with increasing polymer concentration. In addition they also show a decrease in the conductivity with increasing polymer concentration from 0% to 50%. With the assumption that the relaxation time is proportional to the inverse of the conductivity their experimental data agree qualitatively well with the present study. This provides an independent confirmation of our previously stated
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connection [13] between the fast diffusion and the ionic conductivity. Concerning the segmental relaxation of the polymer matrix our data suggests (see Fig. 3) a weak concentration dependence within the examined polymer concentration range, but all changes are well within experimental errors. A comparison with the above stated increase in the viscosity with increasing polymer concentration then yields that the segmental relaxation time may not exclusively determine the viscosity. One possible interpretation is that the viscosity is to a large extent determined by the amount of low viscosity solvent present in the system compared to the amount of viscous polymer. An extrapolation of a concentration independent segmental relaxation time to the one of bulk PMMA is clearly inconsistent with an attribution of this process to the a -relaxation, i.e. the structural relaxation of the polymer backbone. This is because the present experiments is performed approximately 80 K below the glass transition and hence the relaxation should be immeasurably long. This apparent problem is less troublesome considering the low concentration of polymer investigated in this study. It is likely that there will be a crossover when the PMMA concentration increases further, causing the segmental relaxation time to diverge towards the PMMA bulk value. From an extrapolation of the relaxation time data it is plausible that the onset of the increasing tseg will occur around 50–60% PMMA where tseg ¯ tfast . At higher concentrations the extrapolated values of tseg and tfast merge and it is reasonable to assume that the two processes become coupled and indistinguishable to form an effective a -process of plasticized PMMA. These ideas follow the work of Williams concerning merging of relaxations [32]. Below the merging concentration the polymer segment is fully plasticized and further increase of the solvent concentration only marginally effects the segmental relaxation.
4. Conclusion We have performed Raman and photon correlation spectroscopy experiments that reveal an intimate relation between the chemical composition and the dynamical behavior in gel electrolytes. Our study
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show that diffusion of solvent within the polymer matrix is slowed down by an increase in the polymer concentration. In contrast, the time scale of the segmental motion reveals no or alternatively a very weak concentration dependence. We therefore conclude that increasing the polymer concentration in order to increase the mechanical stability, will give a decrease in ionic conductivity as it is governed by the mobility of the solvents. Keeping this in mind our results suggest a possibility to optimize the amount of polymer in the gel to improve the overall performance in terms of mechanical stability and ionic conductivity.
Acknowledgements Financial support from the Swedish Natural Science Research Council and the Swedish Foundation for Strategic Research is gratefully acknowledged.
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