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Network structure of poly(methyl methacrylate)-based gels and gel electrolytes
Electrochimica Acta 51 (2006) 4153–4156
Network structure of poly(methyl methacrylate)-based gels and gel electrolytes C. Svanberg a,∗ , W. Pyckhout-Hintzen b , L. B¨orjesson a a
Department of Applied Physics, Chalmers University of Technology, SE-412 96 G¨oteborg, Sweden b Institut f¨ ur Festk¨orperforschung, Forschungszentrum J¨ulich, D-52425 J¨ulich, Germany
Received 26 August 2005; received in revised form 25 November 2005; accepted 26 November 2005 Available online 6 January 2006
Abstract The large scale structure of poly(methyl methacrylate)-based gels and gel electrolytes has been investigated using small angle neutron scattering. ˚ while the larger is 200–300 A. ˚ Comparison between the The data reveal two different structural length scales: the shorter being typically 4–25 A, gel electrolytes, obtained by doping the gels with lithium salt, and the corresponding salt-free systems shows that the determined length scales are very similar. Thus the dissolved salt has only minor influence on the structure of the polymer network. We also discuss the important relations between structure, dynamics and the performance of the gel electrolytes. © 2005 Elsevier Ltd. All rights reserved. PACS: 61.41.+e; 82.70.Gg; 61.12.Ex Keywords: Gel electrolytes; Polymer; SANS; Structure; Physical cross-links
1. Introduction Polymer gels are viscoelastic materials that combines microscopic liquid-like dynamics with macroscopic mechanical stability. From a fundamental point of view it is of high interest to investigate the solvent and polymer dynamics in such inhomogeneous systems in order to determine the relation between structure and dynamics [1,2]. Experiments on the large scale structure have shown that in general at least two characteristic length scales are required to describe experimental data of polymer gels [3]. The shorter of these length scales is the polymer–polymer correlation length that is also observed in the corresponding non-cross-linked polymer solution [3]. At longer length scales, an excess scattering is generally observed for gel systems that is not present for the corresponding noncross-linked system. The excess scattering is therefore believed to be related to heterogeneity induced by the cross-links of the gels [4]. However, the details of the experimental observation differs between different types of gel systems [3] and is occasionally even influenced by the sample preparation procedure [5]. ∗
Corresponding author. Tel.: +46 31 772 31 78; fax: +46 31 772 20 90. E-mail address: [email protected] (C. Svanberg).
0013-4686/$ – see front matter © 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.electacta.2005.11.035
One application of polymer gels are as solid electrolytes suitable for high capacity polymer batteries [6]. An ion conducting polymer gel electrolyte can be obtained by mixing poly(methyl methacrylate) (PMMA) with a liquid electrolyte consisting of a lithium salt dissolved in ethylene carbonate (EC)/propylene carbonate (PC) [7]. To optimize the performance of gel electrolytes two factors are of utmost importance: the mechanical stability and the ionic conductivity. For PMMA-based gel electrolytes dynamical studies have revealed that the ion conduction mechanism is closely coupled to a diffusive relaxation process in the system [8–10]. The macroscopic mechanical strength on the other hand originates from the structure of the polymer network. Therefore, knowledge of the large scale structure of polymer gel electrolytes is essential for improving their performance. In this paper, we report, to the best of our knowledge, the first small angle neutron scattering (SANS) study of a polymer gel electrolyte. SANS is an experimental technique well suited to probe the structure of polymers over the range from a few up to ˚ several hundred Angstr¨ oms [11–13]. Of particular interest here is possibility to use deuterium labelling to enhance the contrast between the polymer and the solvent. This enables us to address the question of the concentration dependence of the distance between the polymer chains and the large scale heterogeneities in PMMA-based gels and gel electrolytes. By comparing gel elec-
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trolytes with the corresponding salt-free systems we show that the salt only has marginal effects on the large scale structure. Instead the key parameter is the polymer concentration dependence that determines the typical mesh size of the system. 2. Experimental In this study, syndiotactic and fully deuterated poly(methyl methacrylate) (PMMA) (MW = 1,587,000, Polymer Source Inc.) was used. Deuterated PMMA was used to achieve the desired contrast in scattering efficiency compared to the hydrogenous solvent and salt. The salt-free samples were prepared by mixing propylene carbonate (PC) with PMMA at room temperature. The salt-doped samples were prepared by first mixing ethylene carbonate (EC) with PC and then adding lithium perchlorate (LiClO4 ), with the ratios EC/PC/LiClO4 : 10/4/1. After a homogenous solution was obtained the polymer was added. All the samples were equilibrated at an elevated temperature, T = 390 K. Some of the samples were prepared directly in the sample cell, while others were prepared in test tubes and subsequently transferred to the sample cells. The sample preparation procedure was performed under argon atmosphere. The sample thickness was 1 mm and the samples were completely transparent with occasional argon bubbles trapped in some of the samples. The small angle neutron scattering (SANS) experiments were performed at the small angle neutron diffractometer KSW1 at FZ J¨ulich, Germany. Experimental details of neutron scattering in general, and SANS in particular, are given in Refs. [11–13]. ˚ was used and In our experiments an incident wavelength of 7 A two sample-detector distances, 2 and 8 m, enables us to cover ˚ −1 < Q < 0.15 A ˚ −1 . the momentum transfer range of 0.006 A All the experiments were performed at room temperature. The data were corrected according to standard procedures; empty cell subtraction, background subtraction and intensity calibration using a polyethylene standard. The incoherent background scattering, obtained from reference sample consisting of hydrogenated PC and PMMA, was also subtracted. However, the presence of argon-bubbles in some samples increase the uncertainty of the absolute values of I(Q) of those samples. We will therefore in this paper refrain from comparing the absolute values of the scattered intensity.
Fig. 1. Intensity vs. wave vector for samples with and without salt. Filled symbols correspond to salt-doped system and open symbols are salt-free. The circles are for two samples with roughly 30% PMMA and the triangles around 10%. The lines are curve-fits to the experimental data using Eq. (1). The data for the 30% samples are vertically shifted for clarity.
for both polymer gels and gel electrolytes. The first term in Eq. (1) is a so-called Ornstein–Zernike (OZ) function [3,4]. The Ornstein–Zernike function describes the data at large values of Q, i.e. short distances, with ξ as the characteristic size of fluctuations in polymer concentration [3]. The second term in Eq. (1) is a so-called Debye–Bueche (DB) function [3,4,14,15]. The Debye–Bueche function was originally derived for a medium with two species randomly distributed and is here used to describe large scale non-homogeneities with a as the characteristic length scale. Eq. (1) has previously been used to describe polystyrene gels [5] and gives a good description of our experimental data. However, for some of the samples the experimental accuracy and reproducibility are not completely satisfactorily at low Q, which is probably due to the sample preparation proce˚ and systemdure. We observe that ξ is in the range of 4–25 A atically decreases with increasing polymer concentration. The ˚ and without any obtained values of a are in the range 200–300 A significant changes with polymer concentration. However, these values are close to the lower limit of our experimental range and therefore somewhat uncertain.
3. Results 4. Discussion In Fig. 1 the scattered intensity of two salt-free gels are compared with two gel electrolytes with similar polymer concentrations. The figure clearly shows two distinct regions with large decrease in intensity, which is typical for polymer gels, and that the scattering functions are very similar for the two systems. This implies that the interpretation established for SANS experiments on standard polymer gels (see Ref. [12] and references therein) can be applied also to polymer gel electrolytes. As seen in Fig. 1 the scattering intensity is well described by I(Q) =
I1 I2 a3 + 1 + Q2 ξ 2 (1 + Q2 a2 )2
(1)
In order to be able to compare the polymer concentration dependence of the length scales with theoretical predictions it is often more straightforward to use volume percent than weight percent. We therefore used semi-empirical electron density calculations in order to, at least approximately, describe the volume ratios of the components in the system [16]. The volumes ob˚ 3 , VPC = 114 tained from the calculations are: VPMMA = 155 A 3 3 3 ˚ , VEC = 93 A ˚ and VLi+ClO4 = 88 A ˚ . The PMMA volume is A calculated for the monomer and the salt volume is the sum of the ion volumes, since previous Raman experiments have shown that ion pairs are scarce in the present gel electrolyte system [17].
C. Svanberg et al. / Electrochimica Acta 51 (2006) 4153–4156
Fig. 2. Curve-fit parameters ξ (circles) and a (squares) as a function of volume fraction polymer. Salt-doped samples are marked with a cross. The full line is the relation ξ = ξp ϕ−s discussed in the text.
In Fig. 2 we show ξ and a as a function of the calculated volume fraction of PMMA, ϕ. In accordance with previous studies of both polymer gels and polymer solutions we attribute the shorter length scale, ξ, to the polymer–polymer correlation length, see Ref. [12] and references therein. We observe, as expected, a marked decrease of ξ with increasing polymer content. Using scaling arguments de Gennes [1] predicted a power law behavior in the semi-dilute regime between the correlation length ξ and the volume fraction ϕ of polymer ξ = ξp ϕ−s
(2)
where ξp is the distance extrapolated to the pure polymer. The power law behavior can be understood by modeling the semidilute polymer solution as closely packed solvent domains separated by the polymer network, where ξ is the average size of the domains [1]. The exponent s in Eq. (2) is related to the fractal 1 dimension df of the polymer chains at infinite dilution s = 3−d f [12]. The curve-fit of Eq. (2) to the experimental data for the salt˚ Comfree samples yields s = 1.0 ± 0.1 and ξp = 3.0 ± 0.5 A. paring the solubility parameters for PC and PMMA with those of for example PMMA and toluene [18] implies that the PC is a good solvent for PMMA and therefore that s should be 3/4. However, according to the theoretical work by Schaefer et al. [19,20] a theta solvent behavior, i.e. s = 1, is expected at high polymer concentrations due to the appearance of ternary junctions between the polymer chains. We also note that s equal to unity has been reported previously for other gel systems [21]. At low wave vectors we observe a second contribution as previously observed for cross-linked gel systems [12]. However, a generally accepted explanation of this excess scattering is still lacking [12]. The excess scattering we observe is best described by the Debye–Bueche function, which was originally derived as the scattering of a random two phase system [14,15]. In the
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PMMA-gels investigated here such large scale heterogeneities must be caused by fluctuations in the polymer concentration. In the present system there are no permanent chemical bonds, but syndiotactic PMMA can form helices that can that evolve into small crystalline structures [22–26]. Potentially such regions could acts as physical cross-links. Another idea is that locally vitrified regions hinders the chains from disentangle [27,28]. In either case these regions have a different concentration and density than the rest of the sample and therefore can be observed in a SANS experiment. This is in contrast to chemical gels, with permanent bonds between the polymer chains, where the excess scattering normally is not observed, although it can be observed after swelling or deswelling [4]. Another important observation is that, within the experimental uncertainty, the larger length scale is independent of polymer concentration. This is in distinct contrast to the macroscopic viscosity that dramatically increases with polymer concentrations. It thus appears as the large length scale observed here is only a prerequisite for the mechanical stability of the system. Also parameters such as the number of different chains in one cross-link and their lifetime could be of importance for the macroscopic viscosity. Furthermore, an alternative idea is that this large scales structure could be related to some of the slower process observable in dynamic light scattering experiments, but this requires further studies. Establishing the true physical origin of the excess scattering at low wave vectors is indeed central for our understanding of the network structure in polymer gels and thus also polymer gel electrolytes. Concerning gel electrolytes the introduction of salt in general changes the electrochemical properties, which could also effect the network structure. However, the data looks very similar for both systems and the same curve-fit procedure can be applied. Furthermore, the obtained length scales are similar for samples with and without salt, as seen in Fig. 2. We therefore make the same attribution for the polymer gel electrolytes as for the salt-free systems: the shorter scale to the polymer–polymer correlation length and the larger length scale to polymer-rich regions. We also conclude that the introduction of ions in the system has only minor effects on the medium and large scale network structure. This in turn implies that the mesh size is mainly determined by the fraction of polymer, which thus is a key parameter for achieving high mechanical stability and high ionic conductivity simultaneously. We have previously shown that in this system the ionic conductivity is related to a fast diffusive process, the so-called collective diffusion [8–10]. However, the dynamics of the salt-free samples is at least three times faster than the corresponding electrolytes. This study shows that this slowing down is not due to changes in the large scale structure. Instead a plausible explanation is that the slower dynamics is due to the coordination between the cations and the carbonyl groups of the solvent molecules [29,30]. Such complexes should increase the local viscosity and therefore reduce the diffusion rate. Also note that dynamical experiments have shown that the relaxation time of the collective diffusion is almost identical for pure PC and mixtures of EC/PC, and thus changes in dynamics due to the different solvents in the samples is very small.
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This study shows that understanding the large scale structure is crucial for the development of new, improved polymer electrolytes. A key parameter for both structure and dynamics is the polymer concentration. Generally high polymer concentration yields improved mechanical stability but reduced ionic conductivity. However, an improved understanding of the network structure, combined with previous information of the dynamics, enables further optimization of the performance of the polymer gel electrolytes in applications such as batteries. 5. Conclusions We have shown that two length scales can be observed in PMMA-based polymer gels and polymer gel electrolytes, and that the structure of the polymer network is very similar for the two systems. The shorter characteristic distance is the polymer– polymer chain distance, for which we observe a power law dependence of the polymer-chain distance that indicates theta solvent conditions. At low wave vectors a significant excess scattering is observed, which is typical for gel systems. We argue that for this excess scattering is due polymer-rich regions that could acts as physical cross-links. Acknowledgements Financial support from the Swedish Research Council is gratefully acknowledged. Dr. Patrik Johansson is acknowledged for electron density calculations to determine the volumes of the molecules. The authors also would like to thank Prof. Kell Mortensen at Risø National Laboratory for valuable comments. References [1] P.-G. de Gennes, Scaling Concepts in Polymer Physics, Cornell University Press, London, 1979. [2] M. Doi, S.F. Edwards, The Theory of Polymer Dynamics, Oxford Science Publications, Oxford, 1986. [3] J. Bastide, S.J. Candau, in: J.P. Cohen-Addad (Ed.), Physical Properties of Polymeric Gels, John Wiley, Chichester, 1996, p. 143. [4] M. Shibayama, Spatial inhomogenity and dynamic fluctuations of polymer gels, Macromol. Chem. Phys. 199 (1998) 1. [5] J.T. Koberstein, C. Picot, H. Benoit, Polymer 26 (1985) 673. [6] B. Scrosati, Challenge of portable power, Nature 373 (1995) 557. [7] G.B. Appetecchi, F. Croce, B. Scrosati, Kinteics and stability of the lithium electrode in poly(methyl methacrylate)-based gel electrolytes, Electrochim. Acta 40 (1995) 991. [8] C. Svanberg, J. Adebahr, H. Ericson, L. B¨orjesson, L.M. Torell, B. Scrosati, Diffusive and segmental dynamics in polymer gel electrolytes, J. Chem. Phys. 111 (1999) 11216.
[9] C. Svanberg, J. Adebahr, R. Bergman, L. B¨orjesson, B. Scrosati, P. Jacobsson, Polymer concentration dependence of the dynamics in gel electrolytes, Solid State Ionics 136–137 (2000) 1147. [10] C. Svanberg, R. Bergman, L. B¨orjesson, P. Jacobsson, Diffusion of solvent/salt and segmental relaxation in polymer gel electrolytes, Electrochim. Acta 46 (2001) 1447. [11] J.S. Higgins, H.C. Benoit, Polymers and Neutron Scattering, Oxford University Press, Oxford, 1994. [12] J.P. Cohen-Addad (Ed.), Physical Properties of Polymeric Gels, John Wiley, Chichester, 1996. [13] G.W. Wignall, Y.B. Melnichenko, Recent applications of small-angle neutron scattering in strongly interacting soft condensed matter, Rep. Prog. Phys. 68 (2005) 1761. [14] P. Debye, A.M. Bueche, Scattering by an inhomogenous solid, J. Appl. Phys. 20 (1949) 518. [15] P. Debye, H.R. Anderson, H. Brumberger, Scattering by an inhomogenous solid. II. The correlation function and its application, J. Appl. Phys. 28 (1957) 679. [16] TITAN v1.0 using the default cut-off electron density 0.002 electrons/A˚ 3 . [17] D. Ostrovskii, A. Brodin, L.M. Torell, G.B. Appetecchi, B. Scrosati, Molecular and ionic interactions in polacrylonitrile- and poly(methylmetacrylate)-based gel electrolytes, J. Chem. Phys. 109 (1998) 7618. [18] J. Brandrup, E.H. Imergut (Eds.), Polymer Handbook, Wiley–Interscience, New York, 1989. [19] D.W. Schaefer, Polymer 25 (1984) 387. [20] D.W. Schaefer, C.C. Han, Quasielastic Light Scattering from Dilute and Semidilute Polymer Solution, Plenum Press, New York, 1985, p. 181. [21] S. Mallam, F. Horkay, A.M. Hecht, A.R. Rennie, E. Geissler, Microscopic and macroscopic thermodynamic observations in swollen poly(dimethylsiloxane) networks, Macromolecules 24 (1991) 543. [22] H. Berghams, A. Donkers, L. Fenay, W. Stoks, F.E. de Schryver, P. Moldenaers, J. Mewis, Thermoreversible gelation of syndiotactic poly(methyl methacrylate), Polymer 28 (1987) 97. [23] M. Berghmans, S. Thijs, M. Cornette, H. Berghmans, F.C. de Schryver, P. Moldenaers, J. Mewis, Thermoreversible gleation of solutions of syndiotactic poly(methyl methacrylate) in toluene: a two-step mechanism, Macromolecules 27 (1994) 7669. [24] J. Dybal, J. Spevacek, An investigation of the self-aggregation process of syndiotactic poly(methyl methacrylate) in solution by using infrared spectra, Macromol. Chem. 189 (1988) 2099. [25] B. Sedlacek, J. Spevacek, L. Mrkvickova, J. Stejskal, J. Horska, J. Baldrian, O. Quadrat, Aggregation of syndiotactic poly(methyl methacrylate) in dilute solutions, Macromolecules 17 (1984) 825. [26] N. Fazel, Z. Fazel, A. Brulet, J.M. Guenet, Molecular structure of polymethyl methacrylate thermoreversible gels, J. Phys. II 2 (1992) 1617. [27] K. te Nijenhuis, Thermoreversible Networks Viscoelastic Properties and Structure of Gels, vol. 130, Springer-Verlag, Berlin, 1997. [28] A. Keller, Introductory lecture: aspectes of polymer gels, Faraday Discuss. 101 (1995) 1. [29] J.-C. Soetens, C. Millot, B. Maigret, Molecular dynamics simulations of LiBF4 − in ethylene carbonate, propylene carbonate and dimethyl carbonate solvents, J. Phys. Chem. A 102 (1998) 1055. [30] P. Johansson, M. Edvardsson, J. Adebahr, P. Jacobsson, Mixed solvent and polymer coordination in PAN and PMMA gel polymer electrolytes studied by ab initio calculations and Raman spectroscopy, J. Phys. Chem. B 107 (2003) 12622.
Network structure of poly(methyl methacrylate)-based gels and gel electrolytes C. Svanberg a,∗ , W. Pyckhout-Hintzen b , L. B¨orjesson a a
Department of Applied Physics, Chalmers University of Technology, SE-412 96 G¨oteborg, Sweden b Institut f¨ ur Festk¨orperforschung, Forschungszentrum J¨ulich, D-52425 J¨ulich, Germany
Received 26 August 2005; received in revised form 25 November 2005; accepted 26 November 2005 Available online 6 January 2006
Abstract The large scale structure of poly(methyl methacrylate)-based gels and gel electrolytes has been investigated using small angle neutron scattering. ˚ while the larger is 200–300 A. ˚ Comparison between the The data reveal two different structural length scales: the shorter being typically 4–25 A, gel electrolytes, obtained by doping the gels with lithium salt, and the corresponding salt-free systems shows that the determined length scales are very similar. Thus the dissolved salt has only minor influence on the structure of the polymer network. We also discuss the important relations between structure, dynamics and the performance of the gel electrolytes. © 2005 Elsevier Ltd. All rights reserved. PACS: 61.41.+e; 82.70.Gg; 61.12.Ex Keywords: Gel electrolytes; Polymer; SANS; Structure; Physical cross-links
1. Introduction Polymer gels are viscoelastic materials that combines microscopic liquid-like dynamics with macroscopic mechanical stability. From a fundamental point of view it is of high interest to investigate the solvent and polymer dynamics in such inhomogeneous systems in order to determine the relation between structure and dynamics [1,2]. Experiments on the large scale structure have shown that in general at least two characteristic length scales are required to describe experimental data of polymer gels [3]. The shorter of these length scales is the polymer–polymer correlation length that is also observed in the corresponding non-cross-linked polymer solution [3]. At longer length scales, an excess scattering is generally observed for gel systems that is not present for the corresponding noncross-linked system. The excess scattering is therefore believed to be related to heterogeneity induced by the cross-links of the gels [4]. However, the details of the experimental observation differs between different types of gel systems [3] and is occasionally even influenced by the sample preparation procedure [5]. ∗
Corresponding author. Tel.: +46 31 772 31 78; fax: +46 31 772 20 90. E-mail address: [email protected] (C. Svanberg).
0013-4686/$ – see front matter © 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.electacta.2005.11.035
One application of polymer gels are as solid electrolytes suitable for high capacity polymer batteries [6]. An ion conducting polymer gel electrolyte can be obtained by mixing poly(methyl methacrylate) (PMMA) with a liquid electrolyte consisting of a lithium salt dissolved in ethylene carbonate (EC)/propylene carbonate (PC) [7]. To optimize the performance of gel electrolytes two factors are of utmost importance: the mechanical stability and the ionic conductivity. For PMMA-based gel electrolytes dynamical studies have revealed that the ion conduction mechanism is closely coupled to a diffusive relaxation process in the system [8–10]. The macroscopic mechanical strength on the other hand originates from the structure of the polymer network. Therefore, knowledge of the large scale structure of polymer gel electrolytes is essential for improving their performance. In this paper, we report, to the best of our knowledge, the first small angle neutron scattering (SANS) study of a polymer gel electrolyte. SANS is an experimental technique well suited to probe the structure of polymers over the range from a few up to ˚ several hundred Angstr¨ oms [11–13]. Of particular interest here is possibility to use deuterium labelling to enhance the contrast between the polymer and the solvent. This enables us to address the question of the concentration dependence of the distance between the polymer chains and the large scale heterogeneities in PMMA-based gels and gel electrolytes. By comparing gel elec-
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trolytes with the corresponding salt-free systems we show that the salt only has marginal effects on the large scale structure. Instead the key parameter is the polymer concentration dependence that determines the typical mesh size of the system. 2. Experimental In this study, syndiotactic and fully deuterated poly(methyl methacrylate) (PMMA) (MW = 1,587,000, Polymer Source Inc.) was used. Deuterated PMMA was used to achieve the desired contrast in scattering efficiency compared to the hydrogenous solvent and salt. The salt-free samples were prepared by mixing propylene carbonate (PC) with PMMA at room temperature. The salt-doped samples were prepared by first mixing ethylene carbonate (EC) with PC and then adding lithium perchlorate (LiClO4 ), with the ratios EC/PC/LiClO4 : 10/4/1. After a homogenous solution was obtained the polymer was added. All the samples were equilibrated at an elevated temperature, T = 390 K. Some of the samples were prepared directly in the sample cell, while others were prepared in test tubes and subsequently transferred to the sample cells. The sample preparation procedure was performed under argon atmosphere. The sample thickness was 1 mm and the samples were completely transparent with occasional argon bubbles trapped in some of the samples. The small angle neutron scattering (SANS) experiments were performed at the small angle neutron diffractometer KSW1 at FZ J¨ulich, Germany. Experimental details of neutron scattering in general, and SANS in particular, are given in Refs. [11–13]. ˚ was used and In our experiments an incident wavelength of 7 A two sample-detector distances, 2 and 8 m, enables us to cover ˚ −1 < Q < 0.15 A ˚ −1 . the momentum transfer range of 0.006 A All the experiments were performed at room temperature. The data were corrected according to standard procedures; empty cell subtraction, background subtraction and intensity calibration using a polyethylene standard. The incoherent background scattering, obtained from reference sample consisting of hydrogenated PC and PMMA, was also subtracted. However, the presence of argon-bubbles in some samples increase the uncertainty of the absolute values of I(Q) of those samples. We will therefore in this paper refrain from comparing the absolute values of the scattered intensity.
Fig. 1. Intensity vs. wave vector for samples with and without salt. Filled symbols correspond to salt-doped system and open symbols are salt-free. The circles are for two samples with roughly 30% PMMA and the triangles around 10%. The lines are curve-fits to the experimental data using Eq. (1). The data for the 30% samples are vertically shifted for clarity.
for both polymer gels and gel electrolytes. The first term in Eq. (1) is a so-called Ornstein–Zernike (OZ) function [3,4]. The Ornstein–Zernike function describes the data at large values of Q, i.e. short distances, with ξ as the characteristic size of fluctuations in polymer concentration [3]. The second term in Eq. (1) is a so-called Debye–Bueche (DB) function [3,4,14,15]. The Debye–Bueche function was originally derived for a medium with two species randomly distributed and is here used to describe large scale non-homogeneities with a as the characteristic length scale. Eq. (1) has previously been used to describe polystyrene gels [5] and gives a good description of our experimental data. However, for some of the samples the experimental accuracy and reproducibility are not completely satisfactorily at low Q, which is probably due to the sample preparation proce˚ and systemdure. We observe that ξ is in the range of 4–25 A atically decreases with increasing polymer concentration. The ˚ and without any obtained values of a are in the range 200–300 A significant changes with polymer concentration. However, these values are close to the lower limit of our experimental range and therefore somewhat uncertain.
3. Results 4. Discussion In Fig. 1 the scattered intensity of two salt-free gels are compared with two gel electrolytes with similar polymer concentrations. The figure clearly shows two distinct regions with large decrease in intensity, which is typical for polymer gels, and that the scattering functions are very similar for the two systems. This implies that the interpretation established for SANS experiments on standard polymer gels (see Ref. [12] and references therein) can be applied also to polymer gel electrolytes. As seen in Fig. 1 the scattering intensity is well described by I(Q) =
I1 I2 a3 + 1 + Q2 ξ 2 (1 + Q2 a2 )2
(1)
In order to be able to compare the polymer concentration dependence of the length scales with theoretical predictions it is often more straightforward to use volume percent than weight percent. We therefore used semi-empirical electron density calculations in order to, at least approximately, describe the volume ratios of the components in the system [16]. The volumes ob˚ 3 , VPC = 114 tained from the calculations are: VPMMA = 155 A 3 3 3 ˚ , VEC = 93 A ˚ and VLi+ClO4 = 88 A ˚ . The PMMA volume is A calculated for the monomer and the salt volume is the sum of the ion volumes, since previous Raman experiments have shown that ion pairs are scarce in the present gel electrolyte system [17].
C. Svanberg et al. / Electrochimica Acta 51 (2006) 4153–4156
Fig. 2. Curve-fit parameters ξ (circles) and a (squares) as a function of volume fraction polymer. Salt-doped samples are marked with a cross. The full line is the relation ξ = ξp ϕ−s discussed in the text.
In Fig. 2 we show ξ and a as a function of the calculated volume fraction of PMMA, ϕ. In accordance with previous studies of both polymer gels and polymer solutions we attribute the shorter length scale, ξ, to the polymer–polymer correlation length, see Ref. [12] and references therein. We observe, as expected, a marked decrease of ξ with increasing polymer content. Using scaling arguments de Gennes [1] predicted a power law behavior in the semi-dilute regime between the correlation length ξ and the volume fraction ϕ of polymer ξ = ξp ϕ−s
(2)
where ξp is the distance extrapolated to the pure polymer. The power law behavior can be understood by modeling the semidilute polymer solution as closely packed solvent domains separated by the polymer network, where ξ is the average size of the domains [1]. The exponent s in Eq. (2) is related to the fractal 1 dimension df of the polymer chains at infinite dilution s = 3−d f [12]. The curve-fit of Eq. (2) to the experimental data for the salt˚ Comfree samples yields s = 1.0 ± 0.1 and ξp = 3.0 ± 0.5 A. paring the solubility parameters for PC and PMMA with those of for example PMMA and toluene [18] implies that the PC is a good solvent for PMMA and therefore that s should be 3/4. However, according to the theoretical work by Schaefer et al. [19,20] a theta solvent behavior, i.e. s = 1, is expected at high polymer concentrations due to the appearance of ternary junctions between the polymer chains. We also note that s equal to unity has been reported previously for other gel systems [21]. At low wave vectors we observe a second contribution as previously observed for cross-linked gel systems [12]. However, a generally accepted explanation of this excess scattering is still lacking [12]. The excess scattering we observe is best described by the Debye–Bueche function, which was originally derived as the scattering of a random two phase system [14,15]. In the
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PMMA-gels investigated here such large scale heterogeneities must be caused by fluctuations in the polymer concentration. In the present system there are no permanent chemical bonds, but syndiotactic PMMA can form helices that can that evolve into small crystalline structures [22–26]. Potentially such regions could acts as physical cross-links. Another idea is that locally vitrified regions hinders the chains from disentangle [27,28]. In either case these regions have a different concentration and density than the rest of the sample and therefore can be observed in a SANS experiment. This is in contrast to chemical gels, with permanent bonds between the polymer chains, where the excess scattering normally is not observed, although it can be observed after swelling or deswelling [4]. Another important observation is that, within the experimental uncertainty, the larger length scale is independent of polymer concentration. This is in distinct contrast to the macroscopic viscosity that dramatically increases with polymer concentrations. It thus appears as the large length scale observed here is only a prerequisite for the mechanical stability of the system. Also parameters such as the number of different chains in one cross-link and their lifetime could be of importance for the macroscopic viscosity. Furthermore, an alternative idea is that this large scales structure could be related to some of the slower process observable in dynamic light scattering experiments, but this requires further studies. Establishing the true physical origin of the excess scattering at low wave vectors is indeed central for our understanding of the network structure in polymer gels and thus also polymer gel electrolytes. Concerning gel electrolytes the introduction of salt in general changes the electrochemical properties, which could also effect the network structure. However, the data looks very similar for both systems and the same curve-fit procedure can be applied. Furthermore, the obtained length scales are similar for samples with and without salt, as seen in Fig. 2. We therefore make the same attribution for the polymer gel electrolytes as for the salt-free systems: the shorter scale to the polymer–polymer correlation length and the larger length scale to polymer-rich regions. We also conclude that the introduction of ions in the system has only minor effects on the medium and large scale network structure. This in turn implies that the mesh size is mainly determined by the fraction of polymer, which thus is a key parameter for achieving high mechanical stability and high ionic conductivity simultaneously. We have previously shown that in this system the ionic conductivity is related to a fast diffusive process, the so-called collective diffusion [8–10]. However, the dynamics of the salt-free samples is at least three times faster than the corresponding electrolytes. This study shows that this slowing down is not due to changes in the large scale structure. Instead a plausible explanation is that the slower dynamics is due to the coordination between the cations and the carbonyl groups of the solvent molecules [29,30]. Such complexes should increase the local viscosity and therefore reduce the diffusion rate. Also note that dynamical experiments have shown that the relaxation time of the collective diffusion is almost identical for pure PC and mixtures of EC/PC, and thus changes in dynamics due to the different solvents in the samples is very small.
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This study shows that understanding the large scale structure is crucial for the development of new, improved polymer electrolytes. A key parameter for both structure and dynamics is the polymer concentration. Generally high polymer concentration yields improved mechanical stability but reduced ionic conductivity. However, an improved understanding of the network structure, combined with previous information of the dynamics, enables further optimization of the performance of the polymer gel electrolytes in applications such as batteries. 5. Conclusions We have shown that two length scales can be observed in PMMA-based polymer gels and polymer gel electrolytes, and that the structure of the polymer network is very similar for the two systems. The shorter characteristic distance is the polymer– polymer chain distance, for which we observe a power law dependence of the polymer-chain distance that indicates theta solvent conditions. At low wave vectors a significant excess scattering is observed, which is typical for gel systems. We argue that for this excess scattering is due polymer-rich regions that could acts as physical cross-links. Acknowledgements Financial support from the Swedish Research Council is gratefully acknowledged. Dr. Patrik Johansson is acknowledged for electron density calculations to determine the volumes of the molecules. The authors also would like to thank Prof. Kell Mortensen at Risø National Laboratory for valuable comments. References [1] P.-G. de Gennes, Scaling Concepts in Polymer Physics, Cornell University Press, London, 1979. [2] M. Doi, S.F. Edwards, The Theory of Polymer Dynamics, Oxford Science Publications, Oxford, 1986. [3] J. Bastide, S.J. Candau, in: J.P. Cohen-Addad (Ed.), Physical Properties of Polymeric Gels, John Wiley, Chichester, 1996, p. 143. [4] M. Shibayama, Spatial inhomogenity and dynamic fluctuations of polymer gels, Macromol. Chem. Phys. 199 (1998) 1. [5] J.T. Koberstein, C. Picot, H. Benoit, Polymer 26 (1985) 673. [6] B. Scrosati, Challenge of portable power, Nature 373 (1995) 557. [7] G.B. Appetecchi, F. Croce, B. Scrosati, Kinteics and stability of the lithium electrode in poly(methyl methacrylate)-based gel electrolytes, Electrochim. Acta 40 (1995) 991. [8] C. Svanberg, J. Adebahr, H. Ericson, L. B¨orjesson, L.M. Torell, B. Scrosati, Diffusive and segmental dynamics in polymer gel electrolytes, J. Chem. Phys. 111 (1999) 11216.
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