Conformations and Vibrations in Polymer Electrolytes
by Patrik Johansson
Dissertation for the Degree of Doctor of Philosophy in Inorganic Chemistry presented at Uppsala University in 1998
Abstract
Johansson, P. 1998. Conformations and Vibrations in Polymer Electrolytes. Acta Univ. Ups. Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 366. 56 pp. Uppsala. ISBN 91-554-4216-1.
Solvent-free solid electrolytes can be formed by dissolving a salt in a polymer matrix (e.g. poly (ethylene oxide), PEO). Such compounds are of interest due to their proposed use as solid electrolytes in new types of electrochemical devices e.g. all solid-state thin-film lithium polymer batteries for the consumer electronics market.
Polymer electrolytes are highly complex materials. The present work has used vibrational spectroscopy in combination with ab initio quantum mechanical calculations to assign vibrational spectra and to study conformational changes in the polymer matrix and the dissolved species.
PEO based polymer electrolytes are often multi-phase systems, which is regarded as a major problem since the cations (lithium ions) are conducted only in the amorphous phase, while the crystalline phases can only serve as salt reservoirs. Therefore liquid model compounds, methyl end-capped oligomers of PEO, known as "glymes", have been used to facilitate both the experimental as well as the computational part of the investigation.
In an ideal polymer electrolyte the cations are conducted by means of the segmental motion of the polymer host while the anions are thought to diffuse freely using free space created in the polymer matrix. The cation-polymer complex formation and cation transport have been modelled and features in the vibrational spectra arising from the formation of local salt-polymer complexes have been explained. The internal flexibility, stable structures and the vibrational spectra of the often used TFSI anion, [(CF3SO2)2N-], and the corresponding acid HTFSI have been investigated.
A molecular level model for lithium ion transport in PEO based on transition state theory is outlined where an ion transport can be envisaged which requires low energy.
Patrik Johansson, Ångström Laboratory, Inorganic Chemistry, Uppsala University, Box 538, SE-751 21 Uppsala, Sweden
Copyrigth Patrik Johansson 1998
ISSN 1104-232X
ISBN 91-554-4216-1
Printed in Sweden by Eklundshofs Grafiska AB, Uppsala 1998
Word of Wisdom
In emptiness there is good but no evil. Wisdom exists, logic exists, the Way exists, mind is empty.
Miyamoto Musashi, 1645
Preface
This thesis comprises the present summary and the following publications which are referred to in the text by their Roman numerals.
New materials have always been the forerunners of the technical achievements of mankind. In the modern society these new materials become more sophisticated and are especially designed to enhance specific properties and meet the requirements of highly specialised devices. In the energy storage area very few new materials have found practical applications since the construction of a battery [1]. The proposed fabrication of an all solid-state thin-film battery clearly requires new types of materials, involving the electrodes as well as the electrolyte, although solid electrolytes were already considered by Faraday in 1838 [2]. An inorganic salt dissolved in a polymer matrix, a polymer electrolyte or a solid polymer electrolyte, SPE, provides one possible solid electrolyte concept with several advantages as compared to liquid or other solid electrolytes [3]. These new materials may also pave the way for some new applications never before imagined except in science fiction novels, e.g. electrochromic windows [4].
Ever since the discovery of the poly (ethylene oxide), PEO, polymer's ability to dissolve inorganic salts [5-8] and the launching of its proposed use in all solid-state thin-film batteries [9,10], there has been extensive research in the area of (PEO) SPE's and their applications. For general articles, reviews and books see references 1 and 11-25.
This thesis will treat the basic aspects of SPE's and their constituents, focusing on PEO, its analogues and the lithium salts used. The nature of the local environments of the dissolved species and how the polymer matrix on a molecular level is changed when dissolving a salt will be the main issues addressed. Therefore, knowledge of the local surrounding of the dissolved salt species is of primary importance and vibrational spectroscopy is a highly viable experimental tool for analysis of SPE's. Small shifts and/or splittings in vibrational bands can be detected and studied as function of temperature, concentration, cation, anion, polymer chain length, additives...etc.
In this work experimental observations are correlated with ab initio quantum mechanical (QM) calculations to assist in the interpretation of changes in spectra. Furthermore, these QM calculations are used on an independent basis to propose a mechanism for lithium ion transport in PEO based SPE's, a phenomenon which still has not been fully clarified and still lacks a basic understanding on a molecular level. Clearly, the development in the area of SPE's has reached beyond the original PEO systems. The usefulness of the present studies for these new concepts and materials will be discussed.
2.1 General concepts
When a salt is dissolved into a polymer matrix, a solid polymer electrolyte, SPE, is formed. To make these SPE's, the salts used are often of low-lattice energy and the polymer matrix must be polar, at least locally. The free energy change of dissolving a salt can be written:
D
Gm = DHm - TDSm ; if DGm < 0 spontaneous reaction (1)The mixing entropy, DSm, consists of two main components: translational entropy and configurational entropy. The introduction of salt reduces the freedom of the polymer chain motion, via the formation of cation-polymer bonds, and therefore causes a reduction in translational entropy. The flexibility of the polymer on the other hand, provides the possibility to adopt several conformations suitable for multidentate cation coordination which may contribute with a positive configurational entropy. At first, it was believed that the total entropy of solvation was always likely to be positive [26]. However, SPE's have been observed to behave in an opposite way to most liquid electrolytes as a function of temperature. Salt precipitation has been observed when increasing the temperature, an indication of a negative entropy contribution to the solvation [27].
The mixing enthalpy, DHm, includes the starting components' lattice energies, the Coulombic ion-ion interaction energy and the ion solvation energy. A spontaneous solvation, i.e. a negative DGm, often requires a salt of low lattice energy which can be overcome by the ion-solvent interactions. However, although the laws of thermodynamics can be applied to some extent on these materials, the materials' kinetics are extremely slow, and equilibrium can require, depending on the preparation method, years to reach [28].
In an ideal SPE, the dissolved cations bind electrostatically to the polymer backbone and the anions are believed to diffuse more or less freely in the matrix. In non-ideal materials ion-pairs or more complex species might form (Fig. 2.1). The plan of study in this thesis is to choose the polymer and salt so as to minimise the ion-pairing, and thus to be able to study the cation-polymer complex formation in these complexes independently of the dissolved anion. By doing so, the anion can also be studied independently.
Figure 2.1 : Schematic representation of possible local interactions in a polymer electrolyte. A: dissolved "free" anion, B: cation-polymer complex and C: contact ion-pair [29].
This is also a general goal in the search for good SPE's - high transport numbers for the cation being of primary importance, local cell concentrations are avoided to ensure a high ionic conductivity. The ion conduction mechanisms of the anion and cation clearly differ; the anion diffuses more or less freely, while the cation is believed to "hop" between polymer chains and between "hops" use the segmental motion of the polymer while temporarily bonded. The possible conformations (Latin conformatio = any spatial arrangement of atoms in a molecule derived from the rotation of part of the molecule about a single bond) of the polymer in the cation-polymer complexes locally obtained are of importance for the solvation as stated above in eq. (1), as well as for the cation conduction mechanism.
2.2 Polymers
2.2.1 PEO
The archetype polymer in SPE studies is poly (ethylene oxide), PEO, (-CH2CH2O-)n [30]. The use of PEO relies on the solvating power of the -CH2CH2O- units and its high chemical and thermal stability. PEO itself is stable up to 350°C in the absence of O2 [31]. The PEO polymer chain is highly flexible, i.e. it contains no double bonds, and it can therefore coordinate various alkali-metal, alkaline-earth-metal, transition-metal and lanthanide ions in a remarkably tight fashion by the ether oxygens' electron lone pairs [15]. The concentration of the electron lone pairs (~1022 cm-3) and the polarisability of the ether groups gives it properties resembling those of water [24,32]. However, when acting as a ligand the coordination strength of the polyether might be expected to be enhanced due to the multidentate nature and the flexibility of the polymer chain. Several low energy conformations can be adopted, exact appearances and relative amounts depending on the cation coordinated.
However, the flexibility, which clearly governs some of the highly desirable properties of this polymer, does have the disadvantage that PEO based systems are prone to crystallisation [33], which is prominent in pure PEO, and reaches a crystallinity maximum of ~95 % for Mw= 6000 Daltons [34]. Above this Mw the long range disorder entanglement efficiently prevents the same magnitude of crystallisation. The multi-phase nature of PEO is most often regarded as a major problem in real working systems, since the ion conduction has been shown to take place mainly in the amorphous phase [35]. Furthermore, the same is true for the study of specific properties, where the effect of a variable can be concealed by the changes in the relative amounts of each phase.
Figure 2.2 : PEO viewed perpendicular to the crystalline helix.
Several crystal structures of alkali-metal complexes MXPEOn have been determined, all with high salt concentrations (n=3,4) [36-42] and also the crystal structure of long chain PEO itself [33,43] (Table 1). All crystallise in helical structures, with the geometry and chain conformation varying both depending on the nature of the cation and anion. Some general tendencies are evident from these studies; the anion never interacts directly with the polymer chain in any of these structures, nor does any cation coordinate to more than one PEO helix strand. No cation has a higher coordination number (CN) than 7 and for lithium CN is equal to 5.
Table 1 : Crystal structure determinations of MXPEOn, n = 3,4 and pure PEO.
|
Structural formula |
CN of M+ |
Conformation sequence of PEO (with respect to O-C-C-O)* |
Reference |
|
PEO |
- |
aG+aaG+a |
33,43 |
|
NaIPEO3 |
5 |
aG+aaG+aaGa |
36 |
|
NaClO4PEO3 |
6 |
aG+aaG+aaGa |
37 |
|
NaSCNPEO3 |
5 |
aG+aaG+aaGa |
38 |
|
LiCF3SO3PEO3 |
5 |
aG+aaG+aaGa |
39 |
|
KSCNPEO4 |
7 |
aG+aaG+aaGaaGa |
40 |
|
NH4SCNPEO4 |
7 |
aG+aaG+aaGaaGa |
40 |
|
RbSCNPEO4 |
7 |
aG+aaG+aaGaaGa |
41 |
|
LiN(CF3SO2)2PEO3 |
5 |
aG+aaG+aaGa |
42 |
* Note: a denoting an anti arrangement, G+ a gauche and G a gauche in opposite direction with respect to G+. For further explanation see section 5.1.1
However, little is known of the "structure" in the amorphous phase; a notable exception is the study of amorphous LiCF3SO3PEO3 by Frech et al. [44]. This is especially true for lower salt concentrations (higher O/M ratios), which more closely resemble real working systems. For these most of the structural work has been done indirectly using vibrational spectroscopy [45-47] and NMR [35,48]. An exception is an interesting report on using neutrons to study LiIPEO5, although this represents a high salt concentration [49]. The limitation is often the occurrence of a crystalline PEO phase at these lower concentrations. Therefore, in order to study the conformation of amorphous PEO and the complexation of lithium ions in such systems, suitable model compounds for PEO have been used - the so-called "glymes".
2.2.2 Glymes
A number of compounds with the general formula, CH3-O-(CH2CH2O)n-CH3, n=1-6, are more well-known as glymes (glyme = glycol dimethyl ether). These homologues (oligomers) of PEO are liquids at room temperature, i.e. they contain no crystalline phases, and can therefore be used as model systems for long chain PEO, without the risk of crystallisation, at least at ambient temperature and, in polymer electrolyte studies, for reasonable salt concentrations.
However, the usefulness of glymes to model the ionic conductivity of SPE's is limited, since the oligomers can self-diffuse in a liquid-like manner while incorporating a cation [27,50], and the long chain PEO cannot. This is due to the chain entanglement limit of PEO at approximately 3000 Daltons as predicted by de Gennes [51,52]. However, to reveal the local interactions between the ether oxygens in PEO and the solvated cation, glymes can be extremely useful. Their limited size further provides the possibility to perform high-quality quantum mechanical calculations, to an extent not possible for long-chain PEO. In this thesis diglyme, n=2, has been the most studied glyme (Fig. 2.3).
Figure 2.3 : The diglyme molecule coordinating a lithium ion (see also [53]).
Diglyme is the shortest homologue of PEO which is useful for the purpose of studying cation coordination since none of the crystalline MXPEOn structures has a cation CN of ether oxygens lower than three and moreover it crystallises in the same conformation as long-chain PEO [54]. In the present thesis, its conformational states, "chain geometry", have been studied, both using vibrational spectroscopy (I) and QM calculations (II and VI). The results and the knowledge from the diglyme studies have subsequently been applied to longer glymes for a more reasonable total CN (see Table 1) for the cation in more dilute systems (III and VII). There are numerous crystalline structures determined for complexes of the glymes, and for the -OH terminated homologues - the glycols, with divalent and trivalent cations [55,56], but no crystal structure determination with lithium as the coordinating cation exists.
Some of the glymes have been thoroughly examined for use in liquid electrolyte mixtures [57]. They have also been used as additives in so-called gel-polymer electrolytes, where they can coordinate the cations as a (co-)solvent in an almost rigid 3D polymer network [58]. Their role in such systems is to act as carrier/shell for the cation in a liquid manner. However, this aspect will not be discussed in this thesis.
2.2.3 Other polymers
Although PEO/lithium salt mixtures have been by far the most common systems studied, several other polymers or co-polymers are regarded as possible fruitful alternatives. Examples include poly (propylene oxide), PPO [9], poly (vinyl chloride), PVC [59], polyether-urethanes [60] and many more. However, none of these appear to have the same ability to solvate salts as PEO, unless they in some way include PEO in units longer than 4 EO monomers as sidechains or copolymers in their structure [24]. Another approach is to include a secondary solvent (e.g. glymes) in the polymer matrix to facilitate solvation and conduction.
An interesting line of work is on PEO-PPO-PEO copolymers where PPO prevents crystallisation, while PEO coordinates and participates in conduction [32,61]. To summarise: in these and in general classical SPE's, the ion conduction and solvation still rely on the ethylene oxide units. This emphasises the need for basic research on PEO systems although the pure PEO/lithium salt mixtures probably never will be the SPE of choice in most applications due to their low ion conductivity at room-temperature [21].
2.3 Salts
2.3.1 Which salts and why ?
When reviewing the field of SPE's, the dominant use of lithium salts is obvious. The reason is the proposed use of these salts in the all solid-state thin-film batteries where lithium provides the largest possible potential window. Also it is the lightest of all metals, providing high gravimetric Coulombic density despite the low transition number of one electron per lithium atom. For the reaction:
2 Li + F2 - 2 LiF (2)
the cell voltage is theoretically ~6 V [62]. In practice other components than F2 are used, but still a cell voltage above 3 V is easily reached. The anode, previously often pure lithium metal, now is often a carbon-based intercalation compound which prevents some mortal phenomena to occur i.e. dendrite growth of lithium which would result in a short-circuit. Lithium is the obvious choice of cation, although work considering sodium have also received attention [47,63].
The ionic conductivity, s, for a dilute homogenous system at a given temperature, can generally be expressed as:
s
= S niqiµi (3)where ni is the number of charge carriers i, qi their charge and µi their mobility. The ionic conductivity should thus increase with salt concentration, if all dissolved species were to carry charge at the same rate as for lower concentrations. However, this is not true in SPE's as increasing the concentration leads to formation of neutral ion-pairs which are insensitive to the applied field (reduced ni) and in addition higher aggregates, e.g. triplets, although charged, should move slower due to their higher mass. At the same time, the cations that coordinate the ether oxygens of the polymer chains cause the polymer chains to "stiffen". This decreases the number of free sites along the chains available for further coordination, which decreases µi. Furthermore, equation (3) is valid when the system is dilute and this is not the case for a general polymer electrolyte as shown below.
One way to enhance the ionic conductivity, is by using anions that do not easily form ion-pairs - which results in a large number of solvated charge carriers, even at modest concentrations. The salt used still must have a low enough lattice energy to fulfill eq. (1). Here "modest" concentrations, O/M=20-40, would be regarded as fairly high concentrations in any aqueous system - ~1-0.5 M. This fact (and the occurrence of ion-pairs in non-ideal systems) has resulted in a debate on whether the polymer-salt mixtures should be regarded as strong or weak electrolytes [64].
The charge density of the anion should be low to reduce the number of ion-pairs with lithium. The ion conductivity increases for a given cation (i.e. lithium) in the series:
F < Cl < Br < I < ClO4 < CF3SO3 (triflate) < [(CF3SO2)2N] (TFSI) [32]
Because of the need for even more non-coordinating anions the current attention is mainly focused on large anions with an extensively delocalised negative charge. These are in many cases derived from the triflate anion and their lithium salts provide even higher ionic conductivities. One of the most prominent among them is the "imide" or TFSI anion.
2.3.2 The TFSI anion
The "imide" or the "double triflate" ion, [(CF3SO2)2N], more accurately named bis-(trifluoromethanesulphone) imide ion, for short TFSI, (Fig. 2.4), was synthesised [65] and first used in the SPE field [66-68] with the explicit purpose of being extremely non-coordinating. Another unforeseen advantage in SPE systems was discovered later: the anion prevented crystallisation - acted as a plasticiser, a property attributed to the large size and internal flexibility of the ion (apart from the cations being "free" and able to coordinate the ether oxygens). This is a major advantage since tendencies of crystallisation can be observed in almost all salt/PEO systems. In line with the previous discussion on the cation, the lithium salt of the anion is a most interesting compound in the context of polymer electrolytes. The LiTFSI salt is a white, highly hygroscopic powder with a melting point of 234°C [65]. The phase diagram for LiN(CF3SO2)2PEOn, MwPEO=4000 Daltons, was determined by Vallée et al. [65]. In the phase diagram the most striking feature is the crystallinity gap for 6 < n < 12 where these concentrations provide the best ionic conductivity in these systems - up to 4×10-5 S cm-1 at 25°C [65].
Figure 2.4 : The TFSI anion in its C1 conformation as calculated in IV.
As the main purpose of introducing this anion was to avoid formation of ion-pairs and since this could be coupled to the enhanced ionic conductivity, the effect of ion-pair formation would be of interest to detect. The TFSI anion might form ion-pairs with lithium in several ways due to the highly delocalised negative charge of the anion. However, the effect of such ion-pairing had not been observed until recently. These results provide evidence for LiTFSI ion-pairing by vibrational spectroscopy [69,70] and examples of geometries of such ion-pairs through quantum mechanical calculations [71]. Vibrational spectroscopy, both infrared and Raman, provides the means to distinguish between ion-pairs and "free" anions, and larger aggregates, as shown for many SPE's of both PEO and other polymers. Therefore, in this thesis a combined experimental (vibrational spectroscopy) and computational (ab initio quantum mechanical) study was undertaken to clarify the assignments of the observed bands and to analyse the possible presence of ion-pairs (V). The internal flexibility, believed to be one of the reasons for the plasticising effect of the anion, was also examined by an ab initio study (IV). The approach of a combined vibrational spectroscopy and computational study has also been used for the next anion in the series of compounds with the formula [(CxFySO2)2N] - the PFSI anion, x=2 and y=5 [72].
2.4 Ion transport
Almost ever since the first mixing of PEO with a lithium salt there has been controversy about and interest in the ion transport in these systems. During the first years the ion conduction was believed to take place mainly in the crystalline phase, inside the PEO helices [9,73]. Later it was realised that the amorphous phase was the main contributor to the ion conduction [35] - whereas the crystalline phases are basically insulators. This discovery raised new questions about the ion conduction mechanism and how to best describe it. Regardless whether it should be described as liquid-like [15] or use the concept of an immobile solvent [74], the fact is that the description of mass transfer in an electrolytic solution is complex [75]. As was suggested by NMR and DSC experiments coupled to ionic conductivity measurements, the cations coordinate the polymer chains, making the chains stiffer. This reduces the segmental motion [76], raises the glass transition temperature, Tg and increases viscosity [26,77]. This leads to a drop in ionic conductivity at high salt concentrations [78] which primarily is attributed to the increase in Tg [79], apart from the formation of ion-pairs [16]. Thus the long range charge transport of cations is believed to be intimately coupled to the segmental motion of the polymer [80-82], although the contribution to the overall ionic conductivity differs due to the species present [83]. However, there still is no general mechanistic description on a molecular level.
The dynamic bond percolation theory (DBPT) is one approach generally considered to be applicable - for a review see ref. 18 [84-87]. The ion transport as interpreted in the DBPT for SPE's is performed through the making and breaking of cation-ether oxygen bonds/interactions by the segmental motion of the polymer. Proton NMR measurements further suggest that the indirectly observed activation energy, Ea, relates to rotational barriers in the polymer chain [88] and furthermore that it is confined to a small part of that chain [89]. Thus the labile cation-polymer bond is a necessary condition for long-range cation transport, and the cation transport is mainly dependent on the local surroundings of the ion.
The anions, with only weak interactions with the polymer host, are generally believed to diffuse more or less freely in the matrix using free spaces created by the segmental motion of the polymer. Also here the DBPT together with free volume theory can be applied. As high a transference number as 0.71 has been observed for TFSI which is an indirect proof of the small interaction with the polymer (and for TFSI - with the cation) [90-92]. Much less attention has been directed to the transport of anions than to that of the cations, perhaps due to this apparent simplicity. Similarly, the anion transport has not been in the focus for this thesis.
However, to interpret ion transport processes only in terms of discrete species is undoubtedly an oversimplification.
2.5 New concepts
Not only new salts and new polymers are used in the search for the "perfect" SPE's, but moreover the whole concept of what constitutes a polymer electrolyte is being revised. Comb-polymers [93], nanocomposites [94], anion "trapping" groups in the polymer chain [95], rubbery polymer-in-salt systems [96,97] and xerogel materials [98] are just a few of these new concepts. Their way of enhancing the ionic conductivity is multifaceted and only a few examples will be given here to show the diversity. Incorporating boroxine rings (B3O3) in the PEO chain which coordinate the anions strongly via B-X bonds leaves the lithium ions "free", resulting in high cation transference numbers (t+=0.88) [95]. The ion conduction mechanism itself can be altered as in the case of nanocomposites, where the negative charge is being dispersed over the anionic lattice [94], resulting in weaker interaction with the cations and an increased value of µi in eq. (3).
However, most of these promising SPE concepts still contain ethylene oxide units as the cation promoting part of the materials. From this point of view the need for a thorough knowledge of the "simple and old-fashioned" PEO systems still remain of utmost importance.
3. Experimental techniques
In the study of the properties of SPE's it is clear that there is a need for several different techniques of analysis due to the complexity of these materials. Many phenomena have to be understood: crystallinity, local structure, which species are present, the glass transition temperature, diffusion, mobility of ions, flexibility, thermal and electrochemical stability, ionic conductivity...etc. Many of these properties can be analysed using different spectroscopic methods. In particular vibrational spectroscopy provides invaluable information which forms a major part of this thesis.
3.1 Vibrational spectroscopy
3.1.1 General
One of the main techniques for analysis of SPE's has been and still is vibrational spectroscopy. Here a brief introduction will be given to the properties suitable for analysis of polymer electrolytes using infrared (IR) and Raman techniques. Also some general vibrational theory will be briefly described.
Traditionally, vibrational spectroscopy has been used to investigate the nature of species present in the polymer electrolytes. In particular, by observing shifts and/or splittings in bands originating from the anions of the added salts [99,100] one can distinguish between dissolved "free" anions, ion-pairs (contact or solvent-separated) and higher aggregates e.g. triplets [101,102]. Quantum mechanical calculations of vibrational spectra for the anions and the ion-pairs [103-105] and isotopic substitutions [106] can facilitate the interpretation of the observed spectra.
Additional information can be obtained by analysing bands arising from the polymer to clarify if and how the cation interacts with the ether oxygens of the polymer backbone or in relevant cases the oxygens from the -OH or -OCH3 ends. Here the C-O-C stretching bands at ~1100 cm-1 have been most useful [45,107,108] together with the relevant end-group bands [45,109,110].
Conformational changes of the polymer when a salt is dissolved have been analysed via changes in the CH2-rocking and wagging bands in the lower wavenumber region 1000 cm-1 to about 800 cm-1 [111-113]. These bands arise from normal modes with contributions also from C-C and C-O stretchings and are complex to analyse, but may give important information about the materials.
Vibrational spectroscopy can also be used when crystalline and amorphous phases are found simultaneously in a material; heating PEO above Tm (~66°C) [114] clearly eliminates the bands present from the crystalline PEO phase and a fingerprint of the amorphous phase can thus be obtained. Of course changing the temperature can induce other changes (e.g. ion-pair formation) in the system of interest as well.
Although many useful observations can be made using vibrational spectroscopy at least two important points should be considered:
i) The measured spectra are related to the time-scale of the experiment (ps) which is vastly different from the conformational changes (µs) - only superimposed spectra of the different conformers can be obtained. Therefore, it is not necessarily so that the ion conduction in the systems in a direct manner relate to the coordination/conformation situations found by spectroscopy.
ii) There exists substantial controversy on how to interpret ion-pairs. The ionic conductivity may drop drastically when increasing the salt concentration without any bands from contact ion-pairs arising in the vibrational spectra. Solvent-separated ion-pairs should be considered.
3.1.2 Infrared Spectroscopy
Molecular spectroscopy is the study of the absorption or emission of electromagnetic radiation by molecules. Intensities and frequencies are obtained as experimental data which then is interpreted as molecular changes in the irradiated sample. Specifically, vibrational spectroscopy relates to changes in the vibrational energy of the molecule.
Classically, the vibration of a single atom can be seen as a displacement x from its equilibrium position which changes its potential energy U as a harmonic oscillator:
U=1/2×kx2 (4)
Of course this is not completely true; if a bond is stretched far enough it will break, thus the vibration is really anharmonic making the potential energy curve more complex, which will have implications when compared to quantum mechanical calculations (see 4.2.4). Neither can the vibrational energy take any continuous value, a true quantum mechanical treatment gives discrete values. In IR spectroscopy the electromagnetic radiation is infrared light of a frequency n which interacts with the sample as:
D
E = hn (5)where DE is a discrete energy difference between two vibrational states. This should lead to infinitely narrow bands in the spectra obtained. In reality the rotational energy levels are superimposed on the vibrational ones in the gas phase, and a Doppler broadening effect can be seen. In condensed samples the interactions within the medium give a broadening often much larger than 2 cm-1 (a resolution often used in spectroscopic measurements). The intensity of a band relates to the population of a certain vibrational state, the change in molecular dipole moment and the number of molecules vibrating at that frequency (i.e. having the same energy, geometry and environment).
The vibration responsible for the interaction with the radiation must cause a change in the dipole moment of the molecule to be IR active. Group theory can specify which modes will be IR active, as this is a result of the symmetry of the molecule and of the type of vibration. An analysis of how many normal coordinates that belong to the various symmetry species determines the number of infrared active fundamental transitions that can occur for a molecule of a given symmetry.
The equipment used for all IR measurements in I was a Bio-Rad FTS 45 spectrometer. KRS-5 (TlI+TlBr) plates were used as infrared windows for data collection at Uppsala University. For acquiring the IR-spectra in V a Nicolet 740 and a Nicolet 20F were used with silicon windows for the liquid and solid samples. For the gaseous samples a 17 cm path-length cylindrical glass cell equipped with KBr windows (University of Bordeaux) was used. Preparation of samples and cells were made in dry air, N2 or Ar glove-boxes.
3.1.3 Raman spectroscopy
Raman spectroscopy [115] should more correctly be named Raman scattering, since it refers to the inelastic scattering of light resulting in a frequency shift of the scattered compared to the incident radiation. The scattering system (the sample) can be a gas, liquid or a solid and the light source (the probe) a monochromatic light source (e.g. a laser). The Raman effect is a second order process with photons being annihilated (incident) and created (scattered), respectively. The differences in frequency relate to discrete energy levels in the scattering system. The intensity of the Raman scattering will depend on the fluctuations in the polarisability of the molecule by a specific internal vibration mode if the incident light frequency is constant.
For a detailed derivation of intensities or activities, a more complex and partly quantum mechanical, partly classical treatment is necessary - with the intensity strongly dependent on the incoming radiation frequency, hence the general use of arbitrary intensity units. Since only vibrations resulting in a polarisability change in the molecule will interact with the incident radiation, not all bands will be observed in the Raman. How many internal modes that may be Raman active for a given system can be determined just as for IR using group theory. In combination with IR spectroscopy almost all vibrations will be accounted for and thus these two methods are highly complementary.
For the Raman measurements in I the light source was the 488.0 nm line (300mW) from a Spectra Physics argon ion laser (University of Oklahoma) and for V a LabRam-Dilor spectrometer using the He/Ne 632.8 nm line with a CCD detector was used (University of Bordeaux).
4. Computational methods
4.1 Introduction
The importance of the vast increase in the use of computers in science, especially in chemistry, cannot be overestimated [116]. Of course the applications are diverse, but often computer calculations are employed to assist in interpreting experiments or to set up models to be tested against experiments. Another line of work is to make specific model systems where selected effects can be studied unperturbed and isolated from other factors present in the real system.
Chemistry is perhaps the one science that has benefited the most from the increasing computational power; chemists are using more than 50% of the CPU-time at the Center for Parallel Computers (PDC) at KTH, Stockholm. A number of chemical computational program packages are commercially available and the algorithms and theories, in general, are well tested. The packages used in this thesis were GAMESS [117], GAUSSIAN94 (and 92) [118] and Spartan [119]. Here, only a brief background of the theory to the performed quantum mechanical (QM) calculations will be given; any textbook or review article in the area provides more details [120-123].
4.2 Quantum mechanical calculations
In this thesis ab initio quantum mechanical calculations have been performed on different systems, divided in two categories. Firstly, lithium-glyme interactions have been calculated to model cation coordination, polymer conformation and cation transport in long chain PEO (II, III, VI and VII). Secondly, QM calculations have been performed on the TFSI anion to reveal structure, flexibility and vibrational assignments (IV and V).
4.2.1 Ab initio methods
There are only a few major disadvantages with ab initio QM calculations - they are time and computer CPU and memory consuming and never give exactly the correct answer. Only systems with relatively few atoms can be considered for a reasonable time of computation. On the other hand a vast number of properties such as total energies, charge distributions, reaction pathways and vibrational frequencies are possible to calculate which often compare reasonably well to experiments.
Basically one has to solve the time-independent Schrödinger equation, which can be written as:
(6)
where 
is the Hamiltonian operator given by :
(7)
Equations such as eq. (6) where a linear operator () acts on a function (here 
) to give back the original function are called eigenvalue equations. Such equations are often difficult to solve and approximations must be considered. In the case of polyatomic molecules the Born-Oppenheimer approximation is most often used and is valid in calculating 95 % of all chemical phenomena [122]. For a polyatomic molecule consisting of n electrons and N nuclei the proper equation then can be written as:
(8)
and simplified to:
(9)
at some fixed nuclear geometry. Replacing the exact Hamiltonian with an approximation - the Fock operator - gives:
(10)
The difference between the Fock operator and the exact Hamiltonian is that the Coulomb operator has been replaced by an operator describing the interaction of each electron with the average field of all the electrons. Thus, the Hartree-Fock (HF) equations (11) will be a set of independent equations for each one-electron orbital.
(11)
The Fock operator itself is a function of the complete set of one-electron orbitals. For this reason the HF equations must be solved iteratively and this is also known as the Self-Consistent Field (SCF) method. The most successful methods of solving the HF equations for molecules involve the expansion of the one-electron molecular orbitals (unknown) as linear combinations of basis functions:
(12)
Substituting this expansion into the HF equations (11) and applying the variation principle yields the Roothan matrix equations which can be solved iteratively using the SCF procedure. The computation of the integrals is greatly simplified by using Gaussian type orbitals (GTOs) as basis functions:
(13)
since a product of two Gaussians can be described as a single Gaussian.
In II-VII HF theory has been used with rather small basis sets (3-21G*, 6-31G*, 6-31+G* and 6-31G**). Better agreement with reality, or at least with experiments, may be reached either by changing the theory or increasing the size of the basis set, or both.
The HF equations take no explicit electron-electron correlations into account, each electron instead experiences a mean field of other electrons. Møller-Plesset (MP) perturbation theory [124] may be used to reintroduce the electron correlation via perturbing the HF solution. Corrections can be derived to desired orders, but most often second order perturbations (MP2) are used (VI).
A recent development, in computational QM methods, is the use of Density Functional Theory, DFT. These methods are less CPU demanding and generally provide better mean absolute deviations from experiments than MP2 calculations [125]. Therefore DFT-B3LYP calculations [126-128] have been used to evaluate the total energies, for geometries obtained at HF level of theory (VII).
4.2.2 Geometry optimisations
In most cases the QM calculations reported are concerned with an energy minimum geometry for a given chemical system, resulting in a stable structure. A stable structure, or computationally, a zero-slope energy derivative point can often be found fairly easily and accurately by using standard algorithms for finding extrema on a multidimensional surface. This surface, the potential energy surface (PES), is created by the chemical formula and by the choice of method - theory and basis set, which together give an energy value for each geometry arrangement of the nuclei.
However, these calculations are only approximations to the real system, and no method should be expected to give the real global minimum. Instead the optimised structures obtained should always be considered as local minima or false/approximate global minima. The aspect or risk of the optimisation procedure to end up in a transition state (TS) on the PES must always be considered. Locating stable structures, global and local minima, has been one of the main purposes of II, III, IV and VII.
4.2.3 Potential energy surfaces
Often only small parts of the multidimensional potential energy surface (PES) are of interest - the stationary points, the extrema. Another use of the PES is to perform a partial optimisation of a given system, e.g. a molecule, by freezing one or more variables which construct the surface, often internal coordinates such as bond lengths or angles. In IV the frozen variables for the TFSI ion were the two C-S-N-S dihedral angles and partial optimisations at HF/6-31G* were performed. In addition, the studies of the PES can generate estimations of energy barriers between different extrema on the surface as in IV.
4.2.4 Vibrational properties
Vibrational frequencies can be calculated as the second partial derivatives of the potential energy with respect to geometry parameters. This can be done for any extremum on the PES; local or global energy minima or transition states, and the applications are diverse. The calculations can verify whether the structures obtained correspond to energy minima, with no imaginary frequencies, or other extrema such as transition states - which will have one and only one imaginary frequency. By calculating the IR intensities and/or Raman activities for the vibrational modes, the resulting theoretical spectra can be compared to experimental vibrational spectra. Furthermore, by specifying internal coordinates for the system and calculating the vibrations, the potential energy distribution (PED) can reveal the relative contribution of each internal coordinate to each vibration.
However, ab initio calculated harmonic vibrational frequencies are typically larger than the experimentally observed by 5-10 % - dependent on the choice of theory and basis set. A major source of this disagreement is the neglect of anharmonicity effects in the theoretical treatment. Errors also arise because of the incomplete incorporation of electron correlation. HF theory tends to overestimate the vibrational frequencies because of improper dissociation behaviour, a shortcoming that can be partially compensated for by explicit inclusion of electron correlation (e.g. MP perturbation theory).
The overestimation is, however, found to be relatively uniform and thus generic scaling factors are often applied to the calculated frequencies. Several investigations on the scaling factor to be applied for the different theories and basis sets exist - a fairly recent and extensive one is given by Scott et al. [129]. A scaling factor of 0.9 has been applied on all calculated vibrational frequencies in this thesis (V-VII). Higher accuracy in the scaling would be unneccessary since the calculations performed on species in vacuum are (mainly) compared to experimental spectra of species in condensed phases.
4.2.5 Transition states and reaction paths
So far, the calculations described have been using, more or less, standard methods. Some more intricate calculations and theory will be described below. For an extensive coverage of this field a book edited by D. Heidrich is highly recommended [130].
Chemical reactions are often illustrated in textbooks using energy profiles which are functions of so-called "reaction coordinates" (RC) (Fig. 4.1). This is a general feature of transition state theory (TST). However, the term RC might be misleading since for a reaction more than one internal coordinate may contribute, and therefore a general "reaction path" (RP), in a multidimensional sense should be used.
Figure 4.1 : Potential energy as function of reaction coordinate.
If the RP connects a particular minimum (defined as reactant, R), with another minimum (defined as product, P) along points of lowest potential energy on a multidimensional PES, then it describes the "minimum energy path" - MEP. RP is often used as synonymous to MEP. The stationary points, of chemical interest, along a RP, are the minima (equilibrium structures) and the first order saddle points, which represent the transition state structures (TSs) in TST.
A TS is the point of highest energy along a RP and is associated with one, and only one, imaginary vibrational frequency. When calculating a RP the TS is the starting point, the RP will follow the negative gradient starting along the eigenvector direction of the imaginary frequency (the eigenvector following method). The gradient is equal to zero at the TS. The mass-weighted path of steepest descent (in cartesian coordinates) is termed the "intrinsic reaction coordinate" (IRC). IRC calculations are now well-analysed and well-accepted and are included as a feature in GAUSSIAN94 [118]. Whenever appropriate, an IRC calculation of the RP should be performed in both directions from the TS to verify that the TS truly connects the expected reactant and product. By extracting the structural information in points along the RP from an IRC calculation, a model of a reaction can be envisaged. In VI IRC calculations have been performed to model lithium ion transport in PEO.
In practice the most difficult part is to guess the nature of the connecting TS, when the stable structures (reactant and product) have been obtained. "Chemical intuition" is perhaps the most appropriate tool, but clearly preliminary calculations may provide insight into what guesses might be fruitful. Remember that, from the minima, all directions increase in energy. The shallowest ascent path might be followed, but there is no guarantee that the TS sought for will be reached. In VI several HF single-point calculations have been performed via variation of one or more internal coordinates to locate suitable guesses for the starting point. Each guess was then combined with the reactant and product using the recently developed QST3 (quadratic synchronous transit) feature in GAUSSIAN94 to locate the TS(s).
The QST3 method [131] searches for a maximum along a parabola connecting the three structures, and a minimum in all directions perpendicular to the parabola.
Note that the RP, however defined, cannot be interpreted as illustrating the stereochemical course of a chemical reaction (in which the trajectories hypothetically pass the neighbourhood of a transition structure), since it is a static path neglecting all kinetic energy terms, and thus is fundamentally different from the "real" solution. It does not have direct physical meaning and is a fiction of chemical thinking, however this conceptual model is extremely valuable in overcoming the dimensionality dilemma of a chemical reaction.
5. Results
5.1 Structural information
The articles II, III, IV and VII concern mainly conformational and structural results from quantum mechanical calculations.
5.1.1 Cation-glyme complexes
The solvation of a lithium salt in a polymer leads to a rearrangement of the polymer matrix and a change in the statistical distribution of conformations. The interaction with the lithium ions and the induced changes in the amorphous 3D structure of the polymer have previously been modelled using primarily molecular dynamics [132,133]. The present work has focused on ab initio calculations of lithium ions in oligomers of PEO to reveal the local interactions in an amorphous phase PEO polymer electrolyte, when the anion is a non-coordinating species.
In the present thesis the shortest oligomer used to model PEO is diglyme, which has the possibility of tridentate coordination of lithium ions and other cations. In most PEO/lithium salt crystal structures the number of ether oxygens coordinated by each lithium is three or four with additional coordination from the anions. Thus, diglyme is suitable to model the interaction of the ether oxygens with the lithium ion, although the coordination number (CN) for lithium may be unrealistic. However, the main purpose was to gain information which could be of subsequent use for longer glymes and PEO. Two tridentate structures, 1 and 2, were found (Fig. 5.1), with different conformation of the oligomer chain and with only ~7 kJ mol-1 difference in total energy. In addition a bidentate structure was also found, with a distinctly higher energy by ~100 kJ mol-1 (II). A combination of a bidentate and a tridentate diglyme provided a pentacoordinated lithium-(diglyme)2 complex in a trigonal bipyramidal geometry. No stable hexacoordinated complex could be found, although the corresponding sodium-(diglyme)2 complex has been reported [134].
a)
b)
Figure 5.1 : Li+-diglyme a) structure 1 and b) structure 2.
The conformation of the diglyme chains with respect to the bond sequence O-C-C-O is aGa aG+a (structure 1) and aG+ag+G+a (or equiv. aG+g+aG+a) (structure 2), respectively. The a refers to an anti arrangement about a single bond, g+ is a gauche arrangement and g is a gauche arrangement in the opposite direction with respect to g+ (Fig. 5.2). Upper-case letters are used to identify O-C-C-O dihedral angles, and lower-case for C-C-O-C (C-O-C-C) dihedral angles.
a)
b)
Figure 5.2 : a) an anti (A) arrangement and b) a gauche (G) arrangement about a C-C bond.
The conformational sequence g+G+a found in 2 is referred to as a "genuine corner" and does give rise to a sharp bend [135]. Structure 1 can be considered as a fragment of a crown ether with its alternating aG-a and aG+a conformations [136]. Also in metallo-organic crystals the diglyme has been observed to adopt this conformation [137]. Some work, both computationally [138,139] and experimentally [140,141], have used monoglyme as a model system for lithium ion coordination in PEO. Monoglyme, with two ether oxygens, can not coordinate lithium in a multidentate fashion and is therefore less suited as a model system for a conformational study, although higher levels of accuracy can be used in the QM calculations.
Using the data from the investigation of Li+-diglyme complexes and earlier discussions by Dale [135] the study was extended to cover triglyme complexes with several alkali-metal and alkaline-earth-metal ions (III) and tetra-, penta- and hexaglyme complexes with lithium ions (VII) . In these studies all unique combinations of 1 and 2 (5, 16, 45 and 126, respectively) were used as starting conformations for the different oligomer chains in a systematic way. These were then optimised using semi-empirical PM3 methods before the subsequent final geometry optimisations at HF/3-21G* level (the triglyme complexes were directly optimised at HF level).
The resulting geometries from the calculations show a large variation in geometric appearance with small relative energy differences, which further emphasises the flexibility and multidentate nature of the polyethers. The energy barriers for rotations about the C-C and C-O bonds in diglyme have been calculated earlier by ab initio methods to be less than 10 kJ mol-1 [142]. All complexes obtained incorporate the conformational sequences 1 and 2 and can be nearly completely described using only these two prototype structures, although the dihedral angles vary for the different cations, and to a small extent with the oligomer chain length.
The geometries of the cation-triglyme complexes obtained in III, range from tetrahedral to square planar arrangements of the ether oxygens. The T5 structure (Fig. 5.3) is interesting in the sense that all oxygens are found "on the same side" of the metal ion. This would be a favourable geometry for delivering the metal ion to the anode or cathode in a working battery system [143].
Lithium ions have been observed to coordinate on average five ligands in the first solvation shell in water [144] and recent computational results for different ether oxygen containing ligands also suggest a CN of four to five for lithium [145]. This also seems to be true in PEO polymer electrolyte systems, although the oxygens coordinated not always originate from the polymer [146,147]. Therefore, tetraglyme, with its five ether oxygens, should be the preferable model.
Figure 5.3 : The T5 structure of Na+-triglyme. Hydrogens omitted for clarity.
In addition, to consider the possibility of hexa- or even heptacoordination calculations for penta- and hexaglyme lithium ion complexes were performed (VII). From the resulting structures, no heptacoordinated complexes were found, and by extrapolation of the resulting bonding energies to CN=7 it is stated that heptacoordination of lithium in PEO/lithium salt systems seems less likely (Fig. 5.4). The total and bonding energies for these systems were calculated at B3LYP/6-31G*//HF/3-21G*.
Figure 5.4 : The total bonding energy as a function of CN of lithium.
Three different geometries dominate among the calculated complexes; the quadratic pyramid and the trigonal bipyramid geometries (CN=5) and trigonal prism geometry (CN=6) (Fig. 5.5a-c).
a)
b)
c)
Figure 5.5 : a) quadratic pyramid (Te5 in VII) b) trigonal bipyramid (Te9) and c) trigonal prism (P7). Hydrogens omitted for clarity.
The lithium-oxygen distances are comparable to those obtained in MD simulations [133] and neutron scattering experiments [49] on LiI in PEO. Our "radial distribution function", "rdf", (Fig. 5.6) shows good agreement with these studies, in spite of the fact that the statistics of our distribution clearly is inferior. If a correction of +0.09Å is applied to the Li+-O distances, deduced from calculations on lithium-diglyme at HF/6-31G** (II), our maximum peak value is similar to that obtained in the neutron experiments, ~2.1Å.
For some of the complexes obtained, the relative energies show very good agreement with the rotational barrier calculations on pure diglyme in reference 142; if no change in the CN for lithium occurs, changes in the chain conformation modifies the relative energy according to the rotational barrier potential curve.
The calculational method chosen thus appears to describe the relative energies and geometries of the complexes well, especially when considering the rather poor basis set used. Test calculations to evaluate the usefulness of a larger basis set and/or more accurate theory were performed on the lithium-hexaglyme H3 complex obtained in VII.
Figure 5.6 : "rdf" of Li+-O distances in the Li+-tetra-, penta- and hexaglyme complexes.
Geometry optimisations were performed at HF/6-31G* and B3LYP/6-31G*, both starting from the HF/3-21G* optimised geometry. The calculations took ~112 and ~502 CPU hours, respectively (on an SGI Power Indigo2 R8000 using GAUSSIAN94). At present these large demands for CPU time clearly limit the usage of such large basis sets and accuracy methods for our purposes. The resulting energies and geometries show only minor changes compared to the single-point calculations performed on the HF/3-21G* optimised geometry.
In VI the conformational and vibrational data for the lithium-diglyme and lithium-triglyme complexes are used to obtain transition states and conversions between the stable structures (see section 5.3).
5.1.2 The TFSI anion
The LiTFSI salt and thus the TFSI anion has been extensively used in SPE studies. Recently, more detailed experimental IR-spectroscopy [69,148] and computational studies [71,149] have appeared in the literature for the TFSI ion and LiTFSI. However, the structure in solution, the vibrational assignments and the proposed origin of the plasticising effect still appeared to contain discrepancies.
A combined experimental and computational ab initio study of the TFSI anion was, therefore, undertaken with the purpose of:
i) identifying the stable structure(s)
ii) revealing the origin of the reported plasticising effect
iii) calculating and assigning the vibrational spectra (see section 5.2.2.)
The potential energy surface for rotations about the two central S-N bonds (i.e. varying the C-S-N-S dihedral angles) of TFSI in steps of 30° was calculated at the HF/6-31G* level to obtain the minimum energy structure(s). Two non-equivalent energy minima were observed and the geometries of these grid points were then fully optimised and two different minimum energy structures were obtained. Their vibrational spectra were calculated to confirm the minima and to serve of subsequent use in the assignment of experimental spectra (section 5.2.2). Diffuse functions were added to the basis set used (6-31G* - 6-31+G*), due to their often argued obligatory use on anions, but no significant changes were obtained. The conformation with C2 symmetry (Fig. 5.7) has the lowest energy by 2.3 kJ mol-1, the other being of C1 symmetry. Their relative population is ~5:2 according to the Boltzmann distribution at 25°C. The rotamer with C2 symmetry has two equal gauche C-S-N-S dihedral angles (93°), whereas the C1 rotamer has one trans(anti) (-168°) and one gauche angle (100°).
Figure 5.7 : The TFSI anion in its lowest energy conformation with C2 symmetry.
A distorted local C2 axis has been observed for the anion in a crystal structure determination of [Mg(H2O)6][(CF3SO2)2N]2×2H2O, and also the corresponding acid HTFSI has been found to have C2 symmetry [150]. The calculated geometries agree well with the reported structures. This is especially important for the S-N-S angle which earlier has been reported to be as large as 156° and was subsequently used for calculating LiTFSI complexes [71,149]. Our values, 128° and 126° for C2 and C1 respectively, are closer to both the salt hydrate structure (125°) and the HTFSI structure (128°). Both crystal structures have C-S-N-S angles of approximately equal gauche values (91-95°), but no evidence of a trans-gauche conformation as in our C1 symmetry structure has been reported to our knowledge. In the highly relevant LiN(CF3SO2)2PEO3 crystal structure [42] the TFSI entity has C-S-N-S dihedral angles of -82° and 116° [151].
There is a low energy barrier between the two minima: ~3.9 kJ mol-1 according to the calculated PES (Fig. 5.8) (IV) and confirmed by the calculation of a TS connecting the two minima [152]. Furthermore, a low energy region exists in the PES where the energy variation does not exceed 15 kJ mol-1 for a 60-240° angle variation in both dihedral angles. These values are clearly of most importance when compared to the barriers for rotations about the single bonds in the PEO systems. The low energy barrier found is comparable to or less than the barriers found for rotations around the C-C and C-O bonds in diglyme [142]. This observation is interesting from the point of view of the TFSI anion acting as a plasticiser in PEO based polymer electrolytes.
Figure 5.8 : The PES of TFSI for rotations about the S-N bonds in a 30° grid (IV). The C-S-N-S dihedral angles denoted as dh5 and dh6, cis = 0°.
The TFSI anion has been observed to suppress crystallisation of the PEO systems - which may mainly be attributed to the low tendency of ion-pair formation, thus leaving the cation free to coordinate the ether oxygens of the polymer chains. Moreover, the plasticising effect of any anion could be explained as resulting from the creation of more space between the polymer chains combined with the possibility for the anion to be removed by a conformational change occurring in the polymer. In addition to these effects, according to the rotational barriers, the TFSI anion could, at a low energy cost, perform a concerted conformational change with the polymer. This may be one reason why LiTFSI usually has a better reported ionic conductivity in SPE's than any other lithium salt.
On the other hand, the variation of the S-N-S angle has little or no correlation with the present PES and only small changes of the S-N-S angle are within a low energy area (IV). The PES will most probably change with cation coordination, but at least for the free TFSI anion the S-N-S angle does not seem to contribute significantly to the mechanical flexibility, and thereby to the plasticising effect, as the changing C-S-N-S dihedral angles might.
5.2 Spectroscopic information
The articles I and V concern mainly spectroscopic information obtained both by experiments and via quantum mechanical calculations.
5.2.1 Cation-glyme complexes
One of the original intentions and major purposes of calculating the stable structures of several lithium-glyme complexes was to compare spectroscopic information in the chain conformation sensitive wavenumber region 1000 - 800 cm-1 to experimental data. As the frequency of the CH2 rocking motion should be sensitive to the conformation, i.e. to the dihedral angles in the polymer backbone, the calculations should allow one to identify those conformations producing the vibrational spectra. Several early studies both on the pure glymes and the pure PEO exist, where both liquid and solid systems were studied by spectroscopic methods [54,107]. More recent studies are by Frech et al. [140] and Matsuura et al. [108].
It was originally proposed that by studying these conformation sensitive bands at low temperature (annealing the samples at -80°C) as a function of O/M=4 - 20 for LiCF3SO3-diglyme, spectra originating from a single type of cation-diglyme conformation should be obtained (I). The resulting spectra (Fig. 5.9) suggest occurrence of a lithium-(diglyme)2 complex for most concentrations together with a lithium-(diglyme)(triflate) complex for the highest salt concentrations.
Figure 5.9 : IR spectra of LiCF3SO3-diglyme after annealing and recorded at -80°C.
Also bands arising from crystalline pure diglyme were obtained, which decreased with increasing salt content. In these spectra the triflate anion is non-coordinated for all concentrations except the highest (O/Li=4), as could be detected as a single band in the 770 - 750 cm-1 region.
In the room-temperature spectra the bands arising from the complex increase with salt concentration, but bands from pure diglyme can be seen for all concentrations. The interaction with the anion is obvious for all concentrations studied. It is thus more likely that the complex present at RT is of the lithium-(diglyme)(triflate) type rather than the lithium-(diglyme)2 type. The calculated shifts for the different diglyme conformers after lithium coordination were small and hard to correlate with the observed spectra in I [153]. Clearly more sophisticated studies and a more detailed analysis needs to be done before any strict conclusions can be drawn on the conformational state of the diglyme molecule, or longer glymes, in the complexes.
However, by comparing with earlier studies on PEO-systems [45], some tentative suggestions about the conformations of pure diglyme at -80°C and RT can be made. The absence of bands at ~990 and ~770 cm-1 for both RT and -80°C can be interpreted as no anti O-C-C-O sequences present. Bands arising at ~940 and ~880 cm-1 are interpreted as occurrence of gauche O-C-C-O sequences. For the low temperature infrared spectra of pure diglyme only four distinct bands are obtained in the region; 943, 861, 852 and 841 cm-1. These are interpreted as crystallised diglyme in the aG+a aG+a conformation (I).
For the corresponding tri- and tetraglyme - LiCF3SO3 mixtures the spectra obtained [154] show no similar sharp "one conformer only" bands, but rather a mixture of conformations - broad bands - which is consistent with the present calculations indicating that several stable conformations may be present simultaneously (III and VII). For the complexes involving the larger glymes the vibrational frequencies have been calculated mainly to certify the postulated structures to be minima and not transition states. Clearly, a thorough investigation of these complexes could reveal information of interest also for the purpose of assigning the vibrational spectra with respect to chain conformation.
Another interesting common feature in the spectra of lithium salt/PEO mixtures is the band observed at ~860 cm-1 [155] (in V at 862 cm-1) which is not present in pure PEO. This is a strong Raman band and has been assigned to a so-called "breathing" mode of a PEO segment solvating the lithium ion and adopting a kind of "crown-ether conformation". The corresponding calculated modes for the lithium-tetraglyme, and indeed also for the penta- and hexaglyme complexes, reveal that regardless of chain conformation, a band calculated at ~830 ±9 cm-1 (scaled) with a high Raman intensity exists (VII). Visualisation of these modes gives a "breathing" mode where all coordinated oxygen atoms move towards the metal ion in phase. The vibrations are mainly due to C-O and C-O-C coordinate changes with the lithium ion more or less fixed. The behaviour of the C-O and C-O-C units as independent oscillators with similar force constants may explain the insensitivity of the vibrational band to the chain conformation.
5.2.2 The TFSI anion and the HTFSI acid
The TFSI anion is often used as a counterion to lithium in SPE's and therefore, an understanding and assignment of the bands in the vibrational spectra is of interest in order to identify possible ion-pair formation.
Much debate has occurred concerning interpretation of ion-pairs as seen or not seen by IR or Raman compared to other techniques. Contact ion-pairs of LiTFSI in SPE's have recently been observed spectroscopically by Rey et al., but seem negligible for O/Li ratios = 8 [69]. In V the LiTFSI salt has been dissolved in several polymers to obtain spectra of the "free" anion. Furthermore, vibrational spectra of the corresponding acid, HTFSI, have been measured. The HTFSI acid will serve as a reference system in discussions of differences in the spectra, both with respect to differences between the two compounds, and with respect to experimental observations by IR and Raman and calculations.
Both stable conformations of TFSI obtained in IV, show similar calculated vibrational patterns, differing mainly in the region below 700 cm-1 (V). An artificial spectrum can be derived and compared with the IR spectrum of LiTFSIPEO9 (Fig. 5.10). The experimental spectrum cannot be reproduced in all detail using only one conformer.
The band calculated at 733 cm-1, a highly intense Raman line and also present in IR is observed at 740 cm-1. It shows no significant changes with temperature in the interval investigated (-20° - +80°) and furthermore the calculated intensity for that band is the same for the two TFSI conformers. Thus a change in this band is not likely to result from a change in the relative amount of the two conformers.
Figure 5.10 : The simulated IR spectra of the C1 and C2 conformers compared to experiment.
In order to facilitate comparison with HTFSI and experiments only the C2 symmetry conformer will be considered in the following section (Fig. 5.11). If the TFSI anion adopts the C2 symmetry, its 39 internal vibrations can be classified into 20 A and 19 B modes; the former (generally) having high Raman intensities and the latter (generally) being more intense in IR.
The band observed in Raman and IR at ~740 cm-1 has been extensively used a probe of ion-pairs present. The assignment for this band, by comparison with similar compounds, especially the triflate ion with a band at 754 cm-1 [101,156], has been suggested to be dsCF3. From the calculated PED, and indeed also for the PED for the triflate ion [156], this assignment can be questioned. In our PED this mode is a complex mixing of internal coordinates, but with no F-C-F bending contribution among the four largest ones. We assign this band as mainly a nsSNS mode. The large Raman intensity can be easily envisaged by visualising the mode, in which the whole molecule is expanding and contracting making a large polarisability change of the molecule. For the triflate ion the C-F contribution dominates (53%), accompanied by many other contributions, but the authors have not further commented on this problem [156]. The assignment is retained for the HTFSI acid where the most intense Raman line is observed and calculated at ~765 cm-1, and the normal mode according to the PED is dominated by C-F, C-S and S-N stretching coordinates.
In our calculation on TFSI, the F-C-F bending coordinates contribute largely to the modes at 549, 541 and 526 cm-1. From visualising these modes a decoupling can be seen with either one or two of the C-F bonds taking part in bending motions. This in fact implies the existence of approximate local mirror planes rather than C3 axes at each end of the TFSI anion. In addition this is confirmed by the HTFSI calculation (549, 545 and 520 cm-1).
1400 ....................1200.................... 1000...................... 800.................... 600......................400...................... 200
Wavenumbers cm-1
Figure 5.11 : Comparison of the experimental and calculated IR (a) and Raman (b) spectra of the TFSI anion. The experimental IR and Raman spectra of LiTFSIPEO8 at 80°C (with the PEO subtracted). The asterisk indicates a line not due to the anion but coming from the PEO breathing mode.
The spectra and the calculations also show other significant features, some of which will be summarised below:
For the TFSI ion a very large splitting between the naSNS band, only observed in IR, and the nsSNS band is observed: 300 cm-1, the high frequency (~1060 cm-1) of the former is in part justified by the partial double-bond character of the S-N-S group. This behaviour is changed in HTFSI (Fig. 5.12), where the ~1060 cm-1 band has disappeared and a new strong band is present at 859 cm-1 (calculated at 882 cm-1). This is consistent with the evaluation of the double-bond character which decreases for the acid, by comparing the S-N distances of 1.58 (0.02 Å and 1.64 (0.02 Å found for the anion and acid, respectively. The S-O bonds in HTFSI become slightly shorter, the S-O force constants become larger and the S-N force constants decrease which further supports this suggestion (V).
The IR spectra of gaseous HTFSI can be compared to the Raman spectra for the solid. The formation of N-H...O bonds in the solid can be detected in the shift from 3394 cm-1 in the gas state to 3197 cm-1 in the solid for the nNH mode, calculated at 3410 cm-1 (V). The hydrogen bonds are not very strong d(H...O)=2.26 Å [150], but changes in all bands involving N-H can be detected; in the out-of-plane deformation mode gNH an upshift from 460 cm-1 (calculated at 464 cm-1) to either 495 or 526 cm-1 is observed.
1400.................1200.................1000..................800.....................600.....................400.....................200
Wavenumbers cm-1
Figure 5.12 : The vibrational spectra of HTFSI a) gas phase IR b) solid phase Raman and the calculated IR and Raman spectra of the isolated HTFSI molecule.
Although, the absolute frequencies calculated for the naSO2 bands (A and B symmetry) for TFSI are too low compared to the experimental values, a naSO2 mode splitting of 25 cm-1 is calculated, with A higher than B, which is in very good agreement with the observed splitting of 20 to 24 cm-1. The prediction of the naSO2 and naCF3 vibrations still remains difficult. Furthermore, in HTFSI, strong coupling between the naSO2 and the dNH stretching coordinates is found for the modes calculated at 1422 and 1335 cm-1 (B symmetry) (V). This coupling is somewhat unexpected since no bonds are in common for the definition of the NH in-plane bending and the S-O stretching coordinates. The observed increase in naSO2 for the HTFSI, observed as a band at 1463 cm-1 with a shoulder at 1440 cm-1, compared to 1300 cm-1 for TFSI, is reflected also in the S-O force constants which show a 20% increase relative to TFSI.
To summarise, problems remain in the comparison between the calculations and experiments. However, the assignment for several bands has been assisted by the calculations and the spectra obtained can be used as fingerprints in the regions of interest. The validity of the calculated geometries, and especially the debated S-N-S angle, has been further confirmed as the vibrational modes calculated involving this entity correlate well with experimental spectra.
5.3 Modelling lithium ion transport
As mentioned in 2.4 the consensus at present for a model of lithium ion transport is that the cation transport is promoted by conformational changes due to the segmental motion of the polymer chain via making and breaking of cation-oxygen bonds (the cation mainly regarded being lithium). The total transport of lithium ions probably consists of both inter-chain and intra-chain movements. A single chain model can be applied to model the latter. Here a quantum mechanical modelling of such ion transport will be described and evaluated (VI). However, to allow for the electronic structure to be explicitly treated in QM calculations the system must, however, be severely limited in size for computational reasons. Using the stable minimum energy structures obtained for lithium-diglyme (II) and lithium-triglyme (III), the method chosen here is to calculate the transition states (TSs) for processes involving a change in coordination number of the cation. For diglyme as the chosen model compound for PEO, this change involves the tridentate and bidentate coordinations. The changes between the stable structures can be modelled as a conformational change, described by dihedral angles as the reaction coordinate, which is coupled to the segmental motion description above.
Two different types of TSs were found for the lithium-diglyme and lithium- triglyme systems. The first TS found, TS1 (Fig. 5.13), involves the transition from a tridentate lithium-diglyme complex (structure 1) to a bidentate lithium-diglyme complex, both from II. This requires only one major internal change, one O-C-C-O dihedral angle going from gauche to anti, aGa aG+a to aAa aG+a.
Figure 5.13 : The calculated TS1 structure of lithium-diglyme.
A vibrational frequency calculation verified the TS, an imaginary frequency of -112 cm-1 was obtained, which was almost solely due to a changing O-C-C-O dihedral angle. The O-C-C-O dihedral angle for the TS was -131°. An IRC calculation was made to verify TS1 as the TS sought for, i.e. the RP connecting structure 1 and the bidentate structure (Fig. 5.14).
Figure 5.14 : The IRC-RP for the transition from 1 to the bidentate complex.
An elongation of the oligomer chain in these TS calculations also seems appropriate, as we have proposed that 1 and 2 should be necessarily regarded as the unique substructures. The same procedure as for the lithium-diglyme system was applied to lithium-triglyme using the T4 structure from III. The TS obtained, TS3, differs by only 0.1° in the relevant O-C-C-O dihedral angle as compared with TS1, 5 cm-1 in frequency and the small energy barrier (i.e. from tridentate to TS3) differs only by 0.6 kJ mol-1 (VI).
However, for this type of RP by using TS1/TS3, shows no obvious way for making the lithium move along the PEO chain.
The second TS found for lithium-diglyme, TS2, is more complex, involving the transition from aG+g+ aG+a, structure 2, to the bidentate structure aAa aG+a. Clearly this transition requires at least two internal dihedral angles to be changed, which made the starting guess(es) harder to propose. Therefore, several single-point calculations were made by varying the two dihedral angles systematically, to construct a surface to locate suitable TS guesses. Using these guesses, one single TS emerged and an imaginary frequency of -120 cm-1 verified the TS.
However, the imaginary mode, the subsequent IRC calculation and the resulting RP (Fig. 5.15) show both more complex and more interesting features than found for TS1 and TS3. From a visualisation of the imaginary mode it was unclear if TS2 was the TS searched for and an IRC calculation was in this case deemed necessary. The part of the RP from TS2 to the bidentate structure was without complications. On the other hand, the part of the RP leading from TS2 to 2, reaches a bifurcation point, (end of filled symbols), where the geometry of the complex has an approximate C2 symmetry. From this point the RP can follow either one of two equivalent paths and the products will be two energetically identical aG+g+ aG+a complexes. However, the IRC calculation can not proceed through a bifurcation point and therefore the frequencies of this point were calculated and the imaginary modes evaluated. The imaginary mode involving a conformational change was used to force a displacement from the bifurcation point and a new IRC calculation was started from this new point [157]. This IRC calculation resulted in a RP to the expected product(s). The changes in energy for the RPs as a function of the dihedral angle changes involved are shown in Fig. 5.15.
Also in this case the lithium-triglyme TS equivalent, TS4, was calculated using T1 from III. The differences obtained compared to TS2 are negligible: 0.3° (0.2°) in the relevant O-C-C-O (C-C-O-C) dihedral angle, 2 cm-1 in frequency and 0.4 kJ mol-1 in the small energy barrier (VI).
Figure 5.15 : The IRC-RP for the transition from 2 to the bidentate complex. Circles for the O-C-C-O dihedral and squares for the C-C-O-C dihedral.
The more complex behaviour of the latter part of this RP offers an interesting possibility for lithium ion transport. The lithium-oxygen distances show a difference of 0.15Å by a change between 2 and a point slightly above the bifurcation point, which can be accomplished with little energy cost (VI). Furthermore, the two equivalent structures that can be reached from the bifurcation point in diglyme, result in two non-equivalent positions of lithium in a real polymer or longer oligomer. By a co-operative change in this manner for several monomer units a "channel" for lithium ion transport can be formed with each small step being ~0.15Å.
This proposed mechanism was evaluated by further calculations to construct a transport path in the lithium-triglyme system. The oligomer backbone dihedral angles were restricted at certain values and only the lithium position optimised. The dihedral angles were intially chosen to mimic a coordination of lithium resembling structure 2 of lithium-diglyme (A1) (Fig. 5.16a). Then the dihedral angles were changed in a systematic way to reach a structure with all O-C-C-O dihedral angles equal (40°) and all C-C-O-C (C-O-C-C) dihedral angles within 160-165° and thus having a C2 symmetry similar to the bifurcation point of lithium-diglyme (A11) (Fig. 5.16b). Finally dihedral angle changes were made to reach a structure 2 type of coordination (A21) (Fig. 5.16c), but at the other end of the triglyme chain. In this way the lithium ion has been allowed to move along the chain using a "TS" resembling the bifurcation point, involving coordination changes from tri- to "tetra-" and back to tridentate coordination (Fig. 5.16a-c).
a)
c)
b)
Figure 5.16 : The modelled reaction path for Li+ transport a) structure A1 b) structure A11 and c) structure A21(VI).
The changes in the lithium-oxygen distances along the transport path are shown in Fig. 5.17. The energy changes along this path are less than 10 kJ mol-1 (Fig. 5.18) and a further optimisation of the path would most likely result in even smaller changes. This can be compared with MD results which show that Li+ transport can be performed via consecutive changes from penta- to tetra- to pentadentate coordination along a polymer strand [133]. From the MD work no detailed information about the energy barriers or demands are given and also the co-operation of an anion or an ether oxygen from another polymer strand is suggested. Our suggested mechanism leaves the lithium ion "open" on one side allowing for a possibility to coordinate in this manner.
Figure 5.17 : The modelled reaction path for Li+ transport and the lithium-oxygen distances.
Figure 5.18 : The modelled reaction path for Li+ transport and the relative energy.
The modelling of a conformational change may be compared to experimental results. However, appropriate NMR experiments for lithium - containing systems such as the PEO or oligomers, do not seem to exist. Therefore, a comparison with an analogous Sr2+ system - having approximately the same charge-to-radius ratio as lithium (both ~1.7) was made. From NMR measurements of T1r relaxation data for protons of the PEO chain (Mw=4×106) of Sr[N(CF3SO2)2]2PEO9 , an activation energy of 61 kJ mol-1 in the amorphous phase was evaluated [158]. In that system, the glass transition temperature (Tg) has been determined to 0°C [159], and the correlation times calculated from the relaxation measurements follow an Arrhenius behaviour in the temperature interval investigated (25-120°C). The experimentally determined activation energy, 61 kJ mol-1, can be compared with our calculated one of ~80 kJ mol-1 for a change from a tetra- to tridentate coordination in the lithium-triglyme complex. The experimental result is an average over all types of conformational changes, and some of these are not necessarily involving metal-ion coordinated ether oxygens. This probably explains the main difference between our calculated and the experimentally determined activation energies.
6. Concluding remarks
Writing a thesis would mean very little without a summary of the main results and giving the perspective of what the present results and status of knowledge implies for future work. Predictions of what will happen are of course not possible, perhaps not even what is likely to happen can be imagined, but that should certainly not be the limitation for one's wishes and thoughts of what could happen.
6.1 The present and the future
Crystal ball gazing is always an activity fraught with peril! However, a few trends are becoming apparent in SPE studies. The systems used and studied as polymer electrolytes do become more complex - more specially designed components are mixed together in multi-component blends. Certainly, to be used in all solid-state batteries, the SPE's need to considerably enhance their quality (e.g. their ionic conductivity). This is at least true for usage in devices designed and intended to work at ambient temperature.
The efforts to create a convincing basic model of ion transport mechanisms in SPE's are still concerned with the "simplest" PEO/lithium salt mixtures. The development of a first general model which can be applied to more complex systems is not unrealistic. The increasing quality and number of experimental techniques, computational power and knowledge of mechanisms makes this the most intriguing scientific question in the SPE area. If then a way would be found to predict which SPE could be suitable in a specific electrochemical application in a real working system "a priori"; the success story would be complete. In forthcoming work the use of the present TST approach used on PEO together with QM calculations could be neatly combined with time-resolved experimental techniques to verify reaction paths and the structures present as reactants and products. This can perhaps also be performed on more sophisticated SPE's including also the more recent concepts.
Nanocomposite materials comprise one of the present scientific trends that recently also has become of use for the preparation of SPE's. Syntheses can be controlled in several manners and the ion transport mechanism may be altered. Batteries with also their electrodes being constructed from organic compounds have been launched recently - using redoxpolymers which is a whole new concept of working environment for the polymer electrolyte.
Clearly, regardless if any of these or any other new concept will be dominant in the future, there is need for thorough investigation of the ion conduction mechanism. In situ studies of several properties in conjunction in real working batteries will probably be more common. In this perspective, macroscopic as well as fundamental modelling of whole batteries - not only all different components separately will become of importance. Such highly complex problems need new algorithms /approaches to be formulated and applied.
6.2 Brief summary of results
- The applicability of ab initio computational methods to the components and problems of polymer electrolytes has been proven possible and successful.
- A potential energy surface for the TFSI anion has been calculated and two stable conformers were obtained.
- The vibrational spectra of both the TFSI ion and the corresponding HTFSI acid have been assigned using a combined theoretical and experimental approach.
- Visualising molecular vibrations as a scientific tool in band assignments has been proven very useful for several disputed vibrational modes.
- The local surrounding of the lithium ion in PEO has been modelled using different lengths of methyl end-capped PEO oligomers - glymes - as models for PEO. The lithium ions seem to have a CN of 5 or 6 in these systems.
- The flexibility of both the oligomer chains in the lithium-glyme complexes and the TFSI anion has been evaluated.
- A new possible lithium ion transport mechanism in PEO based on quantum mechanical model calculations is suggested.
Svensk sammanfattning / Swedish summary
Nya material har alltid varit föregångare till stora uppfinningar och stora språng i den teknologiska utvecklingen i mänsklighetens historia. Polymerelektrolyter som denna avhandling handlar om har, kanske, inte ännu nått fram till att användas teknologiskt, men har definitivt potentialen och är förvisso utmärkt intressanta material att studera, från en forskares synvinkel.
Användningsområde för materialen är främst som en vital komponent i tunnfilmsbatterier. Konsumentprodukter där dessa batterier kan få användning innefattar mobiltelefoner, videokameror, verktyg och bärbara datorer.
Polymerelektrolyter har ett flertal egenskaper, t ex deras jonledande förmåga, som kan studeras med hjälp av olika metoder och modeller. Kvantmekaniska beräkningar och spektroskopiska mätningar bildar i detta arbete en grund för tolkningar av hur jonledningen går till och vad som styr den. Kopplingen mellan experiment och beräkningar är ett utmärkt exempel på hur metoder tillsammans ger mer information än de enskilda delarna var för sig. De resultat som erhållits är främst kopplade till hur en av de ledande jonerna - litiumjonen - binds upp av polymeren, komplexbinds, och vilka energier som krävs för att den ska transporteras.
En modell för hur litiumjontransporten går till har satts upp med utgångspunkt från de kvantmekaniska beräkningsresultaten. Dessutom har den inre flexibiliteten och vibrationsspektra för TFSI-jonen, en vanlig anjon till litiumjonen i polymerelektrolyter, beräknats och detta har avsevärt underlättat tolkningen av experimentella spektra.
Acknowledgements
First of all I would like to express my deep gratitude to Jan for being the teacher everyone would like to have. You possess great knowledge not only in "ordinary" chemistry, but also in the perhaps even more difficult field of personal chemistry. You've been a never-ending source of encouragement and shared my ideas, joy in science and sometimes my frustration. "May the power be with you" and your enthusiasm never fade.
My "second supervisor" Jörgen I would like to thank for his for scientific suggestions and discussions about the computational part of the work and Bob Delaplane for saving the thesis from my not always so brilliant English. I would also like to thank Profs. Kersti Hermansson and Josh Thomas for your enthusiasm for science and life - it's contagious...
All my invaluable co-workers for all the effort you've put down - it's a lot of hard work.
The technical assistance from the computer-wizards Dick Jarklint, Hans Ollaiver and Bo Fredriksson has been valuable, and to the secretarial staff, especially Barbro Lange - many thanks.
I would also like to thank all the members of the 'Structure & Dynamics' group - present and past. Special thanks to the "polymer-babes" for all the fun we've had together around the world and at home. My gratitude also to all "normal" friends, very near or very far, reminding me of the world outside and especially to all my friends in the floorball-teams and in the dojo - the physics are also important.
Financial support for this work has been given from the Swedish Research Council for the Engineering Sciences (TFR) and the Swedish Natural Science Research Council (NFR). The Royal Academy of Science (KVA) - T. H. Nordströms stip. - and Uppsala University - C. F. Liljewalchs stip. - have provided travel funds. The High-Performance Computing Council (HPDR) has provided supercomputer time. All these contributors have given me a solid ground of research support and is gratefully acknowledged.
Finally, I want to thank my parents for always believing in me and giving all thinkable support - more than you perhaps know yourselves. Ett stort TACK. Och ......, ... ....... ...!
Uppsala, April 1998.
References
1. B. Scrosati, Nature, 1995, 373, 557.
2. M. Faraday, Philos. Mag., 1838, Feb 8, §1339.
3. M. Gauthier, A. Bélanger, B. Kapfer, G. Vassort and M. Armand in Polymer Electrolyte Reviews 2, J. R. MacCallum and C. A. Vincent, Eds., Elsevier, London, 1989, p. 285.
4. A. M. Andersson, J. R. Stevens and C. G. Granqvist in Large Area Chromogenics- Materials and Devices for Transmittance Control Vol. IS4, C. M. Lampert and C. G. Granqvist, Eds., Institute series, opt. Eng. Press Bellingham, USA, 1990.
5. R. D. Lundberg, F. E. Bailey and R. W. Callard, J. Polym. Sci. Part A1, 1966, 4, 1563.
6. D. E. Fenton, J. M. Parker and P. V. Wright, Polymer, 1973, 14, 589.
7. P. V. Wright, J. Poly. Sci., Poly. Phys. Ed., 1976, 14, 955.
8. P. V. Wright, Br. Polym. J., 1975, 7, 319.
9. M. B. Armand, J. M. Chabagno and M. J. Duclot in Fast Ion Transport in Solids, P. Vashista, J. N. Mundy and G. K. Shenoy, Eds., Elsevier North Holland, New York, 1979, p. 131.
10. M. Armand, J. M. Chabagno and M. Duclot in Second International Meeting on Solid Electrolytes ( extended abstracts ), C. A. Vincent, Ed., St. Andrews University Press, St. Andrews, Scotland, 1978.
11. N. Oyama, T. Tatsuma, T. Sato and T. Sotomura, Nature, 1995, 373, 598.
12. A. R. Armstrong and P. G. Bruce, Nature, 1996, 381, 499.
13. W. Li, J. R. Dahn and D. S. Wainwright, Science, 1994, 264, 1115.
14. Polymer Electrolyte Reviews 1&2, J. R. MacCallum and C. A. Vincent, Eds., Elsevier, London, 1987 and 1989.
15. P. G. Bruce and C. A. Vincent, J. Chem. Soc. Faraday Trans., 1993, 89, 3187.
16. Solid Polymer Electrolytes, Fundamentals and Technological Applications, F. M. Gray, VCH, New York, 1991.
17. C. A. Vincent, Progress in Solid State Chemistry, 1987, 17, 145.
18. M. A. Ratner and D. F. Shriver, Chem Rev., 1988, 88, 109.
19. M. B. Armand, Ann. Rev. Mater. Sci., 1986, 16, 245.
20. Solid State Electrochemistry, P. G. Bruce, Ed., Cambridge Univ. Press, 1995.
21. Applications of Electroactive Polymers, B. Scrosati, Ed., Chapman & Hall, 1993.
22. Lithium Batteries; New Materials, Developments and Perspectives, G. Pistoia, Ed., Elsevier Science B.V., 1994.
23. M. Armand, J-Y. Sanchez, M. Gauthier and Y. Choquette in Electrochemistry of Novel Materials, J. Lipkowski and P. N. Ross, Eds., VCH, New York, 1994, p. 65.
24. D. Baril, C. Michot and M. Armand, Solid State Ionics, 1997, 94, 35.
25. S. Megahed and B. Scrosati, Interface, 1995, Winter, 34.
26. C. A. Vincent in Electrochemical Science and Technology of Polymers 2, R. G. Linford, Ed., Elsevier Applied Science, London, 1990.
27. G. Cameron and M. D. Ingram in Polymer Electrolyte Reviews 2, J. R. MacCallum and C. A. Vincent, Eds., Elsevier, London, 1989, p. 157.
28. A. Johansson and J. Tegenfeldt, Solid State Ionics, 1993, 67, 115.
29. Molecule images in the summary made by using ymol, ( D. Spångberg, 1997-1998 and POV-Ray( 3.0, ( POV-Team, 1991-1997.
30. M. S. Mendolia and G. C. Farrington, Adv. Chem. Ser., 1995, 245, 107.
31. G. K. Jones, G. C. Farrington and A. R. McGhie in Proc. Second Int. Symp. on Polymer Electrolytes, B. Scrosati, Ed., Elsevier Applied Science, New York, 1990, p. 239.
32. A. Bakker, Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, Uppsala, 1995, 113.
33. Y. Takahashi and H. Tadokoro, Macromolecules, 1973, 6, 672.
34. B. D. Brown and D. J. deLong in Kirk-Othmer Encyclopedia of Chemical Technology Vol. 18 ( 3rd ed.), H. F. Mark, Ed., John Wiley & Sons, New York, 1982, p. 616.
35. C. Berthier, W. Gorecki, M. Minier, M. B. Armand, J. M. Chabagno and P. Rigaud, Solid State Ionics, 1983, 11, 91.
36. Y. Chatani and S. Okamura, Polymer, 1987, 28, 1815.
37. P. Lightfoot, M. A. Mehta and P. G. Bruce, J. Mater. Chem., 1992, 2, 379.
38. Y. Chatani, Y. Fujji, T. Takayanagi and A. Honma, Polymer, 1990, 31, 2238.
39. P. Lightfoot, M. A. Mehta and P.G. Bruce, Science, 1993, 262, 883.
40. P. Lightfoot, J. L. Nowinski and P. G. Bruce, J. Am. Chem. Soc., 1994, 116, 7469.
41. J. B. Thomson, P. Lightfoot and P. G. Bruce, Solid State Ionics, 1996, 86, 203.
42. Y. G. Andreev, P. Lightfoot and P. G. Bruce, Chem. Commun., 1996, 18, 2169.
43. H. Tadokoro, Y. Chatani, T. Yoshihara, S. Tahara and S. Muramashi, Makromol. Chem., 1964, 73, 109.
44. R. Frech, S. Chintapalli, P. G. Bruce and C. A. Vincent, Chem. Commun., 1997, 6, 157.
45. A. Bernson, J. Lindgren, W. Huang and R. Frech, Polymer, 1995, 36, 4471.
46. Å. Wendsjö, J. Lindgren and C. Paluszkiewicz, Electrochimica Acta, 1992, 37, 1689.
47. A. Ferry, Thesis, Umeå University, 1996.
48. A. Johansson, Å. Wendsjö and J. Tegenfeldt, Electrochimica Acta, 1992, 37, 1487.
49. B. K. Annis, J. D. Londono and J. Z. Turner, ISIS Exp. Report, 1996, Vol II, A413.
50. J. Shi and C. A. Vincent, Solid State Ionics, 1993, 60, 11.
51. Scaling Concepts in Polymer Physics, P. G. de Gennes, Cornell University Press, Ithaca, New York, 1979.
52. M. S. Mendolia and G. C. Farrington, Chem. Mater., 1993, 5, 174.
53. Lithium Batteries for Electric Road Vehicle Applications, NUTEK ( Swedish National Board for Industrial and Technical Development ) report, 1995, 45, front cover.
54. H. Matsuura, T. Miyazawa and K. Machida, Spectrochim. Acta, 1973, 29A, 771.
55. Y. Y. Wei, B. Tinant, J-P. Declercq, M. van Meerssche and J. Dale, Acta Cryst., 1987, C43, 1076, 1080, 1270, 1274 and 1279.
56. R. D. Rogers, J. Zhang and C. B. Bauer, J. Alloys and Compounds, 1997, 249, 41 and references therein.
57. J. T. Dudley, D. P. Wilkinson, G. Thomas, R. LeVae, S. Woo, H. Blom, C. Horvath, M. W. Juzkow, B. Denis, P. Juric, P. Aghakian and J. R. Dahn, J.Power Sources, 1991, 35, 59.
58. M. Forsyth, D. R. MacFarlane, J. Sun, J. M. Hey and P. Meakin, Adv. Sci. Technol., 1995, 4, 262.
59. A. M. Sukeshini, A. Nishimoto and M. Watanabe, Solid State Ionics, 1996, 86-88, 385.
60. J. Sun, D. R. MacFarlane and M. Forsyth, Solid State Ionics, 1996, 85, 137.
61. J. Przyluski and W. Wieczorek, Solid State Ionics, 1992, 53-56, 1071.
62. SI Chemical Data ( 3rd ed. ), G. Aylward and T. Findlay, J. Wiley & Sons, Brisbane, 1994.
63. M. M. Doeff, S. J. Visco, Y. Ma, M. Peng, L. Ding and L. C. De Jonghe, Electrochimica Acta, 1995, 40, 2205 and references therein.
64. J-L Souquet, M. Duclot and M. Levy, Solid State Ionics, 1996, 85, 149.
65. J. Foropoulos and D.D. DesMarteau, Inorg. Chem., 1984, 23, 3720.
66. A. Vallée, S. Besner and J. Prud'homme, Electrochimica Acta, 1992, 37, 1579.
67. M. Armand, M. Gaulthier and R. Andréani in Proc. Second Int. Symp. on Polymer Electrolytes, B. Scrosati, Ed., Elsevier Applied Science, New York, 1990.
68. M. Armand, M. Gaulthier and D. Muller, U.S. Patent #5,021,308, 1991.
69. I. Rey, J. C. Lassègues, J. Grondin and L. Servant, Electrochimica Acta, 1998, in press.
70. S. Abbrent, J. Lindgren, J. Tegenfeldt and Å. Wendsjö, Electrochimica Acta, 1998, in press.
71. R. Arnaud, D. Benrabah and J.-Y. Sanchez, J. Phys. Chem., 1996, 100, 10882.
72. P. Johansson, J. Tegenfeldt and J. Lindgren, to be published.
73. J. M. Parker, P. V. Wright and C. C. Lee, Polymer, 1981, 22, 1305.
74. M. B. Armand and M. Gauthier in High-Conductivity Solid Ionic Conductors, T. Takahashi, Ed., World Scientific Press, Singapore, 1989.
75. Electrochemical Methods, A. J. Bard and L. R. Faulkner, J. Wiley & Sons, New York, 1980.
76. J. F. LeNest, A. Gandini and H. Cheradame, Br. Polym. J. 1988, 20, 253.
77. W. Wixwat, Y. Fu and J. R. Stevens, Polymer, 1991, 32, 1181.
78. F. M. Gray, Solid State Ionics, 1990, 40/41, 637.
79. M. J. Smith, C. J. Silva and M. M. Silva, Solid State Ionics, 1993, 60, 73.
80. S. Harris, D. F. Shriver and M. A. Ratner, Macromolecules, 1986, 19, 987.
81. A. L. Tipton, M. C. Lonergan, M. A. Ratner, D. F. Shriver, T. T. Y. Wong and K. Han, J. Phys. Chem., 1994, 98, 4148.
82. J. J. Fontanella, M. C. Wintersgill, M. K. Smith, J. Semancik and C. G. Andeen, J. Appl. Phys., 1986, 60, 2665.
83. P. G. Bruce and C.A. Vincent, Faraday Discuss. Chem. Soc., 1989, 88, 43.
84. S. D. Druger, A. Nitzan and M. A. Ratner, J. Chem. Phys, 1983, 79, 3133.
85. S. D. Druger, M. A. Ratner and A. Nitzan, Solid State Ionics, 1983, 9/10, 1115.
86. M. A. Ratner and A. Nitzan, Faraday Discuss. Chem. Soc., 1989, 88, 19.
87. M. A. Ratner in Polymer Electrolyte Reviews 1, J. R. MacCallum and C. A. Vincent, Eds., Elsevier, London, 1987, p. 173.
88. A. Johansson and J. Tegenfeldt, J. Chem. Phys., 1996, 104, 5317.
89. K. Hikichi and J. Furuichi, J. Polym. Sci.:A, 1965, 3, 3003.
90. I. Rey, Thesis, University of Bordeaux I, 1997.
91. J-C. Lasssgues, J-L. Bruneel, I. Rey, L. Servant and L. Vigneau, Mol. Cryst. Liq. Cryst., in press.
92. I. Rey, J-L. Bruneel, J. Grondin, L. Servant and J-C. Lassgues, J. Electrochem. Soc., in press.
93. P. M. Blonsky, D. F. Shriver, P. Austin and H. R. Allcock, J. Am. Chem. Soc., 1984, 106, 6854.
94. J. C. Hutchinson, R. Bissessur and D. F. Shriver in Nanotechnology : Molecularly Designed Materials, ACS Symp. Ser. 622, G-M Chow and K. E. Gonsalves, Eds., 1996, chap. 18.
95. M. A. Mehta and T. Fujinami, Chem. Lett., 1997, 9, 915.
96. C. A. Angell, C. Liu and E. Sanchez, Nature, 1993, 362, 137.
97. M. D. Ingram, Nature, 1993, 362, 112.
98. G. M. Kloster, J. A. Thomas, P. W. Brazis, C. R. Kannewurf and D. F. Shriver, Chem. Mater., 1996, 8, 2418.
99. B. L. Papke, R. Dupon, M. A. Ratner and D. F. Shriver, Solid State Ionics, 1981, 5, 685.
100. R. Dupon, B. L. Papke, M. A. Ratner, D. H. Whitmore and D. F. Shriver, J. Am. Chem. Soc., 1982, 104, 6247.
101. S. Schantz, J. Sandahl, L. Börjesson, L. M. Torell and J. R. Stevens, Solid State Ionics, 1988, 28-30, 1047.
102. A. Bernson and J. Lindgren, Solid State Ionics, 1993, 60, 37.
103. W. Huang, R. Frech and R. A. Wheeler, J. Phys. Chem, 1994, 98, 100.
104. S. P. Gejji, K. Hermansson and J. Lindgren, J. Phys. Chem., 1993, 97, 3712.
105. S. P. Gejji, K. Hermansson, J. Tegenfeldt and J. Lindgren, J. Phys. Chem., 1993, 97, 11402.
106. D. H. Johnston and D. F. Shriver, Inorg. Chem., 1993, 32, 1045.
107. T. Yoshihara, H. Tadokoro and S. Murimashi, J. Chem. Phys, 1964, 41, 2902.
108. H. Matsuura and K. Fukuhara, J. Polym. Sci. Part B : Polym. Phys., 1986, 24, 1383.
109. A. Bernson and J. Lindgren, Polymer, 1994, 35, 4842.
110. A. Bernson and J. Lindgren, Polymer, 1994, 35, 4848.
111. R. Frech and W. Huang, Macromolecules, 1995, 28, 1246.
112. J. Maxfield and W. I. Shepherd, Polymer, 1975, 16, 505.
113. H. Matsuura and T. Miyazawa, J. Polym. Sci.: Part 2A, 1969, 7, 1735.
114. P. V. Wright in Polymer Electrolyte Reviews 1, J. R. MacCallum and C. A. Vincent, Eds., Elsevier, London, 1987, p. 61.
115. C. V. Raman and K. S. Krishnan, Nature, 1928, 121, 501.
116. Ronald Alsop, Wall Street Journal, 1983, Aug 23: 2, 1.
117. M. W. Schmidt, K. K. Baldridge, J. A. Boatz, S. T. Elbert, M. S. Gordon, J. H. Jensen, S. Koseki, N. Matsunaga, K. A. Nguyen, S. Su, T. L. Windus, M. Dupuis and J. A. Montogomery Jr., J. Comp. Chem., 1993, 14, 1347.
118. GAUSSIAN 94, Revision B.2;(E.2), M. J. Frisch, G. W. Trucks, H. B. Schlegel, P. M. W. Gill, B. G. Johnson, M. A. Robb, J. R. Cheeseman, T. Keith, G. A. Petersson, J. A. Montgomery, K. Raghavachari, M. A. Al-Laham, V. G. Zakrzewski, J. V. Ortiz, J. B. Foresman, J. Cioslowski, B. B. Stefanov, A. Nanayakkara, M. Challacombe, C. Y. Peng, P. Y. Ayala, W. Chen, M. W. Wong, J. L. Andres, E. S. Replogle, R. Gomperts, R. L. Martin, D. J. Fox, J. S. Binkley, D. J. Defrees, J. Baker, J. P. Stewart, M. Head-Gordon, C. Gonzalez, and J. A. Pople, Gaussian, Inc., Pittsburgh PA, 1995.
119. Spartan 4.1, Wavefunction, Inc., 18401 Von Karman Ave.,#370, Irvine, CA, 92715 U.S.A., ©1995 Wavefunction Inc..
120. Ab Initio Molecular Orbital Theory, W. J. Hehre, L. Radom, P. V. R. Schleyer and J. A. Pople,Wiley, New York, 1986.
121. Modern Quantum Chemistry ( revised 1st ed. ), A. Szabo and N. S. Ostlund, McGraw-Hill, New York, 1989.
122. Computational Quantum Chemistry, A. Hinchliffe, John Wiley & Sons, Chichester, 1988.
123. J. Sauer, Chem. Rev., 1989, 89, 199.
124. C. Møller and M. S. Plesset, Phys. Rev., 1934, 46, 618.
125. Exploring Chemistry with Electronic Structure Methods ( 2nd ed.), J. B. Foresman and Æ. Frisch, Gaussian Inc. 1996.
126. A. D. Becke, J. Chem. Phys., 1988, 88, 2547.
127. C. Lee, W. Yang and R. G. Parr, Phys. Rev. B, 1988, 37, 785.
128. A. D. Becke, J. Chem. Phys., 1993, 98, 5648.
129. A. P. Scott and L. Radom, J. Phys. Chem., 1996, 100, 16502.
130. The Reaction Path in Chemistry: Current Approaches and Perspectives, D. Heidrich, Ed., Kluwer Acad. Publ., Dordrecht, 1995.
131. C. Peng and H. B. Schlegel, Israel J. Chem., 1993, 33, 449.
132. F. Müller-Plathe, Acta Polymer, 1994, 45, 259.
133. F. Müller-Plathe and W. F. van Gunsteren, J. Chem. Phys., 1995, 103, 4745.
134. E. O. John, R. D. Willett, B. Scott, R. L. Kirchmeier and J. M. Shreeve, Inorg. Chem., 1989, 28, 893.
135. J. Dale, Israel J. Chem., 1980, 20, 3.
136. R. Hilgenfeld and W. Saenger in Topics in Current Chemistry 101: Host Guest Complex Chemistry II, F.Vögtle, Ed., Springer-Verlag,Heidelberg, 1982, p. 1.
137. H. -J. Gais, J. Vollhardt, G. Hellmann, H. Paulus and H. J. Lindner, Tetrahedron Lett., 1988, 29, 1259.
138. G. D. Smith, R. L. Jaffe and H. Partridge, J.Phys.Chem., 1997, 101, 1705.
139. P. T. Boinske, L. Curtiss, J. W. Halley, B. Lin and A. Sutjianto, J. Computer-Aided Materials Design, 1996, 3, 385.
140. R. Frech and W. Huang, Solid State Ionics, 1994, 72, 103.
141. R. Kreitner, J. Park, M. Xu, E. M. Eyring and S. Petrucci, Macromolecules, 1996, 29, 4722.
142. S. P. Gejji, J. Tegenfeldt and J. Lindgren, Chem. Phys. Letters, 1994, 226, 427.
143. D. Aurbach, Y. Ein-Eli, O. Chusid, Y. Carmeli, M. Babai and H. Yamin, J. Electrochem. Soc., 1994, 141, 603.
144. Ions in solution: basic principles of chemical interactions, J. Burgess, Ellis Horwood Ltd., Chichester, 1988.
145. R. J. Blint, J. Electrochem. Soc., 1995, 142, 696.
146. P. G. Bruce, Electrochimica Acta, 1995, 40, 2077.
147. P. G. Bruce, Faraday Discuss. Chem. Soc., 1989, 88, 91.
148. S. J. Wen, T. J. Richardson, D. I. Ghantous, K. A. Striebel, P. N. Ross and E. J. Cairns, J. Electroanal. Chem., 1996, 408, 113.
149. D. Benrabah, R. Arnaud and J.-Y. Sanchez, Electrochimica Acta, 1995, 40, 2437.
150. A. Haas, Ch. Klare, P. Betz, J. Bruckmann, C. Krüger, Y. -H. Tsay and F. Aubke, Inorg. Chem., 1996, 35, 1918.
151. Dr. Yuri Andreev, personal communication.
152. P. Johansson, J. Tegenfeldt and J. Lindgren, unpublished results.
153. P. Johansson, J. Tegenfeldt and J. Lindgren, unpublished results.
154. P. Johansson, J. Tegenfeldt and J. Lindgren, unpublished results.
155. A. Brodin, B. Mattsson, K. Nilsson, L. M. Torell and J. Hamara, Solid State Ionics, 1996, 85, 111.
156. W. Huang, R. A. Wheeler and R. Frech, Spectrochim. Acta, 1994, 50A, 985.
157. Following suggestions from Dr. Jan Jensen, who is gratefully acknowledged.
158. Å. Lauenstein, Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, Uppsala, 1996, 232.
159. A. Bakker, S. P. Gejji, J. Lindgren, K. Hermansson and M. M. Probst, Polymer, 1995, 36, 4371.