摘要:

317 333 35 1 General Discussion 361 List of Posters 363 Index of Names Polyanilines: A Novel Class of Conducting Polymers A. G . MacDiarmid and A. J. Epstein The Structural Background of Charge-carrier Motion in Conducting Polymers G. Wegner and J. Ruhe317 333 35 1 General Discussion 361 List of Posters 363 Index of Names Polyanilines: A Novel Class of Conducting Polymers A. G . MacDiarmid and A. J. Epstein The Structural Background of Charge-carrier Motion in Conducting Polymers G. Wegner and J. Ruhe

ISSN:0301-7249    

DOI:10.1039/DC98988FX001

出版商:RSC    

年代:1989

数据来源: RSC

摘要:

GENERAL DISCUSSIONS OF THE FARADAY SOCIETY/FARADAY DISCUSSIONS OF T H E CHEMICAL SOCIETY Dare I907 1907 1910 191 I 1912 1913 1913 1913 1914 1914 1915 1916 1916 1917 1917 1917 1918 1918 1918 1918 1919 1919 I920 I920 I920 I920 1921 1921 1921 1921 1922 I922 1923 I923 I923 1923 I923 I924 I924 1924 1924 I924 1925 I925 1926 1926 1927 1927 1927 1928 1929 1929 I929 Subjecr Osmotic Pressure Hydrates in Solution The Constitution of Water High Temperature Work Magnetic Properties of Alloys Colloids and their Viscosity The Corrosion of Iron and Steel The Passivity of Metals Optical Rotatory Power The Hardening of Metals The Transformation of Pure Iron Methods and Appliances for the Attainment of High Temperatures i n a Refractory Materials Training and Work of the Chemical Engineer Osmotic Pressure Pyrometers and Pyrometry The Setting of Cements and Plasters Electrical Furnaces Co-ordination of Scientific Publication The Occlusion of Gases by Metals The Present Position of the Theory of Ionization The Examination of Materials by X-Rays The Microscope: Its Design, Construction and Applications Basic Slags: Their Production and Utilization in Agriculture Physics and Chemistry of Colloids Electrodeposition and Electroplating Capillarity The Failure of Metals under Internal and Prolonged Stress Physico-Chemical Problems Relating to the Soil Catalysis with special reference to Newer Theories of Chemical Action Some Properties of Powders with special reference to Grading by Elutriation The Generation and Utilization of Cold Alloys Resistant to Corrosion The Physical Chemistry of the Photographic Process The Electronic Theory of Valency Electrode Reactions and Equilibria Atmospheric Corrosion.First Report Investigation on Oppau Ammonium Sulphate-Nitrate Fluxes and Slags in Metal Melting and Working Physical and Physico-Chemical Problems relating to Textile Fibres The Physical Chemistry of Igneous Rock Formation Base Exchange in Soils The Physical Chemistry of Steel-Making Processes Photochemical Reactions in Liquids and Gases Explosive Reactions i n Gaseous Media Physical Phenomena at Interfaces, with special reference to Molecular Atmospheric Corrosion. Second Report The Theory of Strong Electrolytes Cohesion and Related Problems Homogeneous Catalysis Crystal Structure and Chemical Constitution Atmospheric Corrosion of Metals.Third Report Molecular Spectra and Molecular Structure Laboratory Orientation I930 Colloid Science Applied to Biology Volume Trans. 3* 3* 6* 7* 8* 9* 9* 9* 1 o* I I 12* 12* 13* 13* 13* 14* 14* 14* 14* 15* 15* 16* 16* 16* 16* 17* 17* 17* 17* 18* 18 19* 19 19* 19 19* 20* 20* 20 20* 21 21* 22* 22* 23* 23* 24* 24 * 25* 25* 26* 26 10: 20;Faraday Discussions of the Chemical Society Date 1931 1932 1932 1933 1933 I934 I934 1935 1935 1936 I936 1937 I937 1938 1938 I939 1939 1940 1941 1941 I942 1943 I944 1945 1945 I946 I946 I947 1947 1947 I947 I948 1948 1949 1949 1949 1950 1950 I950 1950 1951 195 I 1952 1952 I952 I953 1953 I954 I954 1955 I955 I956 I956 1957 I958 1957 I958 1959 1959 I960 1960 1961 1961 1962 I962 I963 Subject Photochemical Processes The Adsorption of Gases by Solids The Colloid Aspect of Textile Materials Liquid Crystals and Anisotropic Melts Free Radicals Dipole Moments Colloidal Electrolytes The Structure of Metallic Coatings, Films and Surfaces The Phenomena of Polymerization and Condensation Disperse Systems i n Gases: Dust, Smoke and Fog Structure and Molecular Forces in ( a ) Pure Liquids, and ( h ) Solutions The Properties and Functions of Membranes, Natural and Artificial Reaction Kinetics Chemical Reactions Involving Solids Luminescence Hydrocarbon Chemistry The Electrical Double Layer (owing to the outbreak of war the meeting was The Hydrogen Bond The Oil-Water Interface The Mechanism and Chemical Kinetics of Organic Reactions in Liquid The Structure and Reactions of Rubber Modes of Drug Action Molecular Weight and Molecular Weight Distribution in High Polymers (Joint Meeting with the Plastics Group, Society of Chemical Industry) The Application of Infra-red Spectra to Chemical Problems Oxidation Dielectrics Swelling and Shrinking Electrode Processes The Labile Molecule Surface Chemistry (Jointly with the Societe de Chimie Physique at Bordeaux) Colloidal Electrolytes and Solutions The Interaction of Water and Porous Materials The Physical Chemistry of Process Metallurgy Crystal Growth Lipo-protei ns Chromatographic Analysis Heterogeneous Catalysis Physico-chemical Properties and Behaviour of Nuclear Acids Spectroscopy and Molecular Structure and Optical Methods of Investigating Electrical Double Layer Hydrocarbons The Size and Shape Factor in Colloidal Systems Radiation Chemistry The Physical Chemistry of Proteins The Reactivity of Free Radicals The Equilibrium Properties of Solutions on Non-electrolytes The Physical Chemistry of Dyeing and Tanning The Study of Fast Reactions Coagulation and Flocculation Microwave and Radio-frequency Spectroscopy Physical Chemistry of Enzymes Membrane Phenomena Physical Chemistry of Processes at High Pressures Molecular Mechanism of Rate Processes in Solids Interactions in Ionic Solutions Configurations and Interactions of Macromolecules and Liquid Crystals Ions of the Transition Elements Energy Transfer with special reference to Biological Systems Crystal Imperfections and the Chemical Reactivity of Solids Oxidation-Reduction Reactions i n Ionizing Solvents The Physical Chemistry of Aerosols Radiation Effects in Inorganic Solids The Structure and Properties of Ionic Melts Inelastic Collisions of Atoms and Simple Molecules High Resolution Nulcear Magnetic Resonance The Structure of Electronically Excited Species in the Gas Phahe abandoned, but the papers were printed in the Transactions) Systems Published by Butterworths Scientific Publications, Ltd Cell Structure Volume 27* 28 29 29* 30* 30 31* 31* 32* 32* 33* 33* 34" 34* 35* 35* 35" 36* 37* 37* 38 39* 401 41 42* 42 A* 42 B Disc.I * 2 Trans. 43" Disc. 3 4* 5* 6 7* 8* Trans. 46" Disc. 9* Trans. 47* Disc. 10* 1 I * 12* 13 14 IS 16* 17 18* 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33* 34 35Date 1963 1964 1964 1965 1965 1966 1966 1967 1967 1968 1968 1969 1969 1970 1970 197 1 1971 1972 1972 1973 1973 1974 1974 1975 1975 1976 1977 1977 1977 1978 1978 1979 1979 1980 1980 1981 1981 1982 1982 1983 1983 1984 1984 1985 1985 1986 1986 1987 1987 1988 1988 1989 Faraday Discussions of the Chemical Society Subject Fundamental Processes in Radiation Chemistry Chemical Reactions in the Atmosphere Dislocations in Solids The Kinetics of Proton Transfer Processes Intermolecular Forces The Role of the Adsorbed State in Heterogeneous Catalysis Colloid Stability in Aqueous and Non-aqueous Media The Structure and Properties of Liquids Molecular Dynamics of the Chemical Reactions of Gases Electrode Reactions of Organic Compounds Homogeneous Catalysis with Special Reference to Hydrogenation and Bonding in Metallo-organic Compounds Motions in Molecular Crystals Polymer Solutions The Vitreous State Electrical Conduction in Organic Solids Surface Chemistry of Oxides Reactions of Small Molecules in Excited States The Photoelectron Spectroscopy of Molecules Molecular Beam Scattering Intermediates in Electrochemical Reactions Gels and Gelling Processes Photo-effects in Adsorbed Species Physical Adsorption in Condensed Phases Electron Spectroscopy of Solids and Surfaces Precipitation Potential Energy Surfaces Radiation Effects in Liquids and Solids Ion-Ion and Ion-Solvent Interactions Colloid Stability Structure and Motion in Molecular Liquids Kinetics of State Selected Species Organization of Macromolecules in the Condensed Phase Phase Transitions in Molecular Solids Photoelectrochemistry High Resolution Spectroscopy Selectivity in Heterogeneous Catalysis Van der Waals Molecules Electron and Proton Transfer Intramolecular Kinetics Concentrated Colloidal Dispersions Interfacial Kinetics in Solution Radicals in Condensed Phases Polymer Liquid Crystals Physical Interactions and Energy Exchange at the Gas-Solid Interface Lipid Vesicles and Membranes Dynamics of Molecular Photofragmentation Brownian Motion Dynamics of Elementary Gas-phase Reactions Solvation Spectroscopy at Low Temperatures Catalysis by Well Characterised Materials Oxidation Volume 36 37 38 39 40 41 * 42* 43 44 45 46 47 4% 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65* 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 * Not available; for current information on prices etc., of available volumes, please contact the Marketing Oficer, Royal Society of Chemistry, Thomas Graham House, Science Park, Milton Road, Cambridge CB4 4 WF, stating whether or not you are a member of the Society.

ISSN:0301-7249    

DOI:10.1039/DC989880X003

出版商:RSC    

年代:1989

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1989, 88, 19-42 Conductivity in Polymer Ionics Dynamic Disorder and Correlation Mark A. Ratner* Department of Chemistry and Materials Research Center, Northwestern University, Evanston, IL 60208, U.S.A. Abraham Nitzan Department of Chemistry, Tel Aviv University, Tel Aviv, Israel Theoretical constructs are developed for discussing diffusivity and conduc- tivity in polymer ionic materials. Such materials are characterized by exten- sive disorder, either static (lack of long-range order) or static and dynamic (lack of long-range order with short-range order evolving with time). Begin- ning with a dynamic percolation model, we show that, in general, so long as the mean-square displacement of the charged particle obeys a certain growth law, the observed charged-particle motion will be diffusive, both in the ballistic regime, corresponding to electronic motion with strong scatter- ing, and in the ionic-hopping regime, corresponding to dynamic disorder renewal of the hopping situation.Some general behaviour for transport under these conditions is predicted, including definite statements about the frequency dependence of the conduction, the relationship between the growth law in a single interval and the growth law for observation times long compared to scattering or renewal times, and the behaviour in the neighbourhood of the percolation threshold for the static problem. Interpre- tations are suggested both for ion and electron-hopping situations. A statistical thermodynamic model is developed for analysis of contact ion pair formation and its effect on conductivity in ion-conducting polymer systems.In this model, the energy (due to solvation and polarization) favouring formation of a homogeneous complex in which the cations are solvated by the polymer host, competes with an entropic term favouring the separated structures (free polymer and contact ion pairs). We derive general conditions for this phase separation, and an expression for the number of polymer-bound, homogeneously solvated ions. We show that this number will, in general, decrease monotonically with increase in temperature, due to entropic favouring of the phase-separated material, this is reminiscent of the lower consolute temperature phenomenon in liquid mixtures. 1. Introduction Polymer conductive ionics, or polymeric solid electrolytes, are the newest and most actively investigated area of solid electrolytes.'-' These materials were first developed at Sheffield,77s Grenoble' and EvanstonlO in the 1970s, and interest in them is now very widespread indeed.Part of this interest arises from possible applications as electrolyte materials in electroactive devices; the remainder arises from their intrinsic scientific interest as dynamically disordered solid materials exhibiting ionic diffusivity of a magni- tude more characteristic of that of ionic liquids or solutions. The class of polymer conductive ionics now includes, in addition to the originally prepared and investigated polymer-salt complex solvent-free polyelectrolytes"-'' and mixed ionic-electronic conductors.14-" The mixed conductors 1920 Conductivity in Polymer Ionics really lie outside the scope of our discussion here, although a number of other contribu- tions to this Faraday Discussion will centre on so-called redox polymers, a specific example of such materials. 1 7 , ' * Similarly, we will not discuss polyelectrolytes per se, though solvent-free polyelectrolytes in fact exhibit behaviour very similar to the polymer- salt complexes, differing only in the transference-number behaviour. Our discussion, then, like most of the experiments reported to date in the field, will centre on simple polymer-salt complex materials. These solvent-free polymer ionics are generally prepared by dissolving or suspending the polymeric host material and a uni-univalent salt in a joint solvent and then driving off the solvent to prepare either a bulk material or a thin film of the polymer-salt complex.That a new compound, rather than a simple physical mixture, has been prepared is obvious from such physical characteristics as glass-transition temperature (it generally increases, by at least 60 K), viscosity, relaxation time and vibrational spectra. The simple chemical reaction P(ru),, + MX - P(ru);MX represents the formation of the complex, where MX is the salt, ru is the repeating unit of the polymer and n gives the relative stoichiometry of repeating units to salt. In the earliest materials to be studied, the repeating units were polyethers, with Lewis-base oxygens in the backbone. In particular, polyethylene oxide( PE0)- and polypropylene oxide( PP0)-based materials were studied extensively in the 1970s.More recent work is concentrated on more flexible polymer materials, including in particular so-called comb polymers, in which a very flexible backbone such as ~ i l o x a n e ' ~ - ~ ' or phosphazene22323 is substituted with short-chain oligoethers to provide the Lewis-base sites for complexing to the alkali M. The polymer-salt complex electrolyte indicated on the right-hand side of eqn ( 1 ) can be structurally quite intricate. It has been convincingly demonstrated experimentally that the homogeneous elastomeric amorphous phase of the polymer-salt complex in fact provides the conductivity; partially crystalline phases reduce overall ionic mobility. We will therefore concentrate, in our discussion, on ion dynamics in the homogeneous elastomeric (melt) phase.Much of the intrinsic interest in these materials arises from their unusual conduction mechanism. In sharp contrast to ionic conductors based on crystalline solids or glasses, in these materials the Walden relation, stating that diffusivity is proportional to inverse viscosity, holds quite well. In this sense, these materials are more like liquid electrolytes, or ionic fluids, than like characteristic solid electrolytes. The applicability of the Walden relation argues that the polymeric host environment actively promotes ionic transport in these substances. This is in fact true, as will be detailed in Section 3 , and comprises the basis for mechanistic understanding of transport in these substances.Just as the polymer electrolytes differ from crystalline and glassy conductors because of the importance of host-chain dynamics in promoting transport, so they differ from simple liquid electrolytes such as aqueous solutions or molten salts, because the host itself is a high polymer, and exhibits the slow relaxation times, long-range correlations and high configurational entropies characteristic of high polymers. The earliest suggestions for describing mechanistically the transport in these materials were based on simple hopping models, taken from crystalline solid electrolytes.8 Such models were introduced for several reasons, partly because the earlier materials (such as PEO), were in fact partially crystalline. The fundamental assumption of these suggestions, that ionic motion occurred in structurally fixed pathways, is incorrect.A number of experimental observations demonstrate clearly the unusual and interesting mechanistic behaviour of ionic transport in these complex materials. Examples include: (1) For a number of these substances, there is a linear relationship between the logarithm of the conductivity, and the logarithm of the so-called shift factor,M. A. Ratner and A. Nitzan 21 0.5 b ' on 0.6 - 0.7 Fig. 1. Correlation between the shift factor uT describing physical relaxation and the conductivity for PEO networks, with low concentrations of salt. The direct proportionality, with slope of unity, implies conductivity inversely proportional to viscosity, as assumed in the Stokes- Einstein relation- ship or Walden relationship.From ref. (25). E - I c b 1 0 cations per polymer repeat unit Fig. 2. Conductivity and glass-transition temperature of MEEP complexes containing AgCF3S03. Note that the glass-transition temperature increases monotonically with salt concentration, and that the ionic conductivity maximizes at relatively low salt concentration. From ref. (22). which describes structural relaxation in polymeric systems. Such correlation, measured by the Grenoble group,2s is illustrated in fig. 1 . (2) Upon change in stoichiometry, conductivity exhibits a highly non-monotonic behaviour with salt concentration. An example, for phosphazine-based material, is shown in fig. 2.22 0.10 0.08 Conductivity in Polymer Ionics 0 .- Y 2 A c Y .- ln Y .- I o - ~ Id8 1 o-' c I E c I \ c: b 0 5 10 15 20 25 30 35 Fig.3. The relative intensities of the vibrational components of the SO3 symmetric stretch in the triflate ion versus inverse salt concentration for modes due to free ions (O), ion pairs (0) and multiple ion aggregates ( A).41 The right-hand scale shows ionic conductivity. Note the reduction in free ions for either high or low salt concentrations. The measurements were made in polypropy- lene glycol, based on vibrational spectra. From ref. (41). (3) The number of free ions in such materials changes non-monotonically as a function of concentration. An example, based on observations22 of vibrational spectra, is shown in fig. 3. (4) In hosts such as PPO, which have relatively lower stability constants for formation of Lewis acid-base adducts with the alkali, a 'salting out' phenomenon is observed at high temperatures, with the crystalline salt precipitating from the complex, which was homogeneous at lower temperatures.26 ( 5 ) Addition of crown ethers or cryptates, which form tight cages around the cation, results in increased Our aim here is to discuss microscopic models for describing such behaviour.Observations ( 1 ) and (2) can be understood straightforwardly on the basis of the diffusion of independent ions in a dynamically disordered polymer host, and are the subject of sections 2 and 3. The last three results are due to the Coulomb interaction of the ions in the material, which corresponds to a highly concentrated Coulomb fluid. Their explanation is more complex, but some steps in that direction are made in Section 4.Finally, Section 5 gives a current view of mechanistic behaviour in these ionic materials, and relates them to other conduction processes in polymers. as a function of temperature, shown in fig. 4.M. A. Ratner and A. Nitzan T / "C -5.0 - -5.5 - - 1 E - 5 -6.0 b M -7.0 -7.5 1 8 10 12 1 0 3 ( ~ - TJ~/K-' 23 Fig. 4. Temperature dependence of the conductivities for a sulphonate polyelectrolyte based on a siloxane backbone, with increasing amounts of polyelectrolyte charge. The symbols A, 0 and 0 indicate 20, 30 and 50% charged groups on the comb backbone, respectively, with Na+ as the mobile ion. The symbols, 0, 0, and 4 are the conductivities measured after adding tetra- ethylene glycol, dimethyl tetra-ethylene glycol, MPEG and 18-crown-6, respectively, at a 1 : 1 concentration ratio to sodium cation.Note the increase in conductivity, due to the break-up of contact ion pairs, on adding sequestering agents. From ref. (61). 2. Some Experimental Observations: Requirements for Mechanism We consider single-phase, homogeneous elastomeric polymer-salt complex materials. These exhibit purely ionic diffusivity and conductivity. The materials in question contain no small-molecule solvents, with the polymer phase itself acting as a solvent for the salt MX. The materials are characterized by both static and dynamic disorder. The static disorder simply arises from the structure and morphology of the polymer chain itself. These materials are non-crystalline, and although the polymer may exhibit helical regions (as PPO does), no crystalline phases occur; no crystalline scattering patterns are seen either in optical microscopy or X-ray scattering. The dynamic disorder is a slightly more complicated process.Polymer ionics, unlike glassy ionic materials, are always studied well above their glass-transition temperature, Tg. While the glass transition is a rather complicated phenomenon, at temperatures exceeding Tg, the local structure is in fact molten, with rapid changes in local bond and dihedral angles. The materials above Tg are soft and plastic, exhibiting high viscosities and solid-like physical properties. These arise from the entanglements of the long chains; very short-chain materials flow easily above Tg, and would not normally be considered solids. While static disorder (the absence of crystallographic long-range24 Conductivity in Polymer Ionics order) is found in the glassy materials such as sodium silicate, these glasses do not exhibit dynamic disorder: in glasses, local metrical information is preserved in time.In dynamically disordered systems, like liquid water or polymer electrolytes, the nearest- neighbour, next-nearest-neighbour, next-next-nearest-neighbour, etc., shells around a given atom or ion will change in time, as orientational and vibrational modes of low frequency and high amplitude are excited. Experimental studies, such as those already discussed in Section 1, place several stringent requirements on a mechanistic picture describing ionic mobility in these materials.Perhaps the most important observation is the necessity, as is clear from the relationship in fig. 1 between relaxation properties and conductivity, for the dynamical motions in the polymer host itself to promote ion transfer. In this sense, we deal with a coupled process between ionic motion and host dynamics. Angel12”3’ has provided a very useful description of the coupling between ionic diffusivity and host motion. He defines the decoupling index, R, by where T, and r, are, respectively, relaxation times corresponding to conductivity and structural relaxation. In molten salts or liquid electrolytes, the structural relaxation is intimately connected with the conductivity relaxation and this ratio is roughly unity. As a molten electrolyte is cooled, if it forms a glassy electrolyte, below a certain fictive temperature,” at which the relaxation processes fall out of equilibrium, there will be a decoupling of the large-scale orientational (structural relaxation) modes of the host and the hopping diffusion of the ions. Thus, in typical glassy electrolytes, the decoupling index, R,, can approach values of lo’?, as relaxation times, or at least the longer relaxation times, approach a macroscopic size of the order of seconds, minutes or hours.In the polymer electrolytes, this ratio is generally of the order of unity; indeed, it will often fall below unity for concentrated electrolytes, as certain motions that contribute to structural relaxation do not promote ion transfer. This is evidence for interionic correlation, and will be discussed in Section 4. That segmental motion of the polymer host is required to promote ion transport is obvious from a number of experiments.Perhaps the most striking is the fact that in many materials the thermal dependence of the conductivity can be expressed in the so-called Vogel-Tamman- Fulcher I - h * 3 3 9 i 4 form of aT = uo exp[ - B / ( T - To)] ( 3 ) where a is the conductivity, B is a constant related to the inverse expansivity of the material, and To is a reference temperature, generally ca. 50 degrees below the glass- transition temperature. This form was originally used to discuss the viscosity of polymeric materials; the fact that viscosity and conductivity are inversely related, essentially the physical content of the Walden relationship, suggests very strongly that structural motions of the polymer are required for diffusive motions leading to conduction. The explanation of a large number of other experimental facts, conveniently reviewed elsewhere, also requires a dynamical coupling of the segmental motion of the polymer host with ion diffusion.Physically, the picture is simply that well defined passageways, or channels, such as are characteristic of crystalline ionic conductors like AgI or Ag-S are simply not present in these soft polymeric substances. Rather, spaces for ionic motion to occur must form due to activated motions of the polymer host. This physical picture underlies free-volume theory,” the quasi-macroscopic model that has been extensively, and very usefully, employed in the polymer electrolytes Although host motions are required for conductivity, by themselves they are not sufficient.Thus, for example, the conductivity of NaBH, complexes in PEO is quite small,38 as is, characteristically, ionic diffusion in most non-ethereal polymer hosts.M. A. Ratner and A. Nitzan 25 Thus, it appears necessai-y that the acid-base interaction between the polymer hosts and the salt is strong enough to cause solvation, but not so strong as to militate against exchange of the coordination environment of the mobile ion. 3. Independent Particle Transport: Dynamic Percolation Theory Formulation of Model The results of extensive experimental investigation of polymeric electrolytes, including those just discussed, place substantial constraints both on the mechanism of ion transport and on any model that might be formulated to discuss ion transport in these materials.Perhaps the most important result is that the motion of the ions is strongly dependent on segmental motion of the polymer host. This is clear both from the near-unity value of the decoupling index R,, and from the adequacy of the VTF form of eqn (3) in describing the conductivity. The equivalent WLF form," it should be remembered, is originally defined for structural and relaxation properties; the close similarity of the dependence upon temperature of ionic conduction and polymer relaxation, as indicated in fig. 1, requires that the dynamics of the chain be linked to the transport process. Additionally, the fairly good relative agreement of the Nernst-Einstein relationship between conductivity and diffusivity, with no substantial correction factor^,^' argues that while interionic interaction effects may be important, they are to a first approximation not needed for understanding the dominant conductivity mechanism in most of these systems. This conclusion is underscored by recent spectroscopic experiments that demonstrate quite convincingly that contact ion pair formation, while important, is not dominant in determining the c ~ n d u c t i o n .~ ' ~ ~ ' Based on these two ideas (coupled dynamics of ions and polymer hosts, and fairly weak dependence of conductivity on interionic interactions), it is reasonable to define an independent particle, hopping-type model for ionic motion. We will see later (Section 3) that such a model can be substantially generalized, and thus describe the physics of ionic motion fairly well.The simplest model, then, involves ionic hopping among sites, defined by simple geometry, in the continuous elastomeric phase of the polymer elec- trolyte. Note that, in contrast to crystalline ceramic electrolytes, or heavy-metal elec- trolytes like silver iodide, the sites are not fixed by the crystal structure, but are simply the nodes of a net arbitrarily defined within the continuous phase. The ions will then, under rather general conditions, obey a generalized master equation, or hopping-type equation, of the form: f; == c ( wjpj - W&). (4) Here f, is the probability of finding a mobile ion at site i, and W,I is the probability per unit time that an ion will hop from site j to site i.For simplicity it is generally assumed that W,I is zero except between nearest-neighbour sites; in a continuous elastomeric network, this assumption is eminently justified. The sites are not necessarily defined in terms of any particular binding geometry; for cations, it is reasonable to assume that sites are defined by a locally attractive coordination environment of, say, tetrahedrally disposed oxygens or nitrogens. In contrast, for anion motion the sites are perhaps best defined simply in terms of sufficient geometric space to accommodate such large anions as triflate or tetraphenylborate. In either case, in any given metrically defined region of the continuous material, a stable site for ion occupancy may not exist at any given time; there may be insufficient volume for the anions, or inappropriate coordination environment for the cations.Under such conditions, the probability Wl, for hopping from s i t e j to site i may be zero, if a favourable environment is not available26 Conductivity in Polymer Ionics around site i. Under these conditions, it is appropriate to simplify the jumping prob- abilities as: 0 probability 1 -f w probability f ' Here w is an average hopping rate between two sites available for ionic occupancy, and the relative probability of the site i being available is denoted f: The probability distribution of eqn ( 5 ) is essentially that of a random hopping in which it is assumed that particles can hop between sites, with random jump probabilities chosen from some given distribution.The percolation model is highly appropriate for statically disordered systems, and has been extensively used in glasses, alloys and related materials. The polymer electrolytes are always investigated at temperatures above Tg. In this regime, the materials are both statically and dynamically disordered; in terms of our percolation model, then, a pathway between two sites which was unavailable at a certain time may become available at a slightly later time, as segmental motions of the polymer chain change the local void volume and/or the local coordination environment. It is then appropriate to generalize the static percolation model given by eqn (4) and ( 5 ) to a dynamic percolation model or a dynamic disorder hopping model, 1,3,37*44-53 in which the assignment of any given hopping probability Wg between sites i a n d j as available ( y.i = w ) are unavailable ( y.i = 0) changes in time.The process by which such changes occur is referred to as renewal, or reinitialization, or reassignment and is characterized by a particular average time, called the renewal time, T,,, . Just as one can define different (random) hopping models depending on the details of the distribution of the Wjis and their values among different sites, so one can define different dynamical percolation models depending on how the renewal process occurs. The simplest renewal process assumes that on a given average interval T , ~ ~ , the assignment of which jumps are available and which are unavailable instantly changes.The simplest dynamic percolation theory picture, then, involves use of eqn (4) and ( 5 ) , describing the static percolation, with the additional feature that after a given time-interval the W,is are reassigned. This is fixed by the parameters w, J; and T,,, . These can be related to such system parameters as ion size, free volume, temperature and pressure. In fact, the most important of these parameters is the renewal time, characterizing the rate of change of the availability of a given intersite hop. This rate of change is determined by the dynamics of the polymer host, and therefore T,~" is simply a characteristic relaxation time for a polymer's configurational degrees of freedom. This simplest dynamic percolation model has been rather extensively applied in discussing ionic motion in polymer electrolyte^.^^-^' Some results and applications are discussed in the next subsection, and extensions of the model, which illuminate precisely what is and what is not important about the restrictions defined on this point, are discussed in the subsection following the next.Results: Applications of Dynamic Percolation Models to Polymer Electrolytes A number of very general results follow from the simple definition of the dynamic percolation model; we will first discuss these, then mention briefly some applications to experiments. ( 1 ) For any observation time, fobs, that is long compared to the renewal time, the ionic motion in any dimensionality is always This is illustrated in fig. 5 , in which it is clear that, although over a short time compared to the renewal time, the mean-squared displacement can become asymptotically con- stant (for a system below the static percolation threshold), the renewal processM. A.Ratner and A. Nitzan 27 0 10 20 30 &O Fig. 5. Mean-square displacement as a function of time, for dynamic percolation on a one- dimensional chain. Notice that within each small interval (of relative size 5 time units) the transport becomes limited by the size of the connective cluster, but over many renewal epochs mean-square displacement is indeed linear in temperature. From ref. (44). permits concatenation of such motions resulting in overall diffusive behaviour, with mean-squared displacement proportional to time. This has been shown to hold in any integer dimensionality.(2) For motion in one dimension, the closed-form result of eqn (6) holds for the diffusion Here a is the mean distance between sites. Dependence onf describes essentially how far an ion travels before the renewal process must occur, and the dependence on l / ~ ~ ~ ~ arises from the renewal process itself. (3) In static percolation models, there is generally a percolation threshold, that is there exists a value f t h below which diffusion is not observed.43 No such thresholds exist in renewal models, consistent with experimental observation; nevertheless, a remnant of the threshold behaviour is found in that the value of the diffusion coefficient changes substantially in the region of This is more extensively discussed in the next subsection.(4) The frequency-dependent diffusion coefficient can be rigorously related to the diffusion coefficient Do in the analogous static percolation lattice [ i.e. the problem defined by eqn (4) and ( 5 ) without renewal] by the analytic continuation formula45 This formal result can be quite important, since closed-form expressions often exist, on different lattices with different hopping probabilities, for the mean- squared displacement or static percolation coefficient.28 Conductivity in Polymer Ionics ( 5 ) If certain reasonable assumptions are made relating viscosity to the relaxation, a Walden product can be obtained as: Dq- = mc2(x2),en f l a ' . Here c is the speed of sound in the elastomer, and the notation ( x ' ) , ~ ~ , indicates mean-squared displacement in a single renewal interval.The Walden product is thus predicted to be only weakly temperature dependent, and to depend upon such material properties as the speed of sound and the segment length. The near constancy of this product is in agreement with the results of fig. 1, and with the near constancy of the decoupling ratio R, (which, assuming the validity of Nernst-Einstein relationships, is essentially proportional to the Walden product). (6) The predicted dependence of the diffusivity of system properties is entirely dominated by the dependence upon the polymer renewal relaxation time T,,,. This is in agreement with experimental results. Indeed, it can be shown in general that44*47 (9a 1 where nd = 1/2d with d the space dimension of the hopping net, and the brackets and bar corresponding to averaging over a thermal ensemble and the distribution of renewal times, respectively.The (7) If the conductivity is plotted as a function of frequency on a log-log plot (fig. 6) one notices substantially different behaviour for the mean polymer host and the elastomeric ionic conductor. At frequencies above ca. 10GHz these two responses are essentially identical; this may reflect displacive motions of charges or dipoles within the polymer host. For lower frequencies, only the ions them- selves continue to respond diffusively over longer and longer time scales. Thus the response of the neat polymer drops essentially to zero, while that of the electrolyte flattens out to an asymptotic value at low frequency, corresponding to the d.c.diffusion arising from the renewal process. This is shown in fig. 6, where the results of the dynamic percolation model are contrasted with experiment." (8) Depending on the size of the continuous region over which static percolative diffusion can be observed, the overall diffusivity or conductivity show different dependences upon the renewal rate. This is illustrated in fig. 7, showing two limits. In the small cluster limit (fig. 7) the mean-squared displacement, assuming no unavailable bonds, would be very much larger than the mean size of the connected cluster, Under these conditions, renewal is clearly necessary for diffusion to occur, and the diffusion coefficient is given by eqn ( 9 a ) . On the other hand, if the connected cluster is large enough that the mean-square displacement for simple hopping in the given time is smaller than the extent of the connected cluster, one expects the motion to be independent of the dynamic renewal process.Under these conditions one finds, as expected, - D = nd (r2LrenI ?re" is for a single renewal interval. D = Do= w(r2)nd. Note here that the result is indeed independent of the re-initialization in the host. Eqn ( 9 a ) and ( 9 b ) describe, respectively, conduction in polymer elec- trolytes above Tg and the glassy solid electrolytes below Tg. In the former case, dynamic host motion is necessary to promote ionic diffusivity, whereas in the latter case dynamic diffusion occurs in a relatively fixed host environment, promoted by thermal motions of the host. ( 9 ) The result ( 9 a ) implies thatM.A. Ratner and A. Nitzan 29 t I -5.01 ' I ' I ' ' ' I ' I ' -1.5 -1.0 -0.5 0.0 0.5 log(w/rad s-I) IOMHz 0.IGHt IGHr 10GHz f K ' Fig. 6. (a) Calculated frequency-dependent conductivity for a simple dynamic percolation model. The lower line is the diffusion coefficient without renewal, the upper line that with renewal. (b) For comparison, the frequency-dependent conductivity of pure PEO (- - - - -) and PEO salt complex (-) at 22°C. Only the salt ions are capable of long-distance diffusive motion, corresponding to renewed diffusion. From ref. (51). where F( T ) is the correlation factor correction to the Nernst-Einstein relation- ship. Writing the shift factor as the combination of (loa) and ( l o b ) explains the linear curve of fig.1, if correlation corrections to Nernst- Einstein are relatively unimportant. Other applications of the dynamic percolation model, including comparison of relation to semicrystalline and fully amorphous material^,^^ frequency30 Conductivity in Polymer Ionics Fig. 7. Different diffusion limits for dynamic percolation. In the upper cartoon, the blob represent- ing the mean connected cluster is small compared to the line, representing root-mean-square displacement within a renewal epoch. Under these conditions, conduction will be proportional to the inverse renewal time. The lower cartoon shows the opposite situation, with large mean connected cluster. Under these conditions, the medium will renew before the local connected region is filled and D will be independent of the renewal time. quasimacroscopic transport theorie~,~’ threshold behaviour and the importance of c ~ r c e l a t i o n s , ~ ~ - ~ ~ , ’ ~ are discussed in later papers on dynamic percolation.Aspects and Extensions of the Dynamic Percolation Model In addition to the specific applications discussed above, the dynamic percolation model has been extended to apply beyond the simple independent hopping of particles on a regular lattice. A number of generalizations have in fact been published. Perhaps the most important conclusions to be drawn from these generalizations are as follows. The important results, particularly in the analytic continuation rule, the diffusive nature of the transport and the monotonic increase of diffusion coefficient with frequency for low frequencies, can be shown to hold under much more general condtions.One can relax the site model, permit certain correlations among the different renewal processes and allow the renewal times to be chosen from nearly arbitrary d i ~ t r i b u t i o n s . ~ ” ~ ~ , ~ ~ ~ ~ ~ In fact, the only real requirement for these general results to hold is that the displacements obey a particular growth law?’ The growth law is illustrated in fig. 8, showing an arbitrary function, F, such as the mean-square displacement for a specific sequence of renewal or reassignment events. Analytically, it can be expressed as: Here g ( 7 ) is the growth that would be observed, without further renewal, starting from an arbitrary time 0, before which random renewal had been an on-going process.f ( ~ ~ )M. A. Ratner and A. Nitzan 31 I I 1 1 tl t 2 t time Fig. 8. An illustration of the growth law for mean-square displacement. The solid lines represent the mean-square displacement addition within each time interval. Notice that the growth law, in the sense that the mean-square displacement is additively incremented within each time interval, is obeyed. From ref. (50). of t is the growth that would be observed without further renewal, starting from a previous renewal at t = 0. The time sequences are defined by i=O T, = t , + l - t t , O < i < N . ( 1 W [ : - t N i = N Physically, fig. 8 and eqn (1 1) mean that a particular property ( F might, for example, be associated with mean-square displacement) grows by addition of finite increments, and these finite increments depend upon time intervals.The behaviour illustrated in fig. 8 is precisely that expected for ionic diffusion in a dynamically disordered medium (including both polymer electrolytes and liquid solution), and therefor? the growth law will hold, and the results of the simplest dynamic percolation model will be applicable, for these situations also. The growth law clearly does not require a lattice with sites, nor approximations involving either the correlation of subsequent renewals or the distribution of renewal times. An alternative proof that important results of dynamic disorder hopping apply under more general conditions can be derived in quantum mechanics, starting with the linear response expression for the conductivity.One can then show that the analytic continuation rule of eqn (7) will hold if and only if the velocity auto-correlation functions sat is fy ( u6( 0 ) c, ( t + i h a ) ) d a = exp ( - A t ) (u<( 0 ) u, ( t + i da. (12) Here 5 and 17 represent space variables x, y or z, A is the inverse mean renewal time, p k g T = 1 and the expectation values on the left and right sides are evaluated in a renewing lattice and a static lattice, respectively. The importance of eqn (12) lies in providing yet a further generalization of dynamic disorder motion to quantum behaviour. For example, fig. 9 shows the effective renewal as a function of time for two situations. The upper situation corresponds to hopping-like transport, in which the mean-square displacement is beginning to flatten out asymptotically with time, before renewal occurs.32 Conductivity in Polymer Ionics h * v h L v t2 time Fig.9. The effective renewal times, at t , , t , , . . . ( a ) on a concave-down and (6) on a concave-up mean square displacement ( r2( t)),, dependence, corresponding relatively to hopping-like (ionic) and coherent or ballistic (electronic) transport. Notice that the growth law is obeyed in both cases, guaranteeing diffusive conductivity along times. From ref. (50). This is characteristic of diffusive hopping transport. On the other hand, fig. 9 ( b ) shows a coherent-like transport situation, corresponding to scattering in band conduction. Here the mean-square displacement without renewal is quadratic in time; the renewal process in fact reduces the expected growth in the mean-square displacement, in sharp contrast to the diffusive situation.The applicability of dynamic disorder hopping models in both the quantum ( c ~ h e r e n t ) ~ ~ and classical (hopping) cases makes the results useful both for ionic conductors and for electronic conductors of relatively short mean free path, such as redox polymers and molecular metals. While correlations in the renewal process will generally have rather small effects on the growth law and the diffusion coefficient, spatial correlations in the renewal pattern can in fact change the rate substantially. Harris et al.55 show by means of simple simulations that if bond renewals are restricted to occur between nearest-neighbour sites, the d.c. conductivity is reduced relative to that for random renewal since the carrier must occasionally wait for the slower renewal chain of events before it can proceed along the chain.More recent work has extended these considerations substantially, by examining a situation in which there are two renewal processes. The first corresponds to a simple fluctuation of each site with a characteristic renewal rate 1 / ~ ~ ~ ~ between open and closed, or available and unavailable, positions. The second renewal process corresponds to pairs of adjacent bonds interchanging their status as available or unavail- able; this rearrangement occurs at a rate a. The interchange is related to models such as the Grotthus picture for proton transport in hydrogen-bonded systems, in which case the rotation of water molecules permits protonic hopping.Granek and Nitzan and other^^',^^ have analysed a renewal problem containing such processes in the effective medium approximation. Fig. 10 shows, for a two-dimensional square lattice, the effective medium rate of transport as a function of the bond filling factor, f; for the situation in which only adjacent-bond interchange is permitted ( T , ~ ~ goes to infinity). Notice that the threshold, which for the two-dimensional square latticeM. A. Ratner and A. Nitzan 33 P Fig. 10. The effective medium diffusion rate as a function of p (equivalent to the f of text), the percentage of available bonds. The static percolation threshold for this square lattice system is at 0.5; notice that the dynamic renewal process (in this case corresponding to correlated renewal, the exchange of nearest-neighbour bonds) drops the percolation threshold to much lower values of p.The different curves are for different rates of interchange of status (open s closed) between adjacent jumps; this rate increases by a factor of 3750 from ( e ) to ( a ) . From ref. (47) and (49). 0.0 1.0 2.0 -0.60 log(w) Fig. 11. Calculated frequency-dependent conductivity for dynamic percolation, or for general growth-law diffusion. The different curves have slightly different renewal processes, but the generalized behaviour (flat near the origin, monotonically upward, flattening out at high frequen- cies) is common for all growth law or renewal processes. From ref. (50).34 Conductivity in Polymer Ionics occurs at f = 0.5 in the static, a = 0 limit, is downshifted to f = 0.34.This threshold is independent of the actual magnitude of a, so long as a # 0. Notice that for increasing a, the effective medium transport rate increases montonically, as expected, with increas- ing a ; for large enough a, this increase is unimportant. Some generalized results on the frequency dependence of dynamic percolation models follow from the growth law itself.”’353 Fig. 11 shows the calculated dependence of the diffusion coefficient on frequency. The high-frequency, asymptotically flat result is an artifact of the hopping model, since any real conductivity must eventually roll over and vanish as the mobile species, due to its inertia, cannot follow the instantaneous reversals of the field.The more important behaviour is the relatively flat slope at very low frequencies, becoming monotonically upward in the intermediate frequency range. While it is generally true that any hopping model must yield an increasing diffusion coefficient with frequency at low freq~encies,~’ the general roll-over behaviour observed in fig. 11 will always hold in dynamic percolation models. Thus the dynamic percolation model has been extended to deal with situations far beyond the original simple picture discussed at the beginning of this section. While correlations among renewals can affect the diffusivity, unless such correlations are very StrOng47,49,53.55 the effects are quite small. This is not necessarily true with correlation effects among the ions, arising from Coulombic forces.4. Ionic Correlation Effects: Coulomb Interactions Characteristically, the ionic concentration in polymer-salt complex electrolytes is roughly one molar, and the mean distance between ions is of the order of 6 A. This means that all ionic motion is within a relatively strong Coulomb field of other ionic particles, and therefore that the material can be considered as a solvated Coulomb fluid, rather than a simple set of independently hopping particles. Under these conditions, one seriously questions not only the simple independent particle description of diffusivity which underlies both the free-volume theory and the dynamic percolation model just discussed, but also any simple extension in terms of ion-pair formation. Indeed, spectroscopic studies, both in liquid polymer and in actual polymer electrolytes,3 1,38.41,42,59 indicate strongly that independent ions, ion pairs, ion triples, and higher ion multiples can be observed.Moreover, the experimental data seem to argue that both solvent-separated ion pairs and tight, or contact, ion pairs exist in these materials. Before proceeding to some simple theoretical considerations concerning ionic interactions in polymer electrolytes, we discuss some of the critical experimental observa- tions. Greenbaum and collaborators 13,2h noted that complexes based on PPO, when heated, often broke down into a remaining complex phase and isolated salt crystals. This was not so clearly observed in the more strongly solvating PEO, nor has it been repeated in ionic conductors of stronger solvating ability, such as the comb polymers.Nevertheless, the observation itself indicates that, especially with weakly solvating hosts, there is a substantial thermodynamic driving force at higher temperatures toward the formation of separated salt structures and polymer host (the latter possibly containing some salt). early on that one could modify the simple WLF form of eqn (3) for the conductivity, by including an activation form relating the stoichiometric concentration of ions to the concentration of mobile ions. This results in: Cheradame aT= uo exp ( - A E F / R T ) exp [ - B / ( T - To)] where AEF is the activation energy involved in forming mobile ions from immobile ions. It was suggested that this is the energy necessary to break up ion pairs, to produce free carriers.This form has been used in several subsequent investigations,“ and indeedM. A. Ratner and A. Nitzan 35 Watanabe repordo6 values of the activation energy AEF, of the order of 0.3 eV for polypropylene oxide electrolytes. More recent investigations, as well as older investigations in the general solvation literature, indicate that the situation may in fact be more complicated. Thus, Torell has d i s c ~ s s e d ~ ~ ' ~ ~ vibrational spectra in terms not only of concentration effects, as indicated in fig. 3, but also of temperature dependence. Indeed, she suggests that the number of contact ion pairs actually increases with temperature; this is consonant with the spirit of Greebaum's observation of salt precipitation. Extensive work in the simpler situations of ethereal solvents has also shown that the concentration of contact ion pairs, as opposed to looser solvent separated ion pairs, in fact increases with increasing temperature.61 That ion pairs are relevant to conductivity in ionic conductors has been demonstrated several times, notably in the early work of Shriver and collaborators in PEO hosts3' These studies show that ions, such as BH,, spectroscopically demonstrating contact pair formation yielded much less conductive complexes than ions such as BF,, for which no vibrational spectroscopic evidence for pairing occurred. Analogously, several workers have shown (compare fig.4) that addition of a sequestering agent, capable of fully and selectively solvating the cation, can often increase the ionic conductivity.27328,6' One obvious argument is that the chelating agent, such as 18-crown-6, tetraethylene glycol or various cryptands, form such a tight sheath around the cation that no contact ion pairs can in fact be formed. Watanabe suggest^'^ that remnant cation-anion attrac- tions, whose strength is indicated by the cohesive energy of the parent salt, can actually reduce overall ionic conductivity in polymer-salt complexes. Finally, as has already been pointed out, the value of considerably less than unity for Angell's decoupling index R, might well indicate reduction of conductivity by means of Coulombic attraction to counterions. From the viewpoint of simple thermodynamics, the free-energy of desolvation to form pairs can always be written where the subscript p indicates pair formation, and enthalpies and energies are taken to be equal.Simple thermodynamics then suggests Thus, the stabilization of the homogeneous complex in free energy will become less favourable with increasing temperature, if the entropy for the contact ion-paired, or salt-separated, material is in fact greater than the entropy of the homogeneously dis- tributed ionic complex. To assess, then, the free-energy for desolvation to form ion pairs is necessary to evalaute both the energy term A Up and entropy term AS,. An actual derivation of these terms, involving some fairly elaborate arithmetic, is given elsewhere.62 We recap here the important physical points involved, and discuss how this theoretical approach relates to experiment. We first consider the energetics involved.Generalizing the approach of Debye, Huckel and Onsager,63 we can consider forming a dipole within a cavity in the uniform fluid of charges. For the polymer electrolytes, however, the concentrations are in fact extremely high. The inverse Debye screening length is given by with n, the charge density of carriers with charge q1 and E the static dielectric constant. For most polymer electrolytes, the high concentration makes this inverse Debye length of the order of 1 bohr-I.? This means that the usual expansion, to first order in inverse is n o longer justified. Instead, one must treat the problem numerically A G, = A Up - T AS, (14) (a AG,/~T),,,,,",, = -AS,. (15) k = J ( 4 r r X 1 n , q ' / ~ k B T ) (16) $1 bohrz5.291 77x l o - ' ' m36 Conductivity in Polymer Ionics to evaluate the energetic contribution A Up of eqn (14).Our preliminary calculations62 indicate that for the complex electrolytes of interest, for which the concentration is near one molar, the energetic term will always favour separation of the contact ion pairs, to form solvated ions. This of course is evaluated in the continuum-cavity model, and ignores specific solvation effects and the molecularity of the solvent. These latter would in general tend to favour pair separation even more strongly,65 so in the absence of entropic terms contact pairs would not be very favourable even at high concentrations. This is in accord with a number of experiments, which indicate that at relatively low temperatures contact ion pairs are less probable than quasi-free ions.One caveat must be remembered: specific energetic interactions may in fact over- whelm the solvation stabilization of separated pairs, and result in contact pair formation. This has been observed with very small anions39 such as BH,, and with very strong Lewis-base anions, such as tetra-alkoxy alum in ate^.^^ Also, simple mass action suggests that the equilibrium polymer solvent M :olvated + x - t % MX will in fact favour the right-hand side (contact ion pairs) to a greater extent as the overall concentration of salt increases. This is in accord with the simple physical expectation, as well as the observations of Torell, Smid, Shriver and others. Finally, we should remember that ‘quasi-free’ in this context means that the ions are separated to their stoichiometric average distance.In highly concentrated salt solutions, this average distance will be a number ca. 6-10 A, rather than the large separations familiar from dilute electrolyte situations. The temperature dependence of ion pairs really depends, as suggested in eqn ( 1 9 , on the entropic changes that arise from the formation of contact pairs. A very simple statistical model has recently been developed62 to characterize this entropy change, and it suggests [in agreement with most experiments, and contrary to the implication of eqn (13)] that with increasing temperature contact ion pair formation, and salt separation, might in fact be favoured. This model is based upon the effective cross-linking between polymer strands brought upon by coordination to the alkali cation.Such cross-links reduce the configurational entropy of the polymer chain, and thereby the overall configurational entropy of the system. While this effect will be exaggerated in polymer systems, it will hold even in polar solvents, where strong coordination to cationic metal species will substantially limit the translational entropy, and orientational entropy, available to the solvent itself. This extra entropic contribution will be proportional to the number of such cross-links. If we denote by n; the number of free polymer segments, then this entropic contribution can be written n: In A, where A is the contribution to the entropy from each free polymer strand; that is, if the free polymer strands are complexed, and therefore immobilized, the entropy cost will be proportional to n ; In A.We consider then, the formation of contact ion pairs according to the simplified relation pc+a ;-+ p+ac. (18) Here we have denoted by p, c and a, respectively, polymer segments, cations and anions. When reaction (18) proceeds to the right, the cation complexed by the polymer strand decomplexes and forms a contact ion pair. The polymer segments and cations can then exist in two states: we denote by n:, n:, n:, respectively, the number of bound (to solvent) cations, the number of free (unsolvated) cations and the number of bound (complexed) polymer segments. Since the total number of segments and ions must be conserved, we have N,= nL+ n i (19)M. A. Ratner and A. Nitzan 37 N,=n:+nL (20) where Nb and N , are, respectively, the number of polymer segments and the number of cations (equal to the number of anions).There will then be three independent stoichiometric variables: N , and N p describe the overall make-up of the material, and nb = n: = n i is the number of bound (complexed) cation-polymer segment pairs. The energetic component for the free-energy can be defined by setting the zero of energy as the fully uncomplexed material (separated salt and polymer). Then we can write the thermodynamic energy term as where we expect the constant E to be negative, corresponding to energetic favouring of the formation of the homogeneous polymer salt complex. If E were in fact positive, the thermodynamic driving force for complexation would not exist, and the complex would never form.Indeed, it was noted early on in studies of PEO materials that for salts of sufficiently high lattice energy, there is not sufficient energy gain on complexation to overcome the cohesive energy of the lattice, and complexes simply never do If indeed the constant E is negative, then the energy will be minimal when all cations are complexed, and no contact ion pairs exist. -AU,,= Enb (21) Using simple combinations, the entropy can be written as Here the factorial quantities simply refer to the division of polymer segments and cations among the two categories free and bound; the A-dependent term is the extra entropy contribution that arises when the polymer segments are not limited by being complexed to cations. The term proportional to N , is simply a volume term, that arises from all the different ways to distribute bound pairs, free cation segments and free polymer segments over all the sites in a lattice model of the system. (We have already discussed extensively in Sections 2 and 3 that although no real lattice exists in these systems, an effective lattice can be defined simply as a spatial net in the amorphous material.) This form is reminiscent of the term in the Sackur-Tetrode equation in which the entropy is proportional to the number of particles times the logarithm of the volume per particle: the role of the volume is taken by N , , the number of sites.In fact, this simple form is valid only in the dilute limit, which we can assume here since the lattice spacing is entirely arbitrary.Inserting the energy and entropy expressions of eqn (21) and (22) into the thermo- dynamic form of eqn (14), and minimizing the energy with respect to the constitutive parameter, nb dF/dnb = 0 (23) we obtain the temperature dependence of the number of bound pairs as N P Nc - nb( N p + N,) + n t exp ( E / kT) = Anb N S This can be solved for nb itself, yielding: nb = +{ N P + Nc + A ex p ( E / k T) Ns * v'( [ N p + Nc- + A ex p ( E / k T) N, 3' - 4 NpNc-)}. ( 25) This is, then, the desired expression for the temperature dependence of the number of ion pairs. Taking derivatives and rearranging, we obtain EhnbN!, exp ( E / kT) = (3) [ N , + N, - 2nb + h N, exp ( E / k T)]. kT2 Since E is in fact a negative quantity, and the factor in the second parenthesis on the38 Conductivity in Polymer lonics right-hand side of eqn (26) must be positive, we have d n b -<o.aT This shows, in agreement with experiment, that the number of cations bound to the polymer, and therefore not tied up in contact ion pairs, decreases with temperature. This is in agreement with the experiments, both those showing the number of contact ion pairs increasing with temperature, and those observing actual segregation of salt with increase in temperature. The general phenomenon of phase separation with increase in temperature is contrary to naive interpretations of entropy in terms of disorder, since fully dispersed phases would appear to have lower distributional order, and therefore higher distributional entropy, than partially separated phases.On the other hand, precisely such behaviour occurs in liquid mixtures exhibiting lower consolute temperatures;66 we suggest that perhaps the same sort of energy contributions (configurational entropy decreases with increasing temperature overwhelming simple arguments) may be operative in such thermodynamic systems. In any case, such a model appears entirely reasonable for the polymer salt complex electrolytes, and the simple model contained in eqn (18)-(22) does yield, in agreement with experiment but in contrast to arguments based solely on energy [such as the negative value of E or the activated form of eqn (13)], that ion pair formation will be increased with rising temperature. Several obvious limiting cases of eqn (25) for the number of complexed cations can be derived.When e / k T becomes very large, nb = 0. This is reasonable, since under these conditions there is an energy cost associated with separation of cation and anion, and this energy is unavailable. A second obvious limit is when & / k T becomes a very large negative number. Under these conditions, nh is equal to the smaller of N , and N,. Once again this is reasonable; at very low temperatures the cations will be entirely complexed if the energy change is negative for complexation. The third obvious limit is the high-temperature limit, where r / k T vanishes. Here nb also vanishes, since at very high temperatures only the entropic terms are important, and the entropic terms favour formation of contact pairs according to eqn (18).This thermodynamic model is simple and reasonable, and gives the correct experi- mental observations. The important fundamental inputs to the model are the energy difference upon solvation of a contact ion pair, called E and the entropic penalty involved in complexation associated with the A term of eqn (22). For any given substance, a generalized Debye-Huckel treatment is available to calculate e ; a number of terms can contribute to A, including configurational entropy of the polymer, and even vibrational entropy, since vibrational frequencies are higher in complexed solvents (either polymeric or small molecule) than in free solvents. The term involving configurational entropy reduction upon complexation would suggest that at smaller chain lengths the entropic favouring contact ion pair formation, and salt separation, should be reduced.Notice that A and E enter the expression for nb only in the combination A exp ( e / k T ) . Thus kT In A is in some sense equivalent to E , and a change in the value of A from h < 1 to A > 1, like a change in E from negative to positive, favours decomplexation and ion-pair formation; this agrees with the interpretation of h as an increase factor for the number of configurations available to the free solvent. 5. Comments Polymer ionic materials are always characterized by the presence of static disorder, arising from the disordered polymer host. Above the glass-transition temperature, they additionally have dynamic disorder, by which we mean that the local environment of any given site will undergo substantial change with time, due to liquid-like local motions.M.A. Ratner and A. Nitzan 39 These two types of disorder have important roles to play in determining charge transport in these polymeric materials. For temperatures above Tg , we are in the realm of dynamic disorder. Here substantial changes in the local structure arise; this change in the local geometry results in 'renewal' processes, or reinitialization processes, which can modulate either ion transport (in electrolyte materials) or electron transport. Examples of electron transport modulated by dynamic disorder include situations in which ion motion is needed to provide homogeneous doping, as in a large class of doped conductive polymer ~ystems.'~ A second example is provided by redox processes on polymer-modified electrodes; for example, recent work from several group^'^,^^ has utilized a network of donor-acceptor relays, or electron-transfer modulators, suspended along a polymer chain leading from a modified electrode to a redox active terminating group, such as a redox enzyme.Under these conditions, the relays along the chain (for example, ferrocene/ferrocenium sites) can provide efficient ET pathways from the redox enzyme to the electrode; the electronic motion is promoted by large-scale motions of the host polymer chain, which permit the sites to become close enough for efficient hopping transport to occur. Thus, very flexible chains, with low glass-transition temperatures, such as are provided by siloxanes, have proven optimal for the design of such relay systems. The role of dynamic disorder in promoting ion transport in polymer electrolytes and polyelectrolytes has been extensively discussed in Sections 2 and 3.For temperatures below Tg , local ionic sites undergo quasiharmonic vibrations, and no easy diffusion pathways will exist. Electrons can still move, but such motion occurs in largely static structures. Under these conditions, electron transfer over very short distances is ballistic or band-like. Scattering processes can then lead to growth laws, with the conductivity being diffusive over long times [as is clear from fig. 9 ( b ) ] . Under these conditions, the temperature dependence arises from the scattering problems, but the diffusive transport is due to the growth law.s0*56 Thus the role of static and dynamic disorder in promoting charge transport in polymer ionics can vary from situations reminiscent of glass-like substances ( T < Tg) to those more characteristic of liquids ( T > 7'').Charge-transport mechanisms in polymer ionics are unusual, and understanding requires models, like the dynamic disorder hopping model discussed in section 2, that differ substantially from those more appropriate for crystalline solids. Polymer ionics contain charged species, and therefore the issue of Coulombic interactions among charge sites is highly relevant. For doped polymers in the glassy state below Tg , Mott-type transitions7' are possible. Under these conditions, the ions are not mobile, but electrons or holes can be, if the local screening length becomes comparable to the hopping distance. Analogous ideas are relevant for ion hopping in these materials, if appropriate pathways for long-range ion transfer exist.7' In polymer electrolytes and polyelectrolytes, Coulomb interactions are important because they can lead to segregation of charged species either as ion pairs or as more highly charged multiples, and thus impede conductivity.If the lattice energy of the salt, or the inter-ionic Coulombic interaction attraction, is too large no complexes will form, no ions will become free and relatively low conductivity will be observed. If, on the other hand, the solvation energy is strong enough, formation of contact ion pairs will be energetically unfavourable compared to solvent-separated pairs, leading to quasi-free ions and substantial ionic conduction.s9-61 Solvation energy clearly must be larger than the ion-pairing stabilization, as indexed by the lattice energy of the parent salt.If the stabilization energy to separate the contact ion pair is very large, the material will remain a homogeneous conductive substance over broad temperature ranges. If, on the other hand, the stabilization energy is smaller, entropic effects can lead to instability of the separated pair compared to contact ion pairs, and to the formation of contact ion pairs (with concomitant reduction in the number of charge carriers) with increasing40 Conductivity in Polymer Ionics temperature. Such a situation can be described by a quasi-thermodynamic model, as discussed in Section 4.The overall temperature dependence, then, of the mobility and the concentration terms will differ: the mobility will increase with temperature according to the usual VTF, but the number of free carriers may decrease with temperature due to ion-pair formation at higher thermal energies. For very low concentrations of ions, the inverse Debye length will be small, and a simple analytic extension of Debye-Huckel theory can be used to estimate the energy involved in separating charged pairs.62 For the concentrations appropriate for most polymer electrolyte systems, however, the inverse screening lengths are quite large (of the order of 1 bohr-'), and the analytic treatment (involving expansion in the smallness parameter proportional to inverse t e m p e r a t ~ r e ) ~ ~ is no longer valid.Under these condi- tions the energy of solvation stabilization must be calculated numerically. The dominant concentration effect for many systems will come from raising the glass-transition tem- perature due to effective cross-linking of polymer strands arising from ion complexation; this decrease in mobility dominates the stoichiometry dependence of conduction in most regimes. Perhaps the most interesting theoretical insight arising from the models discussed here is that there are significant commonalities in the charge transport processes due to ionic and electronic motion in polymer ionics. The effects of the dynamical events and the growth law as well as Coulomb interactions are similar in both sorts of materials. The dynamic and static disorder of the polymers is the dominant effect on all dynamical processes, including charge transport.In this sense, the polymer ionic materials offer an interesting continuum of behaviour, ranging from liquid-like transport in the high- temperature regime (where dynamic motions of the solvent are involved in the charge transport) to glass-like, hopping behaviour for temperatures below the glass-transition temperature. We are grateful to the Northwestern Ionics group, particularly D. F. Shriver and S. Druger, for long-standing and enjoyable collaborations. We thank R. Granek for important contributions to the dynamic disorder hopping problem. Partial support was provided by the National Science Foundation through the Northwestern University Materials Research Center (grant DMR 8821571) and by the Department of Energy (grant DE FG02 85ER 45220).References 1 2 3 4 5 6 7 8 9 10 11 12 J. R. MacCallum and C. A. 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M. Khan and J. Smid, Polym. Preprints Am. Chem. SOC., Diu. Po1.v. Chem., 1989, 30(1). 43 cj: e.g., D Stauffer, Introduction to Percolation Theory (Taylor and Francis, London, 1975). 44 S. D. Druger, A. Nitzan and M. A. Ratner, J. Chem. Phys., 1983, 79, 3133. 45 S. D. Druger, M.A. Ratner and A. Nitzan, Phys. Rev., 1985, B31, 3939; Solid State lonics, 1986, 18/19, 106. 46 S. D. Druger, in Transport and Relaxation Processes in Random Materials, ed. J. Klafter, R. J. Rubin and M. F. Shlesinger (World Scientific, Singapore, 1986). 47 M. A. Ratner and A. Nitzan, Solid Stare lonics, 1988, 28-30, 3; R. Granek, A. Nitzan, S. D. Druger and M. A. Ratner, Solid State lonics, 1988, 28/30, 120. 48 A. Nitzan, S. D. Druger and M. A. Ratner, Philos. Mag., 1987, B56, 853. 49 R. Granek and A. Nitzan, J. Chem. Phys., in press. 50 S. D. Druger and M. A. Ratner, Phys. Rev. B, 1988, 38, 12589; Chem. Phjx Lett., 1988, 151, 434. 51 S. M. Ansari, M. Brodwin, M. Stainer, S D. Druger, M. A. Ratner and D. F. Shriver, Solid State lonics, 1985, 17, 101. 52 A. K. Harrison and R. Zwanzig, Phys. Rev. A , 1985, 32, 1072. 53 R. Hilfer and R. Orbach, Chem. Phjx, 1988, 128, 275. 54 S. D. Druger, M. A. Ratner, A. Nitzan and D. Skinner, J. Chem. Phys., submitted. 55 C . Harris, A. Nitzan, M. A. Ratner and D. F. Shriver, Solid State lonics, 1986, 18/19, 151. 56 H. Scher and M. Lax, Phys. Rev. B, 1973, 7, 4491; M. Lax, Phys. Rev., 1958, 109, 1921. 57 J . C . Kimball and L. W. Adams, Phys. Rev. B, 1978, 18, 5851. 58 J. R. MacCallum, A. S. Tomlin and C. A. Vincent, Eur. Polym. J., 1986, 22, 787. 59 J. F. LeNest, H. Cheradame and A. Gandini, Solid State lonics, 1988, 28/30, 1032. 18/19, 271. 25, 37. G . S. Fulcher, J. Am. Ceram. SOC., 1925, 8, 339. Phys., 1981, 48, 41. 6247; B. Papke, R. Dupon, M. A. Ratner and D. F. Shriver, Solid State lonics, 1981, 5 , 685.42 Conductivity in Polymer Ionics 60 ( a ) M. A. Ratner, S . D. Druger and A. Nitzan, in ref. (46), p. 13. ( b ) M. Watanabe, Br. Polym. J., 61 G . Zhou, I . M. Khan and J . Smid, ACS Polymer Preprints, 1989, 30, 416. 62 A. Nitzan and M. A. Ratner, work in progress. 63 cf: e.g., R. A. Robinson and R. H. Stokes, Electrolyte Solutions (Butterworths, London, 1968). 64 N. Davidson, Statistical Mechanics (McGraw-Hill, New York, 1962), chap. 21. 65 cf: e.g., E. C. Zhong and H. L. Friedman, J. Phys. Chem., 1988, 92, 1685; P. G. Kusalik and G. N. Patey, J. Chem. Phys., 1988, 88, 7715; J. K. Buckner and W. L. Jorgensen, J. Am. Chem. SOC., 1989, 11 1, 2507. 66 For example, 'In this case (of lower consolute temperatures) the two kinds of molecules form a weak complex, which enhances their mutual solubility. At higher temperatures, the complexes break up and the two types of molecules cluster together in swarms of their own kind.' [From P. W. Atkins, Physical Chemistry (Oxford University Press, Oxford, 1986), p. 294.1 1988, 20, 182. 67 cf: e.g., M. Aldissi (ed.), Synthetic Metals, (Elsevier, Lausanne, 1988), vol. 27; 1989, vol. 28. 68 Y. Degani and A. Heller, J. Am. Chem. SOC., 1988, 110, 2615; M. A. Lange and J. Q. Chambers, Anal. Chim. Acta, 1985, 175, 89; A. E. G. Cass, G. Davis, G. D. Francis, H. A. 0. Hill, W. Aston, I . J . Higgins, E. V. Plotkin, L. D. L. Scott and A. P. F. Turner, Anal. Chem., 1984, 56, 667. 69 P. D. Hale, T. Inagaki, H. I. Karan, Y. Okamoto and T. A. Skotheim, J. Am. Chem. SOC., 1989,111,3482. 70 N. F. Mott, The Metal-Insulator Transition (Taylor and Francis, London, 1974). 71 K. E. Doan, S. D. Druger, D. F. Shriver, M. A. Ratner and A. Nitzan, Mol. Cryst. Liq. Cryst., 1988, 160, 311. Paper 9/02135C; Received 18th May, 1989

ISSN:0301-7249    

DOI:10.1039/DC9898800019

出版商:RSC    

年代:1989

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1989, 88, 43-54 Effect of Ion Association on Transport in Polymer Electrolytes Peter G . Bruce” Department of Chemistry, Heriot- Watt University, Riccarton, Edinburgh EH14 4AS Colin A. Vincent Department of Chemistry, University of St Andrews, St Andrews, Fife KY16 9ST Numerous techniques have been employed in an attempt to elucidate details of the conductivity mechanism in polymer electrolytes, and in particular to determine whether cations, anions or both are mobile. Until recently, most of these studies have assumed a ‘strong electrolyte’ model. Here we examine the effect of ion association on the interpretation of different techniques, including Hittorf, concentration cell, centrifugal cell, ratio-tracer, pulsed field gradient n.m.r. and d.c.polarisation methods. The circumstances under which certain of these experiments yield individual ionic transport numbers are described. it is also shown that, in general, measured diffusion coefficients may not be sensibly compared with mobilities from conductivity measurements using the Nernst-Einstein relationship. The d.c. polarisation technique is examined in some detail and the value of the steady-state conductivity in assessing polymer electrolytes for battery applications is described. Finally, some experimental evidence is presented which appears to support the existence of ion association in polymer electrolytes. High-molecular-weight polar polymers such as poly( ethylene oxide), ( -CH2CH20-)), , can offer an attractive alternative to conventional low-molecular-weight organic solvents as media for non-aqueous electrochemistry.Polymer electrolytes generally have the form of flexible solids, but their behaviour is more closely related to liquid systems than to classical solid electrolytes such as sodium p-alumina. It is instructive to compare solid polymer electrolytes and non-aqueous liquid electrolytes. Similarities: (i) Both have conductances that are in general lower than those of aqueous solutions of comparable salt concentration; (ii) owing to the low relative permittivity of the host (solvent), ion association leading to the formation of long-lived ion pairs, triples efc. is considered to occur; (iii) both exhibit a wide electrochemical stability window, which in practice is further enhanced in the case of polymer electrolytes because of the slow kinetics of decomposition in the solid state. Differences: (i) Entanglement of long polymer chains, or chemical crosslinking in the case of networks, precludes long-range motion of the ion-coordinating atoms, in contrast to the situation in low-molecular-weight liquids where a solvation sheath can move with the ions.One consequence of this is that ions which can undergo long-range motion in low-molecular-weight systems may be immobile in polymer electrolytes. A second and more subtle consequence concerns the significance of the transport numbers as measured by, say, the Hittorf method. In liquid solutions in order to define a transport number it is necessary to establish an imaginary reference plane fixed with respect to the solvent, since transport of molecules of the latter in the ionic solvation sheaths makes it impossible to determine ‘absolute’ or ‘true’ transport numbers.(Attempts to evaluate the latter by relating ionic migration to a non-conducting reference substance, or by using membranes have not been successful’). In polymer electrolytes since there is no net transport of solvent by the ions, absolute transport numbers may be determined. 4344 Transport in Polymer Electrolytes (ii) In polymer electrolytes there is no significant convective flow, so that stable concentra- tion gradients can be established. This is of considerable importance since in practical devices (batteries, displays, etc.), where polymer electrolytes are generally used in the form of thin films, a concentration gradient may extend throughout the thickness of the film.While considerable progress has been made in the past decade both in the synthesis of new polymer electrolytes and in the understanding of their properties, many detailed questions concerning mass and charge transport remain unanswered. In particular, there is still little direct evidence for ion association in polymer electrolytes, nor has there been any rigorous treatment of the effect of such a phenomenon on the interpretation of the various transport experiments. The low relative permittivity of ether-based polymers suggests the likelihood of strong ion-ion interactions, and there is indeed some support for the idea of intimate cation-anion contact from Raman spectroscopy.”’ Conductivity measurements on short-chain liquid polyethers with low concentrations of salt have been interpreted on the basis of ion a~sociation.~ It is very likely that similar simple ion pairs, ion triples or other small ion clusters exist in solid polymer electrolytes, but it is not clear whether they play a significant role in determining transport properties over the range of salt concentrations which may be encountered in these systems.A variety of techniques has been employed to probe transport processes in polymer electrolytes, ranging from experimentally simple measurements such as d.c. conductivity to more sophisticated methods such as radio-tracer diffusion studies, Hittorf transference number determinations, e t ~ . ~ Results derived from these techniques often appear to be in conflict; this we consider may be attributed, in part, to the simple model of a fully dissociated polymer electrolyte which is often used to interpret the measurements. The presence of ion association considerably complicates the interpretation of transport processes.For simplicity we here restrict our attention to a solid polymer electrolyte based on a monovalent salt MX, which contains only the species M+, X-, MX, M2X+ and MX2-. In some cases we will further restrict our attention to electrolytes containing only M+, X- and MX. Extension of the treatment to more complex salts such as MX2 or to higher associated species makes the analysis more tedious, but does not introduce significant fundamental differences. We examine the effects of ion association on the methods used to study ion transport, showing that each technique measures the motion of a combination of species and that the various techniques are influenced in different ways by the motion of the species involved.The different methods may be divided into four classes. Class I: Small Signal A.C. and D.C. Conductance Measurements For low fields, transport of each charged species is directly proportional to the field strength, the mobility and the concentration of the species. The latter may be written in terms of the total salt concentration, c, as follows: [M+] = a , c ; [X-] = a,c; [M2X+] = a4c and [MX2-] = a5c. (The concentration of the neutral species MX, which does not contribute to the conduc- tivity is given by [MX] = a3c.) Thus the total conductivity (T is given by l O O O a = ( a l u l + a2u,+ a4u4+ a#g}c where ui is the mobility of species i in unit field strength.Class I1 As in the case of conductance measurements (class I ) , methods in this class probe only the transport of charged species.P. G. Bruce and C. A. Vincent 45 HittorfITubandt Experiments This method involves the passage of a measured quantity of charge through a cell and subsequent determination of changes in the composition of the electrolyte in the vicinity of the anode and cathode. For a cell of the type M( s) Ipolymer-MX( s)/polymer- MX( s) Ipolymer-MX( s)lM( s) in which all three electrolyte compartments are identical, on passage of 1 F of charge, 1 mol of M is stripped from the anode and is deposited on the cathode.Current is carried by the motion of M' and M2X+ towards the cathode and of X- and MXT towards the anode. Provided that the central compartment remains invariant throughout the experiment, neutral ion pairs are not involved in the flux between the electrode compartments and the central compartment. Measurement of the change in salt con- centration in the cathode Compartment gives directly the change in the concentration of X. In the case of a completely dissociated electrolyte, this would lead to a direct determination of the anion transport number. For an associated electrolyte, analysis of the cathode compartment leads only to the determination of the net transfer of the X-constituent of the salt due to the transport of MIX' into the compartment and the transport of X- and MX, out.For the system considered, the transference number for the X-constituent, Tx (given by the change in the number of moles of X in the cathode compartment) may be related to the individual transport number for X-containing species by Similarly Also, Quite generally the transference number of a constituent cation or anion is defined' as the net number of Faradays carried by that constituent in the direction of the cathode or anode, respectively, on the passage of 1 F of charge through the cell. To date there have been few reliable measurements of Hittorf transference numbers in solid polymer electrolytes because of experimental difficulties in applying the tech- nique. Cheradame and co-workers6 have, however, successfully applied it to highly cross-linked networks where cells could be formed using a series of non-adherent thin sections.When the anion was immobilised by attachment to the polymer host, the transport number of the cation was shown to be equal to unity. E.M.F. Measurements on Electrolyte Concentration Cells A cell of the form M(s)lpolymer-MX(s)l Ipolymer-MX(s)lM(s) for c1 > c2 has an e.m.f. due to the tendency of the cell to equalise the concentration of the salt on either side of the electrolyte junction. Passage of 1 F of charge through such a cell has the effect of forming a mole of M' at the anode, depositing it at the cathode and transferring TM moles of M-constituent across the junction towards the cathode, and Tx moles of X-constituent in the opposite direction. The net result is the transfer of Tx moles of salt across the junction.In the situation where c1 and c2 differ by an infinitesimal amount, the e.m.f. of the cell is given by c1 c2 dE,,,, = -( RT/ F ) Tx d In a46 Transport in Polymer Electrolytes where a is the combined activity of the ionic species. It is thus possible to determine Tx by measurement of the e.m.f. of suitable cells ( i e . without involving the actual passage of current) using the relationship Tx = -( F / R T ) dECel,/d In a It is, of course, necessary to know how the activity of the ions varies with concentration. In their application of this method to PEO/LiI systems, Armand and CO-workers' determined this by making e.m.f. measurements of the cell Li(s)lPEO- LiI(s)(PbI,(s)lPb(s). In a later paper,' the same authors circumvented the problem by making e.m.f.measurements on equivalent cells with and without transference, namely Li(s)lPEO-LiC104(8 : 1)1 IPEO-LiC1O4( M : 1 for M > 8)ILi(s) (1) and Li(s)IPEO-LiC104(8 : 1)1 poly ( DV2+, 2C104-), poly (DV+, C1O4-)/PE0-LiC1O4( M : l)ILi(s) ~c,04- = dE,/dE2 for which (DV = decaviologen). E.M.F. Measurements on Cells in Force Fields If a symmetrical cell of the form M(s)lMX-polymer host (s)lM( s) is placed radially on a spinning rotor, an e.m.f. is developed due to the fact that there is a difference in the kinetic energy of the reagents at the two electrodes. The kinetic energy of a mass W at a distance r from the centre of rotation is given by E = 22"' Wr2 where f is the frequency of rotation. Hence the energy difference involved in moving the mass from rl to r2 is A& = 27r2f2 W ( r i - r ; ) .Thus, by considering the transfer of mass occurring in the cell during the passage of 1 F of charge in a reversible manner, an expression for the cell e.m.f. may be obtained: W = ( M , - V , p ) - T ~ ( M M . - V , X p ) . Here MM and MMx are the relative molar masses of M and MX, respectively, vM and vMx their partial molar volumes, and p is the density of the polymer electrolyte. Note that this equation assumes a relatively fluid polymer electrolyte. The cell potential is given by E~~~~ = 2.rr2f2 W<rf - r : ) / F and Tx may be obtained by measuring Ecel, as a function of rotation speed. This technique was developed by MacInnes for aqueous solution electrolytes but has not been widely applied. It does, however, seem to be particularly suited to solid polymer electrolytes and is currently being studied by the present authors.Unlike the Hittorf method it does not depend on the analysis of relatively small concentration changes; nor is it necessary to establish reproducible electrolyte junctions as in the concentration cell method.P. G. Bruce and C. A. Vincent 47 Class 111 The methods in this group are concerned with the measurement of diffusion coefficients of species in the electrolyte. Unlike the situation for class I and class 11, these methods are affected by the flux of both charged and electrically neutral species containing the particular constituent under investigation. Radio-tracer Methods Experiments using serial-sectioning techniques have been applied by Chadwick et aZ?' I to study, for example, PPO-NaSCN polymer electrolytes by measuring the distribution of "Na and I4C following diffusion into a solid sample from a thin layer deposited on its surface.In an associated electrolyte, the total flux of a radioactive species *M is given by d[*M'] d[*MX] dx dx D*MX ~ J*, 1 -D*M+ -- d[ * M (M )X+] dx The concentration of each species may be expressed as a function of the total (radioactive) salt concentration, *c: [*M+] = a,*c; ["MX] = a,*c; [*M(M)X+] = a4*c and [*MX,-] = as*c d[*MXJ dx - D * M X , - D*M(M)Xi so that Similarly, where DLM and DLx are the diffusion coefficients obtained experimentally for con- stituents *M and *X, respectively, and D*MX = DM*x, D*M(M)X+ = DM2*X+, D*MX2- = DM*x(x)-.It is evident that if the sum of second and subsequent terms in the expressions for D L M and DLx are large in comparison with the initial terms, then the cation component flux will tend to equal the anion component flux. It is possible to consider that the drift velocity of ions under the influence of unit force is the same, no matter what the origin of the force. This enables the mobility of a species such as M', under unit electric field, u+ (as noted in class I above) to be related to its diffusion coefficient D, by the Nernst-Einstein relationship: D+ = RTu+/F. For an ideal electrolyte containing a fully dissociated salt, application of this relationship enables the individual transport numbers to be defined in terms of their diffusion coefficients: and If the electrolyte is associated, such that DA= DL then t+ and t - as calculated on this basis will both approach 0.5.Clearly it is not generally valid to apply the Nernst-Einstein equation to such composite diffusion coefficients. A number of workers have attempted to make a rough estimate of the degree of ion pairing by comparing the experimental conductivity with that calculated from the Nernst- Einstein relationship, on the assumptions that the correlation coefficient is unity t+ = D+/( D, + D-) t- = D-/( D, + D-).48 Transport in Polymer Electrolytes and that there are no associated species higher than ion pairs. Lack of information on the ion pair diffusion coefficient makes this very difficult. Note, too, that if relatively immobile ion pairs are present, the flux in both the diffusion and the conductivity measurements would be lowered, and thus no information is obtained on the concentra- tion of the free ions.We have so far ignored the fact that the radio-tracer technique leads to the determina- tion of the tracer diffusion coefficient for any given constituent. In the absence of ion association, this is equal to the self-diffusion coefficient (as used in the Nernst-Einstein relationship) only in the absence of correlation. At high salt concentrations where polymer electrolytes may resemble molten salts more closely than non-aqueous solutions, mechanisms of ion motion may be envisaged in which the correlation coefficient f in the equation is less than unity. For example, if a vacancy mechanism for ionic conduction is dominant or if a cooperative rearrangement of charges occurs in each step of the conduction process, values off which depart significantly from unity may be expected.Furthermore, in molten salts it is well known'* that deviations from Nernst-Einstein behaviour occur since favoured motion in the same direction by a neighbouring pair of oppositely charged ions contributes to diffusional flux, but not to conductivity. In such systems pair correlation need only last for periods of ca. 2 x s, i.e. there is no need for the formation of long-lived ion pairs, Pulsed Field Gradient N.M.R. Experiments This is similar to the radio-tracer diffusion method in that a small proportion of a salt constituent is labelled, in this case magnetically.Generally ca. 10'' atoms are labelled so that the experimental conditions are to all intents and purposes identical to those of the radio-tracer method. Measurements of component diffusion coefficients have been made in polymer electrolytes by a number of workers, notably Berthier and co-worker~'~ and Whitmore and c o - w ~ r k e r s ' ~ , ' ~ by following the motion of 7Li and 19F in polyether- LiCF3S03 systems. As in the case of radio-tracer derived measurements, interpretation of the results of diffusion coefficient measurements is difficult if the latter are indeed composite quantities because of ion association. A comment is appropriate here on the distinction between the self-diffusion coefficient of ions D+ and D- and the salt diffusion coefficient which in the case of a fully dissociated salt may be written as Dsa,, = 2D+D-/( D, + 0-).In macroscopic measurements of salt diffusion, maintenance of electrical neutrality requires that cations and anions move at the same speed with a flux determined by Dsalt. In contrast, in radio-tracer and n.m.r. pulsed field gradient methods, the diffusion potential is negligibly small, i.e. the motion of an ion is not tied to that of other ions. We therefore find it difficult to understand the inference of Bhattacharja et al.14 that the conductivity should be related to D,,,, rather than to ( D , + D-) in a fully dissociated system. Cottrell Equation-based Methods Recently an electrochemical method based on the Cottrell equation has been described.I6 Here polymer- NaC F3S03 systems were doped with millimolar levels of electroactive cations such as Ag+ or anions such as I - and the diffusion behaviour of these was studied by chronoamperometry. Again, the conditions of these experiments are, in principle, similar to those of the radio-tracer method described above, a compositeP.G. Bruce and C. A. Vincent 49 diffusion coefficient for the electroactive constituent being measured. Note that in this experiment there is likely to be association between the electroactive ion and the ions of the supporting electrolyte (e.g. AgNaCF,SO,+ triples). Thus the measured diffusion coefficient could depend markedly on the nature of the supporting electrolyte. Class IV Methods in this class involve the transport of charged and electrically neutral species, but the presence of both electrical and chemical potential gradients distinguishes them from class I11 methods in which an electric field is absent.This distinction has an important influence on the way in which the charged species contribute to the net flux. D.C. and A.C. Polarisation Methods Let us consider first a fully dissociated electrolyte. If a cell of the form M(s)lMX-polymer host(s)(M(s) in which the electrode reactions are reversible and the electrolyte is ideal, is polarised by the application of a constant potential difference between the electrodes, the current, whose initial value, I o , is determined by the conductivity of the electrolyte, is found to fall with time until a steady-state value, I+, is eventually observed. The fall in current is due to the establishment of a linear salt concentration gradient across the cell which reduces and finally stops the net motion of anions.A linear relationship is predicted between the steady-state current and the applied voltage only for small concentration gradients and hence only for small values of the latter. Under these circumstances, and assuming the Nernst-Einstein relationship to hold, the transport number of the cation t+ is given simply by I + / I o . The theory of this method for completely dissociated electrolytes was developed by the present authors.” The technique was first applied to polymer electrolytes by Shriver and co-workers.” The basis of the method is exactly the same as an earlier technique suggested by Sgrensen and Jacobsen” who applied a variable frequency a.c.signal to the same type of symmetrical cell. At very low frequen- cies the (alternating) current is affected by concentration gradients which give rise to a characteristic feature in the complex plane called a diffusional impedance. Again, for fully dissociated electrolytes, it is straightforward, in principle, to evaluate the cation transport number from such measurements. This a.c. method is by far the most widely used technique for the practical estimation of transport numbers in polymer electrolytes, on the implicit assumption that the electrolyte is completely dissociated. (Note that both this method, and the d.c. polarisation method require correction for the effects of finite electrode kinetics, electrode passivating layers, e t ~ .’ ” * ~ In many cases allowance for such electrode phenomena has not been properly made.) However, as in the situation considered in I11 above for direct diffusion coefficient measurements, it is not possible to derive transport numbers directly from d.c. or a.c. polarisation experiments when mobile associated species are present. On the other hand, the understanding of cation transport across a thin film of polymer electrolyte under the combined influence of an electric field and a concentration gradient is of great practical importance, since such circumstances are likely to be encountered regularly in practical devices such as polymer electrolyte batteries under load. We have therefore examined in some detail the theory of the steady-state current response of the cell M(s)lMX-polymer host(sj)M(s) where the polymer electrolyte contains mobile ion-associated species, such as ion pairs and triples, and have undertaken a full analysis for model systems containing simple mobile ions and ion pairs” A qualitative description of the establishment of a steady state following the polarisa- tion of the cell M(s)lMX-polymer host)M(s) in which the ideal electrolyte contains50 Transport in Polymer Electrolytes mobile M', X- and MX species and the electrodes are reversible to M+ may be given as follows.Following the application of a constant voltage, the current is initially carried by migration of cations and anions in the electric field. While cations are continuously supplied by oxidation of M(s) at the anode, and consumed at the cathode by reduction, this is not the case for anions which do not react at either electrode.As a consequence of electroneutrality, a concentration gradient of M+ and X- ions develops across the electrolyte. Since the ion pairs are assumed to be in fast dynamic equilibrium with the free ions, a concentration gradient of MX is also established. Eventually a steady state is achieved where the net flux of X due to field-driven migration from cathode to anode is balanced by the sum of diffusional fluxes of free X- ions and MX ions pairs in the opposite direction. No further changes in concentrations now occur. The steady-state current I+ is due to the migration of M' cations in the field, together with the diffusion of M+ cations and MX ion pairs down their respective concentration gradients.Expressions may be derived for the steady-state current and voltage as follows. In the steady state, we have for the anions K l ' dx dx anion anion ion-pair migration diffusion diffusion d 4 dx where D- and Do are the anion and ion-pair diffusion coefficients, respectively, - is the electric field gradient and we assume that u- is related to D- by the Nernst-Einstein relationship, u = D- F/ RT. Hence d + RT d[X-] Do d[MX] - dx-F[X-] [ dx + ( K ) T ] . Considering now the cations, we can write for the steady-state current: d[MX] F2D+[Mf] d+ dx dx RT dx I+ = - FD+ -- d[M+I FDO-- - cation ion-pair cation diffusion diffusion migration where D, is the diffusion coefficient of the cation and u+ = D+F/ RT. By introducing the equilibrium constant for ion association, K = [ MX]/ [ M'][X-], and integrating, where [M'Ia and [M'Ic represent the steady-state concentration of M+ adjacent to the anode and cathode, respectively.Similarly, by noting that [M+] = [X-] and [MX] = KIM']' an expression may be obtained for the potential drop across the electrolyte: 2 KDo A + = RT [ In (s) + - ([ M'Ia - [ M+]J} . F D- Now for reversible electrodes, the electrode potential difference is so that the potential difference across the cell is given by A V = A+ -+ AE.P. G. Bruce and C. A. Vincent 51 It is now possible to combine the equations for I+ and AV to obtain an expression for I+/AV. Under certain conditions this ratio is a constant and may therefore be called the effective conductivity, C T , ~ , of the cell at steady state.An explicit expression for ueff may be derived as follows.21 When the difference between the cation concentration at the cathode and the anode is small, and then, where [M'l0 is the initial concentration of free ions in the electrolyte and is equal to ([M+Ia+[M+lc)/2. [M'l0 may also be expressed as ac where CY is the degree of dissociation of the salt, and c is the total salt concentration. Two special cases may be considered. First, when the concentration and/or the diffusion coefficient of the ion pairs is small compared with those of the anions, KDo[ M+],/ D- << 1, the equation for the effective conductivity simplifies to aeff = F2D+[ Mi],/ RT and the steady-state current is seen to be principally due to the flux of M+.Secondly, and in contrast, when the ion pairs dominate, KDo[M+],/D- >> 1, and ueff = F'[ M+],( D+ + D-)/ RT which is identical to the (initial) electrolyte conductivity, u. Here the anion flux has been balanced almost exclusively by the flux of ion pairs. This latter situation has been described by Ingram et al.22,23 A number of conclusions may be drawn from the above analysis. (i) The presence of ion pairing in polymer electrolytes has important implications for the operation of practical devices such as solid-state batteries of the type M( s) Ipol ymer- MX( s) lintercalation host. On discharge, the electroactive constituent, M, is carried by both M+ and MX. Provided that the total flux of M from anode to cathode is high, it is not important which species carries the current, so that apparently, significant ion pairing is of no disadvantage in a battery electrolyte provided that Do is high.This, however, is not necessarily the case since a high concentration of ion pairs implies a low concentration of ions, and hence a low ( T , ~ (since ( T , ~ = (T in this situation as noted above). In the exceptional circum- stances where cations are completely immobile, then ion pairs would, nevertheless, provide the only means of transporting M. (ii) In contrast to the case of the completely dissociated electrolyte, the ratio (~,*/u does not yield the transport or transference number of M+, since by definition, a transference number measures the contribution of charged species to transport under the influence of an electric field alone.Furthermore, this ratio does not even furnish information on the transport parameters of all the species contributing to the steady-state flux; as noted above, the equation for (T,~ for an electrolyte dominated by mobile ion pairs contains neither the concentration nor the diffusion coefficient of this species. Despite this, trends in the ratio of aeff/u with variations in temperature, salt, concentra- tion, etc., provide a useful insight into the nature of the transport process, as is demonstrated by fig. 1 which presents data for a PEO-LiC104 electrolyte at a number52 I I I I I I Transport in Polymer Electrolytes 2.0 - - 1.5 - - 1 - 0.0 1 .o 2.0 3 .O concentration/mol dm-3 Fig. 2. Total and 'effective' conductivities as a function of concentration for the cell Li(s)lPEO- LiClO,(Li(s); (- - -) 100 "C, (-) 140 "C.of temperature^.^^'^^ In fig. 2 the total conductivity of the electrolyte is compared with the effective conductivity of the cell Li(s)lPEO-LiClO,(s)lLi(s) (corrected for electrode effects) at two temperatures. At 140°C despite the significant rise in total conductivity with concentration, it is seen that nee rises only marginally. This is probably indicative of changes in the association equilibria as the salt concentra- tion is increased.P. G. Bruce and C. A. Vincent 53 Table 1". total final d.c. corrected applied steady-state electrode electrode applied voltage current ( I , ) resistance iR drop voltage (AV) A V / I+ ueff / m v 1 PA /a / m v /mv la /S cm-' 20.0 136.5 24 3.3 16.7 122.3 2.21 X 40.0 226.7 54 12.2 27.8 122.6 2.20 x 60.0 354.0 46 16.3 43.7 123.4 2.19 x 80.0 498.0 37 18.4 61.6 123.6 2.19 x lop4 100.0 684.0 27 18.5 81.4 119.0 2.26 X lop4 a Cell : LilPEO-LiC104(8: 1)ILi at 120 "C.Cell constant = 0.0270 cm-'. (iii) Extending the equations to include triple ions introduces further variables, namely an association constant and a diffusion coefficient for each triple ion. Since X-containing species are transported in both directions by an electric field, the concentra- tion gradient which develops due to the non-discharge of X may run from anode to cathode, or vice versa, depending on the direction of the net flux of X following initial application of the field. In either case, the net flux of X is zero and ueff remains a measure of the net flux of the M constituent in the steady state.Where the concentration and mobility of ion pairs are high, the comments made in (ii) above are valid, mutatis mutandis. The model may be further simplified in practice since as Cheradame has suggested,26 the mobility of MX2- is likely to be much higher than that of M2X+ in practical polymer electrolytes. The reason for this is that the latter species are likely to be solvated by two polymer chains and thus will be 'anchored' to the matrix. Note that for MX2-, diffusion down the concentration gradient will be opposed by migration in the opposite direction due to the electric field, thus reducing the flux of the M component from anode to cathode. This contrasts with the situation for neutral ion pairs, MX, for which there can be no migratory flux. (iv) In the case of a fully dissociated ideal electrolyte, ueff is independent of the applied potential only for A V S 10 mV." In contrast, we have shown by computer simulation for systems containing M+, X- and MX that if the concentration of mobile ion pairs is high, oeff may remain independent of the applied voltage up to much higher limits, exceeding 10 V in some cases2' In consequence, measurements of aefi as a function A V may be useful as a test for ion association in polymer electrolytes.In table 1 results are summarised for a series of measurernent~~~ where the applied potential has been corrected for electrode effects. aeff clearly remains constant until values well in excess of 10mV, and it may be concluded that this result gives useful additional evidence for ion association in this system, complementing that from spectroscopic measurements. Conclusions Where simple ion-pair formation is the only form of ion association in solid polymer electrolytes, the Hittorf, concentration cell and force-field methods yield individual ion-transport numbers since these techniques are not affected by neutral species whether these are mobile or not.Even for such simple association, however, radio-tracer, pulsed field gradient n.m.r., Cottrell and electrochemical polarisation methods do not yield transport numbers when the measurements are affected by contributions from mobile ion pairs. Full analysis requires knowledge of both the association constant and the mobilities of ions and ion pairs.On the other hand, if the ion pairs are immobile, these techniques do permit the transport number of the ions to be evaluated. Where there is54 Transport in Polymer Electrolytes higher association (triples and above) none of the methods yield ionic transport numbers if any of the more highly charged species are mobile. Despite this, it is probable that a combination of techniques from classes I-IV will lead to a clearer insight into the nature of transport in polymer electrolytes, since the different techniques provide different and possibly complementary information. Study of d.c. polarisation of cells of the form M( s) Ipolymer-MX( s) 1 M( s) leads to evaluation of the term ueff which is a useful parameter for determining the practical merit of a polymer electrolyte in devices such as power sources.We thank the S.E.R.C. for financial support, and Mr M. T. Hardgrave for making available some of the results of his electrochemical measurements. References 1 M. Spiro, in Physical Methods ofchemistry, ed. A. Weissberger and B. W. Rossiter ( Wiley-Interscience, New York, 1971), vol. 1, part I 1 A, chapt. IV. 2 S. Schantz, J. Sandahl, L. Borjesson, L. M. Torell and J. R. Stevens, Solid State Ionics, 1988,28-30, 1047. 3 L. M. Torell and S. Schantz, in Polymer Electrolyte Reviews I I , ed. J. R. MacCallum and C. A. Vincent, 4 J. R. MacCallum, A. S. Tomlin and C. A. Vincent, Europ. Polym. J. 1986, 2, 787. 5 C. A. Vincent, Prog. Solid State Chem., 1987, 17, 145. 6 M. Leveque, J. F. Le Noest, A. Gandini and H. Cheradame, Marcromol. Chem. Rapid Commun., 1983, 7 A. Bouridah, F. Dalard, D. Deroo and M. B. Armand, Solid State Ionics, 1986, 18-19, 287. 8 A. Bourdiah, F. Dalard and M. B. Armand, Solid State lonics, 1988, 28-30, 950. 9 A. V. Chadwick, J. H. Strange and M. K. Worboys, Solid State lonics, 1983, 9-10, 1155. (Elsevier, London, 1989), chap. 1. 4, 497. 10 C. Bridges, A. V. Chadwick and M. R. Worboys, Br. Poly. J. 1988, 20, 207. 11 A. A. Al-Mudaris and A. V. Chadwick, Br. Polym. J., 1988, 20, 213. 12 S. I. Smedley, in The Interpretation of Ionic Conductivity in Liquids (Plenum Press, New York, 1980). 13 M. Minier, C. Berthier and W. Gorecki, J. Phys. (Paris), 1984, 45, 739. 14 S. Bhattacharja, S. W. Smoot and D. H. Whitmore, Solid Stare lonics, 1986, 18-19, 306. 15 S. E. Lindsey, D. H. Whitmore, W. P. Halperin and J. M. Torkelson, Polym. Preprints, 1989, 30, 442. 16 M. McLin and C. A. Angell, Polym. Preprints, 1989, 30, 439. 17 P. G. Bruce and C. A. Vincent, J. Electroanal. Chem., 1987, 225, 1. 18 P. M. Blonsky, D. F. Shriver, P. Austin and H. R Allcock, Solid Stare lonics, 1986, 18-19, 258. 19 P. R. Sprrensen and T. Jacobsen, Electrochim. Acta, 1982, 27, 1671. 20 P. G. Bruce, J. Evans and C. A. Vincent, Polymer, 1987, 28, 2324. 21 P. G. Bruce, M. T. Hardgrave and C. A. Vincent, J. Electroanal. Chem., in press. 22 M. D. Ingram, personnel communication. 23 G. G. Cameron, J . L. Harvie and M. D. Ingram, Solid State Ionics, in press. 24 M. T. Hardgrave, Ph.D. Thesis, (University of St Andrews; 0000). 25 P. G. Bruce, M. T. Hardgrave and C. A. Vincent, to be published. 26 H. Cheradame, personal communication. Paper 9/02349F; Received 5th June, 1989

ISSN:0301-7249    

DOI:10.1039/DC9898800043

出版商:RSC    

年代:1989

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1989, 88, 55-63 Ion Transport in Polymer Electrolytes G. Gordon Cameron,* Malcolm D. Ingram” and James L. Harvie Department of Chemistry, University of Aberdeen, Meston Building, Meston Walk, Old Aberdeen AB9 2UE Transference numbers determined by the classical Hittorf method for liquid polymer electrolytes (solutions of NaSCN etc. in copolymers of ethylene and propylene oxide) yield consistently low values of t, (ca. 0.05). This points to a model in which cations are immobilised by interaction with the polymeric solvent and anions are the principal charge carriers, seemingly at variance with the successful operation of prototype lithium batteries. This paradox is resolved by postulating the ‘transport’ of Li+ ions from anode to cathode via the diffusion of ion pairs down a concentration gradient.A similar mechanism would also explain the higher values of t , (ca. 0.5) determined by the ‘steady-state current’ method and reported elsewhere in the literature. Transference numbers in polymer electrolytes are needed partly to clarify the mechanisms of ion transport, and partly to predict the performance of practical battery systems. As it is difficult to apply the well established (e.g. Hittorf or moving boundary) techniques, a variety of new approaches have been tried, including pulsed-field gradient n.m.r.”* and the a.c. impedan~el.~ (or steady-state current) analysis.536 Typically, cationic trans- port numbers determined in this way lie in the range 0.3-0.5, indicating that both cations and anions are mobile. We report for the first time ‘classical’ Hittorf-style transference numbers measured in liquid polymer electrolytes.The systems under investigation are essentially the same solutions of LiSCN, NaSCN and KSCN in copolymers of ethylene and propylene oxide, whose conductivities and viscosities were studied previously.’ Notably, the conductivities of these electrolytes were unaffected by changes in molecular weight in the range 1700-10000. This indicated [see also ref. (S)] that ion mobility even in liquid systems is primarily a function of local or segmental motions, rather than of the ‘centre of gravity’ movement of entire polymer chains. This is precisely the situation which pertains in the normal elastomeric polymer electrolytes,’ so it is reasonable to suppose that there is no major difference in the ion-migration mechanism.It is significant therefore that in all Hittorf experiments values of t+=0.05 are obtained,” indicating that the cations are largely immobilised in polymer electrolytes. A careful consideration of the ‘kinetic entities’ likely to be present in polymer electrolytes shows that this is not a surprising result, and that the earlier transport data can be reinterpreted in a consistent manner. Experimental Transport Measurements Polymers were kindly supplied to us by Hythe Chemicals Ltd. (U.K.) under the trade name BREOX. I3C n.m.r. spectroscopic experiments (performed by F. Heatley and co-workers’ in Manchester) showed that these are statistical copolymers of ethylene oxide (EO) and propylene oxide (PO).The two polymers most commonly used were labelled ‘75 WDO’ and ‘75 W1800’. These are both 75% EO by weight and are terminated at each end by n-butyl and OH groups, respectively. They differ in viscosity and in 5556 Ion Transport in Polymer Electrolytes electrodes Fig. 1. ‘Hittorf’ cell A, used in determination of transference numbers. ent Fig. 2. Hittorf cell B, used in determination of transference numbers. molecular weights (the latter being nominally 2300 and 13 000, respectively). These liquids were used without further purification except for drying over molecular sieve and rotary evaporation. In some cases, the OH groups were removed by acetylation as described previ~usly.~ After recrystallisation from methanol and vacuum drying at 110 “C, Li, Na and K thiocyanates were dissolved in the minimum amount of methanol, and mixed with the polymer. The methanol was removed subsequently by rotary evaporation.(The final level of H 2 0 impurity was ca. 2 x lo-* mol dm-3, as indicated by Karl-Fischer titration.) Two ‘Hittorf cells specially designed for use with liquid polymer electrolytes (LPEs) are illustrated in fig. 1 and 2. Cell A (fig. 1) has the usual three-compartment configur- ation. It permitted the mercury amalgam electrodes (prepared ‘in house’ using standardG. G. Cameron, M. D. Ingram and J. L. Harvie 57 methods) located in the anode and cathode compartments to be analysed after electroly- sis, so that checks could be made on the current efficiences of these electrode reactions, namely at the anode, M --* M+ + e-, and at the cathode, M+ + e- + M.A steady current supply (in the range 0.5-10 mA) was obtained from a Vokam SAE 2761 power supply (Shadon Southern), and the current was logged at intervals during the electrolyses (over 12-24 h) on a Keithley 175 Digital Multimeter. No attempt was made to thermostat the experiments performed under ambient conditions, but because of Joule heating the electrolyte temperature rose 2-3 "C and then remained close to 25 "C. In other experi- ments, the entire cell assembly was thermostatted in an Instron environmental chamber to within 70.3 "C. The transport number of the SCN- ion ( t - ) was defined as the number of moles of thiocyanate ion leaving the cathode compartment (or entering the anode) per mole of electrons ( F ) passed during electrolysis. The starting quantities of thiocyanate were obtained from the original concentration of the electrolyte and the total mass of solution in each electrode compartment. The final quantities were determined directly by draining the electrode compartments and collecting all the washings.Uncertainties in this measurement included a small (but occasionally significant) Aow of electrolyte into the cathode compartment caused by electro-osmosis, and the absence of sharp boundaries between the compartments. Also, at high current densities a black or. greyish deposit appeared on the anode as a result of side reactions involving the thiocyanate ion. This effect could be controlled by stirring the anolyte, but the 'cathode derived' transference numbers were generally considered more reliable because of the absence of such complications.Some of these problems were minimised in cell B, fig. 2, where the centre compartment was replaced by a hollow-barrel tap. After electrolysis was completed, the level of the catholyte could be readjusted to its original level (by blowing down one of the narrow side arms, if necessary) and thus any electro-osmotic flow could be reversed. Once the tap was closed, the contents of the cathode compartment could be washed out and analysed at leisure. Results and Interpretation The main results of the Hittorf experiments are summarised in tables 1 and 2. With very few exceptions, the data are seen to fit into a very simple pattern. The cationic transference numbers are very low, usually in the range 0-0.1.The 'best' value might be ca. t+ = 0.07 70.05, but there is obviously a fair amount of scatter in the experimental data. Nevertheless, we regard these results as experimentally significant, and highly relevant to any discussions of the transport mechanism. First, the low values of t+ do not indicate that 'nothing happened' during electrolysis. On the contrary, the high values of t - (0.9370.05) derive from large decreases in concentration near the cathode and large increases near the anode. Secondly, any 'back-diffusion' of salt into the cathode compartment would have resulted in lower t- values and correspondingly higher t+ values. A test experiment using cell A (table 1) showed that no increase in t+ was observed when the stirrer in the anode compartment was left switched on after completion of electrolysis, and draining of the electrode compartments was delayed for 12 h.Noting also that there are no systematic differences between data from cells A and B, we conclude that back diffusion is not a problem in these experiments. Thirdly, although corrections have not been made for density changes occurring during electrolysis, we consider that the t+ values listed in tables 1 and 2 do give a good indication of ion mobilities, relative to the solvent as a reference frame. We have reported earlier' that similar additions of NaSCN to these liquid EO/PO copolymers produce little change (<5%) in the molar volume of the polymer. Observing the movement of ions into and out of fixed volumes of solution (which is what we have58 Ion Transport in Polymer Electrolytes Table 1.Transference numbers in 75 W270 copolymer electrolyte solution results I , = (1 - 1 - ) values concentration C.E. salt /mol kg-’ T/”C (cathodic) anodic cathodic “NaSCN “ NaSCN “NaSCN “NaSCN “NaSCN “NaSCN KSCN LiSCN bc NaSC N ‘NaSCN NaSCN NaSCN NaSCN NaSCN 0.056 0.095 0.397 0.397 0.890 1.180 0.870 0.371 0.507 0.475 0.37 0.48 0.40 0.45 25 25 25 25 25 25 25 25 25 25 90 95 95 100 - 98 100 98 96 95 98 96 - - -0.04 0.10 0.10 0.15 0.08 0.07 0.00 0.16 (0.04) 0.00 0.03 0.10 0.04 0.08 0.05 0.01 0.02 0.08 0.05 0.19 0.07 0.05 0.12 “ Data from cell A, Test for back diffusion. ‘ Data from cell B. Table 2. Transference numbers in other liquid polymers polymer electrolyte results concentration t, = ( - t - ) polymer salt /mol kg-’ T/”C C.E.(cathodic) 75 W1800 KSCN 0.62 25 99.5 0.09 75 W270 (Ac) KSCN 0.44 25 95 0.09 25% PC 25% DME NaSCN NaSCN 1 .oo 0.46 25 - 25 - 0.06 0.08 done) corresponds, therefore, to observing the movement of ions into and out of fixed quantities of solvent. Finally, it emerges quite clearly from tables 1 and 2 that low values of t+ are found in Li, Na and K thiocyanates, over wide ranges of concentration, at different temperatures and in the presence of substantial amounts of ‘plasticiser’ such as PC (propylene carbonate) and DME (dimethoxyethane). Furthermore, t+ seems to be independent of melt viscosity (and/or molecular weight). It is difficult to escape the conclusion that all the monovalent alkali cations (Li,, Na+ and K+) are effectively immobilised in liquid polymer electrolytes.Ion Migration Mechanisms Kinetic Entities in Polymer Electrolytes The discovery of these ‘low’ cationic transference numbers is not surprising in the light of the strong cation-polymer interactions which exist, and the for intramolecular solvation to occur (i.e. for part of a single polymer chain to wrap itselfG. G. Cameron, M. D. Ingram and J. L. Harvie n 59 Fig. 3. Kinetic entities in liquid (PEO-based) polymer electrolytes. The arrows show increasing order of mobility cations <ion pairs <anions. ( a ) ‘Free’ cation, ( b ) solvent shared ion pair, ( c ) ‘free’ anion. around each cation in solution). Anions, which are not so strongly solvated, will be comparatively more mobile. However, where are the anions located if there are no specific interactions with the functional groups in the polyether chain? The obvious answer is that they will pair up with cations and thereby weaken the cation-polymer interaction.The expectation would be, therefore, that ion pairs are more mobile than ‘free’ cations and less mobile than anions. This is the thinking behind fig. 3 which shows (schematically) the local structure around these ‘kinetic entities’, and their relative mobility as expressed by the thickness of the arrows. Since the ion pairs have no electrical mobility, they can have no influence on the results of the Hittorf experiments, which quite clearly highlight the relative mobilities of the cations and anions. An obvious question concerns the possible role to be played by triple ions, such as [Na2SCN]+ and [Na(SCN),]-.If the above reasoning is correct, then the positive (dicationic) triple ions will have to be much less mobile than the negatively charged entities. One could then envisage the more mobile [ Na(SCN),]- ion migrating either as a discrete entity, or else breaking up and passing on one of its anions to a neighbouring ion pair: [ (SCN),Na( SCN)J + [ Na( SCN),] -+ [ (SCN),Na] + [ (SCN),Na( SCN),]-. The second process seems more likely (since no cation desolvation is involved) and indeed this process can be regarded simply as a mechanism for facilitated anion transport. Our decision not to consider triple ions as kinetic entities in their own right is consistent both with the above reasoning, and also with the fact that we have never observed negative transference numbers in the Hittorf experiments (the value of t , = -0.04 found in one case lies within the limits of experimental error).In effect we are saying that the t+ values listed in tables 1 and 2 do reflect the share of the current actually carried by ‘free’ cations, and are true ‘transport numbers’ according to Spiro’s definitions. l 3 Finally, one of us (in collaboration with scientists at G r e n ~ b l e ’ ~ ) has shown by experiments with pulsed field gradient n.m.r. that cations and anions both diffuse some 10 times faster than the polymer chains in these same electrolyte systems. The existence60 Ion Transport in Polymer Electrolytes salt concentration L i+ ions cathode - L i + ions anode - t distance across cell -+ Fig.4. The steady state in a ‘simple’ polymer electrolyte where ion pairs are absent (after Bruce and Vincent’). of such a large difference implies that migrating ions do not drag any solvent along with them, and furthermore it supports the idea that the conductivity mechanism in LPE resembles that found in polymer electrolytes of much higher molecular weight. Concentration Polarisation in Polymer Batteries Concentration changes which might occur during the charging of thick-film polymer batteries are simulated in the measurements of ‘transport numbers’ by the ‘steady-state’ current m e t h ~ d . ~ * ~ * ’ ~ , ’ ~ The situation where a d.c. current is passed between two Li/Li+ reversible electrodes is exemplified in fig. 4. The Li’ ions enter at the anode and are discharged at the cathode just as in the Hittorf experiments described above.The difference is that in fig. 4 there is no attempt to separate the cell into three compartments. On the contrary, the concentration is required to vary smoothly (and linearly) across the entire cell. At the steady state, there is no net flow of anions (migration towards is balanced by diffusion away from the anode) and all the current is carried by cations. If the kinetic entities are free cations and free anions (as in fig. 4), then Bruce and Vincents have shown that t+ = I,/ I o , where I, and I. are the steady state and initial currents, respectively. Cationic transport numbers measured by this technique tend to lie in the range 0.5-0.7. The difference between these latter figures and those derived fronl the Hittorf experiments needs to be properly explained.We can startI6 by considering the steady state in a simple cell, with electrodes reversible to Li+ ions, and where for simplicity t+ = 0, (see fig. 5). The only processes under consideration are the migration of anions under the applied electric field (towards the anode), and diffusion of both ion pairs and ‘free’ anions down the concentration gradient (towards the cathode). Under the steady-state conditions, the diffusive flux of ion pairs, Jip, is exactly balanced by the net anionic flux, J,. This net flux is proportional to the anionic current, I,, since J,F = I,, when J , is in mol s-l and I, is in A. In theG. G. Cameron, M. D. Ingram and J.L. Harvie 61 salt concentration Li + ions cathode - c distance across cell +. I L i + ions anode - Fig. 5. The steady state in a ‘real’ polymer electrolyte where the diffusion of ion pairs is more important than the migration of free cations, after Cameron et dL6 steady state, the ion pair flux carries all the cations formed at the anode across the cell to be reduced at the cathode. A steady-state current can thus be observed even if t+ = 0, so it is apparent that I s / & cannot be regarded as a valid measure of the cationic transference number. A Theory of Steady-state Currents As Bruce and Vincent have already shown,’ steady state currents ( I , ) can only be accurately analysed if the applied voltages are small (ca. 10 mV), and the concentration gradients (see fig.4 and 5 ) are correspondingly small. We shall make the further assumption that, under these conditions, the fraction of the salt existing as free ions ( a ) remains constant across the cell. Hence, the concentration of ions Cion = Ca, and the concentration of ion pairs Ci, = Cp, where p = (1 - a ) . The effect of the concentration gradient is to set up a back e.m.f. ( A E ) , which opposes the applied voltage (AV), and reduces the potential difference ( A 4 ) acting across the electrolyte, i.e. A @ = A V - A E ( 1 ) where by the Nernst equation: C, and C, are the concentrations of salt at the anode and cathode, respectively. If the ionic mobilities and ionic diffusion coefficients are related by the Nernst- Einstein equation, the conductance of a unit cell (G) is given by: G = F’D,C~/RT ( 3 )62 Ion Transport in Polymer Electrolytes where D, is the diffusion coefficient of the free anions. The corresponding (Ohmic) current is given by GA4.There is also an anion diffusional current given by Idiff= FJ,. Assuming Fick’s law, then I d i f f = ( C, - C,) D,a F. (4) The final (steady-state) current of anions is thus given by the difference between these Ohmic and diffusional currents: I , = GA4 - FJ, = [A V - ( R T / F ) In (C,/ C,)] F’D,Ca/ RT - ( C , - C,)D,aF. ( 5 ) By making the substitution C, = ( C + 6 ) and C, = (C - S), eqn ( 5 ) may be rewritten as RT ( 25 +,) F’:TCa - 2SD,aF. I,=AV--In ___ F C-6 For small values of S this simplifies”’“ to: 2RTS F‘D,Ca I,= AV-- -2SD,aF. ( F C ) RT (7) In the Bruce-Vincent treatment,5 I , = 0, because in the absence of ion pairs this satisfies the condition that there is no net movement of anions.However, by assuming that a net flow of anions to the anode can be balanced by a flow of ion pairs in the reverse direction, we obtain I,/ F = 2pSDi, (8) where Dip is the diffusion coefficient of the ion pairs. Substituting for S from eqn (8) into eqn (7), and rearranging gives I,= I , = F ’ D , C ~ A V RT I+- I ( ?;). (9) Two special cases can be identified. (i) When D,a >> DipP under these conditions, I , -+ 0, which is the ‘expected’ result, if the cations are immobile and ion pairs make no contribution to the diffusion processes. (ii) When D,a << DipP under these conditions, I ---* F2D,Ca A V/ RT, which is the normal ‘Ohmic’ current, I,, before any concentration polarisation occurs.Therefore, the ratio I,/ I , can equal unity (in theory) even if t , = 0. The contribution of a true ‘cationic’ current to the cell conductivity serves only to enhance the value of the steady-state current by an amountI6 equal to (F’D,Ca A V/ RT). If t , = 0.07 (as is indicated by the Hittorf experiments), then this term will be rather small (since D, >> DJ. Accordingly, the diffusion of ion pairs will be responsible for most of the observed steady-state current. Conclusions On the basis of the above discussion, we can make two suggestions concerning ion transport in polymer electrolytes. (i) There is still a clear need for ‘classical’ transference numbers to be measured for the high molecular weight (viscoelastic) polymer electrolytes if the mechanism is to be properly understood. Such data wi!l not come from the steady-state current method or the corresponding a.c.impedance methods3” for the reasons just given, nor will they come from the pulsed field gradient n.m.r. experiments,‘.’ which in effect” measure a ‘diffusion number’, D+/( D+ + 0-), where the diffusion coefficients are average values reflecting the motions of both charged and uncharged entities. (ii) From a practical standpoint, the factors which control the steady-state current ( I , ) also influence the performance of polymer batteries. A ‘large’ value of I , will result (other things being equal) in a ‘good’ battery electrolyte.G. G. Cameron, M. D. Ingram and J. L. Harvie 63 This is the most interesting aspect of eqn (9).It is apparent that the value of the limiting current can be enhanced by increasing both a and Dip. If the aim is to design the ideal polymer electrolyte which, ( a ) is highly conductive and (6) does not ‘polarise’ during electrolysis one has to consider ways of increasing both the degree of dissociation and the diffusivity of the ion pairs. This is the strategy which we are presently pursuing in our own laboratory. J. L. H. thanks the Carnegie Institute for the Universities of Scotland for a Research Scholarship, and also Dr M. B. Armand for the opportunity to visit Grenoble. References 1 W. Gorecki, R. Andreani, C. Berthier, M. B. Armand, M. Mali, J. Roos and D. Brinkmann, Solid State lonics, 1986, 18/19, 295. 2 S. Bhattacharja, S. W. Smoot and D. H. Whitmore, Solid State Zonics, 1986, 18/19, 306. 3 J. R. MacDonald, J. Chem. Phys., 1973, 58, 4952; 1974, 61, 3977. 4 P. R. Sorensen and T. Jacobsen, Electrochim. Acta, 1982, 27, 1671. 5 P. G. Bruce and C. A. Vincent, J. Electroanal. Chem., 1987, 225, 1 . 6 P. G. Bruce, J. Evans and C. A. Vincent, Solid State Zonics, 1988, 28/30, 918. 7 G. G. Cameron, M. D. Ingram and G. A. Sorrie, J. Chem. Soc., Faraday Trans. 1, 1987,83, 3, 3345. 8 L. M. Torrel and C. A. Angel], Br. Polym. J., 1988, 20, 173. 9 C. A. Vincent, Chem. Br., 1989, 25, 391. 10 G. G. Cameron, J. L. Harvie, M. D. Ingram and G. A. Sorrie, Br. Polym. J., 1988, 20, 199. 1 1 F. Heatley, Y-Z. Luo, J-F. Ding, R. H. Mobbs and C. Booth, Macromolecules, in press. 12 Y. Chatani and S. Okamura, Polymer, 1987, 28, 1815. 13 M. Spiro, in Techniques of Chemistry, ed. A. Weissberger and S. W. Rossiter (Wiley, New York, 1970), 14 M. B. Armand, W. Gorecki and J. L. Harvie, unpublished work. 15 J. Evans, C. A. Vincent and P. G. Bruce, Polymer, 1987, 28, 2324. 16 G. G. Cameron, J. L. Harvie and M. D. Ingram, Solid State lonics, 1989, 34, 65. 17 J. L. Harvie, PhD. Thesis (Aberdeen, 1989). vol. 1, part 1A. Paper 9/02120E; Received 17th May, 1989

ISSN:0301-7249    

DOI:10.1039/DC9898800055

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年代:1989

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Faraday Discuss. Chem. SOC., 1989, 88, 65-76 Charge Transfer at Polymer Electrolytes Michel Armand Laboratoire d' Ionique et d' Electrochimie du Solide CNRS UA 1213, ENSEE-Grenoble B. P. 75 Domaine Universitaire, 38402 Saint-Martin-d' Hkres, France Polymer electrolytes ( PEs) are ion-conducting complexes formed between a metal salt and a solvating polymer, usually a polyether like poly(ethy1ene oxide). Electrochemical reactions at PEs/electrode interfaces are reviewed and compared with those of liquid electrolytes. One characteristic of these materials is their exceptional inertness which spans the 0-4.6 V/Li+ : Li" stability window. Nevertheless, the conduction mechanism, a solvation- desolvation of the cation along the chain, governs the kinetics: only cations with fast ligand exchange are electroactive, irrespective of thermodynamics; anions, which are not solvated are always mobile.Transfer of ions into intercalation compounds is usually well defined, with no solvent co-intercala- tion. The possibility is discussed that some level of redox conduction appears in PEs at potentials either cathodic (metal solubility) or anodic beyond the stability window (oxonium radical). Polymer electrolytes (PEs) cover a wide variety of materials in which ions exist and are mobile in the absence of any solvent or low molecular weight pla~ticizer.'-~ In this respect, they are termed 'immobile solvents' as the ionic motion does not correspond to a net displacement (centre of gravity) of the macromolecule. This is especially evident with cross-linked materials in which the chains are bound together to form a single three-dimensional network.The most frequently studied compounds are those obtained from the dissolution of an alkali-metal salt in a poly(ethy1ene oxide) [CH2-CH2-O-], (PE0)- or poly(propy- lene oxide) [CH,-CH(CH,)-0-1, (PP0)-based polymer. poly( ethylene oxide)( PEO) \ 0 / CH2-c~C H 2 - b C q A p o I poly( propylene oxide) (PPO) \ 1 0 The corresponding units can be arranged with a linear chain, comb or network structure, keeping the basic solvation properties of the pol yether. For highly symmetrical monomer units, like PEO, both the pristine polymer and the corresponding stoichiometric com- plexes (usually 3 : 1 and 6 : 1 repeat units per salt) tend to form regular non-conductive structures (crystallites). A conductive eutectic (elastomeric) is formed at 40-60 "C between these two phases.Modifications of the linear chain structure favour the existence of the conductive amorphous phase; in addition, cross-links improve the mechanical properties. Typical conductivities for PEs are within 10-6-10-3 0 cm-' for temperatures ranging from 25 to 120 "C. The best electrolytes reach conductivities of LR cm-' at room temperature. 6566 H C l o t , CF3SOT +LI+ Be .> + + "Ne' 'Mg+ Al - + t + + - K+ + C i +SC r T 1 + V +I9Cr+*M;' Fe+ goQ:Ni +Cu ' 2 : Ga Go - + + ++ + 3 + 2 + + 2 + + + 2 + + + + + 2 + + + + I- + ' + + + + 4 + 5 + 5 + 2 - + + + + + 2 + . +-). + + + Rb Sr Y Zr Nb Mo Tc Ru R h P d Ag'+Cd+ In +Sn+ Sb Cs Be + L a Hf ;a W Re 0 s Ir Pt A u TI P b +Bi P o * + + + + + + + ' + + + + + + 5 + 3 + 4 +% 1 + + + 3 Fr Ra Ac Charge Transfer at Polymer Electrolytes - + +4 + + Y + + t + + + Ce Pr Nd Pm Sm Eu Gd + + + + + + + + t 2/3t+ ++ Th Pa LO,' + + 2 + , + +4 ++ +I+ + + +I+ +r+ + Tb +Dy+ Ho+ Er Tm Yb Lu + + + + + + + + + + In addition to the alkali metals, by far the most studied, a wide variety of other derivatives including alkaline, rare-earth and transition metals are now known, though they are not yet fully characterized, neither by phase diagram nor by electrochemistry (fig.1). Polyethylene imine with the repeat unit [CH2-CH2-NH-] poly(ethy1ene imine)( PEI) \ / C H 2 - C \ H 2 n n NH NH NH NH NH forms similar complexes, which are especially stable in the case of the 'soft' transition- metal cations (cu*+, Zn2+, co2+ etc.).Charge Transfer at Electrodes Charge Transfer within the Electrolytic Domain A distinguishing feature of the polymer electrolytes is, among other technological advantages, their expected lack of reactivity. This is especially the case for PEO, which shows the well known chemical inertness of ethers. As a result, electron transfer is limited in most cases to the solute and the redox reaction limited at the electrode interface. We shall discuss here the reduction and oxidation processes accessible with polymer electrolytes. Metal Deposition and Alloy Formation At cathodic potentials, a variety of metal cations have been shown to be reduced to the metal. M''+(e/ectro/yte) 4- ne-(e/ecrrode) ---* (M"). The alkali metals have received most attention, especially lithium deposition onto a metallic substrate for battery applications.6-8 Research in this field has been discussedM.Armand r 67 -0.8 voltage/V Fig. 2. Cyclic voltammetry for P( E0)9LiCF3S03 electrolyte at 80 "C. 20 mV s-' on non-alloying nickel substrate. Cycle number indicated on figure. From ref. (8). t I I I 1 1 1 1 I I 1 1 - 4 -3 -2 -1 0 1 2 3 4 voltage/V Fig. 3. Cyclic voltammetry trace for P(EO),,,NaCF3S03 ; platinum electrode, 85 "C; sweep rate 60 mV s-'; reference Ag"/Ag,SI. recently by Bilanger;' the metal can be reversibly plated and stripped at low overpotential when using a salt derived from a thermodynamically (I-) or kinetically (C104-, CF,SO,-) stable anion as shown in fig. 2. The well known difficulties associated with an electrode of the first kind (Li+/ Li") appear much less dramatic with PEs.Dendrite formation, an especially preoccupying problem with liquid electrolytes, can be elminated for > 1000 deep cycles in batteries with surface capacities of ca. 2 C cm'. Sodium deposition as shown in fig. 3 is also observed as a reversible process and even a potassium reduction wave can be obtained despite the higher reactivity of the metal. Nevertheless, the electrochemical activity is dependent upon the transport number of the species, i.e. how68 Charge Transfer at Polymer Electrolytes voltage/ V Fig. 4. Cyclic voltammogram for P(EO),-(0.9)LiC10,-(0.1)Mg(C104)2 ; platinum electrode, 85 "C; 40 mV s-'; reference Ag"/Ag,SI. fast the electroactive species are supplied to the electrode.As pointed out by Vincent, the transference number of the cations can be very small, yet they can diffuse as neutral ion pairs, MX, or triplets, XMX-. Such species are expected to exist in appreciable concentrations in these iow dielectric constant media ( E = 5-10). Neutral species do not appear to be mobile in PEs, as shown by the coincidence of the conductivity values directly measured using various electrochemical techniques and of those deduced from NMR pulsed field gradient measurements through the Nernst-Einstein equation."?' This implies that ionization is the required step for motion and diffusion in PEs, and thus these materials differ markedly from liquids. Strong polymer-cation interactions tend to limit the mobility of the positive charges ( t + = 0), despite an appreciable ionization.This is the case for Mg2+; Mg(CIO,), in PEO has no apparent redox activity, as shown in fig. 4. Conversely, the larger Ba2+, which is less strongly solvated, is able to move towards the electrode and can be reversibly plated and stripped at a potential of ca. 500mV, positive of the Li couple, as shown in fig. 5. An interesting correlation can be made between the motion of cations in PEs and the measured rates at which the same ions exchange water molecules within their solvation shell, drawn in fig. 6 and covering 18 orders of magnitude. Only cations with exchange rates exceeding lo8 sC' are expected to have an appreci- able mobility in polyethers whose solvation characteristics are quite similar to those of water. Tieline at Zn2+ ( t f = 0.05) corroborates the observation of electroactivity of the heavier alkaline- and rare-earth metals with the addition of the 's' metals and the larger transition-metal cations, or those sensitive to the Jahn-Teller effect with high ligand liability (see fig.7 for an example on lead deposition and stripping): Sn2+, Pb2+, Hg", Mn2+, Cu2' etc. Alloy formation is also possible with many host metals and lithium; in fact, this element forms alloys with almost all metals except those with high lattice energy (Fe, Ni, Mo, W, Cr) and the diffusion is fast enough to be observed around room temperature.M. Armand 69 - L - 3 -2 -1 1 2 3 4 voltage/ V Fig. 5. Cyclic voltammogram for P(EO),- (0.9)LiCI04-(0. l)Ba(ClO,), ; platinum electrode, 85 "C; 40 mV s-'.Arrow shows the Ba" deposition peak; reference Ago/Ag,SI. I : t i P6 Co' Fc" V" TI'' Mn'j Lanthanides 1 1 I I ' dl - 8 -6 - 4 - 2 0 2 4 b 8 10 Fig. 6. Rate constants (C1) at 25°C for exchange of water ligand in aqueous solutions. From ref. (23). In fig. 8, the cyclic voltammetry scan of a mixture of LiC10, and LiI (10%) shows in the cathodic domain a reduction wave superposing the formation of a Li/R alloy ( 1 : 2) and Li" deposition, while the two processes of dissolution and de-alloying are well separated on the following anodic sweep. Lithium dissolution in aluminium has been well studied in various electrolytic media, again for battery applications. With the PEO electrolyte, the coulometric titration curve as shown in fig. 9 clearly indicates the transformation of the cy aluminium structure ( < 7 at.% Li) into the p phase which possesses a wide range of non-stoichiometry, 0.85 < y < 1.15, in Li,,Al, in agreement with the phase diagram.Similarly, zinc and magnesium form alloys with lithium which are either stoichiometric compounds (Zn) or true solid solution (Mg). The existence of intermetallic compounds with sodium and potassium is limited to 'softer', more electronegative elements like Pb or Bi.70 Charge Transfer at Polymer Electrolytes + 2 +1 i -1 -2 +3 +4 voltage/V Fig. 7. Cyclic voltammetry trace for P(E0)30Pb(CF3S03),; 90 “C platinum electrode; 10 mV s-’. From ref. (12). Proton-conducting PEs, exemplified by the PEO--H3PO3l3 complexes or the L ~ r m ~ l y t e ~ ’ 1 4 \ NH2 NH2 NH2 NH2 which are intermediates between glasses and polymers both show hydrogen evolution at cathodic potentials, a reversible process on platinum electrodes.Intercalation The most general solid-state redox reaction is intercalation, where an ion (+ne or -ne) diffuses into a solid host structure (H) together with a compensating electronic chargeM. Armand 71 4 - 2 -1 0 - 2 - 4 - -4 -3 -2 -1 0 1 2 3 4 voltage/V Fig. 8. Cyclic voltammogram for P( EO),-(0.9)LiC104-(0. 1)LiI platinum electrode, 85 "C; 40 mV s-'. A", Li dissolution peak from LiPt, alloy; reference Ag"/Ag,SI. 4 0 0 300 > iu < 200 0 - , , I . . . . , . . . . 0 1 0.5 1.5 y(Al-Li, ) Fig. 9. EMF us. composition (coulometric titration curve) for the lithium dissolution in aluminium; reference Li" 65 "C electrolyte P( E0)8LiC104.(e- or h+), keeping the basic structure-building bonds mainly intact (topochemical reaction). Further refinements of this simple description are in terms of a higher order structure (stages, sublattice ordering, site exchange) which allows minimization of the strains (mechanical, electrostatic, Jahn-Teller) due to charge injection. The insertion reaction, written in its electrochemical form as xM+(e/ecrro/yre) + Xe-(e/ecrrode) + (H) ( M ~ H ) o<x<x,,,72 Charge Transfer at Polymer Electrolytes > 0 02 01, 0 6 08 1 X Fig. 10. Ultra-slow scan voltammetry trace for lithium insertion in ZrSe,,,,, ; electrolyte P(EO),LiClO,; 1.2 mA h electrode capacity; reference Li"; 100 "C; 10 mV h-'; from ref. (16). ( a ) CV curve; ( b ) integral EMF=f(x).consists of a simple charge transfer across the electrode interface. Again, such a process has been studied in detail with various host (H) structures like TiS2, W03 or V205 for battery applications, the most immediate driving force in the field of PEs. The reversibil- ity, stability and absence of co-intercalation of the polymer are among the main advan- tages. This latter phenomenon is often seen with liquid electrolytes and two-dimensional structures which are not sterically selective, and occurs when the cations entering the structure are too strongly solvated to shed their coordination shell. As a result, the structure exfoliates and loses its reversibility. For instance, it is not possible to prepare electrochemically the graphite-alkali-metal intercalate with any liquid electrolytes, while they are readily obtained from PEO-MX electr01ytes.l~ Recently, Chabre et have taken advantage of the absence of side-reactions in PE electrochemical cells to set up digital ultra-slow scan voltammetry ( V s-'). This technique allows direct differen- tiation between the sites according to their energies in the intercalation compound.A good example is given with the cyclic voltammetry trace for sub-stoichoimetric zirconium selenide [fig. 10( a ) ] interpreted as the preferential occupancy of the sites created in the vicinity of the Zr-Zr pairs within the slabs, followed by the van der Waals sites. Integration of the cyclic voltammetry trace gives directly the thermodynamic coulometric titration curve [fig. 10( b ) ] .Another aspect of intercalation chemistry, misnamed as 'doping', is observed with conjugated polymers (CPs). Either reduction or oxidation reactions are possible, the latter corresponds to an ingress of anions to compensate for delocalized carbocationsM. Armand 73 40 2 0 - 2 0 I - 4 0 V( Li/ Li') Fig. 11. Cyclic voltammetry trace for solid-state cell Li/ P( E0)8LiC104/polyviologen; sweep rate = 0.5 mV s-', temperature = 90 "C. formed on the polymer backbone: The superposition of both conductivities, ionic in PEs and electronic in CPs, is very appealing. Simple mechanical contact between the two polymers gives poor overall kinetics due to the sluggish diffusion of X- in CPs, yet the elegance of an all polymeric system: (CH),/PEO-NaI/(CH), is certain. l 7 Combination at the molecular level, as for instance oligoPEO-grafted polypyrrole, shows much improved kinetics of charge transfer in the bulk of the composite.'* A non-conjugated redox polymer, like the polyviologen.has been studied in an all solid-state cell, for various MX and n:19 - Li/ P( EO) MX/ polyviologen+. The reversible electroactivity of the viologen is clearly demonstrated on the cyclic voltammogram of fig. 11, showing the formation of the radical cation and of the neutral species: v2+ + e-(elecrrode) a V'+ e V". The pol viologen electrode was thus used as an anion-specific electrode at the equivalent point Vr+2X-/V*+X- to determine the activity of MX in PEO.I974 Redox Processes and Conduction in the Electrolyte Metal Solubility An interesting possibility is that alkali metals are soluble in the polymer, in a similar way to in ether solvents (THF, glymes) where the metals form ion pairs in concentrations up to ca.10-3moldm-3: Charge Transfer at Polymer Electrolytes The formation of solvated electrons, as in ammonia MTOruoted eLolUated is less likely due to the lower dielectric constant of ethers. The high solvation ability of polyethers should favour the metal solubility, and PEO has been shown to increase markedly the solubility of K in THF mol dm-3).20 Such ion pairs in polymers could lead to 'n'-type electronic conductivity, similar in principle to that of 'electrides' formed from cryptates and alkali metals. 7nnn-r :o: :o: :o+ ro: :o: In any case, the solubility is expected to become negligible in the presence of salts, a situation normally encountered when operating PEs ('salting-out' effect).The possibility remains that, under prolonged cathodic polarization with Mo deposition, the concentra- tion gradient due to the anion transference number results in local salt depletion, allowing for metal solubility. Such a phenomenon may have been observed with Lio as a coloured layer moving away from the cathode surface and may explain the 'soft dendrite' healing mode of solid-state lithium batteries: a cell short-circuited by a dendritic growth recovers after a few cycles with little effect on life span. Anodic reactions are also limited to the solute within the 0-4.6 V/Li: Li+ stability window of the polyethers. A good example is given again in fig. 8 where the oxidation of the minority carrier I- into 1,- appears as a reversible reaction.In this case considering the low concentration on the polyiodide species, the reaction is controlled by diffusion of the ionic species, the anions always being mobile. The polysulphides M2S, behave similarly and both systems have been used in photoelectrochemical A different situation is encountered with higher iodine concentrations, as shown in fig. 12 for CsI, which displays an almost linear current-voltage relationship, indicative of predominant electronic conductivity. Similarly, Wright and Siddiqui have found high redox conductivity in the system PEO TCNQO-NaTCNQO-. Again, the polymers differ from simple solutions since the attainable concentrations are higher than those of liquids, corresponding to shorter average distances betwen species, a situation favourable to electron hopping.There are no clear examples yet of a redox conduction mechanism obtained with the same metal at two different oxidation states. Good candidates are the Fe""", Cu"", , UOZ1'" systems which are known or expected to give complexes either in PEO or PEI. However, relatively low levels of redox conduction are expected as the elements often require a different coordination environment when changing valency; this would lead to polaron-type conductivity. Eu I I / 111M. Armand 75 - 4 -3 -2 -1 1 2 3 4 voltage/V Fig. 12. Cyclic voltammetry trace for the complex P( EO)&sI, ; 65 "C, platinum electrode; reference Ago/ Ag, S I. Beyond the anodic stability limit, in the presence of oxidation-resistant anions, the transient formation of oxonium radical cations is possible: 7Af7AAf- :o: :o: :o+ :o: :o: X- = C104-, CF3S03- and could lead to 'p'-type conductivity before chain degradation takes place.The latter process is in fact markedly accelerated by impurities, like CI-. For instance DDQ (dichlorodicyanoquinone) gives DDQ'- in the presence of purified PEO with a minimal loss in molecular weight; addition of chloride results in almost immediate chain scission. Liquid electrolytes like THF or dioxolane also form a cation radical which initiates an irreversible polymerization with the formation of a passivating layer, a problem which was long underestimated with battery electrolytes. Conclusions A decade after their discovery, the electrochemistry of polymer electrolytes has begun to be well documented. It is now clear that the behaviour of these materials cannot be transposed directly from that of liquids: the mechanism for conductivity is unique and more selective, restricting the number of potentially electroactive species from the larger choice based on the thermodynamics alone.On the other hand, this is a definite advantage in terms of stability and absence of side-reaction at the electrode interface. We should also retain the possibility of working under high vacuum, as for in situ SEM76 Charge Transfer at Polymer Electrolytes observation of electrode reactions.23 PEs appear, in fact, to be the best compromise between liquids and true solid electrolytes (AgI, p alumina, glasses), which are even more selective but very limited in choice, and for which the realization of complete electrochemical systems is a challenge, with arduous material processing and interfacial problems.The almost infinite choices offered by macromolecular chemistry present many interesting possibilities for a variety of applications, including alloys of conjugated polymers and polymer electrolytes, the attachment of redox centres to the backbone to mediate or catalyse redox processes, or the confinement of reagent or species to a predesigned spatial location, based on specific ion-polymer interactions ( e.g. Cu2+ in PEI); shuttle redox couples may also be used to reveal the electroactivity of species immobilized in the macromolecule. References 1 M. B. Armand, Ann.Rev. Muter. Sci., 1986, 16, 245. 2 Polymer Electrolytes Reviews 1, ed. J. R. MacCallum and C. A. Vincent (Elsevier, London, 1987). 3 C. A. Vincent, Prog. Solid State Chem., 1987, 17-3. 4 M. Gauthier, M. Armand and D. Muller, in Electroresponsive Molecular and Polymeric Systems, ed. T. Skotheim (Marcel Dekker, New York, 1988), vol. 1, p. 41. 5 M. Armand and M. Gauthier, in Solids with High Conductivity, ed. T. Takahashi (World Publishers, Singapore, 1989), in press. 6 M. Gauthier, A. BClanger, B. Kapfer, G. Vassort and M. Armand, in Polymer Electrolytes Review IZ ed. J. R. MacCallum and C. A. Vincent (Elsevier, London, 1989), in press. 7 C. A. C. Sequeira and A. Hooper, Solid State Ionics, 1983, 9/10, 1131. 8 F. Bonino, B. Scrosati and A. Selvaggi, Solid State Ionics, 1986, 18/19, 1050. 9 A. BClanger, Proc. 2nd Int. Meeting Polymer Electrolytes, Sienna, Italy, June 14-17, 1989. 10 W. Gorecki, R. AndrCani, C. Berthier, M. B. Armand, M. Mali, J. Roos and D. Brinkman, Solid State Zonics, 1986, 18/19, 295. 11 S. Bhattacharja, S. W. Smoot and D. H. Whitmore, Solid Sfate Ionics, 1986, 18/19, 306. 12 A. Bouridah, F. Dalard, D. Deroo and M. Armand, Solid State Zonics, 1986, 18/19, 287. 13 F. Defendini, M. Armand, W. Gorecki and C. Berthier, Electrochemical Society Sun Diego Meeting, 1986, 86-2 extended abstract No. 3. 14 Y. Charbouillot, D. Ravaine, M. Armand and C. Poinsignon, J. Non Cryst. Solids, 1988, 103, 325. 15 R. Yazami, P. Touzain, J. Power Sources, 1983, 9, 365. 16 Y. Chabre, P. Deniard and R. Yazami, Solid State Ionics, 1988, 28/30, 1153. 17 C. K. Chiang, Polymer, 1981, 22, 1651. 18 M. G. Minett and J. R. Owen, Solid Sfate Zonics, 1988, 28/30, 1193. 19 A. Bouridah, F. Dalard and M. Armand, Solid Stare Ionics, 1988, 28/30, 950. 20 I . M. Panayotov, C. B. Tsvettanov, I. V. Berlinova and R. S. Velchkova, Makromol. Chem., 1970, 134, 21 T. A. Skotheim, S. W. Feldberg and M. B. Armand, J. Phys. (Paris), 1983, C344, 615. 22 B. Marsan, Ph.D. Thesis, UniversitC du QuCbec INRS Energie, 1988. 23 P. Baudry, M. Armand, M. Gauthier and J. Massounave, Solid State Zonics, 1988, 28/30, 1567. 24 D. W. Margerum et al., in Coordination Chemistry, ed. A. E. Martell (ACS Monograph No. 174, 313. Washington, D. C., 1978) vol. 2. Paper 9/02136A; Received 19th May, 1989

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DOI:10.1039/DC9898800065

出版商:RSC    

年代:1989

数据来源: RSC

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Faraday Discuss. Chem. SOC., 1989, 88, 77-86 Discussion of the Mechanism of Charge Transfer in Amorphous Ionically Conducting Networks H. Cheradame” and P. Niddam-Mercier Laboratoire de Chimie Macromole‘ctdaire et Papetiire de 1’Institut National Polytechnique de Grenoble, E.E P. B. P. 65, 38402 Saint-Martin d ’HGres, France A model is presented of ionic conduction in the amorphous phase of poly(ethy1ene oxide) containing low amounts of salt. A scheme is given which describes qualitatively charge carrier generation, and a WLF law describes quantitatively the conductivity variations with temperature. The concentration of positive charge carriers remains approximately constant in the concentration range studied, and variations in the positive transference number are also explained.The model predicts the optimum value of the salt concentration. This paper aims at presenting an overall explanation of ionic conductivity behaviour for amorphous polyether networks containing an ionisable salt at low concentration. It is worth specifying first that only materials without a noticeable quantity of solvent, i.e. materials which are ionically conducting in bulk, are dealt with here. In the context of our research, polymers of high crystallinity are not ionically conducting, at least in the range of conductivity high enough to be of use as a solid electrolyte, since movements of atoms are prevented by the rigidity of the matrix. The materials under discussion here are assumed to be totally or almost totally amorphous. For the same reason, commonly used polyelectrolytes are not of interest in the present context.Finally, in our laboratory, most of the salient results concerning the ionic conduction mechanism were obtained with polyether networks, more specifically cross-linked poly( ethylene oxide). Complete experimental details will be found in the various papers published by our laboratory, and mostly in ref.(l)-(4). Nature of Charge Carriers Before discussing the mechanism of charge transfer in ionically conducting materials, it is of outstanding importance to know the nature of charge carriers. It is assumed in the following that the conductivity is mostly due to the movements of unpaired ions. In the case of polyether-based materials containing alkali-metal salts, it was initially thought that the charge transport was mainly due to the movements of cations.This assumption was later ruled out.’-’’ We verified using Tubandt’s in the case of pol yether networks filled with alkali-metal salts of strong acids that the cationic transference number was lower than the anionic one, and was independent of the applied voltage and the current d e n ~ i t y . ” ” ~ The cationic transference number varies appreciably with the nature of the anion associated with the alkali-metal cation (mainly lithium cation). No significant change in t + was observed in the systems studied in our laboratory when the temperature was varied, in one instance between 70 and 120°C. This result confirmed previous results obtained with complex impedance determinations6 In the case of PEO-1000-based networks, t+ decreases monotonically with increasing salt concentration up to a ‘critical’ value corresponding to one lithium cation per polyether chain, i.e.corresponding to a molar ratio of ether oxygen atoms to Li’ cations, O/Li, of 22. Above this concentration, t + tends to level off to a constant value ( t + = 0.2). The 7778 t Charge Transfer in Amorphous Networks 1 I I I I * -1 -0.5 0 log (C/mol dm-') Fig. 1. Plot of the logarithm of the conductivity of PEO-1000-based networks versus the logarithm of the salt concentration at constant reduced temperature [from ref. (l)]. 0, 75 "C; A, 100 "C; X , 125 "C. same behaviour was observed in the case of PEO-2000-based networks. In the case of networks prepared from a triblock POE(2000)-b.POP( 1000)-b.POE(2000) copolymer the cationic transport numbers were also found to decrease with increasing salt concentra- tion but the 'critical' concentration, if any, could hardly be detected, and was lower than 0.05 for the highest salt concentration^.'^ For most materials based on polyether networks, t+ is much lower than t - so that the conductivity behaviour mainly charac- terises the movements of the negative charge carriers.An interesting exception to this conclusion is obviously brought about by the self-ionisable polyelectrolytes for which the anions are covalently bound to the macromolecular network. Indeed, it was verified that for these materials which contain pol yether macromolecular chains and ionisable functions the cationic transport number is equal to unity within experimental This expected result on the other hand gave the opportunity to study the conductivity behaviour of the cations alone.Conductivity Behaviour It was first demonstrated that the ionic conductivity follows a free volume law, expressed in the domain of macromolecular materials as a WLF law. This behaviour was initially demonstrated years ago for the ionic conduction of compositions based on linear polymers.16 It was suggested that it could also hold for ionically conducting polyether networks," and then extensively verified on this type of Self-ionisable electrolytes, in which the anionic moiety of the lithium-based ionisable functional group is bound to the macromolecular backbone, allowed us to demonstrate that the movements of the cations are similar to those of the anions." In order to achieve a better understanding of the conductivity mechanism, the contributions of the ionic mobility and of the number of charge carriers to the conduc- tivity had to be appraised separately.Indeed, it is known that for macromolecular materials the mobility of chain segments is constant at constant reduced temperature, i.e. constant T-T,. This type of analysis, performed for the first time on ionically conducting materials, proved to be a useful tool.'* A plot of the logarithm of the conductivity versus the logarithm of the salt concentration at constant reduced tem- perature showed a linear relationship up to a critical salt concentration, with the occurrence of minima and maxima above this critical concentration (fig.1). The slopeH. Cheradame and P. Niddam-Mercier 79 1 I I -03 -1 log (C/mol kg-') ' Fig. 2. Plot of the logarithm of the conductivity of PEO-400-based networks containing sodium tetraphenyleborate versus the logarithm of the salt concentration at constant reduced temperature, [f'rom ref. (2), p. 2521. of the linear relationship was found to be unity in most of the experiments carried out with PEO-based In other words, the conductivity was found to be proportional to salt concentration. This result was also found to hold in the case of sodium tetraphenyl borate (fig. 2). In the case of the poly(propy1ene oxide) and sodium salt system, the slope for such plots was ca. 3 , and for poly(oxytetramethy1ene) with sodium salt, the slope was 1.5.2 A full discussion of this behaviour will be given below.Unexpectedly, these plots showed that a decrease in the conductivity appeared for a salt concentration of around one salt molecule per chain in the case of PEO-1000-based networks and three salt molecules per chain for PEO-2000-based networks. In other words, a decrease in conductivity was observed when the molecular weight between crosslinks and cations, or between cations, was 500, assuming a homogeneous distribu- tion of cations in the network. Discussion of the Conductivity Mechanism This finding was assessed on the basis of the various equilibria describing the interplay between the different possible ionic species which could be met in such media. Assuming that aggregates of order n are present and that ionisation takes place from these aggregates, it is easy to show that direct proportionality between unpaired ions and overall salt concentration cannot be obtained by ionic dissociation of aggregates rep- resenting the dominant form for the salt.On the other hand, if it is assumed that ionic dissociation takes place from higher aggregates present in minor proportions the following calculation can be done from the set of equilibria: which involves not only the generation of negative charge carriers by the first equilibrium but also fragmentation into neutral smaller aggregates by the second. It is likely that there is one dominant form of aggregation, most probably the dipoles as will be shown below, and consequently we have: n - q = q, i.e. q = n / 2 . Then the various concentrations can be calculted from:80 and Charge Transfer in Amorphous Networks K , I 1 = E (AB i n / ?I2/ (AB n 1 [(AB),,-,B’l= [A-I Kl,l/K2,1 = [A-I’E(AB),,,,I2 and with electroneutrality we have and finally which shows proportionality between the main charge carrier concentration and salt concentration at constant temperature.More generally, it is possible to find materials in which aggregates of order n are present in minor proportions and dissociate into aggregates of order n / i: (AB),, (AB),,-lB’ +Ap; K , , (AB),, * W v , 1 / z ; Kll,!. It is convenient to assume that there is one dominant form of aggregation of order n/i, then KIn = [(AB)n lBtIIA-I/[(A~)nI and Kn/i = E(AB)n/rI’/[(AB)111 and with electroneutrality we have and finally which shows proportionality between negative charge carrier concentration, which are the main charge carriers, and salt concentration to the power i / 2 , at constant temperature.This explains the case of the materials based on poly(propy1ene oxide) or poly(oxy- tetramethylene) for which i/2 is, respectively, ca. 3 and 1.5. These networks are less solvating and, according to the conclusion of this calculation, the salt is also present in aggregates of high order, respectively, around 6 and 3, while the species of major proportion are of the lowest order, ie. dipoles as will be shown below. It is assumed that these species are dipoles according to the situation which prevails in the case of PEO-based networks, but this point would deserve some investigation. Another aspect of this discussion is worthy of further comment: it is assumed that the aggregates of highest order present in the material produce most of the charge carriers by dissociation.Indeed, it is obvious that the energy required to separate a given ion from an aggregate decreases when the size of the aggregate increases. Consequently ionization takes place mainly from the aggregates of the highest possible size present in the network. Also, the fact that t + decreases when salt concentration increases, and that t + does not change with temperature, can be explained by the equilibria in scheme 1 together with: (AB)2 S (AB)B’+A-; K?, scheme 2 I (AB), i= 2(AB); K , (AB)B+ i= (AB)+B+; K , responsible for the production of positive charge carriers. As it is written, the third equation of scheme 2 describes the results better than (AB), (AB)A-+B’; KH. Cheradame and P.Niddam- Mercier 81 u I I I 1 2 3 4 Fig. 3. Plot of the reciprocal transference number versus salt concentration (expressed as O/Li mol%) for two different PEO networks [PEO 1000 (0) and 2000 (W), at 90 “C). t + values from ref. (4). for two reasons. First, the charge separation involved in the former is energetically more favourable than the dissociation involved in the latter. Secondly, this type of positive charge generation involved in the latter means that the concentration of positive charge carriers would be proportional to the concentration of salt, as in the case of the negative ones. Consequently, the ratio of the concentrations of the positive and negative charge carriers would be independent of salt concentration, as would the transport number, t t .It is easy to show using a very simple approximation that scheme 2 implies that t + decreases when the salt concentration increases. From the equilibrium constants K,, and K7, and assuming, as a rough approximation, that the positively charged species present in the largest proportion are the triple ions, the concentration of which is consequently close to the concentration of the negative charge carriers, it follows that [A-] = ( K2,/Kl)”’[AB] and similarly which shows that the positive charge carrier concentration (unpaired positive ions) is approximately constant. Denoting the mobility of the positive charge carriers as rn’ and that of the negative ones as rn- it is easy to obtain t+ = [ B+] m’/ ([ A--]rn + [ B+]rn+).As it has been demonstrated that in our materials the cationic and anionic mobilities differ only by a constant of proportionality (see section on conductivity behaviour, above), then m--/rn’= a and since [A- it can be seen that the reciprocal t t has a linear relationship with salt concentration, and will be independent of temperature if K,, does not vary appreciably with temperature, as will be discussed below, i.e. I / t’ = 1 + a[AB]/ K2,. This conclusion is reasonably verified for PEO-2000 and 1000 based networks in our work (fig. 3). Also, Vincent recently published the determination of an ‘effective’ lithium82 Charge Transfer in Amorphous Networks conductivity at 100 and 140 "C for PEO-LiC104 amorphous phases.22 It was shown that the lithium-ion conductivity is roughly constant at constant temperature when the salt concentration is increased.Scheme 2 presented here, with the simplifying assumptions used, accounts exactly for this result, since it predicts that the number of positive charge carriers at constant temperature is constant. The fact that t + remains constant is observed by Vincent at lOO"C, but not perfectly at 140°C. We think that for the highest salt concentration used by Vincent, it is no longer possible to neglect the dissociation of the multiplets at high temperatures giving negative multiple ions and unpaired positive ions. Accordingly, this dissociation begins to contribute to the cationic transport. On the other hand, this scheme allows us to explain why t + increases when the concentration of the urethane linkages increases, i.e. when the molecular weight between crosslinks decreases. We assign this effect to the presence of the urethane linkages. It was shown that these functions, which are less solvating than the poly(ethy1ene oxide) segments, decrease the extent of the salt i ~ n i s a t i o n . ~ ~ The effect of the urethane linkage concentration on t+ can be accounted for assuming that the dissociation constant K , increases when the urethane concentration increases and consequently the slopes of the lines in fig. 3 increase when the molecular weight between crosslinks increases. This effect is easily explained by the Lewis-base behaviour of the urethane linkages which are a better solvent for cations than for anions, in the context of acid-base interactions.Now, the fact that the conductivity is proportional to salt concentration at constant reduced temperature must be explained. Indeed, the temperature is not constant when we consider the materials at constant T - Tg, since Tg increases with increasing salt concentration. It is possible to give a quantitative answer to this question: for a dissociation equilibrium for an ionisable salt dissolved in polar medium, the dissociation enthalpy is currently found at ca. 5 kJmol-'. Since the equilibrium constants have the usual form: K = A exp ( - A H / R T ) it is easy to show that when the temperature increases by 20 K at an average temperature of 330 K, the constant K varies only by ca. 10%.This variation is at the limit of sensitivity on the plots under discussion (fig. 1 and 2). This calculation is even more appropriate considering that the concentration of negative charge carriers is given by the ratio of two dissociation constants, K 2 , / K l , (scheme2) which vary in the same way with temperature. In other words, so long as the energy of dissociation of the aggregates into smaller aggregates does not exceed energy of dissociation of these aggregates into one unpaired ion and the corresponding multiple ion by more than 5 kJmol-I, the conductivity of PEO-based networks at constant reduced temperature ( T - Tg) will be found to be approximately proportional to the salt concentration, without any noticeable deviation from linearity. The above calculation was evidently oversimplified in the sense that it was carried out for materials having a t - transport number higher than t + .However, it was mentioned above that the transport numbers do not vary with temperature. Since it was shown that the mobility of both types of charge carriers varies according to the same WLF law with temperature there cannot be a compensation effect between mobility and concentra- tion of charge carriers, and the constancy of transport numbers is to be assigned to the constancy of the ratio of unpaired positive ions concentration to the negative one. According to the formalism described above (scheme 2), it was found that [A-] = (K21/K,)"2[AB] [B'] = (K2,/K1)1'2K2, the ratio of the concentrations of the charge carriers is:H.Cheradame and P. Niddam-Mercier 83 I I I I I * 5 10 15 20 LiCIO, (w/ w o/o ) Fig. 4. Plot of the equilibrium swelling ratio of different networks containing various amounts of lithium perchlorate (w/w "/o). 0, PEO 1000 networks; X, PEO 2000 networks, swelling solvent CH2C12 [from ref. ( l ) ] . and the constancy of t+ with temperature means that K , corresponds to an equilibrium of low energy of dissociation. This assumption is supported by the fact that the dissociation of a positive triple ion to give an unpaired positive ion requires less energy than the dissociation of the corresponding dipole itself, since the leaving cation is only exposed to the electric field of a dipole. Quantitatively, considering the accuracy of the determination of transport numbers, it is clear that the same calculation as above can be made, leading to the same conclusion that the transport numbers do not vary with temperature. Indeed it was found that for network based on PEO-1000 containing lithium perchlorate, no significant change in f t was observed when the temperature was varied between 70 and 120 OC.*' Assuming that a variation of 10% is inside the possible error, on a temperature range of 50°C, it is calculated that the dissociation energy of the dissociation reaction giving specifically the unpaired cations must not exceed ca.2 kJmol-'. Accurate data are missing to appraise this conclusion quantitatively. However, taking into account the argument given above that the cation is within the electric field of only a dipole from which it has to be separated [eqn (3) of scheme 21, it seems likely that the energy required to operate this separation is low, so that the corresponding constant of equilibrium do not vary appreciably with temperature.Swelling properties allow us to shed more light on this mechanism. Indeed, it is well known that when a salt is dissolved in a weakly polar solvent, it is present in solution as aggregates, and increasing the polarity allows it to dissociate. Consequently, if we assume that the salt is present as dipoles, the introduction of a solvent of high polarity must not induce a change in the state of aggregation of the salt and must not change the number of elastic chains in the network. As a result the equilibrium swelling ratio must not change with salt concentration. This is effectively observed when methyl- ene chloride is used as swelling solvent, at least within the salt concentration range of interest for this discussion, i.e.three lithium cations per chain of PEO-2000, correspond- ing to ca. 12% w/w' (fig. 4). The decrease of the equilibrium swelling ratio was larger when chloroform was used, showing a tendency to aggregation. The decrease of the equilibrium swelling ratio when using solvents of low dielectric constant was found to follow the same law with molecular weight between crosslinks whether they are covalent84 Charge Transfer in Amorphous Networks I I I I I I * 5 10 15 20 25 LiCIO, (w/w % ) Fig. 5. Plot of the variations of equilibrium swelling ratio for different networks containing various amounts of lithium perchlorate (w/w YO).The swelling solvent is C6H6 [from ref. (l)]. 0, PEO-1000; x PEO-2000. 0.015 1 350 40 0 T / K Fig. 6. Variations of the ratio of the elastic modulus to absolute temperature of PEO-2000-based networks containing various amounts of lithium perchlorate uerws temperature. O/ Li molar ratio: 0, 12; m, 38; a, 00.H. Cheradame and P. Niddam-Mercier 85 or due to the presence of salt, assuming a chain partitioning by each lithium cation It is worth mentioning here that for PEO-1000-based networks the conductivity increases linearly with salt concentration up to one lithium cation per macromolecular chain. In the context of our mechanism which implies that the salt is present in the networks mostly as single molecules solvated by the polymer chain, as long as the number of salt molecules (dipoles) is lower than the number of free chains, these remaining chains can accommodate one dipole each, and ‘saturation’ is obtained when all chains contain one lithium cation, when the molecular weight between crosslinks is 1000.However, if these dipoles are associated in aggregates while each cation is solvated individually by a chain, it follows that each aggregate should play the role of a crosslink, as demonstrated by the swelling behaviour in non-polar solvent (fig. 5). As a result the elastic modulus (on the rubbery plateau) should increase with salt concentration. This assumption can be checked by the determination of the elastic modulus of the various materials containing different amount of salt.It is well known that in the proper temperature range, the elastic modulus is proportional to absolute temperature. Con- sequently, the ratio of the modulus to temperature must increase with salt concentration if the ionic crosslink concentration increases. On the other hand, if the salt is present as dipoles, each solvated by a polymer chain, this ratio must be independent of salt concentration and equal to that of the same network without salt. We have verified that this last behaviour is observed in the case of poly(ethy1ene oxide) networks containing lithium perchlorate in a relatively large range of salt concentration (fig. 6). This result directly supports the conclusion that the salt is present as dipoles and is in tune with the conclusion drawn above from swelling measurements.(fig. 5).24 Conclusion The model presented here for ionic conduction in the amorphous phase of poly( ethylene oxide)-containing salt operates at two levels. Scheme 2 describes qualitatively the charge carrier generation, and the WLF lab describes quantitatively the conductivity variations with temperature. It has obvious limits, those for instance of the free-volume model as recently recalled by Ratner.’ It has been designed for low salt concentration and for a temperature range from Tg to T’,+ 100 “C. However, as such it gives non-trivial results, for instance that the concentration of positive charge carriers is approximately constant in the usual salt concentration range, and explains the variations of the positive transfer- ence number.It is worth recalling here that the combination of both aspects of this model predicts that the optimum value of the salt concentration to choose. For mem- branes to be used in solid-state electrochemical generators this value is the lowest for which the ‘plateau’ concentration for the positive charge carriers is reached, i.e. at the lower limit of the validity of schems 2, obviously for mobility reasons. HydroQuebec is gratefully acknowledged for supporting this research. References 1 H. Cheradame and J . F. Le Nest, Polj.iner Elec-trolj.te Reciews 1, ed. J. R. MacCallum and C. A. Vincent (Elsevier Applied Sci., Amsterdam, 1087), p. 103. 2 A. Killis, TIi6.w de Doctorat d ’ Etat ( University of Grenoble, 1983 ). 3 J . F. Le Nest, A. Gandini and H. Cheradame, Br.Polyrn. J., 1988, 20, 253. 4 M. Leveque, Tliise d’lt~gr‘nieur-Doctrrrr (National Polytechnic Institute of Grenoble, France, 1986 1. 5 J . E. Weston and B. C . H . Steele, Solid State lotiics, 1982, 7, 81. 6 P. R. Sorensen and T. Jacobsen, Elec~rrochirri. Acta, 1982, 27, 1671. 7 P. R. Sorensen and T. Jacobsen, Solid Stare lonics, 1983, 9, 1147. 8 A. V. Chadwick, J. H. Strange and M. R. Worboys, Solid State lonics, 1983, 9, 1155. 9 M. Mali, J . Roos and D. Brinkmann, Ampere Congress, Zurich 1984, p. 177.86 Charge Transfer in Amorphous Networks 10 A. Bouridah, F. Dalard, D. Deroo, H. Djellab and R. Mauger, ISE 35th Meeting, Berkeley, California 11 C. Tubandt, Handbuch der Experimental Physik, ed. W. Wien and F. Harms (Akadem. Verlag, Leipzig, 12 M. Jagla and J. 0. Isard, Natl. Res. Bull., 1980, 15, 1327. 13 MI Leveque, J. F. Le Nest, A. Gandini and H. Cheradame, Makromol. Chem., Rapid Commun., 1983, 14 M. Leveque, J. F. Le Nest, A. Gandini and H. Cheradame, J. Power Sources, 1985, 14, 27. 15 J. F. Le Nest, H. Cheradame, A. Gandini and J. P. Cohen-Addad, Polym. Commun., 1987, 28, 302. 16 T. Miyamoto and K. Shibayama, J. Appl. Phys., 1973, 44, 5372. 17 H. Cheradame, J. L. Souquet and J. M. Latour, Muter. Res. Bull. 1980, 15, 1173. 18 H. Cheradame, IUPAC Macromolecules, ed. H. Benoit and P. Rempp (Pergamon Press, Oxford, 1982), 19 A. Killis, J. F. Lenest, H. Cheradame and A. Gandini, Makromol. Chem., 1982, 183, 2835. 20 A. Killis, J. F. Lenest, A. Gandini, H. Cheradame and J. P. Cohen-Addad, Solid State lonics, 1984, 14, 21 A. Killis, J. F. Lenest, A. Gandini and H. Cheradame, Macromolecules, 1984, 17, 63. 22 C. A. Vincent, Pol-vm. Prepr., 1989, 30, 422, papers presented at the ACS Dallas Meeting 1989. 23 H. Cheradame, A. Killis, L. Lestel and S. Boileau, Polym. Prepr., 1989, 30, 420, papers presented at the ACS Dallas meeting. 24 J. F. Lenest, J. P. Cohen-Addad, A. Gandini, F. Defendini and H. Cheradame, Zntegrarion of Funda- mental Polymer Science and Technology, ed. L. A. Kleintjens and P. J. Lemstra (Elsevier, Amsterdam, 1986), p. 246. (USA), 5-10th August, 1984. 1932), vol. XIII, part 1, p. 383. 4, 497. p. 251. 231. 25 M. A. Ratner and D. F. Shriver, Chem. Rev., 1988, 88, 109. Paper 9/02 12 1 C; Received 18 th May, 1989

ISSN:0301-7249    

DOI:10.1039/DC9898800077

出版商:RSC    

年代:1989

数据来源: RSC

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Faraday Discuss. Chem. SOC., 1989, 88, 87-101 GENERAL DISCUSSION Prof. W. J. Albery (Imperial College, London) addressed Prof. Murray: I was inter- ested in the exponentially rising current-voltage curve you showed us in your fig. 2. Normally when one considers systems with many small hops, the potential difference driving each hop is so small that one can linearize the equations and hence obtain a linear current-voltage curve. To obtain your exponential curve I imagine that you must be using rather a large potential difference to drive electron transfer through rather a small number of layers. Is this true'? Dr A. R. Hillman (University of Bristol) asked: 'Intersite potential differences' of tens of mV across molecular distances result in very large fields. Can Prof. Murray explain the physical significance of this situation? Prof.R. W. Murray ( University of North Carolina) replied: We indeed have a situation of large voltage gradients in the poly-[O~(bpy)~(vpy)~]X~,~ mixed-valent films. A typical film would contain the equivalent of a few hundred monolayers of metal complex sites, would be a few hundred nanometers thick, and for applied voltage biases of, for example, 1-5 V, would experience voltage gradients in the lo5 V cm-' range and intersite potentials ( # ) of 10-50 mV. These values are large enough that the exponential dependence of hopping rate on the free-energy difference between sites (i.e. -nF#) does not linearize in the usual way. This situation permits our detection of the ' p ' multiplier term which we speculate may be a consequence of a clustered structure in the metal complex polymer.Note that our calculation of the intersite voltage 4 relies on a metal complex centre-to-centre value and one might choose to argue that we should employ edge-to-edge distances. Prof. T. J. Lewis (University College of North Wales, Bangor) commented: In one form or another the hopping mechanism is invoked to explain electronic conduction in the doped polymers considered in this Discussion. An essential element of the mechan- ism is electron tunnelling between localized states, and inter- as well as intra-molecular transitions are involved. Thus the conductivity may be expected to be extremely sensitive to structure and, in particular, to the degree of swelling induced when ions move into or out of the polymer during oxidation-reduction cycles.The direct effect of swelling on the electronic processes appears to have received little attention in the face of arguments based solely on the accommodation of counterions in the polymer network. Prof. Murray replied: The model used in the paper, of electron hopping between poly-0s" and poly-0s"' sites, under conditions of immobile counterions, comes directly from classical Marcus theory and takes AG,,,, =-n@ to connect the reaction free energy to the applied voltage. So there is no particular novelty to our theory; what is novel is its application to obtaining electron self-exchange rate constants from the electrical conductivity of mixed-valent materials. We further accommodate conductivity data by the theory that is not in the usual linear i-E regime (low intersite voltage #) but corresponds to currents that rise exponentially with voltage.The exponential rise, and the Arrhenius temperature behaviour that we see at temperatures above ca. -40 "C, furthermore label the hopping as an activated process. Only at the lowest temperatures do we see non-Arrhenius behaviour indicative of tunnelling, which we have modelled with a vibronic coupling theory of Holstein. 8788 General Discussion Your point about the possible relation between electron-hopping rates and the swelling of the polymer structure caused by insertion of charge-compensating counter- ions, is a very good one. The variation of intersite distances, and of the dielectric properties surrounding sites, with counterion has indeed not been much considered, but could be an important kinetic factor.We have varied the counterion from ClO, to PF, to tosylate with no perceptible effect, for 1: 1 0s""" mixed-valent compositions. With even larger counterions now being examined, there may be a rate diminution, based on preliminary experiments. There needs to be a great deal more work done on the counterion topic. Prof. G. G. Cameron (University of Aberdeen) said: One of Prof. Murray's diagrams showed an Arrhenius plot of the diffusion coefficients of ferrocene in two distinct forms: (i) as a 'label' covalently bonded to a polyether chain end, and (ii) as a small molecule 'probe' dissolved in polyether. Two questions concerning this diagram arise. First, does the discontinuity shown by both systems coincide with a phase change, e.g.a crystalline melting point? Secondly, I would have expected the label with its long polymer tail to diffuse much more slowly than the probe over a wide temperature range; can Prof. Murray speculate as to why the two diffusion coefficients are so similar in magnitude? Prof. Murray replied: In reference to the diagram showing an Arrhenius plot of log D versus 1/ T for the diffusion of ferrocene monomer and of the ferrocene-labelled PEO polymer Fc-MePEG: ( a ) The discontinuity shown by both plots at 53 "C coincides with the temperature of a DCS-determined endotherm which we interpret as a phase change from a partly crystalline wax to an amorphous melt. ( b ) The monomer and polymer diffusion coefficients (DFc and DFc-MepEG differ by a factor of three in the melt state ( T = TM) and by a factor of eight at room temperature in the waxy polymer.The difference at the lower temperature we believe signifies that the intrinsic diffusivity of the polymer chain (in itself) is, at these temperatures, appreciably lower than that of the ferrocene moiety itself, and that DFc-MepEG gives a good measure of the polymer chain self-diffusion dynamics. In the polymer melt, the smaller difference between the DFc-MepEG values must mean that the ferrocene and chain have similar diffusivities so that DFc-MepEG is only an approximate measure of the intrinsic polymer chain self- diffusion. As to why the similar diffusivities occur, we can only note that while the linear polymer chain must undergo a tortuous reptation like diffusion it is laterally less bulky than the ferrocene group.Prof. C. A. Vincent (University of St Andrews) said to Prof. Ratner: I was most interested in section 4 of your paper which was devoted to Coulombic interactions and correlation in the ionic motion, and would like you to comment on two sets of conduc- tivity measurements which we have made. Fig. 1 is a plot of molar conductivity (i-e. conductivity normalized by the total number of potential ionic charge carriers) as a function of concentration. While these results were obtained for a low-molecular-weight polyether (and are similar to those reported by Ingram and co-workers' and by Ward and co-workers2), it has recently been shown by Gray in our laboratories that essentially similar behaviour, but with a markedly sharper minimum, is found using an amorphous 300 000 molecular weight polyether-based system.Fig. 2 shows results from the other extreme of the concentration range. Here we have taken a low-melting fused salt ( NH4N03-LiN03-NH4C1) and have added, with some care, increasing quantities of a polar molecular solute. Since poly(ethy1ene oxide) was insoluble in this melt, ethylene carbonate (EC) was used. Again a normalized conductivity is plotted, i.e. we have measured the density of each sample, and have allowed for the reduction in the number of ions per unit volume as the molecular solute was added. I would draw your attention, in particular, to the low EC concentration region where the normalised conductivity0.1 0 0.09 0.08 0.07 0.06 c 0.3 - - z z 'p 0.2- 8 m \ x U .d c) a 0 L cd 0.1 - - 2 General Discussion 0.4 0.00 0.02 0.04 0.06 0.08 LiClO, concentration/mol dm-3 Fig.1 89 0.0 0.2 0.4 0.6 0.8 1 .o mole fraction of EC Fig. 2 falls rapidly with EC content. (The rise in conductivity at higher EC concentrations is likely to be due mainly to the decrease in the viscosity of the system.) 1 G. G. Cameron, M. D. Ingram and G. '4. Sorrie, J. Elecfroanal. Chem., 1986, 198, 205. 2 P. G. Hall, G. R. Davies, I. M. Ward and J. E. McIntyre, Polym. Commun., 1986, 27, 100. Prof. M. A. Ratner (Northwestern University, Illinois) (communicated). The result in fig. 1 is characteristic of the standard situation, in which the mobility of ions is reduced owing to longer renewal times in the polymer host.At very low concentrations of salt, correlation effects among the ions themselves can be ignored, and the simple dynamic percolation model that we have discussed is valid: the renewal time scales with the viscosity, and increases as cations reduce the configurational motion available to the polymer chains.90 General Discussion In higher concentrations, correlations among the ions can become important, and the simple uncorrelated model that we have discussed is invalid. I suggest that perhaps the slowly rising portion of fig. 1 is due to correlated motions of the ions, but this concentration range really lies outside the simple independent hop models that we have discussed. In fig. 2, likewise, the entire curve really lies outside the simple dynamic percolation picture.One might again suspect that (starting from the right) the initial decrease is due to stiffening of the entire system, and the behaviour at very high salt concentrations arises from strongly correlated motions. Nevertheless, unfortunately, these regimes are again outside the range of the simple model we have discussed. Prof. A. J. Heeger (University of California, Santa Barbara) turned to Prof. Ratner: Could you please give us a better intuitive feeling for the renewal time, T:“,:? Prof. Ratner replied: The fundamental difference between ceramic or vitreous solid electrolytes such as LiA1Si04 or ( Na20)xA1203 and polymer electrolytes is that the latter transport ions effectively only above Tg , the glass-transition temperature. The near- unitary value of Angell’s decoupling index R, of eqn (2) means that the timescales corresponding to structural relaxation and ionic motion are essentially the same.This timescale can be thought of as that on which the polymer host reorganizes or relaxes so as to present differing local geometries to the mobile ions. For anions, which do not strongly complex to any particular solvent geometry (at least in ether-based materials), this local geometry can be thought of in simple free-volume terms; for the cations, it is the average time to change coordination environments (exchange inner-shell oxygens j about the cation. Thus for cation motion, it will correlate with the exchange time for inner-sphere solvent exchange in liquid solution which, as Armand has suggested, in his paper, correlates well with conduction in polyether immobile solvent materials.For cations, then (or for neutral pairs, whose mobility is determined by the more strongly complexed species), the renewal time, related to the diffusion by eqn ( 9 a ) , will shorten for faster-exchanging cation-solvent pairs. The renewal time is, thus, essentially the local structural relaxation time, for materials above To. Below To this time diverges, since the structural relaxation is frozen. Prof. T. J. Lewis (University College of North Wales, Bangor) said: I would like to ask Prof. Ratner whether the relaxation time for ion solvation and equilibrium polariz- ation in the polymer lattice is likely to be different from that of the polymer renewal relaxation time? If so in what way might these polaron-like effects influence ion motion? Prof.Ratner replied: Several different timescales and phenomena are involved in this comment. Polarons per se are really not relevant here, since the moving charges are ionic, and therefore the electron-phonon coupling that is responsible for polaron motion does not enter the physics of ion motion. There is a conceptual similarity, since the ‘coincidence event’ timescale for small polaron motion’ refers to the time needed before the electronic states on donor and acceptor are isoenergetic-the renewal time also refers to the time that elapses, on average, before a formerly forbidden jump becomes available. The renewal time itself, as explained in the text, largely determines ion mobility.The polarization relaxation time in the neat host is important, but more relevant is the relaxation in the presence of the ions. If the relaxation spectrum is of the Debye type (with a single time, which is not true of polymers in general), then it must be related to the renewal time, but as the question makes clear, there are probably several relevant timescales. The solvation relaxation time is relevant to the renewal time for cations in polyethers, and the relaxation time for segment motion (dielectric loss) is relevant for the (not specifically solvated) anions. 1 D. Emin, Phys. Rev. B, 1971, 4, 3639.General Discussion 91 Prof. M. Armand (E.N.S.E.E.G., St Martin d'hleres) commented: From pulsed field gradient NMR, as we get more precise data, there seem to be two different types of behaviour regarding the variation of the diffusion coefficients with temperature: on one hand 'H and 7Li give straight Arrhenius lines, but I9F from the anion fits into the classical WLF.Does this imply a decoupling of the transport processes at the microscopic level? Prof. Ratner replied: The nature of the polymer motion needed to provide a renewal may be entirely different from that needed to provide a PFG diffusion signal. For renewal, the polymer simply needs to undergo enough of a local excursion to allow the coordination shell about the cation to exchange at least one coordinate oxygen with an oxygen on the uncomplexed host, (for cation motion). For anions, a local void volume must be made available. For PFG diffusion, on the other hand, long-range motions, perhaps arising from reptation, are required.In fact, the frequency-dependent response of the polymer in the very-low-frequency regime should show distinct peaks from these two motions. Thus the 'H or I3C diffusion spectra would be expected to show smaller 0, with possibly quite different temperature dependence from the I9F. If it is experi- mentally true that Li diffusion looks more like 'H than I9F, then one would conclude that on the (long) time and distance scale of the PFG NMR experiment, there is no effective decoupling of the cation from the PEO, while the anion diffuses quite differently, being largely sensitive to local renewal (faster, WLF-like) motions. Thus there are really two different, decoupled behaviours (again assuming WLF for I9F, Arrhenius for 'Li and 'H): the slower diffuser remains strongly bound to the chains, and 'rides' them to diffuse on the appropriate (slow) polymer diffusion timescale.The anion motion, conversely, is fixed by the local, rapid excursions of the polymer, not seen in PFG NMR. Prof. R. G. Linford (Leicester Polytechnic) asked: What is the effect on dynamic percolation theory of substituting divalent salts for monovalent salts? Is the behaviour essentially dominated by the polymer matrix rather than the ions? Prof. Ratner replied: In the simplest dynamic percolation picture, all correlations of any type are ignored. Then assuming that the material does not undergo partial phase separation, the only effect of changing ions is on the renewal time, since D - (x2)7/ T,,, .Divalents, having higher charge density, would be expected to raise viscosity, Tg and therefore T , ~ , , which is related to Tg in ref. (37) of my paper. Two other important effects of increasing the cation charge may appear. One is to order the polymer such that partial crystallinity appears. In this case, one will have a mixture of static and dynamic percolation, and one expects a real threshold under some conditions. The second is an increase in ion association, bringing with it lower numbers of carriers and the (observed) lower conductivity. Finally, one suspects that both ion-pair and ion-triplet motion will be substantially reduced, due to stronger dipositive ion-host bonding. Dr P. G . Bruce (Heriot- Watt Uniuersity, Edinburgh) (communicated): I found Prof.Ratner's discussion of the competition between contact ion pair formation and solvated ions most stimulating. I would like to offer a possible extension to his discussion. In solid polymer electrolytes such as those based on polyethylene oxide the ether oxygens which coordinate the cations are constrained since they form part of the polymer chains, and as a result the polymer may not be capable of surrounding the cations in such a way that all of the possible sites in the first coordination sphere are occupied. If this is so then the formation of a contact ion pair between a cation and an anion of the salt may not necessarily be in competition with the formation of a solvent-separated ion pair. We may speculate on two classes of polymer electrolyte, those in which the ions may form contact ion pairs without displacing ether oxygens (depending, at least92 General Discussion in part, on the size of the anion) and those in which the contact ion pairs are in competition with solvent-separated ions.Prof. Albery asked: Can Dr Bruce give us a qualitative understanding of his finding in the d.c. experiment that in the absence of ion pairs ueff becomes non-linear when E = 10 mV whereas in the presence of ion pairs ueff remains constant up to 10 V. Dr Bruce replied: I believe I can offer a qualitative explanation for this. Take first an ideal polymer electrolyte containing only M+ and X- ions in a cell with electrodes, M, reversible to the M+cations. On application of a constant potential a steady state develops at which the field-driven migration of X- towards the anode is exactly opposed by the diffusion of X- towards the cathode, owing to the establishment of a concentration gradient in X-.As a consequence of electroneutrality, an identical concentration gradient in M+ also develops. It has been shown' that the steady-state current I + , which is due solely to the transport of M+ is a linear function of the concentration difference of M+ between the anode, [M+],, and cathode, [M+],, where D+ is the diffusion coefficient of the cations. The voltage across the cell, A K may also be expressed in terms of the concentrations of M+ at the anode and cathode but in this case the dependence is logarithmic: I + = -2FD+([M'],-[M+],) (1) The logarithmic term may be expanded as a series and for small differences in the cation concentration between anode and cathode, and thus small values of AV (less than lOmV), truncated to yield Under these circumstances AV and I , are both linear functions of [M+Ia and [M'],; hence eqn ( 1 ) and ( 2 ) may be combined to give: - F2 I - - D+[M+],A V + - RT (4) where [MIo is the initial cation concentration.Hence I+ is linearly related to A V but only up to ca. 10 mV. Introducing mobile ion pairs, MX, then at steady state the migration of X- is opposed by the diffusion of X- and MX. On application of a large potential difference in circumstances where the concentration and diffusion coefficient of MX ion pairs are high, then the large migrational flux of X- is balanced mainly by the ion pairs. A large difference in free anion and hence cation concentration between anode and cathode is not induced and thus the logarithmic term may still be linearized. In this way a linear current-voltage relationship may be maintained to high values of the applied potential.Prof. Linford addressed Dr Bruce: Have you considered the implications of your approach when applied to divalent salt systems? In particular, the two-atom entity for your monovalent materials is a neutral ion pair, whereas for a divalent salt such as MX2 the two-atom species is the cation MX+. Do you think that transport processes in divalent salts are essentially similar to, or significantly different from, those in monovalent systems? Dr Bruce replied: Although the paper, for simplicity of presentation, concentrates on the information which may be obtained from different transport measurements whenGeneral Discussion 93 applied to polymer electrolytes containing a uni-univalent salt, MX, with a variety of associated species, MX, M2X+, MX2--, etc., the essential features of the discussion apply equally to electrolytes containing salts with multivalent constituents.Considering the special case of a salt with a divalent cation and monovalent anion, e.g. Cd(C104)2, the role of the neutral ion pair in the uni-univalent case is taken by the ion triple [Cd( C1O,)Jo so that, for example, the ion pair [CdClO,]+ would contribute to transport in the Hittorf/ Tubandt experiment. In response to your second point concerning the mechanism of ion transport in divalent cation salts, I believe that the basic nature of the transport processes are similar but that there are differences of magnitude.In particular, the cation-polymer interaction is now sufficiently strong in some cases to immobilize this constituent, and ion association is expected to be even more pronounced than in the monovalent cation systems. Prof. M. Cheradame (E.F.P., St Martin d’Heres) said to Drs Cameron and Ingram: You demonstrate in the experimental section of your paper that there is no back diffusion of dipoles during your Hittorf experiments. However, at the same time you use this back diffusion in order to explain the difference in the values of transference numbers between your measurements and others, for instance those based on Tubandt’s method which were carried out in my laboratory.Could you comment on this apparent contra- diction? Dr M. D. Ingram (University of Aberdeen) replied: The reason why the Hittorf and ‘steady-state current’ methods give different values for the transference numbers (typi- cally <0.1 in the former case and ca. 0.5 in the latter) is that back diffusion should be absent in the former, but is certainly important in the latter. No steady state is achieved in the Hittorf experiment, and all concentration changes are localized within the anodic and cathodic compartments. Back-diffusion effects are therefore also localized within the electrode compartments. This is essentially the reason why the Hittorf experiment measures ‘true’ transference numbers and the steady-state method does not.The Hittorf experiment on its own gives no indication of the ion-pair diffusion current. This comes from comparisons made between different methods. In principle, the Hittorf and Tubandt methods should give the same answers. Prof. G. G. Cameron (University of Aberdeen) said to Prof. Armand: You stated in your presentation that you did not think that ion pairs are mobile species. Our contrary opinion is based on the fact that classical electrochemical experiments, such as Hittorf measurements on liquid polymer electrolytes, give very low cation transport numbers, consistent with the view that ‘free’ cations are strongly complexed, and hence critically immobilized by the polymer. By contrast, techniques such as radio-tracing and pulsed field gradient NMR give cation transport numbers closer to 0.5.The Hittorf method is sensitive only to the migration of charged species while the latter two experiments are affected by the flux of both charged and electrically neutral species. We have therefore concluded that the radio-tracer and PFG NMR experiments yield a kind of ‘diffusion number’ which is strongly influenced by the migration of mobile ion pairs. What are your grounds for asserting that ion pairs are largely immobile? Prof. Armand replied: The question of the transport number in polymer electrolytes is still the most controversial topic in this field. We believe that the transport numbers for the precise example of LiClO, in PEO-based electrolytes are t+ = 0.3, t- = 0.7 with no diffusion of ion pairs on a macroscopic scale [i.e.ionization is the required step for the motion of a given atom (Li) or ionophoretic group (ClO,)]. These can be deduced from the coincidence of t+ and t - determinations from three different techniques: (i) Potentiometric measurements in concentration cells; this technique is sensitive to charged94 General Discussion species only, influenced by triple ions if present. (ii) Tubandt's method applied to PEO-based networks whose mechanical properties allow the three segments of the electrolyte to be separated and weighed easily; again, this technique is sensitive to charged species only, dependent on the mass difference between the cationic and anionic species. (iii) Pulsed field gradient NMR responds to a chosen nucleus, irrespective of its charge and chemical environment.The values you quote ( t + = t - = 0 . 5 ) have been obtained by Prof. Whitmore's group at high temperatures (> 150 "C) and for a different system (LiCF,SO,). It is known that for liquids and molten salts, the t values tend to become equal at high temperatures. NMR/PFG yields 0.25 < t+ < 0.35 for PEO-LiC104 for the temperature range 30-100 "C, a good indication that ion pairs are not the most mobile species. LiCF3S03 does not give concordant values with the above-mentioned techniques, a result which could be interpreted as suggesting the existence of triple ions, Li(CF3S03)2. The Hittorf experiments could be explained if we suppose that the short-chain polymer molecules and the solvated cations move as single entities under the influence of the electric field.In such a case the apparent cationic transport number measured against a fixed reference frame (glass frit) is then zero, as the concentration in the cathodic compartment stays constant. The complex would then behave like a molten salt and not like a classical solution where only part of the solvent (solvation shell) moves with the ions. It would be possible to verify this hypothesis by labelling the end OH groups of the polymer (with deuterium or fluorescent dye) in one compartment and then following their migration across the separator. There is possibly a threshold value of molecular weight beyond which chain entanglement prevents a net motion of the polymer chains along with the ions ('immobile solvent'). However, the 'H NMR/PFG seems to contradict such a model as diffusion coefficients for the protons are found one order of magnitude lower than those for 'Li or I9F (in CF,SO,).It should be recalled that the significance of this number for a macromolecule is far from evident: chain segments of the,same chain move at different speeds (reptation and 'blobs') and the non-ionized salt molecules act as temporary crosslinks. For instance, NMR/PFG yields similar " D values for low (ca. 2000) and high (ca. lo6) molecular weight PEO. Dr Ingram added: Whereas in molten salts there is a problem in selecting an appropriate reference frame for transport numbers, this is not the case for liquid polymer electrolytes where the solvent is the obvious reference frame in the Hittorf experiments.Our measurements of t , in 0.5 mol dmP3 NaSCN in liquid polymers should be just as valid in this regard as for 0.5 moldmP3 solutions of salts in any liquid solvent. Our results demonstrate that the cations are immobile relative to the solvent. However, the pattern of results which emerges in liquid polymers is very similar to that which is found in higher molecular weight (elastomeric) systems when pulsed field gradient NMR is the chosen technique. Thus Gorecki and Harvie (unpublished work) find a pattern of Li, F and H diffusion for solutions of CF,SO,Li in liquid EO/PO copolymers very like that found in 'solid' polymers and described today by Armand. There does not, therefore, seem to be any apparent difference in ion and polymer dynamics in low-molecular-weight (2000- 10 000) and high-molecular-weight (ca.lo6) systems. Prof. P. Meares (University of Exeter) said: Cameron, Ingram and Harvie refer to electro-osmosis in their Hittorf cell. I presume this was generated in the pores of the sintered glass dividers. It implies that there is a separation of the charge and a double layer at the pore walls. Thus there must be a contribution from surface conduction and the net transport numbers in the pores will differ from those in the bulk solution. As the area for conduction in the sinters is restricted, the potential gradient in the poresGeneral Discussion 95 U t ‘=. 2 i 13; 12 1 1 10 9 8 7 0 2 0 40 60 80 100 120 140 160 180 time/min Fig. 3 must be greater than in the bulk. Consequently, the concentration changes in the electrode compartments may be determined mainly by the transport numbers in the sinters.In view of my lack of familiarity with the structure and dimensions of the electrical double layer in polymeric electrolytes, I would be glad to have the author’s comments on whether surface conductance may have a significant influence on their results. Dr Ingrarn answered: As Prof. Meares has indicated, the use of glass frits can be a problem, not only because electro-osmosis can occur involving the bulk flow of electro- lyte, but also because the actual transport of ions can be influenced by double-layer effects (surface conduction). The latter problem is more insidious since it could be ‘invisible’. The experimental evidence, however, is that these effects did not influence our published data.We obtained the same (or similar) transport numbers from cell A, which included two glass frits, as from cell B, which included only the hollow-barrelled tap. As regards the structure of the electrical double layer at glass/polymer electrolyte interfaces, speculation is probably premature until more is known about the species actually present in the bulk electrolyte. (See also Prof. Vincent’s reply to Prof. Lewis’s question below.) Prof. Murray commented: Regarding the 12 h period allowed for back diffusion in Dr Ingram’s paper, and other steady-state experiments where diffusion is required, one really should justify the experimental times and distances in terms of the diffusion rates of the ions involved. For example, if D = lop8 cm2 s-’ ( I think probably a typical value) and the pathlength is 0.1 cm, an experimental timescale of lo6 s is required.I recommend that authors be more explicit on experimental details where diffusion times are involved. Dr Ingrarn replied: The Hittorf experiment differs crucially from the ‘steady-state current’ experiment (see paper of Bruce and Vincent) in that it is essential that a steady state is not achieved. The rises in concentration at the anode (and the corresponding falls at the cathode) must be kept confined within each electrode compartment. The figures just quoted, with an estimated timescale of lo6 s (300 h) for reaching the steady96 General Discussion state would be very favourable to our success (in that 300 h is much longer than the experimental timescale).However, other effects (notably convection) can result in an enhanced mixing of the electrolyte so the 12 h waiting period was introduced as an additional test to show that such mixing had not occurred and so invalidated our data. (Compare with reply to question by Cheradame.) Prof. Vincent added: We agree with Prof. Murray’s estimate that it would take of the order of lo6 s (1 1 days) to establish a steady state across a 0.1 cm polymer electrolyte cell if the mean ionic diffusion coefficient was 1 x lo-* cm2 s-I. However, for the cells we use in our study of steady-state currents, which have thicknesses in the range of 150-250 pm, this period is calculated to be of the order of only 3-9 h for the same value of diffusion coefficient. In fig.3 we show a typical plot of current versus time for an amorphous PEO-LiCF3S03 electrolyte at 108 “C. Here equilibration was attained in just over 3 h. Measurements on similar systems at lower temperatures or with somewhat thicker cells are found to require 20-30 h for the steady-state current to become estab- lished in some instances. In contrast, for Hittorf/Tubandt measurements we select the thickness of each polymer layer or ‘compartment’ to be 20.1 cm with a view to ensuring that no detectable salt diffusion occurs between the electrode compartments and the central compartment during a 12-24 h electrolysis. Prof. Lewis asked: In the papers introduced by Prof. Vincent and Dr Ingram the polymer electrolyte is treated as a bulk system, largely uninfluenced by the interfacial double layers at the electrodes. Even though such layers may be closely confined to the electrode surfaces, how can one be sure that processes within them, which will include the necessary solvation or desolvation of charged species, will not have at least a partially controlling influence on the conduction? Dr Ingram responded: In a properly run Hittorf experiment, the electrode reactions should influence the outcome only in so far as the stoichiometry is correctly understood.In our experiments, where sodium amalgam electrodes were commonly employed, all the calculations assumed that the cathodic deposition of Na and the anodic liberation of Na+ ions proceeded with 100% current efficiency. This assumption was believed to be less reliable for the anodic reactions, and so we placed more reliance on data coming from the cathode (where current efficiencies were 95% or greater). The crucial ‘interfaces’ in the Hittorf experiment exist between the electrode and centre compartments.It is, of course, necessary to show that the experimental configur- ation does not introduce important electrical effects at these interfaces (see question from Prof. Meares). Prof. Vincent added: There are two points to consider. First, it is generally accepted that polymer electrolytes which have total salt concentrations in the range 0.5- 3.0 mol dmP3, have a relatively high concentration of mobile ions. Even if the concentra- tion of the latter is only 1% of that of the total salt, due, say, to ion pairing, it is easy to show that the reciprocal Debye length would still not be much more than 1 nm assuming a relative permittivity of ca.10, and a temperature of 60 “C. This situation is therefore quite unlike that of lightly doped semiconductors where the thickness of the Garrett-Brattain depletion layer may be significant in comparison to the total thickness of the semiconductor. We therefore suggest that electrical double layers at the electrode interfaces will not influence measurements of the bulk conductivity of polymer electrolyte films which are typically 200 pm thick. On the other hand, the processes of solvation and desolvation by groups which form polymer segments are likely to have a profound influence on the mechanism and henceGeneral Discussion 97 on the kinetics of electrode reactions such as metal-ion deposition.In conventional low- molecular-weight solvents, such reactions are considered to involve a sequence of desolvation steps in which ion-solvent bonds are replaced by adion-metal bonds, during which process the ion being deposited is free to engage in surface or edge diffusion, depending on its state of desolvation. Clearly, continued partial solvation by the polymer will render mechanisms involving surface diffusion difficult to operate, thus leading to an increase in the charge-transfer resistance at the electrode interface. It should be pointed out, however, that in practice a.c. impedance analysis makes it relatively simple to separate the total cell impedance into bulk electrolyte and electrode/interfacial components.Dr Bruce (communicated): Experimental evidence indicating ion association in high-molecular-weight polymer electrolytes is still very limited and in some cases interpretation is ambiguous. However, measurements presented at this Discussion do reveal features of the nature of ion association in such solid-polymer electrolytes. The equivalent conductance measurements at low salt concentrations obtained in our group by Dr Gray point to the existence of mobile or immobile ion pairs at ca. lo-’ mol dm’. The d.c. polarization measurements described by me coupled with the measurements on solvated molten salts (see comment by Prof. Vincent) indicate ion association at high concentrations (> 1 mol dm-’), probably in the form of ion pairs. Dr Ingram replied: The results which have been described briefly by Dr Bruce are interesting in two respects. First, the trends in molar conductivity (A) with increasing concentration (sharp fall followed by steep rise) are exactly the same as we have previously encountered in liquid polymer electrolytes.This is a further indication that the conductivity mechanisms in low-molecular-weight systems (ca. 3000) are very similar to those in conventional polymer electrolytes, and provides further support for the relevance of transport numbers measured in liquid systems. Secondly, the existence of appreciable concentrations of ion pairs in concentrated polymer electrolytes (0 : Li == 8 : 1) points out a little-noticed similarity between polymer electrolytes and molten salt hydrates (extensively studied by Angell, Braunstein, Hester, Moynihan and others in the 1970s).In the case of the salt hydrates the ‘primitive’ model (where cations were solvated only by water molecules) also had to be modified to take account of cation-anion interactions. Dr Bruce turned to Prof. Armand: In simple, low-molecular-weight, liquid solvents the ions of dissolved salts move, each accompanied by a coordination sphere of solvent molecules. However, in high-molecular-weight, solid solvents, such as polar polymers, the ion must dissociate from its coordination sphere, at least in part, for ion transport to occur. As a result, in ethylene oxide-based solvents, and as a function of molecular weight, a transition must occur from liquid to solid electrolyte behaviour. This will have important effects on the measurement of transference numbers by the Hittorf technique since with liquids the solvent moves and true transference numbers are not obtained, whereas they should be obtained with solid solvents.Could you comment on this and, in particular, give your views on the molecular weight at which the transition is likely to occur for polyether-based electrolytes? Prof. Armand replied: I certainly agree with this comment entirely, in the sense that there should be a progressive change from liquid electrolyte to ‘immobile’ solvent behaviour. The corresponding molecular weight is probably of a few thousand Da,? when chain entanglement appears. The discussion with Prof. Cameron and Dr Ingram already deals with this fundamental aspect. t 1 Da = 1.66 x lo-*’ kg.98 General Discussion Prof.A. G. MacDiarmid (University of Pennsylvania) said: I have two questions to ask Prof. Armand. First, why do you not get Li dendrite formation in an Li/polymer electrolyte battery whereas one tends to get dendrite formation in an Li/organic liquid electrolyte battery? Secondly, what is the present status (from a technological aspect) of Li/solid electrolyte batteries? Prof. Armand said in reply to the first question: Metal deposition and cycling is definitely easier with polymer electrolytes than with conventional organic solutions. Lithium and even the more reactive sodium can be repeatedly plated and stripped. Although the exact reason is not yet known, many phenomena can contribute, exclusively or in part: (i) Polyethers like PEO, especially those of high molecular weight, contain only bonds which are known to be chemically inert.(ii) The mechanical properties of the electrolyte may help push back the dendrites towards the interface. (iii) Lower current densities are used with the solid-state thin-film configuration, thus allowing surface re-equilibration from self-diffusion of the metal. This effect may also be electrochemical in nature with the onset of ‘n’-type conduction near the metal surface. Owing to the non-zero anion transference number, the vicinity of the negative electrode becomes depleted in salt during the plating process and the metal dissolves in the polymer to a very limited extent, enough to induce a mixed conductivity, ionic plus electronic; any dendrite will tend to dissolve faster owing to its higher chemical activity (curvature).He then addressed the second question: The completely solid-state battery using polymer electrolytes is now a proven concept, with performances that are very appealing: > 120 W h kg-’ and > 100 W kg-’ in terms of gravimetric energy and power, respectively, and > 1000 deep discharge cycles. For power applications (such as electric vehicles) the system now operates close to room temperature, cJ: ca. 100 “C a few years ago. Many companies worldwide are considering the commercialisation of the batteries. Note that the conventional battery manufacturers are not specialised in film technology, and probably companies with an expertise in coating processes (packaging and magnetic recording industries) are the best candidates. Prof.Cheradame asked: Do you think that possible compression at the top of a dendrite may induce stress inside the polymer matrix and consequently decrease the conductivity? This effect could contribute to the prevention of dendrite growth. Prof. Armand replied: Yes, possibly, the conductivity of polymer electrolyte is known to decrease under isostatic pressure, though I have no idea of the magnitude of the pressure at the tip of the dendrite. Besides, the salt-depletion phenomenon due again to anion transfer is more pronounced at a dendrite where the local current density is larger and this limits its growth through a decrease in ionic conductivity. Prof. Ratner (communicated): I believe, with Armand, that mixed conductor systems based on polymer electrolytes will be of great intrinsic interest, and also of importance as electrode materials in batteries.Is it true, however, that ‘there are no clear examples of a redox conduction mechanism obtained with the same metals at two different oxidation states’ (p. 75)? The redox polymers described by Royce Murray, and based On what basis is the statement that ‘neutral species do not appear to be mobile in polymer electrolytes’ (p. 68) made? The Nernst-Einstein relationship of D,,, and u would not seem to assure this, and it is in direct contradiction to Malcolm Ingram’s notion that ion-pair motion might be responsible for net currents. , would seem to be precisely such a system. on R u ~ ~ ~ ~ ~ ~General Discussion 99 Prof.Armand replied: The choice of redox couples which do not change their coordination habits when exchanging electrons is relatively limited. The success of the systems is due to the stability of the bipyridine ligand which imposes a six-fold coordination shell in both electronic states. In addition to the mechanical rigidity of the aromatic rings, the 'soft' nitrogen centres tend to enhance the outersphere exchange kinetics, as compared to the 'hard' oxygen in water or PEO. Neither the Fe"71'1 nor the Cu"" couples are expected to keep the same coordination number when changing valency, thus only polaron-type conductivity is expected. Poly( ethylene imine) could be a better choice than PEO in this respect. We have shown in preliminary experiments some redox conduction of Eu1'~''' as triflate salt in PEI, though this must be studied further.Regarding the second point raised by Prof. Ratner, it has been explained in the discussion with Prof. Cameron and Prof. Ingram that only the coincidence of t+ values determined from three different techniques which do not respond to the same species gives proof of the actual motion of the cation. Another clue is that most of the multivalent cations are electrochemically inactive; if they could be supplied to the electrode by ion-pair diffusion, some redox processes, e.g. metal plating, would be apparent. RUI1,lll or Osll,lll Prof. Murray commented: Prof. Armand's suggestion in fig. 6 of his paper, that water exchange and cation transport rates in PEs should be parallel properties, is an important one.However, I should point out that electrochemical reactivity (at the polymer/elec- trode interface) is also parallel to water exchange dynamics: slow water exchange typically gives slow (irreversible) electrochemical kinetics for metal ions. So there is a double problem for slow water exchanges, i.e. slow transport and slow electrode reac- tivity. This may be cured by use of appropriate added ligands for the metals, that supplant the polyether oxygens. Prof. Armand replied: I certainly agree with your comment: the ligand exchange around the ions conditions the electrode reversibility; magnesium salts are known to be reduced with extreme difficulty in organic solutions, even inert ethers, because of the slow desolvation step at the electrode and despite a sufficient supply of diffusing ion pairs at the electrode.In polymer electrolytes, both supply to the electrode and reduction kinetics are limited for this type of ion. The importance of this phenomenon is also exemplified by zinc and cobalt, which can still be plated from aqueous solution but are inert in PEO. You have shown in your presentation that weakly interacting ferrocene shows both fast diffusion and redox kinetics. There is a recent report on improved conductivities and exchange currents (ECS abstract 89-2 no. 99) when adding crown ethers to PEO salt solutions. Our experience is that 1 : 1 salt-crown complexes show limited solubility in polyethers owing to the reduced (second layer) interactions with the macromolecule. Tests with aza crowns and copper salts were more successful since the positively charged hydrogens of the NH moieties located at the periphery of the molecule can form hydrogen bonds with PEO.Prof. Linford said to Prof. Cheradame: The Tubandt method is conceptually simple, but its successful application in the determination of transport numbers for many types of solid electrolyte is prevented by the fusion of the separate layers. How did you avoid these problems? Prof. Cheradame replied: Tubandt's method can be applied to our materials. Indeed, there is no possible displacement of the units of the network since these elements are covalently bound to each other and firmly bound to the network by crosslinks. Con- sequently, the macromolecular chains cannot cross the interface between the two com- partments.We have never observed any separation problem using the geometry described100 General Discussion in our papers.’ The successful application of Tubandt’s method to our materials comes from the physical separation of the network from the charge carriers. The latter species are the only ones which are able to cross the border between the two electrochemical compartments. 1 M. Leveque, J. F. Le Nest, A. Gandini and H. Cheradame, J. Power Sources, 1985, 14, 27; Macromol. Chem. Rapid Commun., 1983, 4, 497. Prof. Armand addressed Prof. Cheradame: f+ increases when the PEO segments are shortened. There are two explanations: either the size of the ‘holes’ in the network are becoming too small for the anion, including a mechanical hindrance, or the urethane linkage, which contains an amide NH bond is able to interact with the negative charges, thus reducing their mobility.Do you have any evidence to suggest which is correct? Prof. Cheradame replied: The influence of crosslink concentration on conductivity was discussed recently.’ It was shown that not only the mobility of the charge carriers but also their concentration is influenced by the urethane linkage concentration. From previous studies, it was concluded that the mobility of both types of charge carrier followed the same WLF law with the same C2 constant, at least within the limits of experimental accuracy, whatever the molecular weight of PEO between crosslinks. This result shows that the steric effect of the ‘mesh size’ is probably negligible since it has apparently the same influence on both the positive and negative charge-carrier mobility. On the other hand, from analysis of the conductivity data at constant mobility, i.e.at constant reduced temperature, it is clear that the urethane linkage concentration has a detrimental effect on salt ionisation, that is on the number of charge carriers. This detrimental effect is less important for positive charge carriers than for negative ones, and this is why the positive transference number increases when the urethane linkage concentration increases. 1 ACS Dallas Meeting, Polymer Preprints, 1989, 30, 420. Prof. Meares said: I would like Prof. Cheradame and P. Niddam-Mercier to expand a little their assumption that the mobilities of cations and anions obey the same free-volume law.In the free-volume theory of diffusion in polymers proposed about 30 years ago by Fujita there were two kinds of parameter. The first concerned the concentration dependence of the free volume and would influence simultaneously all penetrants present together. The second was an interaction parameter specific to the polymer and penetrant and which, in general, would have a different value for each penetrant. Prof. Cheradame responded: It is important to keep in mind that both types of ionic species follow the same WLF law with the same C, constant within experimental error.’ The molar volume of both diffusing species is included in the C , constant. This constant might be different for both types of charge carrier, this would not prevent the ratio of their mobilities remaining constant with temperature change.Consequently, the ratio of their volumes is included in the constant, a, of the equation m-/m+ = a. It is also worth recalling that the assumptions given hereby only intend to provide a general description of the conductivity process in the lowest part of the salt concentra- tion range, i.e. for salt concentrations lower than ca. 1 mot dm-3. Above this concentra- tion the interpretation would probably be more complicated. 1 J. F. Le Nest, A. Gandini, H. Cheradarne and J . P. Cohen Addad, Pulym. Cornmun., 1987, 28 302 Prof. Ratner (communicated): The use of chemical concentrations in place of activities is permissible in dilute solution. However, the concentrations found in the electrolytesGeneral Discussion 101 of Prof.Cheradame’s paper are of the order of 1 mol dm-3: is it still valid to approximate activity by concentration, and how will this affect the arguments made here? The structure found near 1.0 mol dm-3 in fig. 1 of your paper is reminiscent of behaviour seen in crystalline materials at high concentrations, where it is usually attributed to some sort of commensurability effect. Do you have a tentative explanation of these maxima and minima? Prof. Cheradame and P. Niddam-Mercier (communicated): In response to your first question, it is true that the use of concentration instead of activity could be a rough approximation. However, our scheme was aimed at providing an explanation of the conductivity behaviour at low salt concentration, ca. 0.1 mol dm-3, since this is the range of interest for the use of these amorphous materials in solid-state batteries. The behaviour met here is quite similar to that observed for electrolytes in organic solvents. Con- sequently, I consider that the approximation used in this context could only affect some quantitative aspects of our description but not the conclusions drawn to explain the general phenomenology. Turning now to your second question, indeed the structure exhibited by the conduc- tivity behaviour, as shown in fig. 1, was tentatively attributed to a saturation effect of the network by the salt. We have some indications that the network is not saturated when there are more than 12 monomer units between ion pairs or between ion pairs and crosslinks. When the salt concentration exceeds this level, which is the case for the network dealt with in fig. 1 when the salt concentration reaches ca. 1 mol dm-3, it could be thought that quadrupoles or (higher aggregates) are formed. We have no evidence for a reason of any kind why this effect should result in a decrease of the number of charge carriers. We suggest that the formation of the higher aggregates takes place on some of the species which are involved in the charge-carrier generation, the concentration of which decreases accordingly. This point is under investigation in my laboratory. Dr D. R. Rosseinsky ( University ofExeter) (communicated): Regarding Prof. Murray’s second response above, it should be noted that self-exchange rate constants, e.g. for Mn0,-/ MnOi-, have in earlier already been derived from solid-state electrical conductivity measurements. In these and other case^^'^ the conductivity inferences have been supported by dielectric relaxation studies of electron-transfer rate. 1 D. R. 2 D. R. 3 D. R. 4 D. R. 231. 5 D. R. Rosseinsky, J. A. Stephan and J. S . Tonge, J. Chem. SOC., Faraday Trans. I , 1981, 77, 1719. Rosseinsky and J. S . Tonge, J. Chern. SOC., Faraday Trans. I , 1982, 78, 3595. Rosseinsky, Faraday Discuss. Chem. SOC., 1982, 74, 105. Rosseinsky, J. S. Tonge, J. Berthelot and J. F. Cassidy, J. Chem. SOC., Faraday Trans. I , 1987, 83, Rosseinsky and J. S . Tonge, J. Chem. SOC., Faraday Trans. I , 1987, 83, 245.

ISSN:0301-7249    

DOI:10.1039/DC9898800087

出版商:RSC    

年代:1989

数据来源: RSC

摘要:

Furuday Discuss. Chern. SOC., 1989, 88, 103-111 Cation-Oxygen Geometry in Polymer Electrolytes: Interpretation of EXAFS Results Roger J. Latham,* Roger G. Linford and Walkiria S. Schlindwein Department of Chemistry, School of Applied Physical Sciences, Leicester Polytechnic, P.O. Box 143, Leicester LE1 9BH Two issues are of current interest in the field of ionically conducting polymers (polymer electrolytes): these are ion pairing and possible interference of the polymer-cation interaction by water. EXAFS was chosen as a suitable technique to probe local structure surrounding the cations. The systems studied were PEO,, : ZnXz, where n = 6-15 and X = C1, Br or I. They were chosen in order to ascertain the reliability of information pertaining to oxygen neighbours when the system under investigation contains heavy counterions.The results reveal, as expected, that the information about numbers of oxygen nearest neighbours is qualitative rather than quantitative, and firmer conclusions can be drawn for the lighter counterions. Cations and anions were found to be in close proximity, thus confirming ion pairing in PEO-zinc polymer electrolytes; this is in accord with recent observations of zinc diffusion. Polymer electrolytes can be considered to be concentrated solutions, which are special in the sense that the solvent is immobile. A given ion within this type of electrolyte can interact not only with its counterions, but also with mobile ligands present as impurities (e.g. water) and with the immobile matrix solvent. The interaction between a chosen mobile ion and its counterions leads to ion pairing; this is important in concentrated electrolytes such as these polymer electrolyte materials.’ The interaction between ion and ligand is similar to that found in normal electrolyte solutions.The solvent sheath has an effect on such parameters as the mobility, polariz- ability and ionic size of the potentially mobile species. The unusual feature in these electrolytes, however, is the interaction between the ion and its immobile matrix, which mimics that found in ionic complexes with crown ethers. If the cation interaction with the polymer host is strong, then the only potentially mobile ion is the anion. If on the other hand the cation is weakly bound, then the polymer electrolyte solution may be unstable and this leads to ‘salting-out’ effects in which the anions and cations recombine to form phase-separated crystallites.It is because of these factors that an understanding of the environment immediately surrounding the anions and cations within a polymeric electrolyte system is particularly important. The system chosen for this study is PEO, : ZnX,, where n = 6-15 and X = CI, Br or I. This was selected for two reasons. The first is that the Leicester group is among several who are interested in exploring the new avenues of behaviour revealed by non-monovalent systems. The complementary reason is that zinc is conveniently access- ible for the EXAFS technique that has been used for the exploration of the local structure. EXAFS is a structural technique that can be used on materials in a variety of forms, including crystalline, amorphous, liquid and glassy states.The absorption of a high- intensity X-ray beam by the sample is recorded over an energy range from ca. l00eV below to ca. 1000 eV above an absorption edge (usually the K-edge) of the chosen target element. The incident X-ray beam is usually provided from a synchrotron storage ring. For dilute samples, it is helpful to record an indirect function of absorbance, such as 103104 EXA FS of Polymer Electrolytes the fluorescent X-ray signal. The EXAFS phenomenon is seen as a series of oscillations on the high-energy side of the edge. It is in fact divided into several sub-regions. Nearest the edge is seen the so-called XANES region which contains information about the number, distance and geometric arrangement of second and third nearest neighbours.Beyond this is the EXAFS region proper which provides similar information about the first-nearest-neighbour shell. At still higher energies, oscillations due to so-called atomic EXAFS are seen which result from interference of the outgoing photoelectron wave with the outer electron shells of the target atom. Finally, a background region is obtained which is free from EXAFS effects. The local structural information provided by EXAFS lies within a spherical region of up to 6 , 4 of the target atom. In contrast with diffraction techniques, there is no long-range structural information and samples in which long-range order is lacking can, therefore, be studied. It is this feature that makes EXAFS so appropriate for the study of polymer electrolytes, in which the region of electrochemical interest is the amorphous phase.' The information contained in the raw EXAFS oscillations is not immediately acces- sible.In order to deconvolute this information, it is necessary to subtract two types of background: pre-edge and post-edge. Unreliable conclusions can be drawn from data for which the background subtraction has been improperly carried out. The background- subtracted data are then Fourier-transformed into a probability function, akin to a radial distribution function. This necessitates the use of phase shifts which are appropriate for both the target atom and the backscattering species. There are tests, which include the use of model compound data, to ascertain the suitability of the selected phase shifts.The aim of the deconvolution procedure is to provide a good fit between the experimental data and that obtained from an optimised theoretical local structure. This fit is carried out in both k space and real space. A region which has become of interest in the study of polymer electrolytes is the effect of small to trace amounts of water. The presence of water can cause remarkable changes in structure, conductivity behaviour and mechanical properties for some electrolytes. These effects could arise from the water acting as a plasticizer or because the water molecules are coordinated with the potentially mobile cations or for other reasons. A way of discriminating between these possibilities is to obtain information about the local structure, and such a study forms the basis for this paper.In earlier work, water was often uncritically and unintentionally incorporated into the films in the form of hydrated salts or imperfectly dried reagents. It is more common in current practice to ensure that the film is dry and this is achieved in one of two essentially different ways. In the first approach, normal quality reagents are used and after casting the film is subjected to a drying regime, typically involving heating to above 100°C for many hours under vacuum. This drying procedure is also unavoidably an annealing process and consequently the morphology of the film is affected. The alterna- tive method, which is being carefully developed to avoid undesirable structural modifications, involves the use of pre-dried reagents under scrupulously dry conditions.The entire procedure is carried out under high-integrity glove-box conditions. It is unusual for water to be employed as a reagent in the preparation of electrolyte films. Since PEO is water soluble, however, some workers are starting to investigate the properties of water-cast films and the samples studied in this investigation were of this type. When water is the chosen casting solvent, it is clearly impossible to use the pre-dried reagent approach to produce dry films. In this work, we have used a post- casting drying regime similar to that employed in non-aqueous systems but with the difference that the film after casting is heated under vacuum for seven days at 50°C.This is to ensure that the PEO melting temperature is not exceeded and so the as-cast morphology is maintained, and the formation of high-melting complexes is not encouraged.R. J. Latham, R. G. Linford and W. S. Schlindwein 105 Both methods give films that are dry, within the detection limits of the normal laboratory. Typical detection methods include thermogravimetric analysis, Karl- Fischer titrations and F.t.i.r. spectroscopy. None of these methods is sufficiently sensitive nor, with the exception to some degree of F.t.i.r. spectroscopy, do they discriminate between water in different sites. For example, it is not easy to separate the contribution of adventitious water, water of crystallisation and water that is present within the film as a plasticizer.The probable lower limit of convenient detection of water is 0.03%. This is a reflection of the character of water itself; it is too light to be easily weighed, and its all-embracing chemical reactivity does not assist in its identification. The aim of the experiments described in this paper was to elucidate the arrangement of the PEO matrix around the mobile cations. The methodology has involved the use of EXAFS to determine oxygen nearest neighbours. Clearly there is a complication in that the PEO-oxygen environment may be influenced by the presence of moisture. A secondary focus was to establish whether or not ion pairing occurred in these divalent systems. Contrary suggestions have been obtained from earlier work on rubidium’ and ca~cium.~ Experimental Film Preparation The films used in this investigation were prepared using water as a casting solvent.PEO of 4x lo6 relative molar mass (BDH) and zinc halides of the highest available purity (BDH) were dissolved in triply distilled water with stirring for 48 h. ‘Wet’ films were cast by allowing the water to evaporate at room temperature and these were then dried at 50°C for 7 days. All subsequent storage and processing was carried out in a high-integrity, sub-ppm-water-level dry box. EXAFS Experiments The EXAFS studies were carried out using the facilities of the synchrotron radiation source at the S.E.R.C. Daresbury Laboratories, Cheshire. Station 7.1 was used and the ring was operated at 2 GeV with a beam current in the region of 50-200 mA in multibunch mode and high-brilliance configuration.This station uses an Si ( 1 11) double-crystal monochromator and 70% harmonic rejection was used. Samples were typically exposed to the X-ray beam for 40 min during each run, and deconvolution was performed using the Daresbury EXAFS suite of programs. The dried films were protected from humid ambient air during transit by prior encapsulation at Leicester into special sample mounts; these consisted of Mylar sheets sealed with a knife-edge seal and have been described fully elsewhere.s The sample mounts were carried in a desiccator to Daresbury Laboratories, where they were stored within a high-integrity dry box prior to use on the EXAFS station. Results and Discussion Polymer electrolytes are likely to behave in a similar fashion to concentrated electrolyte solutions and as such there may be ion pairing in addition to interactions between the cation and the heteroatom from the host polymer backbone.In EXAFS experiments it is difficult to obtain conclusive information about oxygen nearest neighbours as oxygen atoms are weak back-scatterers. This is particularly the case when there may be heavier nearest neighbours, as provided by ion pairing in polymer electrolytes. In order to stu y these effects, electrolytes of the general composition PEO,, : ZnX, (where X = C1, Br, t , ) were selected. Thus, it might be expected that the evidence for oxygen bdfkscatteririg becomes less apparent as the EXAFS spectra are examined for samples OF increasirlg106 EXAFS of Polymer Electrolytes -5 t h L v 4 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 - I ? Y Fig.1. PEO,: ZnC1, ‘dried’ film. Best fit using chlorine nearest neighbours only; ( a ) background subtracted EXAFS spectrum; ( b ) Fourier transform. (-), experiment; (- - -), theory. mass or size of the possible paired ion. When the experimental and theoretical EXAFS spectra are compared together with their corresponding Fourier transformation, it is clear that a satisfactory interpretation of the data cannot be made on the basis of a single back-scattering halide species. This is demonstrated by the typical result shown in fig. 1, which shows the background subtracted EXAFS spectrum and its accompanying Fourier transform.R. J. Latham, R. G. Linford and W. S. Schlindwein 107 Acceptable fitting of the data can only be obtained when oxygen is also considered as a nearest-neighbour species.The lightness of oxygen as a back-scatterer in comparison with the halide means that the information obtained is less well defined. The simplified expression for the EXAFS function does not take into account low energies, otherwise the plane-wave approximation cannot be applied. This is a particular problem when dealing with scattering species that are light (e.g. nitrogen, carbon and oxygen) since they only strongly scatter low-energy electrons. Two features of the EXAFS suite of programs available at the S.E.R.C. Daresbury Laboratories, however, provide the user with the facility to enhance the interpretation of the data. These are ( a ) the plotting of individual theoretical EXAFS spectra and Fourier transforms for each of the near-neighbour species so that the contribution to the total fit can be examined, and (6) a statistical significance test which can be applied to the fitting of the theoretical data.Fig. 2 shows the EXAFS spectrum and accompanying Fourier transform for the same polymer electrolyte film with fitting of the data for both oxygen and halide nearest neighbours. Fig. 3 shows the same spectrum with individual contributions from the oxygen and halogen back-scattering species. As expected at the high-energy end of the spectrum the main contribution is from halide back-scattering species, and the contribu- tion from oxygen is at low energies. For the systems studied the effects of oxygen backscatter are more clearly seen in the presence of the lightest halide species.The distances of the back-scattering species from the target zinc species suggest that the fit corresponds to a ‘split’ shell of two different nearest neighbours rather than a first- and second-nearest-neighbour situation. The results demonstrate that the halogen provides the most substantial contribution towards the observed EXAFS behaviour, and the distances and numbers of the nearest neighbours are shown in table 1 . This provides evidence that ion pairing is present in these polymer electrolytes. In contrast, whilst it is possible to say that there is certainly an interaction with oxygen, it is much more difficult to state precise coordination numbers. This is supported by the use of the statistical tests of Joyner et al.’ which show that there is much greater confidence in the coordination numbers obtained for halide nearest neighbours.There are two essentially different approaches that can be taken to the deconvolution of the experimental data. In the first, the best possible fit with the lowest fit index is sought, regardless of the acceptability or otherwise of the Debye-Waller factor that is finally evaluated. This approach is rationalised on the basis that the samples are expected to be more disordered (and consequently to have a higher Debye-Waller factor) than is the case for model compounds. In contrast, an alternative approach follows the phil- osophy of Joyner el al.’ in which fits where the Debye-Waller factor is not within the suggested range of 0.005-0.025 are rejected for samples where no static disorder is expected.The validity of this approach for polymer electrolytes where some disorder could be expected may be questioned. However, as is demonstrated in fig. 4, a relatively large envelope is obtained at the 1% level for the fits for oxygen nearest neighbours in comparison to the halide. This confirms that the majority of the EXAFS is due to the heavier and larger halide nearest neighbours and demonstrates that ‘intuitive’ fits obtained with high Debye- Waller factors and higher coordinations of oxygen could be less satisfactory. A further difficulty encountered with oxygen relates to the moisture effects encountered with polymer electrolyte systems. The results referred to in this paper are for ‘dried’ films and the films were specially mounted for the EXAFS experiments.If water is present in a polymer electrolyte film it may be difficult, using the EXAFS technique, to distinguish between oxygen backscatterers from the PEO backbone, and those from either water of hydration surrounding the cation or adven- titious water within the film. This more careful analysis has revealed that information on oxygen nearest neigh- bours is qualitative rather than quantitative. In earlier investigations we reported: ( a )108 EXAFS of Polymer Electrolytes c I ? Y Fig. 2. PEO,:ZnCI, ‘dried’ film. Best fit using chlorine and oxygen nearest neighbours; ( a ) background subtracted EXAFS spectrum; ( b ) Fourier transform. (-), experiment; (- - -), theory . the cation in PEO,: CaI, prepared under wet conditions was surrounded by ca.ten nearest n e i g h b ~ u r s , ~ in accord with the results of Enderby.‘ (6) The large number of oxygen nearest neighbours was also found for the same material prepared under dry conditions. Additional studies of other stoichiometries again showed large coordination numbers, and a small dependence of coordination number on overall film stoichiometryR. J. Latham, R. G. Linford and W. S, Schlindwein 109 1.1 t 1 2 3 4 5 6 7 8 9 10 r / 'A Fig. 3. PEO,: ZnC1, 'dried' film. Data from Fourier transform in fig. 2. Shown as individual contributions. (-), experiment; (- - -), theory (oxygen); (- - -) theory (chlorine). Table 1. PEO, : ZnX, 'dried' films nearest neighbour fit sample atom R I A N h cr2/A2 " EIeV index PEO, : ZnI, 0 PEO, : ZnBrz 1 .O- 1.4 0.005-0.007 (1 .O) (0.006) I 2.514 0 PEO, : ZnClz 2.0-3.0 0.009-0.012 (2.4) (0.010) Br 2.324 0 1.0-2.0 0.005-0.018 7.41 1.12 ( 1.40) (0.01 0) 2.054 0.6- 1.1 0.002-0.007 2*196 (0.9) (0.004) c1 Distance of nearest neighbours, coordination number, '' Debye- Waller factor110 EXA FS of Polymer Electrolytes 0.014 0.012 0.010 0.008 0.006 0.OOL 0.002 0 .o o o 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.1 1.6 1.8 2.0 coordination no. 0.020, , ,, , , , ,, , , ,, , 1 k 0.008 D A 0.6 0.8 1.0 1.2 1.C 1.6 1.8 2.0 2.2 2.6 coordination no. Fig. 4. PEOb : ZnC1, ‘dried’ film. Statistical plots using the approach of Joyner et al.’ ( a ) chlorine backscatterers; ( b ) oxygen backscatterers. was observed. ( c ) In contrast, for dry (i.e. those prepared using stringently dry conditions) PEO, : ZnX, films,5 oxygen coordination numbers were smaller than for calcium, showed no dependence on n and apparently were different for bromide and iodide.It remains clear that in these materials calcium is surrounded by more oxygen nearest neighbours than zinc. This implies that the mobility of the cation in calcium electrolytes is likely to be lower than that for zinc. Further, the qualitative nature of the data does not invalidate the conclusion that there is a modest oxygen coordination numberR. J. Latham, R. G. Linford and W. S. Schlindwein 111 dependence for calcium but not for zinc, and that the oxygen coordination varies with the nature of the anion. The only implication of the present work that affects the previously reported studies is that the earlier numerical values may be less precise than quoted.The present studies have reinforced the clarity with which statements about ion- pairing in these systems can be made. Calcium ions do not appear to be ion-paired in a nearest neighbour sense but zinc clearly is. This is in accord with many recent studies of zinc systems in which for zinc, but not Zn*+, transport exists. The authors thank Dr S. Gurman, IJniversity of Leicester, for helpful discussions about the data deconvolution process. References 1 M. A. Ratner and A. Nitzan, Solid Stare lonics, 1988, 28-30, 3. 2 C . Berthier, W. Gorecki, M. Minier, M. B. Armand, J. M. Chabagno and P. Rigaud, Solid Srate lonics, 1983, 11, 91. 3 C. R. A. Catlow, A. V. Chadwick, G. N. Greaves, L. M. Moroney and M. R. Warboys, Solid Stare lonics, 4 K. C. Andrews, M. Cole, R. J. Latham, R. G. Linford, H. M. Williams and B. R. Dobson, Solid Stare 5 M. Cole, M. H. Sheldon, M. D. Glasse, R. J. Latham and R. G. Linford, Appl. Phys. A, 1989, 49, 249. 6 N. A. Hewish, G. W. Nelson and J. E. Enderby, Narure (London), 1982, 297, 138. 7 R. W. Joyner, K. J. Martin and R. Meehan, J. Phys. C, 1987, 20, 4005. 8 H. Yang and G. C. Farrington, Extended Abstracts, The Electrochemical Society 174th Meeting, Abstract 9 G. C . Farrington and R. G. Linford, in Polymer Elecrrolyre Reviews 11, ed. J. R. MacCallum and C. A. 1983, 9-10, 1107. Ionics, 1988, 28-30, 929. no. 728, 1988. Vincent ( Elsevier Applied Science Publishers, London), in press. Paper 9/02162K; Received 22nd May, 1989

ISSN:0301-7249    

DOI:10.1039/DC9898800103

出版商:RSC    

年代:1989

数据来源: RSC

摘要:

Furuduy Discuss. Chern. SOC., 1989, 88, 113-122 Electroactive Films from Poly( ethylene oxide)-Sodium Iodide Complexes with Tetracyanoquinodimethan Jamil A. Siddiqui and Peter V. Wright* School of Materials, University of Shefield, Northumberland Rd, Shefield S10 2TZ The preparation of conducting polymer films from oriented PEO-NaI by exposure to I2 and charge-transfer exchange with tetracyanoquinodimethan (TCNQ) is described. The PEO-NaI had stoichiometries x = [EO]/[NaI] = 3-6. Gravimetric, X-ray and i.r. analysis suggests that crystalline complexes of PEO-Na13 and PEO- NaTCNQ have been prepared having conductivities of lop4 S cm-' and lop's cm-I, respectively. Exchange with TCNQ forms bilayers of PEO-NaTCNQ/PEO-NaI. Exposure of the x = 3 bilayer to I2 vapour brings about a transformation of the exchanged layer (7-10 pm in thickness) to a microcomposite of a more conductive complex salt within a PEO matrix having a conductivity 1 S cm-'.The apparent conductivity of these films falls to a minimum ( S cm-I) at x = 4, but an increase in conductivity of at least two orders of magnitude is observed for x = 5 films which have much thinner exchanged layers and a more integrated structure than the x = 3 materials. The conductivity of the PEO-NaTCNQ/I, layer is found to depend on the 'gate' potential applied between the layer and a silver-epoxy electrode in contact with the PEO-NaI, layer in a triode configuration. A number of years ago, some semicrystalline complexes of poly(ethy1ene oxide) (PEO) with a variety of lithium, sodium, potassium and ammonium salts were prepared in our laboratory.' These materials have been extensively studied by virtue of their significant ionic conductivity through the amorphous phase' and their potential as thin-film 'polymer electrolytes' in batteries incorporating alkali metal electrodes3 or in other devices.Considerable effort has therefore been devoted to the synthesis of various amorphous copolymers or networks of PEO with the aim of maximising ionic cond~ctivity.~ However, we have also begun an investigation of the electrical and thermo-optical properties of the crystalline PEO complexes.5-* Alongside the inorganic salts, a wide variety of complexes with planar organic anions such as phenolates, naphtholates, carboxylates and sulphonates may also be prepared.In the cases of sodium and lithium salt complexes, these anions are considered to stack alongside a helical PEO-cation adduct having a stoichiometry of 1 mol of salt per 3 ethylene oxide units (x = 3). Such a structural model is inferred from unit-cell data9,"' and the detailed crystallographic investigations of PEO- NaI and PEO- NaSCN complexes by Chatani and coworkers. ''*I1 The latter have shown that the PEO adopts a 2/1 helix enclosing two cations per fibre repeat (7.98 and 7.19 A, respectively). In some of the organic anion complexes, self- organised macrodomain textures have been observed6.' which undergo mesomorphic transformations at ca. 60 "C to microdomain or spherulitic textures before melting to isotropic phases at temperatures up to 200 "C. In this paper, we report on the preparation, characterisation and electrical properties of films of crystalline PEO- NaI complexes which have undergone a charge-transfer exchange reaction with tetracyanoquinodimethan (TCNQ) in hydrocarbon solvent and of a crystalline complex of PEO-sodium polyiodide.PEO-NaI +TC"Q PEO-NaTCNQ+$I, (1) 113114 Electroactive Films from EO Complexes PEO-NaI++n12 PEO-NaI, In an initial brief report of the first of these materials6 [eqn (l)] it was shown that the conductivity is maximised if the PEO-NaI precursor film is oriented. In this work we also report studies of PEO-NaTCNQ post-treated with iodine giving films or fibres of enhanced conductivity. Experimental PEO-NaI was prepared by dissolving PEO of molecular weight 5 x lo6 (BDH) and NaI in molar ratios x = [ethylene oxide units]/[NaI] = 3-6 in methanol to give polymer concentrations of ca.10%. Oriented films of PEO-NaI were prepared by slowly shearing small aliquots of this solution between glass surfaces using a motorised rig. The solvent was rapidly removed in a stream of warm air to give an oriented crystalline film of uniform texture and thickness 10-30 pm. Silvery-grey PEO-NaI, films were prepared by exposing oriented PEO-NaI to iodine vapour in a desiccator for 3 days. The charge-transfer reaction with TCNQ was carried out by immersing the slide in a 2% solution of TCNQ in sodium-dried mesitylene. After 36 h the purple film on the slide was removed, washed in dry mesitylene and stored in a desiccator. PEO-NaTCNQ films on glass slides were exposed to I2 vapour by placing in a desiccator in the presence of I2 crystals at atmospheric pressure for 5 days.Following this treatment, the films took on a dull-grey appearance and the I2 was then removed from the desiccator. After leaving to stand in air in the desiccator for a further 3 days, the exchanged surface became a green-gold colour appearing highly lustrous when traces of surface crystalline material were removed. PEO-NaTCNQ fibres were prepared by dry-spinning oriented PEO-NaI fibres from the methanolic solution of the complex which was delivered from a hypodermic syringe onto a rotating wire frame. The frame was then immersed in TCNQ-mesitylene as before. X-Ray fibre photographs were obtained using a flat-plate camera and a Phillips X-ray generator.Attenuated total reflectance infrared spectroscopy was carried out using a Perkin- Elmer 683 spectrometer fitted with a Specac ATR accessory incorporating a KRS-5 crystal in contact with the exchanged surface of the film. Scanning electron micrographs were obtained using a Cambridge 600 instrument. Polarised light optical micrographs were taken using a Polyvar Met microscope. Conductivity measurements were performed using a Solartron 1250 frequency- response analyser and a 1286 Electrochemical interface employing four-probe (surface) techniques and two- or three-electrode cells. The measurements were carried out under vacuum in the presence of P205 as desiccant. Results and Discussion Representative gravimetric data of molar compositions of precursor films on glass slides and exchanged and iodine-doped materials are given in table 1.As the first row of the table shows, the oriented PEO-NaI film with x = 3 absorbs 1 mol of I2 per mol of NaI. As shown by the diffractometer tracings in fig. 1 the film is transformed to give a new crystalline complex which is apparently PEO-NaI, . Differential thermal analysis of this material indicates a melting endotherm at ca. 145 "C (PEO-NaI melts at approximately 190 OC'**) and also an endotherm at 50-70 "C, as commonly observed in PEO-alkali-metal salt complexes.' The latter may arise from uncomplexed PEO or low melting complexedFaraday Discuss. Chem. Soc., 1989, Vol. 88 Plate 1. Scanning electron micrograph of a fracture surface profile of a PEO-NaTCNQ (upper laqer)/PEO-NaI bilayer mounted on a glass slide.Sample was pre-cooled in liquid nitrogen before fracture. Scale bar = 10 pm. Plate 2. Transmission optical micrograph through a PEO-NaTCNQ/PEO-NaI bilayer (x = 3) between crossed polars. Overall thickness is ca. 5 pm. Scale bar = 20 pm. Plate 3. Wide-angle X-ray fibre pattern of PEO-NaTCNQ with fibre axis vertical. J. A. Siddiqui and P. V. Wright (Facing p. 115)J. A. Siddiqui and P. V. Wright 115 Table 1. Molar compositions of films” A B C P( EO), NaI gain after exchange iodine uptake X / lo4 moI / lo5 mol TCNQ /lo4 moI B / A C I A 3 3.5 3 1.2 5 1.3 6 1 .o - 6.7 1.6 0.7 7.2 - 2.1 3.9 0.56 3.3 6.0 0.12 4.6 4.4 0.07 4.5 “ Representative data from a series of experiments as films mounted on microscopic slides all of the same surface area (2.5 cm x 7.5 cm).n n 1 I I I I I 30 20 10 2 e i o Fig. 1. Wide-angle X-ray diffractometer tracings (Cu K , radiation) for ( a ) PEO-NaI, and ( b ) PEO-NaI. The data of the second row of table 1 indicate that in films of 15-20 pm thickness with stoichiometry x = 3 ca. half of the iodide ion was exchanged with TCNQ. Thicker films contained lower proportions of TCNQ. The estimates given in column B of table 1 were made assuming that all the iodine liberated on the right-hand side of eqn ( 1 ) was retained within the film. The compositions of the exchanged PEO-NaTCNQ (x = 3) films suggested that the gravimetric analysis is corroborated by scanning electron microscopy. An SEM photo- graph of the fracture surface of an exchanged film with stoichiometry x = 3 mounted on a glass slide is shown in plate 1.The section is apparently a bilayer of an overall thickness of ca. 15 pm, consisting of an exchanged layer of PEO-NaTCNQ and a layer116 L 000 Electroactive Films from EO Complexes 3000 2000 1000 wavenumber/cm-' Fig. 2. Attenuated total reflectance infrared spectra of (a) PEO, ( b ) PEO-NaTCNQ (x =3), ( c ) NaTCNQ. of unpenetrated PEO- NaI, each layer being of approximately equal thickness. More extensive experiments on films of various thicknesses suggest that, under the preparative conditions described above, the exchanged layer is 7-10 pm in thickness. The last two rows of table 1 also show that a significantly lower proportion of the available iodide ions was exchanged with TCNQ in the films with x = 5 and 6.This apparently indicates reduced swelling of these film surfaces by the reaction medium. Plate 2 is an optical micrograph of a film of PEO-NaTCNQ ( x = 3 ) between crossed polarisers with the orientation direction at 45 O to the plane of polarisation. The film is approximately 5 pm in thickness and is presumed to be almost fully exchanged. The crystallites are ca. 0.9 pm in thickness along the orientation direction. Although some surface crystals are present there are transparent regions where phase-separated crystals of NaTCNQ are smaller than may be observed using visible light if not present as a chemical complex with the PEO. No further structural detail on the crystallites could be discerned using carbon-replica transmission electron microscopy but the structural discontinuities along the draw direction between crystallites were seen to be voids bridged by fibrils.Attenuated total reflectance infrared spectra of a film of PEO, a film of PEO- NaTCNQ and a compressed pellet of NaTCNQ are shown in fig. 2. The spectrum of the film includes the bands which are characteristic of the -CH2- (ca. 2900 cm-') and -C-0- (ca. 1100 cm-') vibrations of the polyether. Since the depth of penetration of the surface by radiation of wavelength A is 0.29A using the KRS-5 c r y ~ t a l , ' ~ the spectra show that the PEO is present in the exchanged layer within 1 pm of the surface. The shift to lower frequency of the -C-0- vibration in PEO following exchange isJ. A. Siddiqui and P. V. Wright 117 observed in other PEO complexes and is consistent with coordination of the oxygens to a cation.An X-ray fibre photograph of PEO-NaTCNQ (x=3) is shown in plate 3. The strongest spots give a pattern of well defined layer lines corresponding to a fibre-repeat distance of 6.6 8, (kO.1 A). However, a more faint layer line may also be discerned, which may suggest the presence of a second oriented phase with repeat distance 11.6 A. Neither repeat distance corresponds to that expected for pure PEO crystals (fibre repeat = 19.3 8,) and a comparison of the scattering angles of hkO diffractions along the layer lines with diffractometer tracings of NaTCNQ powder indicates significant differen- ces in the patterns. A more detailed analysis of the fibre pattern is awaited. Meanwhile, it is tentatively assumed that the principal fibre pattern represents a complexed form of PEO-NaTCNQ. According to the structural investigations of the crystalline phases of PEO-NaI and PEO-NaSCN (form I) by Chatani and coworkers,11,12 the PEO chain adopts a 2/1 helix with six ethylene oxide units per helical repeat.These investigations and the unit-cell measurements of Parker et allo and Hibma' suggest a general model for PEO-Na' complexes in which the PEO-cation 2/1 helical adduct is able to adjust, at least over the range 7.19-8.40 A in order to accommodate various inorganic anions of different dimensions. This spacing should also comfortably accommodate the thickness of two planar aromatic anions stacked alongside the helix. Siddiqui" has determined fibre repeat distances for PEO-sodium phenolate and PEO-sodium 4-phenyl phenolate complexes (which also have crystalline stoichiometry x = 3) and has determined fibre repeats of 7.1 8, (*0.1 A) in each case which is ca.twice the thickness of the phenyl ring. These data are thus consistent with a schematic model consisting of a PEO-cation helical adduct with anions stacked alongside. The interplanar distance of ca. 3.3 8, between TCNQ molecules, which is indicated by the X-ray fibre pattern, is in the range which has been observed16 in crystals of TCNQ salts which display high electronic conductivity. However, highest conductivities are generally observed in complex salts of mixed valence incorporating uncharged TCNQ molecules, which provide vacancies for electron tran~fer.'~ The proportion of 'neutral TCNQ' in TCNQ salts has been estimated" from the higher energy peak of the split band corresponding to the -C_N stretching vibration at ca.2200 cm-'. Fig. 4(6) and (c) suggests the presence of both charged and neutral forms in PEO-NaTCNQ and in our sample of NaTCNQ. In films of PEO-NaTCNQ doped with I2 (x = 3 ) it is clear from optical reflection microscopy that, following the transformation to the green-gold material, there is considerable phase separation of needle-shaped salt crystals of long dimension, ca. 1-3 pm. Such phase separation is also indicated by the similarity between wide angle X-ray diffraction patterns of the exchanged surface of these films and NaTCNQ salt similarly treated with 12. Consideration of other iodine complexes of TCNQ suggests that the complex salt may have the formula NaTCNQ( 13)0.33.Microscopic investigation of the films indicates that the molecular orientation of the precursor PEO-NaI films, though retained following the exchange reaction, is partially lost after doping with 12. The data in table 1 indicate that the overall absorption of iodine by exchanged films is somewhat greater than in the case of the unexchanged PEO-NaI. Since less iodine per mole of NaI should be required by phase-separated microcrystals of NaTCNQ( 13)o.33 than by the non-exchanged PEO-NaI layer, it seems likely that the extra I2 has been taken up by the phase-separated PEO in the exchanged layer, forming an amorphous matrix for the microcrystals. Greater I2 uptake by PEO not engaged in crystalline complex formation with NaI thus accounts for the high absorption by materials with x > 3.Absorption of I2 in excess of that required for conversion to crystalline PEO-Na13 is presumably limited by the Coulombic energy of the ionic lattice.118 h Electroactive Films from EO Complexes -2 - 4 2.6 2 . 8 3.0 3 . 2 3 . 4 lo3 K/ T Fig. 3. log a, versus reciprocal temperature (a, = bulk conductivity) plots for surface measure- ments on films of PEO complexes. For films exchanged with TCNQ, (T, was calculated assuming that the thickness of the exchanged layer is 10 pm (see text). H, Oriented PEO-NaTCNQ-I,/PEO- NaI, bilayer, x = 3; 0, oriented PEO-NaTCNQ/PEO-NaI bilayer, x = 3; 0, oriented PEO- NaTCNQ/PEO-NaI bilayer, x = 4; A, non-oriented PEO-NaTCNQ/PEO-NaI bilayer, x = 3; 0, oriented PEO-NaI,, x = 3. ( - * .) PEO-NaI, x = 3;13 (- - -) PEO-NaI, x = 4' (measurements through compressed pellets). Fig. 3 shows log( conductivity) versus reciprocal temperature plots for bulk and surface measurements of various films. The bulk conductivity is given by a, = a, / t, where a, is the surface conductivity and t is the film thickness. In the case of exchanged films with surface layers of PEO-NaTCNQ and PEO-NaTCNQ-I,, the thickness t was assumed to be 10 pm, as indicated by the gravimetric and SEM analysis described above. The surface conductivity of PEO-NaTCNQ layers is significantly greater for the oriented films than for those prepared from non-oriented, spherulitic precursor films. The conductivity of the oriented PEO-NaTCNQ layer is almost two orders of magnitude greater than that of compressed pellets of NaTCNQ salt (2 x S cm-' at 20°C).Furthermore, the results for the PEO-NaTCNQ film reported here are ca. five-fold larger than reported previously.' The improvement may be attributed to the more uniform machine-oriented texture of the precursor film in the present work and the use of mesitylene rather than toluene as a medium for the exchange reaction. Although TCNQ salts are generally more conductive along the direction of the stack, as noted previously6 there appears to be little anisotropy of conduction in the plane of the drawn films, the conductivities perpendicular to draw being slightly the greater. This is perhaps a consequence of the morphology as shown in plate 2, which features structural discontinuities between crystallites along the draw direction.The voltage-current slow linear sweep data for these materials appear to be linear and reversible throughout theJ. A. Siddiqui and P. V. Wright 119 temperature range ambient to 120°C for both x = 3 and x = 4 testifying to the essential electronic mechanism of conduction with little contribution from the underlying PEO- NaI material. The lower surface conductivity of the PEO-NaTCNQ x = 4 material may thus be attributed to reduced intercrystalline contacts than for x = 3. The crystalline PEO-NaI, material gives an approximately linear plot in log,, 0, vs. 1/T from ambient temperature up to ca. 90°C. Above this temperature, the fall in conductivity may be attributed to loss of Iz.However, a broad endotherm in thermal analysis traces at 120-150°C apparently represents melting of the new complex and indicates that a substantial proportion of iodine is retained in the material at higher temperatures. Shriver and coworkers*' have measured the conductivities of NaI, complexes ( n = 1-9) in an amorphous ethoxy-based comb polymer, polybis( 2-( 2-methoxyethoxy))ethoxylphosphazene (MEEP). They report the conduc- tivity of MEEP,NaI, at 30°C to be 3 x lOP4S cm-' which is approximately the same magnitude as that indicated in fig. 6 for the crystalline PEO-NaI, complex. Using linear sweep voltammetry and complex impedance analysis, Shriver and coworkers concluded that the conduction proceeds by an essentially ionic transport process in their amorphous systems.However, slow linear-sweep data for the crystalline system studied in the present work are essentially linear throughout the temperature range displaying only slight irreversibility at higher temperatures, and a.c. measurements indicate that the conductivity is frequency independent up to lo4 Hz in some experiments. Thus, although some ionic mobility in less-organised regions of the material may account for the slight irreversibility observed in some samples, the conduction process is apparently dominated by electronic transfer in the crystalline complex. The surface conductivities of iodine-doped PEO-NaTCNQ layers at ambient tem- peratures are more than two orders of magnitude greater than those either of the undoped films or of compressed pellets of the iodine-doped free salt which was estimated to be 3 x lo-, S cm-'.The enhanced conductivity in the complexed salt may be attributed to the distribution of the formal negative charge between the TCNQ and iodine atoms. The decrease in conductivity at temperatures above 60 "C coincides with loss of iodine in the exchanged layer and the restoration of the purple colour of the undoped material. However, in these materials some non-ohmic behaviour is apparent from the linear sweep data (as in fig. 5, later). This behaviour could arise, for example, from polyiodide mobility in the supposed amorphous polymer matrix surrounding the phase-separated complex salt in the exchanged layer. The presence of this phase could account for the greater volatility of iodine in this material when compared with the more tightly bound halogen in crystalline PEO-NaI,. Fig.4 shows log,,u, versus stoichiometry, x, for PEO-NaTCNQ and PEO- NaTCNQ-I, at ambient temperature. The uo (apparent) values obtained from four- probe surface measurements on exchanged films were calculated using the overall film thicknesses. As table 1 shows, in films prepared from PEO-NaI with x > 4, significantly lower proportions of available iodide ion exchange with TCNQ than in the case of x = 3. Thus the surface layers vary in thickness with x and are much thinner for x = 5 and 6, exhibiting significantly greater transmission of visible light in optical microscopy than the materials with thicker exchanged layers. The a,(real) values for the surface layers, which have been calculated using the layer thicknesses estimated from gravimetric data, are also plotted in fig.4. In the case of x=5, the estimated thickness of the exchanged layer (ca. 1 pm) was also confirmed using scanning electron microscopy. The conductivity of the PEO-NaTCNQ films appears to decrease with x, becoming too small to measure by the 4-probe surface technique when x>4. The underlying PEO-NaI material clearly makes an insignificant contribution to the conductivity at ambient temperature. However, the iodine-doped material appears to display a minimum in conductivity at x = 4. The conductivity normal to the exchanged, iodine-doped films is, very much120 Electroactive Films from EO Complexes r I 1 I 3 4 5 6 stoichiometry, x Fig. 4. log (apparent conductivity) versus stoichiometry x = [EO]/[Na+] for bilayer films of PEO complexes.0, Surface measurements on the TCNQ-exchanged layer of PEO-NaTCNQ-IJ PEO- Na13 bilayers; a, measurements normal to the latter bilayers; 0, surface measurements on exchanged layers of PEO-NaTCNQ/ PEO- NaI bilayers. (-) Apparent conductivities calcu- lated using the overall bilayer thicknesses; (- - -) real conductivities calculated using exchanged layer thicknesses. less dependent on x than is the corresponding surface conductivity and is of a magnitude (ca. lo-’) consistent with that to be expected for the PEO-NaI, layer. Thus, the variations in surface conductivity with x may be attributed to corresponding variations in the structure of the surfaces. The reason for the significant increase in conductivity at x = 5 is not clear and these systems require further investigation.Inspection by optical reflection microscopy of the x = 5 and 6 materials indicate regions of variable composition but of a finer texture than the phase-separated crystals within the exchanged layer of the x = 3 material. A more integrated structure, either on the molecular level with mixed TCNQ-iodide complexes or at the interfaces of different complexed phases, is perhaps indicated for x > 4. If an electrode of silver-epoxy is placed in contact with the PEO-NaI, layer (an inert electrode remaining in contact with the TCNQ-exchanged layer) linear-sweep voltammetry normal to the surface of the film gives tracings such as that of fig. 5(a). The anodic sweep of the inert electrode meets the voltage axis at +0.67 V.This lies close to the difference between the standard electrode potentials I,+2e- S 31-; +0.5338 V (3) AgI+e- $ Ag+I-; -0.1519 V. (4) This suggests that the pronounced asymmetry in the tracing (which is not observed with PEO-NaI layers in contact with a silver electrode) arises from the rapid formation of a passivating layer ofAgI when the potential on the inert electrode falls below +Oh7 V. Similar traces were observed at sweep rates up to 6 V s-’ and voltage ranges up to A12 V. The system thus behaves as an electrochemical diode. Fig. 5( 6) shows the characteristics of a triode arrangement in which a film of PEO-NaTCNQ-I, is sandwiched between a pair of gold ‘drain’ electrodes in contact with the exchanged layer and a silver-epoxy reference electrode in contact with the PEO-NaI, layer.A gap of ca. 250 pm separatedJ. A. Siddiqui and P. V . Wright 121 1 - V vs. Ag 4 vg = 2 . 0 v 5 2.0-- drain voltage, V,/V Fig. 5. (a) Linear voltage-current sweep data normal to a PEO-NaTCNQ-I,/PEO-NaI, bilayer (x = 3) having a silver-epoxy electrode in contact with the PEO-Na13 layer and a gold electrode in contact with the exchanged layer. (- - -) 200 mV s-'; (-) 50 mV s-'. (b) Triode characteris- tics of a bilayer film (x = 3) between gold (solid shading) and silver (crossed hatching) electrodes. The diagonal hatching is the PEO-NaTCNQ-I, layer and the unmarked layer is PEO-Na13. Film thickness is ca. 30 pm. Separation of gold electrodes is ca. 250 pm. Fig. 6. Schematic diagram of a proposed structure for PEO-NaTCNQ-12, x = 6.Smaller circles (+) are sodium ions; larger circles (-) are polyiodide ions; rectangles are TCNQ anions or neutral molecules and the solid line represents the PEO 2, helix.122 Electroactive Films from EO Complexes the gold electrodes which were ca. 1 cm2 in total area. With a ‘gate’ potential of 0.7 V applied across the bilayer in the conductive mode (Ag negative), the conductivity in the exchanged layer increases to ca. three times that of the open-circuit conductivity. Gate potentials in excess of 0.7 V causes excessive current leakage across the bilayer. The increase in ‘drain’ current for gate potential s0.7 V presumably arises from an increase in the population of neutral TCNQ molecules and/or iodine atoms in the exchanged layer so creating vacancies for electron transfer.The lowering of conductivity by the suppression of such vacancies on reversing the gate potential was not observed. This presumably arises from the presence of the passivating layer on the silver electrode which drastically reduces the conductivity across the film. Further investigations of the structure and mechanisms of conduction in these materials are in progress. References 1 D. E. Fenton, J. M. Parker and P. V. Wright, Polymer, 1973, 14, 589. 2 P. V. Wright, Br. Polym. J., 1975, 7, 319. 3 M. B. Armand, J. M. Chabagno and M. Duclot, in Fast Zon Transport in Solids, ed. P. Vashisha, J. N. 4 J. M. G. Cowie, in Polymer Electrolyte Reviews 1, ed. J. R. MacCallum and C. A. Vincent (Elsevier, 5 J. A. Siddiqui and P. V. Wright, Polymer Commun., 1987, 28, 7. 6 J. A. Siddiqui and P. V. Wright, Polymer Commun., 1987, 28, 89. 7 B. Mussarat, K. Conheeney, J. A. Siddiqui and P. V. Wright, Br. Polym. J., 1988, 20, 293. 8 P. W. Wright, in Polymer Electrolyte Reviews 2, ed. J. R. MacCallum and C. A. Vincent (Elsevier, 9 T. Hibma, Solid Sfate Zonics, 1983, 9/10, 1101. Mundy and G. K. Shenoy (North Holland, New York, 1979), pp. 131-136. London-New York, 1987), chap. 4, pp. 69-102; F. M. Gray, chap. 6, pp. 139-172. London-New York, 1989), chap. 2, to be published. 10 J. M. Parker, P. V. Wright and C. C. Lee, Polymer, 1981, 22, 1305. 1 1 Y. Chatani and S. Okamura, Polymer, 1987, 28, 1815. 12 Y. Chatani, S. Okamura and Y. Fujii, Polym. Prepr., 1989, 30(1), 404. 13 C. C. Lee and P. V. Wright, Polymer, 1982, 23, 681. 14 Manufacturers Handbook, Specac ATR accessories. 15 J. A. Siddiqui, PhD. Thesis (School of Materials, University of Sheffield, 1989), in preparation. 16 G. J. Ashwell, G. Allen, E. P. Goodings, D. A. Kennedy and I. Nowell, Phys. Stat. Sol., 1983, 75, 663. 17 D. S. Ackers, R. J. Harder, W. R. Hertler, W. Mahler, L. R. Melby, R. E. Benson and W. E. Mochel, 18 R. S. Potember, T. 0. Poehler, D. 0. Cowan, F. L. Carter and P. Brant, in Molecular Electronic Devices, 19 M. A. Abkovitz, A. J. Epstein, C. H. Griffiths, J. S. Miller and M. Slade, J. Am. Chem. SOC., 1977, 99, 20 M. M. Lerner, L. J. Lyons, J. S. Tonge and D. F. Shriver, Polym. Prepr. 1989, 30(1), 435. J. Am. Chem. Soc., 1960, 82, 6408. ed. F. L. Carter (Marcel Dekker, New York, 1982), chap. 6, pp.73-85. 5304. Paper 9/02122A; Received 16th May, 1989

ISSN:0301-7249    

DOI:10.1039/DC9898800113

出版商:RSC    

年代:1989

数据来源: RSC