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