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The determination of transference numbers in solid polymer electrolytes using the Hittorf method
SOLID STATE
Solid State lonics 53-56 (1992) 1087-1094 North-Holland
IOIIICS The determination of transference numbers in solid polymer electrolytes using the Hittorf method Peter G. Bruce, M a r t i n T. H a r d g r a v e a n d Colin A. V i n c e n t Centre for Electrochemical and Materials Sciences, (CEMS), Department of Chemistry, University of St. Andrews, St. Andrews, t;tfe KYI6 9ST. Scotland, UK
Actual transference numbers of M ÷ and X- ion-constituents in polymer electrolytes have been determined for an amorphous poly(ethylene oxide )-based polymer electrolyte containing lithium perchlorate at 120°C by means of the Hittorf technique. The indicated value of cation transference number for an 8:1 electrolyte (0.06_+0.05) is significantly lower than those found from other experimental techniques, such as NMR and steady-state polarisation, demonstrating the unsuitability of those methods for estimating this parameter. The Hittorf procedure described should be applicable to other polymer electrolytes.
I. Introduction
Polymer electrolytes are ionic conductors formed by the dissolution of salts (e.g. M X ) in high molecular weight (usually solid) coordinating host polymers. Ionic conductivity in these materials is a property of amorphous electrolyte phases [1], whereby polymer segmental motion is thought to facilitate the transfer of salt species from position to position through the electrolyte, without the long-range transport of the host polymer because of chain entanglement. Various experimental techniques (e.g. N M R [2], radiotracer diffusion [2], a c / d c polarisation [ 3 ] ) show that, in general, M-containing and X-containing species are both mobile, though it is often not known what the compositions and amounts of these mobile species are. Diffusion coefficients obtained from N M R and radiotracer diffusion measurements, and current measurements from dc polarisation studies, have been used in an attempt to calculate transference (or transport) numbers on the assumption that the salts dissolved in the polymer are completely dissociated [2,4,5]. The low dielectric constant of the polymer and the high salt concentration suggest that this may not be the case, and the results provided by the above techniques are often contradictory. These techniques are indiscriminate in their examination of salt spe-
cies - all mobile species, charged and uncharged (e.g. M ÷, MX, M2X +, M X £ ) will contribute to the diffusion coefficients measured by radiotracer diffusion and pulsed field gradient N M R experiments, and it has been shown that the transport o f neutral species through polarised electrolytes at steady-state may occur together with the transport of charged species, affecting the interpretation of steady-state data [ 6,7 ]. Hittorfand Tubandt methods may be employed to determine the net response only of charged species when an electrolyte is polarised. The two techniques are fundamentally identical, with the term Hittorf generally being reserved for experiments on liquid electrolytes whereas Tubandt refers to those on solid electrolytes where weight changes are often used to calculate the transference number. The application of the Hittorf method for the determination o f transference numbers in liquid electrolytes is described by Spiro [ 8 ]. There are both advantages and disadvantages in applying the technique to solid systems. Advantages are that no correction for the transfer o f solvent molecules coordinated to the ions need be applied because the solvent is immobile over significant distances. Further, as convection may not take place in the solid electrolyte, the study of small samples and the use of a long polarisation time is possible. However, the conductivity of these materials is such that low currents must be employed to prevent the use of large potential differences which might
0167-2738/92/$ 05.00 © 1992 Elsevier Science Publishers B.V. All rights reserved.
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P.G. Bruce et al. / The determination ~[tran~/i'rence numbers'
p r o m o t e the degradation o f the p o l y m e r at the elect r o d e / e l e c t r o l y t e interfaces. This p o l y m e r degradation could sustain current without the transfer of the non-blocked species into or out of the electrolyte, invalidating the experiment. Leveque et al. [ 9,10 ] applied the T u b a n d t m e t h o d to cross-linked polymer electrolytes based on low molecular weight p o l y ( e t b y l e n e o x i d e ) containing lithium perchlorate, and found cation transference numbers of a p p r o x i m a t e l y 0.3 between 70 and 120°C. This technique is not suitable for the study of ordinary PEO-based p o l y m e r electrolytes, because the separation o f preweighed electrolyte discs at the end of the experiment is not possible for these materials due to their highly adhesive nature. C a m e r o n et al. [11] applied the related H i t t o r f method to liquid polyether-based electrolytes and obtained cation transference numbers o f zero for NaSCN, suggesting that the mobile species containing sodium which must exist in this system (because an ionic current could be m a i n t a i n e d between nonblocking electrodes) were N a S C N ion-pairs. In this paper the application of the H i t t o r f / T u b andt method to solid p o l y m e r electrolytes is described for a PEO-based p o l y m e r electrolyte containing lithium perchlorate.
2. Transference numbers A uni-univalent salt MX consists o f two constit. These constituents may be dislributed over a n u m b e r of species, e.g. M + is contained within MX, M2 X+, M X 2 and M + itself. The transference number, T, refers to the m o v e m e n t of a constituent n+ ( n ), and has been defined by Spiro as the net n u m b e r of Faradays carried by the constituent n+ ( n ) (due to the m o v e m e n t o f all species containing n + ( n ) ) through an imaginary reference plane in the electrolyte, in the direction of the cathode ( a n o d e ) when one F a r a d a y passes through the plane. The transference n u m b e r of an ion-constituent n thus considers the overall effect of the transport of charged species a, b, c etc. which contain n, and the transference n u m b e r may be related to the transport numbers o f the individual species. If a salt MX only forms M + and X - ions on dissolution then the transport numbers and transference numbers of the individual species will be identical. u e n t s M + and X
Unlike transport numbers, which may not be negative and must be less than or equal to unity, transference numbers may be o f any sign and magnitude. The sign denotes the direction in which net transport o f the ion-constituent takes place (positive for a cation constituent travelling towards the cathode or for an anion constituent travelling towards the anode, negative if the ion constituents travel to the opposite electrodes). The only condition is that T + "F~ = 1. Transference numbers in aqueous solutions have been used to provide information about the composition of the species present in solution: for example, Spiro quotes the case of aqueous potassium silver cyanide, in which the silver transference number is negative and one half that o f the cyanide. This clearly suggests that the silver and cyanide exists as A g ( C N ) 2 ions. Such interpretations are not likely to be possible when polymer electrolytes are examined, as a variety of species may be present and mobile in these systems.
3. Hittorf cells A H i t t o r f cell is basically four or more electrolyte c o m p a r t m e n t s between two non-blocking electrodes, as represented in fig. 1. The electrodes are polarised, causing charge to flow through the electrolyte by ionic migration. After a known a m o u n t o f charge has been passed, the electrolyte compartments are isolated and any change in composition is d e t e r m i n e d using a suitable technique (e.g. conductivity measurements, chemical analysis etc.). A change in composition of the electrolyte c o m p a r t m e n t adjacent to the cathode may occur due to the loss of charge in the form of M + ions at the cathode being balanced by the influx of cationic species from the central c o m p a r t m e n t s and loss of anionic species to the central compartments. In general, it is likely that the a m o u n t of M + in the c o m p a r t m e n t will change. Thus composition changes may occur at the cathode and start to spread towards the bulk electrolyte. A similar situation occurs at the anode. For a solid electrolyte the electrolyte compartments only need to be defined at the stage of sectioning the electrolyte, providing that compositional changes are confined to the end compartments. Thus, in fig. 2 the three cuts used to create the compart-
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P.G. Bruce et al. / The determination of transference numbers
CATHOLYTE
CATHODE
REFERENCE
1
REFERENCE
2
ANOLYTE
ANODE
Fig. 1. Schematic diagram of Hittorfcell.
Z O H p~
H
m
ANODE CATHODE
ACTUAL (LINE) CONCENTRATION HITTORF CELL
A N D B U L K (SHADED) PROFILE OF POLARISED
Fig. 2. Concentration profiles of polarised Hittorf cell.
ments may be made anywhere in the region of constant salt concentration. For a salt MX whose ion-constituents are taken to be M + and X - , the anion transference number is related to the change in the number of moles of M in the catholyte in the following equation: T --
- AmolesMF Q ,
(1)
where Q is the amount of charge passed and F is the
Faraday, such that M is lost from the compartment if the anion has a positive transference number. In the anolyte a gain in M should take place, matching the loss in the catholyte. The transport of neutral species does not occur through the electrolyte in a Hittorf experiment, because the salt concentration gradients (in which diffusion of any neutral species may occur) which start to form through the electrolyte do not have time to spread throughout the electrolyte, though such trans-
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P.G. Bruce et al. / The determination (?/trans'~,rence numbers
U P P E R S E C T I O N OF C E L L ( U P P E R & SIDE VIEWS) SHOWING POSITIONS OF S C R E W H O L E S A N D S E C T I O N I N G SLITS
L O W E R S E C T I O N OF C E L L ( U P P E R & SIDE VIEWS} SHOWING ELECTRODE AND ELECTROLYTE ARRANGEMENT & P O S I T I O N S OF S C R E W A N D T H E R M O C O U P L E HOLES, & D E P R E S S I O N F O R HOLDING THE ELECTROLYTE SLAB
nm
m
. ....
LOWER SECTION SHOWING STEEL CONTACTS
ASSEMBLED
OF CELL ELECTRODE
CELL
Fig. 3. Sectional views of cell for Hittorf measurements on polymer electrolytes. port may take place in the regions near the electrodes, and m a y be the means whereby a supply of M is m a i n t a i n e d at the cathode. Because the reference plane must be in a region of electrolyte whose composition is unchanged (to ensure that all o f the compositional changes are retained and analysed, as shown in fig. 2), no net diffusion o f neutral species takes place through the plane. Consequently, the compositions o f the anolyte and catholyte are determined by the oxidation and reduction of the non-
blocked species at the electrodes together with the m i g r a t i o n o f charged species through the reference plane, permitting the d e t e r m i n a t i o n o f transference numbers. It is i m p o r t a n t to have at least two central comp a r t m e n t s to verify that composition changes are retained in the end compartments. A discrepancy between these reference c o m p a r t m e n t s shows that the polarisation was carried out for too long. If composition changes spread into it, a single central corn-
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U C L.
II "0 m
0 O.
•
D
DO
i
100
[]
[]
D
i
200
[]
[]
i
300
[]
D
a
i
!
400
500
time
600
/minutes
Fig. 4. Polarisation plots for Li IPEO: LiCIO41Li cells: ( [] ) I 0 laA, ( • ) 50 laA.
partment may lose salt at one end and gain it at the other, and this might produce no net change in composition and incorrectly suggest that all composition changes were retained in the end compartments, yielding incorrect transference numbers in the final analysis.
4. Experimental details Polymer electrolytes were prepared using a grinding/hot-pressing technique described elsewhere [ 12,13]. The electrolyte discs produced were 0.951.05 mm thick and 20 mm in diameter. Slabs of electrolyte of dimensions 12 X 16 mm were cut from these discs. The Hittorf cell for the polarisation of solid polymer electrolytes was made from Macor ceramic, and is shown schematically in fig. 3. The base section contains a 12X 16 mm trough 0.25 mm deep to hold the electrolyte in place, and the upper section contains three narrow slits to permit the easy sectioning of the electrolyte into four pieces at the end of a po-
larisation by the use of a razor blade. The anode was generally lithium metal ( 0 . 7 5 X l . 0 X 1 2 mm) punched from lithium ribbon (0.75 mm thick, Alfa Metals). We have also studied Li/A1 alloy anodes and a lead anode. The cathode was lead metal (0.15 mm thick, Fisons) wrapped around the steel electrode contact. The use of the lead cathode allowed the amount of reduced lithium to be determined after the polarisation, to verify that the current passed was due to the reduction of lithium ions and not due to some polymer degradation reaction at the cathode. Dey [14] reports that the reduction of lithium ions at a lead electrode in non-aqueous electrolytes has a coulombic efficiency of 101%. The Hittorf cell used in the experiments is much smaller than conventional Hittorf cells for the examination of liquid electrolytes. This is not a disadvantage, because it takes a long time for composition changes to spread throughout the cell, and this should not happen over the time scale of the experiment. Steady-state polarisation experiments show that cells 0.25 mm thick achieve this fully polarised state within three hours [ 15 ], suggesting that it would
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P.G. Bruce et al. / The determination Ql'tran~/brence numhers
take about 12000 h to fully polarise a H i t t o r f cell [16]. This time is large in comparison with the actual polarisation time o f about 50 h, making it likely that all of the concentration changes are confined to the electrode compartments. However, in one experiment concentration changes were detected in the central c o m p a r t m e n t s , showing that although complete polarisation may take many thousands of hours, some polarisation occurs in less than 100 h. The cell was placed in a Biichi TO-50 oven under thermostatic control at 120°C, with breakthrough electrical contacts to p e r m i t polarisation. All experimental procedures were carried out in a high integrity argon-filled drybox fitted with columns for oxygen and water removal. Cells were polarised at constant current using a galvanostat built in our laboratories. It was important to select a current sufficiently high to produce significant concentration changes in the electrode c o m p a r t m e n t s in, say, a 2 0 - 1 0 0 h polarisation, without subjecting the cell to voltages which might cause decomposition at the electrodes. Fig. 4 shows the effect of applying currents o f 10 laA and 50 gA to a symmetrical Li I PEO : LiCIO41Li cell: only the former current resulted in acceptable polarisation behaviour. In cells with lead cathodes, a non-zero OCV was present, but in all experiments the total voltage, including the polarisation voltage, was not allowed to exceed 2.5 V. After polarisation and sectioning of the electrolyte the cell was d i s m a n t l e d and the electrolyte removed from the electrodes. The cathode was seen to be blackened, due to the formation of a l i t h i u m / l e a d alloy. N o c o n t a m i n a t i o n o f the cathode compartment by this alloy was apparent, and no electrolyte remained attached to the cathode. R e m o v a l of lithium anodes from the anolyte resulted in microscopic amounts of lithium remaining attached to the polymer. No electrolyte was seen to remain on the anode. W h e n L i / A I and Pb anodes were used no contamination of electrolyte or electrode was seen to be present.
5. Analysis of polarised electrolyte using atomic absorption spectroscopy The use of AAS to d e t e r m i n e the lithium content
of polymer electrolytes has been reported before [17], though in that instance the polymer was insoluble and did not enter solution [ 18 ]. In this stud',' the a m o u n t of lithium in each sample was determined using AAS after the p o l y m e r had been destroyed by acid treatment. This destruction proved necessary because of a twentyfold reduction in the lithium signal in the presence of PEO. The samples, weighed on a 7-figure Sartorius microbalance to an accuracy of +_0.001 rag, were heated electrically in a mixture of 3 cm 3 concentrated sulphuric acid and 0.5 cm ~ o f concentrated perchloric acid at 1 0 0 C for one hour, and were then diluted to 100 cm ' with distilled water. The lead cathode underwent the same treatment to extract the lithium. The atomic absorption measurements were calibrated using the H i t t o r f reference c o m p a r t m e n t samples and samples o f stock polymer electrolyte, once it had been shown that the two reference comp a r t m e n t s displayed the same response (i.e. that any composition changes were retained in the electrode compartments). The initial sample mass was known accurately (+_0.001 mg), and the a m o u n t o f lithium was determined by AAS and the calibration graph, for each experiment. This allowed us to determine the amount of salt in the sample and the amount of PEO was then known by subtraction. The a m o u n t of salt originally present in the sample was obtained from the original composition of the electrolyte, so the change in the mass of the salt (thus the change in the number o f moles o f the salt) was found. Together with the charge passed through the electrolyte the transference numbers were then calculated using eq. ( 1 ).
6. Results and discussion The results for four experiments are given in table 1, which includes data from the analysis of both the anolyte and catholyte. In all cases, the central comp a r t m e n t s showed no change in composition, indicating that the diffusion fronts had not advanced beyond the electrode compartments. Analysis of the lead cathode for lithium in each case gave a value for the total charge passed which was consistent with the current-time integral [ 15 ]. In a satisfactory Hittorf experiment, the value o f transference numbers cal-
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P.G. Bruce et al. / The determination of transference numbers
Table 1 Data from four experiments to determine lithium transference numbers in PEOsLiCIO4. Expt. 1 2 3 4
A moles Li (catholyte) / 10-6
A moles Li (anolyte)/10 6
Charge passed/C
T_
T
(catholyte)
(anolyte)
- 10.4 - 16.0 -14.8 - 14.3
+ 11.2 + 17.6 + 17.1 -
1.082 1.692 1.508 1.416
0.93 0.91 0.95 0.97
1.00 1.00 1.10
culated from each electrode c o m p a r t m e n t should be the same. It is seen that the data from the anolyte gave consistently higher values o f T_. We consider that this is due to c o n t a m i n a t i o n o f the electrolyte by small a m o u n t s o f lithium metal remaining attached to the p o l y m e r when the cell was disassembled. Further evidence for this was derived from a recent exp e r i m e n t using a cell which had a lead anode, in which lead ions were injected into the anolyte when current was passed through the cell. In this cell no c o n t a m i n a t i o n o f the electrolyte by the electrode metal was seen, and analysis o f the anolyte for both lithium and lead gave a value for T_ o f 0.90. Assuming the results from the cathode c o m p a r t ments to be the more reliable, we have T_ =0.94_+0.05. This result implies a cation transference n u m b e r o f 0.06_+0.05, which is significantly lower than that suggested by workers using methods assuming strong electrolyte b e h a v i o u r a n d adherence to the N e r n s t Einstein equation. Such m e t h o d s have p r o p o s e d a T+ in the region o f 0.20-0.30 using low frequency ac polarisations [19,20], pulsed magnetic field gradient N M R [21 ], and p o t e n t i o m e t r i c measurements using concentration cells [22]. It should be noted that this last determination, like the H i t t o r f method, is a well established technique which measures the transference numbers o f constituents and makes no assumptions on the state o f the electrolyte. The m e t h o d is, however, subject to considerable experimental error. We have previously noted that the limiting current fraction, F+, d e t e r m i n e d by dc polarisation o f the symmetric cell
this value with the H i t t o r f transference n u m b e r o f T+ = 0.06. If the system under investigation were an ideal strong electrolyte, then both F+ and T+ would be equal to the cation transport n u m b e r and therefore have the same value. Having considered the available t h e r m o d y n a m i c data on activities [23 ], it seems very unlikely that nonideality can account for the difference between F + and T+; a more probable explanation is based on the presence o f mobile associated species in the electrolyte - a hypothesis which is consistent with tests we have performed on this electrolyte at lower concentrations [ 15 ]. In the simplest model for an electrolyte which includes ion association, only ions and ion-pairs are considered to be present. In these circumstances, the larger value o f F ÷ can be ascribed unambiguously to lithium transport by means o f ion-pair diffusion in the concentration gradient set up in a polarised thin film cell. (A similar explanation may be given for the parameters calculated on the basis o f diffusion coefficient measurements.) There are, however, other possible explanations if the electrolyte contains additional mobile species such as triple ions. F o r example, a low value o f T+ may arise if the diffusion coefficient o f M X f triples were significantly greater than that of M2X + triples (assuming comparable concentrations o f each) since the net effect o f this would be to transport M a w a y from the cathode.
Acknowledgement We thank the SERC for financial support and the Royal Society for the award o f a fellowship to PGB.
References
L i ( s ) IPEO, LiC1Oa(s)8:1 fL i ( s ) at 120°C is 0.20 [23]. It is interesting to c o m p a r e
[ 1] C. Berthier, W. Gorecki, M. Minier, M.B. Armand, J.M. Chabagno and P. Rigaud, Solid State lonics 11 (1983) 91.
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P.G. Bruce et al. / The determination of transference numbers
[ 2] A.V. Chadwick and M.R. Warboys, in: Polymer Electrolyte Reviews I, eds. J.R. MacCallum and C.A. Vincent (Elsevier, London, 1987). [ 3 ] P.R. Sorensen and T. Jacobsen, Electrochim. Acta 27 ( 1982 ) 1671. [4] D.F. Shriver, S. Clancy, P.M. Blonsky and L.C. Hardy, Proc. 6th Riso Intern. Symp. Metallurgy and Materials Science, eds. F.W. Poulsen, N. Hassel Anderson, K. Clausen, S. Skaarup and O.T. SCrensen (Riso National Laboratory, Roskilde, 1985 ). [ 5 ] J. Evans, C.A. Vincent and P.G. Bruce, Polymer 28 ( 1987 ) 2324. [6]P.G. Bruce, M.T. Hardgrave and C.A. Vincent, J. Electroanal. Chem. 271 (1989) 27. [7] G.G. Cameron, J.L. Harvie and M.D. Ingram, Solid State lonics 34 (1989) 65. [8]M. Spiro, in: Physical Methods of Chemistry Parl IIA Electrochemical Methods, eds. A. Weissburger and B.W. Rossiter (Wiley-Interscience, New York, 1971 ). [9] M. Leveque, J-F. LeNest, A. Gandini and H. Cheradame, Makromol. Chem., Rapid Commun. 4 (1983) 497. [ 10 ] M. Leveque, J-F. LeNest, A. Gandini and H. Cheradame, J. Power Sources 14 (1985) 27.
[11] G.G. Cameron, M,D. lngram and J.L. Harvie, Faraday Discuss. Chem. Soc. 88 (1989) 5. [ 12] F.M. Gray, J.R. MacCallum and C.A. Vincent, Solid State tonics 18/19 (1986)282. [ 13 ] F.M. Gray, J.R. MaeCallum and C.A. Vincent, Br. Pat. Appl. No. 8619049. [ 14 ] A.N. Dey, J. Electrochem. Soc. 110 ( 1971 ) 1547. [15] M. T. Hardgrave, PhD Thesis (St, Andrews University, 1990). [ 16 ] S. Atlung, Prog. Batteries Solar Cells 2 ( 1979 ) 96. [ 17] Z. Ogumi, Y. Uchimoto, Z. Takehara and F.R. Foulkes, J. Electrochem. Soc. 137 (1990)29. [ 18 ] Z. Ogumi, personal communication. [ 19] P. Ferloni, G. Chiodelli, A. Magistris and M. Sanest, Solid State lonics 18/19 (1986) 265. [20] J.E. Weston and B.C.H. Steele, Solid State lonics 7 (1982) 81. [21 ] W, Gorecki, R. Andrcani, C. Berthier, M. B. Armand, M. Malt, J. Roos and D. Brinkmann, Solid State lonics 18/19 (1986) 295. [22] A. Bouridah, F. Dalard, D. Deroo and M.B. Armand, Solid State lonics 18/19 (1986) 287.
Solid State lonics 53-56 (1992) 1087-1094 North-Holland
IOIIICS The determination of transference numbers in solid polymer electrolytes using the Hittorf method Peter G. Bruce, M a r t i n T. H a r d g r a v e a n d Colin A. V i n c e n t Centre for Electrochemical and Materials Sciences, (CEMS), Department of Chemistry, University of St. Andrews, St. Andrews, t;tfe KYI6 9ST. Scotland, UK
Actual transference numbers of M ÷ and X- ion-constituents in polymer electrolytes have been determined for an amorphous poly(ethylene oxide )-based polymer electrolyte containing lithium perchlorate at 120°C by means of the Hittorf technique. The indicated value of cation transference number for an 8:1 electrolyte (0.06_+0.05) is significantly lower than those found from other experimental techniques, such as NMR and steady-state polarisation, demonstrating the unsuitability of those methods for estimating this parameter. The Hittorf procedure described should be applicable to other polymer electrolytes.
I. Introduction
Polymer electrolytes are ionic conductors formed by the dissolution of salts (e.g. M X ) in high molecular weight (usually solid) coordinating host polymers. Ionic conductivity in these materials is a property of amorphous electrolyte phases [1], whereby polymer segmental motion is thought to facilitate the transfer of salt species from position to position through the electrolyte, without the long-range transport of the host polymer because of chain entanglement. Various experimental techniques (e.g. N M R [2], radiotracer diffusion [2], a c / d c polarisation [ 3 ] ) show that, in general, M-containing and X-containing species are both mobile, though it is often not known what the compositions and amounts of these mobile species are. Diffusion coefficients obtained from N M R and radiotracer diffusion measurements, and current measurements from dc polarisation studies, have been used in an attempt to calculate transference (or transport) numbers on the assumption that the salts dissolved in the polymer are completely dissociated [2,4,5]. The low dielectric constant of the polymer and the high salt concentration suggest that this may not be the case, and the results provided by the above techniques are often contradictory. These techniques are indiscriminate in their examination of salt spe-
cies - all mobile species, charged and uncharged (e.g. M ÷, MX, M2X +, M X £ ) will contribute to the diffusion coefficients measured by radiotracer diffusion and pulsed field gradient N M R experiments, and it has been shown that the transport o f neutral species through polarised electrolytes at steady-state may occur together with the transport of charged species, affecting the interpretation of steady-state data [ 6,7 ]. Hittorfand Tubandt methods may be employed to determine the net response only of charged species when an electrolyte is polarised. The two techniques are fundamentally identical, with the term Hittorf generally being reserved for experiments on liquid electrolytes whereas Tubandt refers to those on solid electrolytes where weight changes are often used to calculate the transference number. The application of the Hittorf method for the determination o f transference numbers in liquid electrolytes is described by Spiro [ 8 ]. There are both advantages and disadvantages in applying the technique to solid systems. Advantages are that no correction for the transfer o f solvent molecules coordinated to the ions need be applied because the solvent is immobile over significant distances. Further, as convection may not take place in the solid electrolyte, the study of small samples and the use of a long polarisation time is possible. However, the conductivity of these materials is such that low currents must be employed to prevent the use of large potential differences which might
0167-2738/92/$ 05.00 © 1992 Elsevier Science Publishers B.V. All rights reserved.
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P.G. Bruce et al. / The determination ~[tran~/i'rence numbers'
p r o m o t e the degradation o f the p o l y m e r at the elect r o d e / e l e c t r o l y t e interfaces. This p o l y m e r degradation could sustain current without the transfer of the non-blocked species into or out of the electrolyte, invalidating the experiment. Leveque et al. [ 9,10 ] applied the T u b a n d t m e t h o d to cross-linked polymer electrolytes based on low molecular weight p o l y ( e t b y l e n e o x i d e ) containing lithium perchlorate, and found cation transference numbers of a p p r o x i m a t e l y 0.3 between 70 and 120°C. This technique is not suitable for the study of ordinary PEO-based p o l y m e r electrolytes, because the separation o f preweighed electrolyte discs at the end of the experiment is not possible for these materials due to their highly adhesive nature. C a m e r o n et al. [11] applied the related H i t t o r f method to liquid polyether-based electrolytes and obtained cation transference numbers o f zero for NaSCN, suggesting that the mobile species containing sodium which must exist in this system (because an ionic current could be m a i n t a i n e d between nonblocking electrodes) were N a S C N ion-pairs. In this paper the application of the H i t t o r f / T u b andt method to solid p o l y m e r electrolytes is described for a PEO-based p o l y m e r electrolyte containing lithium perchlorate.
2. Transference numbers A uni-univalent salt MX consists o f two constit. These constituents may be dislributed over a n u m b e r of species, e.g. M + is contained within MX, M2 X+, M X 2 and M + itself. The transference number, T, refers to the m o v e m e n t of a constituent n+ ( n ), and has been defined by Spiro as the net n u m b e r of Faradays carried by the constituent n+ ( n ) (due to the m o v e m e n t o f all species containing n + ( n ) ) through an imaginary reference plane in the electrolyte, in the direction of the cathode ( a n o d e ) when one F a r a d a y passes through the plane. The transference n u m b e r of an ion-constituent n thus considers the overall effect of the transport of charged species a, b, c etc. which contain n, and the transference n u m b e r may be related to the transport numbers o f the individual species. If a salt MX only forms M + and X - ions on dissolution then the transport numbers and transference numbers of the individual species will be identical. u e n t s M + and X
Unlike transport numbers, which may not be negative and must be less than or equal to unity, transference numbers may be o f any sign and magnitude. The sign denotes the direction in which net transport o f the ion-constituent takes place (positive for a cation constituent travelling towards the cathode or for an anion constituent travelling towards the anode, negative if the ion constituents travel to the opposite electrodes). The only condition is that T + "F~ = 1. Transference numbers in aqueous solutions have been used to provide information about the composition of the species present in solution: for example, Spiro quotes the case of aqueous potassium silver cyanide, in which the silver transference number is negative and one half that o f the cyanide. This clearly suggests that the silver and cyanide exists as A g ( C N ) 2 ions. Such interpretations are not likely to be possible when polymer electrolytes are examined, as a variety of species may be present and mobile in these systems.
3. Hittorf cells A H i t t o r f cell is basically four or more electrolyte c o m p a r t m e n t s between two non-blocking electrodes, as represented in fig. 1. The electrodes are polarised, causing charge to flow through the electrolyte by ionic migration. After a known a m o u n t o f charge has been passed, the electrolyte compartments are isolated and any change in composition is d e t e r m i n e d using a suitable technique (e.g. conductivity measurements, chemical analysis etc.). A change in composition of the electrolyte c o m p a r t m e n t adjacent to the cathode may occur due to the loss of charge in the form of M + ions at the cathode being balanced by the influx of cationic species from the central c o m p a r t m e n t s and loss of anionic species to the central compartments. In general, it is likely that the a m o u n t of M + in the c o m p a r t m e n t will change. Thus composition changes may occur at the cathode and start to spread towards the bulk electrolyte. A similar situation occurs at the anode. For a solid electrolyte the electrolyte compartments only need to be defined at the stage of sectioning the electrolyte, providing that compositional changes are confined to the end compartments. Thus, in fig. 2 the three cuts used to create the compart-
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P.G. Bruce et al. / The determination of transference numbers
CATHOLYTE
CATHODE
REFERENCE
1
REFERENCE
2
ANOLYTE
ANODE
Fig. 1. Schematic diagram of Hittorfcell.
Z O H p~
H
m
ANODE CATHODE
ACTUAL (LINE) CONCENTRATION HITTORF CELL
A N D B U L K (SHADED) PROFILE OF POLARISED
Fig. 2. Concentration profiles of polarised Hittorf cell.
ments may be made anywhere in the region of constant salt concentration. For a salt MX whose ion-constituents are taken to be M + and X - , the anion transference number is related to the change in the number of moles of M in the catholyte in the following equation: T --
- AmolesMF Q ,
(1)
where Q is the amount of charge passed and F is the
Faraday, such that M is lost from the compartment if the anion has a positive transference number. In the anolyte a gain in M should take place, matching the loss in the catholyte. The transport of neutral species does not occur through the electrolyte in a Hittorf experiment, because the salt concentration gradients (in which diffusion of any neutral species may occur) which start to form through the electrolyte do not have time to spread throughout the electrolyte, though such trans-
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P.G. Bruce et al. / The determination (?/trans'~,rence numbers
U P P E R S E C T I O N OF C E L L ( U P P E R & SIDE VIEWS) SHOWING POSITIONS OF S C R E W H O L E S A N D S E C T I O N I N G SLITS
L O W E R S E C T I O N OF C E L L ( U P P E R & SIDE VIEWS} SHOWING ELECTRODE AND ELECTROLYTE ARRANGEMENT & P O S I T I O N S OF S C R E W A N D T H E R M O C O U P L E HOLES, & D E P R E S S I O N F O R HOLDING THE ELECTROLYTE SLAB
nm
m
. ....
LOWER SECTION SHOWING STEEL CONTACTS
ASSEMBLED
OF CELL ELECTRODE
CELL
Fig. 3. Sectional views of cell for Hittorf measurements on polymer electrolytes. port may take place in the regions near the electrodes, and m a y be the means whereby a supply of M is m a i n t a i n e d at the cathode. Because the reference plane must be in a region of electrolyte whose composition is unchanged (to ensure that all o f the compositional changes are retained and analysed, as shown in fig. 2), no net diffusion o f neutral species takes place through the plane. Consequently, the compositions o f the anolyte and catholyte are determined by the oxidation and reduction of the non-
blocked species at the electrodes together with the m i g r a t i o n o f charged species through the reference plane, permitting the d e t e r m i n a t i o n o f transference numbers. It is i m p o r t a n t to have at least two central comp a r t m e n t s to verify that composition changes are retained in the end compartments. A discrepancy between these reference c o m p a r t m e n t s shows that the polarisation was carried out for too long. If composition changes spread into it, a single central corn-
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P.G. Bruce et al / The determination Qf transference numbers
U C L.
II "0 m
0 O.
•
D
DO
i
100
[]
[]
D
i
200
[]
[]
i
300
[]
D
a
i
!
400
500
time
600
/minutes
Fig. 4. Polarisation plots for Li IPEO: LiCIO41Li cells: ( [] ) I 0 laA, ( • ) 50 laA.
partment may lose salt at one end and gain it at the other, and this might produce no net change in composition and incorrectly suggest that all composition changes were retained in the end compartments, yielding incorrect transference numbers in the final analysis.
4. Experimental details Polymer electrolytes were prepared using a grinding/hot-pressing technique described elsewhere [ 12,13]. The electrolyte discs produced were 0.951.05 mm thick and 20 mm in diameter. Slabs of electrolyte of dimensions 12 X 16 mm were cut from these discs. The Hittorf cell for the polarisation of solid polymer electrolytes was made from Macor ceramic, and is shown schematically in fig. 3. The base section contains a 12X 16 mm trough 0.25 mm deep to hold the electrolyte in place, and the upper section contains three narrow slits to permit the easy sectioning of the electrolyte into four pieces at the end of a po-
larisation by the use of a razor blade. The anode was generally lithium metal ( 0 . 7 5 X l . 0 X 1 2 mm) punched from lithium ribbon (0.75 mm thick, Alfa Metals). We have also studied Li/A1 alloy anodes and a lead anode. The cathode was lead metal (0.15 mm thick, Fisons) wrapped around the steel electrode contact. The use of the lead cathode allowed the amount of reduced lithium to be determined after the polarisation, to verify that the current passed was due to the reduction of lithium ions and not due to some polymer degradation reaction at the cathode. Dey [14] reports that the reduction of lithium ions at a lead electrode in non-aqueous electrolytes has a coulombic efficiency of 101%. The Hittorf cell used in the experiments is much smaller than conventional Hittorf cells for the examination of liquid electrolytes. This is not a disadvantage, because it takes a long time for composition changes to spread throughout the cell, and this should not happen over the time scale of the experiment. Steady-state polarisation experiments show that cells 0.25 mm thick achieve this fully polarised state within three hours [ 15 ], suggesting that it would
1092
P.G. Bruce et al. / The determination Ql'tran~/brence numhers
take about 12000 h to fully polarise a H i t t o r f cell [16]. This time is large in comparison with the actual polarisation time o f about 50 h, making it likely that all of the concentration changes are confined to the electrode compartments. However, in one experiment concentration changes were detected in the central c o m p a r t m e n t s , showing that although complete polarisation may take many thousands of hours, some polarisation occurs in less than 100 h. The cell was placed in a Biichi TO-50 oven under thermostatic control at 120°C, with breakthrough electrical contacts to p e r m i t polarisation. All experimental procedures were carried out in a high integrity argon-filled drybox fitted with columns for oxygen and water removal. Cells were polarised at constant current using a galvanostat built in our laboratories. It was important to select a current sufficiently high to produce significant concentration changes in the electrode c o m p a r t m e n t s in, say, a 2 0 - 1 0 0 h polarisation, without subjecting the cell to voltages which might cause decomposition at the electrodes. Fig. 4 shows the effect of applying currents o f 10 laA and 50 gA to a symmetrical Li I PEO : LiCIO41Li cell: only the former current resulted in acceptable polarisation behaviour. In cells with lead cathodes, a non-zero OCV was present, but in all experiments the total voltage, including the polarisation voltage, was not allowed to exceed 2.5 V. After polarisation and sectioning of the electrolyte the cell was d i s m a n t l e d and the electrolyte removed from the electrodes. The cathode was seen to be blackened, due to the formation of a l i t h i u m / l e a d alloy. N o c o n t a m i n a t i o n o f the cathode compartment by this alloy was apparent, and no electrolyte remained attached to the cathode. R e m o v a l of lithium anodes from the anolyte resulted in microscopic amounts of lithium remaining attached to the polymer. No electrolyte was seen to remain on the anode. W h e n L i / A I and Pb anodes were used no contamination of electrolyte or electrode was seen to be present.
5. Analysis of polarised electrolyte using atomic absorption spectroscopy The use of AAS to d e t e r m i n e the lithium content
of polymer electrolytes has been reported before [17], though in that instance the polymer was insoluble and did not enter solution [ 18 ]. In this stud',' the a m o u n t of lithium in each sample was determined using AAS after the p o l y m e r had been destroyed by acid treatment. This destruction proved necessary because of a twentyfold reduction in the lithium signal in the presence of PEO. The samples, weighed on a 7-figure Sartorius microbalance to an accuracy of +_0.001 rag, were heated electrically in a mixture of 3 cm 3 concentrated sulphuric acid and 0.5 cm ~ o f concentrated perchloric acid at 1 0 0 C for one hour, and were then diluted to 100 cm ' with distilled water. The lead cathode underwent the same treatment to extract the lithium. The atomic absorption measurements were calibrated using the H i t t o r f reference c o m p a r t m e n t samples and samples o f stock polymer electrolyte, once it had been shown that the two reference comp a r t m e n t s displayed the same response (i.e. that any composition changes were retained in the electrode compartments). The initial sample mass was known accurately (+_0.001 mg), and the a m o u n t o f lithium was determined by AAS and the calibration graph, for each experiment. This allowed us to determine the amount of salt in the sample and the amount of PEO was then known by subtraction. The a m o u n t of salt originally present in the sample was obtained from the original composition of the electrolyte, so the change in the mass of the salt (thus the change in the number o f moles o f the salt) was found. Together with the charge passed through the electrolyte the transference numbers were then calculated using eq. ( 1 ).
6. Results and discussion The results for four experiments are given in table 1, which includes data from the analysis of both the anolyte and catholyte. In all cases, the central comp a r t m e n t s showed no change in composition, indicating that the diffusion fronts had not advanced beyond the electrode compartments. Analysis of the lead cathode for lithium in each case gave a value for the total charge passed which was consistent with the current-time integral [ 15 ]. In a satisfactory Hittorf experiment, the value o f transference numbers cal-
1093
P.G. Bruce et al. / The determination of transference numbers
Table 1 Data from four experiments to determine lithium transference numbers in PEOsLiCIO4. Expt. 1 2 3 4
A moles Li (catholyte) / 10-6
A moles Li (anolyte)/10 6
Charge passed/C
T_
T
(catholyte)
(anolyte)
- 10.4 - 16.0 -14.8 - 14.3
+ 11.2 + 17.6 + 17.1 -
1.082 1.692 1.508 1.416
0.93 0.91 0.95 0.97
1.00 1.00 1.10
culated from each electrode c o m p a r t m e n t should be the same. It is seen that the data from the anolyte gave consistently higher values o f T_. We consider that this is due to c o n t a m i n a t i o n o f the electrolyte by small a m o u n t s o f lithium metal remaining attached to the p o l y m e r when the cell was disassembled. Further evidence for this was derived from a recent exp e r i m e n t using a cell which had a lead anode, in which lead ions were injected into the anolyte when current was passed through the cell. In this cell no c o n t a m i n a t i o n o f the electrolyte by the electrode metal was seen, and analysis o f the anolyte for both lithium and lead gave a value for T_ o f 0.90. Assuming the results from the cathode c o m p a r t ments to be the more reliable, we have T_ =0.94_+0.05. This result implies a cation transference n u m b e r o f 0.06_+0.05, which is significantly lower than that suggested by workers using methods assuming strong electrolyte b e h a v i o u r a n d adherence to the N e r n s t Einstein equation. Such m e t h o d s have p r o p o s e d a T+ in the region o f 0.20-0.30 using low frequency ac polarisations [19,20], pulsed magnetic field gradient N M R [21 ], and p o t e n t i o m e t r i c measurements using concentration cells [22]. It should be noted that this last determination, like the H i t t o r f method, is a well established technique which measures the transference numbers o f constituents and makes no assumptions on the state o f the electrolyte. The m e t h o d is, however, subject to considerable experimental error. We have previously noted that the limiting current fraction, F+, d e t e r m i n e d by dc polarisation o f the symmetric cell
this value with the H i t t o r f transference n u m b e r o f T+ = 0.06. If the system under investigation were an ideal strong electrolyte, then both F+ and T+ would be equal to the cation transport n u m b e r and therefore have the same value. Having considered the available t h e r m o d y n a m i c data on activities [23 ], it seems very unlikely that nonideality can account for the difference between F + and T+; a more probable explanation is based on the presence o f mobile associated species in the electrolyte - a hypothesis which is consistent with tests we have performed on this electrolyte at lower concentrations [ 15 ]. In the simplest model for an electrolyte which includes ion association, only ions and ion-pairs are considered to be present. In these circumstances, the larger value o f F ÷ can be ascribed unambiguously to lithium transport by means o f ion-pair diffusion in the concentration gradient set up in a polarised thin film cell. (A similar explanation may be given for the parameters calculated on the basis o f diffusion coefficient measurements.) There are, however, other possible explanations if the electrolyte contains additional mobile species such as triple ions. F o r example, a low value o f T+ may arise if the diffusion coefficient o f M X f triples were significantly greater than that of M2X + triples (assuming comparable concentrations o f each) since the net effect o f this would be to transport M a w a y from the cathode.
Acknowledgement We thank the SERC for financial support and the Royal Society for the award o f a fellowship to PGB.
References
L i ( s ) IPEO, LiC1Oa(s)8:1 fL i ( s ) at 120°C is 0.20 [23]. It is interesting to c o m p a r e
[ 1] C. Berthier, W. Gorecki, M. Minier, M.B. Armand, J.M. Chabagno and P. Rigaud, Solid State lonics 11 (1983) 91.
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P.G. Bruce et al. / The determination of transference numbers
[ 2] A.V. Chadwick and M.R. Warboys, in: Polymer Electrolyte Reviews I, eds. J.R. MacCallum and C.A. Vincent (Elsevier, London, 1987). [ 3 ] P.R. Sorensen and T. Jacobsen, Electrochim. Acta 27 ( 1982 ) 1671. [4] D.F. Shriver, S. Clancy, P.M. Blonsky and L.C. Hardy, Proc. 6th Riso Intern. Symp. Metallurgy and Materials Science, eds. F.W. Poulsen, N. Hassel Anderson, K. Clausen, S. Skaarup and O.T. SCrensen (Riso National Laboratory, Roskilde, 1985 ). [ 5 ] J. Evans, C.A. Vincent and P.G. Bruce, Polymer 28 ( 1987 ) 2324. [6]P.G. Bruce, M.T. Hardgrave and C.A. Vincent, J. Electroanal. Chem. 271 (1989) 27. [7] G.G. Cameron, J.L. Harvie and M.D. Ingram, Solid State lonics 34 (1989) 65. [8]M. Spiro, in: Physical Methods of Chemistry Parl IIA Electrochemical Methods, eds. A. Weissburger and B.W. Rossiter (Wiley-Interscience, New York, 1971 ). [9] M. Leveque, J-F. LeNest, A. Gandini and H. Cheradame, Makromol. Chem., Rapid Commun. 4 (1983) 497. [ 10 ] M. Leveque, J-F. LeNest, A. Gandini and H. Cheradame, J. Power Sources 14 (1985) 27.
[11] G.G. Cameron, M,D. lngram and J.L. Harvie, Faraday Discuss. Chem. Soc. 88 (1989) 5. [ 12] F.M. Gray, J.R. MacCallum and C.A. Vincent, Solid State tonics 18/19 (1986)282. [ 13 ] F.M. Gray, J.R. MaeCallum and C.A. Vincent, Br. Pat. Appl. No. 8619049. [ 14 ] A.N. Dey, J. Electrochem. Soc. 110 ( 1971 ) 1547. [15] M. T. Hardgrave, PhD Thesis (St, Andrews University, 1990). [ 16 ] S. Atlung, Prog. Batteries Solar Cells 2 ( 1979 ) 96. [ 17] Z. Ogumi, Y. Uchimoto, Z. Takehara and F.R. Foulkes, J. Electrochem. Soc. 137 (1990)29. [ 18 ] Z. Ogumi, personal communication. [ 19] P. Ferloni, G. Chiodelli, A. Magistris and M. Sanest, Solid State lonics 18/19 (1986) 265. [20] J.E. Weston and B.C.H. Steele, Solid State lonics 7 (1982) 81. [21 ] W, Gorecki, R. Andrcani, C. Berthier, M. B. Armand, M. Malt, J. Roos and D. Brinkmann, Solid State lonics 18/19 (1986) 295. [22] A. Bouridah, F. Dalard, D. Deroo and M.B. Armand, Solid State lonics 18/19 (1986) 287.