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On the electrical conductivity and other transport properties of molten sodium sulphate
Solid State Ionics 48 (1991)
SOLID STATE lowlcs
127-129
North-Holland
On the electrical conductivity and other transport properties of molten sodium sulphate Arnold Lund& Department Received
and Ben@-Erik Mellander
of Physics,Chalmers University of Technology, S-412 96 Giiteborg, Sweden
25 April 199 1; accepted
for publication
18 June 199 1
Kim and Simkovich have recently published a study of transport properties in molten sodium sulphate at 1173 K. Surprisingly enough, their electrical conductivity is one order of magnitude lower than according to all other studies of the pure salt. Their result is also in conflict with the general systematics found for high-conducting melts. The possible sources oferror in conductivity measurements are discussed, and so are also the concept of transport number for pure molten salts and the validity of the NernstEinstein relation. Their transport number experiment is reinterpreted, which has some consequences for the calculated sodium ion mobility and self diffusion coefficient.
1. Introduction The first report concerning electrical conductivities of molten salts came from Faraday in 1833 [ 11. dc techniques were applied from 1845 and onwards in the early attempts of quantitative conductivity measurements [ 21, while an ac technique was introduced by Kohlrausch in 1882 [ 21. The early investigators worked with salts that could be melted in glass vessels. The available temperature range was expanded up to 1100’ C or more by Arndt, who used a U-cell of porcelain [ 2 1. Quite naturally the search for systematics started early, and over the years the conductivities have been compared by a number of authors for sequences of salts with either a common anion and different cations or vice versa. Compilations of conductivity data have been produced occasionally as a service both to scientists and to engineers. E.g., the Molten Salts Data Center has produced critical assessments of data on electrical conductance, density and viscosity [ 3,4] as well as on diffusion coefficients [ 5 ] for single and multi-component molten salt systems. Kim and Simkovich [ 61 have recently reported on a study of transport properties of molten sodium sulphate at 1173 K. They have commented on the fact that their reported conductivity is close to a factor of ten lower than what has been reported by previous 0167-2738/91/$03.50
0 1991 Elsevier Science Publishers
investigators. Their study is no doubt very carefully performed, and they have used equipment that seems to be of high quality. It is easy to overlook that there are fundamental differences between the ion transport mechanisms in solid and molten salts. With all this in mind, it might be understandable that they suggest that the discrepancy is caused by shortcomings of previous conductivity measurements. It is our intention to compare their results with the literature in order to determine which set of data that is most likely to be reliable. Transport numbers, cation mobilities and the Nernst-Einstein relation will be discussed briefly.
2. Discussion
concerning
the electrical conductivity
While Kim and Simkovich report a conductivity of 0.232 S/cm at 1173 K, all previous data known by us are ten times higher. Numerical values are 2.23 [2], 2.31 [7], 2.31 [8], 2.26 [9] and 2.3 [lo] S/ cm. A study for which the results are only reported graphically [ 111 is in good agreement with the listed results. All six studies are consistent with each other in spite of existing differences concerning cell material, purity of chosen salt and instrumentation. Furthermore, a conductivity of about 2.3 S/cm for Na$O, is in sequence with 1.74 S/cm for Na*MoO,
B.V. All rights reserved.
and 1.40 S/cm for NaZWOJ at I1 73 K [3]. It is also consistent with studies of binary sulphate mixtures such as Li2SOI-NaSO, [ 81. With the LJ-cell technique used in our laboratory it has been possible to extend the conductivity studies from the melt into solid phases. As is well-known, techniques based on the USC of pellets are dominating the study of the electrical conductivity of solid salts. We have. on a couple of occasions, studied electrical conductivities of solid salts at rather high temperatures both with the IJ-cell and the pellet technique. and WC have found consistency in the overlapping temperature range. This has been done for Na,SO, [ IO] as well as for LiZSOl [ 121. In the latter case the IJ-cell study covered the melt, the high-conductivity fee phase. and a small part of the monoclinic phase. while the pellet work covered a large range in the latter phase. Kim and Simkovich suggest that the “discrepancy is most probably caused by the facts that the previous investigators had: ( I ) a relatively impure Na,SO,. (2) a reaction between their quartz capillary and molten sodium sulphate, and (3) a reaction with their Pt electrodes.” It is well-known that the introduction of rather small amounts of aliovalent ions or other impurities can cause drastic increases in the conductivity of most solid salt phases. e.g. hexagonal NaSO, [ 13-l 51. but this is not the cast for high-conductivity molten salts [ 3.4, I6 ] or for high-conductivity solid phases [ 12,13.17]. (The situation is of course different for melts with a low conductivity at high purity, such as zinc chloride. ) Their first suggestion is thus a misunderstanding. Furthermore, WC are convinced that the other two suggestions are. at most. of marginal importance for the quoted conductivity studies. Of course one must be aware of the fact that there are different qualities of quartz. etc.
] IX. 191, Kim and Simkovich report a “cation transport number” determined by a method which has been used successfully for ion conducting polymers [ 201. Their obtained cation transport number is very close to unity, and they claim (at least indirectly) that the transport numbers are negligible in pure molten Na,SOJ for “the possible anion species”. From this result it seems that they actually have had the sulphate ions as reference frame relative to which the transport number of sodium ions is unity by definition. It might bc illustrative to compare existing caperimental data on transport numbers and mobilitics in molten salts with solid electrolytes. For the high-conductivity fee phase of LiZSO, the cation transport number was found to be unity within experimental error for the whole studied range 873 K to 1063 K [2l 1. In contrast to this. all experimental evidence available indicates that both cations and anions arc mobile in molten salts. Thus. this has been found for studies of clectromigration as well as of self diffusion. Several types of electromigration experiments ha\,e been performed over the years. If we limit the discussion to isotope effects in pure salts, it has been found for cations [ 221 as well as for anions [ 13 1. that a light isotope is slightly mote mobile than a heavy one. The phenomenological treatment developed by Klemm [ 24,251 is very suitable for discussing transport properties of molten salts for which the electrical conductivity and both diffusion coefficients (II ’ and D ) have been measured. It follows from calculations of friction coefficients. etc. that both cations and anions are mobile in nitrates [ 261, halides [ 271 and carbonates [ 281. It one defines the cation one obtransport number as I + =I>‘/(D’+llY) tains I + =0.64 for Na,COi at I I73 K.
3. Transport
4. The validity of the Nernst-Einstein
numbers
and ionic mobilities
in molten
relation
salts
The concept of transport numbers in molten salts was an important issue in the late 50s and early 60s. The question of reference frame is not as obvious in a melt as in a solid phase, and one must distinguish between internal and external ionic mobilities, which has been demonstrated very clearly by Klemm
Kim and Simkovich have calculated a cation self diffusion coefficient from the Nernst-Einstein equation. However. it must be remembered that the ion transport processes in a melt are completely diffcrent from the situation for which the Nernst-Einstein equation is derived. It is thus not surprising that calculated self diffusion coefficients nearly always turn
A. Lund&. B.-E. Mellander /Molten sodium sulphate
out to be lower than experimentally determined ones [25-281. To our knowledge no self diffusion experiments have been performed on any sulphate melt. If one assumes that the conductivity is of the order of 2.3 S/cm, and that the cation transport number lies between 0.6 and 0.8 a Nernst-Einstein calculation gives 4.8~10~~ to 6.5~10~~ cm2/s for D+ at 1173 K, which fits much better with data for other sodium salts than the 8.1 x 1OC6 cm’/s obtained by Kim and Simkovich. It might be of interest in this connection to mention that the assumptions underlying the Nernst-Einstein relation neither are valid for solid electrolytes [ 29 1, For solid sulphate electrolytes the calculated self-diffusion coefficients are larger than the measured ones [ 301, i.e. the tendency is opposite to the case of molten salts.
5. Final conclusion There is reason to reconsider the interpretation the study of molten sodium sulphate performed Kim and Simkovich.
of by
References [ 1] M. Faraday, Philos. Transact. ( 1833) 507. [2] K. Amdt. Z. Electrochem. 12 (1906) 337. [3] G.J. Jaw, F.W. Dampier. G.R. Lakshminarayanan, P.K. Lorenz and R.P.T. Tomkins, NSRDS-NBS I5 (Natl. Bureau of Standards. Washington, 1968). [ 41 G.J. Jam, U. Krebs, H.F. Siegenthaler. R.P.T. Tomkins, G.L. Gardner, C.B. Allen, J.R. Downey and SK. Singer, J. Phys. Chem. Ref. Data 1 (1972) 581; 3 (1974) 1; 4 (1975) 871; 6(1977)409:8(1979)125;9(1980)791;9(1980)831; 12 (1983) 591. [ 51 G.J. Jam and N.P. Bansal, J. Phys. Chem. Ref. Data I I (1982) 505. [6] D.-H. Kim and G. Stmkovich. Solid State Ionics 45 ( 1991 ) 165.
129
[ 71 A. Kvist, Z. Naturforsch. 22a ( 1967) 467. [ 81 A.-M. Josefson and A. Kvist, Z. Naturforsch. 24a ( 1969) 466. ]9 1K. Matiasovsky, V. Danek and B. Lillebuen, Electrochem. Acta 17 (1972) 463. ]lO M.A. Careem and B.-E. Mellander, Solid State Ionics 15 (1985) 327. ]‘I 1A.F. Polishchuk. T.M. Shurkhal and N.A. Romashchenko. Ukr. Khim. Zh. 39 (1973) 760. ]12 A. Lund&t. Solid State Commun. 65 ( 1988) 1237. ]13 1A. Lunden and M.A.K.L. Dissanayake, J. Solid State Chem. 90 (1991) 179. (14 P.W.S.K. Bandaranayake and B.-E. Mellander, Solid State lonics 26 ( 1988) 33. ]15 P.W.S.K. Bandaranayake and B.-E. Mellander. Solid State Ionics40/41 (1991) 31. ]16 A. Kvist, Z. Naturforsch. 2la (1966) 1601. [ 171 A. Lund&t, A. Bengtzelius. R. Kaber, L. Nilsson, K. Schroeder and R. Tameberg. Solid State lonics 9/ 10 ( 1983) 89. [ 181 A. Klemm, in: Molten Salt Chemistry, ed. M. Blander (Interscience. New York, 1964) p. 535. [ 191 A. Klemm. in: Advances in Molten Salt Chemistry 6, eds. G. Mamantov and C.B. Mamantov (Elsevier, Amsterdam, 1987) p. 1. [20] D.F. Shriver. S. Clancy, P.M. Blonsky and L.C. Hardy, in: 6th Riser Int. Symp. on Met. and Mat. Science, eds. F.W. Poulsen, N. Hessel Andersen, K. Clausen, S. Skaarup and 0. Toft Sorensen (1985) 353. [ 2 I ] A. Lund&, Z. Naturforsch. 17a ( 1962) 142. [ 221 A. Klemm, H. Hintenberger and P. Hoemes, 2. Naturforsch. 2a ( 1947) 245. [23] A. Klemm and A. Lunden, Z. Naturforsch. 10a ( 1955) 282. [24] A. Klemm, Z. Naturforsch. 8a (1953) 397. [ 251 A. Klemm, Z. Naturforsch. 15a ( 1960) 173. [26] A. Lunden, Z. Naturforsch. 15a (1960) 1019. [ 271 C.-A. Sjoblom and A. Lunden. Z. Naturforsch. 18a ( 1963) 942. [ 281 P.L. Spedding and R. Mills. J. Electrochem. Sot. 112 ( 1965) 594. [ 291 G.E. Murch, Solid State Ionics 7 ( 1982) 177. [ 301 A. Lunden, and J.O. Thomas, in: High Conductivity Solid Ionic Conductors, ed. T. Takahashi (World Scientific, Singapore, 1989) p. 45.
SOLID STATE lowlcs
127-129
North-Holland
On the electrical conductivity and other transport properties of molten sodium sulphate Arnold Lund& Department Received
and Ben@-Erik Mellander
of Physics,Chalmers University of Technology, S-412 96 Giiteborg, Sweden
25 April 199 1; accepted
for publication
18 June 199 1
Kim and Simkovich have recently published a study of transport properties in molten sodium sulphate at 1173 K. Surprisingly enough, their electrical conductivity is one order of magnitude lower than according to all other studies of the pure salt. Their result is also in conflict with the general systematics found for high-conducting melts. The possible sources oferror in conductivity measurements are discussed, and so are also the concept of transport number for pure molten salts and the validity of the NernstEinstein relation. Their transport number experiment is reinterpreted, which has some consequences for the calculated sodium ion mobility and self diffusion coefficient.
1. Introduction The first report concerning electrical conductivities of molten salts came from Faraday in 1833 [ 11. dc techniques were applied from 1845 and onwards in the early attempts of quantitative conductivity measurements [ 21, while an ac technique was introduced by Kohlrausch in 1882 [ 21. The early investigators worked with salts that could be melted in glass vessels. The available temperature range was expanded up to 1100’ C or more by Arndt, who used a U-cell of porcelain [ 2 1. Quite naturally the search for systematics started early, and over the years the conductivities have been compared by a number of authors for sequences of salts with either a common anion and different cations or vice versa. Compilations of conductivity data have been produced occasionally as a service both to scientists and to engineers. E.g., the Molten Salts Data Center has produced critical assessments of data on electrical conductance, density and viscosity [ 3,4] as well as on diffusion coefficients [ 5 ] for single and multi-component molten salt systems. Kim and Simkovich [ 61 have recently reported on a study of transport properties of molten sodium sulphate at 1173 K. They have commented on the fact that their reported conductivity is close to a factor of ten lower than what has been reported by previous 0167-2738/91/$03.50
0 1991 Elsevier Science Publishers
investigators. Their study is no doubt very carefully performed, and they have used equipment that seems to be of high quality. It is easy to overlook that there are fundamental differences between the ion transport mechanisms in solid and molten salts. With all this in mind, it might be understandable that they suggest that the discrepancy is caused by shortcomings of previous conductivity measurements. It is our intention to compare their results with the literature in order to determine which set of data that is most likely to be reliable. Transport numbers, cation mobilities and the Nernst-Einstein relation will be discussed briefly.
2. Discussion
concerning
the electrical conductivity
While Kim and Simkovich report a conductivity of 0.232 S/cm at 1173 K, all previous data known by us are ten times higher. Numerical values are 2.23 [2], 2.31 [7], 2.31 [8], 2.26 [9] and 2.3 [lo] S/ cm. A study for which the results are only reported graphically [ 111 is in good agreement with the listed results. All six studies are consistent with each other in spite of existing differences concerning cell material, purity of chosen salt and instrumentation. Furthermore, a conductivity of about 2.3 S/cm for Na$O, is in sequence with 1.74 S/cm for Na*MoO,
B.V. All rights reserved.
and 1.40 S/cm for NaZWOJ at I1 73 K [3]. It is also consistent with studies of binary sulphate mixtures such as Li2SOI-NaSO, [ 81. With the LJ-cell technique used in our laboratory it has been possible to extend the conductivity studies from the melt into solid phases. As is well-known, techniques based on the USC of pellets are dominating the study of the electrical conductivity of solid salts. We have. on a couple of occasions, studied electrical conductivities of solid salts at rather high temperatures both with the IJ-cell and the pellet technique. and WC have found consistency in the overlapping temperature range. This has been done for Na,SO, [ IO] as well as for LiZSOl [ 121. In the latter case the IJ-cell study covered the melt, the high-conductivity fee phase. and a small part of the monoclinic phase. while the pellet work covered a large range in the latter phase. Kim and Simkovich suggest that the “discrepancy is most probably caused by the facts that the previous investigators had: ( I ) a relatively impure Na,SO,. (2) a reaction between their quartz capillary and molten sodium sulphate, and (3) a reaction with their Pt electrodes.” It is well-known that the introduction of rather small amounts of aliovalent ions or other impurities can cause drastic increases in the conductivity of most solid salt phases. e.g. hexagonal NaSO, [ 13-l 51. but this is not the cast for high-conductivity molten salts [ 3.4, I6 ] or for high-conductivity solid phases [ 12,13.17]. (The situation is of course different for melts with a low conductivity at high purity, such as zinc chloride. ) Their first suggestion is thus a misunderstanding. Furthermore, WC are convinced that the other two suggestions are. at most. of marginal importance for the quoted conductivity studies. Of course one must be aware of the fact that there are different qualities of quartz. etc.
] IX. 191, Kim and Simkovich report a “cation transport number” determined by a method which has been used successfully for ion conducting polymers [ 201. Their obtained cation transport number is very close to unity, and they claim (at least indirectly) that the transport numbers are negligible in pure molten Na,SOJ for “the possible anion species”. From this result it seems that they actually have had the sulphate ions as reference frame relative to which the transport number of sodium ions is unity by definition. It might bc illustrative to compare existing caperimental data on transport numbers and mobilitics in molten salts with solid electrolytes. For the high-conductivity fee phase of LiZSO, the cation transport number was found to be unity within experimental error for the whole studied range 873 K to 1063 K [2l 1. In contrast to this. all experimental evidence available indicates that both cations and anions arc mobile in molten salts. Thus. this has been found for studies of clectromigration as well as of self diffusion. Several types of electromigration experiments ha\,e been performed over the years. If we limit the discussion to isotope effects in pure salts, it has been found for cations [ 221 as well as for anions [ 13 1. that a light isotope is slightly mote mobile than a heavy one. The phenomenological treatment developed by Klemm [ 24,251 is very suitable for discussing transport properties of molten salts for which the electrical conductivity and both diffusion coefficients (II ’ and D ) have been measured. It follows from calculations of friction coefficients. etc. that both cations and anions are mobile in nitrates [ 261, halides [ 271 and carbonates [ 281. It one defines the cation one obtransport number as I + =I>‘/(D’+llY) tains I + =0.64 for Na,COi at I I73 K.
3. Transport
4. The validity of the Nernst-Einstein
numbers
and ionic mobilities
in molten
relation
salts
The concept of transport numbers in molten salts was an important issue in the late 50s and early 60s. The question of reference frame is not as obvious in a melt as in a solid phase, and one must distinguish between internal and external ionic mobilities, which has been demonstrated very clearly by Klemm
Kim and Simkovich have calculated a cation self diffusion coefficient from the Nernst-Einstein equation. However. it must be remembered that the ion transport processes in a melt are completely diffcrent from the situation for which the Nernst-Einstein equation is derived. It is thus not surprising that calculated self diffusion coefficients nearly always turn
A. Lund&. B.-E. Mellander /Molten sodium sulphate
out to be lower than experimentally determined ones [25-281. To our knowledge no self diffusion experiments have been performed on any sulphate melt. If one assumes that the conductivity is of the order of 2.3 S/cm, and that the cation transport number lies between 0.6 and 0.8 a Nernst-Einstein calculation gives 4.8~10~~ to 6.5~10~~ cm2/s for D+ at 1173 K, which fits much better with data for other sodium salts than the 8.1 x 1OC6 cm’/s obtained by Kim and Simkovich. It might be of interest in this connection to mention that the assumptions underlying the Nernst-Einstein relation neither are valid for solid electrolytes [ 29 1, For solid sulphate electrolytes the calculated self-diffusion coefficients are larger than the measured ones [ 301, i.e. the tendency is opposite to the case of molten salts.
5. Final conclusion There is reason to reconsider the interpretation the study of molten sodium sulphate performed Kim and Simkovich.
of by
References [ 1] M. Faraday, Philos. Transact. ( 1833) 507. [2] K. Amdt. Z. Electrochem. 12 (1906) 337. [3] G.J. Jaw, F.W. Dampier. G.R. Lakshminarayanan, P.K. Lorenz and R.P.T. Tomkins, NSRDS-NBS I5 (Natl. Bureau of Standards. Washington, 1968). [ 41 G.J. Jam, U. Krebs, H.F. Siegenthaler. R.P.T. Tomkins, G.L. Gardner, C.B. Allen, J.R. Downey and SK. Singer, J. Phys. Chem. Ref. Data 1 (1972) 581; 3 (1974) 1; 4 (1975) 871; 6(1977)409:8(1979)125;9(1980)791;9(1980)831; 12 (1983) 591. [ 51 G.J. Jam and N.P. Bansal, J. Phys. Chem. Ref. Data I I (1982) 505. [6] D.-H. Kim and G. Stmkovich. Solid State Ionics 45 ( 1991 ) 165.
129
[ 71 A. Kvist, Z. Naturforsch. 22a ( 1967) 467. [ 81 A.-M. Josefson and A. Kvist, Z. Naturforsch. 24a ( 1969) 466. ]9 1K. Matiasovsky, V. Danek and B. Lillebuen, Electrochem. Acta 17 (1972) 463. ]lO M.A. Careem and B.-E. Mellander, Solid State Ionics 15 (1985) 327. ]‘I 1A.F. Polishchuk. T.M. Shurkhal and N.A. Romashchenko. Ukr. Khim. Zh. 39 (1973) 760. ]12 A. Lund&t. Solid State Commun. 65 ( 1988) 1237. ]13 1A. Lunden and M.A.K.L. Dissanayake, J. Solid State Chem. 90 (1991) 179. (14 P.W.S.K. Bandaranayake and B.-E. Mellander, Solid State lonics 26 ( 1988) 33. ]15 P.W.S.K. Bandaranayake and B.-E. Mellander. Solid State Ionics40/41 (1991) 31. ]16 A. Kvist, Z. Naturforsch. 2la (1966) 1601. [ 171 A. Lund&t, A. Bengtzelius. R. Kaber, L. Nilsson, K. Schroeder and R. Tameberg. Solid State lonics 9/ 10 ( 1983) 89. [ 181 A. Klemm, in: Molten Salt Chemistry, ed. M. Blander (Interscience. New York, 1964) p. 535. [ 191 A. Klemm. in: Advances in Molten Salt Chemistry 6, eds. G. Mamantov and C.B. Mamantov (Elsevier, Amsterdam, 1987) p. 1. [20] D.F. Shriver. S. Clancy, P.M. Blonsky and L.C. Hardy, in: 6th Riser Int. Symp. on Met. and Mat. Science, eds. F.W. Poulsen, N. Hessel Andersen, K. Clausen, S. Skaarup and 0. Toft Sorensen (1985) 353. [ 2 I ] A. Lund&, Z. Naturforsch. 17a ( 1962) 142. [ 221 A. Klemm, H. Hintenberger and P. Hoemes, 2. Naturforsch. 2a ( 1947) 245. [23] A. Klemm and A. Lunden, Z. Naturforsch. 10a ( 1955) 282. [24] A. Klemm, Z. Naturforsch. 8a (1953) 397. [ 251 A. Klemm, Z. Naturforsch. 15a ( 1960) 173. [26] A. Lunden, Z. Naturforsch. 15a (1960) 1019. [ 271 C.-A. Sjoblom and A. Lunden. Z. Naturforsch. 18a ( 1963) 942. [ 281 P.L. Spedding and R. Mills. J. Electrochem. Sot. 112 ( 1965) 594. [ 291 G.E. Murch, Solid State Ionics 7 ( 1982) 177. [ 301 A. Lunden, and J.O. Thomas, in: High Conductivity Solid Ionic Conductors, ed. T. Takahashi (World Scientific, Singapore, 1989) p. 45.