Thermodynamics of corrosion in fused sulphates

Corrosion Science, 1968, Vol. 8, pp. 393 to 404. P e r g a m o n Press. Printed in Great Britain

THERMODYNAMICS OF CORROSION IN FUSED SULPHATES* G. BOMBARA, G . BAUDO a n d A. TAMBA Centro Sperimentale Metallurgico, Roma, Italia Abstract--Thermodynamic diagrams have been constructed for Fe in contact with Li2SO4-K2SO4 eutectic at 600°C. In these diagrams, which are similar to those produced by Pourbaix for aqueous systems and Littlewood for fused chlorides, equilibrium potentials (relative to a conventional reference electrode) are plotted against the activity of oxide ion pO 2-. The regions outlined the corrosion and immunity of Fe in relation to the redox and acid-base conditions of the melt. R~sum~-Analoguement au traitement de Pourbaix pour les syst~mes aqueux et de Littlewood pour le chlorures fondus, les diagrammes thermodynamiques ont et6 obtenus pour le fer en contact avec l'eutectique Li2SO4-K2SO4 ~t 600°C. Les potentiels d'6quilibre dans ces diagrammes sont exprim6s en fonction de l'activit6 du Fe oxyde pO 2-. Les domaines de corrosion et d'immunit6 pr6voyables du fer par rapport aux conditions redox et acide-base dans le moyen fondu sont 6tablis. Zusammenfasstmg--Ahnlich der Pourbaix-Behndlung ffir die wfisserigen Systeme sowie der Littlewood Behandlung fijr die geschmolzenen Chloride werden die thermodynamischen Schaubilder des Eisens in Bertirung mit dem Eutektikum Li2SO~-K~.SO4bei 600 ° konstruirt. Bei diesen Schaubildern sind die Glechgewichtspotentiale (auf eine konventionelle Verglechselektl ode bezogen) in Abhiingigkeit yon der T~itigkeit des Oxyd-Fe pO 2- gelegt worden. Es werden die Bereiche einer voraussichtlichen Korrosion und die Immunitfit des Eisens in Bezung auf die Redox-Verhiiltnisse und Siiure-Base des geschmolzenen Mittels bestimmt.

INTRODUCTION AS OUTLINED in a recent review on c o r r o s i o n in m o l t e n salts, a research on p r o p e r t i e s o f fused salts has b e c o m e i m p o r t a n t 2,3,4 because o f their a p p l i c a t i o n s as c o o l a n t s in nuclear reactors, h e a t transfer liquids, a n d r e a c t i o n m e d i a for chemical 5 a n d electroc h e m i c a l processes, e A m a j o r p r o b l e m is steam generation by large boilers, where, owing to the alkali salts c o n t a i n e d in fuels, low-melting d e p o s i t s o f c o m p l e x sulphates 7,s f o r m u n d e r n o r m a l o p e r a t i n g c o n d i t i o n s o n super-heater tubes; these deposits cause a high rate o f attack. Effective remedies, either by c h a n g i n g the o p e r a t i n g c o n d i t i o n s or by selecting suitable materials, require a s o u n d knowledge o f the c o r r o s i o n processes. Hence, there is need o f m o r e basic research into the electrochemistry o f m o l t e n salts, p a r t i c u l a r l y sulphates, a n d into their reactions w i t h metals. A n electrochemical treatment, indeed, seems to be quite a p p r o p r i a t e , because o f the very low p o l a r i z a t i o n o f (hight e m p e r a t u r e ) electrode reactions in fused salts in c o m p a r i s o n with those in a q u e o u s solutions. M e t a l - f u s e d salt systems have been m u c h less investigated t h a n a q u e o u s o r high*Manuscript received 9 October 1967. 393

394

G. BOMaAgA, G. BAUDO and A. TAMBA

temperature gas systems. Most of the works carried out concern weight loss experiments under particular conditions, 9,re or measurements of potential differences between metal electrodes and redox electrodes tl in order to establish the equilibration of the metal with the melt. Thermodynamically, fused chlorides have been much more extensively treated ~2,t s.t4 than any other molten salt, because of the particular industrial interest in the less common metals produced via their halides. Corrosion in molten sulphates has been extensively studied at Southampton ~5 and at Leatherhead ~6 under the sponsorship of the British Central Electricity Generating Board, and this work has been recently reviewed, t7 In this paper a simplified thermodynamic treatment is presented for the binary eutectic of Li2SO4 and KzSO4 (80-20 mole ratio) in relation to Fe corrosion. PROPERTIES

OF MOLTEN

SULPHATES

Fused sulphates may be classified as simple oxyanionic liquids like nitrates and carbonates. The melts consist predominantly of free ions, are thermally stable and have low vapour pressures, high thermal and electrical conductivities, and low viscosities, ts The alkali salts are electrochemically the most stable of fused sulphates, although the limiting electrochemical processes for them are much more complicated than for halides. Indeed, because of the high oxidation level of S in the oxyanion, the latter undergoes cathodic reduction before the metal cation may be discharged. Oxyanionic melts contain oxide ions that are anodically oxidizable to O gas, but as compared with aqueous solutions an essential difference is the absence of protonbearing ions, the oxide ion 02- and its derivatives being of major importance and the function pO ~- replaces pH. With regard to corrosion, another significant difference from aqueous systems lies in the possibility of direct dissolution without oxidation of the metal by a simple solubility mechanism similar to that of attack by liquid metals. However, with a few exceptions, metals appear to be appreciably soluble only in their own salts, so these effects can be normally neglected; an exception is where the melt is allowed to become rich, via corrosion, in salts of the metal involved. Nevertheless, too little information on metal-solubility is available and only corrosion with oxidation will be considered.

Acidity definition Aqueous corrosion has been exhaustively treated from the thermodynamic point of view by Pourbaix. 19 In order to construct thermodynamic diagrams for molten salts it is necessary to define a non-protonic function that gives a measure of the acidity of the melt. In accordance with the views of Lux 2° and Flood, 2t the dissociation of oxyanions, such as SO42+, NO~ and CO32-, or of oxides, such as MgO, leads to definite acid-base equilibria SO~- ~ SOs + 0 ~NO~NO~ + 0 ~C032- ~ C02 + 0 ~M g O ~ M g ~+ + 0 2 -

Thermodynamics of corrosion in fused sulphates

395

all of which can be expressed by the equation base ~---acid + 0 2-

(1)

and by the equilibrium constant K = (acid). ( 0 2-) (base) It can be assumed, as a measure of the acidity of an oxyanionic melt, the function pO 2- = -- log ( 0 2-) a high value of which will characterize an acid melt, whilst a low value will characterize a basic one. The two functions, p O 2- and p acid ( = - - l o g (acid)), are obviously linked together by the relationship p O 2- + p acid = p K that results from assuming (base) = 1 in the equilibrium (I). There is a plain analogy with aqueous media, in which pH +pOH

=pKw

In order to determine directly the actual acidity by electrometric methods, an electrod e reversible to oxide ions is required, i.e. an electrode whose potential is an unequivocal function of 0 2- activity according to the Nernst equation. A number of O and oxide electrodes have been tested in fused salts and have been found to be suitable electrodes for 0 2-22,23 and in favourable oxyanionic melts like sulphates, the electrode reaction of O is not appreciably disturbed by formation of peroxide ions x

½ O2 + 0 2- ~ O,2whose equilibrium is strongly displaced to the left.

Stability and redox potential As for aqueous systems, free energies* may be expressed as equilibrium potentials by the relation E ° = -- AG°/ZF. * The equilibrium potential in a sulphate melt is a function of the activities of reducible and oxidizable species resulting from the acid-base dissociation of the oxyanion,

SO~- ~ SO3 + 0 2(2) *The activities of molten phases are based on the pure component as the standard state, while for eutectie mixtures the standard state may be assumed as that of the predominant component. For gaseous phases, an ideal gas at one atmosphere pressure is taken as the standard at unit activity.

396

G. BOMBARA,G. BAUDOand A. TAMBA

whose equilibrium constant may be determined by considering the dissociation as, M2SO40iq. ) ~

SO a --{- M200iq. )

and, K = (M20). (SOa).

(M2SOD If (M2SO4) ----- 1 and the melt is completely ionic, i.e. M 2 0 is also completely dissociated, K = ( 0 2 - ) . (SO3)

and the equilibrium for reaction (2) may be expressed by pO 2- -- log Pso8 = -- log K. For the representative Li2SO4-K2SO4 eutectic, assuming that the heat of mixing of the two sulphates and corresponding oxides is zero (as for ideal mixtures) an equilibrium constant K = 10-2o at 600°C may be calculated from the available thermodynamic data. 24 Thus pO 2 -- log Pso3 = 20.

(3)

The two half reactions involving the active species 02- and SOa, which determine the redox potential, are 02- ~ ½ 02 + 2e-

(4)

and, in accordance with the suggestions of Burrows and Hills iv SO a + 2e- ~ SO2 + 0 2- .

(5)

The overall reaction determining the melt stability is given by the sum of (4) and (5) SOa ~- SO2 + ½ 02.

(6)

This is the dissociation of SOa into the reducing species SO2 and the oxidizing species 02 and an equilibrium constant of 10-°, 98 _~ 10-I at 600°C may be calculated ~ for it. log pso, _ ½ log Po3 = 1.

(7)

PSO~

The potentials for the half reactions (4) and (5) are given by the Nernst equations RT

RT

Eo2 ---- Eo2 + 2.3 ~-~ log Po2 + 2.3 -2-FP

O~" -,

(8)

Thermodynamicsof corrosion in fused sulphates Eso, = Eso~ q- 2.3 RT log Pso3 q_ 2.3 RT ^22---F Pso, -fFP°

397

(9)

It is necessary to define a zero potential and a convenient reference scale of potentials, closely resembling that suggested by Ingrain and Janz 25 for molten carbonates, may be obtained by considering the oxidation of the sulphate ion SO42- -- 2e- ~ SOs + ½0z which, since (SO42-) = I, gives the following expression for the redox potential

RT RT E -----E ° -1- 2"3 - ~ log Pso3 + 2"3 ~-~ log Po~. It may be assumed that this potential equals zero for a stoichiometric mixture of SOs and O3 at 1 atm total pressure, i.e. when (SOs) : (02) = 2 : 1. Substituting the appropriate values in the above equation becomes E -~ 0"0359 + 0"0866 log Pso~ + 0"0433 l o g p o y from which, considering also the equilibrium (3), the final expressions for O~ and SO2 electrode potentials are Eo2 = -- 1"6961 + 0"0866 pO 2- + 0"0433 log po, V

(10)

Eso2 = -- 3-5147 -k 0"1732 pO z- -- 0"0866 log Pso~V

(11)

Equations (10) and (11) express the equilibrium potential of the system in terms of the acidity, activity of the oxidizing component Oz (anodically producible) and of the reducing component SO2 (cathodically producible). By plotting E vs. pO 2-, two systems of parallel straight lines are obtained (Fig. 1) with different slopes: 86-6 mV/pO ~- unit for lines at constant partial pressure of 02 and 2 × 86.6 mV (i.e. 173.2 mV) for lines at constant partial pressure of SOz. The domain of thermodynamic stability of the sulphate melt at I atm. total pressure is that included by the lines corresponding to unit pressure of SO2 and 02, respectively. Below the line Pso22 = 1, SO3 will be reduced to SO2, while above the line Po2 = 1,02 will evolve so leading to an increase ofpO 2-, i.e. to a more acid melt. While there is no doubt about the upper limit of stability (Po, ---- 1 attn.), the lower limit (Pso~ = 1) strictly results from having assumed reaction (5) (towards the right) as the primary cathodic process. If the cathodic reduction could proceed down to S or S"- or even to the cation discharge, the stability region would become larger because of the lower position of the corresponding limiting line. Although there is a strong evidence15,2e for the occurrence of reaction (5), the particular cathodic reaction which must be assumed as the actual limiting process in any particular sulphate system is still a matter of experimental investigation.

G. BOMBARA,O. BAUDOand A. TAMBA

398 20

15

10

5

0 0

-0'5

-1

-1

-1'5

-Z

-2 0 > LLI -2"5

-3

-3" 5'

20

Fro. 1.

pO 215

10

5

0

E / p O =- diagram for Li=SO4-K=SO4 eutectic at 600°C.

Each point within the region of stability indicates a definite equilibrium potential for a given acidity level of the melt, the partial pressure of SO2 and O, determining the equilibrium at that point being given by the lines intersecting in it. From the diagram it appears also that the potential range within which the melt is stable at any acidity strongly narrows as the acidity increases. In principle there are no limits to variation in the acidity. However, some limitations appear for extreme conditions, such as for log Psos = -- 20, i.e. pO 2- = O. This condition is obviously an upper limit for the acidity of the oxide ion, above which this treatment loses its value, since to take pO 2- = O is inconsistent with the assumption (SO~) = 1 made for equilibrium (3). Furthermore, pO 2- = O implies that (SO~-) = (O2-) which is actually the maximum basicity of the melt. With regard to the cation of the fused sulphate, its influence is clearly accounted for by the value of the equilibrium constant in equilibrium (2), i.e. through the value of the standard free energy of formation of 02- in any melt. The higher this value, the lower the relative acidity of the cation, with a consequent displacement of equilibrium (2) to the loft and an enlargement of the acid-base range.

T h e r m o d y n a m i c s of corrosion in fused sulphates 20

I

10

399

5

0

-0 5 - ¢aO"

-1

\'qo..~. "x~,~

0%,

-1.5

-2

--

>o

iii

*%.,

\\-,

-2.5-

-3

-3'5.

pO i

i

i

n

i

20

15

Fio. 2.

2-

i

f

r

lo

i

t

i

5

A c i d - b a s e a n d redox neutrality.

Neutrality concepts (Fig. 2) As for aqueous systems, it is possible to define the conditions for acid-base neutrality and redox neutrality. The former is AO + 0 2- ~ AO~-

with an equilibrium constant given by X,,=

(AO~-)

(14)

( a o ) (02-) . In the case of a basic oxide, this has a tendency to lose oxide ions according to the reaction AO ~ A 2+ + 022-

with an equilibrium constant Ks = (A2+) (02-)

(AO)

(15)

400

G. BOMBARA, G. BAUDO and A. TAMBA

The constants (14) and (15) give a measure of the acidity and the basicity, respectively, of the oxide AO. Remembering now that the condition for acid-base neutrality in the binary eutectic is given by pO ~- = 10 let us consider the case in which, starting from an initially neutral melt, a value pO ~- > i0 is required. To this end, the melt must be saturated with an acid oxide, such as SiO2 or V205, so that (AO) ---- 1 in equation (14). Since, (AO~-) -----(O2-)i~iti~ -- (OZ-)~nal -----10-1° -- (O2-), neglecting the unit compared to K~, from equation (14) the following expression of the final acidity is obtained, pO z- = 10 -t- log Ka = 10 -- pKg.

(16)

Analogously, saturating the melt with a basic oxide, such as MgO, CaO or ZnO, the activity of AO may be assumed to be unity in equation (15) and since ( A 2+) = ( 0 2-) - - (O2-)initial = ( 0 2-) - - 10-10

neglecting the product (02-) . (O2-)initial, from equation (15) the expression of the final acidity is obtained for the case of a basic oxide pO z- = ½p Kb

(17)

If an acid value for the inital pO 2- is required, this may be obtained by adding an acid oxide for which log Ka > O (equation (16)), i.e. Ka > 1. A basic pO 2- may be obtained in the binary eutectic with a basic oxide having pK b < 20. It is apparent from the above that the materials of which the experimental containers are made may significantly affect the acidity of the melt. With regard to the buffering of pO 2- changes in sulphate melts, this may be obtained in the acid range by staturating the melt with both the acid and basic components (equilibrium (14)) of an acid oxide. Since the activities of these two species in the melt are constant, then (02-) will be constant. Any production of ions O 2-, for instance by corrosion reactions, will be buffered by the precipitation of the basic component and the simultaneous dissolution of the acid one. In the basic range the melt will be buffered with a basic oxide and its salt. Since in the solubility product (equation (15)) the activity of the cation is constant owing to constant activity of its salt, the activity of 02- will be constant. Any production of 02- will be buffered through oxide precipitation and cations dissolution. In this case too, the acid component undergoes dissolution, whereas the basic one precipitation.

Fe corrosion (Fig. 3) The E/pO 2- diagram of the melt provides the basis for defining the conditions of

Thermodynamics of corrosion in fused sulphates

401

thermodynamic stability of reaction products between the components of the melt and a metal in contact with it. The stability domain of the fused sulphate may be divided into three regions at least, each corresponding to the presence of one metal phase at unit activity: the metal sulphate, the metal oxide (plus the metal), and the metal alone. More than three phases (and respective stability regions) obviously must be considered if the metal is involved at more than one oxidation level. For Fe, considering for simplicity only the ferrous state, the phases are: FeSO4 (i.e. FeS+), FeO and Fe. In the Fe domain, Fe metal at unit activity will be in equilibrium with its ions Fe s+ according to the half reaction Fe ~ Fe z+ + 2e-,

(18)

EF~2+/F~ = Ev~S+lr ~ + 0"0866 log (FeS+).

(19)

and at 600°C

In order to calculate the standard potential Er~Z+/r,, let us consider the reaction Fe + SOs (-~ atm.) + ½ 02 (~ atm.)

(20)

in which the free energy involved is equivalent to the standard one of reaction (18), since, in accordance with the assumption made for the zero potential, the fr~e energy of formation of SO8 and 02 in the activity ratio 2 : 1 (from the fused sulphate at unit activity) must be taken as zero. From available thermodynamic data ~a AG = q-69.60 kcal at 600°C may be calculated for reaction (20). Hence

--E~2+IF~ ---=

AG° 2F

-- -- 1"5088 V

and equation (19) reduces to

EF¢s+IF~ = -- 1"5088 + 0"0866 log (FeS+).

(21)

By means of this equation isoactivity lines for the ion Fe s+, parallel to the pO s- axis, i.e independent of the acidity of the melt, may be plotted (Fig. 3). The boundary between the area of stability of Fe and that of Fe 2+ is given by the horizontal line E = E~Z+/v. = -- 1"5088 V. This line for standard of Fe potential is well below the lower stability limit for sulphate melts with high pO z-, so that Fe can never achieve equilibrium in this highly acid medium. The boundary between Fe z+ and FeO areas is defined by the conditions: (Fe 2+) = 1 ; (FeO) = 1. The activities of these two phases are interrelated through the solubility product of FeO, (FeS+) " (02-) = Ksp

(FeO)

402

G. BOMaAgA,G. BAUDOand A. TAMBA

that, when (FeO) = (Fe 2+) = 1, reduces to p O ~- = pK~p. 15

20

0

10

.-10 - 0'5

'o

_1 1 -1-5 •

-~p

-1 ( F e a']. 1

i

03 4-s

~. Fe~'~ =

FeC

-2

_.

0 > -2,!5

LId

~

-31 •

-3

-3"5

T

p O a-

FIG.

3.

i

i

i

r

i

10

15

20

E/pO ~- diagram for the system Fe-binary eutectic at 600"C.

Hence the boundary between Fe 2+ and FeO areas is given by a line, parallel to the E axis, whose position is determined by the solubility product o f the oxide. K~p may be calculated ~a as follows Fe + 42 02 ---- FeO Fe = Fe 2+ + 2e ½0~+2e-=O 3-

AG~o, 6o0.c = -- 49.00 kcal AG~¢~+,6oo.c = - - 69.60 kcal AG°o L, 6o0.c = + 78.24 kcal.

The overall reaction FeO ~ Fe 2+ + O zbeing at the equilibrium, implies a free energy change equal to zero. Thus AG~= o = AGF=~+ + 2.3 R T log (Fe 2+) + AGo 2- + 2.3 R T log ( 0 2-)

Thermodynamics of corrosion in fused sulphates

403

and substituting values for 600°C -- log [(Fe ~+) . (OZ-)] = pKsp = 14.43 Therefore, the boundary line Fe~+/FeO will be at pO ~- = 14.43. This means that below pO z- = 14.43 the phase FeO precipitates from pure FeSO4. In the domain of stability of FeO, FeO at unit activity and Fe 2+ and 0 2- are present with the activities of the latter related by the solubility product, according to log (Fe z+) = -- 14.43 + pO z-

(22)

This equation defines vertical lines of isoactivity of ion Fe z+, independently of the redox potential. In the diagram, the boundary between FeO and Fe regions will be given by the coexistence of these two phases at unit activities. On the boundary both relationship (21) and (22) must be fulfilled, as to obtain E = -- 2.7584 + 0"0866 pO z-. This is the equation of the boundary line Fe/FeO, that is parallel to the straight lines corresponding to constant partial pressures of Oz. The Po, at the boundary is that of dissociation of FeO at 600°C, i.e. 10-24.58 atm.

CONCLUSIONS Diagrams like that shown for iron may be constructed for any metal. They give a clear picture of all redox and acid-base equilibria involved in sulphate systems. The main usefulness of the diagrams is that they outline the conditions for corrosion or possible immunity of a metal. Similarly to aqueous systems, 19 the assumption of metal corrosion when the equilibrium concentration of its ions is greater than 10-e M may be conveniently adopted also for sulphate melts (Fig. 3). However, it must be pointed out that the stability of the metal-oxide in the particular region does not mean that passivation occurs. In this area corrosion leads to the formation of an insoluble (or less soluble than 10-6 M) product, but passivation will depend on a number of properties of the oxide film, mainly adherence and coherence. Similar conditions apply to the passivezone in aqueous systems. The diagram for Fe shows that in presence of an 02 atmosphere Fe undergoes corrosion, passivation being theoretically possible only in basic melts. Nevertheless, the only method of preventing Fe corrosion completely seems to be cathodic pro tection by polarizing the metal down to potentials within the immunity region. The txeatment reported, being thermodynamic, is subject to the relative reservations. However, owing to the high reaction and equilibration rates at the temperatures involved in fused salts, these diagrams actually approach the real conditions much better than those for aqueous media. At least, they provide a useful means for wellgrounded predictions about the reactivity of a metal with a sulphate melt under given redox and acid-base conditions.

404

G. BOMBARA,G. BAUDO and A. TAMBA

Acknowledgement--The authors wish to thank Italsider S.p.A. for the permission to publish this paper. REFERENCES D. INMAN and N. S. WRENCH, Br. Corros. Jnl 1, 246 (1966). M. BLANDER, Ed., Molten Salt Chemistry. Interscience, New York (1964). B. R. St,'~X~FEIM,Ed., Fused Salts. MeGraw-I-Iill, New York (1964). Yo. K. DEUMAV,S~X and B. F. MARKOV, Electrochemistry o f Fused Salts. Translated Sigma Press, Washington (1961). 5. W. SUNDERMEYER, Angew. Chem. 77, 241 (1965). 6. T. B. REDDY, Electrochem. Technol. 1, 325 (1963). 7. W. NELSON and C. CAIN, Trans. Am. Soc. mech. Engrs 82, 194 (1960). 8. A. RAHMEL, Arch. EisenhiittenW. 31, 59 (1960). 9. G. J. JANZ, A. CONTE and E. NEUENSCHWANDER, Corrosion 19, 292 (1963). 10. G. J. JANZ and A. CONTE, Corrosion 20, 237 (1964). 11. R. LIrrLEWOOD, 1st Int. Congr. Metallic Corrosion 91. Butterworths, London (1961). 12. C. EDELEANU and R. LrrrLEWOOD, Electrochim. Acta 3, 195 (1960). 13. R. LrrrLEWOOD and C. EDELEANU, Silic. ind. 26, 447 (1961). 14. R. LrrrLEWOOD, J. electrochem. Soc. 109, 525 (1962). 15. B. W. BURROWS, Thesis, University of Southampton (1965). 16. A. J. B. CUTLER, A. B. HART and J. F. MA'rrHEWS, Laboratory Note No. RD/L/N39/65. Central Electricity Research Laboatories, Leatherhead, Surrey (1965). 17. B. W. BURROWS and G. J. HILLS, J. Inst. Fuel39, 168 (1966). 18. G. J. IANZ, A. T. WARD and R. D. REEVES, Molten salt data. Renssalaer Polytechnic Institute, U.S.-AFOSR No. 63-0039 (1964). 19. M. POURBAIX, Thermodynamics o/" Dilute Aqueous Solutions. Arnold, London (1949). 20. H. Lt~x, Z. Elektrochem. 45, 303 (1939). 21. H. FLOOD and T. F6RLAND, Acta chem. Scand. 1, 592 (1947). 22. H. FLOOD, T. F/)RLAND and K. MOTZFELDT, Acta chem. Scand. 6, 257 (1952). 23. A. M. SHAMS EL DIN, A. A. EL HOSARY and A. A. A. GERGES, J. electroanal. Chem. 6, 131 (1963). 24. O. KUBASCHEWSKXand E. L. EVANS, Metallurgical Thermochemistry. Pergamon Press, London (1958). 25. M. D. INGRAM and G. J. JANZ, Eleetrochim. Acta 10, 783 (1965). 26. C. H. LIu, J. phys. Chem. 66, 164 (1962). i. 2. 3. 4.