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The electrical double layer in molten halides
ELECTROANALYTICAL CHEMISTRY AND INTERFACIAL ELECTROCHEMISTRY Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands
283
THE ELECTRICAL DOUBLE LAYER IN MOLTEN HALIDES
E. A. U K S H E AND N. G. B U K U N
New Chemical Problems Institute, Academy of Sciences, Moscow (U.S.S.R.) (Received 21st September 1970; in revised form l l t h March 1971)
The problem of structure and properties of the metal/salt melt interface has recently attracted the attention of numerous investigators 1,2. Significant information on this question may be obtained in two different ways : (a) by measuring the capacitance when the nature and composition of the metal and salt phases, temperature and electrode potential are varied but the a.c. frequency remains fixed ; (b) by studying the effect of frequency on the electrode capacitance and resistance. We have previously investigated the fixed-frequency capacitances of the stationary liquid and solid electrodes in molten alkali and alkaline-earth metal halides 3-11. The results of our work may be summarized as follows : 1. The capacitance of the electrode/alkali halide interface depends significantly on a.c. frequency 3. However for sufficiently large frequencies (above 20 kHz) this dependence becomes small enough and thus this measured capacitance may be considered to differ insignificantly from the double-layer capacitance. 2. The capacitance of the electrode/alkali (or alkaline-earth) metal halides interface depends on the electrode potential. In most cases C-E curves are close to parabolic with a pronounced minimum, but for some systems (Pb/LiCI~CsCI, Pb/NaC1-CaC12, Ag/NaC1-KC1, etc.) the symmetry of the capacitance curves is broken and a step or even a second minimum appears on the cathodic branch 7-9. 3. The potentials of the minimum capacitance (Emin) have been found to be very close to the p.z.c. (electrocapillary maximum) of metals in LiC1-KC1 and NaC1KC1 molten mixtures. 4. The minimum capacitance (C~,~n)rises significantly and C-E curves become narrower as the temperature increases. The dependence of Cmi, on temperature however is not linear and practically disappears as the temperature approaches the melting poin¢ °'11. The absolute values of Cmi n for the lead electrode were 20-70 #F cm -2, depending on temperature and the nature of the melt 7. To explain these high capacitance values it has been suggested that the melt side of the double layer has the alternating sign structure. In the terms of this hypothesis the effect of temperature, d.c. potential and the nature of melt on the capacitance can be qualitatively inferred 7'12-14 In 1964-69 Delimarskij and Kikhno 15'16 undertook the study of the capacitance of some solid metals which had not been investigated before. They have practically confirmed all the regularities enumerated a'. * Recently Alekseeva and Kuznetsov (Elektrokhimiya 4 (1968) 95, 1351) have found systems where the potential of Cm~n does not coincide with the p.z.c, and the value of Cmln is not independent on the nature of the metal.
3. Electroanal. Chem., 32 (1971) 283-291
284
E.A. UKSHE,N. G. BUKUN
Recently Heus et al. 17 and Beck and Liftshits 18 have published the results of their investigations on the capacitance of liquid electrodes in halide melts. Beck and Liftshifts, as well as the authors of this article, have measured the capacitance of lead and some other stationary electrodes in molten LiC1-KC1 (450°C) and NaC1KC1 (800°C). They have found the minimum capacitance for both systems to be 25___5 #F cm-2 and that it depends weakly on temperature and the nature of melt. Heus et al. have studied the capacitance of the dropping electrode in fused LiC1-KC1. The measured capacitance was established to be practically independent of temperature in the range 390-480°C and to be approximately 30/~F cm-2. The results of Beck and Liftshifts will be discussed later. As to the small dependence of the measured capacitance on temperature in Heus' work it does not appear to contradict our observation lo because the effect of temperature on the measured capacitance has been shown to be almost exponential and to approach a constant as temperature decreases. Thus for the eutectic mixture LiC1-KC1 near the melting point the temperature dependence of the capacitance must disappear. However the experimental data obtained some years ago 3- ~~ do not concern pure double-layer capacitance since measured capacitance and resistance of the electrodes in fused halides depend on the a.c. frequency. In order to clear up the difference between the double-layer capacitance and the measured capacitance we have compared the results of double integration of the capacitance curves and the electrocapillary curves obtained under the same conditions. The agreement was quite good, at least for those cases when the capacitance curves were close to parabolic 5,19,20. The results are in favour of a small difference between the double-layer capacitance and the measured value irrespective of polarizability of the electrode, since Lippman's equation -do/dE=Q
(1)
as well as the equation for double-layer capacitance Cd,=dQ/dE
(2)
include the full charge of the electrode. This full charge is
Q=q+nVr
(3)
where q is the free charge and F is the Gibb's adsorption of the electroactive ions (or the electroactive atoms in the metal alloy). This feature has frequently been discussed in the literature and recently has been clearly demonstrated by Frumkin et al. in their fundamental work 21. The agreement between the capacitance and electrocapillary curves confirms that the measured capacitance is close to that of the double layer and depends on the potential in a similar way. Nevertheless even with relatively small dispersion of the measured capacitance in the frequency range above 20 kHz, it differs from the true double-layer capacitance owing to the non-ideal polarizability of electrodes in fused halides. Therefore it is desirable to determine Cd~ for liquid metals more accurately. Such a determination has been attempted by Beck and Liftshifts18. In the case of a liquid electrode, its surface is formed by the metal meniscus in the glass tube. Therefore the capacitance and resistance dispersion may be due to screening of the metal surface by the tube walls or to creeping of the electrolyte between J. Electroanal. Chem;, 32 (1971)283-291
THE ELECTRICALDOUBLELAYERIN MOLTENHALIDES
285
these walls and the metal. This is why Beck and Liftshifts18have used stationary liquid electrodes with a large diameter (about 4 mm). The dispersion observed under these conditions has been explained exclusively as due to shunting of the double layer by the faradaic impedance. To calculate the double-layer capacitance from series capacitances and resistances (Cs, Rs) measured at 19-20 kHz they used the formula Cd~ = [(coC~)-1 - Rs]/eo[1/(e)C~) 2 + R 2]
(4)
This formula may be readily obtained if we suppose the behaviour of the electrode to be described by the equivalent circuit in which the double layer is shunted only by the Warburg impedance Zw = (1-j)a/co ~
(5)
However more detailed studies carried out in our laboratory have shown that the problem cannot be solved in this simple way. Special measurements have confirmed that the dispersion of the capacitance and resistance depends on the tube diameter 2z, but this dependence becomes unimportant for tubes of sufficiently large diameter (more than 5 mm) and for not too low frequencies (above 500 Hz). Yet such large stationary lead electrodes in fused halides cannot be described by a simple equivalent circuit (Fig. la). This can be shown if we represent the impedance of the electrode by means of parallel capacitance and resistance (Cp, Rp). Then taking eqn. (5) into account we obtain
Ra Fig. 1. Equivalentelectrical circuits.
if0 ~' t40 u- t20
~t00 Q:~ 80
eo -o. 40 20
10a to-Vz/sv2
Fig. 2. Plots of Cp and l/ogRp vs. co-~ for Pb/NaC1-KC1(1:1) at 717°C. (O) Cp (V) 1/o~Rp at E= -0.55 V ; (0) Cp (!?) 1/CORpat E= -0.70 V. Here and in the other figures the referenceelectrode is Pb/2.5 molto PbC12+ base electrolyte. J. Electroanal. Chem., 32 (1971) 283-291
286
E.A. UKSHE, N. G. BUKUN Cp = Cdl + (CO~ X 2a)- 1 (~oRp)-I = (o~ × 2a)-1
(6)
where a is constant. Figure 2 shows the results of measuring the capacitance of large stationary lead electrodes in molten NaC1-KC1 (l:l) at 717°C in the frequency range 500 H z - 3 0 kHz. It is not difficult to see t h a t the experimental data are not described by eqn. (6) and some more complex electrical circuit, probably, corresponds to the lead electrode. When analysing the frequency dependence of the capacitance and resistance by the methods described in refs. 23- 25 we have come to the conclusion that the behaviour of the Pb/NaC1-KC1 system m a y be defined by the equivalent circuit shown in Fig. lb. The capacitance curves have been obtained by graphical extrapolation in Cp vs. I/a>Rp plots according de Levie 24'2s. They are close to parabolic and coincide well enough with the results obtained earlier (Fig. 3) 22.
~
sG
It.
. ~ 70 6O 5O
40 I
I
-o4
I
/
I
I
I
.~6 E/~o.s
Fig. 3. Double-layer capacitance-potential curves for Pb/NaCI-KC1 (1:1) at 700°C. (O) Calcd. Ca~,(~') measured C~ at 40 kHz.
The determination of the meniscus electrode capacitance requires knowledge of its true area. It was suggested in our early work 3-11 and in the articles of Beck and Liftshits 18 that the electrode surface area could be determined as the area of hemisphere of diameter equal to that of the glass tube. However this suggestion causes an error which increases rapidly as the tube diameter increases. The surface area of the meniscus can be estimated by means of Sugden's tables 26 giving the m i n i m u m capacitance of the lead electrode (NaC1-KC1, 700°C) as 36.8 ___1.0/~F c m - 2 , . Thus calculation of the double-layer capacitance gives results which are close to our early data 3-7, provided use is made of the modern methods of dispersion analysis 23- 25 and correct determination of the electrode surface area. The behaviour of the metal/fused salt interface in alternating current can be described by means of equivalent circuits providing the frequency independent * It should be noted here that an analogous recalculation of the data of Beck and Lifshitsla concerning Cmin for the system Pb/NaC1-KC1 gives 374-7 #F cm- 2 instead of 25 -t-5/iF cm- 2.
J. Elrctroanal.Chem:,32 (1971) 283-291
THE ELECTRICAL DOUBLE LAYER IN MOLTEN HALIDES
287
capacitance is interpreted as double layer capacitance and the shunting impedance is connected with the electrochemical reactions: • M "+ + n e ~ M Na + + e + x M ~ N a • xM and so on. This method has been used in our work for some solid electrodes in molten halides. Using the dispersion analysis in a sufficiently large frequency range for silver 27, platinum 28'29 and carbon 3° electrodes equivalent circuits formed by capacitances, resistances and Warburg impedances, have been obtained. The silver electrode has been studied in molten NaC1, KC1 and NaC1-KC1 (1 : 1) at 800°C both by changing its potential by d.c. polarization and by adding Ag + ions to the melt. In all cases the system was fairly well described by the circuit shown in Fig. la. The values of Cdl calculated according to eqn. (4) do not depend on a.c. frequency. The characteristic features of C d r E curves are the minimum, and the step on the cathodic branch. The value of Cmi, increases from KCI to NaC1. These two features were also observed in early studies v (Fig. 4). It is worth noting that the Warburg coefficient a for the equilibrium silver electrode Ag/AgC1,MC1 may be calculated according to the equation a = R T ( n F ) - 2 c - x (2D) -~
(7)
where c is concentration and D is a diffusion coefficient of silver ions which has been measured by an independent method35; these calculations are quite satisfactorily precise. However in the case of d.c. polarization, i.e. at more negative potentials 27, the measured Warburg coefficient a deviates significantly from the calculated value. The behaviour of platinum in fused LiC1-KC1 and NaC1-KC1 mixtures has been studied further with the electrode potential changed both by d.c. polarization 8G
70 I.L
50
30 f
-0.2
I
I
-0.4
I
I
-0.6
I
d~
I
-
Ely
Fig. 4. Double layer capacitance-potential curves for silver. (©) NaC1, 815°C; (xT) NaC1-KC1 (1:1), 825°C; ([5])KC1, 825°C. (O), (V), (a) points obtained by adding AgC1 to the melt. Cd, calculated by means of eqn. (4). J. Electroanal. Chem., 32 (1971) 283-291
288
E.A. UKSHE,N. G. BUKUN
and by adding PtC12. The a.c. properties of this electrode were described by the circuit shown in Fig. lb. At d.c. polarization the charge-transfer resistance 0 is negligible. On the contrary, I/~oCa ~ 0 for the equilibrium electrode. The values of Cat calculated from experimental data for the system Pt/LiC1-KC1 (460°C) are compared with values directly measured Cs (20 kHz) and with the data of Graves and Inman, see Fig. 5. These authors employed galvanostatic pulses (to 2 × 10- 7 s) for measuring dot/ble-layer capacitance 31. All the curves compared are very similar in the cathodic branches. One can see the coincidence of the positions of Emin and of the capacitance fall, which is probably connected with the incorporation of an alkali metal. The difference between our results and those of Graves and Inman for anodic potentials may arise from the difficulty in reproducing the surface conditions for platinum. Finally, the double-layer capacitance of platinum appreciably increases with increasing temperature 28. G1 90
E g0 O 60 30 4D 30 0.4 0.3 0.2 0.!
- . t -a ~-0~
E/v
Fig. 5. Capacitance-potential curvesfor Pt/LiC1-KCI,460°C. (©) Calcd. Cdl,(V) measured C, at 20 kHz, (GI) capacitance measured by Graves and Inman. The investigations of the equilibrium plati~num electrode in LiC1-KC1 (460°C) allow the double-layer capacitance at positive potentials (+ 0.88 to +0.97, V) to be estimated. In this range Ca~ increases from 95 to 170/~F cm -2 (these points are not shown in Fig. 5). Also, we succeeded in determining the charge transfer resistance 0 and the exchange current io for the reaction Pt(II)/Pt : io = (45.4_+ 8.2) c °'65 where c is the Pt(II) concentration in mol 1-1. This value conforms to the data of Laitinen et al. 32 obtained by the doublepulse method. Further, results which are of importance for the understanding of the subject in question have been obtained with the smooth carbon electrode (glassy carbon) 31. The measured capacitance of the carbon/molten salt interface practically does not J. Electroanal. Chem., 32 (1971)283-291
THE ELECTRICALDOUBLELAYERIN MOLTENHALIDES
289
80
,~ 7O U
. .60 J 5O 40 30
I
I
+L2
I
I
+0.8
I
I
*0.4-
I
I
0
ElY
I
I
-0.4
Fig. 6. Double layercapacitance-potentialcurvesfor carbon.(O)NaC1,839°C ; ( x ) KC1,796°C ; (V) NaCIKC1 (1:1), 795°C; ([~) NaCI-KCl (1:1), 703°C. depend on the a.c. frequency in the range 2-20 kHz and it may probably be considered close to the double-layer capacitance. The CaI-E curves for carbon are shown in Fig. 6. They are characteristed by the same features as those described for the capacitance curves of liquid metals. As is seen from the above, the regularities dealing with the dependence of capacitance on d.c. potential, temperature and the nature of the molten salt are due to the properties of the melt side of the double layer. The argument that Cdl increases with temperature scarcely at all and that the apparent rise was due to an inadequate analysis of the experimental data, does not seem to us to be well-founded. In any case the analysis of the impedance dispersion for platinum, silver and lead electrodes does not confirm such an assumption. On the contrary the capacitance of these electrodes remains very high at 700 ° after eliminating the frequency-dependent component. However the supposition of Graves and Inman z which explains the dependence of the double-layer capacitance on d.c. potential by the influence of the adsorption terms in eqn. (3) seems more attractive, although supplementary data should be accumulated to permit the reduction of whole capacitance change with d.c. potential to this cause only. For the present we can say that measurements of the carbon electrode capacitance are a variance with this supposition. The capacitance of the carbon electrode, as noted above, is practically independent of frequency although its dependence on the potential and temperature is very close to that for other metals. Finally we should discuss the problem of accumulating alkali-metal atoms in the surface layers of the electrodes at cathodic polarization. This possibility cannot be excluded although in our opinion Graves and Inman 2 rather exaggerate its danger. J. Electroanal. Chem,,32 (1971)283-291
290
E . A . UKSHE, N. G. BUKUN
If such accumulation were significant at potentials at which C a J E and electrocapillary curves are measured, a change of the measured components of the impedance with the time and hysteresis of the capacitance after cathodic polarization would take place. Actually such phenomena occurred only at more negative potentials, while in the range 250-300 mV around the p.z.c, they were not observed. In conclusion, it is necessary to point out an inaccuracy in Graves' article 1. This author claimed that Frumkin had discovered the "empirical" dependence between the p.z.c, of a metal in contact with electrolyte (Eq = 0) and the work function of electrons (w) E'q = 0 - - E"q = 0 ~ W ' - - w" where indexes ' and " denote different metals. This dependence is actually not empirical. It was derived by Frumkin from the fact that the e.m.f, of a cell made from two metals at their p.z.c, can differ from zero only owing to potential differences which are localized in the surface layers of metals at their contact with each other and with a solvent. Apparently, the presence of the solvent is not necessary for the existence of such potential difference, and if one neglects the fact that adsorption of the solvent dipole molecules can vary, the e.m.f, in question must be equal a3 to contact potential difference between the two metals, i.e. w ' - w " . The work of Novakovsky et al. 34 referred to by Graves may be considered rather as the mathematical interpretation of Frumkin's idea. SUMMARY
In most cases the faradaic impedance appreciably contributes to the measured capacitance of the electrodes in molten halides. However this contribution is not so large as to distort significantly the dependence of double-layer capacitance on d.c. potential, temperature and the nature of the melt. Therefore the measurements of capacitance at rather high frequencies reflect the properties of the double layer completely enough. The analysis of the frequency dependence of the capacitance and resistance for silver, lead and platinum electrodes allowed the separation of the frequency independent capacitance which may be considered as the capacitance of the double layer. As to the carbon electrode, the measured capacitance practically does not depend on frequency above 2-3 kHz and the electrode behaviour in molten halides most closely resembles ideal polarizability. REFERENCES 1 2 3 4 5 6 7 8 9 10 11
A. D. GRAVES, J. ElectroanaL Chem., 25 (1970) 349. A. D. GRAVESANO D. INMAN, J. Electroanal. Chem., 25 (1970) 357. E. A. UKSnE, N. G. BUKUN UND D. J. LEIKIS, Zh. Fiz. Khim., 36 (1962) 2322. E. A. UKSHE, N. G. BtJKUN AND D, J. LmKIS, Izv. Akad. Nauk SSSR, Otd. Khim. Nauk, 1, (1963) 31. N. G. BUKUN AND E. A. UKSHE, Zh. Fiz. Khim., 37 (1963) 1401. N. G. BUKUN AND E. A. UKSHE, Zh. Prikl. Khim., 36 (1963) 1965. E. A. UKSHE, N. G. BtJKUN, D. J. LEIK~S AND A. N. FRUMKIN, Electrochim. Acta, 9 (1964) 431. E. A. UKSHE AND N. G. BUKUN, Zh. Neor 9. Khim~ 9 (1964) 944, 1766, 2494; 10 (1965) 552, 729, 1008. N. G. Bt~KUN ANO G. N. SVALOV, Zh. Neor 9. Khim., 11(1966) 1988. E. A. UKSHE AND N. G. BUKUN, Elektrokhimiya, 1 (1965) 113. N. G. BUKUr~ AND G." N. SVALOV,Elektrokhimiya, 1 (1965) 880.
J. Electroanal. Chem:, 32 (1971) 283-291
THE ELECTRICAL DOUBLE LAYER 1N MOLTEN HALIDES
291
12 R. R. DOGONADZE AND J. A. CHIZMADGEV,Dokl. Akad. Nauk SSSR, 157 (1964) 944. 13 A. I. SOTNIKOVAND O. A. ESSIN, Fizi~eskaja Khimia i Electrokhimia Rasplavlenykh Solei i Shlakov, Khimia, Leningrad, 1968, p. 209. 14 N . G . BuKur~ AND E. A. LIKSHE,Fizi?eskqja Khimia i Electrokhimia Rasplavlenykh Solei i Shlakov, p. 214. 15 J. K. DELIMARSKIJAND V. S. I(IKI4NO, Elektrokhimiya, 5 (1969) 145. 16 J. K. DELIMARSKIJAND V. S. KIKnNO, Ukr. Khim. Zh., 30 (1964) 1150; 31 (1965) 116, 872; 35 (1969)468. 17 R. H. HEUS, T. TIDWELL AND J. J. EGAN in G. MAMANTOV (Ed.), Molten Salts: Characterisation and Analysis, M. Decker, New York, 1969. 18 R.. J. BECK AND A. S. LIFSnITS, Izv. Sib. Otd. Akad. Nauk SSSR, Set. Khim., 6 (1967) 70; 5 (1968) 8,13; 6 (1969) 120. 19 E. A. UKSH~, N. G. BUKUN AND D. I. LEKIS, Dokl. Akad. Nauk SSSR, 135 (1960} 1183. 20 E. A. UKSHE AND I. V. TOMSKIKH, Dokl. Akad. Nauk SSSR, 150 (1963) 347. 21 A . N . FRUMKIN, O. A. PETRI AND B. B. DAMASKIN,Electrokhimiya, 6 (1970) 614. 22 E. A. UKSH~, N. G. BUKUr~AND N. S. TKAt~EVA,Elektrokhimiya, 6 0970) 787. 23 E. A. UKsn~, Elektrokhimiya, 4 (1968) 1116. 24 R. DE LEVIE AND L. POSPI~IL, J. Electroanal. Chem., 22 (1969) 277. 25 R. DE LEVIE~J. Electroanal. Chem., 9 (1965) 117. 26 S. SUGDEN,J. Chem. Soc., (1921) 1483. 27 N. G. BUKUN, E. A. UKSHE AND N. S. TKA~EVA~ Elektrokhimiya, 3 (1968) 1409. 28 E. A. UKSHI~,N. G. BUKUN AND N. S. TKAt~EVA,Elektrokhimiya, 5 (1969) 1421. 29 N. G. BUKtrN, N. S. TKA~EVAAND E. A. UKSHE, Elektrokhimiya, 4 (1968) 1231. 30 N. G. BUKUN AND N. S. TKA~EVA, Elektrokhimiya, 5 (1969) 596. 31 A. D. GRAVESAND D. INMAN, Nature, 208 (1966) 481. 32 H. A. LAITINEN, R. P. TISCHER AND D. K. ROE, J. Electrochem. Soc., 107 (1960) 547. 33 A. FRUMKIN AND A. GORODEZKAJA, Z. Phys. Chem., 136 (1928) 451. 34 V. M. NOVAKOVSKY,E. A. UKSHE AND A. J. LEVIN, Zh. giz. Khim., 29 (1955) 1847. 35 E. A. UKSHE, J. M. RJABUKHINAND V. S. VOLKOVA,I2~. Akad. Nauk SSSR, Metal., 4 (1965) 89.
J. Eleetroanal. Chem., 32 0 9 7 i ) 283-291
283
THE ELECTRICAL DOUBLE LAYER IN MOLTEN HALIDES
E. A. U K S H E AND N. G. B U K U N
New Chemical Problems Institute, Academy of Sciences, Moscow (U.S.S.R.) (Received 21st September 1970; in revised form l l t h March 1971)
The problem of structure and properties of the metal/salt melt interface has recently attracted the attention of numerous investigators 1,2. Significant information on this question may be obtained in two different ways : (a) by measuring the capacitance when the nature and composition of the metal and salt phases, temperature and electrode potential are varied but the a.c. frequency remains fixed ; (b) by studying the effect of frequency on the electrode capacitance and resistance. We have previously investigated the fixed-frequency capacitances of the stationary liquid and solid electrodes in molten alkali and alkaline-earth metal halides 3-11. The results of our work may be summarized as follows : 1. The capacitance of the electrode/alkali halide interface depends significantly on a.c. frequency 3. However for sufficiently large frequencies (above 20 kHz) this dependence becomes small enough and thus this measured capacitance may be considered to differ insignificantly from the double-layer capacitance. 2. The capacitance of the electrode/alkali (or alkaline-earth) metal halides interface depends on the electrode potential. In most cases C-E curves are close to parabolic with a pronounced minimum, but for some systems (Pb/LiCI~CsCI, Pb/NaC1-CaC12, Ag/NaC1-KC1, etc.) the symmetry of the capacitance curves is broken and a step or even a second minimum appears on the cathodic branch 7-9. 3. The potentials of the minimum capacitance (Emin) have been found to be very close to the p.z.c. (electrocapillary maximum) of metals in LiC1-KC1 and NaC1KC1 molten mixtures. 4. The minimum capacitance (C~,~n)rises significantly and C-E curves become narrower as the temperature increases. The dependence of Cmi, on temperature however is not linear and practically disappears as the temperature approaches the melting poin¢ °'11. The absolute values of Cmi n for the lead electrode were 20-70 #F cm -2, depending on temperature and the nature of the melt 7. To explain these high capacitance values it has been suggested that the melt side of the double layer has the alternating sign structure. In the terms of this hypothesis the effect of temperature, d.c. potential and the nature of melt on the capacitance can be qualitatively inferred 7'12-14 In 1964-69 Delimarskij and Kikhno 15'16 undertook the study of the capacitance of some solid metals which had not been investigated before. They have practically confirmed all the regularities enumerated a'. * Recently Alekseeva and Kuznetsov (Elektrokhimiya 4 (1968) 95, 1351) have found systems where the potential of Cm~n does not coincide with the p.z.c, and the value of Cmln is not independent on the nature of the metal.
3. Electroanal. Chem., 32 (1971) 283-291
284
E.A. UKSHE,N. G. BUKUN
Recently Heus et al. 17 and Beck and Liftshits 18 have published the results of their investigations on the capacitance of liquid electrodes in halide melts. Beck and Liftshifts, as well as the authors of this article, have measured the capacitance of lead and some other stationary electrodes in molten LiC1-KC1 (450°C) and NaC1KC1 (800°C). They have found the minimum capacitance for both systems to be 25___5 #F cm-2 and that it depends weakly on temperature and the nature of melt. Heus et al. have studied the capacitance of the dropping electrode in fused LiC1-KC1. The measured capacitance was established to be practically independent of temperature in the range 390-480°C and to be approximately 30/~F cm-2. The results of Beck and Liftshifts will be discussed later. As to the small dependence of the measured capacitance on temperature in Heus' work it does not appear to contradict our observation lo because the effect of temperature on the measured capacitance has been shown to be almost exponential and to approach a constant as temperature decreases. Thus for the eutectic mixture LiC1-KC1 near the melting point the temperature dependence of the capacitance must disappear. However the experimental data obtained some years ago 3- ~~ do not concern pure double-layer capacitance since measured capacitance and resistance of the electrodes in fused halides depend on the a.c. frequency. In order to clear up the difference between the double-layer capacitance and the measured capacitance we have compared the results of double integration of the capacitance curves and the electrocapillary curves obtained under the same conditions. The agreement was quite good, at least for those cases when the capacitance curves were close to parabolic 5,19,20. The results are in favour of a small difference between the double-layer capacitance and the measured value irrespective of polarizability of the electrode, since Lippman's equation -do/dE=Q
(1)
as well as the equation for double-layer capacitance Cd,=dQ/dE
(2)
include the full charge of the electrode. This full charge is
Q=q+nVr
(3)
where q is the free charge and F is the Gibb's adsorption of the electroactive ions (or the electroactive atoms in the metal alloy). This feature has frequently been discussed in the literature and recently has been clearly demonstrated by Frumkin et al. in their fundamental work 21. The agreement between the capacitance and electrocapillary curves confirms that the measured capacitance is close to that of the double layer and depends on the potential in a similar way. Nevertheless even with relatively small dispersion of the measured capacitance in the frequency range above 20 kHz, it differs from the true double-layer capacitance owing to the non-ideal polarizability of electrodes in fused halides. Therefore it is desirable to determine Cd~ for liquid metals more accurately. Such a determination has been attempted by Beck and Liftshifts18. In the case of a liquid electrode, its surface is formed by the metal meniscus in the glass tube. Therefore the capacitance and resistance dispersion may be due to screening of the metal surface by the tube walls or to creeping of the electrolyte between J. Electroanal. Chem;, 32 (1971)283-291
THE ELECTRICALDOUBLELAYERIN MOLTENHALIDES
285
these walls and the metal. This is why Beck and Liftshifts18have used stationary liquid electrodes with a large diameter (about 4 mm). The dispersion observed under these conditions has been explained exclusively as due to shunting of the double layer by the faradaic impedance. To calculate the double-layer capacitance from series capacitances and resistances (Cs, Rs) measured at 19-20 kHz they used the formula Cd~ = [(coC~)-1 - Rs]/eo[1/(e)C~) 2 + R 2]
(4)
This formula may be readily obtained if we suppose the behaviour of the electrode to be described by the equivalent circuit in which the double layer is shunted only by the Warburg impedance Zw = (1-j)a/co ~
(5)
However more detailed studies carried out in our laboratory have shown that the problem cannot be solved in this simple way. Special measurements have confirmed that the dispersion of the capacitance and resistance depends on the tube diameter 2z, but this dependence becomes unimportant for tubes of sufficiently large diameter (more than 5 mm) and for not too low frequencies (above 500 Hz). Yet such large stationary lead electrodes in fused halides cannot be described by a simple equivalent circuit (Fig. la). This can be shown if we represent the impedance of the electrode by means of parallel capacitance and resistance (Cp, Rp). Then taking eqn. (5) into account we obtain
Ra Fig. 1. Equivalentelectrical circuits.
if0 ~' t40 u- t20
~t00 Q:~ 80
eo -o. 40 20
10a to-Vz/sv2
Fig. 2. Plots of Cp and l/ogRp vs. co-~ for Pb/NaC1-KC1(1:1) at 717°C. (O) Cp (V) 1/o~Rp at E= -0.55 V ; (0) Cp (!?) 1/CORpat E= -0.70 V. Here and in the other figures the referenceelectrode is Pb/2.5 molto PbC12+ base electrolyte. J. Electroanal. Chem., 32 (1971) 283-291
286
E.A. UKSHE, N. G. BUKUN Cp = Cdl + (CO~ X 2a)- 1 (~oRp)-I = (o~ × 2a)-1
(6)
where a is constant. Figure 2 shows the results of measuring the capacitance of large stationary lead electrodes in molten NaC1-KC1 (l:l) at 717°C in the frequency range 500 H z - 3 0 kHz. It is not difficult to see t h a t the experimental data are not described by eqn. (6) and some more complex electrical circuit, probably, corresponds to the lead electrode. When analysing the frequency dependence of the capacitance and resistance by the methods described in refs. 23- 25 we have come to the conclusion that the behaviour of the Pb/NaC1-KC1 system m a y be defined by the equivalent circuit shown in Fig. lb. The capacitance curves have been obtained by graphical extrapolation in Cp vs. I/a>Rp plots according de Levie 24'2s. They are close to parabolic and coincide well enough with the results obtained earlier (Fig. 3) 22.
~
sG
It.
. ~ 70 6O 5O
40 I
I
-o4
I
/
I
I
I
.~6 E/~o.s
Fig. 3. Double-layer capacitance-potential curves for Pb/NaCI-KC1 (1:1) at 700°C. (O) Calcd. Ca~,(~') measured C~ at 40 kHz.
The determination of the meniscus electrode capacitance requires knowledge of its true area. It was suggested in our early work 3-11 and in the articles of Beck and Liftshits 18 that the electrode surface area could be determined as the area of hemisphere of diameter equal to that of the glass tube. However this suggestion causes an error which increases rapidly as the tube diameter increases. The surface area of the meniscus can be estimated by means of Sugden's tables 26 giving the m i n i m u m capacitance of the lead electrode (NaC1-KC1, 700°C) as 36.8 ___1.0/~F c m - 2 , . Thus calculation of the double-layer capacitance gives results which are close to our early data 3-7, provided use is made of the modern methods of dispersion analysis 23- 25 and correct determination of the electrode surface area. The behaviour of the metal/fused salt interface in alternating current can be described by means of equivalent circuits providing the frequency independent * It should be noted here that an analogous recalculation of the data of Beck and Lifshitsla concerning Cmin for the system Pb/NaC1-KC1 gives 374-7 #F cm- 2 instead of 25 -t-5/iF cm- 2.
J. Elrctroanal.Chem:,32 (1971) 283-291
THE ELECTRICAL DOUBLE LAYER IN MOLTEN HALIDES
287
capacitance is interpreted as double layer capacitance and the shunting impedance is connected with the electrochemical reactions: • M "+ + n e ~ M Na + + e + x M ~ N a • xM and so on. This method has been used in our work for some solid electrodes in molten halides. Using the dispersion analysis in a sufficiently large frequency range for silver 27, platinum 28'29 and carbon 3° electrodes equivalent circuits formed by capacitances, resistances and Warburg impedances, have been obtained. The silver electrode has been studied in molten NaC1, KC1 and NaC1-KC1 (1 : 1) at 800°C both by changing its potential by d.c. polarization and by adding Ag + ions to the melt. In all cases the system was fairly well described by the circuit shown in Fig. la. The values of Cdl calculated according to eqn. (4) do not depend on a.c. frequency. The characteristic features of C d r E curves are the minimum, and the step on the cathodic branch. The value of Cmi, increases from KCI to NaC1. These two features were also observed in early studies v (Fig. 4). It is worth noting that the Warburg coefficient a for the equilibrium silver electrode Ag/AgC1,MC1 may be calculated according to the equation a = R T ( n F ) - 2 c - x (2D) -~
(7)
where c is concentration and D is a diffusion coefficient of silver ions which has been measured by an independent method35; these calculations are quite satisfactorily precise. However in the case of d.c. polarization, i.e. at more negative potentials 27, the measured Warburg coefficient a deviates significantly from the calculated value. The behaviour of platinum in fused LiC1-KC1 and NaC1-KC1 mixtures has been studied further with the electrode potential changed both by d.c. polarization 8G
70 I.L
50
30 f
-0.2
I
I
-0.4
I
I
-0.6
I
d~
I
-
Ely
Fig. 4. Double layer capacitance-potential curves for silver. (©) NaC1, 815°C; (xT) NaC1-KC1 (1:1), 825°C; ([5])KC1, 825°C. (O), (V), (a) points obtained by adding AgC1 to the melt. Cd, calculated by means of eqn. (4). J. Electroanal. Chem., 32 (1971) 283-291
288
E.A. UKSHE,N. G. BUKUN
and by adding PtC12. The a.c. properties of this electrode were described by the circuit shown in Fig. lb. At d.c. polarization the charge-transfer resistance 0 is negligible. On the contrary, I/~oCa ~ 0 for the equilibrium electrode. The values of Cat calculated from experimental data for the system Pt/LiC1-KC1 (460°C) are compared with values directly measured Cs (20 kHz) and with the data of Graves and Inman, see Fig. 5. These authors employed galvanostatic pulses (to 2 × 10- 7 s) for measuring dot/ble-layer capacitance 31. All the curves compared are very similar in the cathodic branches. One can see the coincidence of the positions of Emin and of the capacitance fall, which is probably connected with the incorporation of an alkali metal. The difference between our results and those of Graves and Inman for anodic potentials may arise from the difficulty in reproducing the surface conditions for platinum. Finally, the double-layer capacitance of platinum appreciably increases with increasing temperature 28. G1 90
E g0 O 60 30 4D 30 0.4 0.3 0.2 0.!
- . t -a ~-0~
E/v
Fig. 5. Capacitance-potential curvesfor Pt/LiC1-KCI,460°C. (©) Calcd. Cdl,(V) measured C, at 20 kHz, (GI) capacitance measured by Graves and Inman. The investigations of the equilibrium plati~num electrode in LiC1-KC1 (460°C) allow the double-layer capacitance at positive potentials (+ 0.88 to +0.97, V) to be estimated. In this range Ca~ increases from 95 to 170/~F cm -2 (these points are not shown in Fig. 5). Also, we succeeded in determining the charge transfer resistance 0 and the exchange current io for the reaction Pt(II)/Pt : io = (45.4_+ 8.2) c °'65 where c is the Pt(II) concentration in mol 1-1. This value conforms to the data of Laitinen et al. 32 obtained by the doublepulse method. Further, results which are of importance for the understanding of the subject in question have been obtained with the smooth carbon electrode (glassy carbon) 31. The measured capacitance of the carbon/molten salt interface practically does not J. Electroanal. Chem., 32 (1971)283-291
THE ELECTRICALDOUBLELAYERIN MOLTENHALIDES
289
80
,~ 7O U
. .60 J 5O 40 30
I
I
+L2
I
I
+0.8
I
I
*0.4-
I
I
0
ElY
I
I
-0.4
Fig. 6. Double layercapacitance-potentialcurvesfor carbon.(O)NaC1,839°C ; ( x ) KC1,796°C ; (V) NaCIKC1 (1:1), 795°C; ([~) NaCI-KCl (1:1), 703°C. depend on the a.c. frequency in the range 2-20 kHz and it may probably be considered close to the double-layer capacitance. The CaI-E curves for carbon are shown in Fig. 6. They are characteristed by the same features as those described for the capacitance curves of liquid metals. As is seen from the above, the regularities dealing with the dependence of capacitance on d.c. potential, temperature and the nature of the molten salt are due to the properties of the melt side of the double layer. The argument that Cdl increases with temperature scarcely at all and that the apparent rise was due to an inadequate analysis of the experimental data, does not seem to us to be well-founded. In any case the analysis of the impedance dispersion for platinum, silver and lead electrodes does not confirm such an assumption. On the contrary the capacitance of these electrodes remains very high at 700 ° after eliminating the frequency-dependent component. However the supposition of Graves and Inman z which explains the dependence of the double-layer capacitance on d.c. potential by the influence of the adsorption terms in eqn. (3) seems more attractive, although supplementary data should be accumulated to permit the reduction of whole capacitance change with d.c. potential to this cause only. For the present we can say that measurements of the carbon electrode capacitance are a variance with this supposition. The capacitance of the carbon electrode, as noted above, is practically independent of frequency although its dependence on the potential and temperature is very close to that for other metals. Finally we should discuss the problem of accumulating alkali-metal atoms in the surface layers of the electrodes at cathodic polarization. This possibility cannot be excluded although in our opinion Graves and Inman 2 rather exaggerate its danger. J. Electroanal. Chem,,32 (1971)283-291
290
E . A . UKSHE, N. G. BUKUN
If such accumulation were significant at potentials at which C a J E and electrocapillary curves are measured, a change of the measured components of the impedance with the time and hysteresis of the capacitance after cathodic polarization would take place. Actually such phenomena occurred only at more negative potentials, while in the range 250-300 mV around the p.z.c, they were not observed. In conclusion, it is necessary to point out an inaccuracy in Graves' article 1. This author claimed that Frumkin had discovered the "empirical" dependence between the p.z.c, of a metal in contact with electrolyte (Eq = 0) and the work function of electrons (w) E'q = 0 - - E"q = 0 ~ W ' - - w" where indexes ' and " denote different metals. This dependence is actually not empirical. It was derived by Frumkin from the fact that the e.m.f, of a cell made from two metals at their p.z.c, can differ from zero only owing to potential differences which are localized in the surface layers of metals at their contact with each other and with a solvent. Apparently, the presence of the solvent is not necessary for the existence of such potential difference, and if one neglects the fact that adsorption of the solvent dipole molecules can vary, the e.m.f, in question must be equal a3 to contact potential difference between the two metals, i.e. w ' - w " . The work of Novakovsky et al. 34 referred to by Graves may be considered rather as the mathematical interpretation of Frumkin's idea. SUMMARY
In most cases the faradaic impedance appreciably contributes to the measured capacitance of the electrodes in molten halides. However this contribution is not so large as to distort significantly the dependence of double-layer capacitance on d.c. potential, temperature and the nature of the melt. Therefore the measurements of capacitance at rather high frequencies reflect the properties of the double layer completely enough. The analysis of the frequency dependence of the capacitance and resistance for silver, lead and platinum electrodes allowed the separation of the frequency independent capacitance which may be considered as the capacitance of the double layer. As to the carbon electrode, the measured capacitance practically does not depend on frequency above 2-3 kHz and the electrode behaviour in molten halides most closely resembles ideal polarizability. REFERENCES 1 2 3 4 5 6 7 8 9 10 11
A. D. GRAVES, J. ElectroanaL Chem., 25 (1970) 349. A. D. GRAVESANO D. INMAN, J. Electroanal. Chem., 25 (1970) 357. E. A. UKSnE, N. G. BUKUN UND D. J. LEIKIS, Zh. Fiz. Khim., 36 (1962) 2322. E. A. UKSHE, N. G. BtJKUN AND D, J. LmKIS, Izv. Akad. Nauk SSSR, Otd. Khim. Nauk, 1, (1963) 31. N. G. BUKUN AND E. A. UKSHE, Zh. Fiz. Khim., 37 (1963) 1401. N. G. BUKUN AND E. A. UKSHE, Zh. Prikl. Khim., 36 (1963) 1965. E. A. UKSHE, N. G. BtJKUN, D. J. LEIK~S AND A. N. FRUMKIN, Electrochim. Acta, 9 (1964) 431. E. A. UKSHE AND N. G. BUKUN, Zh. Neor 9. Khim~ 9 (1964) 944, 1766, 2494; 10 (1965) 552, 729, 1008. N. G. Bt~KUN ANO G. N. SVALOV, Zh. Neor 9. Khim., 11(1966) 1988. E. A. UKSHE AND N. G. BUKUN, Elektrokhimiya, 1 (1965) 113. N. G. BUKUr~ AND G." N. SVALOV,Elektrokhimiya, 1 (1965) 880.
J. Electroanal. Chem:, 32 (1971) 283-291
THE ELECTRICAL DOUBLE LAYER 1N MOLTEN HALIDES
291
12 R. R. DOGONADZE AND J. A. CHIZMADGEV,Dokl. Akad. Nauk SSSR, 157 (1964) 944. 13 A. I. SOTNIKOVAND O. A. ESSIN, Fizi~eskaja Khimia i Electrokhimia Rasplavlenykh Solei i Shlakov, Khimia, Leningrad, 1968, p. 209. 14 N . G . BuKur~ AND E. A. LIKSHE,Fizi?eskqja Khimia i Electrokhimia Rasplavlenykh Solei i Shlakov, p. 214. 15 J. K. DELIMARSKIJAND V. S. I(IKI4NO, Elektrokhimiya, 5 (1969) 145. 16 J. K. DELIMARSKIJAND V. S. KIKnNO, Ukr. Khim. Zh., 30 (1964) 1150; 31 (1965) 116, 872; 35 (1969)468. 17 R. H. HEUS, T. TIDWELL AND J. J. EGAN in G. MAMANTOV (Ed.), Molten Salts: Characterisation and Analysis, M. Decker, New York, 1969. 18 R.. J. BECK AND A. S. LIFSnITS, Izv. Sib. Otd. Akad. Nauk SSSR, Set. Khim., 6 (1967) 70; 5 (1968) 8,13; 6 (1969) 120. 19 E. A. UKSH~, N. G. BUKUN AND D. I. LEKIS, Dokl. Akad. Nauk SSSR, 135 (1960} 1183. 20 E. A. UKSHE AND I. V. TOMSKIKH, Dokl. Akad. Nauk SSSR, 150 (1963) 347. 21 A . N . FRUMKIN, O. A. PETRI AND B. B. DAMASKIN,Electrokhimiya, 6 (1970) 614. 22 E. A. UKSH~, N. G. BUKUr~AND N. S. TKAt~EVA,Elektrokhimiya, 6 0970) 787. 23 E. A. UKsn~, Elektrokhimiya, 4 (1968) 1116. 24 R. DE LEVIE AND L. POSPI~IL, J. Electroanal. Chem., 22 (1969) 277. 25 R. DE LEVIE~J. Electroanal. Chem., 9 (1965) 117. 26 S. SUGDEN,J. Chem. Soc., (1921) 1483. 27 N. G. BUKUN, E. A. UKSHE AND N. S. TKA~EVA~ Elektrokhimiya, 3 (1968) 1409. 28 E. A. UKSHI~,N. G. BUKUN AND N. S. TKAt~EVA,Elektrokhimiya, 5 (1969) 1421. 29 N. G. BUKtrN, N. S. TKA~EVAAND E. A. UKSHE, Elektrokhimiya, 4 (1968) 1231. 30 N. G. BUKUN AND N. S. TKA~EVA, Elektrokhimiya, 5 (1969) 596. 31 A. D. GRAVESAND D. INMAN, Nature, 208 (1966) 481. 32 H. A. LAITINEN, R. P. TISCHER AND D. K. ROE, J. Electrochem. Soc., 107 (1960) 547. 33 A. FRUMKIN AND A. GORODEZKAJA, Z. Phys. Chem., 136 (1928) 451. 34 V. M. NOVAKOVSKY,E. A. UKSHE AND A. J. LEVIN, Zh. giz. Khim., 29 (1955) 1847. 35 E. A. UKSHE, J. M. RJABUKHINAND V. S. VOLKOVA,I2~. Akad. Nauk SSSR, Metal., 4 (1965) 89.
J. Eleetroanal. Chem., 32 0 9 7 i ) 283-291