J. Phys. Chem. 1983, 87,1357-1361
The biological systems discussed by Blair12" and by RashevskylZbare a far cry from the chemical system discussed here. However, both can exist in two possible states and can go from one state to the other by a strong enough perturbation. The fact that the perturbation time-in(12)(a) H.A. Blair, J.Gen. Physiol., 15,709(1932);(b) N. Rashevsky, "Mathematical Biophysics", The University of Chicago Press, Chicago, 1948,p 279. (13)P. H.Richter, I. Procaccia, and J. Ross in "Advances in Chemical Physics", Vol. XLIII, I. Prigogine and S. A. Rice, Ed., Wiley, New York, 1980,p 217 ff.
1357
tensity relationship in such different systems is so similar may indicate a deeper connection between seemingly unrelated phenomena. Registry No. Ce, 7440-45-1; Mn, 7439-96-5; bromate, 1554145-4.
Supplementary Material Available: Appendix A concerns the problem of small perturbations to a steady state in an open system and Appendix B shows why the Blair equation gives a rough approximation to the pulse intensity-pulse time relationship (15 pages). Ordering information is available on any current masthead page.
Kinetics of Formation and Dissociation of the Cryptates Ag(2,2,2)+ and K(2,2,2)+ in Acetonitrile Water Mixtures at 25 OC
+
B. G. Cox, Department of Chemistry, Universtty of Stirling, Stir/ing, FK9 4LA Scotland
C. Gumlnski, University of Warsaw, Institute of Fundamental Problems of Chemistry, Warsaw, Poland
P. Firman, and H. Schnelder' Max-Planck-Institut fur biophysikaiische Chemie, 0-3400 GGttingen, West Germany (Received: September I , 1982)
The dissociationrates of Ag(2,2,2)+and K(2,2,2)+in the acetonitrile (AN) + water system show a quite different dependence upon solvent mole fraction. The dissociation rate constant, kd, of Ag(2,2,2)+is almost independent of solvent composition and the rapid decrease of the stability constant, K,, near 3cm = 0 is determined completely by the variation in the formation rate constant, k p The constant value for k d for Ag(2,2,2)+in the mixtures indicates that in the transition state the silver ion is strongly bonded to the (2,2,2)nitrogen atoms in a manner typical of the partially covalent interaction of monovalent dO ' ions with nitrogen donors (e.g., in nitrilic solvents). This result, and the very similar variation of the Gibbs free energies of the transition state and stable cryptate complex with solvent composition, suggests that the transition state is very close to that of the products. The result is striking because for alkali-metal cryptates, particularly in nonaqueous solvents, a very similar solvent dependence is found for the reactants and transition state. The interaction between K+ and (2,2,2)is also found to be very different in this binary solvent system from that of Ag(2,2,2)+.Both k d and kf contribute similarly to the increase of the stability constant of K(2,2,2)+with increasing mole fraction of acetonitrile, and comparisons of the Gibbs free energies of reactants, transition state, and product do not indicate any simple correlations between the solvation behavior of the three over the whole range of solvent composition.
Introduction Most macrocyclic ligands are characterized by their ability to distinguish between metal ions and to form the most stable inclusion complex within a series of related cations, such as the alkali or alkaline-earth metal ions, with the cation that fits optimally into the cavity of the ligand.'-' Rate measurements have shown that the variation (1)J. J. Christensen, D. J. Eatough, and R. M. Izatt, Chem. Rev., 74, 351 (1974). (2)J. M.Lehn, Stmct. Bonding (Berlin), 16,l (1973);Acc. Chem. Res., 11, 49 (1978);Pure Appl. Chem., 50, 871 (1978). (3)B. G. Cox, J. Garcia-Rosas,and H. Schneider, J.Am. Chem. SOC., 103, 1384 (1981). (4)W. Burgermeister and R. Winkler-Oswaitsch, Top. Curr. Chem., 69,91 (1977). (5) B. G. Cox, J. Garcia-Rosas, and H. Schneider, J. Am. Chem. Soc., 103, 1054 (1981).
in stability of the complexes is almost entirely reflected in the dissociation rates, with the most stable complex having the lower dissociation rate. The change in formation rate with ionic radius is generally small.4 This behavior has been demonstrated most clearly for cryptands? i.e., macrobicyclic diazapolyethers, first synthesized by Lehn et a1.: which form exceptionally stable complexes with metal iom2 For these ligands it has been shown that changes in solvent also normally influence the dissociation rates much more strongly than the formation rates.5 Recently complex formation between the cryptand (2,2,2)-N( (CH,CH,0)2CH,CH2J3N-and K+ and Ag+ has (6)J. M.Lehn and J. P. Sauvage, Tetrahedron Lett., 2885, 2889 (1969). (7) B. G.Cox, C. Guminski, and H. Schneider,J.Am. Chem. Soc., 104, 3789 (1982).
0022-3654/83/2087-1357$01.50/00 1983 American Chemical Society
1350
Cox et al.
The Journal of Physical Chemistty, Vol. 87, No. 8. 1983
TABLE I: Rate Constants of Dissociation ( k d ) ,Formation ( k f ) ,and Catalysis ( k H ) for t h e Cryptate Ag(2,2,2)t in Acetonitrile + Water Mixtures a t 2 5 " C "AN
lid
"H20
,'
1 0 - "2 f , S-'
M-I s~ 1
k
15.6 2.5 1.3 1.1 1.1 1.5 2.4 4.3 5.4
4.7
~ M - ',
S
'~
method
kHlkd
I _ _ -
0.00 0.05 0.1 0.2 0.3 0.5 0.7 0.9 0.95 0.98 1.0
1.0
1 .o
1.0 1.0 1.0 1.0
0 . 4 6 I 0.01' 0.69 0.80d 1.00d 1.04 1.06 1.18 0.78 0.70 0.5 t 1 . 2 0.60 r 0.15e 0.5 - 0 . 1 0 . 4 5 O.lf 0.50 L O.1Sf 0 . 6 0 L 0.1 0 . 4 i- 0.2 0.9 i 0.5
5.0 4.2 3.8 4.2 5.0 3.3 r
-
I . ~ )
10''
1.0 x 104
7.4x 103 7.9x 8.9 x
1.1 x 104 9.9x 103 8.9x 103
X
8.8 X 8.9 x 19.1x 23.5 x 33.3 x 51.5 x 1.1 x 5.9 x
9.1x
lo3
8.5 x 8.4 x 1.6 x 3.0 x 4.5 x 1.0 x 1.8 x 1.2 x 2.0 x
103 103 103 103
io3 105 lo3 io3 f,a
(9.5 : 0 . 5 ) x 1 o 3 f S p ( 6 . 9 i 0.5) x ( 3 . 0 0.4) x 1 0 3 p ( 4 . 3 0 . 2 ) x 103 +
1.9x 1.2 x 7.5 x 4.8 x
Ag(2,2,2)+ + HC10, Ag(2,2,2)+ + HCIO, Ag(2,2,2)+ + HC10, Ag(2,2,2)+ + HC10, Ag(2,2,2)+ + HC10, Ag( 2,2,2)' + HC10, Ag(2,2,2)+ t HC10, Ag(2,2,2)+ t HCIO, Ag(2,2,2)+ + HC10, Ag(2,2,2)+ + HC10, Ag(2,2,2)+ + CF,SO,H Ag( 2,2,2)C104 + CH,SO,H Ag(2,2,2)CF,S03 + Pb(CF,SO,), Ag(2,2,2)C104+ Pb(CF,SO,), Ag(2,2,2)C104+ Pb(C10,), Ag(2,2,2)C104 + NaC10, Ag(2,2,2)C104 + F S 0 3 H
103 103 104 104 104
105 105 104 104g 104g 104g 103g 103
i l h = ~ t 3%, if not otherwise stated, 2.hd = t 1 5 % , if not otherwise stated. thesis of H. Schulz. e Determined by extrapolation t o X ~ . N= 1.0. See ref 11.
t h e catalysis b y metal ions or ion pa&.
'...
been studied in acetonitrile + water mixtures in order to show the importance of ion solvation in cryptate format i ~ n .As~ expected, ~ ~ the strong differentiation between the solvation of the free cations in the solvent mixture had a large effect on the overall stabilities of the complexes, but significant effects due to interactions of the cryptand and the complexes (cryptates) with the solvent components were also o b ~ e r v e d . ~ , ~ In this paper we present the results of stopped-flow experiments on K(2,2,2)+ and Ag(2,2,2)+ cryptates in mixtures of acetonitrile + water. I t has been found for K(2,2,2)' that variations in formation and dissociation rates contribute almost equally to the solvent dependence of the stability constant of the complex. However, for Ag(2,2,2)+the dissociation rate is virtually independent of solvent composition and the variation of the stability constant is determined completely by the rates of complex formation. This contrasting behavior of the two cryptates is explained in terms of differences in the solvation of the metal ions and the activated complexes.
Experimental Section and Results Inorganic salts and acids were obtained in the highest purity commercially available and used without further purification: NaC10, (Alfa), AgCF3S03(EGA), Pb(C104)2 (EGA), FS0,H (Fluka), CF,SO,H (EGA), C1,CHC02H (Riedel-de Haen). Pb(CF3S03),was prepared by reacting Pb(CO,), (Merck, p.a.) with CF3S03Hand dried at 130 O C over P4010for 20 h. The preparation of solutions has been discussed in detail p r e v i o u ~ l y .The ~ ~ ~dissociation of the (2,2,2) complexes in aqueous acetonitrile solutions was determined by using a home-built, all-glass, stopped-flow apparatus with conductance detection. When a cryptate solution was mixed rapidly with an excess of perchloric acid or trifluoromethanesulfonic acid, the overall reaction was observed as a pseudo-first-order reaction5 M(2,2,2)++ 2H+
he
M+ + (2,2,2)HZ2+
(1)
The concentration of (2,2,2) was varied between 1 X and 1 x M and the metal ion concentration was always 5-8 times higher, to ensure that the portion of uncom(8) B. G. Cox, D. Gudlin, P. Firman, and H. Schneider, J . Phys. Chem.,86,4988 (1982).
Rechecked result of ref 17. Doctoral I n these experiments IZH corresponds to
plexed ligand was small. The acid was in 8-20-fold excess over (2,2,2). The experimental dissociation rate constant, k,, was always found to be linearly dependent on acid concentration, as in eq 2, where kd, the uncatalyzed dissociation k , = kd + k,[H+] rate constant of reaction 3, was obtained by extrapolation
2M+ + (2,2,2)
M(2,2,2)+
(3) of k , to zero acid concentration after correction to zero ionic ~ t r e n g t h . ~Figure 1 shows some typical results. In pure acetonitrile the proton-catalyzed pathway when strong acids such as perchloric or trifluoromethanesulfonic acids were used was so large that kd values of acceptable accuracy could not be obtained by extrapolation to zero acid concentration. In this case, dichloroacetic acid, which is only partly dissociated in acetonitrile, was used as a scavenger in the determination of kd for K(2,2,2yS5k , was found to be linearly dependent upon total acid concentration. The dissociation of Ag(2,2,2)+in acetonitrile was monitored by adding several different scavengers in excess: trifluoromethanesulfonic acid (CF,SO,H), fluorosulfonic acid (FSO,H), sodium perchlorate, lead trifluoromethanesulfonate, and lead perchlorate. The dissociation was catalyzed by H+ and Na+ and, as shown in detail in a note published recently,'l by the ion pairs Pb(CF3S03)+ and Pb(ClO$+. The resulting kd values (Table I) obtained by using the various scavengers are in good agreement with one another and with the kd value obtained by extrapolation of kd values in the solvent mixtures to x m = 1. The formation rate constants, k f ,were obtained by combining K, (=kf/kd),with previously measured stability con~tants,'~~ kd values determined as described above. The rate constants for the K(2,2,2)+system are listed in Table 11.
Discussion In acetonitrile + water mixtures, the preferential hydration of the potassium ion and the strong partly covalent (9) B.G . Cox, H. Schneider, and J. Stroka, J. Am. Chem.SOC.,100, 4746 (1978). (10) B. G. Cox, J. Garcia-Rosa, and H. Schneider, J . Phys. Chem., 84, 3178 (1980). (11) C. Guminski and H. Schneider, Nouu. J . Chim.,4, 79 (1980).
Cryptates Ag(2,2,2)+ and K(2,2,2)+
The Journal of Physical Chemistry, Vol. 87, No. 8, 1983 1359
TABLE 11: Rate Constants of Dissociation ( k d ) , Formation (kf), and Catalysis ( k H ) for the Cryptate K(2,2,2)' in Acetonitrile t Water Mixtures at 25 "C XAN =
- XH20
0.00 0.1 0.2 0.3 0.4 0.5 0.6 0.9 1.0 a Akd
= +10%.
M-l
kd,' S-'
kf,
7.50 3.70 1.72 0.87 0.66 0.44 0.31 0.057 0.0046
3.0 x l o 6 1.2 x 1 0 7 2.2 x 1 0 7 4.4 x 1 0 7 8 . 3 x 107 1 . 7 5 X 10' 2.46 X 10' 1.14 x 109 1.16 x 109
S-'
h
~ IV-' , S-'~
kH/kd
146.9 108.7 77.8 60.5 46.0 40.7 38.2 99.9
19.6 29.4 45.2 69.5 69.7 92.5 123 1753
scavanger HClO HCIO: HC10, HC10, HC10, HC10, HC10, HC10, C1,CHCOOH
AkH = +3%.
lo
I
CH3CN - H20, 25°C
3 ,O
6
2 ,o
2 1 ,o
0
-Y
log kd.
0 0
0.5
1 ,o
1,5
2
-2
-3
i o CH+ / moldm
.4-A\
-
Reaction between K(2,2,2)+ and HCLO, in acetonitrile + water mixtures at 25 O C . Rate constants corrected to zero ionic strength. Figure 1.
interaction between the silver ion and acet~nitrile'~-'~ are mainly responsible for the dependence of the stability constants of K(2,2,2)+ and Ag(2,2,2)+upon solvent comThere are important variations with mole fraction of the free energies of both the cryptand (2,2,2) and the cryptates, but they are of smaller magnitudes than those of the metal ions and are partially cancel ling.'^^ The net result is that the stability constant of K(2,2,2)+ increases monotonically with xm? whereas there is a rapid decrease in the stability constant of Ag(2,2,2)+at low xm because of preferential solvation of Ag+ by CH,CN.' In the mixtures there is a competition between (2,2,2) and CH&N for the silver ion. Reaction Rates of Ag(2,2,2)+. The results in Figure 2 show that the kinetic behavior of the two cryptates is also strikingly different in the solvent mixtures. The uncatalyzed dissociation rate, kd,of &(2,2,2)+ is only very slightly dependent upon the mole fraction, so that kd may be taken (12)B. G. Cox, R. Natarjan, and W. E. Waghorne, J . Chem. Soc., Faraday Trans. 1,75,86(1979). (13) H. Strehlow and H. M. Koepp, 2.Elektrochem., 62,373 (1958). (14) H.Schneider and H. Strehlow, 2.Phys. Chem. (Frankfurt a m Main), 49,44 (1966).
x r l - x AN H2°
Figure 2. Rates of formation (log k,)and uncatalyzed dissociation (log kd)of Ag(2,2,2)+ and K(2,2,2)+ in acetonitrile water mixtures at 25
+
OC.
as being effectively constant. Thus, the variation in the rate constant for cryptate formation alone is responsible for the change in the stability constant of Ag(2,2,2)+with solvent composition. In order to discuss the variation of stability constants and rate constants more quantitatively in terms of the solvation of the reactants, transition state, and stable cryptate complex, we have calculated their Gibbs free energies of solvation using schematic reaction profiles in water (XAN = 0) and in the acetonitrile + water system ( x A ~ ) , as shown in Figure 3. As complex formation is undoubtely a multistep process, because of the large number of solvent molecules replaced during complexation, there will be various intermediates along the reaction path. These have, however, been omitted from Figure 3 for clarity. The Gibbs free energies in Figure 3 are either free energies of transfer (AGtr), with respect to water as reference state, or Gibbs energies (AG, AG*) which refer to
1360
The Journal of Physical Chemistry, Vol. 87, No. 8, 1983
Cox et al.
-20
Extent of Reaction
I
F w e 3. Schematic profiles of complexation reaction between MCIO, and (2,2,2) in water and in the acetonitrile water system.
A
+
the state of the reactants, MC104 and (2,2,2),in water. In order to avoid discussion in terms of single-ion quantities, the results are discussed with regard to the perchlorate ion, whose Gibbs free energy of transfer from water to acetonitrile is expected to be very ~ma1l.l~ The Gibbs free energy of the transition state, AG* (M+-(2,2,2),ClO4-),at mole fraction xm depends upon the Gibbs free energies of transfer of the reactants, MC104and (2,2,2), and the free energies of activation of the formation reaction (eq 4). AGf*(xAN)may be obtained from the AG*(M+-* .(2,2,2),C104-) = AGtr(MClO4) + AGt,(2,2,2) + A G f * ( X A N ) (4) formation rate kf(xAN)by using eq 5, in which k B is (5)
i
-60
AG(Ag(2,2,21+CIO;)
.
1
02
0
8
1
06
0.L
1
0.8
,
-
1.0
Figure 4. Gibbs free energies of reactants, transition states, and products for the formation of Ag(2,2,2)+ and K(2,2,2)+ in acetonitrile water mixtures at 25 OC. Reference is the state of the reactants in water.
+
[ k J mol-'] -20
-15
-10
-5
0
Boltzmann's constant and h is Planck's constant. The Gibbs free energy of the product AG(M(2,2,2)+C104-),at mole fraction xm, may be calculated from the free energy of transfer of the cryptate salt and the free energy of complex formation, by using eq 6, which follows from AG(M(2,2,2)+C104-)= AGt1(M(2,2,2)+C104-) A G O ( X A N = 0) (6)
+
Figure 3 by inspection. AG'(XAN = 0) is simply related to the stability constant of the cryptate complex in water, Ks(xAN = 0) as in eq 7 . A G O ( X A N = 0) = -RT In Ks(xAN = 0) (7) The rate constants in Table I, together with previously determined stability constants7 and free energies of transfer of AgC104 and (2,2,2) in the solvent mixtures,'~~ have been used to calculate the Gibbs free energies of the transition state (eq 4), the product cryptate salt (eq 6), and the reactants for the AgC104-(2,2,2) system. The results are plotted as a function of xm in Figure 4. There is an obvious similarity in the trends with mole fraction of AG*(Ag+...(2,2,2),C104-) and AG(Ag(2,2,2)+C104-),both of which are less sensitive to solvent composition than AGt,(AgC1O4 + (2,2,2)), the Gibbs free energy of the reactants. The reactant values are the sum of quite strongly negative AGt,(AgC104)values and positive Act,(2,2,2) values. (15)G. B. Cox, Annu. Rep. Prog. Chem., Sect. A , 70, 249 (1973).
Figure 5. Comparison between the variation in the Gibbs free energies of the transition state for Ag(2,2,2)+ and the Gibbs free energies of either the reactants (0)or the product (A)at different mole fractions of the acetonitrile water system at 25 O C .
+
The relationship between the solvent effects upon the transition state and the reactants and products, and hence the extent to which the transition state resembles the reactants or products with regard to solvation, may be best seen from a direct comparison of AG,*(Ag+..-(2,2,2),ClO,) with AGt,(AgC104)+ (2,2,2)) and AGt,(Ag(2,2,2)+C104-). It follows from Figure 3 that the Gibbs free energy of transfer of the transition state is given by eq 8: where the AGt,(Ag+.. .(2,2,2),C104-)= AGt,(AgC104) + AGtI(2,2,2) + AG~*(xAN) - A G f * ( X A N = 0 ) (8) free energies of activation again are given by eq 5. The results are shown in Figure 5. It is clear from Figure 5 that there is no simple relationship between AGtr* and AGJreactants) but that there is an excellent linear correlation between AGt,* and
The Journal of Physical Chemistty, Vol. 87, No. 8, 1983
Cryptates Ag(2,2,2)+ and K(2,2,2)+
I 1
31
0
0,2
0,4 "AN=
0,6
0.8
1,O
-"H~O
Figure 6. Rate constants (log k H )of acid-catalyzed dissociation of Ag(2,2,2)+ and K(2,2,2)+ in acetonitrile -t water mixtures at 25 OC.
AG,(products). The free energy of the transition state is slightly more sensitive to solvent variation than that of the products but otherwise the behaviors are closely similar. The results strongly suggest that, in the case of Ag+, the transition state for complex formation lies very close to that of the product. This means that the well-known property of Ag+ as a univalent d10 cation to form very stable linear complexes with ligand molecules containing nitrogen atoms13J4J6is effective even in the transition state, where Ag+ is strongly bonded to the two nitrogen lone pairs of the cryptand. Therefore, the selectivity in solvent sorting of Ag+, which leads to strong preferential solvation by acetonitrile of the free cation, is lost in the transition state and its properties resemble those of the fully complexed Ag+ in the product cryptate. These results are in agreement with the observation that in pure water the rate of formation of Ag(2,2,2)+is much higher than that of corresponding alkali-metal cryptates and shows a negative enthalpy of activation." Both of these results suggest a strong interaction between Ag+ and the cryptand nitrogen atoms in the transition state. Reaction Rates of K(2,2,2)+.The results for K(2,2,2)+ are quite different (Table I1 and Figure 2). With decreasing water content of the solvent, the formation rate of the potassium cryptate increases and its dissociation rate decreases. The effects are quite large (ca. 3 orders of magnitude) and contribute almost equally to the overall increase in stability constant with increasing xAN. The Gibbs free energies for the K+-(2,2,2) system in Figure 4 show that the pronounced preferential hydration of both reactants, whose free energies of transfer increase with increasing xAN, is considerably reduced in the transition state. However, there is still an increase in the free energy of the transition state as the water content of the solvent approaches zero. The Gibbs free energy of the stable cryptate decreases with increasing xm (if the contribution of C104- is taken into account) and resembles a large tetraalkylammonium ion in its behavior.8 (16) S. E. Manahan and R. T. Iwamoto, J . Electround. Chem., 14,213 (1967). (17) B. G. Cox, H. Schulz, and H. Schneider, to be submitted for
publication.
1361
The dependence upon solvent composition of the free energy of transfer of the transition state, AG,*, in relation to those of the reactants and products leads to no clear-cut decision as to whether the transition state lies closer to the reactants or products. Plots of AGtr'(K+. .42,2,2),ClOJ against AG,(KC104 + (2,2,2)) or AG,(K(2,2,2)+ClO,) leads to curves showing two separate regions of moderate correlation which meet at xAN = 0.5. The results presented here for the K(2,2,2)+ cryptate may be compared with previous results for a wider range of alkali-metal cryptates on transfer between various pure solvents.6 Where both sovlents involved were nonaqueous, changes in stability constant were predominantly the result of changes in kd values, and the solvation properties of the transition state closely resembled those of the reactants. Results in water, however, were exceptional in that formation rates were lower than in all other solvents and did not fit correlations established in nonaqueous media. These effects, which may be attributed to specific interactions of water with both the free cryptand and the resulting cryptate,8 are consistent with the present results for K(2,2,2)+in acetonitrile + water, Le., that both kfand k d vary significantly with solvent composition and that the properties of the transition state cannot be closely related to those of either the reactants or product. Acid Catalysis. The acid-catalyzed dissociation of the two cryptates is only slightly dependent upon mole fraction, up to xm = 0.9 (Tables I and 11, Figure 6). Beyond this, the increase in kH as the water content decreases is presumably a consequence of the pronounced increase in the free energy of the proton.18 As the water content decreases, there will be a higher tendency for the proton to interact with a nitrogen lone pair of the cryptate complex in an exo conformation. In absolute terms, kH values for Ag(2,2,2)+are much higher than those for K(2,2,2)+, and this does not depend upon the fact that different scavenging acids were used for the two cryptates, as both are strong acids.lg This is difficult to interpret in a simple manner. On the one hand, the very strong interaction between Ag+ and the cryptand nitrogens which persists even in the transition state is expected to make interaction between the proton and the nitrogen lone pairs more difficult than in the case of the K+ complex. On the other hand, this strong interaction also makes it more difficult for Ag+ to interact with the solvent during dissociation, and so the dissociation processes for Ag(2,2,2)+ may be much more sensitive to disruption of M+-N interactions by protonation of the nitrogen than for the K+ complex. The observed results suggest that the greater sensitivity of the Ag+-N arrangement to outside disturbances may be the predominant factor." The nearly constant values of k H / k d for Ag(2,2,2)+(Table I) and its increase with mole fraction xm for K(2,2,2)+(Table 11) suggest also differences in the attack of the proton in the catalyzed dissociation reaction of the two cryptates. Registry No. Silver, 7440-22-4; potassium, 7440-09-7; acetonitrile, 75-05-8; cryptate (222), 23978-09-8. (18) I. M. Kolthoff and M. K. Chantooni, J . Phys. Chem., 76, 2024 (1972). (19) T. Fujinaga and K. Sakamoto, J. Electround. Chem., 73, 235 (1973).
