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Adsorption behaviour of dihydrogen phosphate ions on mercury from constant ionic strength solutions
.%cmxhbmlcaAcro. Vd.M.No.2,pp. Rusted inGrutBritrin.
191-197.1985
001346@&,*5
53.00 +
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RrwmcaRsslUd.
ADSORPTION BEHAVIOUR OF PIHYDROGEN PHOSPHATE IONS ON MERCURY FROM CONSTANT IONIC STRENGTH SOLUTIONS E.R. Los Alamos
GONZALEZ,*
National
A. CARUBELLI~ and S.
Laboratory,
MSD429,
SRINIVASAN~
Los Alamos,
NM 87545. U.S.A.
(Received22 August 1983;in reuisedform 3 Jury 1984) Abstract-The adsorptionbhaviour of &PO; anions on mercury has previouslybeen analysed from capacitance-potential relations at the interface of mercury with K&PO,. It is not possible to determine unambiguously the adsorption characteristics of I&PO, ions from siagle salt solution experiments because of the possible existence of a layer of water molecules between the elecmxle and the adsorbed ions. In this work, the adsorption behavior of H*PO; ionson mercuryis analysedfrom experimentalmeasurements of thecapacitanceasa functionof potential at the interface of mercury with constant ionic strength solutions of compositions x M KH,PO, -t (1 -x) M KF. It is shownthattheQlculatedamountsof adsorbedionsdo not depend on the position of these ions relative to the solvent molecules. The double layer parameters were calculated taking into account the variations of activity coefficients of KH,PO, and KF with solution composition. In constant ionic strength solutions, the plot of adsorbed charge vs &&rode charge exhibits a maximum due to competition between the adsorbed H,PO; anions with the solvent or other ionic species. This result is shown to be important in determining the properties of the double layer characteristics in the presence of adsorbed H,PO; ions.
INTRODUCTION The adsorption behaviour of HZ PO; anions on mercury from solution of NaH2P04 was studied by Parsons and Zobel[l]. This work showed interesting features in particular the fact that differences between integrated capacity and experimental surface tension results could be explained by the existence of an ion free layer of water molecules adjacent to the electrode surface. Later, Barradas and Donaldson[2] also investigated the adsorption characteristics of different phosphate ions on Hg from single salt solutions. These authors discussed the effect of ionsolvent interactions on the double layer structure in the presence of phosphate. ions. The surface excesses calculated in these single salt solutions are probably influenced by the existence of a layer of solvent molecules between the electrode and the adsorbed ions. The double layer properties in the presence of weakly adsorbed ions whose centres ofcharge lie nearer the diffuse layer than the metal surface are expected to depend considerably on the ionic concentration in the former region. Thus, it is worthwhile to compare the adsorption characteristics of HIPO; anions from constant ionic strength soIutions, which is the main subject of this paper, with those observed previously in single salt solutions. The present study also has some technological relevance in respect to fuel cell research and development. There is renewed interest in an understanding of * Present address: Institute de Fi&ccia e Ouithica de S&o Car&, USP, C.P. 369, 13560 Sao Carlo& SP. Brazil. + Present address: Metal Leve S.A., Rua Brasilio Lux 535, Cx. Postal 6567.04746. 90 Paulo. SP. Brazil. r Present address: Institute for Hydrogen Systems, 2480 Dunwin Drive, Mississauga, Ontario L5L lJ9, Canada.
the adsorption behaviour of phosphate species as a
function of potentialbecause of its significant influence on oxygen reduction kinetics and hence on the efficiency of phosphoric acid fuel cells. The higher overpotential for this reaction at platinum in concentrated phosphoric acid than in trifluoromethanesulfonic acid (a promising fuel cell electorlyte) is commonly attributed to the influence of anion adsorption in the former electrolyteC3-j. EXPERIMENTAL KH2P04 and KF (both salts from Baker, AR grade) were used to prepare solutions in deionized water, further putied by distillation from alkaline permanganate. The solutions had a composition x M KH2P04 + (1 - x) M KF, the values of x being 0.005, 0.008, 0.01, 0.05, 0.1, 0.25, 0.5, 0.8 and 1.0. The cell, electrodes and apparatus to measure the differential capacity of the interface have been described elsewhere[4]. Potentials of zero charge (E,) were measured using the streaming mercury electrode technique[5]. All experiments were carried out at 25 *O.l”C using a saturated calomel electrode (see) as reference. RESULTS
AND DISCUSSION
Calculation of double layer parameters from capacity meas wemen f s Table 1 shows the experimental values of E, as a function of x. It can be seen that E, varies by only 7 mV when x changes from 0.005 to I .O.Thus, for a system in which only the anions are responsible for specific adsorption, the amount of adsorbed HIPO; ions in 191
E. R.
I92
Table 1. Potentials of zero charge (E,), surface tension (y,), and differential capacitance (C,) at the potential of zero charge for the mercury/x M KH, PO, + (1- x) M KF interface at 25°C
0 0.005
0.008 0.01 0.05
0.1
0.25 0.5 0.8 1.0
-0.4338 -0.4338 -0.4338 -0.4340 - 0.4340 - 0.4348 - 0.4350 -0.4360 -0.4385 -0.4415
!3. SRINIVASAN
GONZALEZ,A.CARUBELLIAND
452.7 425.7 425.7 425.7 425.7
26.12 26.12 26.15 26.18 26.21
425.6 425.6 425.6 425.6 425.6
26.26 26.30 26.40 26.60 26.80
the region of E, must be negligible. Figure I shows the capacity-potential (C-E) curves for the mercury/ (KH2P04 + KF) interface. An examination of the C-E curves confirms the conclusion that the extent of adsorption of H,PO; ions is low because the capacity is nearly independent of x for potentials more negative than E,. From the characteristics in the region around E,, only qualitative condusions can be reached about the behaviow of the system in other potential regions. Recent publications on the adsorption of NH&); [6] and CFsSO; [7, S] show that these anions exhibit a relatively low specific adsorption which, at positive electrode charges, is even less than that of the H,PO; anions[9, lo]. Nevertheless, the values of E, and of the capacity around E, for these anions show more variations with solution composition than those for H,PO;. This shows the importance of anion-solvent interactions in defining the double layer properties ofa given system. Increasing concentrations of HIPO; in the bulk make the capacity rise steeply for potentials anodic to E. and the humps, present in the C-E curves for low values of X, disappear. According to Barradas and Donaldson[2] this happens because, at low values of x, the hump is due to reorientation of solvent molecules in the electric field; for higher values of X, this reorientation is prevented by increasing amounts of highly solvated H2PO; anions at the interface. For x B 0.25, the hump can again be observed, being well defined for x = 0.8 and 1.0. This hump, which cannot be due to the reorientation of solvent molecules, is probably caused by a marked decrease in capacity in the region anodic to E. as the concentration OF H,PO; in the bulk increases This behaviour was observed previously for CF,SO; [7,8] and also for NO; [9] and ClO, [l I]. As discussed in the last two cases[9,11], the hump is due to the contribution of ionic adsorption to the inner layer capacity. Before carrying out a thermodynamic analysis by integrating the set of capacity curves, due attention must be paid to the possibility that activity coefficients may depend on the composition of the electrolyte. When the activity coefficients of the two constituent salts are approximately the same, this variation can generally be neglected as done so in previous publications in constant ionic strength sdutions. Activity coefficients of KHZP04 and KF at a concentration of 1 M are 0.421 and 0.445, respectively[12]. This difference, too large to be ignored, implies that the
45
40
35 r; ,' 2 30
25
20
15
- 0.5
0.0
-1.0
-1.5
E/V
Fig. 1. Differentialcapacity of the electricaldouble layer for a mercuryelectrodein aqueousx M KH,PO, + (1 -x) M KF at 25°C. x = (l)O.ODS,(2) 0.008, (3)0.01.(4)0.05,(5)0.1, (6) 0.25,(7)0.5,(8)0.8,(9)1.0.
activity coefficient of the K+ ion will change with solution composition. Thus, variations in the potential measured with respect to the see (E,) can no longer be considered equal to those of E+, the potential us an electrode reversible to the cation in the electrolyte. Following the treatment of Fawcett and McCarrik [lo], the activity coefficient (yk+) of the K + ion can be expressed by the relationship In yx+ = -
Afi”” 1 + Bni + p”2
+ BKH$o*CHJo; + BKFcF~1
(1)
where A and 3 are the DebyeHuckel constants, a$+ the ion size parameter for K+, p the ionic strength, flKHIso4 the interaction parameter between K+ and H2POz and BKF that between K’ and F-. The parameters &X,PO+ and /?xp were calculated theoretically[l3] from expressions of the type of Equation (I), using known values of A and B[ 121 and of &+ [ 141. The parameter 8, defined as #3= f&HIpo, - &s)k was then calculated to be -0.426 for p = 1. At the same ionic strength, this value of fi for H,PO; is larger than thoscfoundforf[lO]andNOi [15] ions.In termsof this parameter, the relationship between E+ and E, is given by[ 101 dE+ = dE, - 5 dx,
(2)
where f = FIRT. Using the value of fi given above in Equation (2), it can be shown that the capacitypotential curve is displaced by I I mV when x changes from 0.005 to 1.
Dihydrogen phosphateions on mercury Using the values of E, presented in Table 1, the capacity-potential curves were integrated to obtain the electrode charge density (4). A second integration, using the values of a also presented in Table 1, was performed to obtain the surface tension (7) as a function of potential. Thevalues of yZwere obtained by integration of the 4-E curves from - 1.45 V where the common value of y is the same for all electrolytes [for the control electrolyte (KF) at its interface with mercury, y. = 425.7 mN m-l]. This procedure leads to values of yZwhich will be useful for comparison with proposed experimental values, planned to be determined. The electrode charge and the surface tension were combined to obtain Parsons’ function 5, = y + qE+ . The differential of this function with respect to In x at constant q is related to the specifically adsorbed charge (q’) due to H,PO; anions. For exact thermodynamic treatment of results of capacitance measure ments in mixed solutionsC16, 171,it is necessary to take into account the change of activity coefficients with solution composition. The expression for the differential of the Parsons’ function then becomes[lO]
~ f
l+@
- X+
= q’+q1---- Bx 4 1+/k’
( > dlnx
(3)
where qd- is the anionic charge in the diffuse layer. This equation cannot be solved directly because q”_ is a function of q’. The procedure,adopted here was to first obtain the uncorrected values of q’ via the expression f(a< + /a In x& = q’, as described previously[7J. Values of the diffuse layer charge (q’), the potential of the outer Helmholtz plane (9s) and q”_ were then calculated in succession using known expressions from the Gouy-Chapman theory[lS]. With the value of q!_, a new value of q’ was obtained using Equation (3) and the procedure repeated in an iterative way until the difference between two successive values of q’ was less than 0.01 &cm-2. All these calculations were performed by introducing suitable modifications in the computational procedures described earlier[4]. The difference between corrected and uncorrected values of q’ was only 1.5% for x = 0.05 but rose to be as much as 20 % for x = 0.5.
193
solutions[l, 2] where the definition of a solvent layer adjacent to the electrode surface is complicated by the fact that its thickness depends on the electrode charge[ 13. The situation is different in constant ionic strength solutions as will be shown here. The electrocapillary equation for a system of two salts CA and CB with a common cation can be written: -d<+
= -E+dq+F”-
--Fr,,d~, Xl+,0
+
rgm-(
%B
r
XH,O
n,o
GC,.
>
(5)
Following the treatment of Dutkiewicz and Parsons[l9] for mixed solutions in which the ionic strength is kept constant and the change in activity coefficients is considered negligible, the chemical potentials can be expressed by d&Z* = RTdInx
and
dp,-a = - RT&
(61 d In x,
(r)
where x = m,J(m,-- + mcs), m’s being the respective molality. Substituting Equation (6) and (7) into Equation (S), and expressing x and the mole fractions in terms of the respective number of moles (M) the result is -dc,=-E+dq+
-
( rs_--
c
F,--r McA CB
rH
RTdln x
1o >
MC, r M, ---RRTdlnx M t-Lo t-J*0 > MC,
(8)
which leads to the well known expression: -dC;+ = -E+
dq+
FA- -&I-, RTdInx PI ( > used for the determination of q’[19]. It must be noted in Equation (9) that the surface excesses are absolute. In other words, in constant ionic strength solutions the calculated values of q’ are independent of whether the adsorbed ions are in contact with the electrode surface or separated from it by a layer of solvent molecules. The specz$cally adsorbed charge Figure 2 shows the specifically adsorbed charge due In single salt solutions, the differential of Parsons’ to H2P0, ions as a function of electrode charge. The function T+ with respect to In a* leads to relative values of q’ are much smaller than the ones obtained surface excesses defined by for single salt solutions[l] and, as in the latter case, the adsorbed charges even for x = 1 start being significant only for q > 2 PC cm-‘_ Thelower charges in constant ionic strength solutions can be explained in terms of where A- represents an anion, x’s the mole fractions, the electrostatic effect of the diffuse layer. In Fig. 2, it FA the absolute surface excess of the anions and FnZO can be observed that in most of the regions inthat of the water molecules. If anions are contact vestigated, the adsorbed charge is numerically lower adsorbed on the electrode surface, the difference than the electrode charge. This means that the diffuse between FA-(uJ and FA- can be disregarded and the layer charge has the same sign as the specifically values of q’ are obtained by converting the excesses adsorbed charge. The compensating effect of the into charges and subtracting the contribution of the diffuse layer is proportional to the ionic concentration; it will be larger in constant ionic strength than in single diffuse layer[l8]. However, if a layer of solvent molecules exists between the electrode and the ad- salt solutions. Thus, lower values of q’are expected. On sorbed ions, q’ must be calculated from Ir- which has the other hand, if superequivalent adsorption is to be obtained from Equation (4), after making a present, 14’[ > q and the sign of the diffuse layer charge suitable model for the adsorbed water. This was the is opposite to that of the speciBcally adsorbed charge. case for adsorption of HaPOT ions from single salt Because the screening effect will be larger in constant
E. R. GONZALEZ, A. CARUBELLI
194
2
4
6
8
AND
S. SRINIVASAN
10
12
14
16
ia
glpC crli2 Fig. 2. Adsorbed charge density due to H,PO; ions as a function of the electrode charge. Figures on the lines indicate the following concentrations of H,PO; in the bulk: (I) 0.005, (2) 0.008, (3)0.01, (4) 0.05, (5) 0.1. (6) 0.25, (7) 0.5, (S) 0.8, (9) 1.0.
ionic strength solutions, the values of q’ will then be Iarger than those observed in single salt solutions. An interesting point to be observed from Fig. 2 is that contrary to what happens in single salt solutions q’ reaches a maximum and then decreases as q is made increasingly positive. This phenomenon was discussed previousty in connection with the adsorption of CF,SO; anions on Hg[7, X] in terms of a competition between the anions and the water molecules for the electrode surface. According to the results presented (see Fig. 2 in[7]), the competition between the CF,SO; anions and water molecules seems to depend only on the electrode charge and not on the amount adsorbed. The maximum in adsorption shifts to more positive values of q as the concentration of HIP04 in the bulk decreases. It thus appears that the competition between I&PO; anions and water molecules takes place in a region of values of q where particle-particle repulsion is important. Hence, H,PO, anions are more easily displaced from the surface when the coverage is high. The saturation value of q’ for HI,PO; anions adsorbed at the surface has been estimated to be -53 pCcmLz[l]. Although the values of q’ obtained here are relatively small, these correspond to high coverages in terms of anion adsorption. Another possible explanation for the maximum in adsorption observed is a competition between the H,PO; and F- anions. According to the results of Schiffrin[ZO] fluoride anions can present significant adsorption at high values of q. In this situation, the values of q’ determined are actually given by q’ = q$,roi
- 1‘H
PO CF
q&.
(10)
Thus
the real values of the adsorbed charge due to H2P0, anions (q;lzqo, ) should be higher than those of q’. However, according to Equation (10) the effect of F- adsorption should be maximum for cuzpoi = cr-. > cFit should decrease since the more For ‘HzI’Oi strongly adsorbed H,PO, ion must prevent the Fanions from entering the inner layer. This is not supported by the results presented in Fig. 2 where it is apparent that the maximum is more pronounced the larger C,>,o; becomes in comparison with Cr. _Also, it must be noted that the entry of cations to form “ion pairs” as discussed by Damaskin et aI.[21] is not likely in this case since under all circumstances q’ < q_ Thus the diffuse layer charge will always have the same sign as that of the specificalIy adsorbed ion,
The characteristics
of rhe inner layer
Figure 3 shows the potential drop across the inner as a function of the adsorbed Mm-2 = E+ -#z) charge at constant q+ The hehaviour of the system differs notably from the one observed in single salt solutions[I] for other oxyanions in constant ionic strength solutions[6,7,9, Il, 151. In the latter ease, it is usually found that the slope of the plots is positive for low or negative values of q, gradually becoming zero and then negative as q increases. Here, despite the scatter of the points, the slope seems to be positive for all values of q. The points corresponding to x > 0.25 and to q z= 10 pC cm- * naturally present large deviations due to the particular behavior of this system leading to a maximum in q’ (Fig. 2). The potential drop across the inner layer, assumed to have contributions from the electrode charge and the adsorbed charge, can be written as
Dihydrogen
phosphate
-I
ions on mercury
195
and for low values of x, K,2 is 204 PF crne2 and K,l is 31 PF cm-‘, when evaluated at q’ = 0. These capacities can be expressed[22] by the relationship Kj2 = &/4X(X2 - x,) and K,, = ~/41~~ where x1 is the distance between the metal and the iHp and x2 that between the metal and oHp. Assuming that E is constant within the double layer, K&/K,
Fig. 3. Potential drop across the inner layer as a function of the specifically adsorbed charge due to H,PO; anions. Numbers alongside the lines indicate the charge density on the electrode in pC cmm2. (0) Points corresponding to the
base solution.
of the region between the metal and the outer Helmhotz plane (~HP) and KLZ that of the region between the inner Helmholtz plane (iHp) and the oHp. Equation (11) disregards the contribution of the oriented solvent dipoles to &,,-l. This seems to be justified for anions that present a large superequivalent adsorption but not for weakly adsorbed oxyanions that compete for adsorption with the solvent. The contribution of n dipoles, oriented parallel to the field, to the potential drop is 47t&e where p is the effective dipole moment of the solvent molecules and E the dielectric constant of the inner layer. This parameter is difficult to evaluate because (i) an orientation has to be assumed for the dipoles and (ii) ,Y includes an induced dipole moment term that is dependent on thecharge of the electrode. Changes in this dipole potential may take place when water molecules are displaced by H&‘O; anions or when there are preferential structures at the electrode/electrolyte interface involving the electrode, the adsorbed anions and the water molecules[2]. As discussed above, for most points [q’l < q which means that the diff&e layer charge is negative. This charge will be determined by the solvated F- anions for low values of x, while the contribution of H2PO; anions will increase with x. This may explain why the slopes of the plots in Fig. 3 are higher for low values of x than for higher values of x. The integral capacities KLZ and Kn2 in Equation (11) can be obtained from the slope and the separation of the plots in Fig. 3. In the region 6 G q $ 10 pC cm-’ where
KnZ
is
the
integral
capacity
2 = +a -x1)/x2
(12)
and use of the above values of KL2 and K,,,? in this equation gives x1 = 0.85x,. This seems to be reasonable in view of the large size of the phosphate anion (5 3A in radius). For increasing values of x, the slope approaches zero, which means that XIZ 21 a~ or x1 z xZ. Thus, it must be concluded that the iI-Ip and the oHp nearly coincide when H,FO; anions substitute for F- anions in the diffuse layer. In fact, xZ seems to be smaller in the latter case because in the region 6 d q < 10yCcm-2 K,, has a value of 37 ,uFcm at q’ = - 6 @cm-‘. It is of interest to note that, if enough weight is given to the point corresponding to the most concentrated solution, a parabolic shape of the Christie plots (Fig. 3) can be detected for q = 10-14 pC cm-‘. Such a behaviour has not been previously observed in these plots. An explanation of this phenomenon could he given in terms of the formation of new structures in the double layer as the amount of H,PO; increases. However, an analysis of this situation would rest on a point of dubious accuracy because it is the point corresponding to one of the extremes in a differentiation procedure and hence carrying the largest error.
Adsorption
isothermfir
H2PO;
anions
The adsorption of ions on mercury can be described by an isotherm of the form[23,24] In B = In x+Q+ff#,+aq’+bq,
(13)
where B = q’/(q’s -q), q’s being the saturation value of q’ and Q expresses the specific interaction of an isolated adsorbed ion with the electrode surface. @ and the proportional parameters (1 and b depend on the electrode but are usually assumed to be independent of q’. On the basis of the cut-off disc model, a and b are given by[23] +(
1-+)
(14)
and
where g is a parameter that takes into account the self atmosphere potential of the adsorbed ions, and so related to discretness-of-charge effects. The value of this parameter depends on geometric factors in the double layer and has been calculated by Levine and Robinson for two different models of variation of E with distance[25,26]. When adsorption is weak (q + q’) is small and, consequently, a2 is small and can be approximated by the expression Qpf= A(4 + 4’) f
A
’
196
E. R.
A.
GONZALEZ,
CARUJELLI
AND
S.
SRINIVASAN
15
r,
u
10
Y -u
5
cl 0.0
0.2
0.2 91-Pn (8) iv X F
0.6
0.4
. 1
Fig. 4. Plots of adsorption data for H,PO; ions according to the isotherm given in Equation (11). Numbers alongside the lines indicate the charge density on the electrode in pC CZITI-~.
where A = 5.86$” in water at 25°C. Introducing into Equation (13), the result is lnc=Q+(af
+)q’+
(b+f)q.
this
(16)
This isotherm was tested for H2PO; adsorption by plotting q’ us (l/f)111 (O/x) at constant q and the results are shown in Fig. 4. Here q: was assumed to be the value estimated by Parsons and -53 flCcrn_‘, Zobel[l]. Reasonable straight lines are obtained only for high values of q. namely in the range 12 < q < 18 pC cm- *. The contribution of the points corresponding to high values of x had to be neglected for the reasons discussed in connection with the resuIts presented in Fig. 3, that is, the model in which Equation (16) is based does not take into account the dependence of the competition between the anions and the solvent molecules on the electrode charge. For q -c 12 PC cm- ’ the plots become almost vertical lines, suggesting that (0/x) becomes independent of q’. If this is so, the results in this region may be represented by a Henry’s isotherm, ie tl= xexp(-AG’/RT),
(17)
where AGO is the standard free energy of adsorption. This possibility was tested by plotting 0 tls x at constant 4 (for q -e 12 pC cn- ‘) and the results are shown in Fig. 5. It is obvious that in this region, Hem-y’s isotherm approximately describes the adsorption of HSPO; anions. The applicability of this isotherm means that particle-particle interactionscan be neglected This is surprising when it is considered that for q = 10 $2 cm-’ coverages of the order of 20 % are reached. This discussion shows that the adsorption of H*PO; anions from constant ionic strength solutions is far from being a simple process to be described by a single adsorption isotherm with definite parameters.
Fig. 5. Plots of adsorption
data for H,PO;
ing to a Henry’s isotherm.
Numbers
indicate the charge density on the electrode
Acknowledgernent~Thii
anions accord-
alongside the lines in .uCcm-‘.
work was performed
under the
auspices of the U.S. Department of Energy. A. Caruhehi and E. R. Gonzalez wish to thank CNPq, Brazil, for a scholarship and a travel grant, respectively. A. Cart&% carried out this research work in partial fulfillment of his Ph.D. degree from the Instituto de Fisk e Quimica de Sao Carlos, USP, Brazil.
Dihydrogen phosphate ions on mercury REFERENCES 1. R. Parsonsand F. G. R. Zobel, J. electroad. Gem. 9,333 (1965). 2. R. G. Barradas and G. J. Donaldson, J. electroanal Chem. 48. 239 (19731. 3. W.’ E. o’&dy, E. 3. TayIor and S. Srinivaaan, J. electroanal. Chem. 132, 137 (1982). 4. E. R. Gonzalez. J. elecrroand. Chem. 90. 431 (19781. 5. D. C. Grahame,.R. P. Larsen and M. A. P&h, 3. km. c&m. Sot. 71, 2978 (1949) 6. E. R. Gonzalez, Can. J. Chem. 60, 1643 (1982). 7. E. R. Gonzalez and S. Srinivasan, Electrochim. Acta 27, 1425 (I 982). 8. E. R. Go&ez,
9. 10.
11. 12.
A. CarubcJJi and S. Srinivasan (to be published). R. Payne, J. phys. Chem. 69, 4113 (1965). W. R. Rawcett and T. A. M&brick, J. electrochem. Sac. 123, 1352 (1976). R. Payne, J. phys. Chem. 74 204 (1966). R. A. Robinson and R. H. Stokes, Electrolyte Solutions. Butterwoti, London (t 959).
197
13. S. Lakshmanan
and S. K. Rangarajan, J. clect~oanal. Chem. 27, 170 (1970). 14. J. KielJand, J. An &em. Sot. 59. I675 (I 937). 15. W. R. Fawcett and J. B. Sellan, Can. J. Chem. 55, 3871 (1977). Chem. 10, 35 (1965). 16. H, D. Hurwitz, J. elec~roa~l. 17. S. Lakshmanan and S. K. Rangarajan, J. electroanal.
Chem. 27, f27 (1970). DeJahay, Double Layer and Electrode Kinetics. Interscience, New York (1965). E. Dutkiewicz and R Parsons. J. electroanal. Chem. 11, JO0 (1966). D. J. schiffrin, Trans. Faraday Sot. 67, 3318 (3973). 8. Damaskin. L. Kunznetsova, U. Palm, M. Vii&tnZSu and M. Salve, J. elecrroanai. Chem 100, 365 (1979). J. M. Parry and R. Parsons, Trans. Faraday Sot. 59, 241 (I 963). S. Levine, J. colloid inte&ce Sci. 37, 619 (1971). W. R. Fawcett, J. electronnal. Chem 84, 303 (1977). S. Levine and K. Robinson, J. eiectroanal. Chem. 41,159 (f 973). K. Robinson and S. Levine, J. elecfroad. Chem. 47, 395 (1973).
18. P. 19. 20. 21.
22. 23. 24. 25. 26.
191-197.1985
001346@&,*5
53.00 +
o.m
RrwmcaRsslUd.
ADSORPTION BEHAVIOUR OF PIHYDROGEN PHOSPHATE IONS ON MERCURY FROM CONSTANT IONIC STRENGTH SOLUTIONS E.R. Los Alamos
GONZALEZ,*
National
A. CARUBELLI~ and S.
Laboratory,
MSD429,
SRINIVASAN~
Los Alamos,
NM 87545. U.S.A.
(Received22 August 1983;in reuisedform 3 Jury 1984) Abstract-The adsorptionbhaviour of &PO; anions on mercury has previouslybeen analysed from capacitance-potential relations at the interface of mercury with K&PO,. It is not possible to determine unambiguously the adsorption characteristics of I&PO, ions from siagle salt solution experiments because of the possible existence of a layer of water molecules between the elecmxle and the adsorbed ions. In this work, the adsorption behavior of H*PO; ionson mercuryis analysedfrom experimentalmeasurements of thecapacitanceasa functionof potential at the interface of mercury with constant ionic strength solutions of compositions x M KH,PO, -t (1 -x) M KF. It is shownthattheQlculatedamountsof adsorbedionsdo not depend on the position of these ions relative to the solvent molecules. The double layer parameters were calculated taking into account the variations of activity coefficients of KH,PO, and KF with solution composition. In constant ionic strength solutions, the plot of adsorbed charge vs &&rode charge exhibits a maximum due to competition between the adsorbed H,PO; anions with the solvent or other ionic species. This result is shown to be important in determining the properties of the double layer characteristics in the presence of adsorbed H,PO; ions.
INTRODUCTION The adsorption behaviour of HZ PO; anions on mercury from solution of NaH2P04 was studied by Parsons and Zobel[l]. This work showed interesting features in particular the fact that differences between integrated capacity and experimental surface tension results could be explained by the existence of an ion free layer of water molecules adjacent to the electrode surface. Later, Barradas and Donaldson[2] also investigated the adsorption characteristics of different phosphate ions on Hg from single salt solutions. These authors discussed the effect of ionsolvent interactions on the double layer structure in the presence of phosphate. ions. The surface excesses calculated in these single salt solutions are probably influenced by the existence of a layer of solvent molecules between the electrode and the adsorbed ions. The double layer properties in the presence of weakly adsorbed ions whose centres ofcharge lie nearer the diffuse layer than the metal surface are expected to depend considerably on the ionic concentration in the former region. Thus, it is worthwhile to compare the adsorption characteristics of HIPO; anions from constant ionic strength soIutions, which is the main subject of this paper, with those observed previously in single salt solutions. The present study also has some technological relevance in respect to fuel cell research and development. There is renewed interest in an understanding of * Present address: Institute de Fi&ccia e Ouithica de S&o Car&, USP, C.P. 369, 13560 Sao Carlo& SP. Brazil. + Present address: Metal Leve S.A., Rua Brasilio Lux 535, Cx. Postal 6567.04746. 90 Paulo. SP. Brazil. r Present address: Institute for Hydrogen Systems, 2480 Dunwin Drive, Mississauga, Ontario L5L lJ9, Canada.
the adsorption behaviour of phosphate species as a
function of potentialbecause of its significant influence on oxygen reduction kinetics and hence on the efficiency of phosphoric acid fuel cells. The higher overpotential for this reaction at platinum in concentrated phosphoric acid than in trifluoromethanesulfonic acid (a promising fuel cell electorlyte) is commonly attributed to the influence of anion adsorption in the former electrolyteC3-j. EXPERIMENTAL KH2P04 and KF (both salts from Baker, AR grade) were used to prepare solutions in deionized water, further putied by distillation from alkaline permanganate. The solutions had a composition x M KH2P04 + (1 - x) M KF, the values of x being 0.005, 0.008, 0.01, 0.05, 0.1, 0.25, 0.5, 0.8 and 1.0. The cell, electrodes and apparatus to measure the differential capacity of the interface have been described elsewhere[4]. Potentials of zero charge (E,) were measured using the streaming mercury electrode technique[5]. All experiments were carried out at 25 *O.l”C using a saturated calomel electrode (see) as reference. RESULTS
AND DISCUSSION
Calculation of double layer parameters from capacity meas wemen f s Table 1 shows the experimental values of E, as a function of x. It can be seen that E, varies by only 7 mV when x changes from 0.005 to I .O.Thus, for a system in which only the anions are responsible for specific adsorption, the amount of adsorbed HIPO; ions in 191
E. R.
I92
Table 1. Potentials of zero charge (E,), surface tension (y,), and differential capacitance (C,) at the potential of zero charge for the mercury/x M KH, PO, + (1- x) M KF interface at 25°C
0 0.005
0.008 0.01 0.05
0.1
0.25 0.5 0.8 1.0
-0.4338 -0.4338 -0.4338 -0.4340 - 0.4340 - 0.4348 - 0.4350 -0.4360 -0.4385 -0.4415
!3. SRINIVASAN
GONZALEZ,A.CARUBELLIAND
452.7 425.7 425.7 425.7 425.7
26.12 26.12 26.15 26.18 26.21
425.6 425.6 425.6 425.6 425.6
26.26 26.30 26.40 26.60 26.80
the region of E, must be negligible. Figure I shows the capacity-potential (C-E) curves for the mercury/ (KH2P04 + KF) interface. An examination of the C-E curves confirms the conclusion that the extent of adsorption of H,PO; ions is low because the capacity is nearly independent of x for potentials more negative than E,. From the characteristics in the region around E,, only qualitative condusions can be reached about the behaviow of the system in other potential regions. Recent publications on the adsorption of NH&); [6] and CFsSO; [7, S] show that these anions exhibit a relatively low specific adsorption which, at positive electrode charges, is even less than that of the H,PO; anions[9, lo]. Nevertheless, the values of E, and of the capacity around E, for these anions show more variations with solution composition than those for H,PO;. This shows the importance of anion-solvent interactions in defining the double layer properties ofa given system. Increasing concentrations of HIPO; in the bulk make the capacity rise steeply for potentials anodic to E. and the humps, present in the C-E curves for low values of X, disappear. According to Barradas and Donaldson[2] this happens because, at low values of x, the hump is due to reorientation of solvent molecules in the electric field; for higher values of X, this reorientation is prevented by increasing amounts of highly solvated H2PO; anions at the interface. For x B 0.25, the hump can again be observed, being well defined for x = 0.8 and 1.0. This hump, which cannot be due to the reorientation of solvent molecules, is probably caused by a marked decrease in capacity in the region anodic to E. as the concentration OF H,PO; in the bulk increases This behaviour was observed previously for CF,SO; [7,8] and also for NO; [9] and ClO, [l I]. As discussed in the last two cases[9,11], the hump is due to the contribution of ionic adsorption to the inner layer capacity. Before carrying out a thermodynamic analysis by integrating the set of capacity curves, due attention must be paid to the possibility that activity coefficients may depend on the composition of the electrolyte. When the activity coefficients of the two constituent salts are approximately the same, this variation can generally be neglected as done so in previous publications in constant ionic strength sdutions. Activity coefficients of KHZP04 and KF at a concentration of 1 M are 0.421 and 0.445, respectively[12]. This difference, too large to be ignored, implies that the
45
40
35 r; ,' 2 30
25
20
15
- 0.5
0.0
-1.0
-1.5
E/V
Fig. 1. Differentialcapacity of the electricaldouble layer for a mercuryelectrodein aqueousx M KH,PO, + (1 -x) M KF at 25°C. x = (l)O.ODS,(2) 0.008, (3)0.01.(4)0.05,(5)0.1, (6) 0.25,(7)0.5,(8)0.8,(9)1.0.
activity coefficient of the K+ ion will change with solution composition. Thus, variations in the potential measured with respect to the see (E,) can no longer be considered equal to those of E+, the potential us an electrode reversible to the cation in the electrolyte. Following the treatment of Fawcett and McCarrik [lo], the activity coefficient (yk+) of the K + ion can be expressed by the relationship In yx+ = -
Afi”” 1 + Bni + p”2
+ BKH$o*CHJo; + BKFcF~1
(1)
where A and 3 are the DebyeHuckel constants, a$+ the ion size parameter for K+, p the ionic strength, flKHIso4 the interaction parameter between K+ and H2POz and BKF that between K’ and F-. The parameters &X,PO+ and /?xp were calculated theoretically[l3] from expressions of the type of Equation (I), using known values of A and B[ 121 and of &+ [ 141. The parameter 8, defined as #3= f&HIpo, - &s)k was then calculated to be -0.426 for p = 1. At the same ionic strength, this value of fi for H,PO; is larger than thoscfoundforf[lO]andNOi [15] ions.In termsof this parameter, the relationship between E+ and E, is given by[ 101 dE+ = dE, - 5 dx,
(2)
where f = FIRT. Using the value of fi given above in Equation (2), it can be shown that the capacitypotential curve is displaced by I I mV when x changes from 0.005 to 1.
Dihydrogen phosphateions on mercury Using the values of E, presented in Table 1, the capacity-potential curves were integrated to obtain the electrode charge density (4). A second integration, using the values of a also presented in Table 1, was performed to obtain the surface tension (7) as a function of potential. Thevalues of yZwere obtained by integration of the 4-E curves from - 1.45 V where the common value of y is the same for all electrolytes [for the control electrolyte (KF) at its interface with mercury, y. = 425.7 mN m-l]. This procedure leads to values of yZwhich will be useful for comparison with proposed experimental values, planned to be determined. The electrode charge and the surface tension were combined to obtain Parsons’ function 5, = y + qE+ . The differential of this function with respect to In x at constant q is related to the specifically adsorbed charge (q’) due to H,PO; anions. For exact thermodynamic treatment of results of capacitance measure ments in mixed solutionsC16, 171,it is necessary to take into account the change of activity coefficients with solution composition. The expression for the differential of the Parsons’ function then becomes[lO]
~ f
l+@
- X+
= q’+q1---- Bx 4 1+/k’
( > dlnx
(3)
where qd- is the anionic charge in the diffuse layer. This equation cannot be solved directly because q”_ is a function of q’. The procedure,adopted here was to first obtain the uncorrected values of q’ via the expression f(a< + /a In x& = q’, as described previously[7J. Values of the diffuse layer charge (q’), the potential of the outer Helmholtz plane (9s) and q”_ were then calculated in succession using known expressions from the Gouy-Chapman theory[lS]. With the value of q!_, a new value of q’ was obtained using Equation (3) and the procedure repeated in an iterative way until the difference between two successive values of q’ was less than 0.01 &cm-2. All these calculations were performed by introducing suitable modifications in the computational procedures described earlier[4]. The difference between corrected and uncorrected values of q’ was only 1.5% for x = 0.05 but rose to be as much as 20 % for x = 0.5.
193
solutions[l, 2] where the definition of a solvent layer adjacent to the electrode surface is complicated by the fact that its thickness depends on the electrode charge[ 13. The situation is different in constant ionic strength solutions as will be shown here. The electrocapillary equation for a system of two salts CA and CB with a common cation can be written: -d<+
= -E+dq+F”-
--Fr,,d~, Xl+,0
+
rgm-(
%B
r
XH,O
n,o
GC,.
>
(5)
Following the treatment of Dutkiewicz and Parsons[l9] for mixed solutions in which the ionic strength is kept constant and the change in activity coefficients is considered negligible, the chemical potentials can be expressed by d&Z* = RTdInx
and
dp,-a = - RT&
(61 d In x,
(r)
where x = m,J(m,-- + mcs), m’s being the respective molality. Substituting Equation (6) and (7) into Equation (S), and expressing x and the mole fractions in terms of the respective number of moles (M) the result is -dc,=-E+dq+
-
( rs_--
c
F,--r McA CB
rH
RTdln x
1o >
MC, r M, ---RRTdlnx M t-Lo t-J*0 > MC,
(8)
which leads to the well known expression: -dC;+ = -E+
dq+
FA- -&I-, RTdInx PI ( > used for the determination of q’[19]. It must be noted in Equation (9) that the surface excesses are absolute. In other words, in constant ionic strength solutions the calculated values of q’ are independent of whether the adsorbed ions are in contact with the electrode surface or separated from it by a layer of solvent molecules. The specz$cally adsorbed charge Figure 2 shows the specifically adsorbed charge due In single salt solutions, the differential of Parsons’ to H2P0, ions as a function of electrode charge. The function T+ with respect to In a* leads to relative values of q’ are much smaller than the ones obtained surface excesses defined by for single salt solutions[l] and, as in the latter case, the adsorbed charges even for x = 1 start being significant only for q > 2 PC cm-‘_ Thelower charges in constant ionic strength solutions can be explained in terms of where A- represents an anion, x’s the mole fractions, the electrostatic effect of the diffuse layer. In Fig. 2, it FA the absolute surface excess of the anions and FnZO can be observed that in most of the regions inthat of the water molecules. If anions are contact vestigated, the adsorbed charge is numerically lower adsorbed on the electrode surface, the difference than the electrode charge. This means that the diffuse between FA-(uJ and FA- can be disregarded and the layer charge has the same sign as the specifically values of q’ are obtained by converting the excesses adsorbed charge. The compensating effect of the into charges and subtracting the contribution of the diffuse layer is proportional to the ionic concentration; it will be larger in constant ionic strength than in single diffuse layer[l8]. However, if a layer of solvent molecules exists between the electrode and the ad- salt solutions. Thus, lower values of q’are expected. On sorbed ions, q’ must be calculated from Ir- which has the other hand, if superequivalent adsorption is to be obtained from Equation (4), after making a present, 14’[ > q and the sign of the diffuse layer charge suitable model for the adsorbed water. This was the is opposite to that of the speciBcally adsorbed charge. case for adsorption of HaPOT ions from single salt Because the screening effect will be larger in constant
E. R. GONZALEZ, A. CARUBELLI
194
2
4
6
8
AND
S. SRINIVASAN
10
12
14
16
ia
glpC crli2 Fig. 2. Adsorbed charge density due to H,PO; ions as a function of the electrode charge. Figures on the lines indicate the following concentrations of H,PO; in the bulk: (I) 0.005, (2) 0.008, (3)0.01, (4) 0.05, (5) 0.1. (6) 0.25, (7) 0.5, (S) 0.8, (9) 1.0.
ionic strength solutions, the values of q’ will then be Iarger than those observed in single salt solutions. An interesting point to be observed from Fig. 2 is that contrary to what happens in single salt solutions q’ reaches a maximum and then decreases as q is made increasingly positive. This phenomenon was discussed previousty in connection with the adsorption of CF,SO; anions on Hg[7, X] in terms of a competition between the anions and the water molecules for the electrode surface. According to the results presented (see Fig. 2 in[7]), the competition between the CF,SO; anions and water molecules seems to depend only on the electrode charge and not on the amount adsorbed. The maximum in adsorption shifts to more positive values of q as the concentration of HIP04 in the bulk decreases. It thus appears that the competition between I&PO; anions and water molecules takes place in a region of values of q where particle-particle repulsion is important. Hence, H,PO, anions are more easily displaced from the surface when the coverage is high. The saturation value of q’ for HI,PO; anions adsorbed at the surface has been estimated to be -53 pCcmLz[l]. Although the values of q’ obtained here are relatively small, these correspond to high coverages in terms of anion adsorption. Another possible explanation for the maximum in adsorption observed is a competition between the H,PO; and F- anions. According to the results of Schiffrin[ZO] fluoride anions can present significant adsorption at high values of q. In this situation, the values of q’ determined are actually given by q’ = q$,roi
- 1‘H
PO CF
q&.
(10)
Thus
the real values of the adsorbed charge due to H2P0, anions (q;lzqo, ) should be higher than those of q’. However, according to Equation (10) the effect of F- adsorption should be maximum for cuzpoi = cr-. > cFit should decrease since the more For ‘HzI’Oi strongly adsorbed H,PO, ion must prevent the Fanions from entering the inner layer. This is not supported by the results presented in Fig. 2 where it is apparent that the maximum is more pronounced the larger C,>,o; becomes in comparison with Cr. _Also, it must be noted that the entry of cations to form “ion pairs” as discussed by Damaskin et aI.[21] is not likely in this case since under all circumstances q’ < q_ Thus the diffuse layer charge will always have the same sign as that of the specificalIy adsorbed ion,
The characteristics
of rhe inner layer
Figure 3 shows the potential drop across the inner as a function of the adsorbed Mm-2 = E+ -#z) charge at constant q+ The hehaviour of the system differs notably from the one observed in single salt solutions[I] for other oxyanions in constant ionic strength solutions[6,7,9, Il, 151. In the latter ease, it is usually found that the slope of the plots is positive for low or negative values of q, gradually becoming zero and then negative as q increases. Here, despite the scatter of the points, the slope seems to be positive for all values of q. The points corresponding to x > 0.25 and to q z= 10 pC cm- * naturally present large deviations due to the particular behavior of this system leading to a maximum in q’ (Fig. 2). The potential drop across the inner layer, assumed to have contributions from the electrode charge and the adsorbed charge, can be written as
Dihydrogen
phosphate
-I
ions on mercury
195
and for low values of x, K,2 is 204 PF crne2 and K,l is 31 PF cm-‘, when evaluated at q’ = 0. These capacities can be expressed[22] by the relationship Kj2 = &/4X(X2 - x,) and K,, = ~/41~~ where x1 is the distance between the metal and the iHp and x2 that between the metal and oHp. Assuming that E is constant within the double layer, K&/K,
Fig. 3. Potential drop across the inner layer as a function of the specifically adsorbed charge due to H,PO; anions. Numbers alongside the lines indicate the charge density on the electrode in pC cmm2. (0) Points corresponding to the
base solution.
of the region between the metal and the outer Helmhotz plane (~HP) and KLZ that of the region between the inner Helmholtz plane (iHp) and the oHp. Equation (11) disregards the contribution of the oriented solvent dipoles to &,,-l. This seems to be justified for anions that present a large superequivalent adsorption but not for weakly adsorbed oxyanions that compete for adsorption with the solvent. The contribution of n dipoles, oriented parallel to the field, to the potential drop is 47t&e where p is the effective dipole moment of the solvent molecules and E the dielectric constant of the inner layer. This parameter is difficult to evaluate because (i) an orientation has to be assumed for the dipoles and (ii) ,Y includes an induced dipole moment term that is dependent on thecharge of the electrode. Changes in this dipole potential may take place when water molecules are displaced by H&‘O; anions or when there are preferential structures at the electrode/electrolyte interface involving the electrode, the adsorbed anions and the water molecules[2]. As discussed above, for most points [q’l < q which means that the diff&e layer charge is negative. This charge will be determined by the solvated F- anions for low values of x, while the contribution of H2PO; anions will increase with x. This may explain why the slopes of the plots in Fig. 3 are higher for low values of x than for higher values of x. The integral capacities KLZ and Kn2 in Equation (11) can be obtained from the slope and the separation of the plots in Fig. 3. In the region 6 G q $ 10 pC cm-’ where
KnZ
is
the
integral
capacity
2 = +a -x1)/x2
(12)
and use of the above values of KL2 and K,,,? in this equation gives x1 = 0.85x,. This seems to be reasonable in view of the large size of the phosphate anion (5 3A in radius). For increasing values of x, the slope approaches zero, which means that XIZ 21 a~ or x1 z xZ. Thus, it must be concluded that the iI-Ip and the oHp nearly coincide when H,FO; anions substitute for F- anions in the diffuse layer. In fact, xZ seems to be smaller in the latter case because in the region 6 d q < 10yCcm-2 K,, has a value of 37 ,uFcm at q’ = - 6 @cm-‘. It is of interest to note that, if enough weight is given to the point corresponding to the most concentrated solution, a parabolic shape of the Christie plots (Fig. 3) can be detected for q = 10-14 pC cm-‘. Such a behaviour has not been previously observed in these plots. An explanation of this phenomenon could he given in terms of the formation of new structures in the double layer as the amount of H,PO; increases. However, an analysis of this situation would rest on a point of dubious accuracy because it is the point corresponding to one of the extremes in a differentiation procedure and hence carrying the largest error.
Adsorption
isothermfir
H2PO;
anions
The adsorption of ions on mercury can be described by an isotherm of the form[23,24] In B = In x+Q+ff#,+aq’+bq,
(13)
where B = q’/(q’s -q), q’s being the saturation value of q’ and Q expresses the specific interaction of an isolated adsorbed ion with the electrode surface. @ and the proportional parameters (1 and b depend on the electrode but are usually assumed to be independent of q’. On the basis of the cut-off disc model, a and b are given by[23] +(
1-+)
(14)
and
where g is a parameter that takes into account the self atmosphere potential of the adsorbed ions, and so related to discretness-of-charge effects. The value of this parameter depends on geometric factors in the double layer and has been calculated by Levine and Robinson for two different models of variation of E with distance[25,26]. When adsorption is weak (q + q’) is small and, consequently, a2 is small and can be approximated by the expression Qpf= A(4 + 4’) f
A
’
196
E. R.
A.
GONZALEZ,
CARUJELLI
AND
S.
SRINIVASAN
15
r,
u
10
Y -u
5
cl 0.0
0.2
0.2 91-Pn (8) iv X F
0.6
0.4
. 1
Fig. 4. Plots of adsorption data for H,PO; ions according to the isotherm given in Equation (11). Numbers alongside the lines indicate the charge density on the electrode in pC CZITI-~.
where A = 5.86$” in water at 25°C. Introducing into Equation (13), the result is lnc=Q+(af
+)q’+
(b+f)q.
this
(16)
This isotherm was tested for H2PO; adsorption by plotting q’ us (l/f)111 (O/x) at constant q and the results are shown in Fig. 4. Here q: was assumed to be the value estimated by Parsons and -53 flCcrn_‘, Zobel[l]. Reasonable straight lines are obtained only for high values of q. namely in the range 12 < q < 18 pC cm- *. The contribution of the points corresponding to high values of x had to be neglected for the reasons discussed in connection with the resuIts presented in Fig. 3, that is, the model in which Equation (16) is based does not take into account the dependence of the competition between the anions and the solvent molecules on the electrode charge. For q -c 12 PC cm- ’ the plots become almost vertical lines, suggesting that (0/x) becomes independent of q’. If this is so, the results in this region may be represented by a Henry’s isotherm, ie tl= xexp(-AG’/RT),
(17)
where AGO is the standard free energy of adsorption. This possibility was tested by plotting 0 tls x at constant 4 (for q -e 12 pC cn- ‘) and the results are shown in Fig. 5. It is obvious that in this region, Hem-y’s isotherm approximately describes the adsorption of HSPO; anions. The applicability of this isotherm means that particle-particle interactionscan be neglected This is surprising when it is considered that for q = 10 $2 cm-’ coverages of the order of 20 % are reached. This discussion shows that the adsorption of H*PO; anions from constant ionic strength solutions is far from being a simple process to be described by a single adsorption isotherm with definite parameters.
Fig. 5. Plots of adsorption
data for H,PO;
ing to a Henry’s isotherm.
Numbers
indicate the charge density on the electrode
Acknowledgernent~Thii
anions accord-
alongside the lines in .uCcm-‘.
work was performed
under the
auspices of the U.S. Department of Energy. A. Caruhehi and E. R. Gonzalez wish to thank CNPq, Brazil, for a scholarship and a travel grant, respectively. A. Cart&% carried out this research work in partial fulfillment of his Ph.D. degree from the Instituto de Fisk e Quimica de Sao Carlos, USP, Brazil.
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9. 10.
11. 12.
A. CarubcJJi and S. Srinivasan (to be published). R. Payne, J. phys. Chem. 69, 4113 (1965). W. R. Rawcett and T. A. M&brick, J. electrochem. Sac. 123, 1352 (1976). R. Payne, J. phys. Chem. 74 204 (1966). R. A. Robinson and R. H. Stokes, Electrolyte Solutions. Butterwoti, London (t 959).
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13. S. Lakshmanan
and S. K. Rangarajan, J. clect~oanal. Chem. 27, 170 (1970). 14. J. KielJand, J. An &em. Sot. 59. I675 (I 937). 15. W. R. Fawcett and J. B. Sellan, Can. J. Chem. 55, 3871 (1977). Chem. 10, 35 (1965). 16. H, D. Hurwitz, J. elec~roa~l. 17. S. Lakshmanan and S. K. Rangarajan, J. electroanal.
Chem. 27, f27 (1970). DeJahay, Double Layer and Electrode Kinetics. Interscience, New York (1965). E. Dutkiewicz and R Parsons. J. electroanal. Chem. 11, JO0 (1966). D. J. schiffrin, Trans. Faraday Sot. 67, 3318 (3973). 8. Damaskin. L. Kunznetsova, U. Palm, M. Vii&tnZSu and M. Salve, J. elecrroanai. Chem 100, 365 (1979). J. M. Parry and R. Parsons, Trans. Faraday Sot. 59, 241 (I 963). S. Levine, J. colloid inte&ce Sci. 37, 619 (1971). W. R. Fawcett, J. electronnal. Chem 84, 303 (1977). S. Levine and K. Robinson, J. eiectroanal. Chem. 41,159 (f 973). K. Robinson and S. Levine, J. elecfroad. Chem. 47, 395 (1973).
18. P. 19. 20. 21.
22. 23. 24. 25. 26.