2764
LOWELLR. MCCOYAND HARRY B. MARK,JR.
Catalytic Polarographic Current of a Metal Complex.1 VII. Determination of the Charge of the Electroactive Species for the o-Phenylenediamine-Nickel(I1) Prewavez
by Lowell R. McCoy and Harry B. Mark, Jr. Department of Chemistry, University of Michigan, Ann Arbor, Michigan
48104
(Received February 13, 1969)
In previous studies of the polarographic prewave obtained with Ni(I1) and o-phenylenediamine,the dependence of the prewave height on the outer Helmholtz potential, $O, of the electrode double layer required that a charge of 1 be assigned to the electroactive species rather than the value of f 2 expected for a complex formed from Ni(I1) and an uncharged ligand. In those experiments the desired variation in #a was obtained by the use of a range of concentrations of supporting electrolytes, offering the possibility that the charge value obtained in this manner was the result of fortuitous changes in the reactant activities. This problem has been reexamined using a method of analysis which permits a determination of this charge value at a singleelectrolyte concentration, eliminatingthe activity uncertainty and substantiating the charge value found earlier. The propriety of equating the potential, #O, with the potential of the reaction plane in the case of a large organic molecule has been investigated in terms of the probable orientation of the adsorbed ligand. An extension of the Frumkin parallel capacitor electrode model to a three-component surface system indicates that the molecule occupies a planar position for surface concentrations present in the polarographic measurements. In this position the reaction plane is virtually coincident with the outer plane. At higher surface concentrations, reorientation to a vertical position occurs. Analysis of adsorption data for o-phenylenediamineon mercury using the Frumkin isotherm indicates that strong repulsive forces arise between the adsorbed molecules at electrode potentials of concern to the prewave as the surface concentration is decreased to approach the low values present in the polarographic measurements. This fact, taken together with the negative shift of the potential of zero electrode charge with increasing volume concentrations of the organic ligand, suggests that electrolyte anions are coadsorbed with planar-oriented o-phenylenediamine molecules at not too negative electrode potentials. If the coadsorbed anion is an active partner in the surface reaction, a charge of + l would be expected for the electroactive complex.
+
The behavior of the polarographic prewave observed in the reduction of N(I1) in the presence of the organic ligand o-phenylenediamine (OPDA) has been examined in two recent papers.*d,e The dependence of the prewave height on the experimental variables, drop time, and the ligand surface concentration was found consistent with that predicted for a surface reaction between the hexaaquonickel ion and the adsorbed ligand yielding a n electroactive complex. While variations in the prewave height with changes in the electrode double layer substantiated the existence of a surface reaction, the relationship found between the prewave height and the potential, $O, of the outer Helmholtz plane required that the electroactive complex possess a charge of +1 rather than the value of +2 expected for a complex formed from Ni(I1) and a n uncharged ligand. I n the double-layer calculations made previously, the desired variation in $O was necessarily obtained by changing the concentration of the supporting electrolyte. A possibility, therefore, existed that an incorrect charge was obtained as a result of variations in reactant activities. This paper will present an analysis of the prewave a t a single electrolyte concentration which eliminates this source of error and which The Journal of PhgsicaE Chemistry
substantiates the charge value found in the earlier work. I n these calculations it is assumed that the location of the reaction plane is reasonably coincident with the outer plane of the electrode double layer. The physical size of the OPDA molecule requires that it be planar rather than vertically oriented to the electrode surface if this assumption is to be valid. Evidence favoring planar orientation a t concentrations used in the polarographic measurements is given. An explanation for the unexpected charge of the electroactive complex is offered on the basis of evidence of coadsorption of electrolyte anions with OPDA. The surface concentrations of OPDA on mercury and the electrode charge data used in this paper were obtained from differential capacitance measurements. The experimental methods used to make both these and (1) This research was supported in part by grants from the National Science Foundation, NSF GP-4620 and GP-6425, and the U. S. Army Office of Research (Durham), No. DA-31-124-ARO-D-284. (2) For other papers of this series: (a) H. B. Mark, Jr., and C. N. Reilley, J . Electroanal. Chem., 4, 189 (1962); (b) H. B. Mark, Jr., ibid., 7, 276 (1964); (c) H. B. Mark, Jr., L. R. McCoy, E. KirowaEisner, and H. C. MacDonald, Jr., J . Phys. Chem., 72, 1083 (1968); (d) L. R. McCoy, H. B. Mark, Jr., and L. Gierst, ibid., 72, 4637 (1968); (e) L. R. McCoy and H. B. Mark, Jr., ibid., 73, 953 (1969).
CATALYTIC POLAROGRAPHIC CURRENT OF
A
2765
METALCOMPLEX
the polarographic measurements have been described previously.2d+
The Charge of the Electroactive Complex It has been shown previously*d that the height of a prewave resulting from a 1:1 surface reaction between an adsorbed ligand and a metal ion to form an electroactive complex can be related to +O, the potential of the outer plane of the electrode double layer, by the following expression
where X is a rate parameter calculated from the ratio of the observed prewave current to the diffusion limiting current for the metal ion using Koutecky’s3 mathematical relationship derived for a heterogeneous electrode reaction. The term kro is the forward chemical reaction rate constant for the complexation reaction, t is the drop life, D is the diffusion coefficient for the metal ion, [LIads is the surface concentration of the adsorbed ligand, and x is the charge of the electroactive complex, the quantity of interest here. The other terms have their usual electrochemical meaning. Equation 1 is valid only where the electrode process is controlled by the chemical rate of formation of the electroactive complex and, in the case of the OPDANi(I1) prewave, its application is limited to a small (perhaps 50 mT7) 2d+ and ill-defined electrode potential range in any given electrolyte before a significant fraction of the current represents direct reduction of the hexaaquonickel ion. It is for this reason that correlations between the prewave height and were made previously using several electrolyte concentrations a t an electrode potential corresponding to the prewave plateau. While necessary variations in +O were thus obtained under conditions where eq 1 would be applicable, possible variations in the activities of the reactants added an element of uncertainty to the results of these experiments. Analysis of the prewave for a single electrolyte concentration (avoiding changing reactant activities) would be possible if a n expression valid for the entire wave could be written as the electrode potential span available for calculations would then be much expanded. While a rigorous solution to this problem presents some mathematical complexity, an approximate relationship can be developed without difficulty. If an equilibrium condition a t the electrode surface is assumed whereby the rate of depletion of the surface complex by both chemical and electrochemical processes is exactly balanced by its rate of formation, the following relationship will exist. kt [L]ad~[Ni(HzO)al~=m~+ = kb [ N i ( H z o ) ~ L ] a d ~ ~kei + [Ni(HzO)yL]ad,2+ ( 2 )
+
where kb is a pseudo-first-order reaction rate constant
incorporating the water released by the complexation reaction, and kel is the electrochemical rate constant. Equation 2 may be solved for the surface concentration of the electroactive complex in terms of the reactant concentrations a t the electrode surface (x = 0). The dependence of the current on these concentrations then becomes
The current dependence shown here differs from that of the chemical rate limiting case only in the identity of the rate constants.2d The relationship between a new rate parameter (shown here as 6 to distinguish it from X used in the chemical rate limiting case) may therefore be written as
e=---
kelkf
kei
+ kb
[Lladsd
d5
(4)
where
5
=
F(i)
As before, the mathematical relationship between 5 and i / i d is that given by Koutecky4 for a heterogeneous electrode reaction. I n the derivation of eq 1 and 4,it has been assumed that [L]ads is a time-invariant quantity. It has been shown2e that the equilibrium surface concentration, I?, can be substituted for this term in eq 1if the adsorption of the ligand is sufficiently rapid.6 While the same assumption must also be made in the case of eq 4, an additional problem is presented here by the fact that [L]ads must now represent the “free” or noncomplexed portion of the surface concentration of the ligand. At low values of kel, some fraction of the total surface concentration will be present as part of the metalligand complex. Some error must, therefore, result from the substitution of r for [LIadsa t low values of kel even where equilibrium coverage is attained rapidly. While the degree of error from this source depends on the formation constant for the surface complex as well as kel, it will be seen that this problem has least consequence in that portion of the prewave of concern to the immediate problem of determining the charge of the electroactive complex. Equation 4 represents the relationship expected in the absence of any contribution from the electrode double layer. As this situation is contrary to experi( 3 ) .J. Koutecky, Collect. Czech. Chem. Commun., 18, 697 (1953). (4) The original relationship derived by Kouteckys was written in
,,,4K2
x. terms of the symbol x . The symbol E used here equals (6) This substitution is permitted in the case of slow adsorption only if the ratio i / i d is multiplied by the ratio of the equilibrium surface concentration to the actual surface concentration a t time t.*e The “corrected” current ratio may then be used to determine 5. Volume 7.9, Number 8 August 1969
LOWELL R. McCoy
2766 mental evidence,2d it is necessary to correct eq 4 for double-layer effects. The rate constants calculated from this equation will, in any actual experiment, be those described by Giersts as “apparent” rate constants. The relationships between these and the “true” rate constants, ie., those which would be observed if $O were zero, are given by Gierst6as
HARRY B. MARK,JR.
1
I .o aD
h X
ru
(5)
AND
1t
where kro and kelo are the true rate constants, a is the transfer coefficient, nu is the number of electrons transferred in the rate-controlling electrochemical step, and
0.5
1 [l
i
4 x 1 0 ’ 4 ~OPDA 0.1 M KCI
I
0
IU3M Ni2*,5sec
A
I O - 3 ~Ni2+ ,3sec
X SxlC4M Ni2*,3sec I 0.1MlLiCI04 I 0 ~ x I O - ~Ni2*,3sec M
-0.70 -0.75 -0.80 -0.85 -0.90 Potential, Volts,S.C.E. Figure 2. Dependence of the corrected rate parameter on the electrode potential; charge value, z = $2.
a=--&
z’@
0
$/X
f
-d /
Z=+l 4x1Om4Y. OPDA 0.1 M. KCI 0 10-3M Ni2+, 5sec
A 10-3M Ni2’
X5x164M Ni2’ , 3sec 0.1 M LiC104 0 5 x l d 4 M Ni2:
”
, 3sec
with that shown for kr in eq 5, this point will be examined later with reference to the experimental data. After substituting the rate constants shown in eq 5 and 6 into eq 4,replacing [Llads with I’, and performing an algebraic rearrangement, the following relationships are obtained.
5dB
exp(-#o) zF I’dt RT
__
=
3sec
-0.70 -0.75 -0.80 -0.85 -0.90 Potential, Volts, S.C.E.
Figure 1. Dependence of the corrected rate parameter on the electrode potential; charge value, z = +I.
#’ is the rational potential defined by Grahame7 as the difference between the measured electrode potential and that potential corresponding to ~ e r oelectrode charge in the absence of specific adsorption of the ions of the electrolyte. Two charge terms, z and z*, are shown here. The charge of the electroactive complex, as before, is z . Frumkin, et al.,g have shown that z* in eq 6 must refer to the charge of the ion approaching the electrode surface and must in this case be unambiguously assigned a value of +2 corresponding to the charge of the hexaaquonickelion. Correction of the reverse reaction constant, kb, cannot be so easily resolved. If the electroactive complex exists only at the electrode surface, it should not be subject to the concentration polarization in the diffuse zone which, according to Gierst,6 requires the correction for the other rate constants. While a t this time an exponential term will be arbitrarily written for kb identical The Journal of Physical Chemistry
To simplify the following discussion, the left-hand members of eq 7a and b will be designated as a and b, respectively. These may each be regarded as parameters corrected for variations in the potential-dependent terms, I’ and At high values of kel, a must approach a constant value equal to b if these corrections are properly made. Some of the terms of a, 4, and I?, may be determined by experiment; others, D and #O, may be assigned values from the literature. Only the charge z thus remains as an undetermined constant. An arbitrary value may be assigned to z, however, and member a calculated as a function of electrode poten(6) L. Gierst, “Transactions of the Symposium on Electrode Processes,” John Wiley & Sons, Inc., New York, N. Y.,1961,p 109. (7) D. C.Grahame, Chem. Rev., 41, 441 (1947). (8) A. N. Frumkin, 0. A. Petry, and N. V. Nikolaeva-Fedorovich, Electrochim. Acta, 8 , 177 (1963).
CATALYTIC POLAROGRAPHIC CURRENT OF
A
tial. Only if a exhibits the required approach to a constant value can this choice of z have been correct. Experimental determinations of x have been made in this manner from polarograms of the Ni(I1)-OPDA prewave obtained in 0.1 M solutions of potassium chloride and lithium perchlorate. The values for r at polarographic concentrations of OPDA were obtained by empirical extrapolation of surface concentrations calculated from differential capacitance measurements in these electrolytes using ligand concentrations ranging from lop3to 2 X lo-' M.2e Values of $O were taken from the report by Grahame and S ~ d e r b e r g ,the ~ electrode potential scale being corrected to sce from the nce used there. As D for the hexaaquonickel ion is a constant in a given electrolyte and very nearly so for all 0.1 M electrolytes, only (/rz/iwas calculated for each experiment. The results obtained with various drop times and reactant concentrations in two electrolytes appear in Figures 1 and 2 where x has been assigned values of $1 and +2, respectively. Only where x has been given the value of +1 does the corrected rate parameter approach a constant value a t increasingly negative electrode potentials. As this method of analysis presupposes rapid attainment of at least nearequilibrium surface coverage, experiments were also made with a series of OPDA concentrations. As may be seen in Figure 3, the data approach limiting values at volume concentrations of OPDA equal to or greater than low4M , confirming earlier findings in this regard.ze Further information can be obtained from eq 7a and b by examining the potential dependence of a. This may be done conveniently by combining these equations in the manner
v+( Lana
a
logb -a 2.3RT
_ _ I
1>v] +
a
__
b
'-
a
-
- anaF
--E
2.3RT
+ constant'
If the exponential term including the from eq 7a, eq 9 becomes a cm,F log--( E b -a 2.3RT
kb
x X
e
8 X
.
Z:tl 0.1 M KCI I U 3 M Ni2'
.
8 X
.
o 4 x 10-4 M OWA a 2 4, I8 I,
8.
X
X
e
Qc
I
II
01
I1
e0.5
e
I I I I -0.40 -0.75 -0.80 -0.85 -0.90 Potential, Volts, S.C.E.
Figure 3. Dependence of the corrected rate parameter on the electrode potential and OPDA concentration.
E.+J/O
-0.70 -0.75 -0.80 -0.85 -0.90 I
I
I
I
I
constant
(8) The term z in eq 7a has been given the value of +l here. As a first approximation, eq 8 can be simplified by assigning a value of 0.5 t o CY and of 2 to n,. Recalling that +r equals the electrode potential, E , minus a constant, eq 8 is reduced to log
2767
METAL'COMPLEX
(9)
is omitted
+ \Lo) + constant'
(10)
These equations have been tested using the experimental data represented by the average curve in Figure 1 with the results shown in Figure 4. It is evident that the linear relationships predicted by eq 9 or 10 are not obtained although an approach to linearity is present at more negative electrode potentials in each
E , Volts,S.C.E. Figure 4. Dependence of the electrochemical rate on the electrode potential.
case. This departure from linearity should, however, be anticipated in view of the substitution of for the "free" surface concentration of the adsorbed ligand. As noted previously in this paper, the error from this source should be reliably small only at more negative ~ large. Back extrapolation of the potentials where k , is data in this region thus permits an estimate to be made of the percentage of the total ligand surface concentration present as the surface complex. From the data in Figure 4, it may be calculated that about 40% of I' (9) D. C. Grahame and B. A. Soderberg, Technical Report No. 14 to the Office of Naval Research, Feb 18, 1954, Amherst College, Appendix, p 7.
Volume 73, Number 8 August 1969
2768
LOWELL R. McCoy
2
3
4
5
Distance, d
Figure 5. Physical dimensions of the OPDA molecule.
exists as the surface complex at -0.675 V vs. sce, an electrode potential corresponding very nearly to the “foot” of the prewave. A substantial formation constant for the surface complex is thus indicated. From the linear portions of the curves shown in Figure 4, new values of an, may be calculated and inserted into the bracketed member of eq 8 (or its counterpart equation omitting the exponential term from k b ) and the data replotted t o yield successively more correct values of an,. The effect of this reiterative process is small in either case. This product obtained from the first approximations shown in Figure 4 is 0.74 or 0.63 depending on the choice of E or E $O as the abscissa. As the transfer coefficient for most electrode processes are usually less than 0.5, a two electrontransfer reaction is indicated. Unfortunately, this cannot be regarded as a certainty as values of a greater than 0.5 have also been reported in the literature.1° I n the absence of an independent check for a “correct” value of a,this question remains unresolved as does the necessity of providing an exponential $O correction for kb. These calculations do offer a means of checking the consistency of the data with the behavior expected for a surface reaction. I n general, the agreement between theory and experiment is believed to be satisfactory. As these investigations substantiate the earlier conclusions that the charge of the electroactive complex is +1, it is apparent that the charge of one of the reactants shown in eq 3 must be incorrect or some fault must be found in the procedure of correlating the prewave height with $O.
+
Location of the Reaction Plane I n deriving expressions for the theoretical dependence of the prewave height on $0, it has been implicitly assumed that the reaction plane is nearly coincident with the outer plane. If the reaction plane were, in fact, well removed from that location, some doubt might be cast on quantitative results obtained from correlations employing values of $0. The orientation of an adsorbed molecule of the size of OPDA thus assumes The Journal of Physical Chemistry
HARRY B. MARK,JR.
some importance in these studies. If, as shown in Figure 5 , the molecule were vertically oriented, the functional groups would project into the solution well beyond the outer plane. Grahame and Parsons1’ have estimated that the outer plane is located approximately 3-4 A from the electrode surface. If the molecule were planar oriented, it is probable that the protons of the functional groups would be attracted and the donor electrons repelled by the negatively charged (at the electrode potential at which the prewave is observed) electrode surface. In this case the reaction plane would be quite near, though perhaps slightly within, the outer plane. Planar orientation would therefore represent a more agreeable situation in attempting correlations with $*.
Electrode 1
AND
”E
30
$ . 3
w’
z“
g
25
a!
3 -t B 8 k B
20
15
lo
-0.6
-0.8
-1.0 -1.2 -1.4 -1.6 POTENTIAL v9. S.C.E.
-1.8
Figure 6. Differential capacitance curves; OPDA in 0.1 M KCI.
At high bulk concentrations of OPDA (2 X lo-’ M ) and a t electrode potentials in the prewave range the evidence clearly favors a vertical orientation as saturation coverage approaches 5.5 X 10-lo mol/cm2. This surface concentration corresponds t o an area of about 30 k2 per molecule. Although the area occupied by a molecule this size in a planar position is subject to uncertainty in terms of the maximum packing density commensurate with rotational freedom, this area would be at least two to three times the experimental limit given above. While vertical orientation is indicated for high surface coverage, there remains the possibility that reorientation to a planar position occurs as surface concemtrations approach those present at the low volume concentrations used in the polarographic measurements of preM ) . Reorientation as a wave heights (1 to 4 x function of both concentration and electrode potential (or electrode charge) has been shown by Parry and (10) P.Delahay, “Advances in Electrochemistry and Electrochemical Engineering,” Vol. 1, Interscience, New York, N. Y.,1961,p 248. (11) D.C. Grahame and R. Parsons, J . Amer. Chem. Soc., 80, 1291 (1961).
CATALYTIC POLAROGRAPHiC CURRENT OF
A
Parsons12 for the p-toluenesulfonate anion and Damaskin, et uZ.,13 for aniline. Barradas, et ~ 1 . have ~ 1 ~ considered the reorientation of various amines with changing concentrations while Hansen, et u1.,’6 have speculated on this possibility with regard to phenol. Both phenol and p-toluenesulfonate exhibit two cathodic adsorption peaks in their differential capacitance curves which vary with the bulk concentration of the absorbate. A peak appears a t low concentrations which grows and then subsides to be replaced by a new peak at a more negative potential as the concentration of the substance is increased. Parry and Parsonsla have ascribed this phenomenon to a changing orientation with increasing concentration. As may be seen in Figure 6, no such occurrence is observed with OPDA. There is, however, some basis for believing that reorientation does occur with changing surface concentrations of OPDA. The principal evidence for this statement is to be found in an examination of the manner in which the electrode charge varies with the surface concentration. FrumkinIBhas suggested a model of an electrode surface consisting of two parallel capacitors, one representing the fraction of the electrode surface covered with water dipoles, the other, that fraction covered by the adsorbed substance. The electrode charge then varies linearly with the fractional surface coverage, e, in the following manner q = qs=o(l - 0)
2769
METALCOMPLEX
+ qe-10
I
Electrode PotentiaI
0.1 --I 6
1.0
I 2.0
M
KCI
3.0
4 4.0
5.0
U
Surface Cancentrat ion x 10’0moles/cm2
r
Figure
7. Electrode charge-surface concentration data for
OPDA in 0.1 M KCl.
(11)
where q e - 0 is the electrode charge observed in the absence of adsorption and qecl is the electrode charge that would be observed if the surface were covered with a complete monolayer of the adsorbate. The surface concentration in a monolayer condition is represented by r,. This model has been criticized because it makes no provision for lateral interactions.’’ While the model does not, in fact, work well for anion adsorption, possibly for this reason, less difficulty should be expected from this source in the case of electrically neutral adsorbed substances. The linear relationship between q and I’ predicted by eq 11 is clearly not satisfied by the experimental data for OPDA in 0.1 M potassium chloride shown in Figure 7. The failure of the simple, two surface species model might be expected, however, if the adsorbed molecules were present in two orientations a t intermediate values of I’. An adsorbed molecule in a planar position would obviously require a different value for I’, than would the same molecule in a vertical position. Barradas, et aZ.,14note that the effective dipole moments would be different in these two cases and Parry and Parsons12 have discussed the difference in the polarizability of the benzene ring in planar and vertical orientations.
It is reasonable to assume, therefore, that q s = i is not the same for each of these two orientations. Molecules in each orientation would therefore have to be regarded as separate species. I n terms of the Frumkin parallel capacitor model, consideration of a three-component system would be required in such a case. Extension of the Frumkin model to a three component system requires that 6 be redefined. Molecules in a planar position will be arbitrarily assigned to state 1; those in a vertical position to state 2. The symbol f will be used to designate the fraction of adsorbed molecules in state 1. As before, I’ will represent the total surface concentration without regard to state. Then
(12) J. M. Parry and R. Parsons, J . Electrochem. Sac., 113, 992 (1966). (13) B. B. Damaskin, I. P. Mishutushkina, V. M. Gerovich, and R. I. Kaganovich, Zh. Fiz. Khim., 38, 976 (1964). (14) R. G. Barradas, P. G. Hamilton, and B. E. Conway, J . Phys. Chem., 69, 3411 (1965). (15) R.8.Hansen, D. J. Kelsh, and D. H. Grantham, ibid.,67, 2316 (1963). (16) A. N. Frumkin, 2.Phys., 35, 792 (1926). (17) P. Delahay, “Double Layer and Electrode Kinetics,” Interscience, New York, N. Y., 1966,p 94.
Volume 73, Number 8 August 1969
2770
LOWELL R. MCCOYAND HARRY B. MARK,JR.
I
I
I
15
LO 2.0 3.0 Surface Concentration
I 4.0
I
5.0
r x ioto moies/cm2
position at near-zero coverage, a tangent to the curve a t I' = 0 will represent m(1). Extrapolation of the charge-I' data to the limiting surface concentration, rm(2), where the molecules should be forced into a vertical orientation by surface crowding, yields qs 1(2) from which m(2) can be found. I t has already been noted that the capacitance data for OPDA do not show evidence of potential-dependent reorientation within the voltage range considered here. The ratio of the slopes m(1) and m(2) should therefore be quite constant. The results of this test, using the data shown in Figure 7, appear in Table I. The slope ratio is satisfactorily constant within most of the voltage span. Some small increase in the ratio at -0.8 and -0.7 V is apparent, and a comment will be made on this point in the next section of this paper. ~
Figure 8. Graphical determination of single species slopes for the modified Frumkin capacitor model.
If, as before, the electrode charge varies linearly with the fractional surface coverage in each state, q is given by
Concentration Data for o-Phenylenediamine in 0.1 M KC1 Electrode potential, V UB. sce
-1.20 -1.10
-1
.oo
-0.90
(1
- f)JXqs=1(2) - b r m
-0.80 o )
(2)
(13)
The charge difference for a given state of orientation divided by the monolayer surface concentration for that state is the slope of the q us. I' curve that would be observed if the adsorbed molecules were present only in that orientation. Assigning the symbol m to these hypothetical slopes, eq 13 becomes q =
40-0
+ frm(1) + (1 - f)rm(2)
(14)
Differentiating eq 14, one obtains
~~
Table I: Slopes and Slope Ratio of Charge-Surface
-0.70
m(U
m(2)
0.21 0.20 0.17 0.16 0.14 0.11
0.13 0.12 0.11 0,093 0.076 0.057
m(l)/m(2)
1.6 1.7 1.6 1.7
1.8 1.9
While similar data were also taken in 0.1 M solutions of lithium perchlorate and potassium acetate, only in the case of 0.1 M potassium chloride were large enough values of I' calculated to permit extrapolation of the experimental data to I',(2) with any degree of confidence. A comparison may be made, however, of the slopes obtained a t I' = 0 in these electrolytes. These data appear in Table 11. As the values of m(1) should be determined only by the properties of the adsorbed molecule, the agreement obtained in three quite dissimilar electrolytes is reassuring. Table I1 : Initial Slopes of the Charge-Surface Concentration Data for OPDA in Three Different Electrolytes
The slope of the electrode charge-surface concentration curve thus becomes a function of I', a result consistent with the experimental data for OPDA shown in Figure 7. That such slopes must be considered at a constant electrode potential is evident from the fact that q e = l for both states as well as qs=o are potential dependent.'* While eq 14 and 15 are sufficiently "flexible" to fit complex q - I' behavior, a t least one test can be applied to experimental data where much of this mathematical accommodation vanishes. The slopes m(1) and m(2) can be found graphically as shown in Figure 8 using data taken from Figure 7 at E = - 1.0 V us. sce. If it is assumed that the molecules are present only in a planar The Journal of Physical Chemistry
Electrode potential, V UB. soe
-1.30 -1.20 -1.10 -1.00 -0.90 -0.80 -0.70
KC1
Slope, m ( 1 ) LiC104
KCaHtOz
0.22 0.21 0.20 0.17 0.16 0.14 0.11
0.22 0.21 0.19 0.18 0.16 0.14 0.13
0.24 0.22 0.21 0.18 0.16 0.14 0.12
r
(1s) This fact argues against the use of the Frumkin model in conjunction with Esin and Markov as suggested in ref 17, p 93. The Frumkin model states that (bI'/bq)B is a constant whereas eq 13 of this reference requires that (bI?/bq)@be a constant.
CATALYTIC POLAROGRAPHIC CURRENT OF
A
2771
METALCOMPLEX
A second test may be applied to the experimental data to determine compliance to the model. Equation 14 may be solved for f, yielding
f=
9
- Qs=o
m(1) - m(2)
-
m(2)
m(1) - m(2)
(16)
In view of the constancy of the slope ratio over most of the electrode potential range, a similar constancy should be exhibited by f vs. I' values over the same range. I n the absence of any independent means of obtaining values of f, however, judgment as t o the validity of such values must reside in a consideration of whether the results appear reasonable in terms of the size of the molecule and its probable behavior with surface crowding. Again using the data presented in Figure 7, values off were calculated by eq 16. These values appear in Figure 9. Planar orientation is indicated as the sole atate up to about 0.5 X mol/cm2 with some small proportion of vertically oriented molecules appearing at 1 X 10-lo mol cm2. Considermol/cm2, this ing I',(l) to be about 1.5 t o 2.0 X result seems at least intuitively reasonable as surface collisions should result in some vertically oriented molecules long before saturation coverage in planar orientation is reached. The peak displayed by O(1) at about 2.0 X 10-lo mol/cm2 may or may not fortuitously coincide with FW(l). Some small proportion of planar-oriented molecules is apparently retained up t o the limiting concentration. This permits some comment on eq 15. The term containing the partial differential bf/dI' does appear t o be zero at I' = 0, and the use of a tangent to the experimental data at that point should yield a correct measure of m(1). Conversely, the differential term is not zero at r42) and 4 2 ) must be determined from the charge-I' coordinates as shown in Figure 8, not from a tangent to the curve at I',(2). If the above conclusions are correct, the adsorbed OPDA molecule exists almost wholly in a planar orientation at surface concentrations present in the polarographic measurements (I' < 0.5 X lo-'" mol/cm2). As stated in the beginning of this section, this should place the reaction plane in near proximity to the outer plane of the electrode double layer. It is unlikely, therefore, that an anomalous charge value for the electroactive complex can be attributed to errors from this source.
o-Phenylenediamine-AnionCoadsorption As the previous sections indicate no obvious source of error in the double-layer analysis of the prewave, an explanation for the indicated charge of the electroactive complex must be sought in the state of the reactants. Considering the nickel ion first, it can be reasoned that the actual species reacting with the adsorbed organic ligand is of the form Ni(H20)SX+ l , where X-'is either an electrolyte anion or an hydroxyl group. If such an ion
-0.8
c),
E
9
0
V
-1.20 TO -0.80VOLTS, 1.0
2.0
3.0
4.0
50
Surface Concentration x 10'' moles/cm2
r
Figure 9. Surface orientation of ODPA as a function of surface concentration.
existed in rapid equilibrium with the hexaaquonickel ion, a charge of +1 for the electroactive complex would be anticipated. If this explanation is correct, the prewave height should vary significantly in different electrolytes or be greatly affected by changes in pH. Electrolyte anion participation can be ruled out by the fact that the prewave is observed in noncomplexing electrolytes such as nitrates or perchlorates.2d The variations in prewave heights found in various electrolytes under comparable conditions can be well accounted for by known changes in either $0 or OPDA surface concentrations.2dte The possibility that X-' may be a hydroxyl group is contraindicated by the lack of response of the prewave height to changes in pH above 6 where the OPDA is then present almost entirely as the free base.2b If the nickel ion cannot provide an explanation for the charge of the complex, attention must be directed to the other partner in the reaction, the adsorbed OPDA molecule. Coadsorption of electrolyte anions with OPDA offers one solution to this problem for, if the coadsorbed anion were an active partner in the surface reaction, the charge of the reaction product would be that found above.19 That such a possibility exists is suggested by the change of the electrode potential at zero charge with increasing bulk concentrations of the organic ligand as shown in Figure 10. Although nearly all adsorbed neutral organic substances cause the potential a t zero charge to move toward more positive potentials with increasing concentrations, the shift a t (19) The possibility that coadsorption of anions might occur in this case was first suggested by R. Parsons in a private communication t o the authors as an explanation for anomalies observed in differential capacitance curves for OPD.4 in more concentrated electrolytes.
Volume 78, Number 8 August 1969
2772
LOWELL R. McCoy
up to moderate concentrations of OPDA is toward more negative potentials. This behavior parallels that observed with specifically adsorbed anion^.^^^ The reversal of this trend at high concentrations of OPDA is the result of desorption beginning at potentials negative to the potential of zero charge. The only other substance linown to exhibit a similar behavior is phenol.’s The concept of anion coadsorption has been discussed by Damaskin, et a1.,13who suggest that the 7r electrons of planar-oriented aromatic molecules form bonds with a positively charged electrode surface leaving electronic “holes” which attract anions. I n this instance, however, anion coadsorption in the potential range of the prewave would require that the same phenomenon occur a t a negatively charged electrode. OPDA Conc.,Moles
/.
0 10-3
5x
2x10-’
-0.40 -045 -0.50-0.55 POTENTIAL,VOLTS, S.C.E. Figure 10. Variation in the electrode charge-potential relationship as a function of OPDA concentration in 0.1 M KC1.
If anion coadsorption does take place here, some evidence for it should be found in a greater particleparticle interaction between adsorbed molecules bearing a charge as compared to that expected for neutral molecules. In principle, information on this point can be gained by an analysis of experimental data by the use of isotherms containing an interaction term. I n practice, this operation is made difficult by disagreement among experts on some vital points, and the reader is referred to a review of this subject by Delahay.20 Although a number of isotherms contain an interaction term, this discussion will be limited to the Frumkin16 isotherm which has the form
HARRY B. MARK,JR.
where aa is the activity of the adsorbed substance in solution and g is a term representing particle-particle interaction (negative in sign for repulsion, positive for attraction) between the adsorbed molecules.z1 The symbols 8 and I? have already been defined previously in this paper. The term, p, is given by
P
= eXP(-=)aG”
where aGo is the standard electrochemical free energy of adsorption. Equation 17, therefore, represents an attempt to isolate the particle-electrode interactions in the term p, and the particle-particle interactions in the term, g. To study g, it is desirable to maintain p as a constant. This requires the establishment of a constant electrical state. This has been a matter of controversy with constant voltage and constant charge both having been proposed.20 If the activity of the substance being adsorbed is taken as proportional to its concentration, c, and the temperature and electrical state are constant, eq 17 may be rearranged and written as
IO’*
to-‘
AND
log
8
~ (-l 8)
I _ _
2gFF -_ _
2.3Rl’
+ constant
(19)
If the left-hand member of eq 19 is shown graphically as a function of I?, the slope of the curve should reflect only the variations in the particle-particle interaction term, g. The magnitude of Q, particularly at large values of I?, will be greatly affected by the choice of the isotherm; its sign, indicating repulsion or attraction, will not be. At low values of r, the choice of a proper isotherm is of lesser consequence as the additional exponential terms which these containz0 have a smaller effect on the results. I n view of the uncertainty in the choice of a proper electrical state, adsorption data for OPDA in 0.1 M potassium chloride have been plotted in accordance with eq 19 at constant electrode potential in Figure 11 and at constant electrode charge in Figure 12. The results obtained in 0.1 M solutions of lithium perchlorate and potassium acetate are qualitatively the same as those shown in Figures 11 and 12. Attractive forces are evident in both cases at high values of I?, a result consistent with van der Waals forces operating in a closely packed condition. At lower values of I?, the results are seen to be strikingly dependent on the choice of the electrical state. At constant electrode potential, a change from an attraction between the molecules to a repulsion is indicated as the electrode potentials become less negative. This reversal in sign does not occur where the electrode charge is held constant, but an increase in repulsive forces is indicated at lower values of (20) Reference 17, p 81 ff.
(21) Reference 20 employs the same sign convention for g but incorrectly omits the negative sign for the exponential term in eq 17; see ref 13 and 15. The Journal of Phpical Chemistry
CATALYTIC POLAROGRAPHIC CURRENT OF
A
METALCOMPLEX
- 0.6
2773
Volts, S.C.E.
1.2 -
1.0
2.0
3.0
r x IO'O ~
4.0
5.0
O I ~ S I C ~
Figure 11. Frumkin isotherm a t constant electrode potential; OPDA in 0.1 M KCl.
Figure 12. Frumkin isotherm a t constant electrode charge; OPDA in 0.1 M KCI.
electrode charge. In both cases, increased repulsive forces are indicated for the surface concentrations and electrode conditions of interest to the prewave. These results are therefore consistent with anion coadsorption under these conditions. While coadsorption of anions with the organic ligand provides a convenient explanation for the charge of the electroactive complex, it raises some questions with regard to the analyses performed in this paper. I n the study of the orientation of OPDA, anion coadsorption should result in some increase in the slope of the q vs. r curves at I' = 0. That it may do so is indicated by the increase in the slope ratios shown in Table I a t less negative potentials. While this could be attributed to direct adsorption of the chloride ion a t these electrode potentials, it is of interest to note that the initial slopes of the curves shown in Table I1 are very nearly the same, although the acetate and perchlorate ions are not significantly adsorbed on mercury at these potentials." The degree to which these slopes are affected may depend on the site occupied by the anion. If it were located on the aromatic ring as suggested by Damaskin, et aZ.,l3 rather than on the electrode surface itself, the repulsive forces might be somewhat lessened. This still leaves unresolved the problem of anion coadsorption a t negative electrode charges. Some information of inter-
est to this point could be gained from a study, now in progress, of the isomers of OPDA. If, as suggested here, two complexities exist in the case of OPDA (anion coadsorption as a function of electrode potential and reorientation as a function of surface concentration), it would seem unlikely that any isotherm representing the adsorption properties of a single species can be expected to conform to the experimental data. While it is presumptuous to express a preference for an electrical state in view of this statement, the relative constancy found for the ligand orientation data over the total voltage span argues against a physical change in the molecular adsorption state that could account for the change in the sign of g found where the electrode potential was chosen as the constant electrical state. The monotonic changes (at low values of I') at constant electrode charge are at least consistent with this data. No attempt has been made to modify the Frumkin isotherm as was done for the Frumkin capacitor model used in the orientation studies. I n this case it may be preferable to establish a better basis for interpreting deviations of data from simple models of single species isotherms. Even this task would require a greater body of experimental data than is presently available in the literature.
Volume 73, Number 8 August 1969
