Interpretation of isopotential points. Common intersection in families of

guish the most probable structures for the various species described. Further reduction to the -4 oxidation state is shown in Figure 8. In 1 M HC1, the phlorin monocation is reduced in the first two-electron step to the porphomethene (tetrahydroporphyrin). The postulated structure (P( -IV)H,+) presumes further electrophilic attack at the bridge positions. Since its acid-base properties and spectrum are similar to those previously reported (9), we presume its structure to be similar also. The porphomethene is a weak acid having a dissociation constant greater than lop7(18). The non-equivalence of the bridge position substituents creates at least 24 possible isomers. If the orientation of the bridge substituents has

little effect on the chemistry of P(-IV)H?+, then the generalized structure given represents the only possibility. It was not possible to observe clearly defined intermediates such as the -4 oxidation state on reduction of the phlorin. Electron transfer proceeds in a series of overlapping steps to the -6 oxidation state. RECEIVED for review October 18, 1971. Accepted January 27, 1972. This investigation was supported in part by National Science Foundation Grants GP-9484 and GP-28051, and by Biomedical Sciences Support Grant FR-07002 from the General Research Support Branch, Division of Research Resources, Bureau of Health Professions Education and Manpower Training, National Institutes of Health.

(18) B. P. Neri and G. S. Wilson, unpublished results, 1971.

Interpretation of lsopotential Points The Common Intersection in Families of Current-pot ent iaI Curves D. F. Untereker and Stanley Bruckenstein Chemistry Department, State Uniwrsity of New York at Buffulo, Buffalo, N . Y . 14214 A common intersection point can occur in a family of current-potential curves at an electrode provided the potential scanning program is the same for all curves, the electrode surface is partially covered with at least one adsorbed or deposited species at the start of the application of the potential program, the initial amount of the adsorbed or deposited species is different for each curve, and the electrode surface behaves as if i t consists of two independent electrochemical regions the sum of whose areas is constant at all times for all of the current-potential curves. The mathematics interpreting the origin of isopotential points is analogous to that for isosbestic points in spectrophotometry, but must be suitably modified to take into account the nonequili brium electrochemical situation. The experimental systems studied were oxidation of adsorbed SOz on platinum, oxidation and reduction of a heterogeneous gold-platinum surface, oxidation of thin copper films on platinum, and oxidation of a platinum electrode with both absorbed SOz and I - . Some literature examples of isopotential points are discussed, and the validity of the theory is confirmed by a comparison of conclusions with those reached by other techniques.

DURING OUR WORK studying surface processes at solid electrodes, it became apparent that under certain circumstances a series of i-E curves in the same solution could yield a common intersection point. An examination of the recent literature indicates that other workers have also obtained i-E curves with a common intersection point (1-5). For example, Figures 1 and 2 show families of i-E curves we obtained during (1) G. D. Zakumbaeva, F, M. Toktabaeva, and D. V. Sokol’skii, SOC.Electrochem., 6,754 (1970), Engl. transl. ( 2 ) M. Kesten and H. G. Feller, Elecfrochim. Acta, 16, 763 (1971). (3) Jaspal S. Mayell and William A. Barber, J. Electrochem. SOC., 116, 133 (1969). (4) N. Ossendorfova, J. Pradac, and J. Koryta, J . Electroanal. Chem., 28, 311 (1970). (5) T.Biegler, J . Electr&hem. Soc., 116, 1131(1969).

the oxidation of various amounts of sulfite and Au(O), respectively, from the surfaces of rotating platinum electrodes on repetitive linear potential scans. The only difference in the families of i-E curves in Figures 1 and 2 is the amount of sulfite, or Au(O), on the platinum electrode surface at the time the potential scan was begun. During the anodic potential scan in Figure 1, three of these intersection points, which we shall designate as isopotential points (IP), occur. IP-I is at +0.20 V US. SCE, IP-I1 at +0.48 V US. SCE, and IP-I11 at 0.73 V cs. SCE. Two isopotential points occur during the anodic scans in Figure 2, and one occurs during the cathodic scans. An insight into the origin of isopotential points may be obtained by considering the following example. Suppose a platinum electrode of area A is partially covered with a reduced form of substance X at a cathodic potential Et. If the electrode potential is scanned anodically, both X and the platinum not covered by X will eventually be oxidized. In this example, we will assume that the oxidized form of X remains on the platinum surface. The following equation describes the current at any potential in terms of the area covered by both forms of X , A,, and the current densities for the oxidation of X,i,O, and platinum, ipto,on the remaining area of the electrode, ( A - A J . i

=

i,OA,

+ iptO(A - A,)

Upon rearrangement the total current for a particular value of A, is, i = AiptO

+ A,(izo - i p t O )

Now if we assume that the values of ipta and iZodo not depend upon the initial coverage of the reduced form of X,the above equation describes a family of i-E curves that would be obtained by starting with differing amounts of the reduced form of X on the electrode surface. It is seen that this family ANALYTICAL CHEMISTRY, VOL. 44, NO. 6, MAY 1972

1009

1.2

0.4

0.8

0.0

E,-Vo Its Figure 1. i-E curves for oxidation of various amounts of adsorbed SO, from the surface of a rotating platinum disk electrode S ~0.2M, ~ w = 400 rpm, s = 200 mV/sec. Isopotential points are C ~ O=, 4 X 10-6 M , C B ~ = at following potentials 1;s. SCE: I = +0.20 V, I1 = +0.48 V, 111 = +0.73 V. Fractional monolayer coverages of adsorbed SO, on electrode surface for i-E curves are: a = 0.0, b = 0.08, c = 0.20,d = 0.40,e = 0.61

of curves will have a common intersection point if ipto = iso at one or more potentials. This particular system, X on Pt, is a simple one, and has been further simplified because we ignored double layer effects. As we shall demonstrate in the Theoretical section, it is possible to consider other more complicated situations and obtain the necessary conditions for the occurrence of isopotential points. We will show that isopotential points are characteristic of specific types of electrode surface processes. For example, the two most anodic isopotential points in Figure 1 are due to the oxidation of adsorbed sulfite and platinum, while the least anodic is due to the oxidation of adsorbed sulfite and to double layer charging processes. Similarly, the two most cathodic points in Figure 2 are due to the simultaneous oxidation of platinum and gold during the anodic potential scans and to their simultaneous reduction during the cathodic scans. From these i-E curves and similar solid electrode data available to us, we realized that isopotential points are useful as a diagnostic tool and that their significance may have been overlooked even though their occurrence is not an infrequent phenomenon. In some respects, the voltammetric isopotential point is analogous to the spectrophotometric isosbestic point. Isosbestic points give information about the stoichiometry of equilibrium reactions or kinetic processes occurring in solution. Isopotential points give information about the presence of, and reactions of, adsorbed species and thin films on an electrode surface. For example, quantitative information concerning the stoichiometry of surface site occupation by two different species may be obtained as well as qualitative information about the nature of the electrode surface. The occurrence of isopotential points can also be helpful in dis1010

ANALYTICAL CHEMISTRY, VOL. 44, NO. 6, MAY 1972

covering the presence of adsorbable electrolyte impurities that may cause poisoning of the electrode surface. It is important to note that the absence of an isopotential point in a family of i-E curves may be equally as informative as its presence. A theoretical interpretation of isopotential points is developed below for potential scanning conditions. This theory is based on our experimental observation that isopotential points can occur at solid electrodes in situations involving adsorption or thin film formation in the presence or absence of significant double layer charging processes. THEORETICAL

Generalized Model Leading to Isopotential Points. Suppose that the following set of simultaneous reactions, 1.1-1.2 may occur at the surface of an electrode.

+ Redz $ Ox2 + n2e Redl

e Oxl

Redz

$ OXZ

nle

+ nze

(1.Z)

Either none, one, or more than one of the above reactions may occur on a specific region of the electrode of area, Ahill. If there are m of these discrete regions which originate for reasons discussed below, the total area, A , is m

A

=

An[,,

(2)

k(i)=1

k(i) is an integer variable whose value(s) is (are) determined by the values of i. The values of Ah(%) may be time dependent,

-100

a ?0 O

-

100

I *2

0.4

0.8

0.0

E,- V o l t s Figure 2. Cyclic i-E curves for oxidation and reduction of a partially gold covered platinum disk electrode 0.2M, w = 400 rpm, s = 100 mV/sec. Isopotential points are at following potentials us. C H ~ S= O~ SCE: I = +1.06 V, I1 = +1.25 V, I11 = $0.72 V. Fractions of Pt surface covered by Au for &E curves are: a = 0.0, b = 0.35, c = 0.50, d = 0.70. i-E curves were recorded in order of decreasing coverage of gold (d-a). 30 seconds of oxidation at +1.8 V was required between each pair of i-E curves except b and a. 5 minutes was required to remove the last trace of gold

but A is a constant. The faradic current due to reactions 1.1,etc., is given by Equation 3

(3) Z=1

where (z%O)~(~, is the current density for the ith process on the also may be a k(i)th region of the electrode surface. (izo)k(%) time dependent function and may be positive, zero, or negative depending on the nature of the k(i)th region, the potential of the electrode, and the time since the experiment was begun. signify reduction, i.e., the production Negative values of (itO),(t) of Red,. In many instances k(i) = i for all values of i, a situation which corresponds to each reaction taking place on a separate region of the electrode. In such situations, the notation will be simplified by replacing the subscript k(i) with i. However, there are also other examples in which two or more redox processes occur simultaneously on the same region of the electrode, e.g., if Oxl/Redl and Ox3/Redaoccur on Region 1, A I = Ak.1) = A k ( 3 ) . Finally, the total area, A in Equation 2, may be less than the true area of the electrode if part of the electrode surface is initially covered by a constant amount of material during the experiments that yield an isopotential point. This situation will be discussed in more detail below. Current due to charging processes on each region of the electrode, Ah(%), can be added to the current for the faradic processes in Equation 3 by assigning different differential double-layer capacitances, Ck(%), to each of these regions. Then the total current is

E is the imposed potential according to the function, E = E(t), which relates potential to time for the particular electrochemical technique being used. Ek(i)%is the point of zero charge for the k(i)th region. The conventions used assume i as positive for an anodic current and as negative for a cathodic current. The Occurrence of Isopotential Points in I-E Curves for Systems in Which One Redox Couple Partially Covers the Electrode Surface. Several situations of interest may arise, and in each of these cases the electrode material, M , may react according to Equation 1.1 at a time dependent rate. In all these examples, Equation 1.1 is written specifically as H2

M

0

JcM(oxide) + nle

The region over which Reaction 1.1 occurs is the area A1. A second reaction, described by Equation 1.2 occurs, and is subject to the restriction that Red2 and/or Ox2 is/are initially present on a part of the electrode surface. The area of the electrode surface covered by couple 2 , AB,may be a time deAB = A . The value of A2 at t pendent function, and A1 = 0 is Azo. In addition to faradic currents, there is also a charging current on each of the two discrete areas. Reactions, 1.3 l.Z, which generally depend upon one or both members of each of these couples being in solution, may occur on each of the two regions of the electrode at rates characteristic of the particular region and reaction. TWO-COUPLE SYSTEM.We shall first consider a situation in which only two couples, the electrode metal/metal oxide couple and the adsorbable or depositable couple are involved. Under such circumstances Z = 2, k(1) = 1, and k(2) = 2, and the summations in Equation 4 yield

+

-+


1011

We estimate that the value of 4 may be as high as 0.3, although it is frequently negligible compared to 1. In the other situation alluded to above, where the product of Reaction 1.2 is insoluble, as it was in the example of the oxidation of X on platinum cited in the Introduction, A 4 (and hence A1’) = 0. Thus the equation, analogous to Equation 6, is

i

=

Al(iio

+ ClE’) + A2(iz0 + GE’)

(7)

Note that Equations 6 and 7 are of the same form, differing only by the (1 4) term multiplying i2 in Equation 6. In the following examples we shall use Equation 7 rather than Equation 6, regardless of whether the product of Reaction 1.2 is soluble. This is a convenience justified by the fact that when 4 exists, it cannot be readily evaluated and @),is observed in any experiment. only the product, i? ( 1 It is left to the reader to determine whether i t refers to the true faradic current density function for Couple 2 or whether it refers to the product of the true current density function multiplied by (1 4). The area of the electrode not covered by Couple 2, A,, can be eliminated from Equation 7 by substitution from Equation 2 to yield,

+

E

+

+

i

Figure 3. Hypothetical pairs of current density curves which lead to (A) zero, ( B )one, and (c) two isopotential points

i

=

Al(il0

+ ClE’) + A&z0 + C2E’) + CIAI’(E - Eln) + CzAz’(E - Ezn) ( 5 )

where E’, A,’, and A,’ are the time derivatives of E(t),AI, and Ai, respectively. Depending on whether on not the product of Reaction 1.2 is soluble, two situations may arise. Most generally the product of Reaction 1.2 will be soluble and A,’ and A,’ are nonzero. In such cases a general solution for the condition leading to an isopotential point exists, as is shown below. Suppose that Az changes only when a faradic process on A2 occurs, i.e., no desorption of the plated or adsorbed form of Couple 2 occurs. The rate of change of this area, Az’, is then directly proportional to the faradic current involving the second couple. The proportionality constant is numerically equal to l/n2FN2,where n2 and F have their usual electrochemical significance and Nz is the moles/cmz of the adsorbed or plated form of Couple 2 on the electrode surface. Thus we obtain

+

The - sign is applicable for oxidation processes and the sign for reduction processes. Since Equation 2 states that the sum of AI and AZis a constant, Ai’ is equal to -Az’. Substituting this result and the expression for AZ’ into Equation 5 yields

i

1012

=

Ai(iio

+ CiE’) + Az[izO(l + 4) + CzE’l

(6)


=

A(ilo

+ CIE’) + Az(izo+ C2E’ - ilo - C1E’)

(8)

Suppose now that a series of i-E curves are obtained using the same E(t) function and starting at the same initial potential, E,. An isopotential point may be observed if each i-E curve represents a different initial coverage of adsorbed or plated material at the time E(t) is imposed. This experimental situation can arise if mass transfer of one of the species of Couple 2 is important. Under these circumstances, the amount of Couple 2 initially present on the electrode surface will be determined by the time spent at the initial potential, E,, before E(t) is imposed, and the mass-transfer conditions. The differences in the family of i-E curves which produce an isopotential point occur because of the different initial amounts of Couple 2 on the electrode surface-i.e., the value of A t . Thus the condition for an isopotential point in a family of i-E curves will occur at the time (potential) where the current is independent of the initial coverage of Couple 2 i.e., di/dA2 = 0. Differentiating Equation 8 with respect to Azo shows that a common intersection point will occur if at some time and corresponding potential, E,,,

Equation 9 can be interpreted by noting that dAz/dA2will be nonzero anytime A, > 0. Now if circumstances are such that the current densities it, and i2, and the double-layer capacitances C1 and Cz are not functions of Azo-i.e., they are not affected by the fractional coverage of the second couple -it is seen that the bracketed term on the right side of Equation 9 is zero. Hence, under the above circumstances, the condition for an isopotential point simplifies to that the left side of Equation 9 be zero. This condition is, il0

+ C1E’

=

izo

+ CzE‘

(10)

An isopotential point can only be expected to occur over the ranges of Azo values for which the derivatives on the right side of Equation 9 are zero. We discount the unlikely physical situation in which the derivatives on the right side of Equation 9 sum to zero fortuitously.

It is convenient to consider three limiting cases since both faradic processes and charging current may not always be important. CASEA. Both faradic processes yield currents much larger than the charging current in the region where the isopotential point occurs. As will be demonstrated in the Results and Discussion section, one example of a type A isopotential point is the one observed at +0.73 V us. SCE during the oxidation of various amounts of adsorbed sulfite at a platinum electrode in Figure 1 . Another example is the isopotential point in Figure 2 which we attribute to the simultaneous oxidation of differing amounts of gold on a platinum electrode. Since double-layer charging is assumed to be negligible, the condition for an isopotential point in Equation 10 becomes, il 0 = i20

(11)

The current at this potential is then i,,

=

Ai2O

=

Ailo

(12)

It is apparent from Equation 11 that both zt0 terms must have the same sign-i.e., both processes are oxidative or both are reductive whenever Equation 11 is satisfied. Equation 11 specifies the conditions that must be met in order that an isopotential point occur. However, all situations involving redox couples do not necessarily produce an isopotential point(s). Consider curves 1 and 2 in Figure 3A, where curves 1 and 2 represent the current densities for processes 1 and 2. The nature of these i-E curves eliminates the possibility of condition 11 being met at values of il0 and i20 for which double-layer charging currents are negligible. However, in Figure 3B, curves 1 and 2 do intersect, but in a fashion that permits only one isopotential point. In Figure 3C, two intersections occur between curves 1 and 2 and 1 I and 2. Curves of the general shape of 1 and l ’ , in Figure 3C correspond to the current density curves for processes which have or involve insoluble films on the electrode surface-e.g., platinum oxidation, curve 1, and platinum oxide reduction curve 1 I . CASEB. Another limiting case is encountered when one of the couples is not electrochemically active in the potential region where the isopotential point occurs and double-layer charging currents are important. Equation 10 then becomes Equation 1 3 i,O

=

(C, - C,)E’

(13)

where i = 1,j = 2, or i = 2 , j = 1. Usually i,O and E’ will have the same sign. Therefore, if the electrode material is inert in the potential region where the isopotential point occurs, the double-layer capacitance of the electrode material must be greater than that of the region occupied by Couple 2 on the electrode surface. Conversely, if the electrode material is the electrochemically active couple, CZmust be greater than CI in that region. The current at such an isopotential point is proportional to the differential double-layer capacitance of the region associated with the inert couple. Equation 14 summarizes these relationships. it* = C,AE’

Cl =

e*

(15)

The current is then given by Equation 14 where i = 1 or 2. MULTICOUPLE SYSTEMS.Up to this point, we have limited our discussion to situations in which only two electrochemical reactions occurred, each on a different region of the electrode surface. However, there are other circumstances in which the value of k ( i ) in Equation 4 does not equal i for every reaction-i.e., more than one electrochemical reaction can take place on a particular region of the electrode. While there are numerous hypothetical cases that could be treated, we have elected to consider a particular example that illustrates this general situation-i.e., the origin of the isopotential point at 1.25 V us. SCE in Figure 2. Let us consider a platinum electrode in 0.2M HzS04that is partially covered with a thin gold film so that there are two distinct regions exposed to the solution, gold and platinum. As will be shown below, it is a simple matter to prepare a platinum electrode with different initial coverages of gold; hence, it is feasible to obtain a series of i-E curves corresponding to different gold coverages and this was done to obtain Figure 2. I n sulfuric acid solution, both gold and platinum can be oxidized without significant solution of either metal in the potential region shown in Figure 2. Oxidation of water to form oxygen also occurs on both of these metal regions in the most anodic part of the i-E curves but the rate is much greater on platinum than on gold. Platinum oxidation and reduction occurs only on region A I while gold oxidation and reduction occurs only on region A2. Since oxidation of water to produce oxygen can occur on both regions, its current density must be specified for each region. Thus, in Equation 4, k(i) = i for i = 1 and 2 , and k(i) = 1 and 2 for i = 3, where couples 1 , 2 , and 3 are the platinum metal/platinum oxide, gold metal/gold oxide, and water/oxygen couples, respectively. Hence the summations in Equation 4 become, noting that for this example all dA/dt terms are zero,

+

i = Ai[(ilOh f

(i3O)l

+ C1E’l + Ad(i2Oh + (iso)2 + C S ’ ] (16)

Substituting Equation 2 into 16 and rearranging terms yields i

=

A[(i1O)1 4- (i3O)l

+ CIE’] + A2[(h0)2 + (i3O)2 - (Lo)! + (C, - CJE’] (17) (iSo)1

To obtain the conditions for an isopotential point, we differentiate Equation 17 with respect to A? and assume all ( i $ ) k ( , ) and Ck(*)terms are independent of Azo. The result is

Hence, when the sum of all processes producing current flow (partial currents) on one region of the electrode equals those on the other region, an isopotential point will occur. This example suggests the most general situation. If, in Equation 1, Z processes occur, and reactions 1.1 and 1.2 divide the electrode surface into two regions, the general analog of Equation 18 is

(14)

where i = 1, i2O = 0, or i = 2, il0 = 0. CASEC. It is possible to have an isopotential point even if no faradic processes occur. Since C, is a function of potential, Equation 10 may be satisfied if i,O = 0, i = I and 2. Thus, at the isopotential point.

All of the results for the examples discussed up to this point can be obtained from Equation 19 where (i2°)2is understood to contain the 4 term, as defined in Equation 6, in situations where Azis a function of time. ANALYTICAL CHEMISTRY, VOL. 44, NO. 6, M A Y 1972

a

1013

that Couple 3 is at an equilibrium coverage which is determined by the fraction of the electrode not covered by copper. On imposing E(t), oxidation of Cu and of adsorbed hydrogen occurs, but oxidation of the electrode does not take place. For the purposes of the derivation we divide the electrode surface into three regions of areas AI, AB,and A 3 where A = AI A2 As. The amount of hydrogen adsorbed is determined solely by the area nor covered by copper. The area not covered by copper consists of the region covered by hydrogen, As, and the uncovered platinum, A I . Regions A1 and A3 are not independent since equilibrium for hydrogen adsorption on platinum is rapidly obtained. The relationships between these various areas is given in Equation 20.

+ +

A3 = U(A

- A,)

= U(A1

+ A3)

(20)

where U depends only on potential, since hydrogen adsorption on platinum is fast on the time scale of our experiment. The current for the two electrochemical processes which have nonzero rates in the potential region of interest is given by Equation 3 where Z = 3, k(i) = i , and i10 = 0. Substituting Equation 20 into Equation 3 yields Equation 21 which gives the faradic current in terms of Az and A . if = AUi3O

+

- UiaO]

(21)

The charging current on the three regions is given by Equation 22. I

0.8

0.4 Eo - V o l t s

Figure 4. i-E curves for oxidation of submonolayer (a-c) and bulk (d)amounts of copper from a platinum disk electrode Ccu(+2) = 2 X 10-BM, CH,BO~ = 0.2M, w = 2500 rpm, s = 100 mV/sec. Isopotential points are at following potentials us. SCE: I = +0.15 V, II = +OS9 V. Copper coverages in terms of statistical monolayers for the i-E curves are; a = 0, b = 0.16, c = 0.33, d = bulk Cu initially present

Occurrence of Isopotential Points in i-E Curves for Systems in Which Two Redox Couples Partially Cover the Electrode Surface. In the previous discussions, we treated examples for which one redox couple partially covered the electrode surface. We will now consider a situation in which two redox couples partially cover the electrode surface. Again we elect to consider a specific example since the generalized result can be obtained by analogy. The isopotential point observed in Figure 4, which we ascribe in the Results and Discussion section to the oxidation of submonolayer amounts of Cu(0) and adsorbed hydrogen represents an experimental situation of this kind. The model which we will develop is given below:

Couple

Species

1

PtjPt oxide

Comments

Electrode inert in the potential region of interest CujCu(I1) Cu(I1) in solution Hz(ads)/H+ Acid solution

2 3

Suppose the electrode is poised at a potential, E < ,and that up to the time the potential function is imposed the electrode surface coverage of Couple 2 is nor at equilibrium because of mass-transfer limitations, i.e., non-equilibrium coverage of underpotential copper exists (6). On the other hand, assume ( 6 ) G. W. Tindall and Stanley Bruckenstein, ANAL.CHEM., 40, 1637 (1968). 1014

i,

0.0


d [(AICl dt

= -

+ A3C3)(E - Eln) + A&(E

- Ezn)l (22)

Substituting Equation 20 into Equation 22 and differentiating with respect to time yields the charging current in terms of A , A z ,and A z f .

i, - AC3*Ef

+ AZE'[Cz - C3*] + Az'[Cz(E- Ezn) Ca*(E - Eln)] (23)

where,

C8* =

uc3 + ( 1 - U)C,

(24)

Hence the total current, which is the sum of if and i,, is, i

=

+ C3*E'] + A2[iZo(l+ 4) + C2E' -

A[is0

i30*

- C3*E'] (25)

where i30* = Ui30,and 4 is defined in Equation 6. Equation 25 is of the same form as Equation 6 where C1 and ilo are replaced by C1* and iso*. The conditions for the isopotential point in this case follows directly from Equation 10 when ( 1 4) is understood to be associated with iz0. This interesting result occurs because the regions A I and As are related through the right side of Equation 20 and thus are not independent. Effect of E(r) on the Isopotential Point. In the discussions above, we have demonstrated that an isopotential point can occur in a variety of situations. However, we have not discussed the effect of E(t) upon the magnitude of i at the isopotential point, i,,, and upon the potential at which the isopotential point occurs. The behavior of i,, and E,,, as a function of E(t),is related to the electrochemical kinetics and mass-transfer properties of the system, and can be treated fairly generally. We will limit our discussion to the limiting cases A and B, for which only two couples are involved, although the analysis could be applied to other cases. i,O may be written as

+

where Qi (=

LT

ii0dt) represents the charge/cm2 required

for the ith process in the time interval to go between two potentials. Combining this equation with Equation 7 gives an expression for i involving E’.

Equation 27 can be solved for conditions that yield isopotential points in the same manner as was Equation 7. If the charging current is small compared with the faradic current, the condition for an isopotential point becomes

and ii, is then

i,,

=

A

[(g),E’ +

i

($)E],

It is clear that if (%)E’

>>

(z),, i

=

=

1 or 2

1 and 2

(29)

(30)

or the converse relation holds, Equation 28 has no dependence on E’ and E,, is independent of E’. When neither of these conditions is true, a variation of E,, with E’ will be observed. If Equation 30 represents the experimental situation, i,, will be proportional to E‘, while if the converse of Equation 30 is true, i,, will be independent of E’. Frequently both partial derivatives are important for at least one of the couples, and thus both i,, and E,, are functions of E‘. In a situation such as Case B in which charging currents are not negligible, and only one faradic process occurs in the potential region being studied, the condition for an isopotential point is

j = 1 , i = 2,orj= 2 , i = land

We see from Equation 32 that i,, need not be proportional to E’. From Equation 31, E,, will be independent of E’ if (bQi/dE)iE’ >> (bQi/dt)Et. EXPERIMENTAL

Instrumentation. A conventional three-electrode potentiostat consisting of a solid state control amplifier, potential follower, and current follower was used to obtain the i-E curves which were recorded on an EAI, X-Y-Y’ 1131 Variplotter. The platinum ring-platinum disk and platinum ring-gold disk electrodes used in these experiments were constructed in our laboratory. The area of each disk was 0.46 cm2. The electrode rotator was supplied by Pine Instruments of Grove City, Pa. The glass cell and auxiliary equipment was the same as that described elsewhere (7). All data were recorded at near (7) D. C . Johnson and Stanley Bruckenstein, J . Electrochem. Soc., 117,460 (1970).

25OC temperatures. Solutions were deoxygenated with high purity nitrogen which was presaturated with water. A nitrogen atmosphere was maintained above the solution during experiments. A Leeds and Northrup No. 1199-31 fiber junction SCE was used as the reference electrode and all potentials are reported us. it. Chemicals. Solutions were prepared from triply distilled water using reagent grade chemicals. A fresh bottle of Baker Reagent grade sulfuric acid was used to prepare the supporting electrolyte; 0.2M H2S04 was used for supporting electrolyte in all experiments. Preparation of Gold-Plated Platinum Ring Electrode. This electrode was prepared by oxidizing the disk of a gold disk-platinum ring electrode at $1.6 V and collecting the soluble gold species formed at the ring, E, = 0.0 V. The amount of gold on the platinum surface was decreased after recording each i-E curve by oxidizing the electrode at $1.8 V for at least 30 seconds. Determination of Fractional Coverage of Adsorbed or Plated Materials on Platinum Electrode Surfaces. When the fraction of a platinum electrode initially covered with adsorbed or plated material is given, this fraction, 8 , was calculated from the percentage decrease in the area under the hydrogen adsorption peaks in the presence and absence of the adsorbed or plated material. This method can be used for any material that inhibits the adsorption of hydrogen on platinum, provided hydrogen is not adsorbed on it in this potential region. The “fractional coverage” is equal to the “fractional monolayer coverage” if the material deposited forms a uniform layer before additional material deposits. Conventions Used in Designing Isopotential Points and i-E Curves. Isopotential points are designated by Roman numerals in the order they occur on the potential scans. Thus, isopotential points in a family of cyclic i-E curves obtained by scanning anodically then returning to the initial potential with a cathodic scan would have all isopotential points on the anodic scans numbered before those on the cathodic scans. The individual i-E curves are designated by lower case letters in alphabetic order starting with the lowest initial coverage of adsorbed or plated material on the platinum electrode surface. Coverages at isopotential points were not determined. Pretreatment of Electrode Surface. Before each experiment the platinum disk electrode was hand-polished with 0.05 u , alumina and water. The electrode was always electrochemically pretreated, except where noted otherwise, when the freshly polished electrode was put into the supporting electrolyte, or whenever a new species was added to the solution. This treatment consisted of anodizing the electrode at 1.4 V for five minutes; potential cycling the electrode several times between 1.4 V and -0.2 V; and anodizing one more time at +1.4 V for one minute. The rationale for these procedures was that they yielded reproducible L-E curves. On occasion, impurities made their way into our supporting electrolyte without any obvious source, or error, on our part. Our ability to produce solutions of the same level of cleanliness on a day-to-day basis was judged by the shapes of the hydrogen adsorption peaks and the platinum oxidation region of i-Ecurves in 0.2MH2S04.

+

+

RESULTS AND DISCUSSION

It has been shown in the Theoretical section that it is possible to predict the occurrence of isopotential points in families of i-E curves obtained under potential scanning conditions. We will now interpret Figures 1, 2, 4, 5, and 6 and some Figures from recent electrochemical literature on the ANALYTICAL CHEMISTRY, VOL. 44, NO. 6, MAY 1972

1015

basis of the isopotential point theory and support these conclusions, as needed, with other electrochemical arguments. In order to simplify the interpretation of our experimental results as much as possible, we chose a potential-time function of the form E(t) = Ed sr, where E, and s are constants in a particular experiment. E, represents the inital potential, and s the linear sweep rate. In some experiments, cyclic voltammetry was used-i.e., the sign of s was changed at a specified time. Figure 1. Isopotential Points. Figure 1 shows a family of i-E curves obtained during the oxidation of various amounts of adsorbed sulfite from the surface of a rotating platinum disk electrode. We will refer to the adsorbed sulfite species as SO, for convenience, recognizing that major species present in the acid solution are &SO3 and HS03-. Although the reported i-E curves were obtained at a rotating disk electrode because of its convenient hydrodynamic properties, other experiments confirmed that only very minor changes in Figure 1 occurred when the angular velocity was varied between 2500 rpm and 0 rpm, provided the same initial amounts of SOz were on the electrode surface. In all the experiments, SO, was adsorbed on the rotating disk electrode by holding the electrode at E, = 0.0 V for different known times in a 0.2M H2S04solution containing 4 X mole/liter of added K2S03. Adsorption was found to be diffusion-controlled at E, in the range of initial coverages for which IP-I11 was observed. Acid solutions containing H2S03 ( ~ 1 0 - ~ showed M) visible anodic currents at potentials more positive than $0.20 V. However, in our adsorption experiments, the SO2 solutions were very dilute and the current from the steady state oxidation of SOn was negligible compared to the current from the processes determining the isopotential points. The only faradic processes occurring in the potential region of IP-I1 and IP-I11 of Figure 1 are

+

Hz0

+ rile2H20 + SOn(ads))r Sod2+ 4H+ + 2ePt I_ Pt(oxide)

(33) (34) At IP-I11 charging current is negligible compared with the faradic current and hence Equations 11 and 12 apply, while Equations 28 and 29 apply if we wish to consider the effect of E’. At the foot of the wave, where IP-I1 occurs, the charging current is comparable in magnitude to the faradic current from processes 33 and 34, and the general result, Equation 10, must be used to describe this isopotential point. The order of the i-E curves for different ASO? values on either side of IP-I1 is reversed from that on either side of IP-111. If we neglect double-layer charging processes, the explanation for this is seen by examining curves 1 and 2 of Figure 3C, where curve 1 represents the io for platinum oxidation and curve 2 and io for SOn oxidation. Double-layer charging effects can also be treated using Figure 3 by redefining the ordinate, i, to be the sum of faradic and charging processes. Hence, double-layer charging currents do not introduce new conceptual problems. The processes producing IP-I, at f0.20 V are difficult to determine unambigously because all of the processes occurring have low current densities in this potential region. There are three possibilities : (1) Only double-layer charging is involved. In this situation IP-I would occur where the two differential doublelayer capacitances are equal (Equation 15). (2) Double-layer charging and one faradic process cause this isopotential point. This is not ruled out immediately 1016


since even though platinum is not oxidized at these potentials, the steady state oxidation of a 2mM solution of SOz in 0.2M HnS04 showed the first detectable oxidation occurred at +0.20 V. (3) In addition to (21, there may be some adsorbed hydrogen left on the electrode surface at $0.20 V which would contribute to the current at the isopotential point. The occurrence of SO2 oxidation rules out the possibility of (1). From the shapes of the i-E curves between 0.1 V and 0.2 V, and plots of 0~ us. E (8) we discount the effect of adsorbed hydrogen, ruling out (3). Potential scan experiments show that there is a significant difference in double-layer capacitance of a polished and S02-covered platinum electrode in this potential region. Hence we conclude that this isopotential point is an example described by Equations 13 and 14 and results from a single faradic process coupling with double-layer charging currents. In order to test for the possible dependence of E I Pand iIp on E’, as predicted by Equations 26-31, we studied the effect of s on i-E curves for a platinum electrode with 0s02 = 0 and 0.6 as well as on E1p-111 and i1p-111of Figure 1. First, we determined the behavior of platinum in the absence of SOn. “Normalized” i-E curves (i/s cs. E ) for a platinum electrode in 0.2M H2S04showed s to have only a weak effect on the shape of the i/s us. E curve. Second, we found that “normalized” i-E plots for a SOz-covered platinum electrode showed a marked dependence on s in the region of the SOz oxidation peak. Thus it appears that the inequality (or its converse) stated in Equation 30 is not valid for either couple, though in the case of the platinum couple, Equation 30 is not a bad approximation. Hence, in this situation, E1p-111 and iIp-III/s are predicted to be functions of s, and we did find that as s was varied from 200 mV/sec to 50 mV/sec, iIp-III/s increased by about 3% and E1p-111 moved from +0.73 V to +0.69V. The i-E curve in Figure 1 for an initial surface coverage of SOn, 0s02,>0.5 does not quite pass through IP-111, but does go through IP-I and IP-11. Apparently for @so2> 0.5 the assumption that the right side of Equation 9 equals zero is no longer valid in the potential region where a large faradic current is flowing. It was not possible to decide whether dilo/dA20or diz0/dA2Oin Equation 9 became nonzero. However, the continued existence of IP-I and IP-I1 indicate that no problems are arising at more cathodic potentials. Figure 2. Ispotential Points. Figure 2 shows a series of i-E curves, +1.3 > E > -0.2, obtained by oxidizing and reducing a platinum ring electrode covered with different amounts of gold. As mentioned in the Theoretical section, appreciable soluble gold species were not detected in the potential region for which the i-E curves were recorded. The oxidation product of gold in sulfuric acid is reported to be be AU2Op (9), and our experiments show it adheres to the platinum surface. At potentials more anodic than 1.5 V, appreciable solution of the gold film occurs, thus allowing us, by a controlled oxidation procedure, to decrease the amount of gold on the platinum electrode. During each i-E curve, the electrode surface is converted from metallic gold and platinum at negative potentials, to oxidized gold (on platinum metal) and oxidized platinum at very anodic potentials. As has been previously reported (IO) during the anodic potential sweep, platinum oxidation

+

(8) M. W. Breiter, Trans. Faraday Soc., 65, 2197 (1969). (9) Kotaro Ogura, Shiro Haruyama, and Kyuya Nagasaki, J. Electrochem. Soc., 118, 531 (1971). (10) R. Wood, Electrochim. Acra, 16,655 (1971).

starts occurring before gold oxidation. On the cathodic potential sweep, gold oxide reduction occurs before platinum oxide reduction (10,ll). The gold deposit on the platinum ring electrode cannot be uniformly thick, since the gold deposition did not occur under conditions of uniform accessibility. However, the theoretical interpretation of Figure 2 is unaffected by this nonuniform gold thickness if the right side of Equation 9 is zero-i.e., so long as the properties of the gold region are independent of gold thickness, the uniformity of the thickness of the gold film is irrelevant. It should be reemphasized that O.ku still represents fraction of the platinum surface covered, and not able to adsorb hydrogen, and need not be related to the actual weight of deposited gold. Three isopotential points are observed over the large gold coverage range, 0 5 E)Au 5 0.7. IP-I11 at $0.72 V on the cathodic scans occurs because platinum and gold oxides are being reduced simultaneously in this potential region. The current at E1p-111 is small because the two oxide reduction peaks are quite widely separated. Charging current is a significant percentage of iIp-111 and thus Equation 10 gives the best description of the situation a t E1p-111. IP-I is described by Equations 11 and 12. Platinum oxidation starts occurring a t f0.5 V and continues at a relatively constant rate at more anodic potentials (curve a, Figure 2). Gold oxidation does not occur until about +1.0 V (10). At potentials more anodic than 1.O V, the current density curve for gold oxidation becomes very steep and becomes greater than that for platinum oxidation. Hence at some point, E1p-1, the current density curves cross and a single isopotential point is obtained. IP-11, on the anodic scans in Figure 2, is an interesting example of a situation in which more than one process occurs on two different regions of the electrode surface. In the vicinity of IP-11 both gold and platinum oxidation are still occurring. This was established by measuring the magnitude of gold and platinum reduction peaks as functions of the anodic potential limit of electrodes made of each of these metals. In addition, oxygen is being produced by the oxidation of water at different rates on the gold and platinum regions of the electrode, as determined in separate ring-disk electrode studies. In this case the oxygen evolution occurs at a much higher rate on platinum than on gold. Thus, at any potential more oxygen is evolved the lower the coverage of gold. If the only faradic process occurring was the evolution of oxygen from the two electrode regions, no isopotential point would occur since the current density-potential curves would be similar to Figure 3A. However, as noted above, gold and platinum oxidation are still occurring, and at potentials more anodic than E1p-1 the current density for gold oxidation is greater than that for platinum oxidation. Fortuitously, the relative magnitudes of the four current densities are such that Equation 18 is satisfied and an isopotential point occurs. An alternative approach to explain IP-I1 is to use Figure 3B. It is necessary only to assume that i20 represents the difference in current densities for oxygen evolution on platinum and gold, and that ilo represents the difference in the oxidation current densities for gold and platinum to predict the occurrence of IP-II. Figure 4. Isopotential Points. Figure 4 shows i-E curves obtained for the oxidation of underpotential deposited copper on a platinum electrode. The i-E curves in this Figure corre-

c

-400

- 200 4

-? O 0

200

+

(11) D. C. Johnson, D. T. Napp. and S. Bruckenstein. Electrochim.Acta, 15, 1493 (1970).

:I ~

0.6

1-0

0.2

E,-Volts

Figure 5. Figure 1

Cyclic i-E curves for SOz system and conditions in

Curves a-d yield an isopotential point at +0.73 V. Curves A and B are: A , -, i-E curve of freshly polished electrode in absence of SOe. B, - - -, i-E curve recorded after oxidation of electrode at $1.9 V for 5 minutes. Fractional coverages of adsorbed SOZfor curves a-d are between 0 and 0.3

spond to 0

< 8cu < 0.3 and to a

bulk copper deposit (curve

d). The current peak at 0.0 V, curve d, corresponds to the oxidation of bulk copper and that at +0.4 V to underpotential copper (6). The current peaks for curves a-c cathodic to 0.0 V involve oxidation of adsorbed hydrogen (12). For

bulk copper deposits of varying thicknesses, all the curves coincide with curved, E > +0.4 V. There are two isopotential points in Figure 4. One, at $0.79 V, is caused by the oxidation of platinum and the underpotential deposited copper on the platinum, and corresponds to a situation of the type discussed under Case A in the Theoretical section. This isopotential point was observed for 0 5 0cU5 1. Note that at this isopotential point, only a small fraction of the initial coverage of copper remains and that these results do not conflict with the range of 0~:"for which the other isopotential point is observed (See below). The other isopotential point is the example of the situation described by Equations 20-25, and is based on a model involving the oxidation of underpotential copper and adsorbed hydrogen along with double-layer charging processes. Literature citations confirming these processes have been given above. This isopotential point disappears when Bcu > 0.3. Isopotential Points with a Superimposed Constant Initial Coverage. As pointed out in the Theoretical section, the fact that A , in Equation 2, is not equal to the microscopic area of -_

(12) S. J. Cadle and S. Bruckenstein, ANAL.CHEW,in press. ANALYTICAL CHEMISTRY, VOL. 44, NO. 6, MAY 1972

1017

O1

obtain Figure 1 . Note that only four of the i-E plots pass through IP-I, which is at the same potential as IP-I11 in Figure 1. One of these plots, curve A , is the original i-E curve before any SO2 was added to the supporting electrolyte. On the basis of the isopotential point theory, curve A should go through IP-I. Also note that curve a, was recorded under conditions which permitted no detectable amount of SOz to adsorb on the electrode. Thus curve a, and A should be identical, but in fact they are not. Also the platinum oxide reduction peak for curves a-d are identical, but smaller than that for curve A . This discrepancy can be explained on the basis suggested above if some of the SOa is “irreversibly” adsorbed on the electrode surface. The change from curve A to a is always observed the first time a freshly polished and pretreated electrode is exposed to the supporting electrolyte containing SO*. Our normal pretreatment procedure did not restore curve A . Restoration of curve A could be accomplished in two ways: by repolishing the electrode and pretreating it in supporting electrolyte free of SOa;and by oxidizing the electrode at 1.9 V for 5 minutes, then jumping the electrode potential to 0 .O V and immediately scanning anodically (in the solution containing SOa). This second method yielded curve B, in Figure 5 , which is almost the same as curve A . Hence, extremely vigorous oxidation appears to produce a surface approaching that of a freshly polished electrode. This result strongly suggests that some SOaon a constant fraction of the electrode surface is not oxidized during the potential scans of our usual experiment. The particular virtue of the isopotential point approach is that it is a very simple, and sensitive, diagnostic tool, and naturally draws the attention of the investigator to problems that might be overlooked. In this case, the differences between curves a and A in the platinum oxidation and reduction regions alone suggest the solution to the problem. However, the isopotential point theory lends strong, independent support to the hypothesis that small amounts of SOz are “irreversibly” adsorbed at platinum and can be removed only by extremely vigorous treatment. We estimate, on the basis of the oxide reduction region differences, that 25 i 5 pc/cm* of platinum oxidation and reduction is normally inhibited by the “irreversibly” adsorbed SOS. Two Adsorbed Species, An isopotential point was produced in Figure 5 because the area of the electrode covered by the “irreversibly” adsorbed SO? was constant throughout the experiment. Thus A , in Equation 2 was less than the microscopic area. These SOz findings suggested a more general situation that would show the same type of behavior in a more pronounced way. The general situation would involve the adsorption of a substance that is electrochemically active but for which e is constant, in addition to the usual adsorption of another couple for which 8 is variable. The experiment we report takes advantage of the fact that I-, in addition to SOn,is adsorbed on a platinum electrode at 0.0 V GS. SCE. Both the I- and SOnwere simultaneously adsorbed from sulfuric acid solution. The amount of Iadsorbed was held constant while the amount of SO2 adsorbed was varied between i-E curves. This was accomplished by varying the concentration of SO? from 0 to 8 X 10-6M between successive i-E curves while holding the concentration of I- constant at 1 x 10-6M. In each solution, the potential of the rotating disk electrode was jumped from 1 1 . 2 V to 0.0 V, held at 0.0 V for 15 seconds and then an anodic i-E curve recorded. Figure 6 shows the set of i-E curves (a-e)

+

1.2

0.4

0.8

0.0

E,-Volts

Figure 6. i-E curves for oxidation of various amounts of SO2 and a constant amount of I- from the surface of a rotating platinum disk electrode CHlsor = 0.2M, w = 2500 rpm, s = 100 mV/sec. Solution concentrations of SO2 and I- and total fractional electrode coverage, respectively, during each i-E curve is: A 0, 0, 0; a 0, 1 p M , 0.3; b 2 p M , 1 p M , 0.35; c 4 pA4, 1 p M , 0.40; d 6 p M , 1 p M , 0.43; e 8 pA4, 1 pA4, 0.45. Isopotential points are at following potentials cs. SCE: I = $0.22 V, 11 = +OS6 V, I11 = +0.78 V

the electrode does not affect the basic isopotential point theory. This situation could be treated mathematically; however, we feel this to be unnecessary to interpret the experiments we report. Instead, we present the following argument. If some portion of the electrode surface is always initially covered to the same extent by one species, X,and the remaining part of the electrode is divided into two regions in the usual manner by two additional couples, the resulting family of i-E curves obtained should exhibit all of the isopotential points characteristic of the second two couples. This result is obvious if X is electrochemically inert, and maintains its initial coverage throughout the experiment. The true value of A in Equation 2, is then A - A,. If Xis electrochemically active, its surface coverage will be a function of potential, but will be the same function of potential in all the i-E curves, independent of the surface coverage of other adsorbed species, since 8, is held constant at E,. Hence, if the 8, term were included in a mathematical formulation of the problem, it would vanish on differentiation with respect to An0,and would not appear in the condition for the isopotential point. Thus, the isopotential point potential should be unaltered by the presence of X. On the other hand, the observed current at the isopotential point will be a function of the particular X and 8, chosen for the experiment. One Adsorbed Species. Figure 5 shows aseries of i-E curves for the S02-Pt system under the same conditions as used to 1018


obtained, as well as an i-E curve recorded before any species were added to the supporting electrolyte (curve A ) . Curves a-e correspond to 01- = 0.30 and 0 5 @so25 0.15. There are three isopotential points in Figure 6, which have a one-to-one correspondence with those obtained in Figure 1 for oxidation of adsorbed SOn on platinum in the absence of I-. The potentials at which IP-I1 and IP-I11 in Figure 6 occur are shifted 80 and 50 mV anodic with respect to the corresponding isopotential points in Figure 1. This indicates that either or both of the current densities for platinum and SOs oxidation must be a function of @I-. Despite this dependence of the i”(’s) on 01-, isopotential points are still observed. Hence the assumption that @so,does not affect these io’s is still valid (see Equation 9) at constant @I-. Literature Examples of Isopotential Points. A cursory survey of the recent literature yielded a number of examples of systems having isopotential points. The interpretations we give for five examples below are based on the data presented in these papers plus our isopotential point theory. Zakumbaeva et al. ( I ) reported a study on the “adsorption” of Zn, Cd, and TI at platinum electrodes using linear sweep voltammetry. Their Figure 2, which shows 5 anodic i-E curves corresponding to differing amounts of cadmium initially on the platinum electrode at 0.06 V DS NHE, has two isopotential points, one at +0.35 V and the other at +0.85 V. The different amounts of Cd(0) on the electrode surface were obtained by varying the concentration of CdSO, in solution and potentiostating the electrode at +0.06 V for a period of time sufficient to establish equilibrium coverage of Cd in each case. The concentrations of Cd(+2) chosen were such that a wide variation in the coverage of underpotential cadmium was obtained. The interpretation of this situation appears to be analogous to the case of underpotentially deposited copper on platinum that we discussed above. The more cathodic isopotential point is caused by the oxidation of Cd(0) and of hydrogen adsorbed on the platinum not covered by Cd. The other IP, which occurs at a lower current, is due to the oxidation of Cd and Pt. The relative magnitudes of the two I P S and the shapes of the platinum oxidation peaks at different 0 c d values do not appear consistent with the authors’ conclusion that 90% of the Cd(0) has been desorbed from the electrode surface by 0.8 V. Kesten and Feller ( 2 ) studied the anodic dissolution of Ni in sulfuric acid, and interpreted this oxidation in terms of two reaction paths. Both mechanisms yield soluble Ni(+2), but one goes oia adsorbed OH- and the other goes cia adsorbed S04*- through reduction to adsorbed HS-. Two peaks, which are separated by 0.25 V are observed during the anodization of the Ni electrode. Their Figures 5, 7, 8, and 9 present i-E curves involving different 0 ~ 0 and ~ ~each - figure has an IP near +0.2 V. Although the authors report that soluble Ni(+2) is formed by both mechanisms, passivation of the electrode occurs and the existence of isopotential points in their figures indicates film formation is important, and that there are two different electrode regions (as would be required by their mechanisms). Mayell and Barber (3) studied the behavior of Pt-Rh mixed metal electrodes in H,P04 and H,S04 at 100 OC using both porous and smooth electrodes. Their experiments showed that upon cyclic scanning of such electrodes, isopotential points developed in the i-E curves for certain sets of scans. The authors commented on the existence of two isopotential points which they termed ‘‘isoelectronic’’ points. They explain the entire i-E curves in Figures 1 and 4 on the assumption that rhodium oxide is fairly soluble, and suc-

cessfully interpret the behavior of both porous and smooth electrodes. They correctly recognize the cause of the two isopotential points stating, “it is likely that, during cycling, formation and reduction of oxides of rhodium and platinum occurred with the exclusion of other side reactions.” Our detailed interpretation of the isopotential points in their Figures 1 and 4 is consistent with their conclusions. For example, in Figure 1, for a porous electrode in H 3 P 0 4 of initial Pt :Rh ratio of 2 :1, one IP at about 1.O V L’S. NHE is observed on anodic scans 2-25 (last-reported curve) and one IP at about +0.6 V DS. NHE is observed for cathodic scans 2-7. During scans 8-25, deviation from IP behavior occurs on the cathodic scans. The anodic isopotential point at about $ 1.OV is caused by the oxidation of rhodium and platinum. The relative currents for this family of curves indicate that the oxidized rhodium species is soluble to some extent, and is redeposited as rhodium metal on the cathodic cycle. The cathodic isopotential point at f 0 . 6 V corresponds to the reduction of the rhodium and platinum oxides. In Figure 4, two isopotential points are observed at the same potentials as in Figure 1 . However, the relative magnitudes of the currents in this figure are the opposite of that in Figure 1, and indicate that a soluble oxidized rhodium species escapes from the surface of the smooth electrode before it can be redeposited. An isopotential point is also observed at about f0.2 V in Figure 4. Inspection of Figure 1 shows that i-E curves in Figure 1 also cross, but in the double-layer region at about +0.5 V. The interpretation of these isopotential points is analogous to that of IP-I in our Figure 4. The existence of isopotential points demonstrates that two regions, a platinum and a rhodium one, exist, and the sum of the “true” areas of these regions remains constant during potential cycling. This raises interesting conjectures concerning the nature of the exposed electrode surface in the rhodium-platinum alloy. Does the solubility of rhodium at a solid Pt-Rh alloy produce a platinum surface with pits (which rhodium atoms previously filled) or does the surface rearrange rapidly to a relatively smooth platinum surface ? The choice between these two possibilities is not obvious since it is not clear that the pits would change the total surface area measured by the potential point theory. Another example of an isopotential point is to be found in Figure 5 of Ossendorfova, Pradac, and Koryta’s paper ( 4 ) . While studying the behavior of glutathione at gold and platinum electrodes, they adsorbed equilibrium amounts of the reduced and oxidized forms of glutathione on a platinum electrode at $0.6 V cs. NHE from a glutathione solution in 0.5M HzS04. Next they moved the electrode to a glutathione-free solution of 0.5M H2S04and recorded the first six i-E cycles between 0.0 and 1.6 V. The first anodic potential scan showed a large oxidation wave and the cathodic scan showed only a small reduction peak in the potential region of Pt reduction. Scans 2-6 yielded an IP on the anodic cycles which was considerably more cathodic than the halfwave potential of the first oxidation wave, but at about onehalf of the limiting current in scan 1 . Successively larger reduction peaks at the potentials for Pt reduction were obtained in scans 1-6. Curve 6 approaches the size of the platinum reduction peak observed for this electrode in glutathione-free 0.5M H2S04. The authors merely reported experimental results and noted that the reduction of oxidized glutathione was not observed in any of their experiments.

+

+


1019

The presence of the anodic isopotential point on scans 2-6 demonstrates the occurrence of surface processes involving two different electrode regions whose total area is constant. At least one of the couples involved did not exist on the electrode surface during scan 1, since curve 1 does not pass through (or even close to) the isopotential point. These results suggest that an oxidized form of glutathione (species A ) is adsorbed on the electrode during scan 1 , and that on each of the subsequent scans some A is further oxidized to soluble products, baring more and more platinum until all of the A is removed from the electrode by the sixth potential cycle. Thus it seems likely to us that the isopotential point in this figure is due to the oxidation of A and Pt. Our last example comes from a paper by T. Biegler (5) in which he examines the activation of platinum electrodes in 1M H2S04. His Figure 2, which shows the 2nd, 5th, and 200th repetitive scans after his pretreatment method, yields 2 isopotential points on the anodic scans and 4 or 5 (?) IP’s on the cathodic sweeps. Four of the isopotential points on the cathodic sweeps are in the hydrogen adsorption region and the fifth is in the oxide reduction region. The latter IP is not easily distinguishable because of the scale of the figure, and may not be an ideal isopotential point. Biegler interprets his experiments by assuming that, initially, there is a mixture of very active and “normal” platinum sites, and that upon potential cycling the active sites are gradually replaced by the “normal” sites. The existence of an isopotential point supports Biegler’s view that the electrode is divided into two regions during his

experiments. However, it does not demonstrate that an activation mechanism is responsible for the results reported. Our isopotential point theory would require that the nature of the active sites be independent of their number, and that every active site be transformed to one “normal” site upon potential cycling. CONCLUSIONS

Valuable information about the nature of an electrode surface on which there is a deposited or an adsorbed species can be obtained from the isopotential point theory. For example, the disappearance of an isopotential point with increasing coverage of adsorbate can be useful in establishing the occurrence and stoichiometry of surface reactions. Also, as in the glutathione example, the existence of an unsuspected adsorbed intermediate can be established. Third, the presence of adsorbable impurities can be verified, as in the case of SO, on Pt. Changes in the surface coverages of impurities as low as a few per cent are quite obvious. The potential of an isopotential point is characteristic of the couples involved. Hence, the identity of unknown adsorbates may be learned by adding the suspected species to the electrochemical cell. RECEIVED for review August 18, 1971. Accepted January 7, 1972. Research sponsored by the Air Force Office of Scientific Research, Office of Aerospace Research USAF, under Grant No. AFOSR-70-1832.

Radio Frequency Spectral Emission Discharge Detector for Fixed Gases L. E. BOOS,Jr.,’ and J. D. Winefordner, Depurtment of Chemistry, University o/’ Florida, Guinescille, Fla. 32601

A radio frequency spectral emission detector for detection of fixed gases was designed and evaluated. A description of the overall system used in this work is given along with information regarding the response of the detector to air, CO, CO,, SO,, NHa, NO, NOn, N2, and CHa. The radio frequency (8 MHz) plasma was initiated and sustained by a low power-modified Clapp oscillator. The background spectrum (2000-5000 A) resulted from N,, NH, NO, and OH molecular band emission due to impurities in the helium carrier gas. Characteristic lines of helium and of the platinum electrodes were also identified. Limits of detection ranged from 0.3 ppm for carbon monoxide to 2.4 ppm for methane.

siderably more selective than most other types of detectors and should have considerable use for gas analysis as long as they also have adequate sensitivity, linear range of response, speed of response, and versatility of use. In this paper, a new sensitive, selective, simple radio frequency spectral emission detector for fixed gases is described. Analytical characteristics of this detector are presented. Although the radio frequency spectral emission detector is not evaluated for the analysis of fixed gases under gas chromatographic conditions, it should have use as a selective gas chromatographic detector of fixed gases. EXPERIMENTAL SYSTEM

DETECTORS IN GAS ANALYZERS and in gas chromatographic detectors are based on a great number of physical and chemical properties of gases, e.g., thermal conductivity, excitation and emission of radiation, ionization, flame temperature, absorption of radiation, heat of adsorption, velocity of sound, and many others. Gas detectors based upon absorption and emission of electromagnetic radiations should be con1 Present address Texas Neurological Development. Inc., 310 Medical Center Professional Building, Houston, Texas 77025. Author to ujhom requests for reprints should be sent.

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A block diagram of the instrumental system in the configuration for use with a gas chromatograph is shown in Figure 1. The specific components except for the gas flow system and the rf detector cell with associated circuitry are described in Table I. Helium was used as the carrier gas for all studies. Reagent grade helium (Airco Rare and Specialty Gases, New York, N.Y.) resulted in a lower background than ultra-pure helium (Matheson, Inc., Morrow, Ga.). However, essentially the same signal-to-noise ratios were obtained with either grade of helium, and so reagent grade helium was used in all subsequent studies. However,

Interpretation of isopotential points. Common intersection in families of

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