216
ANALYTICAL CHEMISTRY, VOL. 50, NO. 2, FEBRUARY 1978
Fundamental and Second Harmonic Alternating Current Cyclic Voltammetric Theory and Experimental Results for Simple Electrode Reactions Involving Amalgam Formation Alan M. Bond" and Roger J. O'Halloran Department of Inorganic Chemistry, University of Melbourne, Parkville, Victoria, 3052, Australia
I v i c a Ruzic' and Donald E. Smith" Department of Chemistry, Northwestern University, Evanston, Illinois 6020 1
The technique of ac cyclic voltammetry is extended to treat the case involving the simple electrode reaction, 0 ne R, in which the electrode product forms an amalgam. Rate laws are presented for the ac cyclic response at a stationary sphere mercury electrode. Experimental data for several redox systems give excellent agreement with theoretical predictions for both Nernslian and non-Nernstian conditions. The fundamental and second harmonic ac cyclic responses both prove to give sensitive measures of the amalgam and sphericity eflects, and complement conventional dc cyclic measurements.
+
In a previous communication ( I ) , the ac cyclic voltammetric method was studied for simple solution-soluble redox couples. Excellent correlation of theory and experiment was obtained using the versatile digital simulation approach to solve for the dc component of the boundary value problem. The ac component was treated by standard analytical procedures ( I ) . With rate laws derived in this manner, it was found that ac cyclic voltammetry presents a powerful method for elucidating electrochemical kinetic parameters. The investigation will now be extended to cover the analogous case in which the electrode product forms a n amalgam: 0
+
kf
ne _i R( Hg)
(1)
kb
Several investigations of ac polarography and ac anodic stripping \ oltammetry involving amalgam formation have been undertaken elsewhere. It was clearly evident that modifications to existing electrochemical theories were required to account for the amalgam behavior (2-6). For dc cyclic voltammetry of amalgam systems, it is observed that there is a current enhancement on the reverse (anodic or stripping) peak ( 7 ) . Preliminary studies by Blutstein and Bond (6) also have shown that, on the reverse scan of the ac cyclic voltammogram, amalgam formation a t a spherical electrode is associated with a marked increase in current relative to the forward (cathodic) sweep. This phenomenon of enhanced anodic scan current is illustrated in Figure 1 for t h e techniques of dc and fundamental and second harmonic ac cyclic voltammetry. For the ac observables with Nernstian dc processes, the enhanced anodic scan, with its attendant scan rate and switching potential dependence (see below), provides a major and obvious distinction between amalgam-forming systems and those where the reduced form is solution-soluble ( I ) . In the latter case, one predicts and observes negligible differences On leave from the Center for Marine Research, Ruder Boskovic Institute, Zagreb, Yugoslavia, 1972-1976. 0003-2700/78/0350-02 16$01 .OO/O
in forward and reverse scan peaks and no scan rate or switching potential dependence ( I ) . Our ability to quantiatively interpret these special amalgam effects is a question of considerable interest and the prime topic of this report. For the case of dc cyclic voltammetry, Beyerlein and Nicholson ( 7 ) have shown that electrode sphericity has a substantial influence on amalgam systems. The nature of the ac polarographic amalgam response also has been reported to show a marked dependence on spherical diffusion (8-13). From these precedents, it would be anticipated that a significant effect of electrode sphericity should be observed in the ac cyclic voltammetry of amalgam systems.
THEORY The amalgam case defined by Equation 1 can be regarded as a special case of the simple solution-soluble redox couple investigated previously ( I ) . The same set of expressions as defined there (assuming the slow scan limit) will give the ac amalgam response, since all influences of electrode geometry and spherical diffusion (which will be different for the amalgam case) are included only in the dc surface concentration terms. No attempt is made to analytically solve for these dc terms, but digital simulation, as described by Feldberg (14). can successfully account for the electrode geometry and amalgam formation to give accurate estimates for the surface concentrations. The essence of spherical electrode simulation may be found in the work of Ruzic and Feldberg ( 1 5 ) . Simulation parameters were chosen so that further optimization produced negligible improvement. Typical values of simulation parameters used were: (a) a radius increment of 1/900 the drop radius; (b) a t least t h e first 150 of these elements nearest the electrode surface had to be considered, although 350 were employed in most calculations; (c) a dc potential increment of 1.0 mV; (d) a maximum dimensionless simulation diffusion coefficient, DDMAX (14), of 0.32. Notation definitions employed here are conventional and are given elsewhere ( I ) . EXPERIMENTAL Cyclic voltammograms were recorded on a Princeton Applied Research Corp. (PAR) Model 170 Electrochemistry System, modified as detailed previously (1). The working electrode was a Metrohm Hanging Mercury Drop Electrode (HMDE) BM-503. Ag/AgCl (I M NaCl) was used as the reference electrode and platinum wire as the auxiliary electrode. All solutions were deoxygenated with argon and thermostated at 26.0 f 0.1 O C . Positive feedback circuitry was used to minimize iR drop. The following solutions were prepared using supplied AR grade materials: (i) 1.0 X M Cd(I1) in 1.0 M NaC1. (ii) 1.0 X M Cd(I1) in 1.0 M Na2S0,. (iii) 2.0 X M HC1. These systems M Zn(I1) in 1.0 M KCl/1.0 X were chosen to give a range of k , and 01 values that have been extensively investigated by other workers (16-23). C 1978 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 50, NO. 2, FEBRUARY 1978
217
I
40 Y A
!
k
i
I
'
a)
b
T
d) E.; -800 mV
E5- - 6 3 5 m V
I
7
c
r
c ) E; -700
---,
7
-035
~~~~
-045
7 ~
-055
,
-085
-075
-085
-095
E [VOLT] Figure 1. Comparison of dc and fundamental and second harmonic ac cyclic voltammograms for 1 0 X M Cd(I1) in 1 0 M NaCl at a HMDE. A = 0.0086 cm2, T = 25 O C , v = 50 mV s - ' , E , = -0 35 V, Ea = -0.635 V, E, = -0.90 V [all potentials relative to Ag/AgCI ( 1 .O M NaCI)], (L' = 27r X 400 s-', A € = 5 mV. (a) = dc; (b) = second harmonic; (c) = fundamental harmonic Reversible E1,21 values used in theoretical calculations were obtained from dc polarograms, and Eo values were determined using published diffusion coefficients (26-23). The surface area of the HMDE was calculated by weighing 20 mercury drops, and any shielding due to the point of attachment to the capillary was neglected.
RESULTS AND D I S C U S S I O N Because of the large number of independently variable parameters which significantly influence the ac cyclic experiment when amalgam formation occurs, the most expedient way to investigate the theoretical predictions is to discuss several real electrode processes. General predictions (e.g., construction of working curves of Upvs. log h,) are not simple because of the marked dependence on the switching potential and scan rate. Thus, kinetic parameters for three electrochemical systems were obtained from the literature, and the predicted ac cyclic response was computed. Actual experiments were then performed under conditions matching those used in the calculation, and theory-experiment correlation was made. Reversible Case ( d c a n d ac Senses). The first example considered is the reduction of 1.0 X M Cd(1I) in 1.0 M NaCl Cd(I1)
+
2e
Cd(Hg)
(2)
T h e h, and a values for this system have been reported as 1.2 cm s-l and 0.46, respectively (16). This satisfies the requirements for a reversible dc process (24, 25) and the h, is sufficiently large for effectively reversible ac behavior to prevail under the conditions employed here (26). This system should thus enable the effects of amalgam formation to be observed,
I-
Influence of switching potential (E,) on observed fundamental harmonic ac cyclic response for Cd(I1) system as described in Figure 1. E, = -350 mV for all vottammograms, f = forward scan, r = reverse (anodic) scan Figure 2.
uncomplicated by heterogeneous charge transfer kinetic factors. F u n d a m e n t a l Harmonic Case. It is observed that the most i, portant factor in determining the nature of reversible fundamental harmonic ac cyclic voltammograms is the extent to which amalgam formation occurs. This is determined predominantly by the time during which the applied dc potential is more negative than the E l value. Two factors determine this time: the rate of voltage scan (c) and the switching potential (E,). In Figure 2, A series of experimental fundamental harmonic ac cyclic voltammograms with variable E , values are shown. Figure 2(a) illustrates that, if the scan is reversed at the peak potential of the forward sweep, (Ep)f, then the forward and reverse scans overlap within limits of experimental error. As the switching potential is made more negative. the reverse peak becomes progressively larger because of the greater anodic stripping effect. The influence of scan rate on the reverse sweep is shown in Figure 3. As expected, the slower the scan rate, the larger the reverse peak becomes relative to the forward peak, since there is a longer time available for amalgam formation. Another factor which will determine the extent of current enhancement on the reverse scan is the sphericity of the mercury drop. Data in Table I show that the ratio of forward increases with drop size. to reverse peak currents, (Ip)f/(I,,)r, This is qualitatively in agreement with expectation: as the size of the mercury drop increases, the concentration buildup near its surface due to the convergent nature of spherical diffusion decreases, since the inner volume into which the amalgam species diffuses is relative15 larger. Several important observations become apparent on studying experimental data for the cadmium system in 1 M
218
ANALYTICAL CHEMISTRY, VOL. 50, NO.2, FEBRUARY 1978
i t A
-
--,I
,I
I T
t
~
I
A
T
,
40uA I
1 -04
A
-05
-07
-06
-09
-08
E [VI Flgure 4. Theory-experiment comparison for fundamental harmonic ac cyclic response for Cd(II)/ 1 M NaCl as detailed in Figure 1, Do = 0.68 X cm2 s-', D, = 1.6 X cm2 s-', f = forward scan. r l = reverse (anodic) scan, experimental; r2 = theoretical reverse scan, data from Reference 16. f = forward scan for theory and experiment (Experimental results normalized to forward theoretical scan.)
I
Table 11. Theoretical Results Showing Effect of D o and D R on the Fundamental Harmonic ac Cyclic Response of 1.0 x M Cd(II)/l M NaCl System
i
DR
X
lo5
0.68
(em's-') 1.0
1.2 2.0
-0.35 - 0 4 5
-0'55
-0:65
E
-0'75
-0:85
D o X l o 5 0.4 (cm's-') 0.6 0.9 1.2
-0:85
[VOlfl
Figure 3. Influence of scan rate on observed fundamental harmonic ac cyclic response for Cd(II)/l M NaCl as detailed in Fi ure 1. (a) Y = 100 mV s-'; (b) v = 50 mV s-l; (c) v = 20 mV s-
s
Table I. Dependence of Fundamental Harmonic ac Cyclic Peak Currents for 1.0 x M Cd(II)/1.0 M NaCl on Area of Mercury Drop (i,)f (PA) A, cm2
Exptl
Theory
Exptl
(PA) Theory
0.0086 0.0138
21.4 35.0 42.9
21.4 33.8 43.8
39.9 56.8 66.7
43.4 61.6 73.7
0.0180
(ip)r
Ei = - 0.350 V, E , = - 0,900 V, u = 50 mV s-', AE = 5 mV, w = 2n x 400 s - ' , E o = -0.635 V ,T = 298 K. Theoretical figures calculated using data from Reference 16. All potentials measured relative t o Ag/AgCl (1M NaC1). NaC1. T h e position and height of the peak on the forward scan is independent of scan rate within limits of experimental error and, in fact, predictions for the forward scan closely resemble t h e non-amalgam case, except that the current magnitude is larger for t h e amalgam system: e.g., 19.6 pA (theoretical, non-amalgam) vs. 21.4 pA (theoretical, amalgam) for v = 50 mV s-l and A = 0.0086 cm2. The half-width is 45.5 f 0.5 mV for forward and reverse scans, so the waveshape on t h e reverse scan is similar to the forward scan despite the difference in current magnitude. Furthermore, within limits of experimental error, the peak potentials of both scans coincided under all conditions studied. Experimentally, a linear dependence of both the forward scan peak current, and the reverse peak current, (I,),, on A73 was found for AE I5 mV (at 400 Hz). Over the frequency range 100 to 600 Hz, a direct relationship of (I,)fand (I,), with w1/2 was found for AI3 = 5 mV. For both these instances, the scan rate was 50 mV s-l and the drop area 0.0086 cm2. The phase angle at the
Ef -0.6350 -0.6336 -0.6325 -0.6294 -0.6272 -0.6299 -0.6326 -0.6345
If
21.51 21.48 21.46 21.37 16.22 20.07 24.76 28.72
Er -0.6350 -0.6334 -0.6322 -0.6292 -0.6269 -0.6297 -0.6323 -0.6343
ir
38.05 40.12 41.43 45.34 31.92 40.32 51.56 61.87
ifiir 0.5653 0.5354 0.5180 0.4713 0.5081 0.4978 0.4802 0.4642
Unless otherwise stated, Do = 0.68 x l o w 5cm's-l, = 1.6 x cmz s-', Ei = -0.350 V, E, = -0.900 V, E o = -0.635 V, u = 50 mV s-', w = 2n x 400 s-l, A E = 5
D,
mV,A=0.0086cm2,cu=0.5,h,=1.2cms~',T=298K. All potentials are in V (relative to Ag/AgCl (1M NaCl)) and currents in U A and refer to Deak values.
peak potential of the forward scan was 44 f 2'; and for the reverse peak, 42 k lo,at 400 Hz. Within experimental error, all these latter data closely match expectations for the reversible response. Theoretical ac cyclic predictions for the Cd/NaCl system were obtained via digital simulation using the following data ( k s ,Do,D R , and a from Reference 16): k , = 1.2 cm s-', a = 0.5, Do = 0.68 X cm2 sd, DR = 1.6 X cm2 s-l, w = 2s X 400 s-l, AE = 5 mV, Ei = -0.350 V, E f = -0.900 V, Eo = -0.635 V, A = 0.0086 cm2, v = 50 mV s-l. All potentials are relative to Ag/AgCl (1 M NaCl). Theory-experiment fit is very good (see Figure 4). A small discrepancy can be observed in the current magnitude of the reverse sweep. Experimentally, it is found that the reverse peak current (being larger) is more sensitive to iR compensation than the forward peak current. Any degree of uncompensated resistance will thus cause a relative decrease in the magnitude of the observed reverse peak. The discrepancy between observed and calculated values is within acceptable limits. Uncertainties in Do and DR used in the simulation, together with experimental inaccuracies associated with uncompensated resistance and errors in switching potential and scan rate are sufficient to account for the small difference. For this reversible Cd(I1) system, changes in k , and (Y had an insignificant effect on the predicted ac cyclic response, such that any k , > 1 cm s-l gives acceptable experiment-theory fit. The effect of changes in DO and D R on the computed response is shown in Table 11. The diffusion coefficient of the amalgam species, DR, has negligible effect on the magnitude of the forward peak current, b u t the reverse peak increases sub-
ANALYTICAL CHEMISTRY, VOL. 50, NO. 2, FEBRUARY 1978
219
Table 111. Influence of the Size of the Mercury Drop on Simulated Second Harmonic ac Cyclic Voltammograms. I f = (ip+ + iP-)" for Forward Scan, Ir = (ip+ + ip-) for Reverse Scanb Forward scan A , cm2
(Ein- E o )
ip-
lPt
1.039 [23.3]
5.5
1.163 [- 13.21
2.057 [ 22.91
5.6
2.295 [- 12.41
1.659 [23.3]
5.5
1.813 [-13.01
2.918 [23.0]
5.5
3.173 [- 12.31
2.159 [23.4]
5.5
2.333 [- 12.9 J
3.571 [23.1]
5.5
3.842 [-12.31
1
0.0086 I f / I , = 0.55 (exptl) = 0.506 (theor) 0.0138 I f / I , = 0.62 (exptl) = 0.570 (theor) 0.0180 I f / & = 0.68 (exptl) = 0.608 (theor)
Reverse scan E")
(Ein-
1P-
All potena ip+ = peak current of anodic peak (absolute value). in- = peak current of cathodic peak (absolute value). tials in mV, currents in PA. Figures in brackets are peak potentials relative to E o (i,e., E , - E o ) . Ein = inflection (current minimum) potential. Other parameters are the same as those in Table 11. i
i
t
I \
I
I
, .04
.0.5
- 06
196uA
-07
.0.8
.0.9
E (VOLT)
Flgure 5. Simulated fundamental harmonic ac voltammogram for the same system as in Figure 4, but considering the reduced species to be solution-soluble (Le., neglecting amalgam formation); f = forward scan, r = reverse scan
stantially as DR is made larger. The influence of Do is more complicated, affecting both forward and reverse scans to a marked degree. Of course, the position of El,{ and the ac peak potentials, relative to Eo, are also affected by Do/DR. The Cd(II)/NaCl system thus gives reversible behavior, and the ac cyclic results allow no conclusions regarding the precise magnitudes of k , and cy. To show the differences between amalgam and nonamalgam systems, a calculation was performed using the same set of parameters as those for Cd(II)/NaCl, but considering the reduced species to be solution soluble. The differences are quite evident, especially on the reverse scan, as shown in Figure 5 . The very slight inequality in forward and reverse scan peak magnitudes shown in Figure 5 arises from the spherical diffusion effect combined with the more than factor-of-two difference in diffusion coefficients (see Figure 4 legend) (9). While such a diffusion coefficient difference is perfectly realistic for amalgam-forming systems, it is highly unlikely when species 0 and R are solution phase-soluble. The more nearly equal diffusion coefficients characterizing solution-soluble redox couples lead to disappearance of this forward and reverse scan difference (9). The same observations apply to the second harmonic polarogram shown below in Figure 6b. Second Harmonic Case. Figure 6a shows theoretical and experimental second harmonic ac cyclic voltammograms for the reduction of Cd(I1) in 1.0 M NaCl. For comparison, a corresponding voltammogram, calculated using the same parameters, but considering both species to be solution-soluble, also is included (Figure 6b). The influence of amalgam formation can be seen in the current enhancement of the reverse sweep, and in the enlargement of the lobes at more negative potentials. Again, the observed reverse peaks are marginally lower than predicted, and similar discussions as
-04
-05
-06
-07
-08
-09
VOLT
Flgure 6. Second harmonic ac cyclic voltammograms for Cd(II)/ 1.O M NaCl system as detailed in Figure 4. (a) (--) = theoretical prediction = experimental observation (normalized to i,+ on forward scan); (b) theoretical results as for (a) but neglecting influence of amalgam formation: f = forward scan, r = reverse scan (e..)
applied to the fundamental harmonic case are still relevant. Experimental and simulation results showed a linear dependence of the peak currents on both w'/' (for &!? = 5 mV) and &!?' (at 400 Hz), as expected. A drop area of 0.0086 cm2 and scan rate of 50 mV s-l were used in these measurements. The influence of drop size (sphericity) is shown by some data in Table 111. As the drop increases in size, effects due to amalgam formation diminish since, as discussed previously, the concentration buildup of the amalgam near the surface decreases. The predominance of the current lobe a t more negative potential over that at more positive potential decreases, and the enhancement of current on the reverse scan falls off. The effect of scan rate on the second harmonic response was similar to that for the fundamental harmonic. In Table IV, theoretical and experimental data are presented for several scan rates. As the scan rate decreases, the extent of amalgam formation becomes greater, and so its consequences become more marked: cathodic peaks increase their predominance over anodic peaks, and the reverse scan increases in current magnitude.
220
ANALYTICAL CHEMISTRY, VOL. 50, NO. 2, FEBRUARY 1978
Table IV. Dependence of Second Harmonic ac Cyclic Voltammograms on Scan Rate. Experimental System 1.0 x M Cd(II)/l.O M N a W Forward scan v, mV s-I
+,i 1.503 [23.2
20
(theoretical) I f / I r = 0.418
(Ein- E o ) 5.6 5
1.1
20
(exaerimental I f / I i = 0.45
~ 4 1
50
(theoretical) I f l I r = 0.506 50 (experimental I f I I i = 0.55 100 (theoretical) I f / I r = 0.599
+,i 2.518 [22.3
1.3
2.4
[-131
~ 3 1
i,-
3.008 [-12.71
5
2.9 [- 131
5.5
1.163 [- 13.21
2.057 [ 22.9
5.6
2.295 [- 12.41
1.1
5
1.2 [-131
2.0 ~231
5
2.2 [-131
5.6
1.119 [- 12.81
1.729 [23.2]
5.6
1.864 [- 12.21
1.035 [23.5]
1.2 ~ 3
1.1
100
(Ein- E o ) 5.6
-,i 1.257 [-13.51
1.039 [23.3 ~ 4 1
(experimental) I f / I r = 0.62
Reverse scan
~ 4 1
1.9
1.8 ~ 3 1
1
[- 131
a All potentials in mV, currents in PA. Figures in brackets are peak potentials relative to E o (Le., E , - EO). Other parameters as in Table 11.
Table V. Influence of D R o n the Predicted Second Harmonic ac Cyclic Response for 1.0 x M Cd(II)/1.0 M NaCla Forward scan
DR,X 10
Reverse scan
3
cm2 s-
(Ein-
ip+
0.68 1.059 [ 18.01 1.0 1.053 [20.2] 1.2 1.046 [21.4] 2.0 1.031 [24.8]
,
EO)
Ip-
0.7
1.162 [-18.01 1.164 [-15.81 1.161 [-14.91 1.166 [-11.81
2.8
3.6 7.1
ip+
1.848 0.7 [17.8] 1.931 2.8 [19.9] 1.976 3.7 [21.1] 2.125 7 . 2 [24.2]
Notation as in Table 111. DO = 0.68 Other parameters as in Table 11. I
, -0.4
-0.5
.0.6 -0.7 .0.8
(EinEo)
X
ip2.000 [-17.81 2.105 [-15.51 2.178 [-14.21 2.372 [-11.11
lo-’ cm* s-’.
-0.9
VOLT
Figure 7. Predicted second harmonic ac cyclic voltammograms for Cd(II)/l.OM NaCl system as detalled In Figure 4: influence of changin k, (W = 2 7 X 49 s-l). (a) k, = 12.0 cm s-l; (b) k , = 0.12 cm s- ?l , (c) k, = 0.012 cm s-‘
Data in Table V show that the value of D Rmainly influences the reverse scan, similar to the analogous fundamental harmonic predictions, Figure 7 shows voltammograms computed for order of magnitude changes of k , around the accepted value. As would be anticipated for a reversible system, increasing k , has negligible effect, but decreasing k, significantly lowers the current magnitude and increases the peak-to-peak separation, as ac quasi-reversible behavior is reached. Quasi-reversible ac b u t N e r n s t i a n d c Case. Fundamental Harmonic Case. The ac cyclic voltammetric response of 1.0 X M Cd(II)/l.O M Na2S04was studied to provide an example of a system reversible in the dc sense, but with a quasi-reversible ac response. The kinetic parameters for this system (unacidified Na2S04)have been reported as a: = 0.30 and k , = 0.20 cm s-l (21). Other values of 01 = 0.30, k, = 0.15 cm s-l (18);a: = 0.35, h, = 0.20 cm s-l (19); a: = 0.35, k, = 0.19 cm s-l (20); a: = 0.47, k, = 0.27 cm s-’ (23) and a: = 0.22, k, = 0.063 cm s-l (16) are also presented in the literature.
-04
-05
-06
-01
-OB
-09
E (VOLT)
Figure 8. Comparison of theoretical and experimental fundamental M Cd(II)/l.OM harmonic ac cyclic voltammograms for 1 0 X Na,SO,. Experimental parameters: E , = -0.35 V, E , = -0.90 V , Eo = -0.605 V, v = 50 mV s-’, w = 2~ X 400 s-‘, A € = 5 mV, T = 298 K, A = 0.0086 cm2. (-) = theoretical predictions, = experimental. f l and r l are respectively forward (cathodic)and reverse (anodic)scans calculated using k, = 0.20 cm s-’, a: = 0.3, Do = 0.60 X cm2s-’, DR = 1.6 X 10” cm2s-’. f2 and r2 are corresponding results calculated using data from Reference 16 (..e)
ANALYTICAL CHEMISTRY, VOL. 50, NO. 2, FEBRUARY 1978
I
,
221
' ' 1 I
156uA
-04
-05
-06
-07
-08
-09
-04
-05
-06
-07
-08
-09
E (VOLT)
Figure 9. Comparison of theoretical and experimental second harmonic ac cyclic voltammograms for Cd/Na2S04system as detailed in Figure 8. (a) theoretical (from Reference 21); (b) experimental
I -075
-085
-095 -105 E (VOLT)
-115
-125
Figure 11. Comparison of theoretical and experimental fundamental M Zn((II)/l.O M harmonic ac cyclic voltammograms for 2.0 X KCI-10-3 M HCI. Do = 0.7 X cm2 s-', D, = 2.0 X loT5cm2 s-' using parameters from Reference 12 (see text). (--) = theoretical; = experimental. Experimental parameters: E, = -0.75 V, E , = -1.25 V , E o = -1.005 V , v = 50 mV s-', f = 400 Hz, A € = 5 mV, cm s-', CY = 0.3. f = T = 298 K , A = 0.0086 cm2. k , = 4 X forward (cathodic) scan, r = reverse (anodic) scan
'A
(..a)
-04
-05
-06
-07
-08
-09
E (VOLT)
Figure 10. Simulated second harmonic ac cyclic voltammogram as cy = 0.5
for Figure 9, but
As is evident from Figure 8, very good theory-experiment correlation is found using the kinetic data from References 19,20, and 21. The fundamental harmonic current response is practically independent of OL with this k , value, and so no worthwhile conclusions as to its precise magnitude can be drawn. Cot 9 measurements were insufficiently accurate to compute cy by the recommended procedure (26). There is negligible peak potential separation of the forward and reverse scans, but current magnitudes are significantly lower than for the reversible Cd(II)/NaCl case. At a frequency of 400 Hz, AE = 5 mV and u = 50 mV sd, the half-widths of both forward and reverse waves were measured experimentally as 48 f 1 mV, which agrees with a value of 48 mV computed using data from References 19, 20, or 21. The calculated phase angle a t the peak potential of both forward and reverse scans was 3 3 O ; experimentally it was found to be 35 f 2 O . Again, the only noteworthy discrepancy was a small deviation on the reverse scan. Similar discussions as those applied to the reversible case are still pertinent regarding this small disparity. Computations based on data from References 16 and 27 ( k , = 0.063 cm 8)gave unsatisfactory results in regard to current magnitude (see Figure 8) and phase angle (22O). Studies in Reference 27 were performed in acidified (pH 4) Na2S04 media. I t thus seems that, for this Cd(II)/Cd(Hg) system, the apparent k, value is pH dependent, a fact which may have significant implications (23). Second Harmonic. Figure 9 shows experimental and theoretical second harmonic ac cyclic voltammograms for the Cd/NazS04electrode process. The consequences of spherical diffusion and amalgam formation are evidenced by the enhanced reverse sweep current, and in the enlargement of the lobe a t more negative potentials. Comparison of Figures 9a and b indicates good theory-experiment agreement, except
i
I -07s
,
,
,
,
-om -08-10s -11s E (MLn
, -12s
.. . -
.
,
-on -085
-085
-105
,
-11s
,
-12s
E W T )
Figure 12. Calculated fundamental harmonic ac cyclic response for Zn(I1) system as detailed in Figure 11 showing effect of cy. (a) cy = 0.1; (b) cy = 0.5
for the minimum current (especially on the reverse scan) which does not reach zero in the theoretical curve, but nearly does so in the ac cyclic experimental data. Figure 10 depicts a theoretical second harmonic ac cyclic voltammogram for (Y = 0.5 (same k , ) . I t shows better agreement with experiment regarding both the current minimum and the peak current magnitudes. One concludes from the ac cyclic data that (Y = 0.5 for this system. AC polarographic data in both fundamental (16,19,20,23)and second harmonic (18-21) modes clearly disagree on this point (cy E 0.3). T h a t this experimental disparity is real has recently been shown by running successive fundamental harmonic ac polarographic and ac cyclic experiments on the same solution (same day). The digital FFT approach (23) was employed, which provides sufficiently accurate data to permit evaluation of cy from the cot 6 observable. A 0.35 f 0.03 value was indicated for cy by the ac polarographic mode and ac cyclic voltammetry suggested 01 = 0.47 f 0.05, both in complete agreement with the corresponding analog measurements. A plausible qualitative explanation for the disparity has been advanced (23), but it remains to be confirmed by experimental investigations. For present purposes, it is sufficient to recognize that excellent theory-experiment agreement is obtained for the ac cyclic experiment using a k , value which is consistent with literature
222
ANALYTICAL CHEMISTRY, VOL. 50, NO. 2, FEBRUARY 1978
E l = 255mV
l8mV
E-EO
Figure 13. Fundamental harmonic ac cyclic response for Zn(1I) system as detailed in Figure 11 showing effect of switching potential, E,. E , constant at 4-255 mV (relative to Eo). (-) = theoretical; .) = experimental (a
reports and a n a value which agrees better with the fundamental theory of heterogeneous electron transfer (28) than 3 previously advanced. the ~ 0 . value Quasi-reversible in Both d c a n d a c Senses. Fundamental Harmonic. As an example of a dc quasi-reversible amalgam system, the electrode reaction of 2.0 x M Zn(I1) in 1.0 M KCl/10-3 M HC1 was chosen. Literature values of its kinetic parameters have been reported as h , = 3.8 x cm sd, a = 0.30 ( I n ,k , = 4.0 x cm s-l, a = 0.30 (12);and k , = 3.3 X cm s-l, a = 0.27 (22). A comparison of theoretical and experimental curves is shown in Figure 11. The best agreement was obtained using the results quoted in Reference 12. T h e effect of a upon the quasi-reversible system is quite marked, as is evident from Figure 12. Computations using a = 0.1 and a = 0.5 result in significantly different curve shapes, and only a values close to 0.3 give results in agreement = 5 mV and with experiment. At a frequency of 400 Hz, u = 50 mV s-', the peak separation between forward and reverse scans was experimentally 10 mV, a figure which was cm S C ~ . obtained with a = 0.28 and k , = 4.0 X As in the previous systems, the current magnitude of the reverse peak was slightly lower than calculated. For the dc quasi-reversible case, the simulated voltammograms are very sensitive to small changes in the system parameters and this, together with uncompensated resistance effects, could explain the discrepancy. Theoretical calculations predicted that the fundamental harmonic response would be practically independent of frequency in the range 49 to 400 Hz, and this was confirmed experimentally. The phase angle of both forward and reverse peaks was observed to be close to Oo. in good agreement with the computed value of 2' for the forward peak and 4 O for the reverse peak. A selection of voltammograms with different switching potentials is shown in Figure 13. Differences to analogous observations with the reversible case are apparent, especially as the forward and reverse scans do not overlap when the potential scan is switched at potentials more positive than the forward peak, reflecting the dc quasi-reversibility of this process. As can be seen from the figure, theoretical calculations gave similar results. Second Harmonic. Figure 14 shows a comparison of theoretical and experimental second harmonic ac cyclic voltammograms for the zinc system. Good agreement between theory and experiment is observed.
J -0.75 -0.85 -0.95 -1.05
E
-1.15
-1.25
(VOLT)
Figure 14. Comparison of theoretical and experimental second harmonic ac cyclic voltammograms for Zn(I1) system described in Figure 11. (-) = theoretical, f = forward scan, r = reverse scan; (...) = experimental, forward (cathodic)scan; (---) = experimental, reverse scan
'1
I
-075
#
-085
,
-085
.
-1 05
-115
. -125 ,
E (VOLT)
Figure 15. Simulated second harmonic ac cyclic voltammograms for Zn(I1) system as detailed in Figure 11: influence of a. (a) a = 0.5; (b) a = 0.1
In Figure 15, simulated second harmonic ac cyclic voltammograms showing the influence of a a t this low k,, are plotted. A marked a-dependence is evident. As for the fundamental harmonic, observed voltammograms are only
ANALYTICAL CHEMISTRY, VOL. 50, NO. 2, FEBRUARY 1978
consistent with a n a value close to 0.3.
CONCLUSION The combined digital simulation-analytical solution approach to the ac cyclic rate law with amalgam-forming redox systems has proved successful. Kinetic parameters calculated from this theory using fundamental and second harmonic observables agree well with accepted results in most instances. In this case the reverse (anodic) sweep ac response is not so useful as for the non-amalgam case because of its marked sensitivity to many parameters (e.g., scan rate, switching potential, diffusion coefficients), even for the pure reversible (Nernstian) response. For dc quasi-reversible conditions, no parallel with the a-dependent crossover potential (1) is found. However, predictions for the reverse scan are very close to the experimental results presented here, indicating the satisfactory nature of the theoretical model used. To obtain previously unevaluated heterogeneous charge transfer kinetic parameters, k , and a , from experimental ac cyclic data on amalgam-forming systems, the recommended approach is use of the phase angle cotangent in the standard manner (26). This observable remains independent of the troublesome operating parameters like scan rate, switching potential, electrode radius, and scan direction ( I ) , which are invariably of significance with amalgam-forming systems, as shown above. Although phase angle data provided by the instrument used in this work were of insufficient accuracy and precision for this purpose, the desired data quality has been achieved with computerized FFT instrumentation ( 2 3 ) . Should it be necessary to employ current amplitude data, the use of the frequency spectra of the ac cyclic peaks is recommended to obtain reasonable estimates of k , and a. These observable's shape characteristics, and their dc potential dependence, also are negligibly influenced by the "troublesome parameters" mentioned above. Of course, if scan rate, switching potential, and electrode radius are held fixed, and diffusion coefficients are known (usually the case), theoretical working curves of any potentially useful ac cyclic observable
223
(e.g., peak width, peak location, forward and reverse scan peak separation, etc.) can be generated for the specified operating conditions. In short, the message is that insurmountable data analysis problems do not exist with ac cyclic data on amalgam-forming systems following Reaction 1,despite the more complicated parametric dependences. In most cases, the usual cot @ data analysis strategy (26) will suffice, as has been demonstrated (23).
LITERATURE CITED A. M. Bond, R. J. O'Haiioran, I. Ruzic, and D. E. Smith, Anal. Chem., 48, 872 (1976). W. L. Underkofier and I. Shain, Anal. Chem., 37, 218 (1965). N. Veighe and A. Claeys, J . Elecfroanal. Chem., 35, 229 (1972). D. 1. Levitt, Anal. Chem., 45, 1291 (1973). E. D. Moorhead and P. H. Davis, Anal. Chem., 45, 2178 (1973). H. Blutstein and A . M. Bond, Anal. Chem., 46, 1934 (1974). F. H. Beyeriein and R. S. Nicholson, Anal. Chem., 44, 1647 (1972). T. Biegier and H. A . Laitinen, Anal. Chem., 37, 572 (1965). J. R. Delmastro and D. E. Smith, Anal. Chem.. 38, 169 (1966). J. R. Deimastro and D. E. Smith, Anal. Chem., 39, 1050 (1967). T. G. McCord and D. E. Smith, Anal. Chem., 41, 131 (1969). T. G. McCord and D. E. Smith, Anal. Chem., 42, 126 (1970). I. Ruzic and D. E. Smith, Anal. Chem., 47, 530 (1975). S.W. Feidberg in "Eiectroanalyticai Chemistry", Voi. 3, A . J. Bard, Ed., Marcel Dekker, New York, N.Y.. 1969, pp 199-296. I. Ruzic and S. W. Feidberg, J . Necfroanal. Chem., 83, 1 (1975). J. K . Frischmann and A. Tlmnick. Anal. Chem.. 39, 507 (1967). B. Timmer. M. SiwtersRehbach. and J. H. Siwters. . . J. Elschoa~l.Chem.. 14, 181 (1967). T. G. McCord and D. E. Smith, Anal. Chem., 41, 131 (1969). D. E. Giovergnd D. E. Smith, Anal. Chem., 44, 1140 (1972). D. E. Glover and D. E. Smith. Anal. Chem., 45, 1869 (1973). M. Hirota. Y. Umezawa. H. Koiima. and S. Fuiiwara. Bull. Chem. SOC. Jpn., 47, 2486 (1974). M. Hirota, Y. Umezawa, and S. Fujiwara, Bull. Chem. SOC.Jpn., 48, 1053 (1975). A . M. Bond, R. J. Schwall. and D. E. Smith, J . Electroanal. Chem., 85, 231 (1977). R . S. Nicholson and I. Shain, Anal. Chem., 36, 706 (1964). R. S . Nicholson, Anal. Chem., 37, 1351 (1965). D. E. Smith in "Ebctroanalytica Chemistry", Vol. 1, A. J. Bard, Ed., Marcel Dekker, New York, N.Y., 1966, pp 1-155. D. J. Kooijman and J. H. Sluyters, Electrochim. Acfa, 12, 693 (1967). R. A . Marcus, J . Chem. Phys., 43, 679 (1965).
RECEIVED for review August 15, 1977. Accepted October 28, 1977.
Electrochemistry of the Ruthenium(3+,2+) Couple Attached to Graphite Electrodes Carl A. Koval and Fred C. Anson" Arthur A. Noyes Laboratory, California Institute of Technology, Pasadena, California 9 1 125
Procedures are presented for attaching pyridine-pentaamlneruthenium( 11) complexes to graphite electrodes by covalent bonding and irreversible adsorption. Cyclic voltammetry and differential pulse voltammetry are used to compare the electrochemical behavior of the attached complexes and to measure surface concentrations. Different orientations of the anisotropic graphite affect the quantity of reactant that can be attached as well as the voltammetric responses. Attachment by irreversible adsorption yields larger quantities of complex on the electrode surface but the covalently attached complex persists on the surface for a longer time.
A number of schemes for the attachment of a variety of molecules to electrode surfaces have been proposed and tested recently (1-12). In only a few instances have the attached 0003-2700/78/0350-0223$01 .OO/O
molecules exhibited the long-lived, reversible electrochemical behavior that would be essential for effective catalysis of charge transfer reactions involving less reactive substrates to be realized. In preliminary experiments ( 4 ) directed a t such an objective, we reported some examples of reactants containing multiple aromatic rings (e.g., 9,lO-phenanthrenequinone, iron protoporphyrin IX, and iron tetraphenylporphyrin) which attach themselves to graphite electrodes by spontaneous, irreversible adsorption. In media free of attached reactant, these surface species remain adsorbed for hours and can be cycled repeatedly between oxidation states electrochemically. The tendency of sufficiently large, aromatic molecules to adsorb on graphite has also been exploited to attach a simple transition metal complex, Ru(NHJ5L2+(L is the large, aromatic ligand), to a graphite electrode and to examine its electrochemical behavior in the attached state (12). In the present paper, methods similar to those described by Miller and co-workers (2) were used to attach the same C 1978 American Chemical Society
