to 160 x 1O-SM total sulfide. The HMRDE current plot is linear with sulfide concentration over the whole range, whereas curvature is seen in the i-C plot a t the lower concentrations. It is to be noted that the sign of disk current crosses zero only with a significant amount of sulfide present, due largely to other undetermined processes not controlled by convective diffusion. The sign of A i is always positive, as expected for a convective diffusion controlled anodic process. The i-E and Ai-E curves a t 1.6 x 10-‘jM total sulfide are shown in Figure 11. Even a t this level, the i-E residual curve (not shown) has a significant slope, and crosses zero current on the rising part of the well-formed sulfide wave. The corresponding residual current in the HMRDE curve, as inferred from these data, is essentially flat before and after the wave and indicative of the rejection that leads to the better low level linearity in Figure 10.
ocli
1
01
C I
5Gnoi
1
R
/ I
lonoal
I -03
-0 5
I
I
-07
-09
I
E, VOLTS VS SCE
SUMMARY A N D CONCLUSIONS When there is minimal interference from surface and supporting electrolyte redox processes, direct voltammetry a t rotating disk electrodes is generally capable of equaling or bettering the sensitivity of refined polarographic methods. If interfering currents are mass transport independent, then hydrodynamic modulation techniques may be employed to achieve a sensitivity equal to that obtainable with direct disk voltammetry under ideal conditions. We conclude that the RDE and HMRDE approach to electroanalysis is eminently competitive with any of the modern variations of polarography. Its advantages include a firm theoretical foundation, a high inherent sensitivity, the ability to reject faradaic currents not controlled by convective diffusion through hydrodynamic modulation,
Figure 11. RDE and H M R D E curves
of
sulfide at a silver disk
Total sulfide concentration is 1.6pM in O.OlM NaOH. Anodic scan rate, 5 mV sec. = 60 rprnl”, h 1 / 2 = 6 rprn1’2, f = 3 H z , averaging time constant is 3 sec. Zero current levels indicated on right hand axis and current sensitivity as indicated by the markers. Potential scale common to both traces
and the provision of access to the entire electrode material spectrum including mercury.
RECEIVED for review January 25, 1974. Accepted March 9, 1974. Presented a t the I. M. Kolthoff 80th Anniversary Symposium, Division of Analytical Chemistry, 167th National Meeting, ACS, Los Angeles, Calif., April 1974.
I NOTES Rotating Disk Electrode Voltammetry Using Small Sample Volumes Barry Miller and Stanley Bruckenstein’ B e / / L a b o r a t o r i e s , M u r r a y H i / / . N.J. 07974
Since the early work of Riddiford ( I , 2 ) which demonstrated that deviation from the Levich equation occurred for certain electrode shapes a t low rotation speeds, users of the rotating disk electrode (RDE) have been concerned about disk electrode mantle geometries. The usual practical electrode is a compromise between theoretical requirements and convenience of fabrication. In addition, it was originally anticipated, based on theoretical considerations, that it would also be necessary to use electrolysis cells whose dimensions are large compared to those of the disk electrode. The study of Prater and Adams ( 3 ) ,however, Permanent address. D e p a r t m e n t of Chemistry, State C n i v e r sity o f Kew York, B u f f a l o , N.Y. 14214. (1) K F Blurton and A. C . Riddiford. J. Electroanai. C h e m . . 1 0 , 4 5 7 (1965). (2) A. C . Riddiford. Advan. Electrochem. Eiectrochem. Eng., 4, 47 (1966) ( 3 ) K B Prater and R. N. Adarns. Anal. Chem., 38, 153 (1966).
failed to show the existence of any significant effect on current in going from a 100-ml beaker to a 9-liter vessel while Gregory and Riddiford ( 4 ) found that a 5-cm disk operated satisfactorily in vessels only 11 cm or larger in diameter. Furthermore, we have observed, as other workers have (3, 4 ) , that the position of a rotating disk electrode in a cell has little or no effect on the observed current. For example, it makes little difference in the disk current whether the end of the electrode is just below the solution surface, just above the cell bottom, well centered in the cell, or next to one of the cell walls. Many studies using disk electrodes having cylindrical mantles have shown that the Levich equation, I
= 0.62
nFAo112DL3 ~ - ’ / 6 (Cb -
cy\
(1)
(conventional symbology) is followed over a wide range of (4) D
P Gregory and A C Riddiford. J Chem SOC 3756 (1956)
ANALYTICAL CHEMISTRY, VOL. 46, NO.
13, NOVEMBER 1974
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Table I. Disk Electrode Dimensions Electrode
Au 1 Au 2 Pt 1
Disk material
Disk radius, cm
PLASTIC CAP
Disk area, cm2
Mantle radius, c m
Gold
0.147:
Gold
0.092
0.0683 0.0260
0.184
Platinum
0.112
0,0392
0,274
SYRINGE I N L E T PORT FOR SAMPLES
0.135
(bl
I! I
\ti1 I
speeds, provided extremely low rotation speeds are avoided. Thus, we thought it should be possible to reduce dramatically the scale of a rotating disk experiment and that it would be worthwhile to obtain some indication of the minimum cell volumes and electrode dimensions to which the Levich equation would apply. Such data, combined with the submicromolar concentration sensitivities recently established for the RDE and the hydrodynamically modulated RDE (HMRDE) in conventional cells ( 5 ) , would lead to reliable estimates of the minimum absolute quantities of electroactive species determinable by these met hods.
,,EPOXY
COAT
GOLD COUNTER ELECTRODE
0CRACKED 5 - 1 0 ml BEAD W D
I
S
K
tl
Lv-4.2
I
EXPERIMENTAL T h e methodology used in this work, except for the substitution of smaller electrodes a n d low volume cells, was t h e same as described recently ( 5 ) .All disk electrodes had cylindrical insulating mantles. They were fabricated by brazing the desired disk electrode material t o the end of a 0.250-inch diameter stainless steel rod and machining t h e electrode end of the rod to t h e desired diameter. The length of the machined portion corresponded to the anticipated maximum depth of submersion in the solution to be studied. The machined portion was insulated with epoxy resin, which was turned t o the desired mantle diameter after curing. The physical dimensions of the three disk electrodes used in this study are given in Table I. T h e ratio of the mantle radius to disk radius was between 2 and 2.5. Three cells were employed, the largest of which had a capacity of 150-200 ml and is described elsewhere (6). The two others used had capacities of 5 ml a n d 0.5-1.0 ml and are shown schematically in Figures l a and l b , respectively. The 5-ml cell is of conventional three-compartment design and utilizes fritted glass disks as separators. I t was originally intended for use with the dropping mercury electrode. T h e smallest volume cell, in which the 0.5- and 1.0-ml studies were performed, was fabricated from the body of a Leeds and Northrup reference electrode with a cracked glass bead junction in its bottom. The rotating disk electrode a n d auxiliary wire counter electrode were both placed in the body of the cell, which contains 0.5 to 1.0 ml of sample, and the glass bead end of the cell was submerged in a beaker of supporting electrolyte into which the reference electrode dipped. Three test solutions were used: 5.5 x 10-7M Hg(I1) in 0.01M HC104, 2.17rnM Fe(II1) in 1.OM HzS04, and 1.57mM K4Fe(CN)6 in 1M KC1. They were all prepared from reagent chemicals and triply distilled water. T h e Fe(II1) solution was prepared from a standardized stock solution; the other solutions were prepared from solids of known purity. The temperature varied according to the ambient, 24 f 1.5 "C.
RESULTS AND DISCUSSION The 2.17mM Fe(II1)-1M H2S04 solution has previously been examined a t larger disk electrodes using a 200-ml capacity cell (7). Proportionality between limiting current: i. and square root of angular velocity, &2, was found, i . e . , Levich's equation was followed. The solution was studied in the two low volume cells shown in Figures la and l b , using the 0.0392 cm2 Pt disk electrode and the 0.0683 cm2 Au electrode. Levich plots of the data obtained in these experiments are given in Figure 2 and are linear in the (5) B. Miller and S. Bruckenstein, Anal. Chem., 46, 2026 (1974).
(6) R H. Sonner. B. Miller, and R. E. Visco, Ana/ Chem., 41, 1498 (1969). (7) 8 . Miller, M . I . Bellavance, and S. Bruckenstein. J . Electrochem. SOC.,118, 1082 (1971).
2034
S
t
N
,
Figure 1. Schematics of ( a ) 5-ml and ( b ) 0.5-1-ml cells
153
1
3
23
80
6C
4C
&I/?,
rpm
00
112
Figure 2. Limiting reduction current vs. square root of rotation speed for 0.0683 crn* gold disk and 0.0392 cm2 platinum disk in 5 ml and 1 ml, respectively,of 2.17 m M Fe(lll) in 1M H2S04
rotation speed range from 100 to 8100 rpm. From the slopes of the lines in Figure 2, the values obtained for the diffusion coefficient of Fe(III), D F e , I ~ ~ are i , 4.6 x 10-6cmz/sec (gold electrode) and 4.2 x 10-6cm2/sec (platinum electrode). The previously reported value of DFe,III found using the 200-ml capacity cell and a 0.178 cm2 area disk electrode was 4.5 x 10-6cm2/sec (7). The ratio of the areas of the electrodes used to obtain the data presented in Figure 2 is 1.74, compared to the ratio of the slopes of 1.84. This discrepancy of nearly 5% leads to an 8% difference between the calculated values of I I I , , which, considering the various experimental errors, is satisfactory. The uncertainty in the dimensions of the small electrodes is about 2%, while the possible variation in temperature, &1.5 " C , leads to an uncertainty of approximately 2% in the limiting currents. It is difficult to estimate the uncertainty introduced by eccentricity produced during the machining of the small disk electrodes.
ANALYTICAL CHEMISTRY, VOL. 46, NO. 13, NOVEMBER 1974
A more exhaustive study of the solution-volume and cell-dimension effect is shown in Figure 3. The 0.0264 cm2 Au disk electrode was used to study the 1.57rnM K4Fe(CN)6-1M KCl solution in all three cells. Volumes of 0.5 ml and 1.0 ml were used in the smallest cell, 5.0 ml in the intermediate sized cell, and 150 ml in the largest cell. All the experimental data, up to 3600 rpm, fall in the ranges indicated and are internally consistent within the experimental reproducibility. The pairs of points shown in the speed range 4900-8100 rpm demonstrate that linearity exists between i and u1 in the two larger cells, but that there is a slight negative deviation from Levich behavior in the smallest cell above 4900 rpm. This negative deviation appears to be a t least partly due to surface deactivation effects, since an experiment performed with a freshly polished 0.0683 cm2 gold surface, also shown in Figure 3, obeys the Levich equation over the entire velocity range. Surface pretreatment, i . e . , potentiostating briefly a t an oxidizing potential. was required for both the gold and platnium electrodes in order to obtain reproducible limiting current valur?s. Such pretreatments are normally required when using solid electrodes. On cycling the potential of an electrode, the successive i-E curves become more irreversible in appearance, ultimately yielding a sigmoid curve so dragged out over the potential range that the limiting current plateau was completely masked by the current due to supporting electrolyte decomposition. Such surface deactivation occurred fastest in cells with high electrode surface to solution volume ratios, i . e . . it took place more rapidly in the 0.5-ml experiment than in the 150-ml one. The electrode insulation anti cell walls are sources of possible impurities whose effects are heightened in the small cells. [Jsing the data in Figure 3, the value of U F , , C N , ~is- ~ calculated from the original Levich equation to be 5.69 and 6.09 x cm2/sec for the 0.0683 cm2 and 0.0264 cm2 electrodes, respectively. The corresponding values are cm2/sec when Newman's correction 5.9:3 and 6.33 x ( 8 ) for finite Schmidt numbers is made. The generally accepted value of DF?( . ~ , 6 a-t ~25 "C is 6.32 f 0.03 X cm2/sec from von Stackelberg et al. (9). The internal consistency between values of DF,ic.N,6-4 calculated from data obtained in the three cells for electrodes of' different area and mantle size and the agreement of these values of with the generally accepted literature value are convincing evidence that no serious departure from theory occurs in using low volume cells with appropriately dimensioned rotating disk electrodes. Sinusoidal angular velocity modulation ( 5 , IO) in the 1-ml and 200-ml capacity cells gave essentially the same modulated current responses for the F ~ ( C N ) Gsystem. -~ In our experience, if there is no deviation from Levich behavior observable in a conventional i - u1 plot obtained in constant angular velocity experiments, programmed angular velocity experiments are equally successful. For example, Ai - E traces obtained for a 5 x' M Hg(I1)(81 J Newman,d. Phys. Chem.. 70, 1327 (1966). (9) M. yon Stackelberg M. Pilgram, and V. Toorne, Z. Eiektrochem.. 5 7 , 342 (1953). (10) B Millei. M . I Bellavance, and S. Bruckenstein, Ana/. Chem.. 44, 1983 (1972).
~~
" 0
20
40 w"2,
60
80
100"
rpm ''2
Figure 3. Limiting oxidation currents vs. square root of speed for 0.0264 ern' gold disk in 0.5, 1.0, 5, and 150 tion volumes and for 0.0683 cm2 gold disk in 0.5 ml volume. Separate ordinates for each electrode: solution K 4 F e ( C N ) 6in 1M KCI
rotation
ml solusolution
1.57mM
0.01M HC104 solution using the hydrodynamically modulated rotating disk electrode technique ( 5 ) were as good in the 5-ml cell as in the 200-ml cell. In the 5-ml cell, the modulated current response was 0.30 x lo8 nA r p m - l M - l cm-2 as compared to the previously published response of 0.27 nA rpm-l M - l cm-2 found in the 200-ml cell using a larger disk electrode. The results reported above clearly demonstrate that rotating disk electrode techniques are easily applied to small solution volumes and that the data are in good agreement with theory. Therefore, the previous estimate of the practical sensitivity of rotating disk electrode techniques ( 5 ) can be used to estimate the absolute amount of electroactive material that can be quantitatively determined using the 1-ml cell. In these recent studies, it was shown that it is possible to analyze solutions at concentrations of -1 X N to *5% using the 200-ml cell. Hence, it should be possible to determine -1 x 10-lO equivalent with the same accuracy in the 1-ml cell. The previous work established direct and hydrodynamically modulated rotating disk voltammetry as being competitive in concentration sensitivity with modern polarographic techniques ( 5 ) .This work demonstrates that considerations involving voiume and electrode dimension requirements are far less stringent than had been anticipated and that the solution volume requirements are not that different from those of polarography. Thus, rotating electrode techniques must be considered as being competitive with modern DME techniques in both trace and micro analysis.
RECEIVEDfor review January 25, 1974. Accepted March 9, 1974.
ANALYTICAL CHEMISTRY, VOL. 46, NO. 13, NOVEMBER 1974
2035
