ANALYTICAL CHEMISTRY, VOL. 51, NO. 13, NOVEMBER 1979
2287
Effects of Switching Potential and Finite Drop Size on Cyclic Voltammograms at Spherical Electrodes Sir: The past two decades have seen cyclic voltammetry develop from a technique employed only by the specialist to one used by many non-electrochemists in the characterization of a wide variety of chemical systems. Great impetus was given to this development by the application of digital simulation ( I ) (explicit finite difference methods) to the differential equations describing diffusion, and subsequently these methods have found wide use, particularly in studies of electrochemical systems coupled with homogeneous reactions. Even before the development of cyclic voltammetry, the importance of accurately describing current-potential curves a t spherical electrodes in linear scan experiments was recognized and appropriate solutions were obtained by Frankenthal and Shain (2) and by Reinmuth ( 3 ) . Other workers have treated the spherical diffusion problem including its extension to the consideration of amalgam formation (“inner” as well as “outer” diffusion) ( 4 ) . The related problem of finite electrode volume has been addressed by workers studying anodic stripping ( 5 , 6 ) . Guminski and Galus (7) have published an empirical equation which relates the ratio of anodic to cathodic peak current in cyclic voltammetry to diffusion coefficient (d), switching potential ( E A )scan , rate ( v ) , and electrode radius (ro):
O * t
E-E”
0003-2700/79/0351-2287$01 .OO/O
\.olfi
values of 4) : (A) 0.00726,
Table I. Cathodic and Anodic Peak Potentials and Peak Current Ratio as Functions of Switching Potential and @ @
The purpose of this study was to adapt the digital simulation technique to the calculation of cyclic voltammograms at spherical electrodes with amalgam formation and to generate sufficient data to allow one to establish the extent to which the useful diagnostic criteria (peak position, peak separation and peak current ratio) are affected by spherical diffusion and/or finite electrode volume. Calculations were made for a simple reversible system and all diffusion coefficients were assumed to be equal. The usual calculation of linear sweep voltammograms at planar electrodes by either the solution of integral equations or by simulation results in a single current function r1J2x(at) which is independent of scan rate. For spherical electrodes the interaction of scan rate, diffusion coefficient, and electrode radium is most conveniently expressed in terms of the dimensionless parameter 4 = D‘/z/a1/2rowhere a = n F v / R T . As v and ro are increased for a given chemical system, the conditions of linear diffusion are approached. In developing the simulation, the volume element equations suggested by Feldberg ( I ) were employed. Fixed model values of n = 1, D = 0.45, v = 0.25 mV/time increment, and At = 1 were employed. The value of C$ was varied by varying the model radius. The model can be related to a real system through C$ and the switching potential. For a typical experiment (ro = 0.05 cm, D = 6 X lo4 cm2/s, v = 0.1 Vis), the number of volume increments in the drop will be about 300. The effect of finite electrode volume falls naturally out of the use of this model. Single scan currents calculated by the simulation show excellent agreement with those calculated using the empirical correction parameters of Beyerlein and Nicholson ( 4 ) . Anodic peak currents were measured from extensions of the cathodic scans. Current functions generated by varying 4 over a wide range a t constant switching potential are shown in Figure 1. The transition from the usual cyclic voltammogram to that more resembling a stripping experiment is evident.
,
Figure 1. Current functions for different (B) 0.0229, (C) 0.0725, (D) 0.227
0.227 0.0725 0.0229 0.00726 0.00229
a,b
-7 5
-164
E h - E ” , mV -253
-342
-570 1 6b 1.84c -37 28 1.27 -31 32 1.09 -29 33 1.03 -29 33 1.01
-57 10 2.70 -37 24 1.47 -31 28 1.14 -29 30 1.04 -29 30 1.01
-57 6 4.35 -37 22 1.84 -31 27 1.22 -29 28 1.07 -29 29 1.02
-57 7 3.54 -37 23 1.66 -31 28
1.18 -29 29 1.06 -29 29 1.02
Cathodic and anodic peak potentials, E -- EO, mV.
ialic.
-0.075
-0 164
E*-E“
-0.253
-0342
, Volts
Figure 2. Peak current ratio as a function of 4 (logarithmicscale) and switching potential
Unlike the planar system where the ratio of anodic to cathodic peak current is independent of switching potential (assuming the potential scan is reversed no closer than 3 5 / n mV to the cathodic peak (8)),the switching Dotential affects voltammograms in the system under consideration. Results 0 1979 American Chemical Society
2288
ANALYTICAL CHEMISTRY, VOL. 51, NO. 13, NOVEMBER 1979
Table 11. Comparison of Peak Current Ratios from Digital Simulation and from the Eauation of Giminski and Galus E A - E ” , mV i a / i c , sim. i&, calcd @J
0.027 0,119 0.0725 0.0229 0.007 26
-342 -298 -253 -164 -7 5
4.35 2.43 1.66 1.14 1.03
3.42 2.20 1.67 1.17 1.03
of changes in both 4 and switching potential on peak potentials and peak current ratios are given in Table I. Though peak potentials are seen to vary, the separation is little affected. The peak current ratio, the most common diagnostic criterion, undergoes large changes as expected. These results are most easily seen by the use of the pseudo-three-dimensional map shown in Figure 2. Use of this diagram allows one to easily estimate the peak current ratio for a given set of experimental conditions. Finally, measured peak current ratios taken from the simu-
lations were compared to those calculated by the equation of Guminski and Galus. This comparison, shown in Table 11, indicates that the equation is a good predictor under typical experimental conditions. LITERATURE C I T E D Feldberg, S. W. Electroanal. Chem. 1989, 3 , 199-296. Frankenthal, R. P.; Shain, E. J . Am. Chem. SOC., 1958, 78, 2969. Reinmuth, W. H. J . Am. Chem. SOC. 1957, 79, 6358. Beyerlein, F. H.; Nicholson, R. S. Anal. Chem. 1972, 44, 1647. Shain, I.; Lewinson, J. Anal. Chem. 1981, 33, 187. (6) DeVries, W. T.; Van Dalen, E. J . Nectroanal. Chem. 1987, 8 , 366. (7) Guminski, C.; Galus, Z. Rocz. Chem. 1989, 43, 2147; Chem. Abstr. 1970, 72, 106569. (8) Nicholson, R . S.; Shain, I. Anal. Chem. 1984, 36, 706.
(1) (2) (3) (4) (5)
J. Everett Spell Robert H. Philp, Jr.* Department of Chemistry University of South Carolina Columbia, South Carolina 29208 RECEIVED for review March 16,1979. Accepted July 26,1979.
Enhancement of Luminol Chemiluminescence with Halide Ions Sir: Chemiluminescence (CL) analysis of trace Cr(II1) has been reported previously (1). The technique is based upon the Cr(II1)-catalyzed oxidation of luminol by hydrogen peroxide in basic aqueous solution. The intensity of light emission is proportional to the “free” Cr(II1) concentration, if luminol and hydrogen peroxide are present in excess. The detection limit has been reported to be 5 x M (0.025 ppb) (1,2). We have been concerned with the speciation of chromium in marine and freshwater environments. Previous studies have used only C1 analysis for the determination of Cr(II1) in freshwater systems (1-3). While attempting to extend this technique to seawater analysis, we have determined that concentrated inorganic salt solutions can cause an enhancement of the C1 intensity. Table I indicates the ions which were tested for interferences. The concentration of 0.56 M is based upon the chloride concentration in natural seawater ( 4 ) . The anions C1-, F-, S042-have the same effect upon the light emission. The bromide ion is unique with its eightfold increase in luminescence intensity. Some ions, which are not listed in Table I (I-, SCN-, S2032-), reacted with the hydrogen peroxide. For iodide and thiocyanate, a chemiluminescent reaction occurred in the absence of Cr(II1). Upon further investigation of the bromide enhancement, it was discovered that the CL signal remained proportional to the Cr(II1) concentration. Furthermore, as indicated in Table 11,light emission is not a linear function of the bromide concentration. Below M Br-, no signal enhancement is observed. A bromide concentration of 0.5 M was chosen for future CL analysis and in all cases background solutions, of 0.56 M NaBr and M EDTA, were measured for a chemiluminescence signal. This is important because commercial KBr and KC1 have impurities of heavy metals. These anionic enhancements were not observed in earlier reports. One paper (1)used anionic concentrations of 1 x M, which are below the minimum concentration needed to observe the enhancement. Another group reported no effect on the CL signal when high concentrations of NaCl were added (5). Their work used chemiluminescence as a detection system for the chromatographic separation of metals. They chose a cell pH of 12.5 as optimum for their purpose, while the usual cell p H for Cr(II1) is approximately 10.5. The chloride ex0003-2700/79/035 1-2288$01 .OO/O
Table I. Effect of Anions on the Chemiluminescence of Cr(II1) % light % light emission emission anion (Cr only (Cr only anion (0.56 M ) = 100%) (0.56 M) = 100%) c1145 Br800 S0”Z‘ 146 PO,* 0 SO;z- (0.028 M)a a
100
NO-;
100
F140 Concentration found in seawater.
periments ( 5 ) we have repeated a t pH 12.5, and indeed no change in the CL peak intensity was observed. Preliminary results indicate these anionic enhancements are not unique to Cr(II1). Tests with Co(II), Fe(II), and Ni(I1) as catalysts yielded responses with 2-4 times the intensity observed with no C1- or Br- present. The chemiluminescence system of Mn04--luminol (no HzOz present) also gave increased signals in the presence of chloride or bromide ion. Bromide ion appears to be unique for the Cr(II1) system, but peak enhancement was the same for chloride and bromide addition in the metal catalysts used above. It should be stressed that experimental conditions were not optimized for the metals other than chromium, and the final CL enhancements may be greater than those indicated. The mechanism of this bromide effect is thought to be an ion-pairing phenomenon. The formation of a chromiumbromide-peroxide complex is postulated. The bromide, associated with the complex, facilitates the transfer of electrons in the reaction with luminol. A similar mechanism was proposed by Seitz for Co(I1) catalysis (6). Work is now in progress in our laboratory to elucidate the mechanism of bromide interaction. Analyses for this work were obtained using a flow system, which incorporates two 20-mL plastic syringes driven by a Sage Model 351 syringe pump. One syringe contains the chromium(1II) sample to be analyzed, while the second syringe has a solution of luminol and hydrogen peroxide at pH 11.2. The solutions are mixed immediately before entering a quartz flow cell contained in a Perkin-Elmer MPF-44A Fluorescence 0 1979 American Chemlcal Society *---
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