110
ANALYTICAL CHEMISTRY, VOL. 51,
NO. 1, JANUARY 1979 (41) A. W . C. Lin, N. R. Armstrong, and T. Kuwana. Anal. Chem., 49, 1228 ( 1977). (42) J. F. Evans and T. Kuwana, Anal. Chem., 49, 1633 (1977). (43) E. M. Smoiin and L. Rapapport, "s-Triazines and Derivatives", Interscience, New York, 1959. (44) Sadtier Standard Spectra, Spectrum No. 1403, Vol. 2 (1961); Spectrum No. 12499, Vol. 25 (1962); Spectrum No. 12554, Vol. 26 (1962); Sadtler Research Laboratories, PhiladeDhia. Pa. (45) J. H. Scofield, J . Electron Spedtrosc. Relat. Phenom., 8, 129 (1976).
(28) R. F. Lane and A. T. Hubbard, J . Phys. Chem., 77, 1401 (1973). (29) R. F. Lane and A. T. Hubbard, J . Phys. Chem.. 77, 1411 (1973). (30) A. P. Brown, C. Koval. and F. C. Anson, J . Electroanal. Chem., 72, 379 ( 1976). (31) H. L. Landrum, R. T. Salmon, and F. M. Hawkridge, J . Am. Chem. SOC., 99, 3154 (1977). (32) D. G. Davis and R. W. Murray, Anal. Chem., 47, 194 (1977). (33) J. C. Staraardt. F. M. Hawkridae. and H.L. Landrum. Anal. Chem.. 50. 930 (197g). (34) H. Tachikawa and L. R. Faulkner, private communication. (35) L. L. Miller and M. K. Van De Mark, J , Am. Chem. SOC.,100, 639 (1978). (36) A. Merz and A. J. Bard, J . A m . Chem. SOC., 100, 3222 (1978). (37) F. Kaufrnan, Abstracts, IUPAC meeting, Tokyo, Japan, September 1977. (38) M. Fujihira, N. Ohishi, and T. Osa, Nature (London), 268, 226 (1977). (39) A. A. Pilia, J . Electrochem. SOC.,118, 202 (1971). (40) J. W . Strojek and T. Kuwana, J . Elecfroanal. Chem.. 16, 471 (1968).
RECEIVED for review July 5 , 1978. Accepted October 18, 1978. w o r k supported by NSF Grant CHE76-81591 and US PHS Grant GM 19181. The XPS studies were supported in part by NSF Grant CHE76-04911.
Anodic Stripping Semidifferential Electroanalysis with Thin Mercury Film Electrode Formed in situ Masashi Goto, * Kazuhiko Ikenoya, and Daido Ishii Department of Applied Chemistry, Faculty of Engineering, Nagoya University, Chikusa-ku, Nagoya, Japan
observed curve is similar to that of a differential pulse polarogram. It has been demonstrated that the technique greatly improves the sensitivity and resolution in ordinary linear sweep voltammetry. The semidifferential electroanalysis is therefore likely to be an attractive alternative technique to conventional methods for detection in anodic stripping analysis. Application of this technique to stripping analysis with a hanging mercury drop electrode has been made in the preceding paper ( I O ) . In this paper, the theory of anodic stripping semidifferential electroanalysis with a thin mercury film electrode formed in situ on the rotating glassy carbon disk is presented and its experimental verification is tried.
The theory which describes the properties of the semiderivative of the current, e, vs. the electrode potential, E , curves in anodic stripping processes at thin mercury film electrode is presented in response to an imposed ramp signal. The semiderivative, e ( f ) , of the current, i ( f ) , is defined by
Anodic stripping voltammetry from the thin mercury film electrode formed in situ on the rotating glassy carbon disk electrode has been carried out employing semidifferential electroanalysis as a detecting method. Experimental results are shown to be in good agreement with theory. The method is nearly comparable in sensitivity and resolution with the difierential pulse stripping method, but is much faster to perform stripping. Reproducibility and sensitivity with a thin mercury film electrode formed in situ are much better than those with a hanging mercury drop electrode.
THEORY Consider a solution of reduced species, Rd, in a thin layer of mercury, while on oxidation the oxidized species, Ox, diffuses into a solution of infinite thickness. T h e electrode reaction is considered to be reversible without pre- or post-kinetics. According to de Vries and van Dalen (111, the following integral equation for the flux, J ( t ) ,applies under the conditions defined by the dimensionless parameter, H , less than 1.6 x 10 3. H i s equal to l'a/D'and u = nFu/RT, 1 is the mercury film thickness, D ' t h e diffusion coefficient of Rd, n the number of electron transfer, F the Faraday constant, u the potential scan rate, R the gas constant, and T the absolute temperature.
Anodic stripping voltammetry is eminently suited for the trace analysis of heavy metals. Different methods have been applied for detection in anodic stripping analysis. The most common technique used is linear sweep voltammetry. In this technique, very fast scan rates of potential could be easily employed to increase sensitivity, but the shape of the observed curves and the presence of large charging current render the determination of two or more depolarizers present very difficult. I n order to overcome the above problems, Perone and Birk ( 1 ) applied the derivative technique to it, and Osteryoung et al. (2) employed a staircase wave form as the applied signal. More sophisticated wave forms used are square wave ( 3 ) ,phase sensitive ac ( 4 ) ,second harmonic ac ( 5 ) and differential pulse (6). Recently the authors et al. have developed a new voltammetric technique, semidifferential electroanalysis (7-9). The technique measures the semiderivative of the current with respect to time as a function of electrode potential. When a ramp potential is applied to the electrode, the shape of the 0003-2700/79/0351-0110$01 0010
and x = at
(2 )
(3)
(4) where X is the dummy variable of integral, t the electrolysis time, C ' the bulk concentration of Rd, D the diffusion C
1978 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 5 1, NO. 1, JANUARY 1979
Table I. Dependence of d"Zz(x)/d3;1'2on Ymax -
J ~ J *Ymin 250 500 1000 2000 4000 8000 av. a
0.279 0.277 0.277 0.276 0.276 0.276 0.277
Condition:
6
"ma-Xmax
4.87 5.56 6.25 6.94 7.64 8.33
ln(,/HI+) -0.651 -0.655 -0.658 -0.661 -0.654 -0.657 -0,656
I
$/,/Ea
11 1
I
A
XminXma
2.52 2.52 2.52 2.52 2.52 2.52 2.52
2.13 2.12 2.12 2.12 2.12 2.12 2.12
= 0.01 0.08
coefficient of Ox, E, the initial potential, E, the standard potential, and f ' a n d f are the activity coefficients of Rd and Ox, respectively. Equation 1 can be rewritten by using the semiintegrating operator (12),d-'/*/ dx-I/*, being defined by
- 4 - 2
0
4
6
8
- In(L7iYY)
Figure 1. Theoretical shape of e vs. €curve in anodic stripping process at thin mercury film electrode
the d112z(xj/dx1/2 vs. x curves. It appears that d'/2z(x)/dx1/2 is the curve having a maximum and a minimum which is practically independent of the values of $/ t/i7, when plotted vs. x - In (yZ/$). Bearing in mind the definition of x, z ( x ) , and the relation,
as follows
J(t)= where d-'/dx-' represents the first-order integrating operator. Differentiation of Equation 6 with respect to x and rearrangement produce
where d1/*/dx1i2is the semidifferentiating operator (12) and d1/2f(x)/dx1/2 = d]d-'/2f(x)/dx-1;z)/dx. This equation expresses the shape of the curves observed in semidifferential electroanalysis a t the thin mercury film electrode. Equation 7 has been tried to solve numerically for dl/'z(x)/dx1I2by Huber's approximation method for several values of $&. Substituting x = J 6 and d112z(x)/dx1/2 = y ( x ) , one finds the following recurrent semidifferentiated currentpotential curve equation YI
2
x
=
-
i(t) n AF
_-
where i ( t j is the faradaic current and ,4the electrode area, it follows t h a t
From Table I and Equations 2 and 12, it follows t h a t as the electrode potential is linearly changed with time toward positive value, i.e., E = E , + u t , the height from the negative peak to positive one in the e vs. E curve is
the negative peak potential in the e vs. E curve is
E,, = E1;2 - 0.656RT nF ~
+ -___ nF
log H
(14)
where El' is the dc polarographic half-wave potential, and the width between the negative peak and the positive one is
w,,= 2.52RT nF -
where 1-1
s1= kc= l
(Yk - Y k - l ) { ~-
h
I-1
s, = k = l
(Yk
+ 1 1 3 2 ci - h)3/7 -
+ Yk-1)
(9)
(10)
Equations 13 and 14 are the relationships that constitute the base of quantitative and qualitative analysis in the proposed technique, respectively, and Equation 15 indicates the degree of resolution in the technique. Now consider the case that the Rd in thin mercury film is accumulated by pre-electrolyzing the trace of Ox in sample solution at the potential E, so cathodic that reduction reaction occurs. The limiting reduction current of Ox, disregarding the current arising from the reduction of Hg2+ ion when Florence's electrode (13)is used, for the rotating disk electrode ( 1 4 ) in the pre-electrolysis process is given by ,
T h e numerical calculations have been programmed in FORT R A N - ~for computation with a digital computer in accordance with the above equations. Copies of the program are available from the author on request. The results are given in Table I and Figure 1. In Table I, ymaxand ymlnrepresent the maximum and minimum values of d1'2z(x)/dx1/2,and x,, and x,,, represent the x values a t ymaxand y,,,,,, respectively, in
11
=
nF A CD 2 / ( 2 T N ) 1
1.62~"~
where C is the bulk concentration of Ox in solution, Y the kinematic viscosity, and N the number of revolutions of the electrode per second. By Faraday's law, the concentration of Rd in the mercury, being accumulated during the preelectrolysis, is
112
ANALYTICAL CHEMISTRY, VOL. 51, NO. 1, JANUARY 1979 2
(17) where t , is t h e pre-electrolysis time. Combining Equations 13, 16, and 17, t h e desired equation for the height from the negative peak t o the positive one in e vs. E curves for the re-dissolution processes in anodic stripping voltanmetry is 0.429n2."2."AUl.jt ), D2,':{ 1vl i ? C' ePP
=
_.
1
/6R1.5 TI.3
(18)
According to Equation 18, the height is independent o f t h e mercury film thickness. This fact is of particular importance when Florence's electrode is used, as the mercury film is not normally removed between measurements made on the same aliquot. It should be noted that the height is proportional to the concentration of Ox in the original solution, the square rc >tof the rotation speed of electrode and the pre-electrolysis time.
EXPERIMENTAL Instrumentation. A function generator ( S F Co., model FG-121B) was used as the applied potential sweeper. The booster amplifier for cyclic voltammetry (Yanagimoto Co., model PH-C\') was employed for both the potentiostat and the converter from current to voltage. The output of the booster amplifier was fed to the analog circuit for semidifferentiation through a voltage follower and a resister in order to minimize electrical noise as shown in Figure 1 in Ref. 10. An X-Y recorder (LVatanahe Co.. model WA-441) was used to record e vs. E and i vs. E curves. The rotating electrode assembly of the glassy carbon disk (Yanagimoto Co., model P8-RE) was used to form the thin mercury film electrode in situ as the working electrode. The surface of the glassy carbon disk was polished to a mirror finish with A120Jpowder (0.05 gm) on an acrylic resin plate before use. The reference electrode of Ag/AgCI (satd KC1) was made from a silver filter sheet coated with silver chloride immersed in a saturated KC1 solution and separated from the sample solution by an agar salt bridge. The counter electrode was a platinum spiral immersed in supporting electrolyte, being separated from the sample solution by an agar salt bridge. The electrolytic cell which has a capacity of 25 mL was made from a weighing glass vessel. Reagents. The stock solution of 10 mhl Hg(NO,,), wab prepared by dissolving 99.9999% mercury in nitric acid. T h e salts Cd(N03)2.4H20,Pb(N0312,and TlNO3were used the supporting electrolyte, 100 mM KNO, plus 10 m M HNO,j xere used. All reagents used were special or super special grade and all solutions were diluted by distilled and deionized water. The cell and all vessels used for sample preparation were filled with 1 M "OB for a day, rinsed out, and then filled with distilled and deionized water for a day before use. Procedure. The mercuric solution and supporting electrolyte were mixed with the sample in the proper portions. About 25 mL of the mixed solution was poured into the cell and flushed with nitrogen to remove dissolved oxygen for about 10 min. At the end of this period, the nitrogen stream was diverted above the solution, the glassy carbon electrode was rotated at a defined revolution number, and the required potential was applied to it for a defined time. After this pre-electrolysis time, the rotatic,n of electrode was stopped and the potential was anodically swept at a defined scan rate following a rest period of :JO s. For the re-dissolution process of deposited metal, the e VS. E curve was measured at room temperature ( - 2 0 " C ) . RESULTS AND DISCUSSIOh' e vs. E Curves in Anodic Stripping Processes from Thin Mercury Film Electrode. The theoretical predictions were examined by using the sample solutions of Cd'", Pb'", and Tl+ as examples of the species: whose electrode reactions arc two- and one-electron transfer processes, respectively. Figure 2 shows the typical e vs. E curve of the re-dissolution processes for Cd2+and Pb'+,and also shows the corresponding vs, E curve for comparison. In the case for TI', the similar, kit somewhat broad e vs. E and i vs. E curves were observed. j
-4
t---
-c
I
-9L
2
E(V
YS
-C6 Ag/A;Cl)
-38
Figure 2. Typical e vs. E curve for the re-dissolution of Cd and Pb amalgams at the thin mercury film electrode. Sample: 6.5 n M Cd2+ plus 8.6 nM Pb2+ in 100 mM K N 0 3 plus 10 mM HNO, plus 49.2 FM Hg(NO,),; potential scan rate: 160 mV/s; electrode area: 7.07 mm2; pre-electrolysis potential: -0.90 V vs. Ag/AgCI; pre-electrolysis time: 10 min at the rotating electrode and then 30 s at t h e standing one; revolution number of electrode: 1800 rpm
As expected from theory, the shape having a minimum and a maximum was observed in each e vs. E curve including the case for T1+. T h e ratios of minimum e values t o maximum ones in Figure 2 and in the e vs. E curve of Tl(Hg) were 1.94 for Cd(Hg), 2.06 for Pb(Hg), and 2.17 for Tl(Hg),respectively. These values are compared with the theoretical value of 2.12 independent of species (see Table I). In linear sweep anodic stripping voltammetry at a thin mercury film electrode ( 2 1 ) , the observed curve is a n asymmetrical peak and the peak current is given by lp
=
0.298n2PA~ilC' -
RT
(19)
r >
I he ratio of eppto --ip, therefore, is presented as follows
I t is expected from Equation 20 t h a t the signals observed in the proposed technique are larger than those in ordinary linear sweep voltammetry a t higher potential scan rates. This is evident from comparison between the e vs. E curve and t h e corresponding i vs. E curve a t the scan rate of 160 mV/s as an example, as seen in Figure 2. T h e experimental values ( s 1 . 2 ) ofe,,/(-i,) were 3.36 for Cd(Hg), 3.17 for Pb(Hg), and 2.34 for Tl(Hg). These values are compared with t h e theoretical values of 3.31 s '' for the two-electron transfer species for the one-electron transfer species, respectively, and 2.34 s calculated from Equation 20 on the basis of the 160 mV/s a t 2 0 "C. From Figure 2 , it seeins easy t o estimate the height from the negative peak to the positive one in the proposed technique rather than the peak height from the base line, which must be graphically drawn. Dependence of eppon t , , v, N , and C. Figure 3 shows the relationship betweeii P,,, and t , for Cd'+, Pb2+,and T1+, Iieing measured by keeping all other parameters constant. epp was linear with pre-electrolysis time a t rotating electrode u p to about 5 min for Cd'+ and Pb", and about 12 min for T1' at the concentration of about 100 nM. The range of linearity increased when the bulk concentration level decreased, as shown in the case of Cd2+in Figure 3. The positive intercepts with the ordinate in Figure 3 correspond to the pre-electrolysis f'or 30 s under a standing electrode. Figure 4 shows the for the same ions. Linearity was dependence of epp on ry and the lines passed through the origins. T h e s of experimental values from the lines in Figures 3 and 4 seem t o be due mainly to the large mercury film thickness and fast potential scan rate applied, respectively. ~ i ~ . ~ ' '
ANALYTICAL CHEMISTRY, VOL. 51, NO. 1, JANUARY 1979
Table 11. Negative Peak Potential and Width between Negative Peak and Positive One of e vs. E Curves for Re-dissolution Processes a t Different Ionic Concentrationsa
N
n
w p p , mV
species
C, nM
CdZ+
2.10 4.20 6.30 8.40 10.5
TI
E*,W vs. Ay/AgCI) z p t l
+
theor
30 32 30 31 31
--0.607
-0.611 - 0.612 -0.606 0.608 av. -0.609 20.8 - 0.439 - 0.438 41.6 62.4 -- 0.437 83.2 -- 0.434 104 -0.435 av. --0.437 19.6 - 0.564 39.2 - 0.572 58.9 -- 0.562 0.555 78.5 98.1 -0.554 av. --0.561
Pb2+
113
.
~~
32
t,(m
31 31 30 30 32
32
65 66 64 62 62
64
i
n)
Figure 3. Relationship between heights from the negative peak to the positive one of e vs. E curves for re-dissolution processes and preelectrolysis times at the rotating electrode. (0)105 nM Cd", (A) 5.3 nM Cd2+, (0) 104 nM Pb2+, ( 0 )98.1 nM TI'; supporting electrolyte: 100 mM KNO, plus 10 mM HNO, plus 49.2 gM Hg(NO,), for Cd2+, 51.0 pM Hg(NO,), for Pb2' and TI'; other conditions are the Same as in Figure
2
a Supporting electrolyte: 100 mM KNO, plus 1 0 mM HNO, plus 49.2 p M Hg(NO,), for Cd", 51.0 g M Hg(N03), for P b Z +and TI'; potential scan rate: 1 6 0 mV/s; electrode area: 7.07 mm'; pre-electrolysis potential: -- 0.90 V vs. Ag/AgCI; pre-electrolysis time: 1 0 min for Cd" and T i + , 2 min for P b z +a t the rotating electrode and then 30 s a t the standing o n e ; revolution number of electrode: 1800 rpm. E n p is the value at the second sweep. __.
e,,, was linear with the square root of N as predicted by Equation 18 for all ions. Figure 5 shows the relationship between eppand C for Cd'+ and Pb2+at different concentration levels. In both cases, eppwas linear with C and the intercept values with the ordinate correspond to the Cd2+ and Pb'+ amount contained as impurities in the supporting electrolyte solution used, respectively. I t should be noted that the pre-e!.ectrolysis time of 2 min may suffice for the determination of Pb2+a t ppb level. T h e same relationship was tested for TI+ also at different potential scan rates of 60 160 mV/s and it was found t h a t eppis proportional to C independent
-
of
L'.
D e p e n d e n c e of E , , a n d W,, o n C , v, a n d 1. T h e experimental results for three ions are shown in Tables I1 and 111. In all cases, E,, was independent of ionic concentration to be -0.609 V vs. Ag/AgCl for Cd(Hg), --0.437 V for Pb(Hg), a n d -0.561 V for Tl(Hg) under the experimental conditions shown in Table 11, but it shifted to the positive side with L'
vl5(rnV'.5/s'5)
Figure 4. Relationship between heights from the negative peak to the positive one of e vs. E curves for redissolution processes and potential scan rates. (0)105 nM Cd2*, (0) 104 nM Pb", ( 0 )98.1 nM TI'; supporting electrolyte and other conditions are the same as in Figures 3 and 2, respectively
and 1 as shown in Table 111, and there were linear relationships as predicted from Equation 14. W,, between E,, and log (UP) was independent of C, u , and 1 as shown in Tables I1 and 111, and the experimental values for Cd(Hg), Pb(Hg), and Tl(Hg) agreed well with the theoretical values of 32 mV for twoelectron transfer species and 64 mV for one-electron transfer species calculated from Equation 16,respectively. Applicable M a x i m u m P o t e n t i a l Scan Rate. Referring to Equation 18,the magnitude of eppincreases very much with increasing potential scan rate. However the applicable maximum scan rate was limited by the response time of the pen on the X-Y recorder used in this study to be about 200
Table 111. Negative Peak Potential and Width between Negative Peak and Positive One of e vs. E Curve for Re-dissolution Processes at Different Potential Scan Rates and Mercury Film Thicknessesa E,
( V vs. Ag/AgCl)
W P p , mV
.-_____
V, mVjs 20 40 60 80 100 120 140 160 180 200
Cd(Hg) 0.654 0.639 -- 0.630 - - 0.622 -0.617 - 0.610 - 0.604 - 0.600 - 0.594 - 0.590
1 2ab 3a 4a
-
5a 6a 7a
PbWg)
TI(&)
- 0.462
- 0.644
0.448 -0.437 - 0.431 . - 0.427 - 0.421 -0.416 -- 0.413 - 0.408 - 0.406
0.625 0.609 - 0.598 - 0.590 - 0.580 -0.574 -0.570 - 0.561 - 0.559
-
--
--
Cd(Hg) 31 30 32 31
32
Pb(Ilg) 30 30 30 29
T1U-k) 60 65 65 65
31
65
65 34 65 9a 34 32 65 1Oa 35 32 65 1l a 36 32 65 Theor. 32 32 64 a Sample: 1 0 5 nM Cd", 104 nM P b z +98.1 nM TI+;pre-electrolysis time: 2 min at the rotating electrode and then 3 0 s at the standing one; other conditions are the same as in Table 11. a is the mercury film thickness formed during pre-electrolysis of 2 rnin at the rotating electrode and 30 s at the standing one at -- 0.90 V vs. AgiAgC1. . .
-~-
8a
-.
--
.
.
~
~
...
_____
33
30 31
__
114
ANALYTICAL CHEMISTRY, VOL. 51, NO. 1, JANUARY 1979 ChM) 0
20
40
60
60
I
100
Table IV. Relationship between Height from Negative Peak to Positive One of e vs. E Curves for Re-dissolution Processes and Sweep Number"
120 I
P is
l 2 t
eon, E.IAIS"'
sweep no.
Cd(Hg) Pb(Hg) TWg) 4.87 1.31 1.22 2 1.32 5.30 1.31 3 1.32 5.30 1.31 4 1.32 5.39 1.31 5 1.32 5.26 1.28 6 1.33 5.35 1.26 7 1.31 5.32 1.25 a Sample: 5.3 nM C d 2 + ,20.8 nM P b 2 + ,19.6 nM TI'; pre-electrolysis time: 5 min at the rotating electrode and then 30 s at the standing one; other conditions are the same as in Table 11. 1
C(nM)
Figure 5. Relationship between heights from the negative peak to the positive one of e vs. E curves for re-dissolution processes and concentrations of Cd2+ and Pb2+ present in original solutions. (0)Cd2+ in 100 m M KNO, plus 10 m M HNO, plus 49.2 p M Hg(NO,),, (0) Pb2+ in 100 m M KNO:, plus 10 m M HNO, plus 51.0 p M Hg(NO,),; preelectrolysis time 10 min for Cd2+, 2 min for Pb2+at the rotating electrode and then 30 s at the standing one; other conditions are the same as in Figure 2
mV/s. When an oscilloscope is used for recording e vs. E curves, it is limited by the lower time limit of the ladder in the analog circuit for accurate semidifferentiation. The most commonly used ladder is the paralleling geometric ladder ( I s ) , and its lower time limit is about 0.050 s. Therefore about 10 V / s may be applied as the maximum scan rate, and, in such case, about a 26 times larger signal can be obtained for the two-electron transfer species compared with ordinary linear sweep voltammetry. Here it should be noted that as Equation 18 applys only under the condition of H 2 1.6 X 10 and H a 1'0, one must choose the corresponding thin thicknesses of the mercury film electrode on application of the large potential scan rates. Effect of Charging Current. T h e charging current, i,, in ordinary linear sweep anodic stripping voltammetry is given by I,
= -AM
(21)
where c is the differential double-layer capacitance per an unit area of electrode. Its semiderivative, e,, with respect to time is
when t h e differential capacitance is assumed constant. Ordinarily, the differential double-layer capacitance is nearly constant or changes slowly with potential to the faradaic current. Therefore it is expected that the semidifferentiation of the i vs. E curve decreases interference of the charging current under the condition t > l / s.~Furthermore, as long as the background current changes more slowly than the faradaic signal, the semiderivative measurement minimizes background interference. These are qualitatively clear from comparison of the plateau parts between the e vs. E and the i vs. E curve in Figure 2. Perone and Birk ( 1 ) have demonstrated t h a t the adverse effect on sensitivity of a highly potential-dependent background current can be eliminated by measuring the timederivative of the conventional curve with a hanging mercury drop electrode. This approach can also be applied to stripping voltammetry with a thin mercury film electrode. T h e shape of the curve observed in such a case is similar to t h a t in the proposed method, b u t is somewhat more symmetrical. Interference of the charging current may be more eliminated
on differentiation, but the electrical noise arising from the analog circuit for differentiation seems to be much larger than that for semidifferentiation. Analytical Aspects. Suitable mercuric concentration added to sample to form mercury film electrode in situ was 500 pM and it was found investigated in the range of 0.5 that about 50 p M is most suitable to get reproducible data, resulting from a homogeneous, gray mercury film formed. Table IV shows the reproducibility for successive measurements of eppon the same aliquot. In general, the eppvalue in the first sweep tended to be smaller than those in the sweeps after the second. The virtual constant eppvalues were observed in the second to seventh sweeps for all cases; the relative standard deviations for the successive measurements were 10.5% for about 5 nM Cd2+,10.8% for about 20 n M Pb2+, and k2.170 for about 20 nM TI+, respectively. eppvalues were linearly dependent on trace concentrations of metal ions when all other parameters were constant. T h e detection limits were found to be about 0.1 nM for Cd2+and Pb'+, and about 0.5 nM for T1+,respectively, a t the potential scan rate of 160 mV/s and pre-electrolysis time of 10 min.
-
CONCLUSIONS All theoretical predictions concerning anodic stripping semidifferential electroanalysis have been adequately confirmed. Anodic stripping semidifferential electroanalysis with a thin mercury film electrode provides much better sensitivity, resolution and precision than t h a t with a hanging mercury drop electrode, as shown in the preceding paper (IO). T h e proposed method is close to the differmtial pulse anodic stripping method in sensitivity and resolution, but the time required for stripping in this method is much shorter than in the differential pulse method. Semidifferential electroanalysis seems indeed an attractive alternative to both differential pulse and linear sweep methods in stripping analysis, combining the best features of both techniques. ACKNOWLEDGMENT T h e authors are indebted to the Computer Center of Nagoya University for computation, and are grateful to K. Kitagawa and M. Kajihara for computational and experimental assistance, respectively. LITERATURE CITED (1) S. P. Perone and J. R. Birk. Anal. Chern., 37,9 (1965). (2) U. Eisner, J. A. Turner, and R. A . Osteryoung, Anal. Chern.,4 8 , 1608 (1976). (3) G. D. Christian, J . Nectroanal. Chern., 23, 1 (1969). (4)N. Velghe and A. Claeys, J . Nectroanal. Chern., 32, 229 (1972). (5) M. Stulikova and F. Vydra, J . Nectroanal. Chern., 42, 127 (1973). (6) T. R. Copeland, J. H. Christie, R. A . Osteryoung, and R. K. Skogerboe, Anal. Chern., 4 5 , 2171 (1973). (7) M. Goto and D. Ishii, J . Nectroanal. Chern., 61, 361 (1975). (8) P. Dalryrnple-Alford, M. Goto. and K. 8. Oldham, J . Electroanal. Chern., 8 5 , 1 (1977).
ANALYTICAL CHEMISTRY, VOL. 51, NO. 1, JANUARY 1979 (9) P. Dalrymple-Alford, M. Goto, and K . 8. Oldham, Anal. Chem., 49, 1390 (1977). (10) M. Goto, K. Ikenoya, M. Kajihara. and D. Ishii, Anal. Chim. Acta, in press. (1 1) W. T. de Vries and E. van Dalen, J . Nectfoanal. Chem., 14, 315 (1967). (12) K. 6.Oldham and J. Spanier, "The Fractional Calculus", Academic Press, New York, 1974, p 115. (13) T . M. Florence, J . Nectroanal. Chem., 27, 273 (1970).
115
( 14) P. Delahay, "New Instrumental Methods in Electrochemistry", Interscience
Publishers, New York. 1966, p 229. (15) K. 8. Oldham, Anal. Chem., 45, 39 i(1973).
RECEIVEDfor review June 5 , 1978. Accepted September 25, 1978.
Analytical Implications of Differential Pulse Polarography of Irreversible Reactions from Digital Simulation James W. Dillard,' John J. O ' D e a , and R. A. Osteryoung* Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523
polarographic analysis without resort to lengthy empirical studies. Another approach to the problem of the quantitative treatment of quasireversible pulse polarographic wave has recently been developed by Birke, who has obtained a closed form solution for the problem ( 4 ) .
Explicit finite difference simulations of differential pulse polarography have been developed for evaluating the analytical applications of differential pulse polarography to irreversible and quasireversible electron transfer reactions. From simulation data, detailed prediction of polarographic peak shape and position as a function of pulse height, pulse time, and drop time is possible. Optimum conditions for analytical application of differential pulse polarography are discussed.
THEORETICAL Digital simulation as a general method for solving electrochemical diffusion-kinetic problems has been discussed in detail by Feldberg ( 5 ) . A recent publication by Ruzic and Feldberg (6) described an improved simulation of the dropping mercury electrode (DME) with associated compression and sphericity. The siniulator used in this investigation incorporates the improved DME model and the time change method mentioned earlier. All simulator currents are normalized after Feldberg except as rnodified previously ( 3 ) . For electron transfer reduction of the type
Differential pulse polarography has become an increasingly important tool in the analysis of both organic and inorganic electroactive species. With the expanded interest in differential pulse polarography, the systematic evaluation of the analytically important experimental parameters has become necessary. Such an evaluation for reversible electron transfer reactions has already been reported ( I ) . The treatment of irreversible and quasireversible systems will be presented here. Previous coupling of an explicit finite difference simulation for differential pulse polarography with a standard lionlinear least squares fitting program has denionstrated the feasibility of studying electron transfer kinetics b y differential pulse polarography (2). However, the cost of ezecuting such coupled programs usually limits the exhaustive investigation of complex elecron transfer reactions. The ready availability of a minicomputer system in our laboratory normally used for on-line data acquisition prompted a feasibility study of using finite difference simulations to evaluate the analytical applications of differential pulse polarography. 'l'he execution time of these siniulations was greatly reduced by the implementation of an incremental time change during the course of the simulation. T h e details of this expedited simulation technique have been previously published ( 3 ) . 'I'he treatment of quasireversible systems dictates that electron transfer kinetics be included in the simulation model. This elaboration has been incorporated into our programs and will be discussed further in the theoretical section. 'The use of this simulator enables the detailed prediction of polarographic peak shape and position as a function of controlled experimental variables such as pulse height, pulse time, and drop time. Such simulations promise to be of considerable aid to the analyst who wishes to select and optimize the experimental conditions of a differential pulse
ki
OX
+ ne -.RED
the flux of the electron transfer reaction is calculated from Feldberg ( 5 ) (Equation 116)
RATEHFIUU(~,~)-KAI'EHL~*UL~(~,~) zz = _______ (2) 1 + (RATEHF/2*DD)+(RATEHB/2*IID) -
which is derived from the basic surface boundary conditions. T h e surface concentrations ( U U ( l , I ) , U U ( 2 , l ) ) of OX and RED are in simulator units and are assumed to be soluble in the solution. The normalized diffusion coefficient (DD) has been optimized to a value of 0.4 simulator unit. The potential dependent heterogeneous electron transfer rates (RA'I'EHF and RATEHB) must be determined from the apparent standard heterogeneous rate constant. From the general form of the Butler -Volmer equation k f and hb may be deduced
where
n, = 1 G=y+rp
' Present address, Tennessee Valley Authority, River Oaks Building,
Muscle Shoals, Alabama 35660.
0003-2700/79/0351-0115S01 0010
(1)
kb
f
1978 American Chemical Society
