Investigation of A.C. Polarography at Statio nary Electrodes, with Application to Stripping Analysis WILLIAM L. UNDERKOFLER and IRVING SHAlN Chemistry Department, University o f Wisconsin, Madison, Wis.
b The use of stationary electrodes in alternating current polarography was investigated. Theoretical relations were developed to define the conditions under which the alternating and direct components of the current could b e separated, and a direct comparison of theoretical and experimental a.c. polarograms was made. The use of a phase selective detector was investigated, and the method was applied to stripping analysis. This method of detection, combined with the concentration step of stripping analysis, made it possible to obtain a significant increase in sensitivity over the direct stripping analysis method.
A
there have been many applications of a x . polarography in which the dropping mercury electrode was used, relatively few applications with stationary electrodes have been reported. These have included platinum electrodes (12, 29), carbon paste and graphite rod electrodes (29), mercury pool electrodes ( 7 , 8),and the hanging mercury drop electrode (26). A general disadvantage of stationary electrodes is that adsorption, contamination, and other surface phenomena are more frequently encountered, compared to the dropping mercury electrode where the surface is renewed regularly. Nevertheless, where applicable, stationary electrodes have the advantages of decreased charging current, lower electrode resistance, and no interference from capillary noise. Furthermore, the products of the electrode reaction can be accuniulated a t a stationary electrode, and thus are available for further Investigation, or for trace determinations in stripping analysis (26). The procedure used with stationary electrodes is similar to conventional stationary electrode polarography (4). Starting a t some initial 1)otential where no current flows, the potential is scanned linearly with time over the range of interest. Simultaneously, an alternating voltage of sinall amplitude is superimposed on the linear scan. The a.c. portion of the current is plotted as a function of time-i.e., applied direct potential. LTHOUGH
218
ANALYTICAL CHEMISTRY
The theory of a x . polarography with the dropping mercury electrode has been covered extensively ( I B ) , and it has been found that for a reversible charge transfer without chemical kinetic complications, the a x . process operates essentially independently of the d.c. process (10). Thus, the alternating and direct components of the current are experimentally separable, provided the a x . frequency is high compared to the capillary drop time. Similarly, with stationary electrodes, the alternating and direct components of the current should be separable provided the a.c. frequency is high compared to the rate of potential scan. *ilthough this condition was assumed to hold in previous work with stationary electrode a x . polarography, there has been no direct comparison of theory with experimental data. In this vcork, the use of stationary electrodes in a x . polarography was investigated further. Theoretical relations were developed to define the conditions under hich the alternating and direct components of the current are independent, and a coniparison of theoretical and experimental stationary electrode a x . polarograms was made. In addition, the method \\as applied to stripping analysis, and the use of a phase selective detector for rejection of the charging current was investigated. This method of detection made possible a significant increase in sensitivity over the direct stripping analysis technique.
Here, AE is the amplitude of the sine wave, and w is the angular frequency. Other terms used here (as well as in the equations below) are the same as defined previously (18). Combining Equation 1 with the Xernst equation provides the boundary condition defining a reversible reaction in stationary electrode a x . polarography (CO/CR)Zd2
=
B exp(-ut
y = nFAE/RT
Since it is assumed that neither 0 nor the sum of the surface concentrations is related to the bulk concentrations by (5)
+ CR(2=0) =
co* + d m i Z C R *
For a reversible reaction
in which both species are soluble, the boundary value problem for stationary electrode a x . polarography is similar to that for the conventional method aithout the superimposed a x . potential (Reference 18, Case I, Equations 1-5). The major difference is that the electrode potential as a function of time is given by
(1)
(3)
R accumulates a t the electrode surface,
dK/Z
+ ne = R
(2)
The solution to this boundary value problem can be obtained using the method of Sevcik (20) and Reinmuth (19), in which the Laplace transform is applied to the Fick’s law equations to obtain the surface fluxes in terms of the surface concentrations. This provides a single equation
THEORY
t > O , X = 0: E = E , - v t - AE sin wt
y sin ut)
where
CO(Z40)
0
-
(5)
Noting that C R * = 0, Equations 2 and 5 can be combined, and after differentiation, the time dependence of the surface ooncentration of substance 0 is obtained
- [Co*(u sech2[(ln 4 where
+ ywcoswt)/4] x - at -
ysinwt)/2]
(6)
i
=
6
~ F A D o ' ~ ~ C O * ( ~[ l/ /~l )/ ~ ( t
nFdDo1Wo*(yw/4)
and
sech2 [(In $
- a7 -
[ C O S U T / ~ / T-( ~T ) ] sech2 [(ln $ - a7
On combining Equations 4 and 6, an equation for the current is obtained in terms of the experimental parameters. I n Equation 8, the d.c. and a.c. processes interact through the distortion of the linear scan by the superimposed alternating potential, but if the amplitude (y) is small and the frequency (a) is high compared to the rate of voltage scan, this interaction is small. Under these conditions, the first term in Equation 8 primarily describes the d.c. component of the current, and it reduces to the expression for stationary electrode polarography obtained by Sevcik (20) and Reinmuth (19), provided the a.c. terms in the hyperbolic secant are neglected-Le., when y = 0. The second term, which describes primarily the a x . component of the current, would require numerical evaluation if it were to be applied rigorously. However, for the conditions y-, 0
T)]
yw
>>a
the alternating current does not depend on the rate of potential scan, and the potential dependence can be removed from the integral to obtain
+
ysinw~)/2]d~
-
ysinwr)/2]dr (8)
of diffusion to a plane electrode, but it also applies to spherical electrodes under certain conditions. In a x . polarography with the dropping mercury electrode, Gerischer (9) showed that the spherical nature of the electrode may be neglected provided
m
i twtion about an orti(,r of ma giii t utle 1110 rt' tli tu t e , 1 his .sensitivity limit :igrce.; c~loscly with that fouiici liy 1,:rtieldiny for ])haw selrctive polariigralihy at a mercury 1)ool elect1,ode ( 7 ) . Smith and Reinniuth on the other hand i2Zs, 2;) rc~ ) o r t c tan l or(!cr of niagnitutlc niurc senFitivitJ- ior a tcc*hnicjuc~similar to that iireti hcre. In thih \vork a t dilution; grratrr than about 5 x 10-:.11, reI)roduribility of reliliratts !\-a5 iioor and calitiration of concrntration 2's.
Table I.
alternating current was no longer linear. _I hus, . it at)pear.> that the l i r i i i t h 5tated above are realistic for analytival allplications with the eyuilinient described here. A.C. Stripping Analysis. The method of strili1)ing analysis (22) with the hanging mercury droli electrode also was studied in conjunction with phase selective a x . polarography. Recent research on stripping analysis has shown that the method is very sensitive for t,he determination of electroactive materials. The techniqur conskts of a prestep, during which the sample is concentrated by electrodeposition on an electrode. The actual takes place (luring a subelectrodissolution (stripping) step, in which any of several electroanalytical method:: can lie used. I n the p r o c ~ d u r estudied here, the read-out in the stril)i)ingRtq) i t a s by phase selective a .('. polarography . Xn alterriating Imtential was sul)eri n i l m d on the dircct potential throughout the entire esiierimen effect on the pre-~lectrol carried out in the limitin for the reduction of the metal ion to amalgam. .kfter thc timed preinterval in s t i r r d solution, the stirring was stoplied and a 30second interval was allowed for the solution to conic' to rest. The potential t1ic.n was sc,anncd in the anodic direction. The alternating current for the anodic h p p i n g process was nieasured using thr phase wlective detector. I o investigate the precision, accuracy, and a~qilicatiility of thr method, solutions of cadmium ion were studied in the cwncentration range 10-lo.\/. The Iire-elec~trol condurted at -1.0 volt vs. the S.C.E.. with the solution stirred 11y a magnetic stiwing liar drivrn by a synchronous motor. The aplilietl alternating Iiotential \vas 20 niv. Iicak-to-peak a t 100 c . 1 ~ For ~ the stripping btep the potential \vas scanned anodically from the plating potential at a rate of 20 niv. per secfond. Thr result%(Tahlc 1) indicate that the peak altrlnating cwrrent i-; a linear r .
Phase Selective A.C. Polarographic Stripping Analysis of Cadmium in 0.1 M Potassium Chloride
Preelectrolysis time, t
minutes 1 )
i
1.i
80
?LV. p e a k
height, i P pa.
1.50 4.5 P 4 54 1 XS 0 54
i,/r
ix
10:, 9 , 00 9 18 9 08 9 20 R 97
Std. dev.h
VOL. 37, NO. 2, FEBRUARY 1965
5
1 0 2 4 2 1 8 7 1% s
221
function of the concentration of the ion in solution and of the pre-electrolysis time. Sensitivity appeared to be improved by about a n order of magnitude over that reported for the corresponding direct current stripping method (6). Thus, it is possible to perform analyses a t concentration levels about 10-fold more dilute than in the d.c. technique, or alternatively, to achieve a saving in time by employing shorter pre-electrolysis times a t the same concentration levels. LITERATURE CITED
(1) Alberts, G. S., Shain, I., ANAL.CHEW 35, 1859 (1963).
(2) Breyer, B., Bauer, H. H., “Alternating Current Polarography and Tensammetry,” pp. 101-3, Interscience, New York, 1963. (3) Ibid., p. 128. (4) Delahay, P., “New Instrumental
Methods in Electrochemistry,” Chap. 6, Interscience, New York, 1954. ( 5 ) Ibid., p. 54. (13) DeMars. R. D.. Shain., I.., ANAL. -~~ CHEM.29; 1825 (1957). (7) Erbelding, R. F., Ph.D. Thesis, Cornel1 University, 1961. (8) Erhelding, W. F., Cooke, W. D., Division oflAnalytica1 Chemistry, 140th Meeting, A.C.S., Chicago, Ill., September 1961. (9) Gerischer, H., 2. Physik. Chem. 198, \ - I
~
286 (19.51). \----,
(lO)Hung, H. L., Smith, D. E., ANAL. CHEM.36, 922 (1964). (11) Jessop, G., Brit. Patent 640,768 (1950). (12) Juliard, A. L., J . Electroanal. Chem. 1, 101 (1959). (13) Kolthoff, I. SI., Lingane, J. J., “Polarography,” pp. 219-20, Interscience, Kew York, 1952. (14) Lingane, J. J., J . Am. Chem. SOC. 68, 2448 (1946). (15) hlatsuda, H., 2. Elektrochem. 61, 489 (1957). (16) Ibid., 62, 977 (1958). (17) Meites, L., ANAL. CHEM. 27, 416 (1955).
(18) Nicholson, R. S., Shain, I., Ibid., 36, 706 (1964). (19) Reinmuth, W.H., J . Am. Chem. SOC. 79, 6358 (1957). (20) Sevcik, A , , Collection Czech. Chem. Communs. 13, 349 (1948). (21) Senda, XI., Tachi, I., Bull. Chem. Soc. Japan 28, 632 (1955). (22) Shain, “Treatise on Analytical Chemistry,’;’I. XI. Kolthoff and P. J. Elving, eds., Part I , See. D-2, Chap. 50, Interscience, Kew York, 1963. (23) Smith, D. E., ANAL. CHEM.35, 602 (1963). (24) Ibid.) p. 1811. (25) Smith, 11. E., Ph.D. Thesis, Columbia University, 1961. (26) Smith, D. E., Iieinmuth, W. H., A N ~ LCHEM. . 32, 1892 (1960). (27) Ibid., 33, 482 (1961). (28) Underkofler, W. L., Shain, I., Ibid., 35, 1778 (1963). (29) Walker, I). N., Adams, R. N., Juliard. A. L., Ibid., 32, 1526 (1960). RECEIVEDfor review October 21, 1964. Accepted December 11, 3964. This work was suppoited in part by funds received from the U. S. Atomic Energy Commission, under Contract No. AT(11-1)-1083.
Ultratrace Determination of Metals Using Coordination Chain Reactions D. W. MARGERUM and R. K. STEINHAUS Department o f Chemistry, Purdue University, lafayette, Ind.
b A chemical kinetic method is proposed for the detection and determination of ultratrace quantities of metal ions. A coordination chain reaction system involving the exchange of triethylenetetrarnine-nickel(l1) and (ethylenedinitri1o)tetraacetatocup r a t e (11) is used. This exchange proceeds b y a chain mechanism where the chain centers are the free ligands: EDTA and trien. The rate of the exchange reaction is followed by its color change and is responsive to 10-gM concentration changes of EDTA. The theoretical limits for metal determinations suggest that analysis down to the 10-gM level with *5% accuracy should be possible. Experimental results are given down to lO-*M. AS little as mole of sample can b e analyzed with the theoretical limit around mole. Any metal ion which complexes EDTA can b e determined.
CURATE
determination of metal ions in solution becomes increasingly difficult as the concentration of the metal is reduced below 10-6M. Some conventional trace analysis techniques are applicable down to 10-661, but beloa this level it has generally been necessary to use different methods. I n this paper a new kinetic method of analysis is proposed for ultratrace metal 222
ANALYTICAL CHEMISTRY
where trien = triethylenetetramine determinations-for metal concentra(H2NCH2CH2XHCHzCH2XHCHzCH2tions of less than 10-6Jf and samples NH2) and EDTA = (ethylenedinitri1o)containing less than 1 pg. of metaltetraacetate [(OOCCH2)zKCH2CHzPbased on the chemical behavior of coordination chain reactions. (CH2COO)2]-4. The reaction is initiated by the dissociation of very The exchange reaction of two metal small quantities of the complexes or by complexes in aqueous solution can the addition of traces of free E D T A or proceed by a chain reaction mechanism free trien. The two free multidentate (20). This leads to a rate of exchange ligands are the chain reaction centers much faster than the rate of dissociation and the chain-propagating steps are of either complex. The chain centers in these coordination chain reactions are EDTA Nitrien+2--t trace concentrations of the niultidentate KiEDTh-2 trien (2) ligands involved in the complexes. The ligands can originate from the pure trien C u E D T h + -+ complexes or can be added separately. Cutrienf2 EDTA (3) Just as a source of free radicals greatly accelerates a free radical chain reaction, The number of protons and the charge so the addition of a free ligand greatly on the ligands have been omitted in accelerates a coordination chain reEquations 2 and 3 because they vary action. I t is the kinetic response of the with pH. exchange reaction to free ligand at conThe addition of trace quantities of centrations of 1 O - g X and less that perfree ligand to the pure reactants greatly mits the ultratrace determinations. A accelerates the exchange rate and kinetic study of one coordination chain simplifies the rate expression. The exreaction system has been reported change rate is easily adjusted to a first(20). Recent additional kinetic inorder dependence in one of the reactants formation about the reactions in this where the first-order rate constant system (f4,16, 83) makes it possible to depends on the free ligand contreat it in theoretical detail. Thus, the centration. Thus, although the free method is based on the exchange reE D T h concentration may be only action of Fitrien+2 and C U E D T ~ ~ - ~ 10-’.11, it can control the rate of conversion of l O - 3 N ?iitrien+2 to Cutrien+2. NitrienC2 C U E D T A - ~+ The bright blue color of Cutrien+2 is used to follow the progress of the Cutrien+2 4- XiEDTA+ (1)
+
+
+
+
+
