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Anal. Chem. 1988, 60,1177-1179
Concentration Limits of Electrolytic Preconcentration in Instrumental Analysis Roman E. Sioda Department of Chemistry, T h e University of Rhode Island, Kingston, Rhode Island 02881-0801 >
A general mathematical model has been developed descrlblng concentration limits for the process of electrolytic preconcentration of metal Ions by deposttlon. The model shows that the deposition behavlor Is Inltlakoncentratlondependent and leads to a final equlilbrlum concentration of metal Ions In solution, descrlbed by a single generalized equation. The model has appllcatlon for practical electrolytic preconcentratlons performed In connection with the followlng Instrumental determination,
Electrolytic preconcentration is frequently used for improving limits of detection of many instrumental methods of analysis (1-3). By its application as a preliminary step, it is possible to decrease the practical limits of detection by up to 2 orders of magnitude below the usual values for the instrumental methods alone. Various instrumental methods can be coupled with the electrolytic preconcentration, and such methods, as neutron activation analysis (NAA) (4), electrothermal atomization atomic absorption spectroscopy (ETA-AAS) ( 5 , 6 ) ,and recently inductively coupled plasma emission spectroscopy (ICP-ES) (7-11) proved especially valuable. These methods, coupled with the electrolytic preconcentration, achieved limits of detection in the parts-perbillion range, for several environmentally important metals in natural waters and biological fluids. Anodic stripping voltammetry (ASV) is an important method, which intrinsically combines the electrolytic preconcentration and voltammetric determination, performed in the same analytical vessel. The method had been applied most widely, mainly for transition-metal ions as analytes, present in diverse original matrices (12). Under its many variations, the method can boast record low limits of detection in the range of 0.1-0.01 ppb. It is natural to try and envision a further decrease of limits of detection of the combined methods of electrolytic preconcentration and instrumental determination. It, thus, seems that the limits of detection of the combined methods should depend on the efficiency of the metal electrodeposition step. This efficiency will in turn depend on the applied electrolytic potential, and absence of any reactions, which can interfere with the metal deposition. It had been found experimentally that at ultratrace metal ion concentrations the electrodeposition reactions are very slow, much slower than at moderate concentrations, and that stationary metal ion concentrations in solutions are formed during deposition electrolysis (4, 10, 13). A theoretical model had been devised, which explained successfully these two unexpected experimental findings (14, 15). The model was based on an assumption of a simultaneous metal electrodeposition and chemical dissolution of deposit, leading to a formation of an equilibrium concentration of metal ions, usually at ultratrace concentration levels. The purpose of the present work is to show how this model can be unified and confirmed by properly chosen experimental tests. It is believed that the model will help to increase the understanding and applicability of the combined methods of electrolytic
preconcentration and instrumental determination.
RESULTS AND DISCUSSION An electrodeposition reaction can be written in general, as Mnf + ne- = Mo
(1)
where Mn+ denotes metal ion of charge n+ in solution, edenotes electron, and Mo denotes the deposited metal. Reaction 1is reversible, and dependent on the applied deposition potential, according to the Nernst equation. According to the discussed model, reaction 1is often followed by a reaction of chemical dissolution of the deposited metal
Mo + X = Mn+ + Y
(2)
which leads to a partial restoration of the initial substrate, MnC,in solution. Reaction 2 is considered to be a zero-order heterogenous reaction, as it is assumed that the deposit, Mo, is in solid form, and the chemical oxidant in solution, X, is present in excess. The sequence of reactions 1and 2 resembles the catalytic reaction mechanism, EC', which had been treated theoretically by Nicholson and Shain (16,17). However, their work concerned a fully homogeneous system, where participants of both reactions were in solution. It had been shown also that such an EC' mechanism leads to stationary-state limiting currents of the substrate under voltammetric conditions (18). The main idea of the earlier papers on the present model (14, 15, 19) can be stated in the form of a simple equation dc/dt = - s ( ~ , c- xk,) (3) where c (mol/cm3) is the concentration of the electroactive metal ionic species, t (s) is time, s (cm-') is the specific area of the electrolytic cell, i.e. s = A/V
(4)
where A is the electrode geometric area and V is the volume of solution in the cell, kl (cm/s) is the mass-transfer coefficient of the reduction-deposition process, x , which can be timedependent, x = x ( t ) ,is the fraction of the total electrode area A covered by metal deposit, and k2 (mol/(cm2.s))is the specific rate of deposit dissolution. In earlier papers, cited above, eq 3 was integrated for two special, limiting cases: (1)When the initial concentration of the substrate is very low, and there is not enough of substrate in the solution to cover fully the area of the electrode with deposit, then an equilibrium concentration of substrate is set in solution, c,, which is dependent on the starting concentration, co (cell = copk2/lsk1
+~k2)
(5)
where p (cm2/mol) is the so-called molar monolayer area constant, characteristic for a metal in question (approximate values of p for several metals are given in Table I). (2) When the initial concentration of depositing metal ion is moderate or large, so that the area of the electrode is quickly covered fully with deposit, then ( C e h = k2/k1 (6)
0003-2700/88/0360-1177$01.50/00 1988 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 60, NO. 11, JUNE 1, 1988
Table I. CalculatedaMolar Monolayer Areas ( p ) of Several Important and Electrochemically Active Metals
metals
lo-8p, cm2/mol
Ag
4.4 4.3 4.4 4.6 3.4 8.5 3.3 6.4 4.1 2.9 4.1 6.1 3.7 4.4
AU
Bi Cd cu
In Ni Pb Sb
Se Sn
T1 Zn av
c, = kz/kl(l - exp(-y(co - c,))) Cg.
Equation 15 reduces to eq 5 and 6, in the limit of, respectively, very low and high initial substrate concentrations, co. In the intermediate range of co, eq 15 should be solved numerically. Equation 15 can also be presented so ce = (ce)z(l - exp(-y(co - e,)))
meaning that the equilibrium concentration formed is independent of the initial concentration, co, and of the geometric parameter of the cell, s. "he two equilibrium concentrations are very different, as one is initial-concentration dependent, and the other is not, and there does not seem to be an expected smooth transition between them. While ( c , ) ~is expressed very simply by eq 6, eq 5 for (cell can be shown to be dependent on (c,)~and (p/s) ratio
(7) where the new constant y (cm3/mol) is characteristic of the depositing metal, and of the cell (8)
Transition between ( c , ) and ~ ( c , ) ~ It . is natural to expect that there should be a smooth transition between the two equilibria concentration levels, ( c ~ and ) ~ ( c , ) ~ ,when there is a continuous increase of the initial concentration, co, starting at some ultratrace low level. The formulation of such a smooth transition is proposed in the present paper. Coming again to eq 1,one sees that for an equilibrium dc/dt = 0, and eq 1 becomes klc, - ~ k = ,0 (9) Equation 9 contains a term, x , which will normally depend on the amount of deposited metal, m, which can also be expressed by the equivalent electric charge of deposition, q q = mnF/M
(10)
where n is the number of electrons transferred per discharging metal ion, F is the Faraday constant, and M is the atomic weight of the metal. According to the earlier propositions of Rogers and Stehney (20)and Brainina et al. (21,22),and modified by Sioda (15), the fractional electrode area covered by deposit, x , depends on the electric charge of deposition, q, in the following way: x = 1 - exp(-pq/nFA) (11) Substitution of q from eq 10 leads to x = 1 - exp(-mp/MA)
(12)
The ratio present in the exponent can be expressed by the concentration difference (co - c,) m / M = (co - c,)V (13) and eq 12 now becomes x = 1 - exp(-y(co - c,))
(15)
valid for an unlimited range of the initial concentration term,
a From atomic radii, and assuming closest packing of spheres on a Dlane, accounting for 0.9069 occupation of the plane.
Y = P/S
where the parameter y is defined by eq 8. Substitution of x of eq 14 into eq 9 leads to the following general equilibrium equation:
(14)
(16)
where ( c , ) ~is given by eq 6. Graphic Representation of the Equilibrium vs Initial Concentration Dependence. To show graphically the dependence between the initial concentration, co, and the final, equilibrium concentration, c,, of the depositing metal ion, expressed by the general eq 15 and 16, one should adopt some realistic values for the numerical parameters: (c& = k 2 / k l and y . It seems that ( c , ) ~should depend on a metal ion in question and on the composition of applied solution. It will be so, provided that the applied potential of electrolysis is negative enough that the deposition reaction is fully mass-transfer controlled and that the electrochemical oxidation of the deposited metal is practically fully prohibited. Thus, ( c , ) ~of eq 6 will depend on speed of electrolysis, as expressed by the mass-transfer coefficient of deposition, k l , and on the specific rate of the chemical dissolution of a given metal, k2, characteristic for the metal itself and for the oxidative and complexing power of the solution. It is possible to make a tentative estimation of the magnitude of (c& by considering the limits of detection, for a series of metals, of the very powerful analytical method of ASV, which applies an inherent electrolytic preconcentration. This approach is naturally only very approximate, as most of metals determined by ASV form amalgams with the mercury cathode on deposition. The average limit of detection of ASV for a series of 11metals (Ag, Bi, Cd, Co, Cu, In, Pb, Sb, Sn, T1, and Zn) is on the order of 1 X M, i.e. 1 X mol/cm3 (23). Assuming that this value is intrinsic for the electrolytic preconcentration step of ASV, (c,)~can be tentatively estimated, as on average equal to mol/cm3. The estimation of the parameter y is even more straightforward. From Table I, the average value of the molar monolayer areas for a series of 13 metals (Ag, Au, Bi, Cd, Cu, In, Ni, Pb, Sb, Se, Sn, T1, and Zn) is 4.4 X lo8 cm2/mol. On the other hand, it is reasonable to assume that the specific area of a typical electrodeposition cell is of the order of 0.05 cm-l. Thus, according to eq 8, the typical order of magnitude of the parameter y is 1O1O cm3/mol. Figure 1 shows results of calculations, where the circled points represent the calculated values of c, according to eq 16, for y = 1O1O cm3/mol, (c,)~equal to and mol/cm3, and for a range of the initial concentrations, c,, (mol/cm3). The curves shown have three regions. Starting from the low initial concentrations, the curves are linear, and described by ( c , ) ~ of eq 5 and 7. For the middle curve (B), the proportionality constant between (c,)~and co is equal to according to eq 7. This result can be so inter9.99 X preted: for the ultratrace concentration region (W9to M), as also below lo4 M initial concentrations, the obtained equilibrium concentration is equal to approximately 0.1% of the initial concentration of the depositing metal ion. The second definite region of the curves in Figure 1 is that for initial concentrations higher than about 5 X mol/cm3 (5 X M). Here the equilibrium concentrations are invariant with the change of the initial concentration and are
Anal. Chem. 1988, 60, 1179-1185
1179
equilibrium concentration dependence on the initial concentration of a depositing metal ion. The present, and more general model, unites those two limiting approaches of the earlier model by means of the single, nonlinear eq 16, applicable for the full range of the initial concentrations, including the intermediate region. It is also postulated that one way of estimation of (c,)~is by means of eq 6, when the mass-transfer coefficient of deposition, k , , and the specific rate of metal dissolution, k2, are separately measured for a single experiment. It seems that the measurement of k z is more difficult experimentally, than the measurement of kl, which is rather straight-forward under usual experimental conditions.
LITERATURE CITED
v
, -12
-11
109 ic,)
-IO
-6
Flgure 1. Calculated dependence of the equilibrium concentrations, c,, on the initial concentrations, co,of metal ion in solution, according to e 16. Concentrations in mol/cm3; are as follows: lo-'' (A), lo-' (B), and lo-'* (C).
9
equal to the chosen values of (c& of eq 6. These equilibrium concentrations are characteristic for an electrode fully covered by deposit. The third region of the curves in Figure 1 is that between approximately 5 x 10-l' and 5 x mol/cm3 initial concentrations (5 X and 5 X lo-' M) of the metal ion, and corresponds to nonlinear solutions of eq 16. In this region, there is a nonlinear transition between (c,), of eq 5 and (c,)~ of eq 6. This region is relatively narrow (over the range of the initial concentrations of approximately one order) and, hence, practically not the most important. Thus, the earlier and simpler model (14, 19) adequately described the two limiting, and most practically important regions of the
(1) Sloda, R. E., Batiey, G. E.; Lund, W.; Wang, J.; Leach, S. C. Talsnta 1986, 33, 421-428. (2) Leyden, D. E.; Wegschneider, W. Anal. Chem. 1981, 53, 1059A1065A. (3) Krasiishchik, V. 2.;Kuzmin, N. M.; Neiman, E. Ya. Zh. Anal. Khim. 1979, 3 4 , 2045-2056. (4) Jerrstad, K.; Salbu, B. Anal. Chem. 1980, 52, 672-676. (5) Holen, B.; Bye, R.; Lund, W. Anal. Chim. Acta 1981, 130, 257-265. (6) Batiey, G. E.; Matousek, J. P. Anal. Chem. 1977, 49, 2031-2035. (7) Sioda, R. E. Talanta 1984, 3 1 , 135. (8) Salin. E. D.; Habib, M. M. Anal. Chem. 1984, 56, 1186-1188. (9) Habib. M. M.; Salin, E. D. Anal. Chem. 1985, 57, 2055-2059. (10) Matusiewicz, H.; Fish, J.; Malinski, T. Anal. Chem. 1987, 59, 2264-2269. (11) Abduliah, M.: Fuwa, K.; Hiroki, H. Appl. Spectrosc. 1987, 4 1 , 715-721, (12) Wang, J. Stripping Analysis; VCH Publishers: Deerfield, FL, 1985. (13) Brooks, E. E.; Mark, H. B., Jr. J . Environ. Sci. Heafih, Part A 1977, A12, 511-521. (14) Anderson, J. L.; Sioda, R. E. Talanta 1983, 3 0 , 627-629. (15) Sioda, R. E. Talanta 1985, 32, 1083-1087. (16) Nicholson, R. S.; Shain, I. Anal. Chem. 1984, 36, 706-723. (17) Bard, A. J.; Fauikner, L. R. Electrochemical Methods; Wiiey: New York, 1980; Chapter 11. (18) Saveant, J. M.; Vlaneiio, E. Electrochlm. Acta 1985, 10, 905-920. (19) Sioda, R. E. Anal. Lett. 1983, 16, 739-746. (20) Rogers, L. B.; Stehney, A. F. J . Nectrochem. SOC. 1949, 95,25-32. (21) Brainina, Kh. 2.;Kiva, N. K.; Belyavskaya, V. B. Elektrokhimiya 1965, 1 , 311-315. (22) Brainina, Kh. 2. Stripping Vofiammetry in Chemical Analysis; Wlley: New York, 1974; Chapter 1. (23) Rubinson, K. A. Chemlcel Analysis; Little, Brown and Co.: Boston, MA, 1967; Chapter 7.
RECEIVED for review October 23, 1987. Accepted February 5, 1988.
Electrochemical Oxidation of Bilirubin and Biliverdin in Dimethyl Sulfoxide Fathi Moussa,*vl Gaoussou KaDoute, Christine Herrenknecht, Pierre Levillain, and Frangois Trivin Laboratoire de Biochimie Appliquee, Laboratoire de Chimie Analytique et d'Electrochimie organique, Centre d'Etudes Pharmaceutiques Paris-Sud, F 92290 Chatenay-Malabry, France The mechanism of the electrochemicaloxidation of biiirubln was reexamined to explain the dlfferences in behavior reported in previous studies publlshed by various authors. The findings point to an ECEC mechanism. Only the first step of this mechanism is speciflc to bllirubin, and it may consequently be used as a crRerlon of purHy for this molecule.
In man, bilirubin (BR) is the product of the catabolism of the tetrapyrrolic prosthetic groups, mainly from hemoglobin '
Present address: H o p i t a l Saint-Joseph, Laboratoire de Biochimie, 7, rue Pierre Larousse, 75674 Paris Cedex 14, France.
(Figure 1). It constitutes a biological marker of hemolysis and hepatopathies. Neonatal hyperbilirubinemia can generate kernicterus, an encephalopathy with extremely serious clinical and social consequences that must be prevented. It is therefore important to be able to measure precisely the BR concentration in the blood. Some technical and analytical difficulties for measurement of bilirubinemia have not been solved in a satisfactory manner. Different circulating forms and a number of isomers may explain some of these difficulties. Current methods of determination do not take account of all these forms, and yet the latter do not all have the same physiopathologic significance. Moreover, there seems to be
0003-2700/88/0360-1179$01.50/00 1988 American Chemlcal Soclety
