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Anal. Chem. 1989. 6 1 . 570-573
as an associated charged carrier in the membrane phase. Salicylate levels in biological samples can be measured (without significant interference from physiological chloride) with the Sn[TPP]C12-basedelectrode, although pH sensitivity of the existing membrane formulation restricts practical applications to samples buffered below pH 6.0. Under such conditions, for samples containing proteins (e.g. serum), it is not yet clear how measured salicylate levels in diluted samples will correlate to true "free" salicylate levels in undiluted samples under physiological conditions (pH 7.2-7.5) or total salicylate concentrations as determined by the classical Trinder method. Such clinically related correlation studies are currently in progress, as are efforts to decrease the response time and pH sensitivity of this membrane electrode system.
ACKNOWLEDGMENT The authors wish to thank Dana Wang (Oberlin College) for performing the experiments with membranes doped with Sn(OEP)C12. LITERATURE CITED Wuthier, U.: Pham, H. V.; Zund, R.; Welti, D.; Funk, R. J. J.; Bezegh, A.; Ammann, D.; Pretsch, E.; Simon, W. Anal. Chem. 1084, 56, 535-538. Schulthess, P.; Ammann, D.; Krautier, B.; Caderas, C.; Stepanek, R.; Simon, W. Anal. Chem. 1085, 57, 1397-1401. Schulthess, P.; Ammann, D.; Simon, W.: Caderas, C.; Stepanek. R.: Krautler, B. Heiv. Chim. Acta 1084, 67,1026-1032. Chang, Q.;Meyerhoff, M. E. Anal. Chim. Acta 1086. 786,81-90, NishMe, H.; Ohyanagi, M.; Okada, 0.; Tsachkla, E. Macromolecules 1087, 2 0 , 417-422.
(6) Chaniotakis, N. A.; Chasser, A. M.; Meyerhoff, M. E.; Groves, J. T. Anal. Chem. 1088, 60,185-188. (7) Stewart, M. S.;Watson, I. D. Ann. Ciin. Biochem. 1087, 2 4 , 552-565. (8) Smith, M. J. H.; Smith, P. K. The Saiicyiates , A Criticai Bibliographic Review; Interscience: New York, 1966. (9) Trinder, P. Biochem. J . 1054, 57,301-303. (10) Yon, K.; Bittikofer, J. A. Ciin. Chem. 1084, 3 0 , 1549-1551. (11) Walter, L. J.; Biggs, D. F.; Coutts, R. T. J . Pharm. Sci. 1084, 63, 1754-1758. (12) Dadgar, T.; Climax, J.; Lambe, R.; Darragh, A. T. J . Chromatogr. 1085. 342, 315-321. (13) Levy, G. Drug Metab. Rev. 1070, 9 ,3-19. (14) Relman, A. New Engl. J . Med. 1088, 378, 245-246. (15) Choi, K. K.; Fung, K. W. Anal. Chim. Acta 1082, 738,385-390. (16) Mitsana-Papazoglou, A.; Diamantis. E. P.; Hadjioanou, T. P. Anal. Chim. Acta 1084, 759,193-196. (17) Buchler. J. W. S. I n The Porphyrins; Dolphin, D., Ed.; Academic Press: New York, 1978; pp 406 and 436-438. (18) Guibault, G. G.; Durst, R. A.; Frant, M. S.:Freiser, H.; Hansen. E. H.: Light, T. S.;Pungor, E.; Rechnitz, G. A,; Rice, N. M.; Rohm, T. J.; Simon, W.; Thomas, J. D. R. Pure Appi. Chem. 1078, 4 8 , 129-132. (19) Ma, S. C.; Chaniotakis, N. A.; Meyerhoff, M. E. Anal. Chem. 1088, 60,2293-2299. (20) Eisenman, G. Glass Electrodes for Hydrogen and Other Cations; Marcel Dekker: New York, 1967; Chapter 5 . (21) Flower, R. J.; Moncada, S.;Vane, J. R. I n The PharmacoiogicaiBasis of Therapeutics: Gilman. A. G., Goodman, L. S.,Rail, T. W., Murad, F., Eds.; McMillan: New York, 1985; Chapter 29. (22) Brodie, B. B.; Udenfriend, S . ; Coburn, A. F. J . Pharmacoi. Exp. Ther. 1044. 80. 114-117.
RECEIVED for review September 14,1988. Accepted December 5, 1988. We gratefully acknowledge the National Institutes of Health (GM-28882) and Mallinckrodt Sensor Systems for supporting this work.
Effects of Added Plasticizer on Redox Ion Charge Transport in Quaternized Poly(viny1pyridine) Films Kwok-Keung Shiu, Ronald Chemerika, and D. Jed Harrison* Department of Chemistry, University of Alberta, E d m o n t o n , Alberta, Canada T6G 2G2
Ouaternlzed poly(vinylpyrldlne) (QPVP) fllms on carbon electrodes can be modHied by addltlon of dloctyl phthalate (DOP) as a plasticizer. The resulting films are more flexible and less susceptible to dlssolvlng in aqueous solution. Chronoamperometry shows the diffusion coefflcient for charge transport by Fe(CN):-, alizarin red S, and alizarin complexone In plasticized OPVP films is 2-5-fold greater than In unplastlclzed fllms, dependlng on the amount of plasticizer added and the redox Ion examlned.
Charge-transfer rates through polymer films on chemically modified electrodes (CMEs) are fundamental to the behavior and application of such electrodes ( I ) . The overall chargetransport process can be described by the laws of diffusion and its rate expressed as a diffusion coefficient for charge transport, D,, (2-4). Electron transport through modifying polymer films is generally believed to involve electron-hopping reactions between redox centers and/or site-site exchange of redox species, depending on the nature of the redox sites and the polymer film. The overall mechanism and rate are governed by the electron self-exchange rate between redox centers and the diffusion coefficient for mass transport of the redox
* Author to whom correspondence should be addressed. 0003-2700/89/0361-0570$01 50/0
center, which is related to mobility of associated solvent molecules in the film and segmental motion of the polymer chains ( 1 , 3, 5 ) . Frequently, D,, is 2-3 orders of magnitude smaller in the polymer film than the diffusion coefficient for the same redox couple in solution, and this limits the current density attainable for a given film thickness. As well, analytical applications of CMEs can require diffusion of analyte into the film, and this may be hindered by low diffusion coefficients for mass transport, D, (6-10). Increasing the extent of solvent swelling of the polymer matrix (11, 12) and inducing heterogeneity in the polymer film through the use of polymer mixtures (13) are two methods that have been found to increase both D,, and DmV Miller and Majda (14, 15) have reported that lateral charge transport in bilayer assemblies can be increased in the presence of octanol in solution and suggest this is due in part to increased fluidity of the bilayer when octanol is intercalated. In this paper we examine the use of a plasticizer in preparing quaternized poly(viny1pyridine) (QPVP) films and its effect on D,, for redox species ion-exchanged into the film. Addition of plasticizer to a polymer is known to increase the mobility and flexibility of the polymer segments (16,17) and is a commonly used method to improve ionic conductivity in polymer matrices used in ion-sensitive electrodes (18-21). Through this effect, or by direct solvation of redox ions in !C 1989 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 61, NO. 6, MARCH 15, 1969
QPVP, it was expected that D,, could be increased, as was found t o be the case.
EXPERIMENTAL SECTION Dioctyl phthalate (DOP), &,a'-dibromo-p-xylene, alizarin red S, and alizarin complexone were used as received from Aldrich, as was dibromodecane (Eastman). Water was doubly distilled from alkaline permanganate. All other chemicals were of reagent grade. Synthesis of 64% quaternized poly(viny1pyridine) (QPVP) has been reported elsewhere (6). Poly(viny1pyridine) (500000 MW) was a kind gift from Reilly Tar and Chemicals. Cyclic voltammetry was performed with a PAR 273 potentiostat, or a Pine RDE-4, and a Kipp and Zonen BD90 XY recorder. Chronoamperometry was performed with a PAR 273 interfaced to an IBM PC-XT as controller and data acquisition system. Modified carbon electrodes were prepared by allowing a methanol solution of the appropriate components to evaporate under a methanol atmosphere (-3 h) and then heat-treating a t 60 "C (2 h) to promote cross-linking (6). The cross-linking agent was always present a t a constant molar ratio of 5:1, QPVP to reagent, which is sufficient to completely quaternize the remaining free pyridine. Free-standing films were prepared by casting on Teflon substrates, and the density of these films was determined in the dry state. The extent of polymer swelling in aqueous solution was determined by measuring the thickness of freestanding films with a micrometer before and after aqueous soaking for 20 min to 2 h. Coatings of -40-nm thickness on polished Si slides and -5-pm thickness on glass microscope slides were prepared by spin coating, and their change in thickness after aqueous exposure, pH 9.2, was also determined by surface profilometry (Alpha Step Profilometer, Tencor Industries). Thiclmess measurements of the wet polymer were much less precise than those of the dry material for both methods, possibly due to a decrease in polymer hardness. Polymer coverage in moles of pyridine units per square centimeter, rPy, was determined by cyclic voltammetry (10 mV/s) following extended ion exchange of Fe(CN)," into the film at pH 2. The Fe(CN)64-was exchanged back out by exposing the electrode to 4 M KC1 for 1.5 h or longer. At pH 2 any remaining tertiary pyridine is protonated so the total number of pyridine sites can be determined. Only small discrepancies of 1 4 % were observed when rPywas also measured a t pH 7, indicating alkylation by the cross-linking agent leads to nearly complete quaternization of the film. For electrodes on which a known weight of QPVP was deposited over a portion of the electrode surface, rpydetermined by Fe(CN):- exchange was in agreement with the weight of polymer deposited. This confirmed that electrochemical determination of rpywith Fe(CN):- is a relatively reliable method (22). The diffusion coefficient for charge transfer was usually determined by chronoamperometry using the Cottrell equation i = n F A D , 1 / 2 r , ~ o ~ / d ( ~ t where ) 1 ~ 2 ,n, F , A, and t have their usual is the coverage of redox species in mol/cm2, and meanings, rredox d is polymer thickness. A potential step was performed in a solution of supporting electrolyte to determine the charging current, before ion-exchanging the redox ion into the film from a 1 mM solution. This current was then subtracted from the current observed with redox ion present in the film, giving linear Cottrell plots at shorter times, with an intercept of zero. Coverage of redox ion, rdox,was measured by cyclic voltammetry (10 mV/s) immediately following the potential step. For some electrodes D,, was also evaluated by rotating disk, to determine the charge-transfer-limited current by a steady-state method, using thick films to ensure charge transport was the rate-limiting step. This condition was confirmed as described previously (22) by the independence of limiting current on solution concentration of the redox couple and by the agreement between D, values determined by rotating disk and chronoamperometry.
RESULTS AND DISCUSSION Addition of a plasticizing agent t o a polymer commonly produces a composite with thermal and mechanical properties differing from the pure polymer (16,17). Free-standing films of 64% quaternized poly(viny1pyridine) (QPVP), with a constant amount of dibromoxylene as cross-linking agent
571
Table I. Density of QPVP and Plasticized Films molar ratioo DOP / compn QPVP/diBrb QPVP I I1 I11
5 5 5
densitv. g/cmj'
0
0.58
0.5 1
0.68
0.81
molar densitv.c mmol/cm3 "
I
2.4 1.6 1.3
"Molar ratio of components in film casting solution expressed relative to the moles of total pyridine sites. bdiBr is dibromoxvlene In terms of total number of Dvridine sites. sufficient to quaternize the remaining pyridine groups, and a variable amount of dioctyl phthalate (DOP) as plasticizer added were prepared to evaluate properties of the composite films. Films prepared with QPVP and dibromoxylene alone (type I) were very brittle, tending t o shatter when handled or if cut into smaller pieces. Following 24-48-h exposure t o aqueous solution, p H 7, such films were solvent swollen and had broken u p into many smaller pieces. Films were also prepared with DOP added a t a 0.5:l molar ratio of DOP to moles of pyridine moieties (type 11)and a 1:l DOP to pyridine unit molar ratio (type 111). The same amount of cross-linking agent was added to plasticized membranes as to unplasticized QPVP films. Both compositions I1 and I11 gave flexible free-standing films that were durable during handling and were easily cut into smaller pieces without damage. Such films appeared to swell less than type I films after 24-48-h exposure to aqueous solution and did not break apart or lose mechanical strength. The densities of the different film compositions were determined for dry films (Table I). The film composition following solvent evaporation was assumed to be that of the casting solution. The results show that the film density increases with addition of DOP. However, Table I shows that the molar density of the total number of pyridine sites in the composite films decreases with addition of DOP, indicating the contribution from the partial molal volume of DOP is significant. To evaluate the effect of solvent swelling, films were prepared on solid substrates and their thickness was determined by profilometry before and after soaking in aqueous solution. Within experimental error there was no difference in swelling for the three compositions following soaking for 20 min to 2 h, although as noted above extended exposure to aqueous solution swells pure QPVP films more than the other compositions. An increase in thickness of 15-25% was observed for -40 nm thick films on Si after 20 min t o 2 h of soaking, and -5 pm thick films on glass showed an increase of 1 0 4 0 % . Free-standing films of 0.1-0.2-mm thickness also showed a 10-25% increase for all three films. Due to the poor precision in determining wet film thickness, the values of D, have been calculated from the density of the dry films. Since electrodes were studied within the first half t o four hours of exposure to solution, all compositions will have swelled t o about the same extent. The effect of added plasticizer on D,,in QPVP films was examined for three redox systems, Fe(CN)64-, alizarin red s (ARS), and alizarin complexone (AC), at p H values of 7 and
8
?H
II
0
ALIZARIN RED S (ARS)
II 0
CH,COOH
ALIZARIN COMPLEXONE (AC)
9.2. The coverage of QPVP expressed as the number of pyridine moieties, rpy, was in the range 1.4 X lo-* to 2.2 X mol/cm2. The coverage of redox anions incorporated in the
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ANALYTICAL CHEMISTRY, VOL. 61, NO. 6, MARCH 15, 1989
Table 11. Effect of Plasticizer on Do, in QPVP Films
std error ( 9 5 7 0 ) ~ redox anion
polymero compn
Fe(CN),4-d
I I1 I11
I
ARSe
I1 I11
Ace
I I1 I11
no. of obsvns
coverage range,* %
101oD,,, cm2/s
10 5 19 28 28 34 31 31 31
30-60 30-45 25-40 10-70 15-80 15-40 35-95 30-75 25-15
8.0 13 38 1.6 2.0 3.3 0.5 1.2 1.7
x
cm2/s f3.6 f5.6 fll f0.4 f0.5 f0.7 fO.l f0.3 f0.3
'Polymer compositions as in Table I. 'Percentage of pyridinium sites charge-compensated by redox anion. Precision of the mean expressed as the standard eror within 95% confidence limits. dMeasuredby potential step from -0.3 to +0.6 V vs SCE in 0.1 M phosphate, pH 7.0. eMeasured by potential step from -0.4 to -1.1 V vs SCE in 0.1 M NH,Cl, DH 9.2. films varied from (0.22 to 2.2) x lo-@mol/cm2 for Fe(CN)64and (0.26 to 6.8) X lo-@mol/cm2 for the alizarin derivatives. A decrease in D,, was observed as the coverage of redox anion increased for a given value of rpyas is commonly observed for other systems. This is believed to result from the effects of ionic cross-linking on mobility in the polymer matrix (I, 3,5). The data presented in Table I1 was obtained for a range of values of the ratio rredox/rpy, but is given as an average for all ratios to indicate the general trend induced by addition of plasticizer. The range of DCtvalues obtained for a given polymer composition and redox ion was treated by calculating the standard error of the mean to the 95% confidence limit given by eq 1 (23), where p is the true mean, 5 and s are the p -2 =
fts/n1J2
(1)
experimental mean and standard deviation, respectively, n is the number of measurements, t is the value of Student's t for the 95% confidence interval, and ts/n1i2is the standard error for that interval. By use of the Kolmogorov-Smirnov test (24),the data was found to obey a normal distribution, indicating the above analysis is appropriate. The value of D,, for Fe(CN)64-in poly(viny1pyridine) and partially quaternized QPVP is typically (0.5-1) X lo-@cm2/s at low pH (3,22), where the free pyridine sites are protonated and the polymer is apparently more swollen with H 2 0 (9). At pH 7 D,,in the nearly fully quaternized films used in this cm2/s. The data in Table I1 shows study is (8.0 f 3.6) x that when an equimolar ratio of pyridine sites to DOP is used, De, for Fe(CN)64-in the film is increased about 5-fold. Comparison of the standard error of the means indicates the change in De, is statistically significant for a 1:l ratio. However, for a DOP to pyridine site ratio of 0.5:1 the values of D,, do not differ at the 95% confidence interval, although they are statistically different at the 90% interval. This may in part reflect the fact only five measurements were made for the type I1 film. The alizarin derivatives differ considerably from Fe(CN):in being fairly large anions with a potential for hydrophobic interaction with the plasticizer and, in the case of AC, in having well separated charge sites. The charge on these ions at pH 9.2 is 2- for ARS (25) and about 80% is presented as 2- and 20% as 3- for AC (26). These quinones can be used in the analysis of La3+by ion exchange into QPVP films as we have recently shown (6). They are similar in many respects to other complexing ligands that have been bound in modifying films for electroanalysis (7-9). The data in Table I1 shows that both ARS and AC exhibit a statistically significant increase in D,, for composition I11 versus films with no plasticizer (type I), with D,, increased by a factor of about 2 for ARS and 3.5 for AC. For composition I1 both ARS and AC show an increase in D,, over composition I; however, the increase is not significant within the 95% confidence interval
for ARS, while it is for AC. The addition of plasticizer appears to have little other effect on the quinone redox processes: the peak potentials do not change, and the number of electrons in the reduction also remains unchanged. This indicates that the polymer film environment remains relatively unchanged despite the large amount of hydrophobic plasticizer added. The effect of added DOP on metal complexation by ARS and AC in QPVP films was also examined. We have previously reported that La3+is complexed by both quinones in QPVP, resulting in 150-200-mV shifts in peak reduction potential for the ligands (6). However, difficulties with poor mass transport of La3+ in the film require that QPVP films be no more than 30 A thick and result in a detection limit of about 0.1 mM La3+. When a 1:l ratio of pyridine sites to DOP is used, with cross-linking reagent also added, polymer film thicknesses of 100 still respond to La3+ in the manner of the thinner composition I films. More importantly, La3+can be determined at concentrations of 20 pM, indicating improved extraction and transport of the metal ion in the polycationic matrix. The results are consistent with an increase in D,, for La3+ in the plasticized film. The Dahms-Ruff equation has been shown to describe D,, a t least qualitatively in polymer films (27, 28). Following Buttry and Anson (28), we can express this relation as
-
D,, = D,,
a
+ De, = D,, +
r
where De, is the diffusion coefficient for the electron-hopping or self-exchangeprocess. De, depends on the distance between redox sites at which electron transfer occurs, 8, the redox site concentration C, and the apparent electron self-exchange rate in the polymer film, which itself depends on the true electron self-exchange rate k,, and the diffusion-controlled rate constant kd. The magnitude of k d can be estimated by the Smoluchowski equation and is directly proprotional to D,, (28,29), indicating that even when De, > D, the value of the diffusion coefficient for charge transport can still be strongly dependent on the mass transport rate of the redox ion in the film. This dependence arises since motion of the redox sites must occur to allow the species to attain sufficient proximity for electron transfer to occur ( I ) . The above discussion is important since we (6) and others (30) have recently shown that electron hopping plays a dominant role in charge transport by ARS and AC in polycationic films. However, eq 2 shows that the increase in D,, for the redox couples studied, and the apparent increase in D,, for La3+with added plasticizer, can easily be interpreted in terms of an increase in mass transport rates even when De, is dominant, since De, is a function of Dmk An increase in the intrinsic self-exchange rate k,, with added DOP cannot be ruled out, although the similarity of the change in D,, for both Fe(CN),4- and the quinones, which are very dissimilar redox
ANALYTICAL CHEMISTRY, VOL. 61, NO. 6, MARCH 15, 1989
couples, suggests this is not the case. Increased mass transport rates in the presence of DOP could arise from an increase in solvation of the redox ions, although the relatively poor solvation of ions by the ester argues against this. Another possibility is that the decrease in pyridinium site density with added plasticizer results in less effective ionic cross-linking. However, the expected decrease in dielectric strength of the matrix with added DOP would enhance ion pairing with the fixed pyridinium sites, and it is difficult to predict the net effect. The most likely cause for increased transport rates is an increase in the mobility and flexibility of the polymer chain segments. This is a well recognized effect of using plasticizers, and polymer segmental motion has been identified as an important factor in charge transport (1-5). When De, is important, the rate of collisions resulting in electron transfer can be controlled by segmental motion of the polymer (1,5 ) or the viscosity of the polymer matrix. For the more bulky alizarin complexone anion it is possible that both solvation of the polymer chain and AC by added DOP is important. These combined effects could be responsible for AC showing a more significant increase in D,,a t a lower degree of plasticization than does ARS or Fe(CN)64-.
CONCLUSION In addition to increasing charge transport rates, the presence of plasticizer decreases the solvent swelling and increases the durability of the polymer film. This should be of significant benefit, since even with an added cross-linking agent QPVP films on carbon electrodes tend to slowly dissolve when stored in aqueous solution over several days, unless an electrostatic cross-linking agent such as Fe(CN)63-/4-is present. Perhaps more interesting is the possibility of enhancing selectivity of complexing ligands incorporated in the polymer film by judicious choice of the plasticizer. For poly(viny1 chloride) based ion-selective electrode membranes the choice of plasticizer can alter the selectivity of the ion carrier (19-21). Significant effects can arise from relatively subtle changes in the plasticizer, such as found for neutral-carrier-based Na+ electrodes for which the use of dioctyl adipate rather than dioctyl sebacate leads to higher selectivity for K+ than for Na+ (20). Whether such effects on complexation can occur in a more polar matrix such as Q P W is not known and is currently under investigation.
ACKNOWLEDGMENT We thank J. Buechler of Reilly Tar and Chemical Corp. for a generous gift of 400000 and 500000 MW poly(vinylpyridine),
573
and the Alberta Microelectronic Centre for use of the surface profilometer. Registry No. DOP, 117-81-7; ARS, 130-22-3; AC, 3952-78-1; Fe(CN)64-,13408-63-4; ((Up’-dibromo-p-xylene)(vinylpyridine) (copolymer), 49627-73-8.
LITERATURE CITED Murray, R. W. Electroanal. Chem. 1984, 13, 191. Daum, P.; Lenhard, J. R.; Rolison, D. R.; Murray, R. W. J. A m . Chem. SOC.1980, 102, 4649. Oyama, N.;Anson, F. C. J. Hectrochem. SOC. 1980, 127, 640. Peerce, P. J.; Bard, A. J. J. Electroanal. Chem. Interfacial Nectrochem. 1980, 114, 89. Kuo, K. N.; Murray, R. W. J. Nectroanal. Chem. Interfacial Electrochem. 1982, 131, 37. Shlu, K. K.; Harrison, D. J. J. Nectroanal. Chem. Interfacial Nectrochem., in press. Guadalupe, A. R.; AbruRa, H. D. Anal. Chem. 1985, 5 7 , 142. Hurrell, H. C.; AbruRa, H. D. Anal. Chem. 1988, 6 0 , 254. Gehron, M. J.; Brajter-Toth, A. Anal. Chem. 1986, 58, 1488. Cox, J. A.; Kulesza, P. J. Anal. Chim. Acta 1983, 154, 71. Anson, F. C.; Sav6ant, J. M.; Shigehara, T. J. Am. Chem. SOC.1983, 105, 1096. Van Koppenhagen, J. E.: Majda. M. J. Electroanal. Chem. Interfacial Electrochem. 1987, 236, 113. Montgomery, D. D.; Anson, F. C. J. A m . Chem. SOC. 1985, 107, 3431. Miller, C. J.; Majda, M. J. A m . Chem. SOC. 1988, 108, 3118. Miller, C. J.; Majda, M. Anal. Chem. 1988, 6 0 , 1168. Plasticization and Plasticizer Processes; GouM, R. F., Ed.; Advances in Chemistry 48. American Chemical Society: Washington, DC, 1965. The Technology of Plasticizers; Sears, J . K., Darby. J. R., Eds.: John Wiley & Sons: New York, 1982; Chapter 2. Fiedler. U.; Ruzicka, J. Anal. Chim. Acta 1973, 6 7 , 179. Fiedler, U. Anal. Chim. Acta 1977, 8 9 , 111. Fiedler, U. Anal. Chim. Acta 1977, 89, 101. Craggs, A.; Keil. A.; Moody, G. J.; Thomas, J. D. R. Talanta 1975, 2 2 , 907. Harrison, D. J.; Daube, K. A.; Wrighton, M. S. J. Nectroanal. Chem. Interfacial Hectrochem. 1984, 163, 93. Laitinen, H. A.; Harris, W. E. Chemical Analysis, 2nd ed.; McGraw-Hill: New York, 1975; Chapter 26. Sokal, R. R.; Rohlf, F. J. Biometry, 1st ed.; W. H. Freeman & Co.: San Francisco, 1969; Chapters 6, 16. Masoud, M. S.;Tawflk, S. E.; Zayan, S. E. Synth. React. Inorg. Met .-Org. Chem . 1984, 14, 1. Ingman, F. Talanta 1973, 2 0 , 135. White, H. S.;Leddy, J.; Bard. A. J. J. Am. Chem. SOC. 1982. 104, 4811. Buttry, D. A.; Anson, F. C. J . A m . Chem. SOC. 1983, 105, 685. von Smoluchowski, M. Phys. 2. 1918, 17, 557-571, 585-599. Ohaska, T.; Oyama, N.; Takahira, Y.; Nakamura, S. J. Nectroanal. Chem. Interfacial Electrochem. 1988, 247, 339.
RECEIVED for review July 8,1988. Accepted December 1,1988. We thank the Natural Sciences and Engineering Research Council of Canada and the Central Research Fund of the University of Alberta for support of this research.
