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Anal. Chem. 1986, 58, 1488-1492
the response curve, in contrast to conventional methods which rely on a ratio of peak currents of catalytic and diffusioncontrolled voltammograms. Furthermore, an accurate initial guess for kl is not needed for proper convergence-initial errors up to *lOO-fold can be tolerated. The nonlinear regression/digital simulation approach is a general one that can be easily modified, in principle, to apply to any electrochemical mechanism. Although we have considered only reductions here, transposition to oxidations is straightforward. In addition to generality, a major advantage of the procedure is that it provides a reasonable computation time without sacrificing accuracy. For uncomplicated reversible electron transfer, the longest central processing unit (CPU) times for the procedure with experimental data were about 72 s for voltammetry and 130 s for chronocoulometry. This amounts to about 4 computing cycles for the latter and 13 cycles for the former. Regression analysis of experimental electrocatalytic data required approximately 16 min and involved about 20 computation cycles. The expanded grid technique is about 10 times faster than a procedure developed earlier in our laboratory using a uniform space grid simulation with a nonlinear regression technique based on the method of steepest descent (33).
ACKNOWLEDGMENT We are grateful to A1 Fry, Wesleyan University, for a uniform space grid digital simulation program for cyclic voltammetry at planar electrodes, which was a starting point for our work, and to David Gosser for suggesting the benefits in time to be gained with an expanding grid approach. Registry No. 4-Chlorobiphenyl,2051-62-9;phenanthridine, 229-87-8; 9,10-diphenylanthracene,1499-10-1.
(5) Rusling, J. F. Anal. Chem. 1983,5 5 , 1713-1718, 1719-1723. (6) Rusling, J. F.; Connors, T. F. Anal. Chem. 1983,5 5 , 776-781. (7) Shukla, S. S.; Rusling, J. F. J. Phys. Chem. 1985,8 9 , 3353-3358. (8) Evans, D. H.;Jimenez, P. J.; Kelly, M. J. J. Electroanal. Chem. 1984, 163, 145-157. (9) Wojclechowski, M.; O'Dea, J. J.; Osteryoung, J. J. Phys. Chem. 1983,8 7 , 4725-4730. 10) Meites, L.; Shia, G. A. Chemometrics; Kowalski, B. R., Ed., American Chemical Society: Washington, DC, 1977; pp 127-152. 11) Bond, A. M.; Henderson, T. L. E.; Oldham, K. 8. J . Elecfroanal. Chem. 1985, 191, 75-90. 12) Rusling, J. F. Trends Anal. Chem. 1984,3 , 91-94. 13) Feldberg, S. W. Elecfroanal. Chem. 1969,3 , 199-296. 14) J o s h T.; Pletcher, D. J. Electroanal. Chem. 1974, 49, 171-186. 15) Feldberg, S. W. J. Electroanal. Chem. 1981, 127, 1-10, 16) Seeber, R.; Stefani, S. Anal. Chem. 1981,5 3 , 1011-1016. 17) Rusling, J. F.; Kamau, G. N. J. Nectroanal. Chem. 1985, 187, 355-359. (18) MacKay, R. A. I n Microemulsions; Robb, I. D., Ed.; Plenum: New York, 1982; pp 207-219. (19) Andrieux, C. P.; Blocman, C.; Dumas-Bouchlat,J. M.; M'Halla, F.; Saveant, J. M. J. Nectroaflal. Chem. 1980, 113, 19-40. (20) Nicholson, S.; Shain, I. Anal. Chem. 1964,36, 706-723. (21) Santhanam, K. S. V.; Bard, A. J. J. Am. Chem. SOC. 1986, 88, 2669-2675. (22) Connors, T. F.; Rusling, J. F.; Owiia, A. Anal. Chem. 1985, 5 7 , 170-174. (23) Conti, P.; Marassl, R.; Misici, L. J. Elecfroanal. Chem. 1985, 184, 77-85. (24) Marquardt, D. W. J. SOC. Indust. Appl. Math. 1963, 1 1 , 431-441. (25) Christlan, S. D.; Tucker, E. E. Am. Lab. (fairfield, Conn.) 1982,Sept, 31-36. (26) Rusling, J. F.; Arena, J. V. J. Electroanal. Chem. 1985, 186, 225-235. (27) NLLSO Nonlinear Least Squares; CET Research Group: Norman, OK, 1981. (28) Egglns, B. R. J. Chem. SOC. Chem. Commun. 1972,427. (29) Bacon, J.; Adams, R. N. Anal. Chem. 1970,42, 524-525. (30) Bard, A. J.; Santhanam, K. S. V.; Maloy, J. T.; Phelps, J.; Wheeler, L. 0. Discuss. Faraday SOC. 198Er167-174. (31) Johnson, K. J. Numerical Methods in Chemistry; Marcel Dekker: New York, 1980. (32) Nicholson, R. S. Anal. Chem. 1985,3 7 , 1351-1355. (33) Arena, J. V.; Rusling, J. F. Universlty of Connecticut, 1984, unpub-
LITERATURE CITED
(34) Andrleux, C. P.; Saveant, J. M.; Zann, D. Nouv. J . Chim. 1984, 8 , 107-116.
(1) Rusllng, J. F.; Brooks, M. Y. Anal. Chem. 1984,5 6 , 2147-2153. (2) Rusling, J. F.; Brooks, M. Y.; Scheer, B. J.; Chou, T. T.; Shukla, S. S.; Rossi, M. Anal. Chem., in press. (3) Woodard, F. E.; Goodln, R. D.; Kinlen, P. J.; Wagenknecht, J. H. Anal. Chem. 1984,5 6 , 1226-1229. (4) Dombroski, A. J.; Meites, L.: Rose, K. J. Nectroanal. Chem. 1982, 137, 67-75.
lished work.
RECEIVED for review September 11,1985. Accepted February 3, 1986. This work was supported by U S . PHS Grant ES03154 awarded by the National Institute of Environmental Health Sciences.
Voltammetric Behavior of Iron(I I) at Electrodes Modified with Quaternized Poly(4-vinylpyridine) Cross-Linked with Bathophenanthrolinedisulfonic Acid M. J. Gehron and Anna Brajter-Toth* Department of Chemistry, University of Florida, Gainesville, Florida 3261 1
A polymer-modlfied electrode was prepared by use of quaternized poly(4-vinylpyrldine) cross-linked with bathophenanthrolinedisulfonicacid. The structure of the film was evaluated by cycllc voltammetry as a function of pH and the amount of Incorporated Fe( 11). The modified electrode was appiled to the determination of Fe( 11). Linear response was observed In the 10-8-10-7 M range.
In the last few years, development of polymer-modified electrodes has been a very active area of research triggered by their potential electrocatalytic applications (I). The potential for analytical applications of polymer modified elec0003-2700/86/0358-1488$01.50/0
trodes has been recognized (2) and a few practical applications have appeared (3-5). The use of polyelectrolytes containing ion-exchange and/or complexing groups for selective preconcentration of analytes is an attractive and simple way of preparing modified electrodes for analysis (6). Modification with polymers can avoid problems with saturation of sites, which can limit the linear range of similar monomer-modified electrodes. Full benefit of improved sensitivity and limits of detection as a result of preconcentration of analyte into the polymer film can only be obtained if the film permits efficient electron and mass transport. In order to ensure linearity of response, the structure of the polymer, which determines the overall rate of charge transport, should be independent of the com0 1986 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 58, NO. 7, JUNE 1986
position of the analyzed solution. It is clear from work to date that film structure will affect sensitivity, linear range, and limit of detection at polymer-modified electrodes (4-7). In the work described in this paper, a film was prepared in which structure and thickness were controlled, and the analytical response of this film into which analyte was preconcentrated through complexation was evaluated. The work described deals with electrodes modified with quaternized poly(4vinylpyridine) (QPVP), cross-linked with (4,7-diphenyl-l,l0-phenanthroline)disulfonicacid (bathophenanthrolinedisulfonic acid, BP). Modification of SnOz and Pt electrodes with this polymer has recently been described for use as an electrochromic display device (8). In this work, the QPVP/BP groups in the film were the preconcentration sites a t which Fe(I1) was complexed. EXPERIMENTAL SECTION The voltammetric and differential pulse polarographic (DPP) experiments were performed with a BAS 100 electrochemical analyzer. All potentials were measured and are reported vs. SCE. All chemicals were ACS Reagent Grade, unless specified,and were used without purification. PVP was obtained from Reilley Chemicals and was quaternized with freshly distilled CH31 (K & K ICN Pharmaceuticals) (9). The quaternized polymer was dialyzed for 3 days from saturated KC1 to replace I- with C1- in the polymer, Bathophenanthrolinedisulfonicacid (BP) was obtained from Aldrich. The cross-linkedpolymer was prepared by precipitating QPVP with BP from aqueous solutions. QPVP/BP precipitate is soluble in a tertiary 1:810 mixture of water:HCl:dioxane (8), and a known volume (1-5pL) of a 0.1-2% (w/v) solution was used to prepare the modified electrodes. The graphite electrodesubstrate that produced adherent, stable films while providing reasonable background currents was prepared by sealing a piece of pyrolytic graphite (Pfizer) (ca. 0.002 cm2) into glass tubing with epoxy. The electrodes were first polished on 600 grid Sic paper followed by polishing with Fisher Gamal 0.1-pm alumina on a Gamal cloth. Before the polymer film was applied, electrodes were cycled in 0.1M TFAA between 0.5 and 1.0 V to verify the absence of impurities on the electrode surface. Typically the first scan produced higher background current than the successive scans. The cycling was stopped when a steady-state response was obtained. Adherent and stable films were produced when the QPVP/BP polymer coating was dried for ca. 3 h. The electrodes were then used without any further pretreatment. Percent cross-linkingwas estimated from electrochemical results. First the total number of pyridinium sites was determined M from the maximum Fe(CN)63-coverage (obtained from Fe(CN)6" solution in pH 1.0 trifluoroacetic acid (TFAA) as a supporting electrolyte and measured in pure supporting elecM solution, Fe(CN)6" replaces BP from trolyte). At pH 1.0 in the film through ion-exchange. By use of a second electrode of the same area coated with the same amount of QPVP/BP, the number of -NCH3+ sites (BP cross-linkingsites) was determined from the Fe"BP coverage (Fe(I1)was preconcentrated from M solution). By assuming 100% efficiency and a stoichiometry of 1:l for all reactions, a low estimate of 20% cross-linking was calculated from these results. On the assumption of 100% efficiency of the cross-linking reaction, this corresponds to a 20% quaternization of the QPVP. If the stoichiometry favored in the homogeneous solution (1 Fe(CN)63-:3pyridinium sites, 1 BP:2 QPVP, 1 Fe(II):3 BP) is assumed, together with 100% efficiency of all reactions, a high estimate of 40% quaternization of the QPVP is obtained. As a result of the nonuniformity of the graphite substrate, film thickness measurements with a stylus profilometer were not successful. The thickness of the swollen polymer film was calculated from the estimated polymer density of l g/cm3 (IO)and the known amount deposited on the electrode surface. RESULTS AND DISCUSSION Evaluation of the Film Structure. Under conditions of rapid electron and mass transport, voltammetric peak currents for electroactive species incorporated into thin electrode
1489
250mV
/ ?'+ 1000
i
l0,OOO
il
Flgure 1. Cyclic voltammograms obtained in 0.1 M TFAA pH 1.7 at
QPVP/BP coated electrodes following incorporation of Fe(1I) from IO-' M Fe(I1) solution in 0.1 M TFAA. Scan rate was 200 mV s-'.
polymer films should obey the thin-layer equation (12). In the case of QPVP/BP films used to preconcentrate Fe(I1) the polymer bound Fen/InBP complex is the electroactive species. For phenanthroline (phen) complexes of Fe(II/III) the heterogeneous electron transfer rate constants (kso)are moderately high. Considering the structural similarities between phen and BP the kso values for their Fe(I1) complexes should be similar. For Fen/nl(phen), in 0.5 M H2S04at Pt, k,O = 5.8 X cm s-l (22) while, a t high ionic strength, the self-exchange rate constant is 3 X lo8 M-ls-l (23). The value of k,O =2X cm s-l for Fe(CN)63-/4-under similar conditions (14) while the self-exchange rate constant is on the order of lo5M-' 5-l (15). In view of these values, thin-layer behavior should be observed in the thin QPVP/BP/Fe"/'" films if the structure is sufficiently permeable and allows rapid counterion transport. QPVP/BP films with estimated thicknesses of 1000 and 10OOO 8, prepared on polished pyrolytic graphite were exposed to 10 mM Fe(I1) solution in 0.1 M TFAA a t pH 1.7 until steady-state response was reached. The cyclic voltammograms recorded when the electrodes were transferred to iron-free 0.1 M TFAA at pH 1.7 are shown in Figure 1. The potential at which Fe"/"'BP complex in the polymer reacts is ca. 0.820 V vs. SCE, which is in close agreement with the oxidation/reduction potential of the 1:3 Fe"/mBP complex in solution (12). The cyclic voltammograms obtained with the QPVP/BP coated electrodes into which Fe(CN)t- was incorporated in similar fashion are shown in Figure 2. From the comparison of Figures 1 and 2, it can be concluded that surface behavior prevails in 1000-8, and 10 000-8, films containing Fe"/"'BP while diffusional tailing indicating less efficient charge transport is apparent in thicker films with incorporated hexacyanoferrate. The qualitative observations are consistent with the dependence of peak current on scan rate, which is summarized in Table I, for the oxidation of Fe"BP and Fe(CN):- in films of different thickness. For FenImBP the slope of the log i, vs. log u plot at scan rates of 5-200 mV s-l is ca. 1 in films of thickness ranging from 1000 8,to 20000 A, which is characteristic of surface species; for Fe(CN)63-/4-adsorption character is only observed in thinner films with lower Fe(CN)64-coverage and concentration. Nernstian behavior of surface confined noninteracting species is manifested by symmetrical peaks (Up = 0) with
1490
ANALYTICAL CHEMISTRY, VOL. 58, NO. 7, JUNE 1986
Table I. Electrochemical Parameters (0.1 M TFAA, .01 M Fe(II), 0.01 M Fe(CN),4-) electrochemicalparameters at the following film thicknesses 19000 A
11000 A
2000 A
948 A
6.5 X 6.1 x 10-9
1.6 X 2.6 x 10-9
6.4 X lo4 1.6 x 10-9
1.1 x 10-9 1.5 X
0.342 0.032
0.145 0.024
0.320 0.080
0.116 0.016
0.598 0.750
0.672 0.817
0.777
0.895 0.929
50 100
14 84
8 80
0 59
137 141 196 176
86 80 169 147
82 78 176 137
82 78 196 137
2.28 x 10-10 1.07 x 10-7
3.76 X lo-* 1.22 x 104
4.04 x 10-9 8.17 X lo4
rT,mol/cm2 Fe(CN)63Fe(I1) concentration, M Fe(CN)64Fe(I1) log i, vs. log u
Fe(CN)63Fe(I1) AEp, mV Fe(CN):Fe(I1) mV
@ljZ!
Fe(CN)63-c A
Fe(I1) C A
DE,cm2/s Fe(CN)63Fe(I1)
Vi
1000
V l0,OOO
i
Flgure 2. Cyclic voltammograms obtained In 0.1 M TFAA pH 1.7 at QPVP/BP coated electrodes containing Fe(CN),3-,which was incorporated into the film from lo-* M K,Fe(CN),, 0.1 M TFAA solution. Scan rate was 200 mV s-'.
peak half-widths of 90.6/n mV (16). As is apparent from Table I, oxidation and reduction peak half-widths for FenlmBP confined in the QPVP polymer are consistently broader while surface Fe(CN)63-/4-peaks are consistently narrower than predicted for noninteracting Nernstian systems. In addition, Fe"/"'BP cathodic peaks are broader than anodic peaks and the peaks are shifted along the potential axis while Fe(CN)63-/" peaks remain symmetrical. The results show that neither FenimBPnor Fe(CN)63-/Pincorporated into the QPVP films follow the behavior predicted for ideal noninteracting Nernstian systems. Rather, the behavior of Fell/rllBPin the film is consistent with the presence of repulsive interactions (16)while that of Fe(CN)63-/" indicates attractive interactions between electroactive species in the film (16). In the QPVP/BP/Fe"/"' films the observed separation of cathodic and anodic peaks along the potential axis and the dissymmetrybetween the cathodic and anodic peak half-width indicate that in addition to the presence of repulsive interactions in the film the charge transfer between the electrode and the film is slow (16);the fact that thin-layer behavior is observed throughout the scan range indicates that electron and mass transport occur rapidly in the film (16). In contrast in QPVP/BP films containing hexacyanoferrate, when thinlayer behavior is observed, attractive interactions and rapid charge transport in the film as well as between the electrode and the film are indicated. From these results a model of the QPVP/BP film in pH 1.7 0.1 M TFAA can be proposed. As was described in the Experimental Section, percent quaternization of QPVP used
to prepare QPVP/BP films was estimated at 20-40%. In the film,quaternized pyridinium groups are cross-linked with BP. At pH 1.7 in 0.1 M TFAA the remaining pyridine groups in the film can be protonated (pyridine pK, = 5.0) creating a high density of positive charge. The high density of positive charge affects Fe"/"IBP response and is an apparent source of the repulsive interactions that were observed. In contrast, the positive interactions between electroactive species that are apparent when hexacyanoferrate is incorporated into the QPVP/BP film at pH 1.7 from 0.1 M TFAA show that the well-documented electrostatic cross-linking of protonated pyridine by negatively charged Fe(CN)63-/4-(17) causes the film to become more compact and rigid. This is especially pronounced in thicker, highly loaded films where diffusion behavior rather than thin-layer behavior was observed (Table
I).
The above model of the QPVP/BP film in 0.1 M pH 1.7 TFAA is supported by the values of the apparent diffusion coefficients of charge (DE) that were determined by chronocoulometryand are summarized in Table I. The values of DE for Fe'IIIIIBP were approximately 2 orders of magnitude greater than the DE values for Fe(CN)63-/4-in the same films. The values of DE for QPVP/BP/Fell/lll changed from 1.2 X lo+ to 8.2 X cm2s-* with the change in concentration of Fe"/'"BP in the film from 0.024 to 0.080 M while DE in films to 2.3 X containing Fe(CN),3-/P changed from 3.8 X cm2 s-l with the change in hexacyanoferrate concentration from 0.145 to 0.342 M. Although the absolute values of DE are a high estimate reflecting the uncertainty in film thickness measurements, their relative orders of magnitude can be compared. The values of DE were calculated by assuming a swollen polymer density of 1 g/cm3 (10) and the known amount of polymer deposited on the electrode surface. For both systems the DEvalues decreased with the increase in concentration of electroactive species in agreement with the results reported for similar films (18, 19),probably reflecting the effect of increased interactions in the film. The film thickness did not have a systematic effect on DE. The proposed model indicates that the QPVP/BP film is suitable for the determination of Fe(I1) in media where protonation of pyridine groups leads to an open, permeable structure of the film. A small loss in sensitivity can be expected as a result of peak broadening caused by nonideal surface behavior. Application of QPVP/BP Films to the Determination of Fe(I1). The QPVP/BP electrode films were evaluated for
ANALYTICAL CHEMISTRY, VOL. 5 X lO-'M
1491
58, NO. 7,JUNE 1986
Fe!lII
CGII 20,000
8
IO-'M
Fe!nI
2000 i 1 0 ' ' ~ T F A A INC I M TFAA MEAS
INITIAL MEASUREMENT TIMES
(d --
Q
- - _ _ _ _+!
2 MIN
-- - 50
0
100
(MIN
INITIAL MEASUREMENT
150
I
Flgure 5. i,, of Fe"BP/QPVP in 0.1 M TFAA pH 1.7 vs. time of incorporation from 5 X lo-' M Fe(I1) M TFAA pH 5.0. The dashed line represents different incorporation times before the first measurement in 0.1 M TFAA pH 1.7. The solid line represents response in 0.1 M TFAA pH 1.7after shown additional Incorporation time M Fe(I1) pH 5.0. from 5 X -
A. S L R
A
I
30
0
J
(MINI
60
/
,IF T FAA
I
Figure 3. Cyclic voltammetric oxidation current of Fe%P/QPVP vs. time of incorporation of Fe(I1) into the QPVP/BP film from 5 X M Fe(I1): (A) A,0.1 M TFAA, pH 1.5;(E) 0, 0.001 M TFAA pH 3.0; (C) 0, M TFAA/O.l M NaF pH 5.0solution. The last point In (E) and (C) was obtained after electrode transfer to 0.1 M TFAA pH 1.5. 150
, l M T F A A / (01 M
Fe(CN1;-
Fe (E)
d
---0
1
1
E.
I
+0.700
T
1MnR
1
!AL 20,000H 20008
,oo-
4
i
&3-+--
--a
.
I
0
._a
E IUOLT 1
1
0
20
40
60
I
80
(MIN)
Figure 4. i , of Fe(CN);and Fe%P In QPVP films vs. time of incorporation from lo-* M solution in 0.1 M TFAA. ,/ was measured in 0.1 M TFAA pH 1.7 at scan rate 200 mV s-'.
the determination of Fe(I1). Metal ion was preconcentrated through complexation and was determined by measuring current at the oxidation potential of the complex in metal-free solutions. Medium transfer was necessary to avoid mediation effects between polymer bound complex and Fe(I1) in solution (8). The preconcentration/determination approach is similar to that used in stripping analysis (20). Preconcentration conditions into a film whose structure is a function of pH have to be a compromise. Considering 20% quaternized poly(viny1pyridine) as a collection of vinylpyridine groups (molar mass of monomer 103.9 g), the concentration of the vinylpyridine monomer in the film is ca. 7.5 M if the
Flgure 6. Cyclic voltammogram (A) and differential pulse polarogram (E) of Fe"BP/QPVP in 0.1 M TFFA pH 1.7 following 10 min of incorM TFAA pH 5.0 solution, transfer to poration from lo-' M Fe(I1) 0.1 M pH 1.7TFAA solution, and additional 10 min incorporation from Fe(I1) solution. Estimated film thickness 2000 A. (A) Scan rate v = 200 mV/s; (E) scan rate v = 4 mV/s, pulse amplitude = 50 mV, pulse width = 50 ms, drop time = 1000 ms.
density of the swollen film is assumed as 1 g/cm3 (10). At pH
