Anal. Chem. 1989, 6 1 , 1763-1768
1763
Cyclic Voltammetry at Microhole Array Electrodes Koichi Tokuda*
Department of Electronic Chemistry, Graduate School at Nagatsuta, Tokyo Institute of Technology, Nagatsuta, Midori-ku, Yokohama 227, Japan Ken-ichi Morita' and Yoshihiro Shimizu
Basic Research Laboratories, Toray Industry, Inc., 111 1 Tebiro, Kamakura 248, Japan
Mlcrohoie array electrodes have a unique characteristic of exhlbltlng steady-state current. Cyclic voltammograms at microhole array electrodes are treated theoretlcally for a reverslble redox-electrode process, and analytlcai expressions for current-potential curves are presented. Cyclic voltammetry of a [Fe(CN),]4-'S- couple is carrled out at these microhoie array electrodes constructed from a carbon fiberepoxy composite. The theoretical results are applied to the analysis of the experimental results, and a reasonable value for the diffusion coefficient is obtained from the analysis of the ratlos of maximum (peak) currents of cyclic voltammograms to the steady-state currents.
Microhole array electrodes, which can be fabricated by electrochemical etching of a carbon fiber-epoxy composite, have proved to be promising as an oxygen sensor ( I ) , a biosensor (2), and a flowmeter (3). One of the most important features of the microhole array electrodes is that the steady-state current is readily reached. This is because the convection of the bulk solution has little effect on the mass transfer within the microholes, and thus a linear concentration gradient of the electroactive species is established when its concentration just outside of the microholes is kept constant by stirring the solution. Extensive applications of these electrodes for electroanalytical purposes are under consideration, and their design also shows promise in the analysis of kinetic studies. However, since an easy means of construction has only recently been achieved ( I ) , the theory for various voltammetric methods including kinetics with these electrode has not been solved as yet. Understanding of the fundamental characteristics of such microhole array electrodes is desirable for their use in the sensors mentioned above as well as in other fields. Recently Bond et al. ( 4 ) reported a comparison of the chronoamperometric response a t inlaid and recessed disk electrodes. They obtained equations for the transient current response at a single recessed disk electrode under conditions of stirred and quiescent solution. The microhole array electrode fabricated from the carbon fiber-epoxy composite can be regarded as an ensemble of a number of such recessed disk electrodes. This allows amplification of signals. Cyclic voltammograms obtained with the microhole array electrodes are quite similar in shape to those for stationary rotating disk, ultramicrosphere or ultramicrodisk electrodes. In other words, sigmoidal voltammograms are obtained at slow potential sweep rates, which is expected from the linear concentration gradient in the microholes a t the steady state (1, 4 ) .
This paper is devoted to the derivation and the calculation of reversible current-potential curves at microhole array Present address: Toin University of Yokohama, 1614 Kuroganecho, Midori-ku, Yokohama 227, Japan.
electrodes and presents analytical expressions for all sweep rates. Theoretical results have been compared with experimental ones obtained for the redox-electrode reaction of hexacyanoferrate(II/III) at carbon fiber microhole array electrodes of various depths. Relatively good agreement between experimental and theoretical results has been obtained.
THEORY Mathematical Model of the Electrodes. We consider the microhole array electrode as an ensemble of N recessed microdisk electrodes of equal diameter d and depth L as shown in Figure 1A. Although the scanning electron micrographs of the etched carbon fibers (1)have revealed that the surfaces of the carbon fibers are not flat but conical or bullet shaped as schematically shown in Figure lB, it is assumed in the model that each microhole electrode has a surface area equal to the cross-sectional area of the carbon fiber or that of the microhole. Thus the total geometric surface area of the electrode A is equal to N(*d2/4). Since each microhole electrode is regarded as an independent unit, it may suffice to consider mass transport in the single microhole and then the totalcurrent will be obtained from multiplying the current density by the total electrode area A . When the solution is well stirred, the concentration of the electroactive species at the mouths of the microholes may be maintained a t its initial value. Consider a simple redox-electrode reaction
R
2
0 + ne-
(1)
for which we make the following assumptions: (a) both species R and 0 are soluble in solution; (b) the reaction proceeds so rapidly that the Nernst equation holds at the electrode surface; (c) these species have equal diffusion coefficients D ; (d) the solution contains an excess of the supporting electrolyte; (e) before electrolysis only the reduced form R of the redox couple is present in the solution, the concentration of which is denoted by cRo;and (f) initially the electrode potential E is set at a value Ei which is sufficiently less positive than the formal potential E"' of reaction 1so that virtually no faradaic current flows in the cell. The potential sweep is performed according to the program
E = Ei+ u t
for 0 It It , (forward sweep) (2)
and
E = E,- u ( t - t,) = Ei- ut + 2ut, for t
1 t , (reverse sweep)
(3)
where u is the potential sweep rate, t , is the switching time when the direction of the potential sweep is reversed, and E, is the switching potential given by
E, = Ei + ut,
(4)
which may be chosen to be sufficiently positive of Eo'. We seek expressions for reversible current-potential curves for forward and reverse sweep separately.
0003-2700/89/0361-1763$01.50/00 1989 American Chemical Society
1764
ANALYTICAL CHEMISTRY, VOL. 61, NO. 15, AUGUST 1, 1989
.C = ( n F / R T ) ( E
- EO')
(15)
Combining eq 2 and 6 with eq 15 yields
r=
0 (26)
and cR = cRo, and eo = 0
for
= 1, T
>0
27)
This boundary value problem is also solved using the Laplace transformation as shown in Appendix 3. The concen-
ANALYTICAL CHEMISTRY, VOL. 61, NO. 15, AUGUST 1, 1989
1285
trations of R and 0 at the electrode surface are given by CR' = J7B2(O; CO'
=
CRO
- J'O2(0;
T
- U)(CR' - i(u)L/nFAD} du (28)
T
- u ) { c R O - i(u)L/nFAD) d u
(29)
Introducing eq 28 and 29 into eq 26 and following the procedure similar to that employed for the forward potential sweep, we obtain an expression for the reverse sweep voltammogram (the cathodic wave) i, = (nFADcRo/L)[l - ~ m B s ( O ; exp({ y)
(1+ exp({
+ py) X
V I
+ P Y ) ~ dy] - ~ (30)
Thus, analytical expressions for current-potential curves have been evaluated and can be used for all sweep rates.
EXPERIMENTAL SECTION Microhole array electrodes were prepared from high strength carbon fibers (TORAYCA T-300; the number of fibers in a single electrode is 1ooO; 6.93 wm in diameter) using fabrication techrhques described in the previous paper (1). Depths of microholes were controlled by the amount of charge used during the etching process of the carbon fibers. Seven microhole array electrodes of different depths were employed in the present work. After the electrochemical measurements were finished, the actual depth of the microholes were determined from the scanning electron micrographs of the cross-sectional view of the microhole array electrodes. Solutions of 1.0 mmol/dm3 potassium hexacyanoferrate(I1) in 0.4 mol/dm3 potassium sulfate were prepared from reagent grade chemicals without further purification in water purified with an ultrapure water supplier (TORAYPURE LV-OS). Electrochemical measurements were carried out by use of a potentiostat (Model HA-301, Hokuto Denko, Tokyo) and a function generator (Model HB-104, Hokuto Denko, Tokyo) with an x-y recorder (Type 3086, Yokogawa Hokushin Electric, Mitaka, Japan). The electrochemical cell used was a 100-mL beaker with a silicone rubber lid having holes for installation of electrodes and for a nitrogen inlet tube. A saturated calomel electrode (SCE) was used as the reference electrode and all potentials were referred to this electrode. The auxiliary electrode was a platinum wire. The solutions were deaerated with nitrogen. They were stirred by a magnetic bar covered with Teflon during the measurements. Electrochemical measurements were conducted at 30 0.5 "C. Scanning electron micrographs of cross-sectionalview of the microhole array electrodes were obtained with a Hitachi S-800 scanning electron microscope with a field emission gun.
*
RESULTS AND DISCUSSION Characteristics of Cyclic Voltammograms. Theoretical cyclic voltammograms were calculated from eq 22 and 30 on a personal computer (NEC PC-9801RA). The integral from 0 to m was evaluated by dividing it into three integrals over the subintervals [0, 0.041, [0.04, 1.41 and [1.4, -1. Though 03(O;y)is singular a t y = 0, we can avoid the singularity by replacing 03(0;y) by (7ry)-'I2 in the region of 0 < y I0.04 (see eq 20) and by integrating by parts. In the region of y 2 1.4, O,(O;y) is virtually equal to 1 (see eq 19) and the integration is trivial. Other integrals were evaluated by using Simpson's 1/3 rule. The current-potential curves thus calculated are shown in Figure 2 for several values of p = nFvL2/RTD. It should be noted that the anodic and the cathodic waves are symmetric with respect to the point ( E O ' , nFAcRoD/2L). This will be apparent from the relation
ia({) 4- ic(-{) = nFAcRoD/L
(31)
which can readily be derived from eq 22 and 30. When p is less than 0.02, the voltammograms are independent of p, indicating steady-state behavior. Traces of the forward (anodic) sweep and the reverse (cathodic) seeep
- 2 ~ 1 1 " ' 1 ' ~ " ' -10 0
'
"
'
l
'
'
'
'
10
~
~
~
C= ~nF/RTI~E-E"l Flgure 2. Theoretical cyclic voltammograms for a reversible redoxelectrode process. Values of p are (A) 50.02, (e) 1.0, (C) 3, (D) 5, (E) 10, (F) 15, (G) 20, (H) 30, and (I) 40.
0
1
2
3
4
[nFvL2/RTDI Figure 3. Dependence of the normalized maximum current or the ratio of i, to i, on square root of p . Dashed line corresponds to the case of the semiinfinlte linear diffusion conditions.
voltammograms are completely identical and these can be expressed by i = (nFAcR"D/L)/[l + exp(-(nF/RT)(E -E0'))] (32) Thus the current-potential curves are sigmoidal in shape and the limiting current plateau, i.e., the steady-state current i,, is easily obtained. This behavior is the same as that for conventional polarograms and rotating disk voltammograms or at ultramicroelectrodes. In this case the half-wave potential Ellz equals Eo' since DR = Do = D. With an increase in the value of p, Ellz of the anodic wave moves from E O ' , toward less positive values and the cathodic half-wave potential moves toward more positive values. It has been found theoretically that i f p I2, then the sigmoidal form is retained and the reciprocal slope of the conventional logarithmic plot, Le., plot of log {i/(i, - i)) vs E, is equal to 2.3RTlnF. The shift of Ellz is not due to the change in reversibility but is caused by the transition from the steady-state mass transport condition (i.e., a fixed diffusion layer thickness) to a time-dependent diffusion layer thickness. When p is less than 2, the maximum current i, is equal to bu. When the value of p exceeds ca. 2.5, peaks appear on both the forward sweep and the reverse sweep waves. In this case we denote the peak current i, as.,i Figure 3 shows variation of i,,,&/nFADcRo or i,/i, with p'I2. When p L 15, i-/i, is proportional to p'l2 and the slope is equal to 0.446. Then we have iP/& = i,,L/nFADcRo = 0.446~'/~ (33) or using eq 18 i, = 0.446nFAc~~D'/~(nF/RT)'~~u~~~ (34)
1766
ANALYTICAL CHEMISTRY, VOL. 61,NO. 15,AUGUST 1, 1989
-
i30
L.
1.0-
1
, N
c
-
ii: 0.5-
>
p"2= ( n F v f '/RTD)"'
Flgure 4. De endence of the potential of the half-maximum current Emxll on p "'(anodic wave). Right ordinate is for n = 1 and 25 "C.
h/pm
Flgure 6. Plots of reciprocal of steady-state current against depth of ~ from peak the microhole h (A) and plots of @ R T / n f - ~ ) l 'obtained current agalnst h (B).
4:
81
Flgure 5. Cyclic voltammograms for oxidation and rereduction of [Fe(CN),]&in 0.4 mol/dm3 K2S0, aqueous solution at microhole array electrodes of h = 1 1 pm (A) and h = 156 pm (B): potential range, -0.20 to 4-0.60V; potential sweep rate (Al)5 mV/s, (A2)20 mV/s, (A3) 50 mV/s, (Bl)1 mV/s, (82)5 mV/s, and (83)10 mV/s; S = 50 nA (A) and S = 10 nA (8).
This is the same equation as for the peak current of the reversible potential sweep voltammogram under semiinfinite diffusion conditions (9, IO), indicating that when the potential sweep rate u is high enough or the depth of microholes L is deep enough to satisfy p 2 15, then the diffusion layer thickness is less than L at the time the peak appears. The shape of voltammograms is also characterized by the potential of the half-maximum current the dependence of which on p1J2is shown in Figure 4 for anodic wave. For values of p 5 0.25, Emar12= E"' within (2/n)mV at 25 "C, which corresponds to the steady-state condition. When p 2 15, on the other hand, Em,12 = Eo' - l.OS(RT/nF). This corresponds to the half-peak potential for semiinfinite diffusion. This behavior is the same as that in the thin-layer cell mentioned above (8). In order to apply the theoretical results, the redox-electrode reaction of hexacyanoferrate(II/III) was chosen as a reversible system. Typical cyclic voltammograms obtained experimentally for oxidation of 1.0 mmol/dm3 [Fe(CN),J4- in aqueous 0.4 mol/dm3 K2S04solutions are shown in Figure 5 for the microhole array electrodes having depths of about 10 and 150 pm. At the electrode of 10 pm depth, sigmoidal current-potential curves were obtained for the sweep rate range between 2 and 50 mV/s. Some noise seen on the limiting current plateau was due to the turbulent flow caused by the agitation of the solution. Noise of less amplitude was observed at the electrode of 20 pm depth but could not be seen at the 50 pm depth. Since the solution was stirred with a magnetic bar stirrer, the flow in the cell was turbulent. When the electrodes were placed in a laminar flow, such noise was found to be greatly reduced. The traces of the forward and the reverse sweep completely overlapped and showed no hysteresis at the sweep rate of 2
mV/s (10 pm depth), indicating that the redox-electrode process of the hexacyanoferrate couple is reversible under the conditions employed. Although the effect of charging current became more apparent in the higher sweep rate range, the limiting current values were found to be the same when a correction of the charging current was made as described below. The fact that the steady-state behavior is observed at the microhole array electrode of 10 pm depth is predicted from the theoretical results because the value of p lies in the region from 0.01 to 0.38 for 2 mV/s 5 u 5 50 mV/s and for representative D values ranging from 5 X lo4 to 1 X cm2/s. Cyclic voltammograms at the microhole array electrode of 150 pm depth showed well-defined peaks on both anodic and cathodic waves for u I2 mV/s, but the voltammogram recorded at u = 1mV/s was almost sigmoidal. These voltammograms were almost symmetric as expected from the theoretical results. Analysis of the Steady-State Current. The reciprocal of the steady-state current is expected from eq 23 to be proportional to the depth of microholes. In order to compare the theoretical and experimental voltammograms, it is desirable to have values of the depths of the microholes. Although the depth of the microholes can approximately be controlled by the amount of electricity consumed in the etching process as mentioned previously (I),a more reliable value of the actual depth is determined from the scanning electron micrographs of the cross-sectional view of the microholes. The etched tips of carbon fibers were not flat but had a shape like a bullet head as shown in Figure 1 of the previous paper (I) and schematically in Figure lB, and the average length 1, of the etched carbon fiber tips ranged from 2.5 to 13 pm depending on the total microhole depth; the larger the total depth, the larger 1,. We will define the depth of microholes h as a sum of the average distance from the mouths to the t i p of the carbon fibers and half of 1, as shown in Figure 1B. Figure 6 shows plots of the reciprocal of the steady-state current against the microhole depth. The steady-state current values were determined from the chronoamperometric experiments but they agree completely with the limiting current values obtained from cyclic voltammograms with a correction of the charging current. This correction was carried out on the voltammograms by subtracting the current value calculated from the linear extrapolation of the residual current curve preceding the initial rise of the wave, and was used throughout this work. These plots fall on a straight line (line A) which has an intercept at -13 pm on the abscissa. Thus we may write as l / i s s = (h + lI)/nFADcRo (35)
ANALYTICAL CHEMISTRY, VOL. 61, NO. 15, AUGUST 1, 1989
where 11 may be regarded as a length which must be taken into account to include the effect of a layer outside of the mouths of microholes on the diffusion process. This behavior is the same as that for oxygen reduction reported in the previous paper (I) and 11 was considered to be the thickness of the diffusion boundary layer formed on the surface of microhole array under the stirring condition. Thus the thickness of the diffusion layer L is regarded as the sum of h and II as shown in Figure 1B. The value of 13 pm for I, found in this work is somewhat larger than the average value of 7.6 pm found in the previous work for the reduction of oxygen ( I ) . However, a range of I1 values from 4.1 to 12.8 pm was observed in the previous work ( I ) , and the discrepancy may result from possible variation of stirring conditions in the solution. From the slope value of line A in Figure 6, the product of the diffusion coefficient by the total area was evaluated to be 3.46 X cm4/s. If we assume that the diameter of the microholes is equal to that of carbon fibers and the tips of the carbon fibers are flat, the total electrode surface area A is estimated to be 3.8 X 10"' cm2,which yields D = 9.1 x lo4 cm2/s. Inspection of micrographs of the surfaces of microhole array electrodes revealed that some neighboring microholes were connected to each other by thin crevices formed in the epoxy resins during the electrochemical etching process. If we take this observation into account, then, since the effective surface area is larger, the value of D would become somewhat smaller than 9.1 X 10* cm2/s. It is also necessary to consider the effect of the difference in the surface areas of the real electrodes and of the electrode model in Figure 1A on the current intensity. As mentioned above, the real surface area of the electrode is obviously larger than the one estimated above since the carbon fiber tipes have a shape like a bullet. At the early stage of the electrolysis, the diffusion layer has not developed and thus the current value reflects the real surface area. As time passes, however, the diffusion layer develops, the thickness eventually well exceeds le, and the steady-state current i, would become insensitive to 1,. Thus it is expected that the effect of 1, on ,i or on the D value evaluated from i, would be relatively insignificant and i, may be determined by the geometric cross-sectional area of the microholes. However, since it has not been clarified quantitatively how large this effect is, exploration of etching methods to make flat carbon fiber tips is under way. An alternate means of estimating the D value, which is independent of the sufface area value, is described below. Analysis of the Cyclic Voltammograms. When cyclic voltammograms show peaks, we can evaluate p values from the ratio of the peak current to the steady-state current, i,,/i=, using the working curve shown in Figure 3. Values of (pRT/nFv)1/2 thus calculated are plotted against h in Figure 6. These plots also fall on a straight line (line B), which has an intercept at about -13 pm on the abscissa. It is interesting to note that both intercept values of lines A and B are almost the same. This linearity is expected from eq 18 when we write L=h+11 (pRT/nFu)1/2 = D-lI2(h+ 2,)
(36)
From the slope of this line, D is evaluated to be 6.7 X lo* cm2/s. A value of 5.9 X lo* cm2/s has been reported for D of [Fe(CN),I4- in 0.4 mol/dm3 K2S04at 25 OC (11). If we take into account a temperature coefficient of about +2% /"C for diffusion coefficients in aqueous solution ( I 2 ) ,then we have 6.5 X lo4 cm2/s at 30 "C. This value is very close to that evaluated from the ratio of imm/i,. There is some discrepancy (about 30%) between the D value obtained from the steady-state current measurement (line A) and that from cyclic voltammetry (line B). Evaluation of the
1767
D value from i,, requires the value of the electrode surface area A, and thus some uncertainty in A directly influences the estimated D value. The higher value of D obtained from
is, may partly result from the used value of A which would be smaller than the real one. When ,i is attained, the diffusion layer has well-developed although the development is not complete as in the steady state. Thus the shape of carbon fiber tips may affect more or less equally both i, and i-. The effect of uncertainty of the electrode surface area on the evaluated value of p from imm/i, is ruled out because only the ratios of experimental values are used and this may be the reason why a reasonable value of D was obtained from line B in Figure 6. It is concluded that relatively good agreement has been obtained between the theoretical and experimental results for reversible cyclic voltammograms at microhole array electrodes. Extension of the work to examine kinetically controlled systems is also being considered. The amplified current at the microhole array electrode is a great advantage over the single hole electrode (4). The microhole array electrode may be most suited for measurements in stirred solutions or in flow-through systems. Under these conditions, concentrations of the species outside the holes are regarded to be uniform and thus there is no complexity resulting from the overlapping of diffusion layers, which must be taken into account in the case of ensembles of inlaid microdisk electrodes. Application of the microhole array electrode to electrochemical detectors in liquid chromatography and flow injection analysis is under way. APPENDIX Appendix 1. Application of the Laplace transformation with respect to T to eq 7, 9, and 11 yields d2L[C~]/d12= (s/D)L[c,] - cBo/D
(Al)
with dL[cR]/dE = -dL[co]/df
= L[iL/nFAD] for
E =0 (A2)
L[cR]
CRo/s,
L[cO] = 0 for
5=1
(A3)
where L [ f ]denotes the Laplace transform of function f and s is the dummy Laplace variable. General solutions of eq A1 for B = R and 0 may be written as L[cR] = c R O / S
+ AR exp(-s1/2t) + BR exp(s1/2[)
(A4)
+ Bo exp(s1/2f)
(A5)
L[co] = A. exp(-s1/2[)
where coefficients AR, BR, Ao, and Bo are functions of s to be determined from the boundary conditions. Using eq A2A3, we have
+
AR = -A0 = - L [ ~ L / ~ F A D ] s - ' / ~ ( exp(-2~'/~))-I ~
+
BR = -Bo = L [ ~ L / ~ F A D ] S - ' / ~e ~x p~( 2 ~ l / ~ ) ) - l Substituting these equations into eq A4-A5 and rearranging the resulting equation yield L[cRI = cRO
- s-'l2 sinh (s1l2(1-
E ) ) sech ( . S ' / ~ ) L [ ~ L / ~ F A D ] 646)
L[co] = s-l/'sinh ( ~ ' / ~ ( 1E ) } sech ( s ' / ~ ) L [ ~ L / ~ F A D ] (A7)
A t the electrode surface (Le., = 0), these equations reduce to L[cRs] =
CRO
- S-lI2 tanh ( s ' / ~ ) L [ ~ L / ~ F A D(A8) ]
L[cos] = s-lI2 tanh ( . s ~ / ~ ) L [ ~ L / ~ F A D ](A91
Anal. Chem. 1989, 6 1 , 1768-1772
1768
The Laplace inversion transform of eq A8 and A9 by use of the relation ( 5 )
L[CR] = C R O E / S s-l" sinh {s'/'(l -
1) sech (sl/z){L[iL/nFAD] - CR'/S) (A171
L-'[s-'iZ tanh (as'/2)] = u-'O,(O;T/U~) (a, constant) (A10) yields eq 12 and 13, respectively. In the above equation, L-' is the inverse Laplace transform operator. Appendix 2. Applying Laplace transformation to eq 14 and rearranging, we have
L [ ~ ( T ) L / ~ F A=DS-'/' ] coth (s'/')s~[cR0(~ + exp(-{))-l] (All) Inverse transform of eq A l l is obtained by making use of relations (5) s L [ f ( ~ ) 1= L ( d f ( ~ ) / d r I+ f ( 0 )
L[c,] = C R O ( 1 - E ) / s + s-'/'sinh (s'/'(l - E ) ) sech ( S ' / ~ ) ( L [ ~ L / ~ F CAR OD/ S]]
(A181 Letting 6 = 0 in eq A17 and A18 and inverse transforming by use of eq A10 gives eq 28 and 29. ACKNOWLEDGMENT Helpful discussion with Dr. J. F. Cassidy is gratefully acknowledged. Registry No. Fe(CN)6*-,13408-63-4;Fe(CN)63-,13408-62-3; KFe(CN)G,13943-58-3;dipotassium sulfate, 7778-80-5. LITERATURE CITED
and
L-'[S-'/~coth (as'/2)]= a-'O3(0;T/a2) (a, constant) (A121
(1) (2) (3) (4)
and we have eq 19. Appendix 3. Application of the Laplace transformation with respect to T to eq 7 , 25, and 27 using eq 24 yields
(6)
d2L[C~]/dE2 = (S/D)L[CR] - cRoE/D
(A13)
(7)
d2L[co]/dF2 = (S/D)L[co] - C R o ( l - C;)/D (A14)
(8) (9) (10) (11)
with d L [ c ~ ] / d [ = -dL[co]/dt = L [ i L / n F A D ]for
5 =0 (A15)
L[cR] = CRo/S, L[c,] = 0 for
6
= 1
(A16)
Following the procedure similar to Appendix 1, we obtain
(5)
(12)
Morita, K.; Shimizu, Y. Anal. Cbem. 1989, 67, 159. Shimizu, Y.; Morita, K., submitted for publication in Anal. Chem. Morita, K.; Sugiyama, T.; Ohaba, M., unpublished results. Bond, A. M.: Luscombe, D.; Oldham, K. B.; Zoski, C. G. J. Elechoanal. Chem. 1988, 249, 1. Roberts, G. E.; Kaufrnan, H. Table of Laplace Transforms; W. B. Saunders Company: Philadelphia, PA, 1966. Spanier, J.; Oldham, K. B. An At&s of Functions; Hemisphere Publishing Corporation: Washington, DC, 1987; Chapter 27. Aoki, K.; Tokuda, K.; Matsuda. H. J. Electroanal. Chem. 1983, 746, 417. Daruhizi, L.; Tokuda, K.; Farsang, G. J . Electroanal. Chem., in press. Matsuda, H.; Ayabe. Y. 2.Elektrocbem. 1955, 59,494. Nicholson, R. S.; Shain, I. Anal. Chem. 1964, 36, 706. Bruckenstein, S.; Tokuda, K.; Albery, W. J. J. Cbem. Soc. Faraday Trans. 7 1977, 7 3 , 823. Sawyer, D. T.; Roberts, J. L., Jr. Experimental Electrocbemistry for Chemists: John Wiley: New York, 1974; p 153.
RECEIVED for review December 28, 1988. Accepted May 9, 1989.
Fiber-optic Time-Resolved Fluorescence Sensor for the Simultaneous Determination of AI3+ and Ga3+ or In3+ Mary K. Carroll, Frank V. Bright,' and Gary M. Hieftje*
Department of Chemistry, Indiana University, Bloomington, Indiana 47405
A fiber-optic fluorescence sensor for simultaneous two-elemental determlnatlons has been developed. The sensor is based on the formation of a complex between specific metal ions and a metal ion chelator. Several chelator-ion systems and several means of chelator immobilization were studied. The successful fiber-optic sensor design Is based on a pool of chelator solution trapped behind a membrane made of Naflon. The chelator uitlmately chosen, lumogallion, forms strongly fluorescent complexes with trivalent aluminum, gallium, and indium ions. Because of the difference in fiuorescence lifetimes of the various lumogaliion complexes, timeresolved fluorometry enables simultaneous determination of two of these ions.
* Author
t o w h o m correspondence should b e addressed. C u r r e n t address: Department o f Chemistry, State University of N e w York a t Buffalo, Buffalo, NY.
INTRODUCTION Many chelators form strongly fluorescent complexes with metal ions. Often, the fluorescence of the chelator itself is weaker than that of its complexes. As a result, the extent of complexation and, thus, the concentration of an ion in solution can be found from a measurement of fluorescence intensity. However, a chelator will frequently form complexes with several different ions, and the emission spectra of the different complexes are sometimes similar. Hence, interferences plague the determination of any particular metal ion in the presence of one or more of the others. This report describes the development of a fiber-optic-based fluorescence sensor capable of simultaneous two-element determinations under the conditions described above. Others have developed fiber-optic sensors for the determination of metal ions (1-5). Generally, these sensors are fabricated by immobilizing a metal indicator or chelator on
0003-2700/89/0361-1768$01.50/0 0 1989 American Chemical Society
