248
Anal. Chem. 1987, 59,248-252
Simultaneous Electrochemical Determination of Diffusion and Partition Coefficients of Potassium Ferrocyanide for Albumin-Glutaraldehyde Membranes Carl A. Marrese,' Osato Miyawaki,2 and Lemuel B. Wingard, Jr.* Department of Pharmacology, School of Medicine, University of Pittsburgh, Pittsburgh, Pennsylvania 15261
The determlnatlon of true diffusion and partltlon coefflclents for the transport of electroactlve materlals through membranes conslsthg of enzymes or lmmunocompounds lmmoMuzed on electrode surfaces Is an Important topic In Mosensor development. Both (1) chronoaRlperometrywlth a stationary electrode and (2) steadydate dtffuslon lhlted current measurements wlth a rotating disk electrode can be used Independently to obtaln effective dlftuslon coefflctents for membranes attached to electrodes. The effective dlffuslon coefficient Is based on the true dmuslon coelflclent and the equlllbrlum partHion coefflclent. Thls paper describes a sequential procedure In which potentlal step chronoamperoms try Is followed by lhltlng current rotating electrode measurements. The method was applled to the transport of potassium ferrocyanlde through an albumin-glutaraldehyde cross-llnked membrane coating on a ptatlnm electrode. The resultlng data were used to calculate both the true dlffuslon and the partltlon coefficients wlthout the need for addltlonal measurements. The coefflclents were Influenced strongly by the pH of the electrolyte.
The immobilization of proteins that show high substrate selectivity, such as enzymes, antibodies, or cell membrane receptors, on solid supports for the purpose of developing electrochemical biosensors is an exciting and important area of present research (1-4). One of the critical operational parameters for such systems is the extent of resistance that the immobilized protein matrix (i.e., the membrane) imparts to the diffusion of compounds. In most cases convective transport is not present within the membrane (5),and under such conditions the diffusional resistance can be characterized by determination of the true diffusion coefficient for transport of a specific compound within the membrane. The value of the true diffusion coefficient for a substance may differ significantly between that in bulk solution and that in an immobilized protein matrix. Generally the diffusion coefficient must be determined experimentally. The experimental measurement of true diffusion coefficients for transport of specific compounds within an immobilized protein matrix is often difficult to carry out. This limitation occurs because of the lack of practical methodology for accurately measuring the concentration of the compound at precisely known positions within the matrix. This problem may be circumvented by placing a bulk solution on one side of the membrane and a solid electrode surface on the other side and operating the system under conditions where the concentration of the diffusing species can be known accurately both a t the electrode surface and in the bulk solution. For 'Present address: Bacharach, Inc., 625 Alpha Dr., Pittsburgh, PA 15238. On Leave from the Department of Agricultural Chemistry, University of Tokyo, Tokyo, Japan.
a precise description of the system, the measurement of the equilibrium partition coefficient for the distribution of the compound between the matrix and bulk solution also is required. In cases where a less precise description is suitable, an effective diffusion coefficient can be defined that incorporates the true diffusion coefficient and the equilibrium partition coefficient. Two electrochemicaltechniques have proven to be especially useful for the measurement of diffusion coefficients of electroactive compounds. Steady-state diffusion limited currents, obtained with the matrix immobilized on the surface of a rotating disk electrode, have been used to obtain effective diffusion coefficients for the transport of potassium ferrocyanide or other redox compounds through a variety of matrix materials (6-10). Chronoamperometry (11)is another technique that has been used to obtain effective membrane diffusion coefficients. In these referenced studies, separate experimental procedures were required to measure the partition coefficient and thus enable the true membrane diffusion coefficient to be calculated. In the work reported here, we have combined the chronoamperometric and steady-state rotating disk methods to enable both the equilibrium partition coefficient and the true membrane diffusion coefficient to be calculated from a given set of electrochemical measurements. For the immobilized protein matrix we selected glutaraldehyde cross-linked bovine serum albumin because this is a widely used method for the immobilization of enzymes and other proteins onto electrode surfaces. Potassium ferrocyanide was selected as the electroactive species because the diffusion coefficient has been measured under a variety of conditions, and this is a wellcharacterized redox compound.
THEORY The system under study consists of a protein membrane that is attached to and covers the entire surface of a platinum-disk electrode assembly. The geometry of the electrode-membrane unit is described in the Experimental Section. The membrane-disk end of the electrode assembly is immersed in a solution of electrolyte that contains potassium ferrocyanide and in some cases a suitable buffer. The electrode assembly is rotated only during the steady-state measurements. With the electrode held stationary, partition equilibrium occurs when the concentration of potassium ferrocyanide is constant throughout the bulk phase (C*) and throughout the membrane phase (C,) (solid lines in Figure 1A). The partition coefficient, a,is defined by eq 1.
C,/C*
=a
(1) In Figure l A , it is assumed that potassium ferrocyanide is less soluble in the matrix than in the bulk solution. Under these equilibrium conditions, a step in the potential applied to the disk, to a value well in excess of that needed to oxidize ferrocyanide, causes the ferrocyanide concentration at the electrode surface to drop essentially instantaneously to zero.
0003-2700/87/0359-0248$01.50/00 1987 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 59, NO. 2, JANUARY 1987
PI at inum Disc
+
I
J
m
Distance
l
Sufficient rotation to reduce the diffusional resistance associated with the diffusion layer in solution to a minimum (12) often is not attainable with a rotating disk-membrane electrode without risking damage to the membrane. Gough and Leypoldt (6) pointed out a way of circumventing this problem by noting that the steady-state current, following a potential step at the platinum disk, is made up of two components. The f i t component is based on achieving the maximum attainable gradient within the membrane alone and is independent of the electrode rotation rate. The second component describes the current as a function of the electrode rotation speed, as described by Levich (13), and pertains to the fluid in the absence of the membrane. The two components are summarized in reciprocal form in eq 6 (6)
(x)
0
I---.
.-I:
249
/
Flgure 1. Schematic profiles of potassium ferrocyanide concentration C vs. distance X from phtinumdisk surface. Membrane thickness is
denoted as 6, and dlffuslon layer in bulk solution is shown as 6,. Part A: The bulk solution Is unstirred. Part B: The bulk solution is stirred by rotation of the platinumdisk-membrane electrode. This produces a Concentration gradient of ferrocyanide within the matrix and results in the diffusion of ferrocyanide toward the disk. The dashed lines 1, 2, and 3 in Figure 1A are at increasing times. The rate at which ferrocyanide reaches the disk is indicated by the current. If the time duration is limited to a few seconds (i.e., curve 3 in Figure lA), then the concentration changes remain within the matrix, and the transient current i ( t ) for this chronoamperometric measurement can be described by the Cottrell equation, with C, replaced by aC* from eq 1
where
(3) Here D , is the true diffusion coefficient for potassium ferrocyanide movement within the matrix, t is time after the potential step change, A is the area of the platinum disk, F the Faraday constant, and n unity for the number of electrons transferred per molecule oxidized. The effective diffusion coefficient as determined by chronoamperometry, De,,,, is made up of the true diffusion coefficient and the partition coefficient. Values of De(ca)can be obtained by use of eq 2 and plots of i ( t ) vs. t-'l2 for fixed values of C* and short times. At longer times, the value of C, is decreased throughout the membrane, and the concentration of ferrocyanide within the solution diffusion layer also begins to diminish. If the platinum-disk-membrane electrode is now rotated, the resulting convective flux acts to diminish the thickness of the diffusion layer to give the steady-state profile shown by the solid line in Figure 1B. At very high rates of rotation, the diffusion layer is essentially eliminated, so that the steady-state concentration gradient between the bulk solution (C*) and the platinum-disk surface occurs solely within the membrane (Figure lB,dashed line profile). This concentration gradient, aC*/6,, is the maximum obtainable (6, is the thickness of the membrane). The corresponding steady-state current a t the disk, i,,, can be described by eq 4
where v is the kinematic viscosity and o is the rotation rate in radians per second. This equation can be expressed in terms of De(ss)as
Therefore, with the current known at different electrode rotation speeds, the value of i,, can be obtained from the intercept of a plot of l/i vs. Equation 4 can then be used to calculate De(,),and eq 3 and 5 can be solved simultaneously to give the values of a and D,.
EXPERIMENTAL SECTION Electrochemical Instruments. A conventional three-electrode electrochemical cell was employed. The working electrode was a Pine Instrument Co. 0.50-cm- or 0.70-cm-diameter platinum disk mounted on the flat end of a support made of Teflon. A Ag/AgC1(1 M KCl) reference electrode and a platinum-screen auxiliary electrode completed the electrochemical cell. The working electrode was rotated by using a Pine Instrument Model ASR variable-speed drive. Control of the applied disk potential and measurement of the disk current were done with a Pine RDE-3potentiostat connected to a Houston X-Y or strip-chart recorder. Materials. Fraction V bovine serum albumin, 8% aqueous glutaraldehyde, and Tris-HC1 buffer were obtained from Sigma. Only glutaraldehyde that showed no evidence of polymer formation, as determined by spectrophotometry ( 1 4 , was used. Potassium ferrocyanide from Mallinckrodt and all other reagents were of analytical grade. Water of 18 MQ cm specific resistance (Milli-Q System) was used throughout the work. The electrochemical cell was purged with high-purity nitrogen to remove oxygen prior to measurements. Procedure. The working electrode was modified by covering the platinum disk with a matrix of cross-linked albumin. The matrix was prepared by mixing in order 0.680 mL of 15% (w/w) aqueous albumin, 0.826 mL of 0.1 M Tris-HC1 buffer of pH 8.0, and 0.174 mL of 8% aqueous glutaraldehyde. Approximately 15 pL of this solution was spread to overlap the edges of the platinum disk and held for 2 h at room temperature and high humidity to enable cross-linkingof the glutaraldehyde-albumin to occur. The maximum thickness of the wet matrix was 0.025 cm, as determined by optical microscopy. The geometry of the matrix electrode and the arrangement of the humidification chamber are shown in Figure 2. A fresh matrix was prepared for each series of measurements. In a typical experiment, the matrix electrode was rotated at 1000 rpm for 0.5 h in 1 M KCl, or 1 M KCl containing buffer,
250
ANALYTICAL CHEMISTRY, VOL. 59, NO. 2, JANUARY 1987 J
1.5-
7 4
2
1
Figure 2. Cross section schematic of membrane electrode geometry and humldification chamber for albumin cross-linking. The parts are denoted as follows: 1, platinum dlsk; 2, insulation made of Teflon; 3, albumin membrane; 4, rubber O-ring; 5, wet filter paper, 6, metal washer to hold filter paper in place: 7, electrical connection from disk. to rinse out loosely attached albumin and unreacted glutaraldehyde. The rinsed matrix electrode next was placed in the cell, containing about 10 mM potassium ferrocyanide and 1 M KC1. Ten to 20 min was allowed for the ferrocyanide to reach equilibrium partitioning throughout the membrane. The establishment of partition equilibrium was tested by comparing the peak currents for the oxidation of ferrocyanide, using sequential linear sweep voltammograms run between 0.0 V (reference Ag/ AgC1) and +0.6 V at 50 mV/s. Equilibrium was assumed to be present when sequential voltammetric peaks were superimposable. After the potassium ferrocyanide concentration reached equilibrium throughout the matrix, chronoamperometric measurements were made. In the chronoamperometric studies, the electrode was not rotated. The potential applied to the disk, was stepped from 0.0 V to +0.6 V and the current measured as a function of time. The step potential of +0.6 V was selected to place the electrode well in excess of that needed for the oxidation of ferrocyanide. The chronoamperometric measurements were followed immediately by steady-state current determinations at different electrode rotation rates. The diffusion and partition coefficients were calculated by using the chronoamperometric and steady-state current data.
A
U
E 1.0-
Y
c z w a a 0.53
0
1
=
-
1
1
=
I 1
1
-m
I
c
I
1
1
1
.
0.8
0.4 TI
1
,
1.2
(seC)-0.5
Flgure 3. Plots according to Cottrell equation for potassium ferrocyanide diffusion through 0.024-crn-thick albumin-glutaraldehyde membrane attached to a statlonary platinumdisk electrode, following a step in the applied potential. Solution composition: 1 M KCI plus potassium ferrocyanlde at 0.003 M (m), 0.020 M (U),0.042 M (O), 0.061 M (0),0.079 M (A),and 0.095 M (A). Lines fit by linear least squares.
RESULTS AND DISCUSSION Chronoamperometry. Typical chronoamperornetric results for ferrocyanide oxidation at the membrane-coated 0.50-cm-diameter platinum disk, following a step in disk potential, are summarized in Figure 3. The expected linearity for Cottrell equation plots of i ( t ) vs. t-'I2, with the line gassing through the origin, was observed. This was indicative of a E diffusion controlled process. The values of i(t) shown in Figure :7Y 3 represent the Faradaic currents only. 'A control experiment in the absence of ferrocyanide was carried out, and the control current values were subtracted from the results with ferrocyanide present. From the slope of each line and eq 2, the w a effective diffusion coefficient, De(,,, was calculated. Cottrell a equation behavior was observed with all of the matrix-electrode preparations for up to 10 s following the step in disk 3.04 potential. This conclusion was based on the product it1/' remaining constant for at least 10 s (see eq 2). This relatively long time was attributed to the absence of convective fluid flow at the surface of the platinum disk and to moderately slow diffusion of ferrocyanide within the matrix. The Figure 3 results validated the chronoamperometric approach. Rotating Disk Electrode. In this part of the study, potassium ferrocyanide was oxidized a t the membrane-coated Figure 4. Rotating disk electrode data showing how the reciprocal of the measured current varied wlth the reclprocal of the square root of 0.70-cm-diameter platinum-disk electrode, while the electrode rotation speed for several different thicknesses of membrane on the assembly was rotated at a constant rate. The results for platinum disk. Data are for oxidation of 10 mM potassium ferrocyanide several different membrane thicknesses are shown in Figure in 1 M KCI with membrane thickness as follows: (0)bare platinum, 4. As predicted from eq 7, the plots of '-i vs. w-lI2 were linear (0)0.10 mm, (U) 0.17 mm, (A)0.23 mm, ( 0 )0.27 mm. Lines fit by for a given membrane thickness and bulk solution concenlinear least squares. tration of potassium ferrocyanide. For the five seta of data shown in Figure 4, the slopes, defied as ~'/~/(0.62nFA.@/~c*),brane-solution interface. The correlation coefficient squared were very similar, with a mean value of 4.15 mA-l s-'/~ and for each of the five plots was 0.98-0.99. It should also be noted a standard deviation of 0.54 mA-' s-~/*.This commonality that the maximum steady-state current differed by only a few of slope was expected since the term containing w pertains percent from the highest rotation-rate data point on each plot, only to concentration gradients established a t the memcorresponding to an angular rotation rate of 3000 rpm. Thus,
Q
.
O
~
ANALYTICAL CHEMISTRY, VOL. 59, NO. 2, JANUARY 1987
Table I. Membrane Diffusion and Partition Coefficients for Potassium Ferrocyaniden membrane
thickness,
a
De(ca),
cm
cm2/s
De,,), cmz/s
D,, cmz/s
a
0.038 0,019
5.30 X lo4 5.13 X lo4
4.48 X lo* 4.09 X 10”
3.79 X lo4 3.26 X 10”
1.18 1.25
251
0.035
& 0.030 LoE 0.025 0.020
Determined with 1 M KC1 as the electrolyte.
to a first approximation, the current at 3000 rpm could be substituted for iss(,=) with little error. However, the lines in Figure 4 were accurately extrapolated to give the y-axis intercepts as the maximum values of i, for each line. According to eq 7, i,-I should vary linearly with the membrane thickness. This inverse relationship was substantiated in the present work. The line was first fit by linear least squares to give a slope of 39.8 mA-’ mm-l; however, a subsequent t test showed that the origin was well within the 95% confidence interval for the value of y at x = 0. Therefore, the line was refitted by linear least squares to include passage through the origin with the slope now being equal to 38.8 mA-l mm-‘. From eq 7 at high rotation rates, the slope for a plot of iSL1 vs. 6, becomes l/nFAC*D,(,,). The mean calculated value of De(,) with the refitted slope was 6.9 X lo4 cmz/s. The data from Figure 4 and the plot of vs. 6, substantiated the methodology with the rotating disk electrode and steady-state values of current for calculation of De(88). Determination of D , and a. Two different thickness membrane-covered disk electrode assemblies were then examined by using both the chronoamperometric and the rotating disk steady-state methods to give values for both De(ca) and De(,,,. These results, along with the resulting values of D, and a , calculated from eq 3 and 5, are given in Table I. The average value for D, from Table I, 3.53 x lo4 cm2/s, was significantly smaller than the 6.3 X lo4 cm2/s reported for potassium ferrocyanide diffusion in free solution of 1 M KC1 (15). From the partition coefficients of Table I, it is concluded that potassium ferrocyanide was more soluble in the membrane than in aqueous 1 M KC1. Since these results were obtained in unbuffered medium, a subsequent series of measurements of D, and a were carried out at different solution pH values. For the determination of the diffusion and partition coefficients at known solution pH values, the membrane was prepared on the electrode as usual at pH 8.0, and then the membrane-electrode was placed in 10 mM potassium ferrocyanide and 1 M KC1, buffered with 0.1 M acetate, phosphate, or carbonate systems over the pH range from 2.7 to 8.9. Both the chronoamperometric and rotating disk steady-state methods were repeated at each pH value to enable both De(ca) and De(,, to be determined. The resulting calculated values of D, and a are shown in Figure 5. The thickness of the matrix increased from 0.021 cm at pH 2.7 to 0.037 cm at pH 8.9. Therefore, the matrix would appear more open at higher pH values since the same quantities of materials were used in the preparation of each matrix. This would tend to increase the value of De(ca), due to more rapid diffusion, at higher pH values. However, a thicker matrix would produce a smaller concentration gradient between the essentially constant potassium ferrocyanide concentrations in the bulk solution and that at the electrode surface for the rotating disk steady-state experiments; this would produce smaller values of i, at higher pH readings. The value of D, at pH 8.9 in Figure 5 is higher than the diffusion coefficient for potassium ferrocyanide in free solution (15). We believe this is an artifact of the method of calculation; but additional experimental work will be needed to obtain a rational explanation.
1
0 4.0
1.2-
8
1.0-
Figure 5. Matrix diffusion and partition coefficients for potassium ferrocyanide determined at known solution pH values. Data presented as mean and range for duplicate determinations of D ,, and De(ss). Wet matrix thickness measured by optical microscopy.
The above predicted changes in De(ca)and in De(,,)with matrix thickness assume that the thickness did not influence a. The data in Figure 5 show that less potassium ferrocyanide partitioned into the matrix as the pH was increased. This may have been the result of pH-dependent adsorption, possibly of the polar cyanide group, to albumin. However, a more definitive explanation will require additional research. An explanation based on electrostatic effects does not appear likely since chloride ions were present at 100 times the concentration of ferrocyanide ions. By use of the isoelectric point of 4.8 (16) and the presence of 107 free amino groups per molecule of bovine serum albumin plus the stoichiometry of the reaction with glutaraldehyde, it is concluded that the matrix had a net positive charge at solution pH values of 3.0-4.5 and a net negative charge at solution pH readings of 4.5-8.9. These two pH ranges agree closely with the pH values over which ferrocyanide partitioning was accumulated and rejected by the matrix, respectively. However, it is not clear how an electrostatic explanation for the observed partitioning vs. pH could result. There also has been a suggestion that the albumin molecule undergoes an expansion at pH values below the isoelectric point (18); however, this idea does not appear to have been carried any further. In order t o verify the methodology further, a chronoamperometric experiment was carried out with the matrixelectrode rotating at a sufficiently high rate to eliminate the diffusional resistance in the solution. The experiment was continued until a steady-state current was obtained, thereby covering the range from transient currents, described by Cottrell behavior (eq 2), to steady-state currents, defined by extrapolation of eq 7. Peerce and Bard (11) previously presented a mathematical model of how the ratio of transient current, i(t),to steady-state current, i, should vary with time
(In,
252
ANALYTICAL CHEMISTRY, VOL. 59, NO. 2, JANUARY 1987
where y is a nondimensional parameter defined as y =
D,t/6,2.
1 .o
0.010
0 001
0.100
D
100
t
Y=+
6, Flgure 6. Relation between transient current and steady-state current as a function of dimensionless time, following a potential step applied to a matrixavered electrode rotating at a hlgh enough rate to eiirninate solution diffusional resistance. Line is plot of eq 12.
Table 11. Determination of D , by Transient-Steady-State Current Procedure with Electrode Rotated at Rapid Rate" measd currentb
104i, A 4.22 2.55 1.94 1.56 1.08 0.65 0.43 0.35 0.33 0.33
time, s 0.5
1.0 2.0 3.0 6.0 16
y (from
i(t)/iB8 Figure 6) 12.8 7.7 5.9 4.7 3.3
2.0
41 80
1.3 1.1
123 186
1.0
106D,,'
LITERATURE CITED
cm2/s
0.0019 0.0054 0.0091 0.014 0.029 0.079 0.18 0.34
2.8 3.9 3.3 3.4 3.5 3.6 3.2
3.1
1.0 mean 3.4
Conditions: potassium ferrocyanide 9.4 mM; 6 , 0.027 cm; electrode rotation rate 3000 rpm; pH 4.86 (buffered). bMeasured currents corrected t o eliminate charging currents. 'D, = y 6,'/t.
for diffusional transport in both the membrane and solution phases. We have modified this model to omit diffusion within the solution. Our system can be described by the following expressions:
C, ( x , O ) = aC* initial condition C, (0,t) = 0 boundary condition 1 C, (6,,t) = aC* boundary condition 2
Equation 12 is plotted in Figure 6. This plot was used to obtain values of y from experimentally determined current ratios, i(t)/&. Once y was known, then D, could be calculated without the need to know the partition coefficient. This approach is demonstrated in Table I1 for a 0.027-em-thick membrane rotated at 3000 rpm in 0.0094 M potassium ferrocyanide and 1M KC1 buffered at pH 4.86. The transient current was recorded; then i(t)values were read from the plot at the times indicated. From the calculated values of i(t)/iBs, y was read from Figure 6 and used to calculate D,. The mean value of D, of 3.4 X lo4 cm2/s from Table I1 is in reasonably good agreement with the value of 4.14 X lo4 cm2/s at the same pH and membrane thickness that was calculated from De(ca) and De(ss)(see Figure 5 ) . Registry No. K,Fe(CN)6, 13943-58-3; Pt, 7440-06-4.
(9) (10) (11)
Equations 8-11 can be solved in a manner analogous to that used by Peerce and Bard (11) to obtain eq 1 2
(1) Lowe, Christopher, R. Trends Blotechnol. 1984, 2 , 59-65. (2) Rechnitz, Gary A. Science (Washington, D . C . , 1883) 1981, 214, 287-29 1. (3) Gullbault, George G.; Danielsson, Bengt; Mandenius, Carl F.; Mosbach, Klaus Anal. Chem. 1983, 5 5 , 1582-1585. (4) Ianniello, Robert M.; Yacynych, Alexander M. Anal. Chem. 1981, 5 3 , 2090-2095. (5) Gough, David, A.; Leypoldt, John K. AIChE J. 1980, 2 6 , 1013-1019. ( 6 ) Gough, David, A.; Leypoldt, John K. Anal. Chem. 1979, 5 1 , 439-444. (7) Randles, J. E. B. Can. J. Chem. 1959, 3 7 , 238-246. ( 6 ) Aibery, W. J.; Hitchman, M. L. Ring-Disc Electrodes, Oxford University Press: Oxford, 1971; pp 1-171. (9) Castner, James F.; Wingard, Lemuel B., Jr. Biochemistry 1984, 23, 2203-2210. (IO) Ikeda, T.; Schmehi, R.; Denisevich, P.; Willman, K.; Murray, R. W. J. Am. Chem. SOC. 1982, 104, 2683-2691. (11) Peerce, Pamela, J.; Bard, Allen J. J. Electroanal. Chem. Interfacial Electrochem. 1980, 112, 97-1 15. (12) Millis, James, R.; Wingard, Lemuel, B., Jr. Biofechnol. Bioeng. 1981, 2 3 , 965-98 1. (13) Levlch, V. 0. Physicochemical Hydrodynamics ; Prentice-Hall: Englewood Cliffs, NJ, -1962. (14) Wingard, Lemuel, B., Jr.; Cantin, Leslle A.; Castner. James F. Biochlm. Blophys. Acta 1983, 748, 21-27. (15 ) Adams, Ralph, N. Electrochemistry at Solid Electrodes ; Marcel Dekker: New York, 1969; p 220. (16) Radola, B. J. Blochlm. Blophys. Acta 1973, 295, 412-426. (17) Brown, J. R. I n Albumin Strvcture, Biosynthesis, Function; Peters. T.. Sjohoim, I.,Eds.; Pergamon: New York, 1978; pp 1-10, (18) Aoki, K.; Foster, J. J. Am. Chem. SOC. 1957, 79, 3385-3393.
RECEIVED for review July 16,1986. Accepted September 19, 1986. Part of this work was presented at the 11th Federation of Analytical Chemistry and Spectroscopy Societies Meeting, Sept. 16-21,1984, at Philadelphia, PA. This work was supported by Contract DAAG29-82-K-0064 from ARO.
