The determination of noradrenaline using differential double pulse voltammetry

J. Electroanal. Chem., 125 (1981) 205--217

205

Elsevier Sequoia S.A. Lausanne -- Printed in the Netherlands

THE DETERMINATION OF NORADRENALINE USING DIFFERENTIAL DOUBLE PULSE VOLTAMMETRY

W. JOHN ALBERY

Department of Chemistry, Imperial College, London SW7 2A Y (England) T. WILLIAM BECK and WILLIAM N. BROOKS

Physical Chemistry Laboratory, Oxford OX1 3QZ (England) MARIANNE FILLENZ

Department of Physiology, Oxford OX1 3PT (England) (Received 13th August 1979; in revised form 4th February 1981)

ABSTRACT The application of differential double pulse voltammetry (DDPV) for the determination of noradrenaline using various electrode materials is described. From a theoretical description of the shape of DDPV voltammograms for reversible, quasi-reversible and irreversible electrode kinetics, it is shown that the concentration can be simply determined from the product o f the peak height and the peak width. Simple corrections are presented for the effect of the finite difference between the two potentials in each pair of pulses and for finding the true peak height and its position. Experiment and theory are shown to be in good agreement for the determination on a carbon paste electrode of concentrations of noradrenaline from 1 pM to 1 mM.

INTRODUCTION

Electroanalytical techniques are important for the determination of catecholamines because electrodes can be used in vivo to study concentration variations in the brain [1]. In 1976 Lane and Hubbard [2] showed that differential double pulse voltammetry (DDPV) on a stationary platinum electrode was a promising technique for the determination of dopamine and noradrenaline. They have since [3] shown that cyclic voltammetry and ordinary differential pulse voltammetry can be used in vivo. In this paper we describe the development of the theory and practice of the differential double pulse technique for the determination of noradrenaline in vitro. The pulse train for differential double pulse voltammetry is shown in Fig. 1. Between pulses the electrode is at potential E0 where the noradrenaline is not oxidised. The electrode is pulsed into a potential region where the noradrenaline is oxidised and held there in our case for 25 ms. The current is sampled towards the end of each pulse and the difference in current for each pair of pulses is measured. The advantage of the technique [2] is that the electrode spends only 5% of the measuring time at potentials where the noradrenaline is oxidised, and this prevents the build-up of polymerised products which poison the electrode. In ordinary differential pulse 0022-0728/81/0000--0000/$02.50 © 1981 Elsevier Sequoia S.A.

206

E

I~_#._l

Fig. 1. D D P V pulse train. T y p i c a l values are AE = 25 m V , AE! = 14 m V , pulse w i d t h = 25 ms a n d s a m p l e t i m e t s = 17 m s ; t h e t i m e interval b e t w e e n pulses is 0.5 s. As given b y eqn. (21) t h e d i f f e r e n c e in c u r r e n t for e a c h pair o f pulses is p l o t t e d at t h e average p o t e n t i a l E1,2.

voltammetry small-amplitude pulses are imposed on a voltage ramp [4], and so the electrode does n o t spend much of its time at E0. EXPERIMENTAL

Stationary disc electrodes with radii ranging between 0.5 and 4 mm were used throughout; the insulator surrounding the electrodes was e p o x y resin, Araldite MY 753. Carbon paste electrodes were made with Nujol [5] or silicone oil [6]. A block diagram of our control circuit for DDPV is shown in Fig. 2; a detailed circuit diagram may be obtained from the authors. The double pulse generator consists of four linked monostables; this gives great flexibility in the choice of the amplitude and timing of the pulse train. The end of the second

T /

'

' r..Jl NI.~

)

e

I

Pulse1.~

~

I_

I Subtrootor

I From working eliotrode

Fig. 2. B l o c k diagram o f a p p a r a t u s .

' - - +working -electrode

/

ContrOl

Output

207

pulse of each pair of pulses triggers a "staircase generator" the o u t p u t of which is added to the pulse train. The chopper is an analogue switch controlled by the pulses from the double pulse generator; during a pulse the o u t p u t of the chopper is the o u t p u t of the adder, while during the space the o u t p u t is held at 0 V. The o u t p u t of the chopper is added to a dc level and this sum then controls the electrode potential. Each of the pair of pulses triggers a "sample and h o l d " which measured the current; the difference between the "sample and hold outp u t s " is measured by the subtractor during the space after each pair of pulses and is recorded on a Gold Advance Digital Storage Oscilloscope, OS 4000. In our work we used pulse widths of 25 ms separated by spaces of 0.5 s. This ensures that there is sufficient time for the surface concentration of catecholamine to return to its bulk value between each pulse. The difference, AE, in Fig. 1, between the amplitude of the second pulse compared to the first of each pair was 25 mV, and normally the increment in voltage for each pair, AEI, was 14 mV. The current was sampled 17 ms after the start of each pulse; this time was chosen to obtain as large a faradaic c o m p o n e n t to the current as possible, after the double-layer charging is Complete. The solution was contained in a 20 cm 3 thermostatted pot. The counter electrode was a Pt wire and the reference electrode was a saturated calomel electrode (SCE); all potentials are reported with respect to SCE. All experiments were carried out at 25.0°C. All chemicals were of AnalaR quality except for noradrenaline which was supplied by Sigma Chemical Co. and used w i t h o u t further purification. Solutions of noradrenaline were made up by dilution with oxygen-free water and were stored in a refrigerator. Nujol was supplied by Hopkin and Williams and silicone oil by the Aldrich Chemical Co. 17,563-3. Glassy carbon was supplied by the Ringsdorff Carbon Co. (ES 40) and Ultra Carbon Co. UCP1-M graphite was used for making paste electrodes. THEORY

Basic e q u a t i o n s

Lane and Hubbard [ 2] assumed t h a t the electrochemical system was reversible. For this case, using DDPV, a sharp peak is obtained, the height of which is proportional to the concentration. However the maintenance of complete electrode reversibility for periods of several hours or days during an in vivo experiment is a severe restriction. We have examined the effect of the electrode kinetics on the shape of DDPV peaks. For the system k~ A~--~B + ne k~ we assume t h a t A and B each obey Fick's second law of diffusion with diffusion coefficients D A and Dm Before each pulse the initial conditions are a=a~

b =0

where lower-case letters represent concentrations and a~ is the bulk concentration of A. The same boundary conditions are f o u n d as x -* ~ , where x is the

208

distance from the electrode. At the electrode surface we find:

This problem has been solved by Delahay [7] and we find: is = n F A k~a~ exp(~"2) erfc(~')

(1)

where = (k'fD~, '/2 + k ; D ; '/2) .~±'/: and is is the current observed at Q. The function exp(~"2) erfc(~') has been tabulated by Kouteck:~ [8]. To calculate the shape of DDPV curves we first write for the potential dependence of the rate constants: !

--

t

kf-k0exp(aP)

and

l

t

kb=k0exp[-(1-a)P]

where P = n(E - - E ~) F / R T

(2)

and E ~ is the standard electrode potential for the couple in the medium. Then we calculate Ai from eqn. (1) a t P and P + AP. In reporting the results we normalise the current with respect to the maximum current that would be observed for a reversible A, B couple: y

Ais/AP (~i/aP)max

-

-

4x/Tr~ A [ e x p ( a P + ~-2) erfc(~')] AP

(3)

where k'o(tJD) ' n

=

(4)

~" = X exp(aP)[1 + exp(--P)] max

447/"

6/oo

(5) (6)

and we have assumed DA = DB = D. Equation (3) describes the shape of DDPV peaks for any value of AP, where AP is the difference in potential between the first and second pulse of each pair. For small values of AP we can differentiate the square bracket in eqn. (3) to obtain the limiting shape as AP -~ 0, written as Y0, where Yo = 4X exp(aP){ [2x/~r~" exp(~"2) erfc(~') -- 2] X [a~" -- X exp{--(1 -- a) P} ] + ax/~r exp(~"2) erfc(~')}

(7)

For a reversible system, where X > > 1, eqns. (3) and (7) simplify to y ~ 4A[1 + e x p ( - - P ) ] - l / A P

(8)

and Y0 ~-- 4 exp(--P)/[1 + exp(--P)] 2

(9)

209

These equations agree with those derived by Parry and Osteryoung [4] for this particular case. For the irreversible case, where ~ < < 1, we obtain Y ~--

4x/~aA[~ exp(~ 2) erfc(~')] A[ln ~'1

(10)

and Y0 ~- 4a~'[x/~(1 + 2~"2) exp(~"2) erfc(~') -- 2~']

(11)

where ~"~ )~ exp(aP)

(12)

Shape o f peaks for AP -+ 0 We will first discuss the shapes of the peaks for the case where AP -~ 0 using eqns. (7), (9) and (11). We will subsequently consider the effect on the shape of increasing AP. In Table 1 we collect together results from eqns. (9) and (11) for the peak height, Yo,m and peak width at half height, Pw for the reversible and irreversible case. The results for the reversible case agree with those of Parry and Osteryoung [4]. For the irreversible case Fig. 3 shows a plot of eqn. (11) and is the general shape of an irreversible DDPV peak. The form of eqn. (11) means that the peak height is proportional to a, while the form of eqn. (12) means that the peak width is inversely proportional to a. If one integrates the area under a DDPV peak then the result must be the limiting current regardless of the electrode kinetics. In our notation from eqns. (1), (3) and (6): d-oo

f

y dP = 4

(13)

The results in Table 1 show that the product of the peak height and peak width at half height are reasonably close to 4. More important, the results for the two extreme cases differ by only 1%. This suggests that the effect of electrode kinetics on the shape of DDPV peaks can be allowed for by measuring the product of peak height and peak width rather than just the peak height. Having dealt with the two extreme cases we now explore the validity of this approach for the quasi-reversible case. Using eqn. (7), Fig. (4) shows how the peak width and the position of the peak, Pp, with respect to the standard electrode potential (P = 0) depends upon a and )~. The figure is bounded by the

TABLE 1 Peak heights and peak widths at half height

Reversible Irreversible

Eqn.

Peak height/ Y0 ,m

Peak width/ Pw

Product/ Yo,mPw

(9) (11)

1.00 1.28~

3.53 2.79/a

3.53 3.57

210

y/c~

I'0

aP

20

Fig. 3. The shape of the DDPV current voltage curve for the general irreversible case from eqn. (11). The position on the potential axis (but not the shape) depends on k; for this case k = 10 -s.

limiting value of a = 1 and the low value of a = 0.175. For X > 2 the limiting reversible shape is f o u n d at P = 0, with a width of Pw = 3.53. The lower the value of X the more irreversible is the reaction and the peaks appear (for an oxidation) at more positive potentials. For k < 0.01 the limiting irreversible shape is found. As given in Table 1, the peak width is then inversely proportional to a and hence the a contours are parallel to the x-axis. The insets show the shape of peaks for some of the intermediate cases along the a = 0.175 contour. For quasi-reversible systems with low values of a a peak with two maxima is found. This shape has also been f o u n d by Dillard et al. [9], who calculated shapes for differential pulse voltammetry peaks at a dropping mercury electrode using digital simulation. The reason for the double peak is t h a t with a lower value of a a quasi-rever-

//

/

1c X),'025

/

~-0"5 ~

~, ! / I

o

/oo,,o

I -/

~-o.2o

~= 050

).:001

{//

~*

,/o(-o.Ts.~" ~=l'O I

lo

Fig. 4. Diagram showing how the peak width Pw and peak position Pp depends on c~ (shown by solid contours) and k (shown by broken contours). The insets show a set of DDPV current voltage for the case where o~ = 0.175. The reasons for the double peaks are discussed in the text. There is a discontinuity in Pp when the two peaks are of equal height and a discontinuity in Pw when the shoulder is at half height. The discontinuities are indicated by dotted lines. The reversible shape is found at Pp = 0 in the b o t t o m left-hand corner and the irreversible shape when Pp ~ 10.

211

sible system will change from being reversible, when the fast back reaction is still operative for P ~ 0, to irreversible as the back reaction is switched off as P increases. The s w i t c h ~ f f is rather sharp because the back reaction has a large transfer coefficient (1 -- a). The low value of a means t h a t the irreversible peak of the wave is then displaced sufficiently far along the potential axis for two peaks to be observed. The existence of these double-peaked shapes is an unfortunate complication in DDPV since t h e y might lead to the erroneous conclusion that there were two different substances present. The double m a x i m u m is only observed for rather low values of ~ (~ < 0.25), but at larger values of ~ the same effect can cause noticeable shoulders. An advantage of DDPV is t h a t the analytical theory presented here allows one to test the shape of such curves and so distinguish between a quasi-reversible low ~ case and a case containing two different species. The double-peak effect is the reason why in Fig. 4 the peak width for a = 0.175 passes through a m a x i m u m with a sudden change at Pp ~ 11.3. This sudden change is when the lower "reversible" peak drops below the half height. The discontinuity in Pp for a peak width of 17.7 occurs when the two peaks are of equal height. From the peak width and its position on the potential scale one can use Fig. 4 to determine values of k and ~ for any system. We now return to the use of the peak height times the peak width for the determination of the concentration of A. In Fig. 5 we plot a contour diagram which displays a correcting function, f, where f

=

3.55/Yo,mPw

(14)

As shown in Fig. 4 there are some cases where Pp is negative. In this region f

2o

...........................

..~'/_.~A.I.4"

ii

111 / / / / Igl I / /f,o.~. ~I f,o.9o~,, / // /f.o-gB

~.o.9~

/

.~-o.sTs

IVT;-"

.,o.o

.t= 1"00

2

6

,'0

Pp

Fig. 5. Similar diagram to Fig. 4 giving contours {broken ]ines) for the correction function, f, d e f i n e d by eqn. (14). For m o s t cases f is reasonably close to unity, and the values t o use can be f o u n d from the measured values of Pw and Pp.

212

changes so rapidly t h a t the values cannot be displayed conveniently. The shapes are so peculiar t h a t the product of peak height and peak width is not a good estimation of the concentration. Apart from this region the function f is generally close to unity and can be f o u n d to sufficient precision from Fig. 5. Hence, in general, the product of peak height and peak width is a convenient and accurate m e t h o d for estimating concentrations from DDPV peaks.

Effect o f finite We now examine the effect of AE or AP, the difference between the potential of the first and second pulses of each pair. For this purpose we use eqns. (3), (8) and (10). For the reversible case from eqn. (8) we find the same result as Parry and Osteryoung [4] :

and for the peak width we find Pw 21n{2+C+ [3+4C+C21 'n} w - -- 3.53 3.53

(16)

where C = cosh(~AP) and w = 1 as AP -~ 0. The functions Ym and w are shown in Fig. 6 together with the product wym. It can be seen that the effect of increasing AP decreases the peak height and widens the peak. However, the product WYm remains very close to unity; the limiting value of the product at large AP is in fact 1.135. In the region of interest (AP < 7) an approximation which holds to within 3% is

wy~ ~ 1 + AP/80

(17)

For the irreversible case explicit analytical functions cannot be found. However, evaluation of eqn. (3) leads to the results in Fig. 7. Again the product

V

2'0

vym 1.0

. . . . . . .

1-0

.

.

.

.

Ym I 5"0 ,,~P

Ot

5.0 ,~p

Fig. 6. Plots of functions describing the peak height, Ym, peak width, w, and their product from eqns. (15) and (16) as a function of ~P, the difference in potential between the first and second pulses. These functions are for the reversible case. Fig. 7. Plots of functions describing the peak height, Yra, peak width, w, and their product as a function of AP for the irreversible case.

213

wym remains close to unity and may be approximated by wYm ~ 1 + ~AP/60

(18)

Since ~ can be estimated for the peak width using the results in Table 1 we can combine eqs. (17) and (18) to obtain

wym ~- 1 + 0.045 AP/Pw

(19)

This relation holds for both the reversible and irreversible cases where f = 1. Investigation of the quasi-reversible cases, where f < 1, leads to the following correcting function: WYm ~-- f-~[1 + ( 0 . 5 4 5 f - 0.5) AP/Pw]

(20)

This function holds to within 3% for AP/Pw < 2 and for the values of f shown in Fig. 5, always providing t h a t the system is n o t near the discontinuity in peak width. Hence, while the peak height is fairly sensitive to AP -- and this means that one has to use values of AP less than ~ 1 -- the product WYm is much less sensitive and values of AP up to 7 can be used. These larger values of AP will result in wider peaks so t h a t it will be more difficult to resolve two different substances. On the other hand, the absolute values of the current will be larger. The tanh form of eqn. (18) shows t h a t the absolute value will increase for AP < 7. For AP > 7 a limiting value is reached and no further increase will be found; this limit corresponds to having the first pulse at the f o o t of the wave and the second pulse at the top. Finally, the position of the peak on the potential scale with respect to E ~ does n o t alter significantly with AE if one plots Ai for each pair of pulses at the potential E1.2 where E1.2 = E1 + ½AE

(21)

and EI is the potential of the first pulse.

Correction for true peak height and position Because the electrode poisons, we wish to determine the concentration with as few pulses as possible. This means that there may not be a pulse exactly at the m a x i m u m of the polarogram. By treating the top of the DDPV as a parabola, one can show for the three successive readings Ail, Ai2 and Ai3, where Ai2 is the largest reading at potential E2 and Ail and Ai3 are the two adjacent readings, that the true peak height Aim and the true position of the peak Ep are given by Aim = Ai2 +

Ai3 -- All ~E 4 AE

(22)

and Ep - - E 2 AE = 7 + ¼ 7 - 1 -

1 -1)2 111:2 [(7 + 4 7 --

(23)

214 where 2Ai2 -- Ail -- Ai3 Ai3 -- Ail

7 -

We have tested these corrections using the shapes of the irreversible and reversible peaks and have shown that they hold to within 2%, even when Ail and Ai3 is two-thirds of Aim. Hence, in our work, values of peak current and Ep were obtaine~t using eqns. {21), (22) and (23). RESULTS AND DISCUSSION A number of different electrode materials have been investigated. The ideal material would first have a low residual current in the region where the electrode is pulsed. Secondly it is desirable, b u t not essential, that the electrode kinetics of the catecholamine should be as reversible as possible. We have found that Pt electrodes hav e large residual currents, and, although the electrode kinetics are fairly rapid when the electrode is clean (k'/cm ks -1 ~ 6), the electrode poisons rather rapidly. This observation agrees with that of Lane and Hubbard [2]. We have tried coating the Pt electrode with I-, and although we have observed some improvement we have n o t succeeded in obtaining the

AA ~A

~=1"25

~ffi0"50

50

# 0 •

L,

),:0"14

~ =0"30

~A

,l

Ew/mV

A 500

• ~mx

O0

5O

700 500 Et2/mV

700 El.z/mV

"

"is

|+.,

60

I 40

I 580

I 600

I 620

I

640 Ep / mV

Fig. 8. Typical experimental results (X) for the determination of noradrenaline using DDPV. The concentration o f noradrenaline was 4 × 10 -4 M in 1 M H2SO4. The four runs were taken over a period of ~ h. The solid lines show theoretical curves calculated with 0~ = 0.5, E +/mV = 577 and the given values o f k; these values o f k were chosen to give agreement between the experimentally and theoretically determined peak positions. Fig. 9. Results from 136 different experiments showing the peak width E w as a function of the peak position Ep. The solid line is the contour calculated for ~ = 0.5.

215

excellent results reported by Lane and Hubbard [2]. We find the behaviour on Rh to be similar to that on Pt. We have obtained better results on glassy carbon and carbon paste electrodes. For our electrodes the carbon paste electrodes had lower residual currents than the glassy carbon electrode and we found, like Sternson et al. [6] t h a t the silicone oil carbon paste electrode had somewhat faster electrode kinetics than the Nujol past electrode. We have therefore used the silicone oil carbon paste electrode. Typical results taken from a series of successive scans are shown in Fig. 8. It can be seen that the peaks decrease and broaden as the electrode gradually poisons. Figure 9 shows a plot of Ew, the width of the peak at half height, against Ep, the potential at which the peak is observed for 136 different scans on different electrodes. By taking E ~ = 577 m V we can fit the data to a contour of a ~- 0.5 which is equivalent to the contours in Fig. 4. This contour was calculated from eqn. (3) using AE/mV = 25 in AP and n = 2. This shows that the poisoning proceeds principally by a decrease in k'o/cm ks -1 from 20 to 0.2 rather than a change in a. We can now calculate the shapes of the curves shown in Fig. 8. Reasonable agreement is found between experiment and the theoretical shapes. The value of a close to 0.5 means that for a two-electron reaction [5], one electron is transferred in the transition state and suggests t h a t the rate-determining step takes place after a pre-equilibrium electron transfer. The overall reaction is

HO~/~TR~_O~I~R H0 " . . ~ " o,~',,,,~"

.2H ÷ "2~

where R is CHOH CH2NH2. These results suggest t h a t rate-limiting step is the loss of one of the protons after the removal of the first electron forms the "semi-quinone" species. We combine the results of the theoretical section from eqns. (3), (6), {14), (16) and (20) to obtain

fEw(Ais)m 1 + (0.545f -- 0.5)

AEIEw

= Y = 0.50n

AF(D/t,)InAE a~

(24)

where 0.50 = 3.55/4 ~/Tr and a~ is measured in mol cm -3.

/x

-S log(Y/W)

x/ ×/

-4

/,

x

x//

Xj

-6

Iog(a~/M)

-3

Fig. 10. Plot of log Y calculated from eqn. (24) against log (aoo), where aoo is the concentration o f noradrenaline in 1 M H2SO4.

216

3O

,/

Y/FW

,/

(,dE/mV)obs

/,/

?C I0 00 /

/((

IS

,/

I0

fx xs x

J

/f/ I I

50

i

(ts/S)-~

5

I

I

10 15 (,~E/rnV )calc

Fig. 11. Variation of Y, calculated from eqn. (24), with the sample time t s. Fig. 12. Comparison of observed and calculated values of the shift in peak position, ~Ep, on altering ts, assuming a = 0.5.

From Fig. 5 we see that for our values of a and X, f lies between 0.95 and 1.0 and hence the correcting term is always close to unity. Figure 10 shows a plot of log Y against log a~, where a~ is the concentration of noradrenaline in the solution. A good straight line of gradient 1 is f o u n d for concentrations from 1 p.M to 1 mM. Each point in Fig. 10 is the mean of at least 15 different experiments, and for these different experiments the electrode kinetics varied in the manner shown in Fig. 9. From the intercept we obtain a plausible value of D / c m 2 p s - ' = 4.6. The good straight line shows that DPPV can be used to determine concentrations of noradrenaline, even though the electrochemical rate constants are changing by over t w o orders of magnitude. We have further tested eqn. (24) by varying ts from 17 ms up to 54 ms. Figure 11 shows a plot of Y vs. t~ ~/2. Reasonable agreement is found with the straight line calculated from the results in Fig. 10. Increasing t~ n makes the system more reversible and hence Ep shifts towards E ° b y an a m o u n t AEp. Figure 12 compares values of AEp calculated from the position on the a = 0.5 contour with the observed values. Again reasonable agreement is found, thereby confirming our theoretical analysis. Finally, we summarise the improvements we suggest to DDPV for the determination of c o m p o u n d s such as catecholamines: (1) By treating the top of the DDPV peak as a parabola the peak height and peak position can be obtained with a small number of pulses, see eqns. (22) and (23). (2) By measuring the p r o d u c t of peak width and peak height, the effect of poisoning on the electrode kinetics can be reduced to the well-behaved correction function f shown in Fig. 5. (3) For the p r o d u c t of peak width times peak height there is a simple correction function (eqns. 20 and 24) for the effect of AE and this allows an appropriate choice of AE with respect to detection limits and resolution. ACKNOWLEDGEMENT

We thank the M.R.C. for a project grant for the support of this work.

217 REFERENCES 1 2 3 4 5 6 7 8 9

R.N. Adams, Anal. Chem., 48 (1976) 1126A. R.F. Lane and A.T. Hubbard, Anal. Chem., 48 (1976) 1287. R . F . L a n e , A . T . H u b b a r d a n d C.D. B l a h a , B i o e l e c t r o c h e m . B i o e n e r g . , 5 ( 1 9 7 8 ) 5 0 4 . E.P. P a r r y a n d R . A . O s t e r y o u n g , A n a l . C h e m . , 37 ( 1 9 6 5 ) 1 6 3 4 . M.D. H a w l e y , S.V. T a t a w a w a d i , S. P i e k a r s k i a n d R . N . A d a m s , J . A m . C h e m . S o c . , 8 9 ( 1 9 6 7 ) 4 4 7 . L . A . S t e r n s o n , A.W. S t e m s o n a n d S.J. B a n n i s t e r , A n a l . B i o c h e m . , 7 5 ( 1 9 7 6 ) 1 4 2 . P. D e l a h a y , J. A m . C h e m . S o c . , 7 5 ( 1 9 5 3 ) 1 4 3 0 . J. K o u t e c k : ~ , C h e m . L i s t y , 4 7 ( 1 9 5 3 ) 3 2 3 . J . W . D i l l a r d , J . J . O ' D e a a n d R . A . O s t e r y o u n g , A n a l . C h e m . , 51 ( 1 9 7 9 ) 1 1 5 .