J. Electroanal. Chem., 151 (1983)47-64 47 Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands

D I F F R A C T I V E S P E C T R O E L E C T R O C H E M I S T R Y

A S E N S I T I V E P R O B E O F T H E E L E C T R O C H E M I C A L D I F F U S I O N LAYER

PAULA ROSSI and R.L. McCREERY *

Department of Chemistry, The Ohio State Universtty, Columbus, OH 43210 (USA.)

(Received 6th July 1982; in revised form 9th December 1982)

ABSTRACT

The utility of diffracted light for monitoring species generated or consumed at an electrode surface was examined, based on theory presented earlier. When laser light diffracted by an electrode is used to make absorbance measurements, the resulting absorbance vs. time transients are sensitive to the presence of chromophore in the diffusion layer, within as little as 5 /~m of a planar electrode surface. In both theory and experiment the absorbance reaches a constant value after about 200 ms, which is related to the concentration of an electrogenerated absorber via Beer's law. The path length for absorbance equals the electrode length along the optical axis, and was varied from 0.014 to 1.1 cm. The linear range of the method is 5 #M to 6 mM for test systems, and the observed response had the predicted dependence on diffraction angle, time, concentration, path length, and wavelength. A detection limit of 1.2 #M was established for electrogenerated trianisylamine cation radical. The method can be at least 400 times more sensitive than conventional spectroelectrochemical methods.

INTRODUCTION

The value of using U V - V I S spectral techniques to examine electrochemical processes has been recognized since 1964 [1], and spectroelectrochemical methods have been employed to determine E ° ' values, homogeneous and heterogeneous rate constants and spectral properties of species associated with electrochemical charge

transfer [2,3,4]. The major mot iva t ion for using spectrophotometry to moni to r solut ion components generated electrochemically lies in the greater selectivity and in fo rmat ion content resulting from the combina t ion of optical and electrochemical

methods. A variety of configurat ions has been employed for spectroelectrochemistry, inc luding light t ransmission through a part ial ly t ransparent electrode [2,3], external [5,6,7] and in ternal [8] reflection, and an optical beam passing parallel to a p lanar electrode [9-11]. A previous report from this laboratory presented the theory and experimental verification for the combina t ion of U V - V I S absorpt ion spectroelectro- chemistry with the quite distinct p h e n o m e n o n of optical diffraction [12]. A laser

* Author to whom correspondence should be addressed.

0022-0728/83/$03.00 © 1983 Elsevier Sequoia S.A.

48

beam passing parallel to a planar electrode surface is partially scattered into the geometric shadow of the electrode, and the diffracted light can be monitored by a photomultiplier tube. When an absorbing species is generated at the electrode, it diffuses across the beam and attenuates the diffracted light. Because of the Fourier transform relationship between beam cross section and diffraction pattern, the behavior of the diffracted light during electrogeneration of a chromophore can be predicted. It was shown both theoretically and experimentally that absorption spectroelectrochemistry using diffracted light has several advantages over conven- tional methods, including high sensitivity and rapid time response. However, the initial report was primarily theoretical, and involved a limited range of experimental variables, e.g., electrode length, diffraction angle and concentration. The purpose of the present report is to discuss the generality of the phenomenon with respect to a variety of variables and chemical systems. Theoretical and experimental results will be presented for the effect on diffracted light of variations in diffraction angle, electrode length, concentration, and wavelength. Both organic and inorganic systems were studied, in both aqueous and non-aqueous solvents. The results permit assess- ment of the linearity and dynamic range of the technique when applied to micro- molar solutions of certain organic systems.

EXPERIMENTAL

Electrodes

Platinum electrodes were prepared by polishing the edge of sheet metal (Mat- they-Bishop) of 0.014, 0.027 and 0.05 cm thickness. Glassy carbon obtained from Atomergic was cut into squares with lengths of 0.16, 0.63 and 1.12 cm. The active surface of each electrode was prepared by a polishing procedure designed to ensure a microscopically and macroscopically flat surface. Electrodes were mounted inside a pyrex cylinder with Castolite Resin (Buehler) with the edge to be polished exposed on one end. A mechanical polisher was used (Buehler minimet) with a series of abrasives starting with silicon carbide paper (180, 240, 320, 400, 600 grit), "metadi" diamond (15/~m, 6/~m, 1/~m), then alumina A (0.05 #m) and alumina B (0.03/~m). (All abrasives were Buehler products.) This procedure required a total of a few hours and was necessary only once for each electrode. Polishing time on each abrasive was kept brief (a few minutes) to avoid rounding off the surface. After polishing was complete, the resin was dissolved with "Stripsolve" (Cargille Laboratories). A typical electrode lasted for several months of daily use, with occasional cleaning in con- centrated sulfuric acid being necessary.

CeH and lase~

For the platinum electrodes, the capillary cell described earlier was employed [12]. The longer carbon electrodes were mounted as shown in Fig. 1, in a cell made from quartz plate. For either cell, the electrode surface was aligned parallel to the beam by

49

Input BeGm

f Workmg electrode lead

Ref ,~ b

Aox , I / , o I ii I Ill//

2 crn t 0 Meter

PMT

Fig. 1. Experimental configuration for measurements with glassy carbon electrodes (not to scale). Working electrodes consist of a carbon square (a) epoxied to a glass tube, with a platinum wire making contact through mercury (b). An SCE and a platinum auxiliary electrode complete the conventional three electrode circuit. The laser beam has an approximately 2-mm diameter cross section, which is bisected by the electrode plane. Diffracted light appears symmetrically above and below the beam axis, but the photodetector was placed above the beam to rmnimize reflected or other non-diffracted hght. The diffraction angle fl was determined from the position of the PMT above the beam axis.

not ing that the diffracted intensity passed through a min imum when the beam and surface were parallel. This alignment was the same as that obtained f rom the reflection [12], and produced absorbance transients which agreed most closely with theory. A reliable check of electrode alignment was the variation in the limiting absorbance occurring after 0.5 s of electrolysis. The alignment producing the flattest plateau after 0.5 s corresponded to that obtained by the reflection method or by obtaining the min imum diffracted intensity. Three lasers were used in this work, a H e - N e (5 m W at 632.8 nm), a H e - C d ( I0 m W at 442 nm) and an Ar ÷ pumped dye (R6G) laser (570-630 nm, approx. 10 m W at cell). The auxiliary electrode was isolated f rom the main solution by a porous glass (Vycor) tube.

Chemicals

The systems used to test the method included t r i (p-bromophenyl) -amine (TBA), t r i (p-methoxyphenyl)amine (TAA), K4Fe(CN)6, and tetramethyl-p-phenylenedia- mine (TMPD). Relevant physical data on these compounds are shown in Table 1. Te t rae thylammonium perchlorate (TEAP), K4Fe(CN)6 , and K N O 3 were reagent grade and were used without purification. Commercia l T M P D dihydrochloride (Sigma) was converted to free base [16] and recrystallized from benzene, and TBA was synthesized by a published procedure [17]. T A A was a gift f rom Rober t Waiters of the University of Illinois, Chicago Circle.

Optics and electronics

The optical arrangement was identical to that described previously [ 12], except a 1 m focal length lens was used to improve angular resolution. A 0.8 m m aperture

50

m o

8 0

T

T

>

r ~

0

x x x

z z z

51

preceding the photomultiplier yielded an angular resolution of 0.05 °. The ab- sorbance vs. time transients were calculated from the PMT output, as monitored by a Hewlett-Packard computer system. The PMT output was monitored both before and during a potential step applied to the working electrode, and the absorbance was calculated as the common log of the ratio of the initial diffracted intensity to that after the generation of an absorbing species. A PAR 173 potentiostat controlled the potential, with resistance compensation being applied according to PAR proce- dures.

d

Signal averaging was used to improve signal to noise ratio for experiments yielding small absorbance values. For aqueous solutions, five absorbance transients were averaged when the maximum absorbance was less than 0.04 units for platinum electrodes. In acetonitrile, background noise was higher, and 50 runs were averaged when the absorbance was below 0.05 units. For the longer carbon electrodes in acetonitrile, 20 runs were averaged for absorbances below 0.3 units.

RESULTS AND DISCUSSION

• The results are divided into several sections discussing the observed absorbance response in relation to variations in pertinent experimental parameters, such as electrode length, wavelength of the incident beam and the concentration of the electroactive species. Theoretical predictions are compared to experimentally ob- served absorbance vs. time transients where relevant. The theoretical transients are based on the approach described previously, using a 2048 point numerical Fourier transform routine.

Electrode length

For the purpose of predicting diffracted intensity, the electrode was assumed to be infinitely thin along the optical axis [12]. Therefore, the beam cross section at the electrode was attenuated by electrogenerated chromophore using the actual electrode length (thickness), but the diffraction of the attenuated beam was assumed to originate at an infinitely thin edge. In view of this assumption, the question arises of how valid the theory will be when applied to "thick" electrodes, having path lengths of 0.1 to 11 mm along the optical axis. Figure 2 shows a comparison of observed and theoretical diffracted intensity in the absence of any electrogenerated chromophore, for a relatively thin Pt electrode having a length of 0.027 cm along the optical axis. Absolute intensity measurements were not made, so the two curves were scaled in amplitude to allow comparison of their shapes. For diffraction angles of 0.6 ° to 1.3 °, the two curves agree well, indicating that intensity falls off with angle as predicted by theory for this region. At angles outside this range there is significant deviation of theory and experiment. For a longer electrode (0.63 cm) shown in Fig. 3, the comparison of theory and experiment is poor, with no angles producing the expected intensity profile. Furthermore, the experimental intensity is weaker than for the 0.027 cm electrode, and falls off more rapidly than predicted by theory at all angles.

52

0 5

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_ c 0 5

0 9 O

O 8

O 7

O6 0

0 O

O 2

O I

0 I I I I I I

0.5 0.5 07 0 9 I.I I 2 I 4

diffraction ongle/°

Fig. 2. Diffraction by a 0 .027 cm thick Pt electrode in the absence of electrogenerated absorbers. Points are relative intensities measured at various diffraction angles, while the solid curve is the intensity predicted from theory. Absolute intensity was not measured, so the experimental points were scaled to provide the best fit with theory (~, = 633 nm at 5 mW) .

One might expect that absorbance vs. time transients from the thinner electrodes should show the best agreement with theory, since these conditions best approximate the assumption underlying theoretically predictions. Four such transients are shown in Fig. 4, for the generation of TBA ÷ at a 0.027 cm Pt electrode. The theoretical transients were calculated from values of the diffusion coefficient, concentration, and molar absorptivity obtained from independent measurements (see Table 1), and employed no adjustable parameters. Good agreement between theory and experi- ment was observed in the range from 0.65 to 1.2 ° , as shown. At higher angles, the weak diffracted intensity makes measurements difficult due to stray light and at lower angles agreement with theory becomes worse than that shown for 0.29 ° . Disagreement between theory and experiment was most apparent in the transient portion of the absorbance vs. time curve, occurring during the first 200-600 ms of the run. The time independent absorbance reached later in a run was much less

53

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08

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06

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o

0.4 o

= O5

o 2

0

I i I I I I i

0 3 0.5 0.7 0.9 I I I 3 1.5

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Fig. 3. Comparison of theory and experiment for diffraction by a 0.63 cm carbon electrode, using the same approach as Fig. 2. At angles above 1.2 ° the diffracted light was too weak to measure reliably (X = 633 nm at 5 mW).

sensitive to experimental conditions such as angle and alignment, and has the theoretical value even if the transient portion did not.

A representative transient for a thick (1.1 cm) electrode is shown in Fig. 5. At no angle was good agreement between theoretical and observed risetime obtained, but the time independent portion of the curve did reach the expected value, as will be discussed in more detail below. Furthermore, the risetime for long electrodes was difficult to reproduce, because of difficulties with alignment. At short times, the thinness of the diffusion layer makes alignment more critical, and this effect is most pronounced with long electrodes, as would be predicted from simple geometry.

Therefore the theory based on a thin edge approximation is valid for thin electrode (0.27 mm) in the angular range from 0.6 to 1.2 °. This is the same range of angles over which the diffraction pattern itself has the expected shape, as shown in Fig. 2. Since the perturbations on the results caused by an edge of finite thickness have not been treated theoretically, this observation is presently an empirical one. The results shown in Figs. 4 and 5 also indicate that there exists a trade-off between

54

theoretical agreement and sensitivity. Longer electrodes have non-theoretical rise- times, but the limiting absorbance, which does agree with theory, is significant even for low concentrations (e.g. 11 /~M in Fig. 5). Shorter electrodes are less sensitive, but should allow deductions about beam shape and possibly concentration profiles to be made (see below).

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Fig. 4. Experimental and theoretical absorbance vs. time transients for generation of TBA + (c = 15,100 M - i c m - 1 ) at a 0.027 cm thick plat inum electrode. Bulk concentration of the TBA precursor was 2.6 raM, and experimental curves were single runs. Dashed lines are theoreucal, calculated from 2048 point Fourier transforms, and the points represent experimental data. Curve A, 0.29 ° diffraction angle; curve B, 0.65°; curve C, 0.87°; curve D, 1.16 ° ()~ = 633 nm at 5 mW).

55

As pointed out previously the limiting absorbance observed after ca 0.5 s is dictated by Beer's law, where the path length is that of the electrode, the molar absorptivity is that of the electrogenerated chromophore, and the concentration is that of the colorless precursor. A useful analogy is an imaginary Beer's law "cell" placed against the electrode. As electrolysis occurs, this cell is "filled" with chromo- phore, and observation of the diffracted light allows this process to be monitored. Once the cell is "filled", the chromophore concentration is constant and the time independent absorbance is reached. Assuming the cell to have a concentration of chromophore equal to 95% of the bulk concentration of precursor when the plateau is reached, and noting that the plateau is reached in 200 ms at 1.16 ° (Fig. 4D), the "cell" is about 5/~m wide (D = 10 -5 cm 2 s- t ) . Therefore the absorbance measured at 1.16 ° is equivalent to that obtained from an imaginary cell placed against the electrode, with a dimension perpendicular to the electrode plane equal to 5/~m and length equal to that of the electrode along the optical axis.

Concentration

While electrode length determines the transient characteristics of the technique, both theory and experiment show that a time invariant absorbance is reached which

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0.04

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Fig. 5. Theoretical (dashed line), and experimental (points) transients for generation of TAA + at a 1.12 cm carbon electrode. Bulk concentration of TAA is 11.2 /tM and the Beer's law absorbance is 0.135 (A = 633 nm at 5 mW).

56

uD

20, / \"

I 6 t/ . . . .

1.2 t i/---- --

0.4 / ~ / ~

0 0.2 04 0 6 08 I 0

T ime/s

Fig. 6. Theoretical transients for TBA + generation at a 0.027 cm electrode at several concentrations and two diffraction angles. Dashed curves are for a 0.58 ° angle, solid are for 1.16 °. Upper curves are for a bulk concentration of TBA of 4.0 m M (%xbc for TBA + = 1.63); middle curves are for 2.6 m M (%,,bc = 1.06); bottom curves, 0.5 m M (%,,bc = 0.203) (k, = 633 nm at 5 roW).

depends on Beer's law parameters. Theoretical transients for three different con- centrations are shown in Fig. 6 for two different diffraction angles with a 0.027 cm electrode. Provided the absorbance is measured on the time independent portion of the transient, the absorbance is linear with concentration as shown in Fig. 7. At short times, a peak is observed whose magnitude increases disproportionately with concentration, resulting in the non-linear response shown in Fig. 7 at 0.25 s. Strictly speaking, the peak at short times is consequence of high absorbance rather than high concentration, and will appear whenever the Beer's law absorbance is larger than about 0.2. In any case, the non-linear region can be avoided by proper choice of measurement time.

Also shown in Fig. 7 are experimentally observed absorbance values at two measurement times for the TBA system on a 0.027 cm Pt electrode. The concentra- tion range is 12/~M to 3.3 m M , and the absorbance was measured at either 0.25 or 1.0 s after the initiation of generation of TBA + cation radical. As expected, the absorbance at 1.0 s is linear with concentration, and follows Beer's law. The molar absorptivity calculated from the slope is 15 121 1 mol-~ cm-n which is within 0.2% of the value of 15 100 1 mol-~ cm-n determined from independent measurements. The standard deviation of the seven values of molar absorptivity determined for seven different concentrations is 2.5%. At 0.25 s, the observed absorbance has the expected non-linearity, closely following theory.

The dynamic range for a single electrode indicated from Fig. 7 is 270 (12/~M to

57

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2.0

1.6

12

08

0.4

0 0 5 I0 2.0 3.0 40

Concentratton f roM

Fig. 7. Absorbance on a funct ion of concen t ra t ion for two electrolysis t imes for the genera t ion of TBA + at a 0.027 cm Pt electrode. Solid l ines are theoret ical curves for the 0.58 ° d i f f rac t ion angle employed.

Circles are exper imenta l values for the absorbance measured at 1.0 s, t r iangles are at 0.25 s after e lectrolysis began. Concen t ra t ion range is 12 ~ M to 3.3 m M (~ = 633 n m at 5 mW).

3.3 m M for this chromophore). In terms of absorbance, this range is 0.0049 to 1.35, with the lower limit being determined by noise. At absorbance values above about 1.5, stray light collected by the PMT caused negative deviations in absorbance measurements from predicted values. This effect was most pronounced at high angles where the diffracted intensity is weak. Therefore, stray light imposes an upper limit on accurate absorbance measurements. A similar dynamic range would be expected for any chemical system on the Pt electrode, but the specific concentration range would be dictated by the molar absorptivity. The range of values for ccb accessible with the experiment depicted in Fig. 7 is 0.181 to 49.8 cm-1.

To test the conformance of the absorbance plateau to Beer's law, a variety of electrode lengths and three chemical systems were examined. A composite plot of the results is shown in Fig. 8, with the logarithmic axes allowing a wide range of concentration to be covered. In all cases, the experimental absorbance was measured on the time independent portion of the absorbance vs. time transient. The linearity of these plots and the unity values of the slopes clearly indicate that absorbance is linear with concentration over a range of electrode lengths from 0.14 to 1.1 cm. To assess the precision and accuracy of the results, a molar absorptivity was calculated from each run and compared to the value determined independently. The results are shown in Table 2.

The results shown in Table 2 establish the validity of Beer's law for calculating the time independent absorbance from the molar absorptivity of the electrogener- ated chromophore, the electrode length, and the bulk concentration of the precursor. While Table 2 shows overall accuracy and precision, it was noted that the standard deviation became larger and the average value of ~ agreed less well with the expected

0.014 cm

0 027 em

O. 16 crn S

58

Ca O

o

- I

I I I I I -5 -4 -5 -2 - I

log ( concentrofuon f mol -t)

Fig. 8. Composite plot of time-independent adsorbance for TBA + and Fe(CN) 3- . Ordinate is the log of the absorbance measured on the plateau of the transient (between 0.5 and 1.0 s), divided by electrode length. Abscissa is logarithm of bulk precursor concentration. Upper curve is for TBA (concentration range 12/~M to 6 mM), lower curve is Fe(CN)63- (2.1 to 61.6 m M ) (X = 633 nm at 5 mW). TAA + data not shown because of near overlap with TBA +.

value at higher angles and longer electrode lengths. The most likely reason for deviation under such conditions is the increased effect of stray light. At higher angles or with longer electrodes, the diffracted intensity gets weaker, and light from sources other than diffraction begins to interfere. This effect also limits the upper end of the dynamic range for long electrodes. For example, the maximum accurate absorbance for a 1.1 cm electrode was about 0.2. Fortunately, the long electrodes would probably only be necessary in the case of analysis of very dilute solutions where absorbances would be small and stray light would be a minor problem.

TABLE 2

c values from diffraction experiments

Chemical system TBA +" TAA +" Fe(CN)~-

Number of transients measured 13 4 13 Concentration range /m M 0.012-6.0 0.0049-0.25 2.1-61.6 Path length range/cm 0.014-0.63 0.16-1.12 0.027 Range of diffraction angle/degrees 0.58-0.73 0.58-0.73 1.02 Mean experimental c / M - i c m - 1 14469 10 330 554 Deviation of c from value in Table 1 - 2.8% - 3.9% 0.0% Relative standard deviation of ~ 4.7% 8.1% 7.3%

59

Once the Beer's law absorbance has been reached, after ca. 200 ms, the ab- sorbance depends only on the electrode length, concentration, and molar absorptiv- ity, not time or the diffusion coefficient. The diffusion coefficient does determine how rapidly the limiting absorbance is achieved, but has no effect on the absorbance after the plateau is reached. All other transient spectroelectrochemical methods yield an absorbance which depends on the diffusion coefficient, and therefore is tempera- ture and viscosity dependent. An additional feature which distinguishes the diffrac- tion technique from most other techniques is the complete conversion of precursor to chromophore within the region sampled by the diffracted light. Using the capillary cell experimental configuration, the beam need not pass through any solution which is unaffected by electrolysis, as would occur in external reflection or transmission spectroelectrochemistry. Therefore, absorbing precursors may be examined, or cases where both precursor and product adsorb significantly. The beam will not be attenuated by "inactive" solution before it interacts with the diffusion layer.

Given the dependence on different variables, a comparison of the sensitivities of the diffractive method with conventional spectroelectrochemical techniques will depend on experimental conditions. For a transmission experiment using an opti- cally transparent electrode (OTE) [3], the absorbance is given by 2~cb(Dt/~r) 1/2. The Beer's law absorbance from diffraction divided by this value is 7rl/2b/2(Dt) 1/2. For a 1.1 cm electrode and a typical diffusion coefficient (5 × 10 - 6 c m 2 s - 1 ) this ratio is 436 at t = 2 s and 1380 at t = 0.15 s. Therefore, the diffractive technique can be 400-1400 times more sensitive than an OTE experiment, but it should be recognized that this comparison is a strong function of b, D and measurement time.

Effect of wavelength

Figure 9 shows a spectrum of TMPD ÷ cation radical obtained using the diffrac- tive technique with an Ar + pumped dye laser. The molar absorptivity at each wavelength was calculated using Beer's law from the absorbance on the level portion of the absorbance/ t ime transient, and the spectrum shown is the average of six separate runs. The diffraction results agree with the literature spectrum [18] to within 870, indicating that Beer's law applies over the 570-625 nm wavelength range (as well as at 442 and 633 nm). In addition, no perturbation in the spectrum was observed near the X . . . . indicating the absence of any observable anomalous dispersion or other refractive index effects in the time independent portion of the transient. It should also be noted that wavelength will affect the transient character- istics of the technique, with shorter wavelengths yielding more rapid response. However, it should be emphasized that the Beer's law region is unaffected by wavelength, except for the expected changes in molar absorptivity.

Detection limits

The range of concentrations examined during the construction of Fig. 8 was 12 /~M to 6 m M for the TBA system. Below 12 #M, two effects appeared which made the measurements more difficult and caused deviation from Beer's law. At low

60

14

12

I0

3- 8

,, 6

I I I I I I I 570 580 590 600 610 620 630

~/nrn

Fig. 9. Absorbance spectrum for TMPD + measured by diffractive spectroelectrochemistry. Points were taken from the time independent portion of the absorbance transient measured at each wavelength. Six different solutions were used to construct the complete spectrum, but the concentration of TMPD was close to 1 mM in all cases. Light source was a R6G dye laser (Ar + pumped).

absorbance, noise became comparable to signal, with the major noise source appear- ing to be solution convection. Noise was more severe for long electrodes and low viscosity solvents such as acetonitrile. Apparent ly the beam is scattered by refractive index gradients which are caused by convection, and a longer passage through solution, as with a long electrode, worsens the effect. Whatever its source, the noise ranged f rom _+0.002 A.U. in water (b = 0.05 cm) to _0 .01 A.U. in C H 3 C N (b = 1.1 cm), both measured after 20 time-averaged runs. With blank solutions, a background absorbance was observed which could not be neglected at concentrat ions below 5 /~M for TBA. The background signal was more severe in acetonitrile than water and worse on carbon than on platinum. As shown in Fig. 10A, the background in H 2 0 is smaller than the noise below 0.5 s, but is quite appreciable in acetonitrile (Fig. 10B). The origin of the background signal was no t determined, but it appeared to be peculiar to ace ton i t r i l e /TEAP solutions rather than a characteristic of the diffrac- tive technique itself. In any case, a blank run is good practice when performing trace measurements.

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0.004

0.2 0 4 0 6 0.8

Time/s

61

o ~

J o

018

0.14

010

0.06

0 0 2

B

0 2 0.4 0.(5 0 8

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Fig. 10. (A) Background signal for 1 M KNO 3 at a 0.05 cm Pt electrode. Potential was stepped from 0 to +0.8 and 20 runs were time averaged. (B) Dotted curve is a background run on 1.1 cm carbon in 0.1 M TEAP. The peak at 0.1 s varied greatly with different electrodes, but the background "adsorbance" always decayed to noise levels by 0.5 s. Dashed curve is theory for generation of TAA + from a 1.2/xM solution of TAA, and the solid curve is the corresponding experiment (20 time averaged runs). Diffraction angle was 0.80 °, applied potential was 0.8 V. TAA yielded a better detection limit that TBA because the background "absorbance" was higher at the more posiuve potential required for TBA + generaUon.

Figure 10B also shows theoretical and experimental t ransients for a 1.2 /~M solut ion of TALk on a 1.1 cm carbon electrode. Note that the background signal has decreased to the noise level after 0.5 s, and that the observed absorbance is close to the Beer's law value in the range 0.5 to 1.0 s. In this t ime region, the signal to background ratio is approximately two, indicat ing a detect ion l imit of 1.2 # M for

this part icular system. While higher molar absorptivi ty or less noise (as in water) would improve this value, this detect ion limit was the lowest encountered dur ing the course of this work. The peak in the absorbance t ransient at 100 ms is possibly due to adsorbed material which is released as a pulse dur ing electrolysis. While this effect

may prove to be very useful for detecting desorbed species, its effect on the t ransient was over by 0.5 s and it did no t appear to affect the detection limit.

Double step response

By analogy to the imaginary Beer's law "cell" presented earlier, it should be possible to both fill and empty the region sampled by diffracted light. Figure 11 shows an absorbance vs. time t ransient for a potent ia l step which generates chromo-

62

030

o o

R

O 2 0 J~ <

0.10

I 2 3 4 6 7 8 9

T ime s

Fig. l 1. Double step experiment for Fe(CN)36 - generation at a 0.027 cm Pt electrode. With the bulk solution containing 15 mM Fe(CN)64 , the potential was stepped from 0.0 to +0.8 V for 5 s, then returned to 0.0 V. Result is a single run, with no time averaging (X = 442 nm at 10 mW).

phore for 5 s, then returns to a value which removes the electrogenerated chromo- phore. After about 300 ms of generation, the absorbance reaches its Beer's law value, which remains constant for the duration of the forward step. Upon return to the initial potential, the chromophore is rapidly removed and the adsorbance reduced, as expected from the analogy. The diffracted light effectively samples only the region near the electrode surface, which can be rapidly altered by an electrode reaction.

Refractive index effects

The theory discussed here neglects phase shifts caused by refractive index gradients within the diffusion layer. Such gradients accompany any change in absorptivity caused by chromophore generation, and they will affect the diffracted intensity if their magnitude is sufficiently large. Unfortunately, their magnitude is hard to predict since it depends on the chemical system, its concentration, the solvent, and wavelength. Furthermore, refractive index data for dilute organic systems in acetonitrile are not available, nor are data for cation radicals or organic salts. Nevertheless, theoretical calculations were carried out to ascertain what effect refractive index changes in the diffusion layer would have on the absorbance transients. The predicted effect of refractive index gradients on the time independent portion of the absorbance / t ime curves was slight, but was obvious during the transient portion. For example, a - 0.01 change [19] in refractive index per mole of electrogenerated species caused a 25% increase in the peak absorbance (t = 0.06 s) for a 3 m M TBA solution at 1.2 ° diffraction angle. However, at 0.5 s the increase was 2%. At lower concentration (0.3 m M) the effects were substantially smaller with a 1% deviation at 0.5 s and 2% at 80 ms. While quantitative estimates of refractive index effects cannot be made without accurate molar refraction data, it is apparent that they are larger at higher concentrations and that they have little effect on the limiting absorbance.

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Refractive index effects in the experiments depicted in Fig. 4 cannot be ruled out, but appear unlikely given the agreement between theory and experiment. The Beer's law conformance over a wide range of path length and concentration and in different solvents indicates the absence of refractive index effects on the time independent absorbance region. Particularly important is the spectrum of Fig. 9, showing no effect of wavelength on the absorbance except that corresponding to molar absorptivity changes. It is not surprising that refractive index changes upon electrolysis do not affect the time independent absorbance, since this region reflects a situation where all precursor near the electrode has been electrolyzed, and both concentration and refractive index are nearly constant in the region sampled by the diffracted light. With no refractive index gradient, there is no effect on the diffraction pattern.

CONCLUSIONS

When light diffracted by a planar platinum or glassy carbon electrode is used to perform absorbance measurements on an electrogenerated chromophore, the result- ing absorbance vs. time transient has two distinct regions. In one region the absorbance is time independent, with a constant absorbance being reached 200-500 ms after the initiation of electrolysis, depending on diffraction angle. The limiting absorbance is independent of the diffusion coefficients of the electrogenerated species of its precursor, and can be calculated from Beer's law. For a range of absorbances from 0.005 to 1.35 and path lengths from 0.014 to 1.1 cm, Beer's law was valid to within 4% with a standard deviation of 9% or less. The dynamic range for a single electrode length was 270, a range of 12 ~M to 3.3 m M for a test system. The sensitivity of the technique in this region (equal to ~b) depends on both electrode and system, but for TAA on a 1.1 cm electrode, it is 1.2 × 104 M 1. The detection limit for TAA was 1.2/~M.

The second region of the absorbance vs. time transient is the rising portion preceding the Beer's law region, and its behavior depends on many more experimen- tal variables. For short electrodes the entire transient follows theory for diffraction angles between 0.6 and 1.2 °, with faster risetimes being observed at higher angles. Longer electrodes exhibit responses which do not agree with theory in this region, but do reach the expected Beer's law value at times above 0.5 s. The rising portion of the transient is sensitive to alignment, refractive index gradients, if any, and the quality of the electrode surface, although these factors have much smaller effects on the time independent portion of the transients.The trade-off between sensitivity and agreement with theory serves to identify the advantages of the method as presented here. For long electrodes, the technique can be several orders of magnitude more sensitive than OTE experiments, with a very simple, time independent relationship between absorbance and concentration. While sensitivity is lower for short elec- trodes, the transients agree well with theory. Since the theory is based on the Fourier relationship between diffraction pattern and beam cross section, the absorbance transients contain spatial information about the chromophore distribution. Different

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concentration vs. distance profiles yield different beam cross sections and therefore different diffraction patterns. Efforts to deduce diffusion layer structure from diffraction are in progress. Another potential application of the approach is in studying adsorption on electrodes. As indicated in Fig. 10B, desorbing material which leaves the electrode upon electrolysis will cross the optical beam as a pulse, resulting in a high transient absorbance. Diffracted light may provide a sensitive probe for examining the existence and kinetics of adsorption.

ACKNOWLEDGEMENTS

R.I.M. is an Alfred P. Sloan Fellow for 1981-83, and partial support by that foundation is acknowledged. This work was supported by the National Science Foundation through grant CHE-7828068.

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