Laser interferometric investigation of the transfer of concentration polarization between serially polarized drops in polarography

Electroanalytical Chemistry and lnterfucial Electrochemistry, 42 (1973) 25-36

25

~ Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands

LASER INTERFEROMETRIC INVESTIGATION OF THE TRANSFER OF CONCENTRATION POLARIZATION BETWEEN SERIALLY POLARIZED DROPS IN POLAROGRAPHY PART I. CONCENTRATION GRADIENT MEASUREMENTS

R. N. O'BRIEN and F. P. D I E K E N

Chemistry Department, University of Victoria, Victoria, British Columbia (Canada) (Received 12th June 1972)

INTRODUCTION

Previous interferometric investigations of the DME include the work of Antweiler 1 who demonstrated the existence of the diffusion layer around a mature polarized-drop and estimated the distance the diffusion layer extends from the Hg surface to be 0.05 mm. Ibl 2 analyzed Antweiler's optical systems and reported that one produces an artificial diffusion layer. The failure of the Ilkovic equation to describe accurately the instantaneous current-time behavior exhibfted by the DME prompted Airy and Smales 3 to suggest that a new drop begins its ~life in a region of solution diluted by the previous drop. The first use of a pure interferometric technique was by O'Brien and Leja4 who detected large relative concentration gradients at the DME when the drop-time was large (10-12 s) and migration effects were not completely eliminated. These authors did not reduce the interferograms to quantitative concentration data. Therefore, no quantitative investigations about the magnitude of depletion or the extent of depletion that exists under a normal polarographic ~capillary after drop detachment in a normal polarographic analysis, have been undertaken. Quantitative results about the residual depletion between serially polarized drops can be obtained by multiple-beam interferometric methods which provide in situ measurements of changes in refractive index which can readily be related to concentration changes. Accurate measurement, however, requires careful optical adjustment and an analysis scheme adapted to estimate spherical concentration effects occurring in cylindrical space. The optical adjustments are required to minimize optical artifacts arising from interferometer imperfections and the reflecting capacity of the mercury drop. When the artifacts are minimized, the residual effects must be accurately measured so that allowance can be made for them in the final fringe perturbation determination. The geometrical problems can be minimized if a time in the drop life is chosen when the spherical nature of the drop is not imposed upon the depleted region; such a time occurs immediately after drop detachment, when the depleted region has a cylindrical geometry with its axis at right angles to the axis of the cylindrical interferometer. A series of cylindrical shells of increasing diameter can be used and an integral concentration contour found.

R. N. O'BRIEN, F. P. DIEKEN

26

The major theoretical interest is in the concentration of electroactive species (the supporting electrolyte concentration is considered constant), that the emerging drop encounters. In Part II, the experimentally determined magnitude and extent of depletion are related to the failure of theoretical polarographic equations to describe accurately the observed time-dependent diffusion current. INTERFEROMETRYTHEORY In a quiescent cell containing a liquid of refractive index, n, the well-known cosine law describes the position and separation of the fringes. In a wedge-type interferometer, the relationship between the perturbation of a fringe near a working electrode, F, and the change in r~fractive index, An: An = ()~/2t) V

(1)

where 2 is the wavelength of the nearly normal incident laser radiation of 632.8 nm and t is the thickness of the separation of the optical flats, has been described by O'Brien 5. The fringe shift factor, F, represents a ratio of the distance a fringe has shifted from its equilibrium position in the bulk electrolyte to the equilibrium distance between unperturbed fringes in the bulk electrolyte. In a sandwich-type interferometer cell where the optical flats form the cell boundary at the edges of the electrode, the refractive index change occurs throughout the thickness of the cell, from one edge of the electrode to the other. In a polarographic interferometer cell, the geometry of the electrodes and the diffusion layer does not permit the positioning of the optical flats at the solution/diffusion layer boundary. Such a system would create additional depletion in the region of the concentration gradient. Therefore, an interferometer cell was constructed in which the DME was centered between the optical flats which were separated by a distance, T, which is larger than t, the thickness of the region of refractive index change. Calculations of concentration values in a non-homogeneous region which is surrounded on all sides by electrolyte of a uniform concentration have not been previously attempted. Approximations to the concentration of depolarizer in such a depleted region can be made under the capillary after drop detachment. The evolution of depletion regions under the capillary found in this work is consistent with the findings of Antweiler 1 and O'Brien and Leja 4 and is shown in Fig. 1. The diffusion layer which surrounds a mature drop experiencing limiting current conditions (Fig. la) consists of an approximately spherical region, which extends over the majority of the surface of the drop to an average distance of 0.05 mm into the solution, and an approximately cylindrical region at the neck of the drop. This latter region arises due to restricted transport of depolarizer to this region of the drop and the upward natural convection of depleted electrolyte. When the drop falls (Fig. lb), convective stirring by the falling drop does not restore the depolarizer to the bulk concentration value. The accumulation of depleted solution around the neck of the drop is drawn a short distance downward by drop fall into a reasonably regular cylinder. To this depleted solution must be added the diffusion layer which is sheare~l from the drop as it falls. The disposition of the latter depleted electrolyte is again approximately cylindrical. Concentration values within a cylindrical disk element which is taken from Fig. lb and rotated 90 °

27

CONCENTRATION GRADIENT MEASUREMENTS (a) ....

(b)

~!-f/j

:,.

~ - ,,.,,.

Fig. 1. Evolution of depletion under the capillary. (side elevation to plan view) in Fig. 2a and 2b, are estimated by a scheme in which successive layers are dealt with; the thickness of the layers are chosen such that an average value of the concentration within a layer is reasonable. For the first approximation, an average value of the concentration, ~l, along a chord thickness drawn through Xo, X1, X 2 (Fig. 2a) can be calculated from the linear relationship between concentration and refractive index and eqn. (1). The refractive index change is assumed to occur only within the region of diameter Z. The value of ~ along X, represents an average of the higher concentrations near the perimeter of the cylinder and the lower concentration values near the center of the cylinder. The chord thicknesses of the cylinder through X o and X 3 are different and individual t values are required for each refractive index change calculated according to eqn. (1). For the second approximation, the original cylindrical volume of depleted solution was divided into: concentric cylindrical shells, (Fig. 2b). The average concentration ~2, within the cylindrical shell i is calculated by assuming that the average value of the refractive index of the inhomogeneous volume element I, which extends across the entire celt thickness, can be expressed as the sum of the weighted value of the refractive index of the individual, approximately homogeneous volume ele-

(o)

(b)

GLASS FLAT

GLASS

//////////////////////////////

T~

Z

FLAT

I/I///////////////////////////.

T t~2

'

i ~ii ~,il. xo

\

-X

xv x2i /

', ', i/

I //////////////////////////////

Nj,T ~LTjJ

///////////////I//////////////

Fig. 2. First and second approximationsto distributionof depleted electrolytewithin a cylindricaldisk element: (a) First approximation,(b) second approximation.

28

R. N. O'BRIEN, F. P. DIEKEN

ments. In order to facilitate the calculations, the length of the nearly homogeneous volume element was chosen as the weighting factor rather than the proper volume of the volume element. The refractive index of the solution within volume element I, and the corresponding volume element J, denoted Nix and NjT, respectively, is calculated from the refractive index of the bulk solution Nbu~k, and eqn. (1) when the average fringe shift across I and J are given from the data acquired from the first approximation and the value of t is given by the cell thickness, T. According to the second approximation, NjT and Nn. can be expressed as the sum of the individual regions of uniform refractive index which are weighted according to their length. Therefore: =

+

(2)

JYIT= [Nbulk(T - it) ~- Nj(t") +JYi(t'")]/r

(3)

and In eqn. (3), NI is the dependent variable which is evaluated in terms of the previously determined value of Nj. Homogeneous volume elements will occur only in the bulk electrolyte. The diameter of the cylindrical volume element of depleted solution Z1 has been exaggerated for clarity. Under experimental conditions, Z is approximately 10~o of the cell thickness, T. In the region of depleted electrolyte, the choice of length rather than volume for the weighing factor is partially justified since the average fringe shift across the volume element is used in the calculation. Also if the thickness of the cylindrical disk element, AY, is small and the number of cylindrical shells is increased, the difference becomes small. The number of shells is usually chosen such that Z is divided into a series of equally spaced concentric cylinders. Data will be presented which are based on a minimum of 6 and a maximum of 9 shells. APPARATUS An O'Brien-type multiple-beam Fabry-Perot interferometer that produces fringes by division of amplitude, when two partially reflecting glass plates sandwich the working electrodes, was modified to permit easy access of the three electrodes in the polarographic system. An adjustable wedge-type interferometer cell (see Fig. 3a) was constructed entirely of Teflon. The cell was a nominal 1.5 in.* in diameter and 9.271 mm between the internal surfaces of the glass flats. Nylon screws threaded into the optical flat seating face created a reproducible wedge angle which controls the orientation and spacing of the fringes. The 90~o reflecting optical flats (LibbyOwens Ford Glass Co.) which were 1½ in.* in diameter by ¼ in.* thick, and parallel to within 1 thin of arc, were held in position by stainless steel binding straps which also effected an almost leak-proof seal. The assembled interferometer cell Fig. 3c, was sandwiched between two aluminum plates (one plate was locked in the cell holder). Each plate had a fixed plexiglass ring which formed the only region of contact between the cell and the cell holder. The entire assembly was held together by three symmetrically located tie-bars which also provided the final means of adjusting the horizontal fringe pattern. * lin.=-2.54 cm.

29

CONCENTRATION GRADIENT MEASUREMENTS

I;

a

,1

5--

i

Seating Foce

Nylon Screw

I+ "F o0o

7

kil

6

4 [

(a)

(b)

i.

"

I

i i

i l

(c)

Fig. 3. Interferometer cell and supporting apparatus: (1) Metal binding straps, (2) optical glass flat, (3) Teflon cell body, (4) thermostatted plate and support stand, (5) Plexiglass ring, (6) aluminum cell support plate, (7) tie bar, (8) thumb nut.

A model 130-B Spectra-Physics H e - N e c.w. gas laser provided coherent radiation with a wavelength of 632.8 nm. The laser was equipped with a SpectraPhysics model 332 spatial filter and a model 333 collimating lens. The exit beam had a gaussian distribution across its diameter of 20 mm. Although the laser had an intensity control, neutral density filters were required to increase the contrast of the fringe system which was photographed with a 16-ram Paillard-Bolex motion picture camera with a f 1.4 Switar 50 mm lens. The framing speed was calculated to be 36.4 ft.* s -~. Eastman Kodak Plus-X negative film (type 7231), was processed in our laboratory. Corning marine barometer tubing (0.05 mm internal diameter) served as the capillary; 11 cm lengths were obtained by breaking the capillary with a LKB Knife Maker. Capillary cut on this instrument has a nearly perpendicular face and a minimum of tailing on the glass which was carefully removed on a grinding wheel. Great care was taken to obtain a perpendicular face without projections to the tip which might create an unsymmetrical diffusion gradient. A controlled potential modular type polarographic instrument (Heath) served as the polarograph and the instantaneous current was recorded on a Visicorder. The auxiliary electrode (Ag/AgC1 in saturated KC1) and the reference electrode (Hg/HgzC12 in saturated KC1) were prepared in the laboratory. Electrical connection between the half-cells and the interferometer cell was obtained through side-arm salt bridges containing a plug of agar saturated with K N O 3. Coarse fritted * 1 ft.= 30.48 cm.

30

R. N. O'BRIEN, F. P. DIEKEN

disks sealed at the end of the side-arm prevented gross contamination and bulk electrolyte flow. Reagent grade chemicals, conductivity water and triply distilled Hg were used for all experiments. Stock solutions of analyzed Cd(NO3)2 and recrystallized 4 M NaC10 4 (which had" first been filtered) supporting electrolyte were diluted for each test solution. Nitrogen (U.H.P.) was used to remove dissolved oxygen. Maximum suppressors were not added to any test solution since a maximum for Cd z+ ion does not occur in this electrolyte with a 4 s drop-time. Also, the change in refractive index due.to an accumulation of maximum suppressor in the vicinity of the electrode could not be tolerated. EXPERIMENTAL Solutions containing C d ( N O 3 ) 2 at concentrations of 2 x 10 -3, 4 x 10 _3 and 10 2 M with 1.0 M NaC10 4 supporting electrolyte were investigated. Plots of refractive index vs. concentration of reducible electrolyte, with and without supporting electrolyte, were linear (.data to be published in C h e m . E n g . D a t a ) , with slope agreement within 1.5°,o. Residual current polarograms did not indicate the presence of a reducible impurity so pre-electrolysis was dispensed with. Polarographic plots, ia vs. concentration and ia vs. uncorrected height of the mercury column, confirmed the expected diffusion controlled current. The half-wave potential for Cd(II) ion in 1 M NaC104 was found to be -0.551 V vs. SCE. Numerous constant applied voltage ( - 1.00 V vs. SCE) and no applied voltage polarographic sequences of drop growth and detachment were recorded and photographed. The reason for this was the need to determine false fringe shifts or fiinge displacements due to optical artifacts which will subsequently be discussed. Using a magnification of about 200, interferograms were measured by projecting them onto a measuring table, using a 45 ° mirror, and a transparent template overlay. Concentration changes were determined from changes in refractive index which are ¥

1

d,T

-r d, =-

~,

(a)

*,

(b) Fig. 4. Methods of determining fringe shift values: (a) Preliminary method, (b) rigorous method.

CONCENTRATION GRADIENT MEASUREMENTS

31

evaluated in arbitrary units, i.e. fringe shifts. This involves using the equally spaced wedge fringes in the bulk solution as a grid and the transparent template shown in Fig. 4. Line Y is drawn through the Hg thread and represents a vertical reference line. Additional vertical reference lines to A I and Az are located at equivalent distances from the Hg thread and the distance between A1 and A 2 is chosen such that electrochemical processes do not affect the position of the fringes in this region of the electrolyte. Dashed lines through the center of each fringe are used to locate reproducibly a fringe relative to the base of the capillary and the value of d2, the fringe separation in the bulk electrolyte, is determined along Ax or A 2. The remaining distances L1, L2 and L 3 are measured and the fringe shift is determined from: F = [L3 - ½(L2 + L 1 ) ] / d 2 -

ffs

(4)

where ffs is the false fringe shift produced by effects not related to a refractive index change. False fringe shifts are primarily produced by spurious interference effects caused by reflections from the surface of the Hg drop and by dishing of the optical flats which introduces a very small optical path difference between the middle and the edges of the optical flats. Reflected radiation from the surface of the drop affects fringe shift measurements near the surface of the drop and its contribution to the total false fringe shift has been shown elsewhere 6. "Dishing" of the optical flats is produced by the uneven pressure exerted when the tie bars are tightened to establish the wedge and orientate the fringes. The false fringe shift produced by dishing of the flats affects the fringe shift throughout the region of depletion and must be evaluated at each point where a fringe shift is determined. Since the "dishing" of the flats and the optical alignment changes with each experiment, a proper correction for the ffs could only be made when experiments were designed such that the DME was photographed during open circuit voltage conditions and then during limiting current conditions without the slightest alteration of the interferometer cell. The total fringe shift for each fringe, (during limiting current conditions) was calculated with the same template used in the ffs determination (during open circuit conditions) and in order to compensate for any movement of the interference pattern, distances L1, L2 and L 3 were evaluated for each interferogram. The success of this method of fringe shift determination did not depend upon reproducibly locating the base of the capillary. Reproducible fringe shift values could be obtained only by this rigorous method of measurement, followed rigorously each time for each set of experiments. k_

.

.

RESULTS

Concentration gradients around polarized mature drops were obvious and measurable in the 10-; M runs; however the labour involved would have been prohibitive, since 24 individual fringes would.have to be measured to obtain accurate refractive index changes. Of more interest in this work was the determination of concentrations near the base of the capillary immediately after drop detachment. Interferograms of the events surrounding non-polarized drop detachment, and polarized drop detachment are shown in Fig. 5. Consecutive frames (b, d, f) show the nonpolarized nascent drop at an elapsed time of (lj36.4)= 0.027 s after detachment and

32

R. N. O'BR1EN, F. P. DIEKEN

Fig. 5. Interferograms of polarized and non-polarized DME in dilute solns, of Cd(NO3) 2 and 1.0 M NaC104: (g) (h) Non-polarized drop in supporting electrolyte, (i) (j) polarized drop in supporting ~lectrolyte, (k) (1) non-polarized drop in supporting electrolyte and 2.0 mM Cd(NO3) 2.

the p o l a r i z e d d r o p a t a p p r o x i m a t e l y

1/2 ( 1 / 3 6 . 4 ) = 0 . 0 1 4

s a n d 3/2 ( 1 / 3 6 . 4 ) = 0.041

s after drop detachment. Fringe shift measurements were, in general, not obtainable w h e n the latent image of the falling drop was present in the frame. T h e r e f o r e , all

subsequent concentration measurements pertain to an elapsed time when the image of the d r o p d i s a p p e a r s f r o m the frame at 0.027 s or 0.041 s.

Depletion near the base of the capillary was examined by measuring fringe perturbations along the entire length of each horizontal fringe located near the base of the capillary. A 10.0 mM solution of Cd(NO3)2 served as the bulk concentration of depolarizer in 1,0 M NaC104. The drop-time was 3.99 s with an applied voltage of - 1 . 0 0 V v s . SCE and no maximum suppressors present. Corrected fringe shift values and first approximation concentration values are plotted in Fig. 6 as a func-

"C-'bb 0.9 0.8 0.7 0.6 J

0

0.05

i

0.10

I

0.15

/

I

I

0.20

0.25

0.30

0.35

DISTANCE FROM VERTICAL LINE THROUGH Hg THREAD/' /

mm

Fig. 6. First approximation average concn, ratios near base of capillary in a 10.0 mM Cd(NO3) ~ soln. Distance below capillary: (©) 0.12, ([1) 0.20, (~x) 0.25 mm. Cb= 10.0 mM Cd(NO3) a.

33

CONCENTRATION GRADIENT MEASUREMENTS

tion of distance X, the distance from the line Y in Fig. 4. Each fringe shift value represents an average of two readings. Additional pertinent experimental values needed to determine gt values from refractive index changes calculated according to eqn. (1) include 2=632.8 nm, the slope of the refractive index--concentration plot = 2.75 x 10- 2 M - 1, and Z = 0.536 mm, 0.609 mm and 0.634 mm. Additional first approximation concentration values which were obtained at slightly different distances from the base of the capillary are shown in Fig. 7. Each fringe is readily identified by its vertical distance below the capillary. Second approximation concentration values were calculated for fringes A F, according to expansions of eqn. (3). 1.0

Cb

0.9 0.8 ~

0.7

0.6

0.5 i

0

0.05

0/10

0.115

i

i

0.20

0.25

0/30

0/35

O.140

DISTANCE FROM VERTICAL LINE THROUGH Hg THREAD / mm

Fig. 7. Additional first approximation average concn, ratios near base of capillary in a 10.0 mM Cd(NO3)2 soln. Distance below capillary: (O) 0.16, (73) 0.23, (A) 0.28 ram. 1.0

I

I

I

~bb 0.9 0.8 0.7

0.6 0.5

DISTANCE

i

I

I

I

0.05

0.10

0.15

0.20

FROM

VERTICAL

LINE

i

0.25

THROUGH

i

0.30 Hg

0.35

THREAD / mm

Fig. 8. Second approximation average concn, ratios near base of capillary in a 10.0 mM Cd(NOs)2 soln. Distance below capillary: (O) 0.12, (D) 0.20, (A) 0.25 mm.

Corrected fringe shifts were used to determine an average concentration across the entire cell thickness, T -- 9.271 m m as a f u n c t o n o f d i s t a n c e X. T h e n u m b e r

of cylindrical shells varied from 6 for fringe A to 9 for fringe F. Plots of g2/cb against their respective X distances are given in Figs. 8 and 9. The vertical disposition of depolarizer near the base of the capillary can be approximated by plotting concentration ratios at equal X distances against vertical d i s t a n c e b e l o w the c a p i l l a r y (Fig. 10). N e a r the b a s e o f the capillary, the s m a l l e s t

concentration ratios occur near line Y where X is small. Each line represents the

34

R. N. O~BRIEN, F. P. D I E K E N 1.0

Cb 0.9

0.8

0.7 0.6

0.5 i 0.05

J1 o. 0

DISTANCE

FROM

o.J15

i 0.20

VERTICAL

i 0.25

LINE

, 0.30

THROUGH

Hg

i3 o. 5

i4 o. 0

THREAD / r a m

Fig. 9. Additional second approximation average concn, ratios near base of capillary in a 10.0 m M Cd(NO3)2 soln. Distance below capillary: (©) 0.16, ( ~ ) 0.23, ( A ) 0.28 mm.

1.0

C-'b" 0.9

oo

0.8

..........

°

f

X X X X

°

- ....

~

o

~

.

/

= = = "

0 . 2 4 4 mrn 0.195 mm 0.146 mm 0.098 mm

X = 0.049

mm

0.7

0.6

/

• '

X=O.O mm

0.5 I

0.4

0 VERTICAL

i

i

i

i

0.1

0,2

0.3

0,4

DISTANCE

BELOW

CAPILLARY /

mm

Fig. 10. Vertical disposition of depleted electrolyte near base of capillary in a 10.0 m M Cd(NO3)z soln.

vertical concentration profile on either side of line Y and extrapolation of each line back to zero distance from the capillary gives an estimation of the depolarizer concentration in the immediate vicinity of the nascent drop at an elapsed time of 0.027 s after drop detachment. For extrapolation purposes, the data for the first five X distances were fitted to a linear regression program and individual lines are computer generated. DISCUSSION

The limit of accuracy with which concentration values can be estimated has been stated in terms of the location of the center of the perturbed fringe. The necessity of determining ffs values should increase the uncertainty in the final result; however, the overall precision with which corrected fringe shifts were determined was considerably better than 1/20th of a fringe shift. Corrected fringe shift measurements were reproducible to within 1/80th of a fringe shift 7, but the overall precision with which changes in refractive index could be determined was also a function of the precision with which the thickness of the cylindrical region, Z, could be measured.

CONCENFRATION GRADIENT MEASUREMENFS

35

Cylindrical thickness measurements were reproducible to within 53o. Fringe shifts (which include false fringe shift) measured near the capillary in a 10 mM Cd solution are significantly larger than the uncertainty of the fringe shift and a total relative tmcertainty in the final result of about 7"o can be expected. First approximation average concentration values indicate that a region of prominent depletion does exist under the capillary after drop detachment. Linear extrapolation of ~7~ values, measured along line Y (X =0) back to the base of the capillary, indicate that at a distance of 0.025 mm below the capillary, the average concentration across the entire region of depletion is 70'~g,-+ 7°'/o of the bulk value. Second approximation concentration values for the outer cylinders are approximately equal to the corresponding i:1 values. For the inner cylinders, C2 values are much lower than the corresponding Oa values. These observations are consistent with the nature of each approximation. Figure 10 represents a map of the horizontal and vertical depletion near the base of the capillary at an elapsed time of 0.027 s after drop detachment. Linear extrapolation of (72/cb ratios at equivalent X distances, back to the base of the capillary permits the evaluation of average depolarizer concentrations within any cylindrical disk which has a radius equal to or less than 0.195 mm and a depth equal to or less than about 0.3 mm. For example, a cylindrical disk which has a radius of 0.1 mm and extends to a depth of 0.1 mm below the capillary, has a ~2 value of 61°o of the bulk value. The radius of this hypothetical cylinder is approximately 4 times the radius of the orifice and the cylinder has a volume of solution approximately twice the volume of the nascent drop. In the immediate vicinity of the orifice, the depolarizer concentration is only about 50%1;of the bulk value. CONCLUSION Split-fringe multiple-beam interferograms can give reproducible fringe shift measurements within 1/80th of a fringe shift even when optical artifacts are present and appreciable false fringc shift values must be measured and subtracted. This should result in about a 790 error in 0.01 M results and corresponding greater error at lower concentrations of depolarizer. Using corrected fringe shifts converted first to refractive index changes and then from experimentally determined refractive index~oncentration curves to concentrations, areas of depletion below the emerging drop can be determined. Integral concentration values within this region of depletion are evaluated according to two approximations. In Part I, the region of depletion near the base of the capillary and in the immediate vicinity of the nascent drop has been investigated. In Part II, a second region of depletion at moderate distances from the capillary is investigated and the overall disposition of depletion related to current-time curves. SUMMARY A laser interferometric investigation of the concentration gradients encountered by the emerging drop in polarography is reported. The interferometer and two graphical integration methods are described. The results of the two methods are compared for the two regions of depletion, i.e. the solution trapped around the

36

R. N. O'BRIEN, F. P. D1EKEN

neck of the drop, between the drop and the capillary bottom, and the diffusion layer proper around the drop. Only the values near the bottom of the capillary are reported in this test. In Part II values farther away are reported, related to the drop's diffusion layer and compared with theory. REFERENCES 1 H. J. Antweiler, Z. Elektrochem., 44 (1939) 719. 2 N. Ibl, Proceedings of the 7th Meeting, C.I.T,C.E., London, 1955, Butterworths, London, 1957, p. 112. 3 L. Airy and A. A. Smales, Analyst, 75 (1950) 287. 4 R. N. O'Brien and J. Leja, NaU~re, 210 (1966) 1217. 5 R. N. O'Brien, Rev. Sci. Instrum., 35 (1964) 804. 6 F. P. Dieken, Ph.D. Thesis, University of Victoria, 1971. 7 K. Beach,Ph.D. Thesis, University of California, Berkeley, 1971.