A Turbulent Tubular Electrode W. J. Blaedel and G. W. Schieffer Department of Chemistry, University of Wisconsin, Madison, Wis. 53706
The design and construction of a tubular electrode in which turbulence is impressed by a twisted Teflon stirrer rotating inside the tube are described. Current-voltage curves are reported for various stirrer speeds. The limiting current is independent of flow rate for stirrer speeds greater than 1500-2000 rpm and proportional to the cube root of the flow rate at low stirrer speeds. The limiting current is linear with respect to concentration at both low and high stirrer speeds, and a fivefold increase in sensitivity is obtained at the higher stirrer speeds. The effect of changing the shape of the stirrer is studied.
Forced convection electrodes are those to which electroactive material is brought principally by convective processes, rather than by the slower processes of diffusion that are operative a t more conventional electrodes. The general advantages of convective electrodes over diffusive ones are simplicity, greater sensitivity, and the ability to make current-voltage measurements in a steady-state mode rather than the transient mode. Forced convection electrodes have been reviewed by Adams (1)and Nicholson (2). From the standpoint of construction and manipulative techniques, forced convection electrodes may be most conveniently divided into two classes: those in which the electrode moves in a stationary solution, and those in which the solution flows past a stationary electrode. The best known example of a moving convective electrode is the rotated disk electrode (RDE) which has been studied extensively ( 3 ) . The RDE and its modifications, like the rotated ring-disk electrode, have proved to be very useful in the study of electrochemical kinetic mechanisms ( 4 ) and electrode adsorption ( 5 ) . Recent examples of moving convective electrode systems not covered in the above reviews are the rotated line electrode (6) and the rotated hemispherical and ring-hemispherical electrodes (7). There are also numerous examples of stationary electrode systems in flowing solution: conical (8),micro (91, tubular ( I O ) , micromesh screen ( I I ) , and, most recently, the wall-jet electrode ( I Z ) , which consists of a jet of solution flowing from a nozzle and impinging perpendicularly onto a disk electrode. Also in this class are porous or columnar electrodes, which have considerable promise as transformation devices (13, 14) and as coulometric chromatographic Adarns. "Electrochemistry at Solid Electrodes," Marcel Dekker, New York, N.Y., 1969. (2) R. S. Nicholson, Anal. Chem., 42, 13013 (1970). (3) A. C. Riddiford, Advan. Electrochem Electrochem. Eng., 4, 47 (1966). (4) W. J. Albery and M. L. Hitchman, "Ring-Disc Electrodes," Oxford University Press, London, 1971. (5) V. A. Vicente and S. Bruckenstein, Anal. Chem., 45, 2036 (1973). (6) A. Kirnla and F. Strafelda. Collect. Czech. Chem. Commun., 32, 56 (1) R. N.
(1967). (7) D. T. Chin, J. Electrochem. Soc., 118, 1764 (1971). (8) J. Jordan, R. A. Javick, and W. E. Ranz, J. Amer. Chem. Soc., 80, 3846 (1958). (9) G. Nagy, Zs. Feher, and E. Pungor, Anal. Chlm. Acta. 52, 47 (1970). (10) W. J. Blaedel and S. L. Boyer, Anal. Chem., 43, 1538 (1971). (1 1) W. J. Blaedel and S. L. Boyer, Anal. Chem., 45, 258 (1973). (12) J. Yarnada and H. Matsuda. J. Electroanal. Chem., interfacial Electrochem., 44, 189 (1973). (13) R. E. Sioda and W. Kemula, Electrochim. Acta, 17, 1171 (1972). (14) R. Alkire and P. K. Ng, J. Nectrochem. Soc.. 121, 95 (1974).
1564
detectors (15).In particular, tubular electrodes have been the most studied of this class. They are simple, sensitive, have low solution holdup, and are practical quantitation devices for flowing stream analysis (16, 17). Tubular electrodes have also proved to be amenable to pulse polarographic techniques (181, anodic stripping analysis (19),and digital simulation techniques (20). The only example found of a moving electrode in a flowing solution is a rather specialized rotated cylindrical or disk electrode inserted in a flow cell of small volume (21). This cell was designed for the coulometric analysis of liquid chromatographic effluents. Virtually all of the above convective electrodes operate under laminar flow conditions and smooth velocity profiles. Turbulence, characterized by random and chaotic eddy motion, is often specifically avoided, especially in theoretical studies. However, a turbulent hydrodynamic regime might be advantageous if high mass transport rates are desirable for greater sensitivity or for high reaction rates. For this reason, a tubular electrode has been constructed in which turbulence is mechanically impressed by a spiralled strip stirrer whose axis of rotation is parallel to the axis of the tubular electrode. The stirrer wipes the electrode surface and consists of sharp edges which are conducive to the onset of turbulent flow a t relatively low solution flow rates. The characteristics of such a turbulent tubular electrode ( T T E ) are elucidated in this paper.
EXPERIMENTAL Apparatus. A schematic diagram of the cell is shown in Figure 1. The body consisted of three 2-inch diameter Plexiglas blocks (Rohm and Haas Co., Philadelphia, Pa.), one %-inch thick, and two 1-inch thick, held together with four stainless steel bolts (not shown). The silver-silver chloride reference electrode (SSCE) was wound around a Plexiglas post (0.351-inch long and 0.405-inch diameter) which extended from the middle block into a cavity (1.078-inch diameter, 0.402-inch deep) in the lower block. Epo-Tek 349 epoxy (Epoxy Technology Inc., Watertown, Mass.) was used to seal a 0.096-inch thick platinum disk into the cavity of the lower block and the silver wire electrode lead into the middle block. Epo-Tek H80 gold-filled conducting epoxy was used to make the electrical contact between the platinum and a copper lead. A 2.00-mm diameter solution channel was drilled through the platinum and the Plexiglas body to form the tubular electrode in the configuration shown in Figure 1. Bolting the three blocks together exerted pressure on six cation exchange membrane washers (10-mil thick, 0.08-inch (2-mm) i.d., 1.070-inch o.d., Nafion XR-170, E. I. du Pont de Nemours & Co., Wilmington, Del.) located in the cavity of the lower block. This provided a leak-free solution bridge between the working and reference electrodes. T h e stirrer was made simply by placing one end of a strip of Teflon about 40 mm long, 2 mm wide, and 0.5 mm thick into a vise and twisting with pliers to form a spiral shape with about 0.5 turn per centimeter. T h e Teflon, which retained its twisted shape, was then press-fitted into a Kel-F stirrer holder. The fit of the Teflon (15) D. C. Johnson and J. Larochelle, Talanta, 20, 959 (1973). (16) W. J. Blaedel, D. E. Easty, and L. Anderson, Anal. Chem., 43, 509 (1971). (17) W. R. Seitz, R. Jones, L. N. Klatt, and W. D. Mason, Anal. Chem., 45, 840 (1973). (18) A MacDonald and P. D. Duke, J. Chromatogr, 83, 331 (1973). (19) S. H. Lieberman and A. Zlrino, Anal. Chem., 46, 20 (1974) (20) J. B. Flanagan and L. Marcoux, J. Phys. Chem., 78, 718 (1974). (21) G. Johansson, Talanta, 12, 163 (1965).
ANALYTICAL CHEMISTRY, VOL. 46, NO. 11, SEPTEMBER 1974
IO
0-3400 (BKGD)
0.3
I I
L
0.1 -0.1 VOLTAGE, VOLTS VS SSCE
-0.3
Figure 2. Current-voltage curves at the turbulent tubular electrode D
50 p M K3Fe(CN)6.3.75 ml/min. For clarity, original data points are shown only for the 1485 rpm curve
Figure 1. The turbulent tubular electrode A. O-ring; B. Cation exchange membranes: C. Cast epoxy; D. Sample solution inlet; E. Lead to platinum tubular electrode; F. 0.1 M KCI inlet: G. Lead to reference electrode (SSCE); H. Sample solution outlet; J. Twisted Teflon stirrer: K. Nitrogen inlet; L. Kel-F stirrer holder; M. 0.1 MKCl outlet
to the 2.00-mm i.d. channel was snug but not so tight as to restrict free rotation or to cause binding. The Teflon was thin and pliable enough to compensate for any errors in alignment, yet rigid enough to maintain its spiral shape even a t high rotational speeds. The Kel-F stirrer holder did not come in contact with the Plexiglas body. T h e stirrer holder was attached to the chuck of a small motor ( % s H.P. Type NSH-34, B & B Motor and Control Corp., New York, N.Y.). T h e stirring speed was varied from 0 to 3440 rpm with a motor control (Type S-12, Gerald K. Heller Co., Las Vegas, Nev.). The rotational speed was measured by placing an electronic counter (Model 704, Series 700, Modular Instrument, Syosset, N.Y.) in a voltage divider circuit with a &volt battery, a I - K resistor, and a phototransistor (General Electric 2N5780). The motor chuck was painted black and a small strip of aluminum foil was glued to the shaft. When light from a high intensity lamp was reflected by the foil onto the phototransistor, the resist,ance of the phototransistor decreased sharply, generating a voltage pulse of about 1.8 volts which was registered as a count by the counter. T h e counts accumulated for one minute were taken as the stirrer speed in rpm. T h e standard deviation was about 3~0.5%a t speeds of 400 rpm or higher, and fl rpm a t lower speeds. Sample and blank solutions were stored above the cell in 1-liter glass vessels, each containing a fritted glass bubbler for deaeration. For deaeration, a stream of nitrogen was used that had passed through a column of amalgamated zinc and acidic vanadous sulfate solution, a column packed with glass wool, a column of alkaline permanganate solution, and a column of supporting electrolyte. In addition, nitrogen was passed above the stirrer channel through the cavity in the topmost. Plexiglas block. Solution flowed from the glass storage vessels to the cell by gravity uia 2-mm i.d. capillary tubing, the volume flow rate being measured with a calibrated rotameter (No. 9143, Fischer and Porter, Warminster, Pa.) placed upstream from the cell. Plexiglas ball joints were made in the machine shop and used for the solution and nitrogen stirrer channel inlets. T h e remaining inlets and outlets were drilled to receive Tygon tubing ( U S . Stoneware Co., Akron, Ohio), press fitted, and sealed with cyclohexanone. One-tenth molar KCI saturated with AgCl was slowly flushed through the compartment housing the AgAgCl reference electrode. All potentials in this paper are given with respect to this reference electrode. All current-voltage measurements were made with a Sargent Model XV Polarograph. Each current measurement was reported a t steady state, i.e., after sufficient time had elapsed (usually less than 30 seconds after a change in potential or stirrer speed), so that the current no longer changed with time. Reagents. Analytical reagent grade KHzP04 and KzHP04 were
used without further purification to prepare the 0.1 M phosphate p H 7.5 buffer solution which was used as supporting electrolyte. Analytical reagent grade K3Fe(CN)s was recrystallized twice from deionized water. All solutions were prepared from triply distilled water, the second distillation being made from alkaline permanganate, and the third from 3 m M HzS04. A ferricyanide stock solution of 1 m M K3Fe(CN)c in the p H 7.5 phosphate buffer was diluted with buffer to prepare solutions of ferricyanide ranging in concentration from 1 to 100 pM. The 273 pM ferricyanide solution was prepared directly. T h e resistance of the cell with the phosphate buffer supporting electrolyte flowing through was 1370 ohms, measured with a conductance bridge (Model RCM 15B1, A. H. Thomas Co., Philadelphia, Pa.). To attain reproducible electrode behavior, the electrode was pretreated in flowing supporting electrolyte before a series of measurements by alternately holding the potential a t -0.8 L7 and +0.8 V for one minute a t each potential. This cycle was repeated a total of four times, finally ending with the cathodic potential.
RESULTS AND DISCUSSION Dependence of Current upon Applied Voltage, Stirrer Speed, and Flow Rate. The current-voltage curves for a 50.0 p M solution of K3Fe(CN)G at various stirrer speeds and a constant volume flow rate ( V f )of 3.75 ml/min are given in Figure 2. The curves were taken pointwise at steady state since scanning the potential gave adsorption and charging currents which distorted the waves. Potential independent transport limiting current regions were obtainable at all rates of stirring. As expected, the magnitude of the limiting current, i ~ increased , with an increase in stirring rate. Log-log plots of limiting current us. stirrer speed for four flow rates are given in Figure 3. There is a marked dependence of limiting current on flow rate at low stirrer speeds. However, this dependence decreases as the stirrer speed increases, disappearing at stirrer speeds greater than 2000 rpm. Apparently, at high stirring rates, the magnitude of the flow rate has a negligible effect on the rate of mass transport to the electrode surface. The plots in Figure 3 approach linearity a t stirrer speeds for which the current is independent of flow rate. The average slope and standard deviation obtained from six separate sets of experiments performed over a period of time was 0.50 zk 0.03. Since a theoretical study has not yet been made, this apparent square root dependence of limiting current on stirrer speed must be regarded as empirical.
ANALYTICAL CHEMISTRY, VOL. 46, NO. 11, SEPTEMBER 1974
1565
7 " '
I SLOPE.0521
f
3430
1-T 3.75
21 25
I
50
1
I
100
200
I
J
I
I
500 1000 RPM
Zoo0
STIRRFR SPFFD
Figure 3. Dependence of current upon stirrer speed for various flow rates 50 pM K3Fe(CN)6. Applied potential, -0.3 V. For clarity, original data points are shown only for the 5.44 mllrnin curve
Figure 5. Dependence of current upon ferricyanide concentration Applied potential, -0.3 V. 3.75 ml/min
J"/
I I
A
SLOPE, 0 334
l % b i O
2
3
5
FLOW RATE, rnl/MIN
IO
Figure 4. Dependence of current upon flow rate at a low stirrer speed (25 rpm)
Id0
2 b
5
&
4
STIRRER SPEED, RPM
Figure 6. Dependence of current upon stirrer speed: Highly twisted stirrer 273 yMK3Fe(CN)6. Applied potential, -0.3 V. For clarity, original data points are shown only for the 8.30 rnllmin curve
273 puMK3Fe(CN)6.Applied potential, -0.3 V
A log-log plot of limiting current us. flow rate a t a constant stirrer speed of 25 rpm is given in Figure 4. The plot approaches a straight line with a slope of 0.334 for flow rates greater than about 5 ml/min. As the flow rate becomes small, there is a positive deviation from the straight line because an increasing proportion of the total mass transport is generated by the stirrer, even a t this low stirrer speed. The limiting Slope of '/3 a t the higher flow rates, where the mass transport is controlled primarily by the volume flow rate, indicates that laminar flow may exist a t low stirrer speeds. The cube root dependence of current on flow rate under laminar conditions has been obtained both experimentally and theoretically for tubular electrodes (22). Dependence of Current upon Concentration. Plots of limiting current us. concentration (Figure 5 ) a t a constant flow rate were linear up to 100 wLM for both high and low rates of stirring, and for the tubular electrode (with stirrer removed). (Data for higher concentrations were not taken.) The background current was about 10 nA. The sensitivity compared to 0.03 kA/gM for a t 3430 rpm was 0.16 ~ A / w M that a t 0 rpm, the stirring causing more than a fivefold increase in sensitivity over the unstirred tubular electrode. Effect of Stirrer Shape. The reproducibility of current obtained with the cell of Figure 1 was around &l% (relative standard deviation), as long as the geometry was not disturbed. However, the act of disassembling and then reassembling the cell caused changes in the current by as much as 5 to lo%, even though the relative shapes of Figures 2-5 did not change significantly. This was undoubtedly due to the difficulty of realigning the stirrer precisely the same way each time. Slight differences in stirrer depth, lateral (22) W J. Blaedel and L. N. Klatt. Anal. Chem., 38, 879 (1966).
1566
alignment, etc., while not significantly changing the characteristics of the cell, probably caused perceptible differences in mass transport efficiencies. When the number of twists of the stirrer was increased from 0.5 turn per centimeter to 3 turns per centimeter, the log-log plots of limiting current us. stirrer speed shown in Figure 6 were obtained. With this stirrer, the current depended little on stirrer speed until very high stirrer speeds were attained. The sensitivity was only about half that of the original low-pitch stirrer. The high-pitch stirrer possessed poorer mass transport efficiency probably due to the tendency of this stirrer to channel the solution axially with the volume flow rather than radially to the electrode surface, a t least until a high rate of stirring was achieved. The independence of mass transport on stirrer speeds up to moderately high speeds for the high pitch stirrer is markedly different from the behavior of the low pitch stirrer. CONCLUSIONS A turbulent tubular electrode has been designed in which the mass transport of electroactive species is increased with the aid of a mechanical stirrer and a turbulent flow regime. For a stirrer speed greater than about 15002000 rpm, the limiting current is directly proportional to the square root of the stirrer speed ( w ) , to the analytical concentration of electroactive species (C), and independent of the volume flow rate ( V f ) : iL a U ' ' ~ C (high speed) This relationship between the limiting current and stirrer speed is empirical, and its theoretical basis is under investigation. The dependence of limiting current on the diffusion coefficient of the electroactive species is also being investigated.
A N A L Y T I C A L C H E M I S T R Y , VOL. 46, N O . 11, SEPTEMBER 1 9 7 4
At low stirrer speeds (20-30 rpm), the limiting current is directly proportional to the cube root of the flow rate, to the analytical concentration C, and only slightly dependent on stirrer speed: iL
vy3c
(low speed)
Intermediate stirrer speeds probably represent a transition between laminar and turbulent flow. The current also depends to some extent on the relative geometry of the cell, but is constant as long as the electrode position is fixed. A stirrer pitch of about y2 turn per centimeter gives more efficient mass transport than a pitch of about 3 turns per centimeter. The turbulent tubular electrode may have some important advantages. It is relatively simple to construct and is highly sensitive, with a limit of detection below 0.1 gM. I t
also has a limiting current which is independent of flow rate a t high stirrer speeds. The latter would be an important advantage for making measurements in flowing systems with poorly controlled flow rates. The high mass transport rates attainable with this electrode might prove advantageous for hydrodynamic voltammetric studies of electrochemical kinetics.
ACKNOWLEDGMENT The assistance of R. Schmelzer in the machining of the cell is highly appreciated. RECEIVEDfor review January 28, 1974. Accepted April 29, 1974. This research was supported in part by an Office of Water Resources Research Grant, No. A-053-WIS. Additional support in the form of a du Pont Summer Research Assistantship (G.W.S., 1972) is gratefully acknowledged.
Fundamental and Second Harmonic Alternating Current Polarography of Electrode Processes with Coupled First-Order Catalytic Chemical Reactions: Theory and Experimental Results with the Iron Triethanolamine-Chlorite System Kathryn R. Bullock’ and Donald E. Smith2 Department of Chemistry, Northwestern University, Evansfon, 111. 6020 7
Some results of studies on the fundamental and second harmonic ac polarographic responses with the first-order catalytic mechanism are presented. Some unpublished aspects of the theoretical predictions for the ac polarographic behavior with this mechanism are discussed. Theoretical predictions reveal simple schemes for characterizing the homogeneous and heterogeneous rate parameters from current amplitude measurements in kinetic regimes where a previously-applied simple procedure based on phase angle measurements is inapplicable. Experimental data obtained with a previously unreported catalytic process, which occurs when ferric triethanolamine is reduced in the presence of chlorite ion, are given. These data provide additional support for the fidelity of ac polarographic rate laws which have been derived for the catalytic mechanism. Heterogeneous charge transfer rate parameters for the ferric-ferrous triethanolamine redox couple were found to be = 0.21 cm sec-’ and a = 0.50 in an aqueous electrolyte primarily composed of O.lOMNaCI, O.OSOMNaOH, and 0.1OMtriethanolamine. The second-order rate constant for the homogeneous oxidation of ferrous triethanolamine by chlorite ion in the same electrolyte was calculated to be (8.0 X 1 0 3 ) W 1 sec-’ from polarographic data obtained under pseudo firstorder conditions.
The initial fundamental harmonic ac polarographic theory for the first-order catalytic mechanism,
’
Present address, T h e Gates Rubber Co., 999 S o u t h B r o a d w a y , Denver, C o l a 80217. T o w h o m correspondence s h o u l d be addressed.
was derived by Smith in 1963 on the basis of the stationary plane electrode model ( I ) . Quantitative predictions were limited to the phase angle and the current amplitude’s frequency response profile, because these observables were indicated to be insensitive to the electrode model’s accuracy. The phase angle theory was validated experimentally by studying the polarographic reduction of Ti4+to Ti3+in the presence of chlorate ion (2). In 1968, McCord and Smith published a general theory for the fundamental ( 3 )and second harmonic ( 4 ) ac polarography of systems with firstorder homogeneous chemical reactions coupled to a single heterogeneous charge transfer step. These theories were derived on the basis of the expanding plane electrode model and included the case of the catalytic mechanism. Through this development and Delmastro’s theory ( 5 ) for the dc process with a catalytic mechanism, which encompasses all combinations of heterogeneous and homogeneous rate parameters, h,, a , and h,, a quite general theory for the ac polarographic rate law with the catalytic mechanism is made available in the context of the expanding plane electrode model. Subsequently, Sluyters-Rehbach and Sluyters (6, 7 ) extended the theory to include the effects of reactant adsorption under Nernstian conditions and provided expressions for the overall interfacial admittance by introducing the double layer parameters. Efforts to obtain mathematically simpler rate law formulations also characterized their efforts. Despite these apparently successful efforts in developing (1) D. E. Smith, Anal. Chem., 35, 602 (1963). (2) D. E. Smith, Anal. Chem., 35, 610 (1963). (3) T. G. McCord and D. E. Smith, Anal. Chem., 40, 1959 (1968). (4) T. G. McCord and D. E. Smith, Anal. Chem., 40, 1967 (1968). ( 5 ) J. R . Delmastro, Ph.D. Thesis, Northwestern University, Evanston. 111. 1967. (6) J. H. Sluyters and M. Sluyters-Rehbach. J. Nectroanal. Chem., 23, 457 (1969). (7) M. Sluyters-Rehbach and J. H. Sluyters, J. Elecfroanal. Chem., 26, 237 (1970).
A N A L Y T I C A L C H E M I S T R Y , VOL. 46, NO. 11, SEPTEMBER 1974
1567
