Anal. Chem. 1982, 54, 1757-1764 (3) Relchardt. C. "Solvent Effects in Oraanlc Chemistry"; Verlag Chemie: Welnhelm, 1979. Grifflths, T. R.; Pugh, D. C. J . Solutlon Chem. 1979, 8 , 247-258. Snyder. L. R. "Prlnclples of Adsorption Chromatography"; Marcel Dekker: New York, 1968. Snyder, L. R. J . Chronripfogr. 1974, 92,223-230. Keller, R. A.; Karger, E. L.; Snyder, L. R. "Gas Chromatography 1970"; Stock, R., Ed.; Institute of Petroleum, London, 1971. Karger. B. L.; Snyder, L. R.; Eon. C. J . Chromafogr. 1978, 125, 71-88. Karger, B. L.; Snyder, L. R.; Eon, C. Anal. Chem. 1978, 50, 2 126-2 136. Kamlet, M. J.; Abboud, J. L.; Taft, R. W. J . Am. Chem. SOC. 1977, 99,6027-6038. Abboud, J. L.; Kamlet, M. J.; Taft, R. W. J . Am. Chem. SOC. 1977, 99,8325-8327. Abboud, J. L.; Taft, R. VV. J . Phys. Chem. 1979, 83,412-419. Kamlet, M. J.; Taft, R . W. J. Chem. Soc., Perkin Trans. 2 1979, 337-341. Kamlet, M. J.; Jones, M. E.; Taft, R. W.; Abboud, J. L. J. Chem. SOC., Perkin Trans. 2 1979. 342-348. Kamlet, M. J.; Jones, M. E.; Taft, R. W.; Abboud, J. L. J . Chem. Soc., Perkin Trans. 2 1979, 349-356. Taft, R. W.; Kamlet, U. J. J. Chem. Soc., Perkin Trans. 2 1979, 1723-1729. Kamlet, M. J.; Solomonovlcl, A.; Taft, R. W. J . Am. Chem. SOC. 1979, 101, 3734-37311. Kamlet, M. J.; Hall, T. hi.; Boykln, J.; Taft, R. W. J . Org. Chem. 1979, 44, 2599-2604. Taft, R. W.; Plenta, N. J.; Kamlet. M. J.; Arnett, E. M. J . Org. Chem. 1981, 4 8 , 661-667. Taft. R. W.; Abboud, J. L.; Kamlet, M. J. J . Am. ChSm. SOC. 1981, 103, 1080-1086. Kamlet, M. J.; Abboud,, J. L.; Taft, R. W. Prog. Phys. Org. Chem. 1980, 13, 485-630.
1757
(22) Hildebrand, J. H.; Prausnitz, J. M.; Scott, R. L. "Regular and Related Solutions"; Van Nostrand-Reinhold: Princeton, NJ, 1970. (23) Scatchard, 0.Chem. Rev. 1931, 8 ,321-333. (24) Scatchard, G. Chem. Rev. 1949, 4 4 , 7-35. (25) Hlldebrand, J. H. Proc. Nafl. Acad. Sci. 1979, 76, 6040-6041. (26) Halicloglu, T.; Sinanoglu, 0. Ann. N . Y . Acad. Sci. 1969, 158, 308-317. (27) Slnanoglu, 0. Inf. J. Quantum Chem. 1980, IS,381-392. (28) Horvath, C.; Melander, W.; Molnar, I. J. Chromafogr. 1976, 125, 129-158. (29) Melander, W.; Campbell, D. E.; Horvath, C. J. Chromatogr. 1978, 158,215-225. (30) Carr, P. W. J. Chromatogr. 1980, 194, 105-119. (31) Kamlet, M. J.; Carr, P. W.; Taft, R. W.; Abraham, M. H. J. Am. Chem. SOC. 1981, 103, 6062-6066. (32) Bekarek, V. Collect. Czech. Chem. Commun. 1980, 45,2063-2069. (33) Bekarek, V. J. Phys. Chem. 1981, 85,722-723. (34) Ehrenson, S. J. Compuf. Chem. 1981, 2 , 41-52. (35) Hamza, M. A.; Serratrice, G.; Stabe, M. J.; Delpuech, J. J. J . Am. Chem. SOC. 1981, 103, 3733-3738. (36) Block, H.; Walker, S. M. Chem. Phys. Len. 1973, 79,383-364. (37) Klrkwood, J. G. J . Chem. Phys. 1934, 2,351-361. (38) Onsager, L. J . Am. Chem. SOC. 1938, 58, 1486-1493. (39) Bottcher, C. J. F. "Theory of Electric Polarization", 2nd ed.; Elsevier: Amsterdam, 1973; Vol. I. (40) Buckingham, A. D. Proc. R . SOC. London, Ser. A 1958, A248, 169-182. (41) Ehrenson. S.J . Am. Chem. SOC. 1981, 103,6038-8043. (42) Weast, R. C., Ed. "Handbook of Chemistry and Physics", 61st ed.; CRC Press: Boca Raton, FL, 1980.
RECEIVED for review August 20, 1981. Resubmitted and accepted June 1, 1982.
Electrochemical Detection with a Regenerative Flow Cell in Liquid chromatography Stephen 0. Weber" Department of Chemlstty, ildniversi@ of Pittsburgh, Pittsburgh, Pennsylvania
15260
William C. Purdy Department of Chemlstty, McGiIl Unlversl& 80 I Sherbrooke Street, West, Montreal, Quebec, H3A 2K6 Canada
The regenerative detector studied has two worklng electrodes, one an anode arid one a cathode, placed parallel to one another and close to each other. Solution containing depolarizer flows In the thln channel between them. I n such a detector the product of the electrode reaction at one electrode can dlffuse to the1 opposlte electrode where starting material may be recreated. Thls leads to a current ampllflcation with respect to a coulometric detector. A simple theory allows the derivation of equatlons relating current to system variables; for example, for current measured at an anode and a reduced deiaolarizer, i = nFCo(AD/b 4- 0.278) where A Is electrode area, D is dlffusion coefflclent, b is the distance between the electrodes, and U is the volume flow rate. The equatlons expllaln observed data well. To use the cell It Is required that the large nolse current generated by the low cell impedance be defeated. Thls Is possible by swltchlng the worklng electrodes In and out of the current to voltage conversion circuit. A duty cycle of a few percent yields picogram detection limits; for 2,4-toluenedlamlne following chromatography in an aqueous methanol solvent.
In any system of detection it is desirable to increase sensitivity if one can do so with less than a concomitant increase in noise. Expressions for the signal intensity are known for the various sorts of electrochemicaldetectors, the channel (I, 2), the tubular ( 3 , 4 ) ,and the wall-jet (5), and for hydrody-
namic electrode detectors in general (6). Far less is known about the noise. In the absence of specifics it has become custom to assume that the noise is proportional to electrode area (7). Qualitatively, at least, this relationship seems to be followed, although certainly many more variables enter into the relationship. Thus if one can increase the sensitivity of an electrochemical detector without increasing the electrode area, one will likely have a device with improved limits of detection. Regenerative flow cells satisfy this criterion. In a regenerative flow cell one converts analyte which has reacted at a working electrode back to its original form using physical (8, 9) or chemical (IO)methods. The latter cells involve the "catalytic" reaction (11)in which analyte A is regenerated using reagent C
A
B
+C
-
-+ k2
A
B (electrode)
products
(homogeneous)
The current to be expected from this system in a flow cell has been determined by Aoki et al. (12).The physical regeneration occurs because of a second electrode placed parallel and opposite to the first electrode so that one has the following scheme A
B
--
B (electrode 1)
A (electrode 2)
0003-2700/82/0354-1757$01.25/00 1982 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 54, NO. 11, SEPTEMBER 1982
thus the sum of uncompensated resistance and switch resistance represents a possible error. For signals at the lo4 A level, 1ks2 yields 1mV iR drop. Thus only for large signals, and then only at less than optimum applied potentials, will the switch resistance be troublesome.
A
B
AUX
Figure 1. Switching deslgns: (A) alternate switching,(B) simultaneous swkching. W1 and W2 are working electrodes and AUX Is an auxiliary
electrode. This has been called a parallel-opposed dual electrode cell, or PODEC. This cell was f i t used in flowing streams by Fenn et al. (8). Their PODEC demonstrated an enhancement of signal current with respect to a coulometric cell for the same electrode area. Only a brief account of the theory for this cell exists ( I ) . The detailed theory of operation, confirmation of that theory, and conditions for maximum signal to noise ratio for PODEC’s are given in this report.
EXPERIMENTAL SECTION The cells used for this work were made of either Lucite or Kel-F with 10 cm X 1.5 cm glassy carbon electrodes (Tokai Manufacturing, Tokyo,Japan) facing one another across the solution. The two electrodehalves were held apart by a poly(tetrafluoroethy1ene) spacer (Dilectrix). For the comparison of experiment and theory the flow of a solution of potassium hexacyanoferrate(I1 or 111) in 2 M KCl was pushed through the cell with a peristaltic pump (Technicon). The flow rates were checked by timing the filling of a 1.00- or 2.00-mL volumetric test tube. The distance between electrodes was 0.0024 cm, as measured by the method described in ref 1. The chromatographicsystem consisted of a Waters M45 pump, a Valco loop injedor, and an HPLC Technology 10-pm Spherisorb octadecylsilane column 25 cm long. The mobile phase used for the solute 2,4-toluenediaminewas 23% methanol/77% aqueous or lW3 M. The phosphate buffer, pH 5.5, concentration lo-*, M in EDTA. entire mobile phase was made The potentiostat used was an LC4 (BioanalyticalSystems) or a Princeton Applied Research 174A. For control of the second working electrode, a second current to voltage converter was built using the design of Blank (13). The switching circuit required for increasing signal to noise ratio was as diagrammed in Figure 1. The switches were FET switches. Several types were used. CMOS switches (AD 7519, AD 7513, Analog Devices) are fast, but noisy and fragile. For operation at low applied potentials p-channel J-FET switches work well (AH 5012H, National Semiconductor). The switchingsignal was obtained from a 555 timer, the frequency and duty cycle being manipulated using external resistors and capacitors. The FET switches used all have a nonzero impedance. An “on” resistance of a couple of hundred ohms and capacitances on the order of a few picofarads are typical. The time constant of such a system is extremelyshort, thus one need only consider resistance of the switch for low frequency or dc signals. The on resistance is in series with uncompensated resistance and cell impedance;
RESULTS AND DISCUSSION The auxiliary electrode in an electrochemical cell carries the current produced at the working electrode. The auxiliary electrode current is opposite in sign to the working electrode current, Le., for an anodic working electrode current the auxiliary electrode current will be cathodic. In the context of a thin-layer cell, if the auxiliary electrode is placed opposite and parallel to the working electrode, the possibility of the regeneration of starting material by the auxiliary electrode may be seen to occur in the following fashion. A molecule of depolarizer is first oxidized at the working electrode surface. By diffusion it travels away from the electrode surface until it reaches the auxiliary electrode where it may be reduced to yield starting material. The same molecule will diffuse back to the working electrode. The process may continue ad infinitum. Systems such as this with stationary electrolyte have been studied (9). These studies were carried out with a dual working electrode potentiostat. The two working electrodes were aligned parallel and opposed to each other. The potentiostat allowed independent control of the two working electrode potentials. For a cathodic auxiliary electrode, if the potential required to regenerate starting material is less reducing than the potential required to reduce supporting electrolyte or solvent, then virtually all of the oxidized starting material which reaches the auxiliary electrode will be reduced. This is equivalent to the four-electrode system in which the second working electrode is at a large enough potential to ensure complete reduction of oxidized starting material. The two systems can be considered identical under these conditions, and will both be called PODEC. With the diffusion layer treatment (14,15) an approximate description of PODEC current may be obtained. A short review will be beneficial for understanding PODEC. Electrochemical cells of the channel design generally are built so that the solution reaches the electrodes as fully developed laminar flow. Then the solution velocity is a parabolic function of distance from the working electrode, and there is no solution flowing toward or away from the working electrode. The solution velocity is at its maximum halfway between the working electrode and the wall or electrode opposite to it and is zero at the electrode surface. Since there is no component of flow perpendicular to the electrode surface, diffusion is the means by which molecules arrive at the electrode surface in channel cells. This allows one to use the concept of a diffusion layer, a region of the solution in front of the electrode over which the analyte concentration changes from its value at the electrode surface to its value in the bulk of the solution. The thickness of the diffusion layer, 6, is a function of the electrolysis time, among other things. Thus in a flow cell, 6 is a function of distance down the cell. Since current is inversely proportional to diffusion layer thickness
i
C
= nFAD-
6
(1)
(D = solute diffusion coefficient, A = electrode area, C = analyte concentration in the bulk of solution) this means that current is a function of distance along the electrode. I t is convenient to consider the length along the electrode, x , in dimensionless form, r r = x(DW,/Ub)
(2)
where D is the solute diffusion coefficient, W , is the channel width, U is the solvent volume flow rate and b is the channel
ANALYTICAL CHEMISTRY, VOL. 54, NO. 11, SEPTEMBER 1982
coulometric
height. When r is writtm as
r = (3c/Y)/(b2/D)
(3)
abc
I =: LrLi(r)dr
(4)
rL := L(DWc/Ob)
(5)
Here rL is r at x = L At r = 0, 6 = 0, and for r > 0, 6 increases steadily. It is convenient to discuss 6 in dimensionless form, 6
(6)
Thus when 6 = 1,the concentration of analyte changes all the way from the electrode to the opposite wall where it has its bulk value. The length of electrode required for 8 to equal 1is r = 0.33. The total integrated current from an electrochemical detection cell with rL = 0.33 is (I)
IrL=o.33 = 0.60nFC0~(We/Wc)
(7)
where Weis the width of the electrode. Note that coulometric conversion corresponds to an electrode with rL 2 2 ( I ) and the current is
Icoul= nFCoO(We/Wc)
(8)
Let us consider a cell far which rL = 0.33 and inspect more closely the concentration distance relationships at the end of the electrode where 6 = 11. While analyte is being consumed a t the electrode and diffusing toward the electrode, the product(s) of the electrochemical reaction is(are) being produced there and is(are) diiffusing away from the electrode. At 8 = 1 (for reactant and product diffusion coefficients equal) the wall opposite the electrode first becomes exposed to the electrode reaction product. If the opposite wall is an electrode and if the analyte couple is chemically reversible then the reaction product will be (convertedto analyte at 8 = 1. This is a stable system; as analyte goes to product at S = 0, product goes to analyte at 8 = 1, and there is a continuation of the concentration distance rlelationships for all r > 0.33. For a PODEC, then, one may measure current from analyte oxidation or reduction at one electrode, and current from the product reduction or oxidation a t the other. Note that the latter current will be smiiller than the former since there is in principle no current at the opposite electrode for r < 0.33. These concentration dii~tancerelationships are illustrated in Figures 2 and 3. For reference recall that a t r = 0.11,S = 0.5, r = 0.33,6 = 1.0, and coulometric conversion is obtained for r > 2. Note in Figure 2 the analyte and product concentration gradients decrease as r increases. This is in contrast to the case in Figure 3 where, because there is a second electrode, the Concentrationgradient for r > 0.33 is constant and equal to Ca/b. One can now derive equations which will give approximate relationships between current and physical variables/parameters. This will be done for three cases. Consider the reversible electrode oxidation of A to B. 5
A ).
Bn+ Let us measure current a t only one of the electrodes, the anode, W1. The anode is siufficiently oxidizing so [A](z=,, = 0. The opposite electrode, W2, is the cathode at which B
-
e
d
\ I l l
where P is the solvent velocity, it may be seen that r is the ratio of the time spent in the channel to the time required to diffuse the height of t,he channel. The theoretical treatment consists of determining 6 as a function of r, then i as ti function of r. Qnce this is known, integration of the current, over the total electrode length yields the cell current
S = 6/b
1759
WE
f
\
I
!
I
I
l
0
r
l
l
1
2
3
4
concentration profiles at various values of r
r-7j
-------_4
1
i
i---,
i
d ' r i $ i c a l a x i s = ~ ~ ~ & ~ a t i of,nrs4.0 horizontal axis=dlstance between walls
Flgure 2. Concentration profiles as a function of distance along a coulometric flow cell. The length along the cell is glven in dlmenslonless form, r = xDWc/&, where x is distance along the cell, D is the analyte dlffuslon coefflcient, W , is the channel width, U is the average solution volume flow rate, and b is the cell height or thickness. The solutlon flows from left to right. The concentration profiles are drawn with the working electrode on the right: (-) concentration of analyte; (---) concentration of the product of the electrolysis of anaiyte.
PODEC
\=$&-ip\
abc d
.... ....._ I _ > _
WE2
I
0
!
I
2
3
1
i
1
l
r
l 4
Concentration profiles at varlous values of r
Flgure 3. Concentration proflies as a functlon of dlstance along a PODEC. The concentrationprofiles are drawn wlth working electrode 1 (WE1) on the right. Other conventions are the same as in Figure 1.
A and [B](z,,) = 0. The unitless distance 8 is measured from W1. The three cases to consider are as follows: (1)A is in the flow stream at concentration CA,and current is measured at W1. (2) B is in the flow stream at concentration Cg, and current is again measured at W1.(3) A and B are in the flow stream at equal concentrations, CA, and current is measured at W1. It will be convenient to define a dimensionless parameter, the efficiency 4, such that when conversion is coulometric, 4 = 1, so
I = nFC00(We/Wc)4 Case I. For 0 < r
(9)
< 0.33 the cell generates a current
I = nFCAU(We/Wc)@
4 = 0.60
(10)
(11) For the remainder of the electrode (0.33 < r < rL) one has 8 = 1, 6 = b. From eq 1
1780
ANALYTICAL CHEMISTRY, VOL. 54, NO. 11, SEPTEMBER 1982
i = nFADCA/b
(12)
The electrode area is obtained from the width and the length under consideration, which are obtained from r
A = We(rL- 0.33)b0/DWC
(13)
i = ?IFCAD(W e /Wc)(rL- 0.33) 4 = rL - 0.33
(14)
thus
,031 I 0
0 1
The entire electrode will generate the sum of these two currents
4 = rL + 0.27 Case 11. There will be no current for 0 thereafter eq 14 applies
(15)
< r < 0.33 and
4 = rL - 0.33
(16)
Case 111. A will be depleted at W1, and this diffusion layer will grow into the solution as r increases. Likewise A will be produced a t Wz and this diffusion layer will also grow into the solution. At W1, [A] = 0, while at W2, [A] = 2CA, since the A initially in the solution has not been oxidized by W1, and the reduction of [B] to 0 at 6 = 1leads to a production of A a t a [A] = C A which adds to the initial concentration. The depletion diffusion layer from W1 will meet the enhancement diffusion layer from W2 at 6 = 0.5, at which point the concentration gradient is 2 C ~ / band , the steady state is reached. Proceeding along lines similar to case I, for 0 < 6 < 0.5 one has 0 < r < 0.11. The efficiency from this portion of the electrode is ( I )
4 = 0.25 Thereafter (0.11 < r
(17)
< rL) 4 = 2(rL - 0.11)
(18)
The fador of 2 arises from the concentrationgradient of 2 c A /b while the reference for d, = 1 is for a concentration C A and a gradient a t r = 0.33 of CA/b. Then for case 111
4 = (2r + 0.03)
(19)
For W,= W,, a common experimental case, one can rewrite eq 15,16, and 19 in terms of the cell dimensions and physical paramers in such a way that the route to experimental verification by measuring current as a function of flow rate is clear.
+ 0,270
(20)
I/nFCB = LDW,/b - 0.330
(21)
I/nFCA = L D W , / b I/nFCA = 2LDW,/b
+ 0.030
(22)
There is a similar experimental approach to enhanced currents which has been discussed by Kissinger et al. (IO). Instead of regenerating the analyte, say A, with an electrode, one may regenerate analyte with a homogeneous chemical reaction. Here molecule C is in the flow system.
A
B +C
hne-
-+ ka
A
B (electrode)
products
Figure 4. Investigation of a cell with large r . Both axes are in units of cm3s-‘. The lines represent theoretical expectation (eq 20-22) for: a, coulometric system, 1.0 X lo-‘ M K,Fe(CN), in 2 M KCI; b, PODEC, 1.0 X lo-’ M K,Fe(CN), in 2 M KCI; c, a PODEC with 1.0 X M K4Fe(CNI6 In 2 M KCI; d, a PODEC with 1.O X lo-’ M of both K,Fe(CN), and K,Fe(CN), in 2 M KCI. Potential of the working electrode was 950 mV vs. Ag/AgCI button. The points represent experimental data. The error In the theoretical predlctlon ( 3 4 is about 11% ( 1 ) .
reaction to be treated as a simple diffusion problem. In the case of the PODEC,where 6 = b , one must substitute the reaction layer thickness, ( D / k ) 1 / 2for , b in eq 9 to arrive at expressions for the current to an electrode when one has a homogeneous reaction regenerating A, rather than a second electrode regenerating A. The expression thus derived is in good agreement with eq 22 of the work of Aoki et al. who have solved this problem with fewer assumptions (12). Verification of Theory. The theory predicts that, for a given analyte and cell, the measured current ought to be a weak function of flow rate. With solutions of potassium hexacyanoferrate(I1) and -(III) in 2 M KC1 as analytes, the curves in Figure 4 were obtained. The data and theory agree well for both regenerative and coulometric cases. The usefulness of this detector results from allowing a value of 4 > 1 (eq 20-22). This requires large r, which may reasonably be obtained by (a) increasing electrode area (L and W,), (b) decreasing b, and (c) decreasing U. The cells used in these experiments were 10-15 cm2,which represents a large (and expensive) piece of glassy carbon. Also, at constant b, increasing L and W, will increase cell dead volume. Choice b is a good choice but poses the practical difficulty that the two working electrodes can come into physical contact with one another causing a short circuit. Choice c works, but of course one must accept lengthened analysis time. Figure 5 demonstrates the magnitude of the gain possible as the flow rate is lowered. Since application of these detectors will most likely involve the detection of “plugs” of concentration of analyte as peaks rather than the steady-state response illustrated in Figure 4,it is valid to ask whether equations similar to 20-22 exist for peaks. In fact eq 15, 16, and 19 do if one considers 4, the efficiency, to be the ratio of measured coulombs, Q, to (nF) X (moles injected), e.g., for eq 15
(homogeneous)
This homogeneous reaction proceeds with a rate kz[B][C]. If one makes the concentration of C large enough, then the reaction is pseudo first order with an apparent first-order rate constant Iz = k,[C]. The electrochemical current due to A when C is present in excess can be approximated by using the reaction layer thickness. This approach allows the electrochemical current which arises in part due to homogeneous
This is for the case where We = W,, and where one is measuring current from the anode of PODEC in which the anal@ is oxidizable. The charge from the peaks in Figure 5 at the two higher flow rates fall on a straight line with an intercept ( 1 / 0 = 0) of 0.27 in agreement with eq 23. The charge for the 0.1 mL/min flow is 94.5% of that predicted by eq 23. It
ANALYTICAL CHEMISTRY, VOL. 54, NO. 11, SEPTEMBER 1982
100 PI injections of 6.78 pM DOPAC coulometric conversion E 131 ~ C O U I 74 5 1470 6720 p o u l
5 min.
Figure 5. Injections of dihydroxyphenylacetic acid into a PODEC at three flow rates.
is possible that when the solute is in the oxidized (quinone) form for such a long period of time that there is some following chemical reaction which destroys solute. One of the redeeming features of this detector configuration is that the peak current i5 only a weak function of the flow rate. Also, from eq 23 i t can be seen that the number of coulombs in a peak (peak: area) remains practically invariant if sample size (moles) anti flow rate (0are lowered concomitantly. In capillary and microbore liquid chromatography (16) flow rates are low and sample sizes are low. Thus if one were to consider electrochemical detection in chromatography with low flow rates, the most advantageous type of detector would be, in our opinion, the PODEC. In this regard, a major technical difficulty for low dead volume detectors, obtaining a low dead volume connection between column and detector, has been solved (17). A disadvantage of this detector is that, it works best for chemically reversible anrdytes. Chemically irreversible analytes can yield enhanced current if the parallel opposed electrodes are working m d auxiliary electrodes. In this case the species produced at the auxiliary electrode may react’at the working electrode to give a current enhancement. While we have observed enhanced currents for species which react irreversibly (albeit with an efficiency lower than that for reversible species), since tlhe chemical species responsible for the enhancement are not known we have not pursued this for analytical purposes. Clonversely, if the parallel opposed electrodes are both controlled potential electrodes, then one may selectively enhance the current of reversible species (10). Maximizing-Signal-to-Noise Ratio. In the course of still ongoing work we have determined that a large contributor to the noise in the measured current is the voltage noise in the current to voltage converter. This source is one of many contributions to the total noise (18,19). ‘This voltage noise generates a current noise through the cell impedance. Thus if the cell impedance is low, the equivalent current noise measured for a given voltage noise will be high. In the case of regenerative cells, where the double layer capacitance may be a few hundred microfarads,the cell impedance may be low and the noise current, especially at “high”frequencies, is high. The solution resistance lbetween the auxiliary and working electrodes aids in reducing this noise source in normal cell designs. In the PODEC however, two current carrying electrodes, W1 and Wz, are :separated by a very small solution resistance, and a large noise current flows between them. It was felt that a way to defeat this noise source was to force the individual currents at W1 and Wz to flow to the auxiliary
1761
electrode, rather than for each to complete the circuit for the other (which is the normal case). This could be done by alternately switching the working electrodes in and out of electrical contact with the circuit as shown in Figure 1A. For this to work one relies on the slow relaxation of the difference in potential across the double layer to hold the potential at one working electrode near its applied potential while the other working electrode is being driven by the potentiostat. The advantage to this technique is that each working electrode is in electrical contact with the auxiliary electrode (through a relatively large solution resistance) while the two working electrodes are not in electrical contact with each other. Thus the current-to-voltage converter input voltage noise is not converted to a large current through a low cell impedance. The concomitant disadvantage is that while an electrode is in the “off“ state, its potential droops, and when it returns to the “on” state, the auxiliary electrode is required to drive a large current through the solution resistance to charge the double-layer capacitance. This may take a relatively long time. Another option is to switch the two working electrodes on simultaneously as shown in Figure 1B. If one can obtain full signal expression by only having the electrodes “on”for a short period of time (ton)then one can improve the signal-to-noise ratio since the total noise energy (a2 X ton)observed will be decreased; the current-to-voltage converter current noise is nil when the switch to the working electrode is open. The final measured voltage (proportional to cell current) is low-pass filtered to the same degree for both switched and normal potentiostat operation so that the averaging time t,, is the same, thus the measured noise power (azton/tav) is lower in the switched experiment. To be more explicit, let ad: be the experimental noise power in the normally operating potentiostat. In the switched case the noise aeW2will be asw2
=
‘Jd?(ton/(ton
+ teff)) + Uex2
(24)
where tonis the switch “on” time, toffis the switch “off“ time, and ue,2is the excess noise created by the switching. Thus for small duty cycle (ton/(ton+ teff)) the measured noise may indeed be lower for the switched experiment than the normal operation. An improved signal-to-noise ratio is expected for those cases in which signal power is not severely attenuated. These conditions are given in the Appendix. The experimental results demonstrated that the alternate switching approach worked, but the simultaneous switching worked better. Thus more data were obtained for the latter. Because of the long time constant for operation in the alternate
