1744
Anal. Chem. 1984, 56, 1744-1747
varied between 1360 Q cm at 0.01 M TBAP and 107 Q cm at 1.0 M TBAP. There were no significant differences between the values of p in this study utilizing ten nonaqeous solvents and those presented in two more limited studies which included three of our ten investigated solvents (9,21). Values from these earlier studies are presented in parentheses in Table 111. Data for solvents containing TPAP, TEAP, and TMAP are less numerous than those for TBAP due to the limited solubility of these salts in some solvents. However, as seen from Table I11 similar trends in p exist as a function of supporting electrolyte concentration. In a given solvent p is almost identical for TPAP, TEAP, and TMAP, and is slightly smaller than that for TBAP. In addition, the smallest value of p is again observed in CH&N and the largest (where a comparison is possible) is found in CHzClzor EtClZ. Almost all electrochemical studies in nonaqueous media utilize tetraalkylammonium salts as supporting electrolytes, the most commonly being TBAP, TPAP, TEAP, and TMAP. The usual concentration of this supporting electrolyte which has been employed in cyclic voltammetry is 0.1 M, although some studies utilize 0.2 M. In contrast, thin-layer spectroelectrochemistry (which does not use built-in IR compensation) requires much higher concentrations of supporting electrolyte, and concentrations as high as 0.50 M or 1.0 M are often utilized. As seen in Table I11 the need to use highly concentrated solutions of tetraalkylammonium salts is largely justified on the basis of the decreased specific resistance. In an earlier study, Whitson et al. (9) calculated a solution resistance of 230 Q using their specific cell configuration and a specific resistance of 128 Q cm. Using the same configuration in THF and our value of 2670 Q cm (at 0.1 M TBAP) would lead to a solution resistance of almost 5000 Q. This is an extremely high value, and under these experimental and solution conditions, great care must be taken in correcting for IR loss. This value of resistance depends, of course, upon the specific cell configuration. However, for a given electrode configuration, solution resistances can be easily calculated. Finally, we should stress that k” values presented in this paper should not be assumed to be absolute standard rate constants which would be identical by all electrochemical techniques. They are, however, self-consistent measurements obtained by cyclic voltammetry at a Pt electrode using all known precautions to eliminate uncompensated IR loss. We believe that the use and evaluation of these data when looking p
at other heterogeneous electron transfer rate constants should help to eliminate problems associated with the reporting of erroneous resistance-limited rate constants, as well as the erroneous evaluation of peak current shifts as a function of scan rate using cyclic voltammetry and the well-known and often quoted Nicholson-Shain diagnostic criteria (23). Registry No. TBAP, 1923-70-2;TPAP, 15780-02-6; TEAP, 2567-83-1;TMAP, 2537-36-2;DMF, 68-12-2;DMA, 127-19-5;MF, 123-39-7;F, 75-12-7; Py, 110-86-1;THF, 109-99-9;Fc, 102-54-5; Fc’, 12125-80-3; CH3CN, 75-05-8; Me2C0, 67-64-1; CH3NO2, 75-52-5;MeOH, 67-56-1;PrCN, 109-74-0;Me2S0,67-68-5;PhCN, 100-47-0; PhN02, 98-95-3; CH2C12, 75-09-2; EtCl,, 1300-21-6; EtOH, 64-17-5; PrOH, 71-23-8.
LITERATURE CITED (1) Sawyer, D. T.; Roberts, J. L., Jr. “Experimental Electrochemistry for Chemists”; Wiley: New York, 1974. (2) Dobos, D. “Electrochemical Data”; Elsevler: Amsterdam, 1975. (3) Brown, E. R.; McCord, T. G.; Smith, D. E.; DeFord, D. Anal. Chem. 1966, 38, 1119, and references therein. (4) Garreau, D.; Saveant, J. M. J. Electroanal. Chem. 1972, 35, 309. (5) Bezman, R. Anal. Chem. 1972, 4 4 , 1781. (6) Whltson, P. E.; VandenBorn, H. W.; Evans, D. H. Anal. Chem. 1973, 45, 1298. (7) Sedletskii, R. V.; Limin, B. E. Electrokhimiya 1972, 8,22. (8) Thomas, W. E.; Schaap, W. 8. Anal. Chem. 1969, 4 1 , 136. (9) Whltson, P. E.; VanderBorn, H. W.; Evans, D. H. Anal. Chem. 1973, 45, 1298. (10) Belew, W. L.; Fisher, D. J.; Kelley, M. T. Chem. Instrum. 1970, , 297. (11) Garreau, D.; Saveant. J. M. J. Necroanal. Chem. 1978, 86,63. (12) Nicholson, R. S. Anal. Chem. 1965, 37, 1351. (13) Kadish, K. M.; Su, C. H. J. Am. Chem. SOC. 1983, 105, 177. (14) Zhu, T.; Su. C. H.;Lemke, B. K.; Wilson, L. J.; Kadish, K. M. Inorg. Chem. 1963, 22,2527. (15) Bauer, D.; Breant, M. I n ”Electroanalytical Chemistry”; Bard, A. J., Ed.; Marcel Dekker: New York, 1975; Vol. 8. (16) Diggle, J. W.; Parker, A. J. Nectrochim. Acta 1973, 18,975. (17) Sharp, M.; Peterson, M.;Edstrom, K. J . Nectroanal. Chem. 1980, 109, 271. (18) Armstrong, N. R.; Qulnn, K.; Vanderborgh, N. E. J. Nectrochem. SOC. 1976, 123,646. (19) Daum, P. H.; Enke, C. G. Anal. Chem. 1969, 4 1 , 653. (20) Cai, S. M.; Mallnskl, T.; Lln, X. 0.; Ding, J. Q . ; Kadlsh, K. M. Anal. Chem. 1983, 55, 161. (21) House, H. 0.; Feng, E.; Peet, N. P. J. Org. Chem. 1971, 36,2371. (22) Malinski, T.; Ding, J. Q.; Kadish, K. M., manuscript in preparation. (23) Nicholson, R. S.; Shain, I. Anal. Chem. 1964, 3 6 , 706.
RECEIVED for review July 25, 1983. Resubmitted March 16, 1984. Accepted March 26,1984. We are grateful for financial support of this work from the National Institutes of Health (Grant GM 25172), the National Science Foundation (Grant CHE-821557),and Robert A. Welch Foundation (Grant E680).
Enhanced Voltammetric Response by Electrochemical Pretreatment of Carbon Paste Electrodes K. Ravichandran and Richard P. Baldwin* Department of Chemistry, University of Louisville, Louisville, Kentucky 40292 Despite the fact that electrodes constructed from carbon substrates exhibit low background currents over a wide range of potentials and are useful for numerous electrochemical applications, electron transfer rates observed for redox processes at these surfaces are often slower than those at metal electrode surfaces. As a result, carbon electrodes often exhibit substantial overpotentials which cause the related oxidations and reductions to take place at potentials significantly in excess of their thermodynamic potentials. In order to increase the electron transfer rates, various chemical (1-3), thermal ( 4 ) ,and electrochemical (5-12) surface treatment procedures for carbon electrodes have been developed which have been 0003-2700/84/0356-1744$01.50/0
shown to produce improved electrode response compared to that of the native electrode material. Of all these modification methods, the electrochemical pretreatment reported by Engstrom (6, 7)for glassy carbon is one of the simplest to carry out experimentally. In addition, this particular modification strategy has been shown to produce a marked enhancement in the sensitivity and selectivity of liquid chromatography/ electrochemicaldetection (LCEC) for several electrochemically irreversible oxidations which exhibit high overvoltages at untreated glassy carbon (12,13). The systems examined so far have included hydrazines, hydroquinone, ascorbic acid, and nicotinamide adenine dinucleotide (NADH). In nearly 0 1984 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 56, NO. 9, AUGUST 1984
all of the cases reported to date, this kind of electrochemical pretreatment has been carried out on solid carbon electrodes constructed from such substrates as glassy carbon (5-B), pyrolytic carbon fiber (9),and graphite/epoxy (IO). Despite the widespread popularity of carbon paste electrodes for a variety of electroanalytical applications, little analogous work describing the effects of pretreatment procedures on this type of electrode material has yet been reported. Recently, Adams et al. (11)have shown that application of positive potentials greater than +1.2 V vs. SCE to carbon paste results in increased electron transfer rates for the quasi-reversible oxidations of ferrocyanide and 3,4-dihydroxyphenylacetic acid-presumably via formation of oxygen-containing surface states which promote the removal of the inhibitory organic layer from the graphite particles and thereby cause the surface to resemble *dry graphite” more closely. In this paper, the effect of Engstrom’s electrochemical pretreatment on carbon paste electrodes will be examined for a more extensive series of model compounds and compared to that previously seen for glassy carbon. Specifically, it will be shown that the enhancement resulting from electrochemical pretreatment of carbon paste, though qualitatively similar, is shorter-lived than that obtained with glassy carbon and, as a result, is not as well suited for subsequent LCEC applications. EXPERIMENTAL SECTION Reagents. NADH (Grade 111),ascorbic acid (anhydrous), and hydrazine sulfate, obtained from Sigma Chemical Co. (St. Louis, MO), and hydroquinone, obtained from Fisher Scientific Co. (Cincinnati, OH), were used as received without further purification. The supporting electrolyte consisted of a solution containing 0.1 M KN03 and 0.01 M Na2HP04whose pH was adjusted to 7 with 0.015 M HN03. All solutions were prepared with deionized water. Apparatus. Cyclic voltammograms were obtained with a Bioanalytical Systems (West Lafayette, IN) CV-1B cyclic voltammetry unit and a Hewlett-Packard 7015-B X-Y recorder. An Ag/AgCl reference electrode and platinum wire counterelectrode were used along with the carbon paste working electrode in a three-electrode cell. The potential scan rate employed for all experiments was 10 mV/s. Rotating disk experiments were performed with a Pine Instrument Co. (Grove City, PA) Model MSR rotator. Liquid chromatography was performed with a Waters Associates Model M-6000A pump, a Rheodyne Model 7125 injector with a 6-pL sample loop, and a Bioanalytical Systems Model LC-3 amperometric detector equipped with a Model TL-3 thin-layer electrode assembly. The reference electrode was a Ag/AgCl electrode. All experiments were run in a flow injection mode with no column actually placed between the injector and detector; in its place, only a section of 0.010 in. inner diameter stainless steel tubing was inserted. The mobile phase employed was pH 7 phosphate buffer. The mobile phase flow rate was always 1.0 mL/min. Electrodes. Carbon paste electrodes were prepared in conventional fashion by thoroughly hand-mixing 3 mL of Nujol oil (McCarthy Scientific Co., Fullerton, CA) and 5 g of graphite powder (Spectropure grade, Fluka) in a mortar and pestle. The paste was packed into a home-built assembly consisting of two concentric lengths of glass tubing arranged in a pistonlike configuration so that the paste could easily be extruded and a fresh surface exposed. The geometric surface area of the electrode was 0.20 cm2. The electrode pretreatment procedure, identical with that used by Engstrom (6)for glassy carbon, consisted of a 5-min preanodization in buffer/electrolyte at +1.75 V vs. Ag/AgCl followed by precathodization for 10 s at -1.20 V. Unlike glassy carbon electrodes which need to be polished with alumina before pretreatment, carbon paste electrodes needed only to have a freshly smoothed surface prepared prior to the conditioning sequence. RESULTS AND DISCUSSION It is generally believed that electrochemical conditioning of glassy carbon results in the formation of electroactive
1745
Table I. Effect of Electrochemical Pretreatment on Test Systems E,, (oxidation),V vs. Ag/AgCl before after pretreatment pretreatment
system hydroquinonea ascorbic acid hydrazine NADH
+0.24 +0.30 t0.82 +0.48
AE,,mV 130 220 340 80
+0.11
+0.08 +0.48 +0.40
=Data shown are for the oxidation only. E , for hydroquinone reduction was -0.04 V vs. Ag/AgCl before pretreatment and t0.02 V after pretreatment.
+04
+0.2
0.0
-0.2
POTENTIAL VVSAgiAgCl
Figure 1. Cycllc voltammogram of 2.25 mM hydroquinone in pH 7 buffer at a carbon paste electrode: before pretreatment (- -); after
pretreatment
-
(-).
surface compounds which enhance electrode response via unspecified redox mediation processes (5, 7,8). However, in this work, no distinct surface waves indicating the presence of surface species formed by the pretreatment were observed when the pretreated carbon paste electrode was cycled a t positive potentials in a blank buffer solution. In fact, the only noticeable change associated with the pretreatment itself was a larger background current in comparison to that observed at a conventional untreated carbon paste electrode. In previous studies employing pretreated glassy carbon, the most observable effect of pretreatment consisted of a cathodic shift of the oxidation peaks for electrochemically irreversible systems by some 0.24.5 V compared to the behavior seen at the untreated glassy carbon surface (5-7,12). Also, many quasi-reversible systems behaved somewhat more ideally, exhibiting sharper peaks and smaller potential separation between the anodic and cathodic peaks. Data showing a similar comparison for some irreversibly oxidized model systems at untreated and treated carbon paste electrodes are summarized in Table I. Figure 1 shows the cyclic voltammograms obtained for hydroquinone at both untreated and pretreated carbon paste electrodes. The degree of reversibility for this redox system was dramatically enhanced by the electrochemical pretreatment procedure as indicated by the sharper oxidation and reduction waves observed a t the conditioned surface and the corresponding decrease in the separation of the oxidation and reduction peaks from 280 to only 90 mV. Figure 2 shows the voltammograms for the oxidation of ascorbic acid at both a conventional carbon paste electrode and the same surface following electrochemical pretreatment (curve A). It is evident that the pretreatment resulted in a shift of the oxidation potential of ascorbic acid by some 200 mV in the cathodic direction. Also shah is the trace obtained for the same pretreated electrode after 3 h of continuous cycling between -0.1 V and +0.5 V vs. Ag/AgCl
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ANALYTICAL CHEMISTRY, VOL.
56,NO. 9, AUGUST 1984 UNTREATED
TREATED I
I
I5m A
+o.s
+ 0.’3
__ +O.I
-0.1
P O T E N T I A L VvSAg/AgCI Figure 2. Cyclic voitammograms of 1.0 mM ascorbic acid in pH 7 buffer at a carbon paste electrode: before pretreatment (- -); immediately after pretreatment (curve A): and after pretreatment and 3 h of continuous potential cycling (curve 6).
Flgure 3. Chromatograms obtained before and after electrochemical pretreatment for injections repeated at 15-min Intervals for (A) 50 ppm ascorblc acid (Ew = +0.30 V vs. Ag/AgCI) and (B) 50 ppm hydrazine (E, = +0.45 V vs. Ag/AgCi).
(curve B). Although some instability was indicated by a gradual shift of the oxidation wave at the pretreated carbon paste surface back anodically toward its original position (30 mV/h) and a slow decrease in peak current (4%/h), the oxidation still occurred at a much more cathodic potential than at the conventional carbon paste electrode. This behavior is analogous to that which has been reported for the glassy carbon electrode following both thermal (4) and electrochemical (12) pretreatment. In the case of NADH, the cathodic shift due to the pretreatment was somewhat smaller than that at the glassy carbon electrode. However, it should be noted that, at both the electrochemically treated glassy carbon and carbon paste electrodes, the oxidation of NADH occurred at +0.40 V. For hydrazine, the oxidation wave at a pretreated carbon paste electrode was also shifted cathodically, but still remained broad and diffuse as compared to the sharp, well-defined wave that had previously been obtained at the pretreated glassy carbon electrode (10). In both cases, however, the magnitude of the shift was almost the same. In general, the effect of experimental conditions on the redox behavior of the test analytes at pretreated carbon paste electrodes was identical with that at conventional carbon paste electrodes. Thus, the effect of pH and potential scan rate on the peak potentials and peak currents observed for oxidations a t the untreated electrode was paralleled by peak potential and current changes in the same direction and of roughly the same magnitude for the electrochemically conditioned surface. For example, the oxidation potential of ascorbic acid ( ~ K A = 4.17) is well-known to be unchanged over the pH range of 7-4.2 but to shift anodically by 30 mV/pH unit at lower pH values. In our work, ascorbic acid exhibited this behavior at both the untreated and pretreated carbon paste electrodes. However, in all cases, the oxidation potentials at the treated surface were lower by approximately 200 mV. Again, these observations were completely analogous to those made previously with glassy carbon electrodes (13). A primary reason for investigating the effects of electrochemical pretreatment on carbon paste was the possibility that the enhanced response obtained for irreversible systems might be of use in analytical applications such as LCEC. Accordingly, the performance of pretreated electrodes, placed in a typical LCEC thin-layer cell arrangement, was examined by use of ascorbic acid and hydrazine as test analytes. In this work, the potential sequence employed for surface pretreatment was identical with that used above in cyclic voltammetry.
However, the pretreatment potentials could be applied in any of three different cell arrangements: (1)with the thin-layer cell disassembled and the carbon paste surface immersed in electrolyte solution as above for cyclic voltammetry, (2) in situ with the cell assembled and the electrolyte/mobile phase present but not flowing, and (3) in situ with the mobile phase actually flowing. The first two procedures were found to produce roughly equivalent LCEC response and were used interchangeably in the work described below. However, the third approach-with the electrode conditioning performed in a flowing stream-yielded erratic results that were generally inferior to those obtained by the other procedures; therefore, this pretreatment mode was abandoned and will not be considered further. Typical “chromatograms” obtained under flow injection conditions for repeated injections of ascorbic acid and hydrazine are shown in Figure 3. For both analytes, initial injections following electrode treatment produced peak currents 2 to 3 times greater than those observed at the conventional untreated carbon paste surface. But, in both cases, the response declined rapidly on repeated injections and eventually approached the current levels obtained without pretreatment. Subsequent reactivation of the electrode by a second pretreatment sequence initially served to increase the LCEC response still further; but the enhancement was again only temporary, decreasing rapidly upon continuing injections. As the mechanism by which the electrochemical pretreatment is able to effect enhanced response at carbon paste electrodes has not yet been definitely demonstrated, speculation with respect to the mechanism of deactivation in the LCEC configuration would certainly be superfluous. However, the apparent instability of the pretreated electrode upon exposure to the flowing streams was further confirmed by rotating disk experiments in which the carbon paste electrode was pretreated, subjected to precisely controlled convection, and then examined as before by cyclic voltammetry. By use of this approach, it was observed that electrode rotation caused a marked acceleration in the rate at which the enhanced response produced by pretreatment returned to the initial “untreated electrode” behavior. For example, following pretreatment, rotation of the electrode at 500 rpm resulted in a 90 mV/h shift in the oxidation wave for ascorbic acid back anodically toward its original position. This compares to the 30 mV/h rate of return observed earlier for ascorbic acid when
-
Anal. Chem. 1984, 56, 1747-1749
the pretreated electrode was simply held a t -0.1 V in static solution. I t is apparent that the use of simple electrochemical pretreatment procedures can produce enhanced voltammetric response at carbon paste electrodes in a fashion which is analogous in many respects to that previously seen for glassy carbon electrodes. As has been recently suggested by Adams (II),however, it is possible that the mechanism of surface activation-e.g., oxidative formation of catalytic surface oxides (5, 7)or improved interfacial behavior of the oxidized surface (11)-may be quite different for different carbon substrate materials. Further, the potential applications of electrochemically pretreated carbon paste electrodes in analysis appear to be limited by their relatively poor stability in flowing streams, especially compared to pretreated glassy carbon surfaces whose cyclic voltammetric and LCEC response is sufficiently long-lived to provide reproducible current levels over at least a full day’s continuous usage (12,131. In general, it seems that electrochemical conditioning could probably be used to improve response for virtually any carbon matrix electrode. However, unlike conventional chemically modified electrodes whose electrocatalytic response is often very specific toward selected analyte molecules, this pretreatment appears
1747
to produce a relatively nonspecific enhancement of electrode response for a wide range of irreversibly oxidized compounds. Registry No. NADH, 58-68-4; C, 7440-44-0; hydroquinone, 123-31-9; ascorbic acid, 50-81-7; hydrazine, 302-01-2.
LITERATURE CITED Snell, K. D.;Keenan, A. G. Chem. SOC. Rev. 1979, 8 , 259-282. Murray, R. W. Acc. Chem. Res. 1980, 73,135-141. Zak, J.; Kuwana, T. J . Am. Chem. SOC. 1983, 704, 5514. Stutts, K. J.; Kovach, P. M.; Kuhr, W. G.; Wightman, R. M. Anal. Chem. 1983, 55, 1632-1634. Blaedel, W. J.; Jenkins, R. A. Anal. Chem. 1975, 4 7 , 1337-1343. Engstrom, R. C. Anal. Chem. 1982, 54,2310-2314. Engstrom, R. C. Anal. Chem. 1984, 56, 136-141. Cenas, N.; Rozgaite, T.; Pocius, A,; Kulys, J. J . Electroanal. Chem. 1983, 154, 121-128. Gonon, F. G.; Fombarlet, C. M.; Buda, M. J.; Pujol, J. F. Anal. Chem. 1981, 53, 1386-1389. Falat, L.; Cheng, H. Y. J . Electroanal. Chem. 1983, 757,393-397. Rice, M. E.; Galus, 2.; Adams, R. N. J . Electroanal. Chem. 1983, 743,89- 102. Ravichandran, K.; Baldwin, R. P. Anal. Chem. 1983, 55, 1782-1786. Ravichandran, K.; Baldwln, R. P., submitted to J . Liq. Chromatogr.
RECEIVED for review January 30,1984. Accepted April 2,1984. This work was supported by grants from the Commission on Academic Excellence and the College of Arts and Sciences, University of Louisville.
Time and Temperature Controller for Filament Atomizers Joslo P. Oliveira, Eric L. Barish, and Ralph 0. Allen*
Department of Chemistry, university of Virginia, Charlottesville, Virginia 22901 Heated filaments and metal “boats” have been used to introduce samples into several types of analytical devices. The heating rates and temperatures of these electrothermal atomizers often need to be controlled to achieve optimum conditions for vaporizing the sample. The electronic circuit described below allows selection and control of the temperature for a filament (or boat) which is heated by an ac power supply. A microprocessor was used to control the atomization time (as short as 3 X s) and temperature (up to 1400 “C). Our interest in a filament atomizer was a result of our studies on the analytical uses of energy transfer from metastable nitrogen molecules (1, 2). The metastable or active nitrogen is generated in a dielectric discharge operated at 1-10 torr pressure using a 16-kV ac power supply. Since conduction pathways in the dielectric generator have such high resistances, an atomizer filament placed in the system acts as an electric ground. Even though the filament is separated from the dielectric discharge system by 20 cm of low-pressure N2, a filament connected to a grounded power supply becomes the electrical ground for the 15-kV ac spark. For this application it was therefore necessary to float the filament power supply with an isolation transformer and to electrically isolate the controlling electronics from the filament.
EXPERIMENTAL SECTION The block diagram of the electronics used is shown in Figure 1. The filament is heated by an ac voltage from an isolation transformer which is regulated by a feedback system. The regulatory circuit, the feedback loop, and the interface to the computer are all low-voltagedc circuits. A 32-V, 6-A, dc power supply provides power to two parts of the circuit. A low current portion (i < 3 A) provides an electrically isolated power supply for the electronic circuitry. The high current (i = 5 A) portion of the circuit provides the power to the filament at a level controlled via a microcomputer. The voltage for the filament comes from a three-pin regulator (LM338)whose output voltage ( VouJ depends 0003-2700/84/0356-1747$01.50/0
upon the ratio of two resistors, R2 and PR. Vout = (1.25) (1 + R2/PR)V The resistance of R2 is fixed at 8.64 kSE. The resistance of the photoresistor,PR, varies (between 200 SE and 1 MSE) as a function of the intensity of two subminiature incandescent lamps (T-3/4” Sylvania) in the optically isolated feedback circuit (A in Figure 2). The intensities of the lamps are controlled by the application of a voltage to the base of the transistor (2N3904). To isolate the filament,the dc output of the three-pin regulator (LM338)is converted to ac by a 10-kHz oscillator. This ac voltage is applied across the primary windings of a transformer which provides electrical isolation of up to 20 kV for the secondary windings. The ac voltage from the secondary windings powers the filament and is monitored as a dc level by feeding the ac voltage through a full wave rectifier. The ac current through the filament induces an ac voltage in an induction transformer (C in Figure 2) which is proportional to the current. The voltage from this induction transformer is also fed to a full wave rectifier to produce a dc voltage proportional to the filament current. The outputs of both rectifiers are fed into a voltage multiplier (MC1594L) which has an output proportional to the actual power applied to the filament. The multiplier output is compared, in a feedback circuit, to a voltage which is proportional to the desired filament power. The actual power applied to the filament is not measured, but the output from the multiplier is proportional to the applied power and can be calibrated to relate the filament temperature to the multiplier output. Since the filament is heated by passing a 10-kHz alternating current, the effective power We, =Vd-. The two full wave rectifiers (R), which are the inputs to the multiplier, could have been adjusted (using the 5-kQvariable resistors) to give correct RMS values. This, however, required a calibration source of the same wave form as was used in this circuit for supplying power to the filament. Rather than attempting to adjust the full wave rectifiers to give correct RMS values, the multiplier output was compared to the filament temperature as measured by an optical pyrometer. For filament temperatures between 800 and 1400 O C the temperature could 0 1984 American Chemical Society
