2592
Anal. Chem. 1984, 56,2592-2594
ACKNOWLEDGMENT I gratefully acknowledge the technical assistance of C. C. Wu and Leonard Wasicek in constructing the thermospray interface. Special thanks are extended to Curt Brunee and Finnigan/Mat for Lending the CH-5 mass spectrometer used in this work. LITERATURE CITED (1) Blakely, C. R.; Vestal, M. L. Anal. Chem. 1983, 57, 750-754. (2) Vestal, M. L. I n f . 3 . Mass Spectrom. Ions Phys. 1983, 46, 193-197. (3) Vestal, M. L. "Ion Emission From Liquids"; Miinster, A. B. Ed.; Sprlnger-Verlag: Berlin, tg83; pp 246-263. (4) Vestal, M. L. Mass Specfrom. Rev. 1983, 2 , 447-480.
(5) Futrell, J. H.;Wojcik, L. H. Rev. Sci. Instrum. 1971, 42, 244-251. (6) Atklns, P. W. "Physlcal Chemistry", 2nd ed.; Freeman: New York, 1982; pp 900-902.
Marvin L. Vestal Department of Chemistry University of Houston Houston, Texas 77004
RECEIVED for review March 30,1984. Accepted June 20,1984. This research was supported by NIGMS under Grant GM 29031 and by the Robert A. Welch Foundation.
Digital Electrochemical Transient Analysis: Diagnosis of an Elementary Reaction Mechanism as an Illustration of Data Acquisition Strategy Sir: With the advent of the digital and the approach of the cybernetic (1) ages of electroanalytical chemistry, a need has arisen for computational algorithms which might prove to be useful in making decisions concerning the information content of current transients. In this communication, the digitally computed function A(1n i)/A(ln t ) vs. t is offered as a most useful component of the artificial intelligence system of a cybernetic instrument because of its ability to discriminate on line and under high-level software control those processes which may rate limit the current in electroanalysis. We first became aware of the utility of this function during the development of what we have identified as Riemann-Liouville transform polarography (2). Even though it is now our contention that each rate-limiting process produces a unique current response that may be readily distinguished through the computation of this function, we present herein an illustration of its utility only in the treatment of chronoamperometric transient theory for the ECE mechanism. This treatment suggests that this function might find wide use as the digital equivalent of the "working curves" employed so successfully during bygone analogue days in studies of the mechanism of electrode processes. In the development of this illustration we have concurrently been forced to develop the data acquisition strategy that is necessary for the implementation of this method in the analysis of experimental current transients by a cybernetic instrument. This aquisition strategy is also presented herein in prelude to its utilization in subsequent efforts.
THEORY For the ECE mechanism the current subsequent to the application of a potential step to diffusion-limiting conditions has shown ( 3 ) to be
i ( t ) = (nFACD1/2/(~t)1/2)(2 - e-kt)
(1)
where all symbols have conventional electroanalytical meaning, or upon rearrangement This equation may be expressed in logarithmic form and differentiated with respect to In t to obtain an exact expression for the function A(ln i)/A(ln t ) to be digitally computed from the synthetic transient obtained from eq 2 d(ln i)/d(ln t ) = Izt/(2ekt - 1) - 7 2
(3)
Synthetic results for i ( t )were generated within a BASIC program by assigning values to kt in eq 2 in order to obtain a traditional dimensionless working curve (4-8) by plotting the dimensionless current as a function of log k t ; several of these previous treatments suggest ways to perform the appropriate mechanistic diagnosis and to obtain the first-order rate constant k. For comparison, an exact representation of the dimensionless d(ln i)/d(ln t ) working curve was obtained by assigning values to kt in eq 3. This is shown in Figure la. As would be anticipated, a 2 orders of magnitude time domain of kinetic activity separates those periods when the electrode process appears to be diffusion controlled (when, by definition, d(ln i)/d(ln t ) = 0.5). Because this function is completely independent of bulk concentration (C), electrode area (A), and mass transport parameters (D), no further treatment of experimental data would be necessary in the elucidation of the mechanism. This could be accomplished in real time by direct comparison with eq 3; it may be noted that
k = 0.768/tm
(4)
where t , represents the real time associated with the achievement of the maximum value of d(ln i)/d(ln t ) .
RESULTS AND DISCUSSION The theoretical merit of this approach having been demonstrated, a study was undertaken to determine the feasibility of using this method in the interpretation of digitally acquired current transients. This feasibility rests upon the ability to obtain an accurate representation of eq 3 through the computation of A(ln i)/A(ln t ) . The accuracy of the digital computation of the function A(ln i)/A(ln t ) depends upon two factors: (1) the resolution of i ( t )so as to obtain a significant logarithmic difference in the determination of A(1n i) from any two successive data points in the current transient; this resolution depends, to an extent, upon the combined quantization noise (9) and random noise of the measurement of i ( t ) ;and (2) the selection of the proper acquisition rate so as to obtain a significant logarithmic difference in A(ln t ) over all time domains. For example, it is clear that A(ln t ) is not equally spaced for equally spaced time increments used in conventional data acquisition systems. Instead, the value of A(1n t ) tends to become smaller as the value o f t gets larger. To overcome the problem of the variability of A ( h t ) ,we have developed an acquisition strategy that allows A ( h t ) to exhibit a similar variation over all time domains. This strategy calls
0003-2700/84/0356-2592$01.50/00 1984 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 56, NO. 13, NOVEMBER 1984 -0.3-0.4
2593
it\_
a
-
':
-0.5
I
1
a.
n
3.5 3.0 2.5
2.0
-3.0 - 2 . 0 -1.0
0.0
1.0
log(kt)
-2.0
0.0
-2.0
0.0
log ( k t )
Flgure 1. Development of the data acquisition strategy used in the computation of the discrimination function. In each panel the exact expression for d(ln i)ld(ln t ) is compared with A(ln i)/A(ln t ) (0)obtained from eq 2 by the method indicated. Panel a, eq 3; panel b, 32-bit computational accuracy; panel c, 32-bit computation on 12-bit "acquired" data; panel d, as in c with judicious selection of the current maximum at the onset of kinetic actlvt; panel e, as In d with five point movlng average; panel f , obtained by autoranging between 12- and
10-bit acquisition adccuracy with five point moving average. Arrows indicate those points which were obtained from a computation involving a current point having maximum acquisition accuracy.
for the acquaition a small block of data (e.g., 64 data points) at the maximum acquisition rate, followed by the acquisition of half that number of data points (e.g., 32) at one-half the maximum rate, followed by the acquisition of that same number of points (e.g., 32) a t one-fourth the maximum acquisition rate, etc. By proceeding in this manner one may obtain a set of evenly spaced data points equal to the number of points in the initial block of data (e.g., 64) for each time domain of the experiment (where each time domain may be defined as the time necessary to collect that number of data points if every point is collected, or if every other point is collected, or if every fourth point is collected, and so forth). Not only does this strategy provide several blocks of evenly spaced data points over all time domains of the experiment for rapid application of conventional statistical methods (digital fiitering, smoothing, etc.), but it also results in a similar variation in A(ln t ) from one time domain (data block) to another. By keeping the number of points per data block small, one may minimize the variation in A(ln t ) across the data block. For example, in a block of 64 data points, A(ln t ) will vary between 0.693 and 0.016 across the block. Perhaps most importantly, however, this acquisition strategy results in the compression of a great deal of temporal information to a minimum amount of storage; for example, at a maximum acquisition rate of 50 kHz (20 ps/point) 15 blocks of 64 evenly spaced data points may be collected over time domains ranging from 0-1.28 ms to 0-21.0 s and stored within only 512 memory locations of this strategy is employed. Synthetic current time curves were obtained by assigning values to kt in eq 2 in the manner described above and were tested in order to demonstrate the feasibility of this acquisition strategy in the determination of A(ln i)/A(ln t ) . Figure l b shows that very good agreement is obtained between d(ln i)/d(ln t ) and A(ln i)/A(ln t ) for the situation where d(ln i)/d(ln t ) is known, if this acquisition stategy is used to fix a lower limit for A(ln t ) and if i ( t ) is defined to 32-bit computational accuracy. Analogue-to-digital converters, however, usually exhibit between 8- and 16-bit accuracy, and this gives
Flgure 2. Effect of random and quantization noise upon the discrimination function. 10 each panel, curve a shows the computed discrimination function while curve b shows log ( S I N )where N comprises both random and quantization noise. Panel I: no random noise. Panel 11: bidirectional random noise of known, constant amplitude. In both cases, the designated acquisition strategy was employed and the simulated transient was subjected to three Savitzky-Golay digital filterings prior to the computation of the discrimination function.
rise to quantization noise (9) within the acquired signal. With 12-bit A/D acquisition accuracy very poor agreement is obtained between A(ln i)/A(ln t ) and d(ln i)/d(ln t ) due to this quantization noise, as shown in Figure IC,even if the acquisition strategy is employed to minimize the computational error due to t as in Figure lb. This observation makes it clear that additional steps must be taken to optimize the computation of A(ln i) in order to utilize this digital alogorithm. This may be accomplished (1)by judicious selection of the current range so that full-scale 12-bit accuracy in the current measurement coincides with the onset of kinetic activity, (2) by smoothing the data (subjecting it to a modified 5-point Savitzky-Golay (10) moving average with coefficients 1,2, 4, 2, 1,and norm 10) so as to minimize the effects of quantization noise and to artificially provide a higher level of significance in the averaged data than is available in the 12-bit acquired data, and (3) by autoranging the acquisition of the data so that all data has between 12- and 10-bit accuracy. The results of these measures are illustrated in Figure 1, parts d-f, respectively. From the results illustrated, it is clear that if autorangingand smoothing are employed, the results obtained from data having the quantization noise associated with 12-bit acquisition accuracy are quite similar to those obtained from data having 32-bit computational accuracy,provided that the previously described strategy is employed to minimize errors due to diminishing A(ln t ) with increasing t. As implied in the aforesaid discusson, however, the feasibility of using A(In i)/A(ln t ) to discriminate experimental events depends not only upon the effect of quantization noise on the computed result but also upon the effect of random noise. The effect of random noise was investigated by adding bidirectional random noise of constant known amplitude to each 32-bit representation of the simulated current prior to introducing quantization noise by expressing the signal to 12-bit accuracy. This imparted to the varying current signal (S) a determinable level of combined quantization and random noise (N) which can be readily expressed in terms of the varying signal as the S I N ratio. The results of two such simulations are shown in Figure 2. The results obtained in Figure 21 show the effect of adding no random noise. (Curve a actually corresponds to Figure If with the exception that Figure 21a shows each properly averaged point that is obtained by using true five point Savitzky-Golay filtering (10)-
2594
Anal. Chem. 1984, 56,2504-2596
coefficients of -3,12,17,12, and -3 with norm of 35-and is superimposed on the equivalent of Figure la.) The SIN ratio shown in logarithmic form in curve Ib indicates the variation of the pure quantization noise during the prescribed autoranging between 12- and 10-bit acquisition accuracy. Curve 211a shows the effect of adding the constant amplitude bidirectional random noise before digitizing the simulated signal. The magnitude of the constant amplitude was selected so as to cause essentially no random noise at short times (when S is large) and up to 5% random noise a t long times (when S is small). While the brevity of this correspondence does not permit a detailed statistical correlation of the variance due to noise with the computed S I N ratio, it is quite clear from Figure 211 that an easily recognized pattern may be obtained (after Savitzky-Golay smoothing) even in the presence of as much as 1% noise. This observation, in turn, suggests that for the application described herein, full 12-bit A/D conversion accuracy may not be necessary with appropriate digital filtering. CONCLUSION The feasibility of using the digitally computed function A(ln i)/A(ln t ) in the elucidation of the rate-limiting mechanism of an electrochemical process has been demonstrated. In that it employs digital filtering to minimize the effect of noise, this method shares some of the advantages of conventional chronocoulometry where this filtering is performed via analogue integration; however, the primary disadvantage of conventional chronocoulometry-the inability to distinguish instantaneously among several time-dependent eventa- is overcome by using this method, and an instantaneous response to variations in the current caused by several different electrode processes may be readily obtained. Since a considerable amount of free computational time is available during the later stages of data acquisition if this strategy is employed, it also appears that on-line computer manipulation and processing of the data would be made more feasible in this manner. Moreover, as this work clearly demonstrates, it is possible to detect variations in d(ln i)/d(ln t ) of the order that would be observed in many electroanalytical experiments. Thus, this work suggests that decision concerning the control of data acquisitions and/or the on-line interpretation of acquired electrochemical data may be based upon the evaluation of this function. Since each rate-limiting process encountered in electroanalysis may be expected to exhibit its own unique d(ln i)/d(ln t ) characteristic, we believe that the experimental evaluation of A(ln i)/A(ln t ) and comparison with known characteristics that may be stored within limited memory as
relatively simple mathematical functions (to thereby minimize memory requirements) will prove to be most useful in the on-line elucidation of the mechanism. This comparison might be made by simplex fitting to a library of results as suggested by Ridgway ( I I ) , or by pattern recognition techniques as suggested by Perone (12),or by deviation-pattern recognition techniques as suggested by Meites (13)or Rusling (14). Regardless of the method of comparison, however, we believe that the computation of this function will prove to be most useful in the identification of the rate-limiting steps in any electrode process, whether that rate be controlled by homogeneous kinetics as in this somewhat trivial illustration or, more germane to electroanalysis, by mass transport, heterogeneous electrode kinetics, or capacitive/adsorptive effects such as double-layer charging. Investigations of the discriminatory capabilities of the function d(ln i)/d(ln t ) in the elucidation of electrode mechanisms under the control of each of these processes either alone or in combination (and the utilization of this information in the complete interpretation of the digitized current transient) are currently under way. LITERATURE CITED He, Pleixin; Avery, James, P.; Faulkner, Larry R. Anal. Chem. 1982, 54, 1313A-1326A. Soong, F. C.; Maloy, J. T. J . Electroanal. Chem. 1983, 153,29-41. Alberts, G. S.; Shain, I.Anal. Chem. 1983, 35, 1859-1866. Adams, Ralph N. “Electrochemistry at Solld Electrodes”; Marcel Dekker: New York, 1969; Chapter 8. Feldberg, S. W. Electroanal. Chem. 1989, 3 , 199-296. Lawson, R. J.; Maloy, J . T. Anal. Chem. 1974, 46,559-562. Bezilla, 8 . M.; Maioy, J. T. J . Electrochem. Soc 1979, 126, 579-583. Maloy, J. T. I n “Laboratory Techniques in Electroanalytical Chemistry”; Kissinger, P. T.,Heineman, W. R., Eds.; Marcel Dekker: New York, 1984; Chapter 16. Kelly, P. C.; Horlick, G. Anal. Chem. 1973, 45,518-527. Savltzky, A.; Golay, M. J . E. Anal. Chem. 1964, 36, 1627-1639. Hanafey, M. K.; Scott, R. L.; Ridgway, T. H.; Rellley, C. N. Anal. Chem. 1978, 50, 116-137. Schachterle, S.D.; Perone, S . P. Anal. Chem. 1981, 53, 1672-1678. Meites, L.; Shia, G. A. I n “Chemometrics”; Kowalski, B. R., Ed.; American Chemical Society: Washington DC 1977; pp 127-152. Rusling, J. F. Anal. Chem. 1983, 55, 1713-1718.
Arunee Therdteppitak J. T. Maloy* Department of Chemistry Seton Hall University South Orange, New Jersey 07079
RECEIVED for review March 26,1984. Accepted July 9,1984. This paper was presented, in part, at the National Meeting of the American Chemical Society, St. Louis, April 1984, as part of the ACS Award Symposium in Analytical Chemistry honoring Professor Allen J. Bard (paper ANYL 26).
Liquid Secondary Ion Time-of-Flight Mass Spectrometry Sir: We have been interested for some time in developing an approach to SIMS-TOF mass spectrometry which uses primary beams with fluxes of the order used in scanning sector instruments ( I ) and desorption of samples from the liquid phase (2). The time-of-flight mass analyzer has the advantage that high mass ranges can be observed without degrading the basic transmission of the analyzer which accompanies lowered accelerating potentials in the sector instruments. For many analyses in biochemistry for which unit resolution is not required, such an instrument may offer a low-cost alternative for molecular weight and sequence ion determination. This paper describes some preliminary investigations of this approach.
EXPERIMENTAL SECTION The instrumental configuration which we have used to test the feasibility of the approach uses a commercially available timeof-flight mass spectrometer (CVC-2000, Rochester, NY) of the type developed by Wiley and McLaren (3) and a Kratos (Ramsey, NJ) Minibeam I ion gun (Figure 1). Modifications to these instruments are minimal. A second 4-in. diffusion pumping system is mounted onto one of the unused ports of the source housing via a vacuum “tee”. The ion gun is mounted on the other side of the “tee” in such a way that it sits directly over the pump. With this additional pump, torr can be used, while the pressures in the ion gun up t o torr. analyzer and source regions are maintained at about 3 X No additional slits are required to maintain differential pressure,
0003-2700/84/0356-2594$01.50/00 1984 Amerlcan Chemical Society
