LITERATURE CITED (1) W. R. Matson and D.K. Roe, "Trace Metal Analysis in Natural Media by Anodic Stripping Voltammetry" in "Analysis Instrumentation", Vol. 7, Plenum Press, New York, N.Y., 1967. (2) W. Kemula, Pure Appl. Chem., 21, 449 (1970). (3) D.E. Robinson, Anal. Chim. Acta, 42, 533 (1968). (4) G. Tolg, Talanta, 19, 1489 (1972). (5) A. W. Struempler. Anal. Chem., 45, 2251 (1973). (6) T. M. Florence, J. Electroanal. Chem., 35, 237 (1972). (7) American Public Health Association, American Water Works Association and Water Pollution Control Federation in "Standard Methods for the Examination of Water and Waste Water", 13th ed., American Public Health Association, Washington, D.C., 1971, p 417. (8) H. E. Allen, W. R. Matson, and K. H. Mancy, J. Water Pollut. Control Fed., 42, 573 (1970). (9) T. Rojahn, Anal. Chim. Acta, 62, 438 (1972). (10) J. Gardiner and M. J. Stiff, WaterRes., 9, 517 (1975). (11) I. M. Kolthoff and J. J. Lingane in "Polarography", Vol. 2, Interscience, New York, N.Y., 1952, p 503.
(12) M. Ariel and V. Eisner, J. Electroanal. Chem., 5, 362 (1963). (13) G. Macchi. J. €lectroanal. Chem., 9, 290 (1965). (14) M. Branica, M. Petek, A. Baric, and L. Jeftic, Rapp. Comm. In?. Mer. Medit., 19, 929 (1969). (15) J. D. Smith and J. D. Redmond, J. Electroanal. Chem., 33, 169 (1971). (16) H. Blutstein. P. L. Boar, A. M. Bond, and K. M. Bone, unpublished results, 1974-1975. (17) R. G. Clem, G. Litton. and L. D. Ornelas, Anal. Chem., 45, 1306 (1973). (18) G. W. Harrington, W. Miles, and S. Vohra in 'Interface", Vol. 13, No. 5, Michigan State University, East Lansing, Mich., 1974. (19) P. J. Elving and A. F. Krivis. Anal. Chem., 30, 1645 (1958). (20) R. G. Clem and A. F. Sciamanna, Anal. Chem., 47, 276 (1975). (21) R. G. Clem, Anal. Chem., 47, 1778 (1975). (22) M. E. Beyer and A. M. Bond, Anal. Chim. Acta. 75, 409 (1975). (23) G. E. Batley and T. M. Florence, J. Hectroanal. Chem., 55, 23 (1974). (24) A. T. Phillips, R. W. Penis. J. E. Harris, A. J. Fabris, P. L. Boar, and K. M. Bone, Proc. Royal Aust. Chem. lnst.. 42, 209 (1975).
RECEIVEDfor review October 15, 1975. Accepted December 23, 1975.
Computer-Assisted Optimization of Anodic Stripping Voltammetry 0. V. Thomas, Lars Kryger,' and S. P. Perone* Purdue University, Department of Chemistry, West Lafayette, Ind. 47907
Computer-assisted optimlzatlon of anodic stripping voltammetry (ASV) measurements has been investigated. The approach taken has been to specify desired performance criteria; then, using a suitable theoretical model, the on-line computer makes initial measurements, imposing subsequently the values of the various experimental parameters required to achieve the desired response. The overall result is to provide the desired quality of analytical data wlth a minimum analysis time. In this study, we have chosen to speclfy signal-to-noise and signal-to-background ratios for linear sweep ASV, studying metal ion soiutlons in the range 1X to 1 X lo-* M. An interactive approach to peak location and current measurement has been used, allowing the analysis of multicomponent solutions to be performed with a minimum of sophisticated programming algorlthms. Careful selectlon of values for the performance criteria will allow a satisfactory automated analysis to be performed over a wide range of concentratlons, while minimizing analysis time for each sample.
Optimization of analytical instrumentation can be described as a process whereby response is made as nearly perfect, effective, or functional as possible. The scientist usually determines which measurable features should be optimized. When the explicit relationships between controlled parameters and measured response are not clear, experimental optimization attempts often follow a "trial and error" method. That is, individual experimental parameters are varied and resulting signal changes are observed. If the variation enhances the signal measurement, the variation is retained. If not, the parameter is returned to its previous value and another parameter is varied. The Simplex ( 1 ) method of optimization offers a more systematic version of the trial-and-error method. Several parameP e r m a n e n t address, D e p a r t m e n t of C h e m i s t r y , A a r h u s U n i v e r sity, Aarhus, D e n m a r k .
ters are varied simultaneously until the optimum response is found, or oscillation is observed. For analytical systems where response can be related mathematically to various experimental variables, a more direct optimization approach may be applied. The procedure would involve, first, establishing performance criteria for system response; then, from first principles and preliminary measurements, the values for various experimental parameters could be chosen to achieve the desired response. If any values are clearly beyond the capabilities of the instrument, new performance criteria may be tried, or the best available settings may be used with the other parameters adjusted accordingly. This process is ideally suited to the computational and control abilities of the laboratory computer. Typical examples of performance criteria which could be considered are the signal-to-noise ratio, signal-to-background ratio, resolution, analysis time, cost, etc. T o demonstrate this approach, we have chosen the technique of Anodic Stripping Voltammetry (ASV) with a linear potential sweep (2). This is a technique which lends itself well to computerized optimization because of the wide dynamic range of the control parameters, which include plating time and scan rate. (Other stripping functions, like a square-wave or staircase sweep, could be used and suggest other considerations for optimizing experimental parameters.) For this study, the signal-to-noise and signalto-(scan-rate-dependent)-background were selected as the performance criteria. As described below, there is no "optimum" response in ASV when plating time is a controlled variable, as the measured signal improves linearly with time. However, for routine handling of multiple samples, a procedure which accomplishes the minimization of analysis time, while simultaneously meeting desired signal quality specifications, can be considered an optimization procedure. In practice, the procedure requires the operator to specify the desired performance criteria. On the basis of a suitable theoretical model, and preliminary experimental measurements, the laboratory computer subsequently calculates and imposes ANALYTICAL CHEMISTRY, VOL. 48, NO. 4, APRIL 1976
761
PLATING POTENTIAL
~
< SCAN RESET x 4
IK
471:
TO POTENTIOSTAT
Figure 1. Analog ramp generator OAl and OA2 are Texas Instrument SN72741. FET is a Teledyne Crystalonics CAG30 TO A R G
the related experimental parameters for the optimized experiment. In this approach, however, the operator dictates the desired response (which will not be the maximum possible), while the feature optimized by the computer is the analysis time.
THEORY For ASV with an HMDE a t sweep rates greater than about 50 mV/sec, the principles of linear diffusion hold, and the peak anodic current may be described for reversible systems by Equation 1.
i, = nFA Ck ( D T ) ~a1/2 / ~x ( a t )
(1)
where a = nFVIRT, V = scan rate, C i = amalgam concenplating time, K = function of convectration = KCit,, t , ; tion parameters, Co = bulk concentration of metal and, at) = theoretically computed current-voltage function (2).All other terms have their usual significance. Gathering the constant terms, we find from Equation 2
i, = K ’ t , v w ; = s
=
CDLV
+
+y
(4)
Values for a , @, and y can be computed by obtaining background current measurements a t three scan rates and solving Equation 4 simultaneously. Experimentally, we are concerned only with the scan-rate-dependent background, B,, because any constant off-set, y,can be minimized instrumentally. Thus, Equation 5 defines B,.
B , = B - y = aV
+ /3V1’2
(5)
In practice, this has proved to be a much better estimate of the background than Equation 3. The system noise may be defined in terms of the standard deviation, u , of the unperturbed signal. Here, the noise level, N , has been defined as 4u to include -95% of the noise contribution. 762
We may define the SIN and SIB, ratios by Equations 6 and 7 :
SIN =
4.u
SIB, = Ip B-Y
(6)
(7)
Initial values for Equations 6 and 7 , (S/N)1 and (S/B,)1, can be established by performing a preliminary run and measuring ipl, B1, y , and u. Combining Equations 2, 4, 6, and 7 defines the relationship between the desired performance criteria, (S/B,)z and (S/N)2, and the required values of the experimental parameters, t,, and V2:
Taking the ratios of Equations 7 to 8 and 6 to 9, we obtain Equations 10 and 11:
(3)
where CDLis the double layer capacitance. However, Equation 3 does not include other background contributions such as residual cathodic and/or anodic currents. For this reason, we have defined an empirical function to represent more realistically the background contributions to ASV measurements. This expression is given in Equation 4.
B = aV
A3 is an Analog Devices P501, all others are SN72741. Gain Select Gates are CAG3O
(2)
that the peak anodic current is directly proportional to bulk concentration of metal ion, plating time, and the square root of the scan rate. Therefore, increasing any of these three will increase the magnitude of the measured signal, S . The primary background contribution to ASV measurements has been attributed to charging current as defined by Equation 3.
i&
Figure 2. General purpose potentiostat
ANALYTICAL CHEMISTRY, VOL. 48, NO. 4 , APRIL 1976
T o define the optimum scan rate, we divide Equation 10 by Equation 11,
(SIN)2(S/B,)i- LYVZ + PVZ”~ (SlN)i(SlB,)2 Bi - y and solve for V2 (Equation 13),
(12)
where R = the LHS of Equation 12. Solving Equation 11 for t p ,defines the optimum plating time.
EXPERIMENTAL Potentiostat and Ramp G e n e r a t o r . A computer-controlled
Analog Ramp Generator (ARG) was constructed to supply a linear voltage scan for the stripping analysis (Figure 1).I t was designed to allow computer selection of scan rates in the range of 1 to 2000 mVlsec. A linear ramp is obtained by application of the appropriate DAC potential to the input of an SN72741 operational amplifi-
= 50, (S/B,), = 20) C,*,M (SIN)1 (SIB”) I v,(mV/s) 177 1 6 50a 3.0 X 46 750 55 1.0 x lo+ .18 13 300 3.0 X lo-’ 13 5 200 1.0 x lo-’ 11 1000 3.5 x l o + 4 1.5 x 1.3 3 1000 a Software-imposed limit. Note: V ,= 300 mV/s. t p , = 300 s.
obtained using non-optimized conditions. The same series of solutions used with SIMPLE above were analyzed by OPT. In this case, the performance criteria never allowed the observed SIN to drop below 10. These data, corrected for the electrolyte blank, are shown in Table 11. Note that, in all cases, the results agree, within experimental limits, with the specified performance criteria. The observed SIN agrees much better with the specified value, ( S / N ) z , than does the observed SIB, with ( S / This is a reflection of slight instrumental changes in y with time which affect calculation of B,. These effects are most noticeable for experiments run a t low scan rates. The results shown in Table I1 indicated essentially linear concentration response in the optimized mode and suggested that both the hardware and the optimization approach were operational. On this basis, we proceeded to investigate analytical capabilities of the optimization technique for a variety of conditions. Table I11 contains the results of a study a t 1 X lo-$ M Cd(I1) designed to determine the practical response limitations of the system. T h a t is, a variety of performance criteria values were imposed for several different runs. As can be seen, the results obtained agreed reasonably with the specified performance criteria in all cases where the arbitrary limits were not imposed for both scan rate ( V Z )and plating time (tP2).I t should also be pointed out that, when using limiting values for both t,, and Vz, we do not necessarily observe the largest values of SIN and SIB,. Examination of Equations 8 and 9 shows that this is what we expect theoretically. While increasing plating time should increase the SIN and SIB, values, increasing the scan rate may have the opposite effect on the SIB,, depending upon the values of 01 and p. Therefore, i t is not generally possible to use a single set of tp, and Vg values to obtain maximum SIN and SIB, results. Moreover, the specific values of t , and V required to give satisfactory performance will vary with the sample concentration. This factor is investigated below. Automated Analysis. I t is often desirable to operate an analytical instrument in an automated fashion where a series of widely varying concentrations may be presented for
tp2(s)
(S/N)obsd
(S/B,)obsd
203 167 86 5 1418 1800a 1800a
55 52 44 44 37 18
11
24 20 10 6 10
analysis. In order to determine what range of concentrations MULTI could analyze satisfactorily in an automated mode, a series of solutions were analyzed where the Cd(I1) concentration ranged from 3 X to 1 X lo-* M. The performance criteria were established a t values of SIN = 50 and S / B = 20 for all analyses regardless of concentration. In this mode, the operator had only to change and deoxygenate the solutions, and then specify the peak range interactively as before. Although the results in Table IV are shown for a single component solution, the procedure is applicable to multicomponent mixtures, as described in the Experimental section. The results shown in Table IV suggest several things. First, while the specified performance criteria were not attained a t concentrations below 1 X lo-$ M, the optimization procedure substantially improved the results over the initial run, ( S I N ) l and ( S / B v ) l .Second, there is a range of concentrations which may be analyzed in an automatic mode without exceeding the hardware constraints on scan rate and plating time. This range would be expected to change as the specified performance criteria are varied. For example, high values for the criteria will make the concentration range fairly narrow while low values should increase the range. Third, no one set of performance criteria will be appropriate for analysis of a very wide range of concentrations, unless a correspondingly broad range of experimental variables are available. Finally, as pointed out in the Experimental section, if the specified performance criteria are met during the initial run (using VI, t P 1 )there , is no need to proceed to the “optimized” run. This occurs a t the high concentrations in Table IV; however, the “optimized” run was executed anyway in this study, simply to illustrate what conditions would have been sufficient to meet the specified criteria.
CONCLUSION This work has demonstrated an operator-interactive computer-assisted approach to optimization of an analytical method. The approach should be directly applicable to any system where the experimental variable-response characteristics can be defined, theoretically or empirically, and ANALYTICAL CHEMISTRY, VOL. 48, NO. 4, APRIL 1976
765
placed under computer control. When applied to an analytical system this offers the analyst the advantage of knowing a priori the performance of the instrument for any sample. This is limited, of course, by the ability of the instrument to supply the required values of experimental parameters. Because of the wide range of easily-controlled experimental variables available, ASV represents an ideal illustration of the optimization principles described here. I t should be kept in mind, however, that the application to ASV analyses on a routine basis may require different specific experimentalhheoretical considerations if alternative electrodes (e.g., thin-film mercury) or alternative stripping techniques (e.&.,differential pulse, or staircase sweep) are used. Nevertheless, the same general principles are applicable.
LITERATURE CITED (1) S. N. Deming and S.L. Morgan, Anal. Chem., 45, 278A-282A (1973). (2) I. Shain, "Treatise on Analytical Chemistry", I. M. Kolthoff and P. J. Elving. Ed.. Part I, Section D-2, Chap. 50, Interscience, New York, 1963. (3) G. L. Booman and W. B. Holbrook, Anal. Chem., 35, 1793 (1963). (4) L. Meites, Anal. Chim. Acta, 18, 364 (1958). (5) S. P. Perone and J. F. Eagleston, J. Chem. Educ., 48, 317 (1971). (6) S. P. Perone, J. W. Frazer, and Arthur Kray, Anal. Chem., 43, 1485 (1971). (7) R . N. Adams. "Electrochemistry at Solid Electrodes", Marcel Dekker, New York, 1969, p 126.
RECEIVEDfor review July 31, 1975. Accepted November 24, 1975. This work supported by the Office of Naval Research under Contract No. N00014-75-C-0874.
Determination of Acrylamide Monomer by Differential Pulse Polarography S. R. Betso* and J. D. McLean The Do w Chemical Company, Analytical Laboratories, 574 Building, Midland, Mich. 48640
A differential pulse polarographic (DPP) technique is described for the determination of acrylamide monomer in polyacrylamide. A measurement of the acrylamide electrochemical reduction peak current is used to quantitate the acrylamide concentration. The DPP technique also yields a well-defined acrylamide reduction peak at ca. -2.0 V vs. SCE, suitable for qualitatively detecting the presence of acrylamide. The procedure discussed involves an extraction of the acrylamide monomer from the polyacrylamide, a treatment of the extraction solution on mixed resin to remove interfering cationic and anionic species, and polarsgraphic reduction in an 80120 (v:v) methanoVwater solvent with tetra-n-butylammonium hydroxide as the supporting electrolyte. Acrylic acid is polarographically distinguishable from acrylamide in a neutral medium. Ethyl acrylate is an Interference in the analysls. Acrylonitrile is removed, from interfering, by treatment on mixed resin. The DPP procedure given should be applicable to the detection and determination of acrylamide monomer in a wide variety of substances. The detection limit of acrylamide monomer by the DPP technique is less than 1 ppm.
Exposure to toxic substances is a problem of which the chemical industry is most acutely aware. The concern over the toxicity of acrylamide monomer necessitated a rapid, high-sensitivity analytical technique capable of detecting and quantitating this substance in polymeric materials such as polyacrylamide. This report shows the applicability and sensitivity of a Differential Pulse Polarographic (DPP) analysis of acrylamide monomer. There are a variety of methods reported in the literature for determining acrylamide (1-15). Chromatography and polarography seem, however, to be the two methods cited most often. The one major disadvantage that most methods, other than polarography, suffer is the large effort involved in derivatization and sample preparation. The other disadvantage is that most analytical methods which require little sample preparation have poor sensitivity characteris766
ANALYTICAL CHEMISTRY, VOL. 48, NO. 4, APRIL 1976
tics. Polarography overcomes both by requiring minimal sample preparation and exhibiting high sensitivity. The polarographic procedure described herein is essentially a modification of the classical procedure of MacWilliams, Kaufman, and Waling (6). Considerable progress has been made in the areas of electroanalytical chemistry and instrumentation since that publication in 1965. The polarographic study and methodology presented in this report encompass the use of that progress. The MacWilliams (6) procedure pressed the polarographic methodology of their time to its maximum response in the acrylamide analysis. The acrylamide reduction occurs a t ca. -2.0 V vs. saturated calomel electrode (SCE) a t the dropping mercury electrode. A t high acrylamide concentrations, above 100 ppm, the dc polarographic wave is fairly well-defined and resolvable from the background. However, the dc polarographic wave is irreversible and quite broad; a t low acrylamide levels, it is impossible to distinguish it from the background. Furthermore, the relatively long drop times employed, ca. 3 s, allowed maximum interference from reducible, adsorbing species ( 1 6 ) . The instrumentation employed by MacWilliams et al. (6) was a two-electrode polarograph and suffered from all the resistance problems associated with a two-electrode system in a poorly conducting medium ( I 7). Since 1965, two major advances in electroanalytical chemistry have been made. 1) Because of advances in electronic circuitry components, the differential pulse polarographic technique was elevated from its status as a complicated research tool to a usable routine method, and 2) an inexpensive (under $5000), commercially available, all-purpose polarographic instrument incorporating the DPP technique became available from Princeton Applied Research Corporation. With these considerations, the authors felt a need to reconfirm the method of MacWilliams et al. (6) and use the differential pulse polarographic technique in an attempt to enhance resolution and sensitivity.
EXPERIMENTAL Apparatus. A P r i n c e t o n A p p l i e d Research Corporation ( P A R C ) (Princeton, N.J.) M o d e l 174 Polarographic Analyzer equipped
