B. G. Willis. J. A. Bittikoter. H. L. Pardue. and D. W. Margerum, Anal.
(18) J.-C. Lhuguenot, 8.F. Maume, J . Chromatogr. Scl., 12, 411 (1974). (19) P. T. Klsslnger. R . M. Rlggln, R. L. Alcorn, and Leh-Daw Rau, Blochem. Med., 13, 299 (1975). (20) E. Pelizzetti, E. Mentastl, E. Pramauro, and G. Glraudi, Anal. Chim. Acta, 8 5 , 161 (1976). (21) G. D. Owens and D. W. Margerum, unpublished data. (22) F. S.Sadek, R. W. Schmid, and C. N. Reliley, Talanta, 2, 38 (1959). (23) A. Ringbom, G. Pensar, and E. Wanninen, Anal. Chim. Acta, 18, 525 (1958). (24) L. Hunter and C. B. Roberts, J . Chem. SOC.,1941, 820. (25) R. Wizlnger. and V . Blro, Helv. Chlm. Acta, 32, 901 (1949). (26) D. L. Janes and D. W. Margerum, Inorg. Chem., 5 , 1135 (1966). (27) W. E. Wentworth, J . Chem. Educ., 42, 96 (1965). (28) W. E. Wentworth, J . Chem. Educ., 42, 162 (1965). (29) D. W. Marquardt, J . SOC. 1nd. Appl. Math., 2 , 431 (1963).
Chem., 42, 1340 (1970). B. G. Wlllis, W. H. Woodruff, J . M. Frysinger, D. W. Margerum, and H. L. Pardue. Anal. Chem.. 42. 1350 (1970). L. Cl Coombsl J . Vaslllades,’and D.’W. Margerum, Anal. Chem., 44, 2325 (1972). H. B. Mark and 0.A. Rechnltz, “Klnetlcs In Analytical Chemistry”, Intersclence, New York, N.Y., 1968, p 167. N. R . Draper and H. Smith, “Applied Regression Analysis”, Wiley, New York, N.Y., 1966, p 145. H. L. Pardue, T. E. Hewitt, and M. J. M h o . Clln. Chem.. ( Winston-Salem, N . C . ) , 20, 1028 (1974). R. M. Rush and J. H. Yoe, Anal. Chem., 28, 1345 (1954). S . C. Chattoraj, in “Fundamentals of Clinical Chemistry”, N. W. Tletz, Ed., W. B. Saunders ComDanv, Philadebhla, Pa., 1976. D 803. A. Lund, Acta Pharmacal:, 5,.231 (1949). H. Well-Malherbe, and A. D. Bone, Biochem. J . , 51, 311 (1952). J. T. Wright, Lancet, 1958-11, 1155. N. Kirshner and M. C. Goodall, J . Bioi. Cbem., 228, 207 (1957). R. Laverty and K. M. Taylor, Anal. Biochem., 22, 269 (1968). R. F. c. Vochten, J. Hoste, A. L. Delaunols, and A. F. DeSchaepdryver, Anal. Chim. Acta, 40, 443 (1968). M. J. Oesterling and R. L. Tse, Am. J . Med. rechnol., 27, 112 (1961).
RECEIVED for review March 7,1977. Accepted August 18,1977. The work was supported by grants from the Air Force Office of scientific ~~~~~~~h[AFOSR 71-19881 and the National Science Foundation [CHE - 76243691.
Simultaneous Kinetic and Spectral Analysis with a Vidicon Rapid-Scanning Stopped-Flow Spectrometer Gregg M. Rldder and Dale W. Margerum” Department of Chemistry, Purdue University, West La fayette, Indiana
47907
A rapld-scannlng vldlcon spectrometer system Is reported wlth Improved stopped-flow mlxlng, spectral characterlstlcs, and speed of data handllng. Thls system is evaluated in regard to determlnant errors (stray Ilght, resolutlon, vldlcon lag tlme) and random errors In absorbance measurements. Welghtlng factors are determlned from the uncertalntles predlcted by the propagatlon of errors of the measurements. The system Is programmed to glve ( 1) welghted linear least-squares regresslon analysis of firstorder reacttons at multiple wavelength, (2) repetltlve spectra of reactlons or translent Intermediates, and (3) weighted least-squares regresslon analysls of two parallel flrst-order reactlons uslng the response surface (the absorbance measured slmultaneousty as a function of t h e and wavelength). The system Is tested by monltorlng the dissoclatlon reactlons of Hg( 11) and Zn( 11) Zlncon complexes under condltlons where the rate constants and spectral changes are slmllar so that a three-dimensional response Improves the accuracy and preclslon In the determlnatlon of the metal Ion concentratlons.
Multiple component analysis performed by the direct measurement of the physical properties of the components or their reaction products must meet several general requirements. (1) The number of measurements obtained at different values of the independent variable (i.e., wavelength, time, etc.) must be at least equal to the number of components to be determined. (However, additional data may improve the precision.) (2) The relative contributions of the components a t each measurement must not be redundant (Le., there must be at least as many nondegenerate equations as there are components). (3) The absolute and relative contribution of each component to the measurements must be large enough to achieve the sensitivity desired. 2098
ANALYTICAL CHEMISTRY, VOL. 4 9 , NO. 13, NOVEMBER 1977
One such technique is the analysis at multiple wavelengths in which the response such as absorbance, fluorescence, or phosphorescence (1-3), is measured as a function of wavelength. When the responses of the individual components overlap one another, simultaneous equations must be solved. Another technique of multiple component analysis, which has been investigated extensively in this laboratory, is simultaneous kinetic analysis (4-8). The absorbance of a mixture of components undergoing parallel first-order reactions is measured at one wavelength as a function of time. The initial concentrations of the individual components are calculated by a least-squares fit of all the data to a linear sum of exponential response curves (6). Array detectors have led to new techniques of rapid scanning spectrometry (9-12). Vidicon systems are particularly useful for visible and ultraviolet absorption studies. A number of computerized vidicon systems have been developed (13, 14) and can be used to obtain spectral and kinetics information simultaneously (13, 15, 16). Other types of computer-coupled rapid-scanning stopped-flow systems have been developed (17, 18). In the present work, an improved vidicon rapid-scanning stopped-flow system is constructed [the basic design is that given by Milano, Pardue, Santini, Margerum, and co-workers (13, I S ) ] . It is used to measure rate constants at multiple wavelengths, to measure transient spectra, and to perform multicomponent analysis. The absorbance of reaction systems undergoing parallel first-order reactions is measured as a function of two independent variables, wavelength and time, simultaneously. A three-dimensional output results in a response surface which contains all the rate and spectral information within the boundaries of the experiment. Wilson and Miller used three-dimensional plots of luminescence vs. time vs. wavelength to give time-resolved and componentresolved phosphorescence spectra (3). Their data were obtained using a photomultiplier with a motor-driven wavelength
teletype
scope
tape
zj-1
~1-1
Flgure 1. Block diagram of vidicon stopped-flow rapid scanning spectrometer interfaced to a minicomputer
control in which about 100 decay curves were measured at each wavelength and the process was repeated about 100 times as the wavelength wm advanced. In our system, the vidicon tube monitors the radiation intensity a t all wavelengths simultaneously and can be interrogated a t rapid intervals. The application of the resulting response surface (absorbance vs. time vs. wavelength) to multiple component analysis can be advantageous. Whereas the aforementioned general requirements may not be met by measuring the absorbance against only one of the independent variables, the addition of the extra dimension of the second variable may fulfill the requirements, making an analysis possible at the desired level of precision and accuracy. The new vidicon rapid scan system is improved in regard to the stopped-flow mixing capabilities, the spectral dispersion unit, and the speed and efficiency of data acquisition and processing. This system can be used from 200 to 1100 nm with scanning widths of either 200 or 400 nm. It is useful in determining the spectra of transient species as well as in multicomponent analysis. In the latter application, the technique for best calculating the initial concentrations of reactants needs to consider the measurement uncertainties which may vary greatly as a function of signal intensity due to the characteristics of the vidicon system. This requires a weighted least-squares regression analysis in which the weighting factor is determined from the uncertainties predicted by the propagation of errors of the measurements. The vidicon system is evaluated in regard to error analysis and instrumental characteristics that are important in its application.
EXPERIMENTAL Apparatus. A block diagram of the rapid scan instrument is shown in Figure 1. Two radiation sources are available; a deuterium lamp (Oriel 6316) and a tungsten lamp (Oriel 6335), which are mounted in an air-cooled housing (Oriel 6324) with an interchangeable top and with a collimating lens assembly (Oriel 6304). The output from the 50-W deuterium lamp (Oriel 6310 power supply) is useable from 200 to 650 nm, but the tungsten lamp has greater throughput above 400 nm and can be used up to 1100 nm. The W-lamp can use up to 100 W from its power supply (Hewlett-Packard 6286). One fused quartz lens (f/2.5,10-cm focal length) is used to focus the radiation through the flow cell (0.2-cm diameter and 1.0-cm lmgth) and another cf/1.25, 5-cm focal length) to refocus the
radiation onto the slit of the dispersion unit. An Aminco-Morrow stopped-flow unit (4-8478), thermostated by a Lauda/Brinkmann circulator (132-D, K-2/R) to 4=0.02 "C is used. This unit permits smaller samples, gives improved mixing, and has a longer pathlength than the previously used (13)Sturtevant-type mixing cell with a 0.3-cm pathlength. The tradeoff for these improvements is a decrease in radiant energy throughput because of a smaller cross-sectional area of the flow cell. The slight energy loss is important only in the ultraviolet spectral region where lamp output is weak. A low resolution dispersion unit is needed because it is desirable to scan a reasonably wide spectral region with the vidicon, but at the same time it is important to minimize stray light. A long focal length for the output mirror is helpful to avoid spectral distortion on the face of the vidicon tube. A SPEX monochromator (1670 Minimate) equipped with 250, 50, and 25 fim interchangeable entrance slits was modified by removing the exit slit and by increasing the focal length of the exit mirror to 30 cm. The focal plane of this dispersion unit is thereby moved outside the original housing to facilitate its positioning on the face of the vidicon tube. The range of wavelengths scanned is determined by the dispersion of three interchangeable gratings (SPEX) which have reciprocal dispersions of 16 nm/mm (500 nm blaze angle), 16 nm/mm (300 nm blaze angle), and 32 nm/mm (500 nm blaze angle). The useful width of the vidicon face is approximately 12.5 mm so that these gratings allow spectral widths of 200 or 400 nm to be observed for each scan. The grating blazed at 300 nm is used in the far UV because it has a greater efficiency at 200 nm by a factor of four than does the grating blazed at 500 nm. The vidicon tube is an RCA C23246 with a fused silica faceplate; its scanning circuitry and its characteristics have been described earlier (13, 16). The rapid scanning spectrometer is interfaced t o a HewlettPackard 2100 computer equipped with direct memory access. The computer core memory is extended to 28K (Fabri-tek A100 core memory). It has a cassette magnetic tape system (Dicom 344) for permanent storage and retrieval of data. It has a storage oscilloscope (Tektronix 603) interfaced by a H P 1255A DAC to give absorbance vs. time and other plots. Only a few minutes are required to initialize the system, set up data acquisition, and process all the data. The availability of extended core memory greatly reduces the time needed for the entire process compared to the system previously described (13). Timing Circuitry. The variable frequency clock of the scanning circuitry is input to an 8-bit DAC circuit which controls the horizontal deflection of the electron beam and provides sync pulses whenever a new scan is initiated (13). Two hundred pulses from the clock are used before the DAC is reset. A timing circuit ANALYTICAL CHEMISTRY, VOL. 49, NO. 13, NOVEMBER 1977
2099
(Figure 2) outputs every other clock pulse to trigger a high speed ( - 5 /IS throughput) 12-bit ADC which provides 100 data points per scan. Thus an entire scan can be obtained in as little as 0.5 ms. The timing circuit assures a proper sequence of events to initiate data acquisition. (a) The clock is disabled t o the trigger circuit and the divide-by-twocounter is reset. (b) The experiment is initiated by closing either a manual trigger or the stopped-flow trigger. (c) The next sync pulse arrives at the trigger circuit. (d) Only after these three steps have occurred in this order is the clock enabled and trigger pulses sent to the ADC. The output of the ADC is loaded into memory in blocks of 100 words (one scan) under direct memory access control. The frequency at which these blocks are taken into memory is determined in software by counting the appropriate number of sync pulses before returning control t o the direct memory access for data acquisition. Thus every scan can be taken into memory or the time between taking scans can be delayed by any integral value of the scan period. The number of scans acquired also is determined by software, which provides a very flexible data acquisition system in which data rates may be changed any number of times during an experiment. Reagents. Zincon (2-carboxy-2’-hydroxy-5’-sulfoformazylbenzene), obtained from Sigma Chemical Co., was standardized spectrophotometrically with a Zn(C104):!solution which had been standardized by CyDTA titration. Zincon was introduced (19) as a colorimetric reagent for zinc and we have shown (8)that it can be used for the simultaneous kinetic analysis of Zn2+,Cd2+, and Hg”. CyDTA (truns-1,2-diaminocyclohexane-N,N,N’,N’tetraacetate) from LaMont Laboratories was recrystallized from acidic solutions. Solutions of Hg(C10& were prepared and standardized. Borate buffer (pH 7.8) was prepared from boric acid and NaOH.
THEORY The Regression Analysis. Regression Equation. The general system which we shall consider is a mixture of two components, R and S, which undergo first-order reactions with rate constants k1 and k2 to form products, P and Q, (Equations l a and 1b)
~ ~ w ~ =, minimum ~ p i , ~
(5)
ht
where the residual ( k ) is the difference between the observed and expected absorbance difference (Equation 6), ph,t
= (At
- A,)
- AARPh(max) XRphe-k’t
**sQA(max)XSQh e-kzt
(6)
and the weighting factor (w)is the reciprocal of the variance (a2) of the residual (Equation 7 ) .
At the minimum, the partial with respect to each of the parameters must equal zero:
providing the normal Equations 8 and 9.
(9)
k
(la)
R A P
When solved simultaneously these equations yield the least-squares best estimates of the maximum changes in S% Q (Ib) absorbance due to each reaction. Of course, knowing the difference in the molar absorptivities of products and reactants The absorbance a t any wavelength and time is given by at the wavelength of maximum change of absorbance allows Equation 2 the calculation of the initial concentration. Weighting Factor. The weighting factor, w,,~,required to solve Equations 8 and 9 is the reciprocal of the variance of where AAHP,~ and AAsQ,, are the total changes of absorbance the residual (Equation 7). The variance of the residual, a;hL, due to their respective reactions at any particular wavelength. is the cumulative effect of errors in the measurements of all The value of Ax,- is the measured absorbance at time infinity the variables and is calculated from the experimentally deand includes all time-independent background absorbance a t termined uncertainties in the variable measurements and from that wavelength. The values of the rate constants are dethe regression equation by the propagation of errors (20). termined from independent experiments with the individual The uncertainties due to the timing circuitry are very small components. Similarly the individual components are used and determine the precision of measuring the time interval to obtain the difference spectra (AA,) between reactants and between scans and the wavelength positions on the face of the products. The value of X, is defined by Equation 3 vidicon. Because the uncertainties of measuring the signal intensities are much larger, only the variance of the intensity (3) measurements is considered. The inaccuracy of measuring the time after mixing due to the lack of coincidence of the and is used to normalize each difference spectrum relative to stopping of the flow with the start of the first scan is conits maximum change of absorbance (AAAm,). If Equation 3 sidered later along with the time response characteristics of is substituted into Equation 2, the regression Equation the vidicon. (Equation 4),results. The expression which allows the prediction of as a function of the variable terms whose uncertainties are de(At - A m ) & = A A R P ~ ( ~ ~ ~ ) X R P ~ ~ - ~ ~ ~ termined by the variance in intensity measurements is given -k,t by Equation 10. (4) AA SQ h( max ) sQ e
+
Weighted Multiple Linear Leust-Squares Regression Analysis. The goal of this calculation is to find the values ~ ~ , minimize the sum of the of AARP~(,) and A A s Q ~which squares of the weighteh residuals over all wavelengths and times (Equation 5 ) , 2100
ANALYTICAL CHEMISTRY, VOL. 49, NO. 13, NOVEMBER 1977
5v
?
igger
Figure 2. Circuit diagram of time logic
Because the Ah,- and x h values are determined from ensemble-averaged time-independent measurements, the uncertainity in the residual due to these terms is small and Equation 10 can be simplified to Equation 11.
which is independent of transmittance and one which is proportional to the transmittance. The variance of any intensity measurement, u?,,,,is then given by Equation 18.
SI,0and SI,1are defined as error coefficients. Equation 19 can be shown to be an equivalent expression for this system. The variance of the absorbance measurement is calculated by Equation 13 from Equation 12 which expresses the absorbance as a function of intensities and from the variances of the intensity measurements.
A A ,=~ ( l o g ( I o 1 - l O g ( I t ))A
(12)
The value of is the signal intensity a t 100% transmittance minus the signal intensity due to the dark current (Equation 14). The signal intensities for 100% transmittance and for the dark current are measured during an initialization procedure which is described later. The value of ZA,t is the signal intensity attenuated by the sample solution at time, t , minus the dark current (Equation 15).
The variances of I,,o and Ih,[required to solve Equation 13 are given by Equations 16 and 17, respectively.
The values of utA,,,,and utADare measured during the to be deinitialization procedure allowing the value of ujA,,, termined. However, it is impossible to determine the value of u:,,, for a single reaction event and i t is an inefficient use of computer time and memory to do so for ensemble-averaged reactions. A relationship is needed to predict US,,, from more readily obtainable data to solve Equation 13 for the value of 2 UAh I.
The sources of photometric errors have been studied by several investigators (16, 21, 22). Milano and Pardue (16) examined the errors in intensity measurements using a vidicon rapid scanning system and have found the random errors a t any given wavelength are made up of two components: one
If Equation 19 is substituted into Equation 13, Equation 20 results.
Equation 20 allows the variance of the absorbance value at any time or wavelength due to random errors to be calculated simply by knowing the intensities Io and I,, and the variances of the extreme output voltage intensity values, ut,,, and utD. The weighting factor defined by Equations 7 and 11is the inverse of Equation 20. The values of Io, u$,,,, and ubDare determined at each wavelength during the initial calibration of the vidicon system, and the values of I k , t are determined during the experiment. The weighting factor is necessary only if the variance of the absorbance measurement is significantly different as a function of wavelength or the absorbance value. As shown by Equation 20, the variance of the absorbance measurement varies as a function of Io and the absorbance value as determined by the ratio of It/Io. Because the source output, grating efficiency, and vidicon response are not uniform over all wavelengths, the Io value is different for each wavelength. The example shown in Figure 3 illustrates this effect and the necessity of using weighting factors as a function of wavelength. Shown in Figure 3a is the raw output voltage intensity data for the reaction given in Equation 21. Zn(Zincon) + CyDTA
obsd
Zn(CyDTA) t Zincon
(21)
The conditions of the reaction are adjusted so that [CyDTA] > [Zn] > [Zincon]. The bottom line represents the dark ) , top line represents the 100% T reference current ( V x , ~the spectrum (VA,,,,) and the series of lines between are from individual points representing 50 scans of the reacting mixture taken at 100 ms between scans ( VA,Jand a scan of the solution after reaching equilibrium ( V A , J .When the data from these scans are calculated as absorbance values, the series of spectra (only eleven of which are shown) displayed in Figure 3b are produced. The decreasing absorbance change at the ZnANALYTICAL CHEMISTRY, VOL. 4 9 , NO. 13, NOVEMBER 1977
2101
+IO-
vout A BS
(volts) a)
b)
.OOL
- 10-
I
366
366
Wavelength
.40c
Wavelength
-
737
t.01 .40
+.Ol
?ES
ABS
AB5
C)
RES
d)
.oo- 1 0.0
Time ( s e d
1
-.OI
.oc
7.51
-.o I 1.0
751
Time ( s e d
Flgure 3. Output of vidicon system following a reaction taking a spectrum in 10 ms every 150 ms. (a) Raw data for the series of scans, (b) data calculated as absorbance; results of first-order nonlinear regression analysis at 622 nm (c) and at 488 nm (d)
(Zincon) peak (A = 622) when subjected to a first-order analysis yields a rate constant of 0.475 f 0.008 s-' and a residual plot with uez = 0.0005 as shown in Figure 3c. Shown in Figure 3d is the absorbance increase and residual plot at the Zincon peak (A = 488) where a first-order analysis yields a rate constant of 0.46 f 0.04 s-l and uWa= 0.003. Although the magnitude of the absorbance change is approximately the same at both wavelengths, the actual intensity change is much less at 488 nm than a t 622 nm due to the characteristics of the instrument (source output, grating efficiency, and vidicon response) as a function of wavelength. A regression analysis of these data using all wavelengths obviously requires a weighting factor as a function of wavelength.
INSTRUMENT EVALUATION Random Errors. Experiments were carried out which measured Io, I t , u$,,, u $ ~ ,and ut, a t several wavelengths and a t several values of absorbance using neutral density filters to attentuate the signal. The observed variance, uiobd,was calculated by Equation 13, and the predicted variance, uipred, was calculated by Equation 20 for each wavelength and absorbance value. A plot of vs. I o for zero absorbance shown in Figure 4 demonstrates the large effect the differences in radiation throughput as a function of wavelength can have on the uncertainity of the absorbance measurements. A plot of log uiObdvs. absorbance for I o near the maximum allowable value shown in Figure 5 demonstrates the significance of incor2102
ANALYTICAL CHEMISTRY, VOL.
49,NO. 13,NOVEMBER 1977
105%2 OQI
05
0
I
2 Relative Io
3
1
4
x
Flgure 4. Plot of u2A,obsd vs. Io for an absorbance of zero
porating the dependence of the variance of the absorbance measurement on the absorbance value. This dependence is important only for larger absorbance values (A > 0.5). When the system is adjusted to give maximum resolution of the ADC at the wavelength of largest Io value, the quantization errors of the ADC at wavelengths with relatively low lovalues especially for higher absorbance levels are the major source of uncertainty in absorbance measurements. A plot of log uiOM vs. log flipred for one representative wavelength with the
-",
I
-7
Absorbance
Figure 5. Plot of log ( T ~ (calculated ~ , ~ from ~ Equation 13 and observed values of cr;,) vs. the absorbance value
maximum Io value for absorbance values from 0.0 to -3.0 gives a slope of 0.98 f 0.06, an intercept of 0.04 f 0.2, and a correlation coefficient of 0.990 which shows that Equation 20 and Equation 13 agree. Instrument Characteristics. In order to understand the sources of determinant errors, several characteristics of the system must be defined. These include: (1)stray light, (2) resolution, and (3) response lag time. All monochromators produce some unwanted stray radiation. This is a particular problem in regions of the spectrum where either the source is relatively weak or the detector response is relatively poor. Scattered light can come from long wavelength radiation being doubly diffracted (especially with coarse gratings as used with the vidicon), scattering from flaws and edges of mirrors and gratings, and light leaks. The stray radiation of this system is measured a t 240 nm to be 0.6% while observing the spectrum from 200 to 400 nm and 2.5% while observing from 200 to 600 nm. These values of stray radiation are determined by measuring the transmittance of a 1.0 M NaI solution which has a sharp absorption edge absorbing most of the intensity below 250 nm and assuming all the transmittance is due to stray radiation (23). At longer wavelengths, the stray irradiation, is much less and at shorter wavelengths it is greater. One of the tradeoffs in observing larger portions of the spectrum is that coarse gratings with lower dispersion which necessarily produce more stray radiation are required. For comparison, the SPEX monochromator as typically used with a 4 nm/mm reciprocal dispersion grating will produce 0.1% stray radiation in this region. For slit widths of 50 I.cm or less, the resolution of the vidicon system is limited by the scanning process to -0.5% of the total scan range (for example, 1 nm resolution for a 200-nm wide scan range) as estimated by the full width half maximum of the peak formed by the image of the slit. For slit widths greater than 50 Fm, the resolution is defined by the ratio of the slit image width to the width of the area scanned. Using a slit width of 0.25 mm, scanning 12.5 mm of the vidicon face, and observing a spectral width of 200 nm, the expected resolution would be 4 nm. The response lag time (the time required to achieve 90% of the total signal transition) of the vidicon is a complex function of the magnitude of target radiation before the transition occurs, the size and direction of the transition, the magnitude of the dark current, and the voltages supplied t o the various grids of the tube. Our experiments show the lag time to be virtually independent of the scan rate as long as the vertical sweep rate remains faster than the horizontal rate. The lag time is due to a combination of beam discharge lag in which a finite time is required to recharge the target and photoconductive lag resulting from the delayed photoconductive response of the target to radiation changes. In general,
-
I
0.0
1
Time (sed
0.I
a
0.0
Time ( s e d b
0.I
Figure 8. Response of vldlcon system at 585 nm (2 rns/spectra, taking consecutive spectra) to step functions of intensify change. (a) Step function response of 100% Tto 0% Tchange. (b) Step function response of 0% Tto 100% Tchange. Intensity of 100% Tvalue produces a 430 nA signal from vidicon tube
the lag time is much longer for decreasing radiation transitions (increasing absorbance) than it is for increasing radiation transitions (decreasing absorbance) (24). An experiment using a fast electronic shutter was performed to measure the response time of the system to 100% T to 0% T (increasing absorbance) and 0% T to 100% T (decreasing absorbance) transitions. The response curves of an increasing absorbance change shown in Figure 6a and of a decreasing absorbance change shown in Figure 6b can be used to estimate the time required for this system to respond to various absorbance changes. The lag time will also depend on the initial intensity of the radiation. To reach 2.0 absorbance unit when the radiation is completely blocked requires about 100 ms if the initial beam current is 430 nA and about 150 ms if the initial current is 75 nA. However, typical absorbance increases of 0.2 unit or less from low initial absorbance values require only 20 to 30 ms to attain 90% of the total response. In using stopped-flow techniques it must be remembered that, even for very slow reactions, a very rapid absorbance transition can occur during the push as products of the previous run are swept out of the flow cell by new reactants if the absorbance change is large. Therefore, the duration of the push must be long enough to allow the vidicon to reach a steady state before the flow stops. Distortion of kinetic data should not occur for reactions with half-lives longer than the ANALYTICAL CHEMISTRY, VOL. 49, NO. 13, NOVEMBER 1977
2103
‘F‘ Start
Table I. Values of Rate Constants Determined Using Durrum and Vidicon Stopped-Flow Systems Durrum Reaction
AAa
A B
-0.1 -0.3 + 0.3
75 + 1 61 * 1
-0.9
53
C
+0.9
Vidicon
on CPU scope to allow goln B offset adjustment
*
2
D
-0.4
14.6 + 0 . 2
E
+0.4 -0.5 +0.5
0.19 i 0.01
k 5 55+ 3 50+ 3
56
5 0 t 1
31
*
4 + 0.2 13.9 + 0.2 0.21 * 0.01 0.22 * 0.01 14.2
Negative absorbance changes were monitored at
a n d LT‘
I
620
nm; positive absorbance changes were monitored at 500 nm.
lag time which depends on factors discussed earlier. The average age of the mixed reagents in the observation cell of the Amino-Morrow unit is approximately 5 ms when the flow is stopped. As a result the full absorbance change ( A , - Ao)will not be observed for very fast reactions, a fact that may reduce the lag time of the vidicon response. The initial absorbance observed, Ai,approaches A , as the firstorder rate constant, k , becomes greater than lo3 s-’, so that this is an upper limit imposed by the flow system. On the other hand if k < 10 s-’ then Ai is close to A0 but, in general, the vidicon lag time will not limit the observation. When the k values are between 10 and lo3 s-’ the vidicon response time is of concern. Thus, for k = lo2 s-’ the ratio of (A, - A,)/ (A, - A,) is 0.79 and Figure 6a shows that, for a large absorbance increase, the lag time is greater than the reaction half life (e.g., for A, - A. = 1.0 the A , - Aivalue will be 0.79 and the lag time will be more than 20 ms compared to the half life of 6.9 ms). On the other hand, for a similar absorbance decrease, the vidicon response time will be much faster. For spectral changes of the type shown in Figure 3b and for large k values, this could result in apparently different rate constants in regions of increasing absorbance vs. regions of decreasing absorbance. The first-order rate constants of ligand exchange reactions of metal zincon complexes reacting with CyDTA under various conditions as determined by using a Durrum stopped-flow system are listed in Table I with those determined for the same solutions using the vidicon stopped-flow system at two different wavelengths. Reaction A is obviously too fast for the vidicon to accurately rerpond even though the absorbance change is small and negative. Reaction B is slower, but for both the positive and negative absorbance change, the accuracy appears still limited by the response time of the vidicon. Reaction C can be followed accurately as a negative absorbance change but the dependence of the lag time for a positive absorbance change on the magnitude of the transition causes an increased response time and an inaccurate observed rate constant. The analysis of reactions D and E agree well for both the Durrum and vidicon systems. A practical upper limit of observed rate constants measured accurately for reactions with absorbance changes of less than 0.3 and low initial absorbance is approximately 50 s-’. Although the vidicon system can acquire data for one complete scan every 0.5 ms, a practical limit is imposed by the scanning circuitry of 2 ms. At this rate the system can acquire only about 20 scans during three half lives of a reaction with a first-order rate constant of 50 s-’ making this value an upper limit from the standpoint of data acquisition as well as lag time. Another factor is the uncertainty of determining the time of the reaction after mixing due to the lack of coincidence between the stopping of the flow with the start of the first scan. A t 2 ms/scan, the uncertainty is f l ms which 2104
ANALYTICAL CHEMISTRY, VOL. 49, NO. 13, NOVEMBER 1977
Calculate X values from holmium oxlde spec t r u TP
Input data rate (or rate constants, Take 50 scans of V, and 20 01 V, Plot raw data and calculate A B S I
Input # s of spectra to be plotted and scaling f a c t o r s , plot spectra on scope
I< Input area of response surface to be analyzed and perform one of three regression analyses (see procedure), output results and plot A B S and residuals versus time
Figure 7. Generalized flowchart for saftware written for computerized vidicon stopped-flow rapid scanning spectrometer
is slightly less than 10% of the half life of a reaction with a first-order rate constant of 50 s-’. Procedure. The procedure for the use of the system is defined by the software for which a flowchart is shown in Figure 7 . In order to obtain spectral and kinetic data from the vidicon system an initialization procedure must first be performed. The gain and offset of the amplifier is set to maximize the resolution of the analog to digital convertor at the wavelength of maximum signal intensity. A dark current “spectrum” ( VAp) is measured under computer control with the radiation completely blocked in front of the flow cell and is subtracted from all subsequent spectra. Next, a reference spectrum, (Vi,lm),is taken with water or any suitable reference solution in the flow cell to provide values of I o for all wavelengths (Io = Vloo - VD). The spectrum of a holmium oxide spectral calibration filter is taken and displayed for which factors are calculated from known peak locations to define the wavelength of each data point. At this stage, the system is ready to acquire data for the reactions of interest. The spectrum of each of the two reagents is taken and used to calculate the expected spectrum of the mixed reactants at time zero. If a single reaction is being investigated to determine the first-order rate constant or to give information about the transient spectra, the operator inputs the desired data rate through the teletype; however, in the simultaneous kinetic and spectral analysis, the previously determined rate constants are input and the computer calculates the series of data rates. For each push of the stopped flow, the system acquires 50 scans at the predetermined rate or series of rates and averages 20 scans of the reaction mixture when it reaches equilibrium (AA,-). Any number of pushes can be ensemble
averaged to improve the signal to noise. The raw data are converted to absorbance values and can be plotted either vs. wavelength or vs. time. If the data are plotted against wavelength, the computer can display any number of spectra obtained during the reaction in their chronological order allowing the observer to dynamically recreate the experiment at a rate convenient for visual inspection (3 to 4 s for the computer to plot 50 spectra). This use of the system is extremely helpful in detecting isosbestic points as shown in Figure 3b and in characterizing short-lived intermediates. Although all programs written for the system can display the data vs. wavelength or time, three different first-order regression analyses are performed depending on which program is used. (1)A weighted linear least-squares regression analysis of a single first-order reaction can be performed a t any one wavelength to solve Equation 22 for the rate constant, k , and the magnitude of the absorbance change ( A , - Ao).
.?a-
a ) ABS
.oo-
1
1
505
Wave Iengt h
697
0.0
Time ( s e d
3.5
505
Wave Ieng t h
697
.m-
+
Cw,,u: = C w,(ln(A, - A , ) ht - ln(A, - A,))’ = minimum
(22)
The weighting factor, wt,is the reciprocal of the variance of the residual and is calculated from the propagation of error in measuring A,.
b) ABS
.ooThis is followed by a weighted nonlinear least-squares regression analysis accomplished by Taylor’s expansion series linearization to solve Equation 23 for the best values of k , Ao, and A .
I
I
C w t p : = C w t ( A t- A , + ( A , - A o ) e - k t )=2 minimum where w t = 11.4,. This program is used primarily to investigate transient spectra and their first-order kinetic behavior and is particularly useful where the A , value may be difficult to measure because of subsequent slower reactions. Plots of the absorbances and residuals as a function of time are displayed as in Figures 3c and 3d. (2) A difference spectrum between reactants and products is measured from which xh and uCAvalues are calculated and stored on magnetic tape for later use. A plot of xh vs. wavelength is displayed as in Figures 8c and 9c. This program then performs a weighted linear least-squares regression analysis of a single first-order reaction to calculate the best values of k and ( A , - Ao)x,a,from Equation 24 a t any number of wavelengths simultaneously.
In ( A , - AO)h,,,
1
= minimum
J
The weighting factor is calculated from the propagation of errors in the measurements of A,.
Plots of the absorbances and residuals are displayed as a function of time as shown in Figures 8b and 9b. If the signal-to-noise ratio is small for a given reaction, this program can be used to advantage by calculating one rate constant for all the data, thus improving the precision of the estimate. An
I
-1.00
Flgure 8. (a)Series of absorbance ataken during the dissociation of the Hg-Zincon complex; (b) First-order regression analysis of absorbance at 622 nm; (c)Values of x ~calculated , ~ from difference
spectra
examination of the residuals a t all the wavelengths for bias demonstrates whether the absorbance change can be accounted for by a single first-order reaction or whether a more complex mechanism is necessary to describe the observed behavior. This program is also used to obtain the information required to perform simultaneous kinetic and spectral analysis. (3) A weighted least-square regression analysis of two parallel first-order reactions is performed a t any number of wavelengths over any range of reaction time to solve Equation 25 for the initial concentration of each species for which the rate constant and xx values have been determined. This program performs the simultaneous kinetic and spectral analysis. EzWhtPit = ht
z E W h t [ ( A , - At)h At
A ARP,hma, XRP,he-klt -
A A s ~ , h , , , x S Q , h e - ~= ~minimum ~]~ ANALYTICAL CHEMISTRY, VOL. 49, NO. 13, NOVEMBER 1977
(25) 2105
ABS
.oo-
I
I
505
Wave I engt h
697
Time (sec 1
50
.a-
ABS
.oo-
c
0.0
I
1.00-
-1.00-
I
505
Wavelength
I
697
Flgure 9. (a) Series of absorbance specira taken during the dissociation of the Zn-Zincon complex; (b) first-order regression analysis of ab, ~ from ~ difference sorbance at 622 nm; (c) values of x ~calculated
spectra
The weighting factor as discussed earlier is defined by Equations 7 , 11, and 20. The techniques of centering the data and use of the correlation matrix described previously (8) to minimize the effects of round-off errors were not used in order to minimize the execution time (- 1min for 4500 data points). However, the use of these techniques would be advisable as the number of components increases or as the rate constants and x h values become more similar. Test Application. The reactions of Zn(Zincon) and Hg(Zincon) with CyDTA have been used for the simultaneous kinetic analysis of these metal ions under conditions where the rate constants are well separated (8). As a test system for simultaneous kinetic and spectral analysis, the reaction conditions were purposely adjusted so that the rate constants 2106
ANALYTICAL CHEMISTRY, VOL. 49, NO. 13, NOVEMBER 1977
for Zn2+ and Hg2+ would be close together. This binary mixture was also attractive as a test case because their difference spectra are only slightly dissimilar. This chemical system is an example of a difficult problem where neither simultaneous spectral analysis nor simultaneous kinetic analysis are expected to produce satisfactory results, but the combination of the two analyses is advantageous. Simultaneous Analysis of He2+and Zn2+. The vidicon rapid scanning stopped-flow system is used first to investigate the ligand exchange reactions of Hg(Zincon) and Zn(Zincon) with CyDTA individually. Two experiments performed under identical conditions chosen for the simultaneous kinetic and wavelength analysis of the mixture are prerequisite to the multicomponent analysis. First, the rate constants for each reaction are determined, and second, the difference spectrum, ( A , - AJh, is measured so that x h values can be calculated. Once these experiments are carefully done, the analysis of mixtures can begin. A calculated time-independent spectrum of the reaction mixture at time zero is performed as described earlier. Next, for each push of the stopped flow, 50 scans a t a predetermined series of rates and an ensemble average of 20 scans of the reaction mixture at equilibrium are acquired. Three such pushes are ensemble averaged for each solution. The multiple data rates are determined from the values of the rate constants and are calculated to distribute the number of data points taken during four half lives of each of the reactions evenly. This is done to prevent overemphasizing one segment of the reaction over another (8). At this point the data are displayed and the operator inputs the ranges of wavelengths and times defining the area of the response surface measured which is to be used to calculate the least squares best estimates of AARP~,,,) and A A S Q ~ ~ ~ ~
RESULTS When a solution (pH 7.8) containing 1.5 X M Zincon, 0.02 M borate, and 1 x M CyDTA is mixed with a solution M Zincon, 0.02 M borate, and (pH 7.8) containing 1.5 X 1X M metal, the series of spectra, represented by Figure 8a if the metal is Hg2+and Figure 9a if the metal is Zn2+,is recorded using the vidicon rapid scan system. These spectra show the disappearance of the metal complex leaving only the spectrum of the free ligand which is in large excess. A first-order regression analysis of these reactions at the wavelengths of maximum absorbance change yields fist-order rate constants of 1.21 for Hg2+and 0.74 s-l for Zn2+. Residual plots (center line) of the first-order analysis are shown along with the absorbance vs. time for Hg2+in Figure 8b and for Zn2+in Figure 9b. The difference spectra for the Hg2+and Zn2+reactions are shown in Figure 8c and Figure 9c respectively. The response surfaces of five different reaction mixtures of Zn2+and Hg2+are measured as previously described. For each surface the data within five different domains determined by sets of wavelength and time boundaries are subjected to the mathematical treatment developed earlier (Equations 8 and 9) to solve for the least squares best estimates of AAY,,~and A A z ~ , ~ , , . The wavelength boundaries are determined , ~ X Z ~as , ~shown in Figure from a composite plot of X H ~ and 10. In the wavelength region from 600 t o 640 nm, the Hg2+ and Zn2+ x values are very similar, but in the wavelength region from 640 nm to 680 nm the x values are somewhat different. The two time boundaries are defined by using either the difference spectrum at time equal zero calculated from 50 ensemble averaged time independent spectra of the individual reactant solutions and the product solution, or by using the 50 kinetic spectra of the reacting mixture. By using the calculated spectrum at time zero, the analysis contains no kinetic information and is simply a simultaneous spectral
Table 11. Molar Absorptivity Differences, Intercepts, and Correlation Coefficients Calculated from Beer's Law Plots of Simultaneous Kinetic and Spectral Analyses Performed over Different Data Domains of the ResDonse Surfaces for Hg and Zn Domain
Available information
Calibration runs a similar x's; no rate data b different x ' s ; no rate data c similar x's; with rate data d different x's; with rate data e different x ' s ; with rate data
I
505
1
A
M-' cm-'
M-l cm-'
Intercept
AeHg
2.90 i 0.04 2.0 i 0.5 3.2 i 0.2
0.034 i 0.01
-0.007
AEZIl
0.840
2.36 i 0.04 2.0 i 0.8
-0.005
0.020
0.730
-0.003 t 0.005
0.981
0.004
0.993
2.4 i 0 . 2
i
0.002
0.997
2.0 r 0.4
0.009
i
0.009
0.922
0.1
0.004
t
0.003
0.994
0.004
t
0.002
0.997
i
0.08
2.94
t
0.1
-0.002
i
0.003
0.997
2.2
2.96
i
0.08
-0.005
I0.002
0.998
2.28
I
B C Wave Ieng t h
*
R kn
i
2.32
I
0.009
Intercept
Rkg
I
D
J
697
A = 525 B=600 C = 640 D=f330 Figure 10. Composite plot of and x ~vs. ,wavelength ~ ~ in order to show similarities and differences of dependences of these functions on wavelength
analysis of a single curve rather than an area; however, the total number of data points used remains the same as a kinetic analysis since the curve is ensemble averaged. The five different domains are as follows: (a) the wavelength region from 600 to 640 nm and the spectrum a t time zero, (b) the wavelength region from 640 to 680 nm and the spectrum a t time zero, (c) the wavelength region from 600 to 640 nm and 50 kinetic spectra, (d) the wavelength region from 640 to 680 nm and 50 kinetic spectra, and (e) the wavelength region from 525 to 680 nm and 50 kinetic spectra. The values obtained for A A H ~ , ~and , A A Z , , ~ are ~ _ plotted for each of the five domains vs. the concentrations of each of the species in mixtures numbered 1 through 5 . The values of and At&,& calculated from the slopes of these plots are listed along with the intercepts and correlation coefficients in Table 11.
DISCUSSION A comparison of the results (see Table 11) obtained from analyzing the five different domains of the response surface illustrates the versatility of the system and the advantages of simultaneous kinetic and spectral analysis. Comparing domain (a) with (b), neither of which contain any kinetic information, confirms that (b) has greater spectral information
i
i
0.08
for simultaneous spectral analysis of the mixture. Comparing domain (a) with (c), both of which contain very little spectral information, shows clearly the advantages of simultaneous kinetic analysis. Domain (d) which contains both spectral and kinetic information yields a superior analysis in terms of accuracy and precision over either (b)or (c) and demonstrates the advantage of extracting all the information available from the data at hand. The further improvement of the results by analyzing over domain (e) which uses essentially all of the data obtained during the experiment appears slight, but the only cost is a slightly longer execution time. In this paper, we have described an experimental technique and mathematical method of best calculating the parameters of a simultaneous kinetic and spectral analysis based on the understanding of not only the chemical but also the measurement process. Analyzing over both wavelength and time allows all the useful information acquired by this instrument to be extracted for the determination. Including the measurement uncertainties, which may vary greatly because of irregular source output grating efficiency, instrument response, and spectral character of the chemical system injects a much higher degree of reliability and versatility. Multiple component analysis is only one application of this system. The procedures given will permit individual rate constants to be measured based on data from the entire spectral region or any portion of the region being scanned. This procedure can be used to verify that absorbance changes a t different wavelengths are due to the same reaction or to show that additional reactions are occurring. There are a number of instances where dual wavelength data are useful in kinetics studies to correct for other effects. In our system, any number of wavelengths can be observed simultaneously. Another important application is the ability to obtain the spectra of transient species. As shown in Figure 3b, the quality of these spectra are excellent. We have been able to determine the spectra of a number of short-lived intermediates with this system including those that absorb only in the UV as well as those with visible spectra.
LITERATURE CITED (1) J. J. Mousa and J. D. Winefordner, Anal. Chem., 46, 1195 (1974). (2) K. F. Harbauah, C. M. O'Donnell, and J. D. Winefordner. Anal. Chem.. 46, 1206 (1c74). (3) R . M. Wilson and T. L. Miller, Anal. Chem., 47, 256 (1975). (4) J. B. Pausch and D. W. Maroerum. Anal. Chem.. 41. 226 11969). (5) D. W. Margerum, J. B. Pausch: G. A. Nyssen. and F G. Smith; Anal. Chem., 4 1 233 (1969). (6) 8 . G. Willis, W. H. Woodruff, J. M. Frysinger, D . W. Margerum. and H. L. Pardue. Anal. Chem.. 42. 1350 (1970). (7) L. C. Coombs, J. Vasiliades, and D.'W. Margerum, Anal. Chem., 44, 2325 (1972). (8) G. M. Ridder and D. W. Margerum, preceding paper in this issue. (9) . , R. E. Santini. M. J. Mibno. H. L. Pardue. and D. W. Maraerum. Anal. Chem.. 44, 626 (1972). (10) R. E. Santini, M. J. Milano, and H. L. Pardue, Anal. Chem., 45, 915A 11973). (11) Y . Taimi, Anal. Chem., 47, 658A (1975) ANALYTICAL
CHEMISTRY, VOL. 49, NO. 13, NOVEMBER 1977
2107
(12) Y. Talmi, Anal. Chern.. 47, 697A (1975). (13) M. J. Milano, H. L. Pardue, T. E. Cook, R. E. Santini, D. W . Margerum, and J. M. T. Raycheba, Anal. Chern., 46, 374 (1974). (14) T. A . Nieman and C.G. Enke, Anal. Chem., 48, 619 (1976). (15) M. J. Milano and H. L. Pardue, Clin. Chern. (Winston-Salem, N.C.), 21, 21 (1975). (16) M. J. Miiano and H. L. Pardue, Anal. Chern.. 47, 25 (1975). (17) R. M. Wghtman, R. L. Scott, C. N. Reiliey, and R. W. Murray, Anal. Chem., 46, 1492 (1974). (18) R. B. Coolen, N. Papadakis, J. Avery. C. G. Enke, and J. L. Dye, Anal. Chern., 47, 1649 (1975). (19) R. M. Rush and J. H. Yoe, Anal. Chem., 26, 1345 (1954).
(20) . . D. P. Shoemaker and C. W. Garbnd, ‘‘Exwriments in physical Chemistry”, McGraw-Hill, New York, N.Y., 1967. (21) J. D. Ingle. Jr., and S. R. Crouch, Anal. Chern., 44, 1375 (1972). (221 L. D. Rothman and S. R. Crouch. Anal. Chern.. 47. 1226 (1975). (23) W Slavin, Anal Chern , 35, 561 (1963) (24) 0 Yoshida and Y Kiuchi, Jpn J Appl Phys , IO, 1203 (1971)
RECEIVED for review March 11, 1977. Accepted August 18, 1977. This work was supported by National Science Foundation Grant CHE75-15500.
CORRESPONDENCE Voltammetric Determination of Ultratraces of Albumin, Cysteine, and Cystine at the Hanging Mercury Drop Electrode Sir: During the past few years several authors (1-3) have studied so-called BrdiEka currents observed with albumin and some other proteins ( I ) at the hanging mercury drop electrode (HMDE). These catalytic hydrogen currents were first described by BrdiEka (4)at the dropping mercury electrode and observed with disulfide and/or sulfhydryl-containing proteins (and low molecular weight thiols or disulfides) in ammoniacal buffers containing cobalt(II1)hexammine chloride, [Co(III)], or cobalt(II)chloride, [Co(II)],and only Co(I1) with the low molecular weight compounds. From studies (1-3) at the HMDE it appears that a diffusion controlled irreversible adsorption of albumin (1-3) (and a few other proteins ( I ) ) occurs on the mercury surface from ammoniacal and other buffers. For example, in 3 X M albumin it takes about 2 to 3 min at room temperature to get a monolayer adsorbed; from more dilute solutions, it takes a longer time. The completely or incompletely adsorbed albumin is not desorbed ( I , 3 )upon keeping in ammoniacal buffers, unless a potential more negative than -1.5 V vs. SCE (saturated calomel electrode) is applied. When the rate of adsorption of protein is promoted by stirring, and pure water is used as the solvent, it has been possible to detect and determine as little as lo-’’ M bovine serum albumin (BSA) by measuring the two BrdiEka currents in 0.1 M ammonia buffer of pH 9.3 which is M in Co(II1) or Co(I1). In the present communication, we briefly describe characteristics of a newly discovered catalytic hydrogen current observed at the HMDE on which some “active cobalt” has been deposited and oxidized anodically, followed by cathodic scanning. The procedure allows the detection and M BSA in 100 mL. The estimation of as little as electrodeposition at about -1.0 V (vs. SCE) of “active cobalt” on a HMDE from 0.1 M ammoniacal buffer (pH 9.3) containing a low molecular weight thiol or disulfide and Co(I1) was first described in several papers by Anzenbacher and Kalous ( 5 ) . This “active cobalt” yielded one or two anodic waves with peaks at about -0.25 and -0.05 V. We have observed a large catalytic hydrogen wave with peak at about -1.45 V in 0.1 M ammonia buffer (pH 9.3) containing Co(II1) or Co(I1) and high or low molecular weight thiol or disulfide when the anodic scanning is followed by cathodic scanning. This new catalytic current is denoted in this communication by the symbol i,. The HMDE, the polarographic analyzer and recorder, a magnetic stirrer, the various samples of BSA, as well as purity of chemicals used, have been described previously (3). Unless stated otherwise, all experiments were carried out at 21 “C 2108
ANALYTICAL CHEMISTRY, VOL. 49, NO. 13, NOVEMBER 1977
and with a scanning rate of 500 mV/s. Reported values of the new current, i,, refer to that at the peak potential of about -1.45 V. All potentials refer to the SCE. The buffer used was 0.1 M in ammonia, 0.1 M in ammonium chloride, and 5 X M in cobalt(II1) or Co(I1) (BrdiEka buffer). All solutions used were made and kept air-free during an experiment. The HMDE was placed in the BrdiEka buffer containing a known concentration of BSA, the solution was allowed to stand (or stirred) for a given time and (without stirring) the voltammogram was run from 0 V to -1.05 V, the potential was kept at this potential for 30 s, the scanning reversed to $0.1 V (sometimes to -0.1 or -0.2 V) and after 1 to 2 s the voltammogram run cathodically to -2.0 V. In order to study various factors to be described in a subsequent paper, it was necessary to place the HMDE after adsorption of protein in a protein-free solution in which the scanning was carried out. At a given BSA concentration, adsorption, and therefore i,, increases with increasing time of standing or stirring the solution until about of the mercury surface is covered with protein. Figure 1 illustrates the shape of complete voltammograms obtained in extremely dilute BSA solutions. [For the sake of saving space, the potential range between -0.8 and -0.5 V is omitted in Figure 1.1 After different times of adsorption, the anodic waves exhibited a peak between -0.14 and -0.2 V. At the smallest BSA concentrations, the Co(I1) to Co(0) reduction wave is hardly affected by ultratraces of adsorbed protein; with increasing adsorption, this wave is displaced to less negative potentials (up to 0.2 V) and merges with the wave of the (new) catalytic current, i,. Under conditions of Figure 1the peak potential of i, is between -1.47 and -1.5 V, and when i, is less than 50 g A it is proportional to the concentration of BSA. At larger currents, the plot of i, VI. concentration of BSA is hyperbolic. At larger concentrations of BSA than in Figure 1, a maximum in the hyperbolic curve was found when i, was of the order of 180 FA, to decrease when more BSA was adsorbed on the mercury surface. At concentrations of Co(II1) between 1 and 8 X M, i, has been found proportional to the cobalt concentration; at larger cobalt concentrations, i, became less than proportional. At concentrations greater than 2.5 X M Co(III), stirring around the mercury surface affected values of i,. The scanning rate has a very large effect on i,. In one set of experiments the following results were obtained: at scan rates of 500, 200,100, and 20 mV/s, peak i, values of 73, 34, 4,
