Table I. Analysis of Mercury(I1) Solutionsa Titration, CI -
K n o w n sample
A (MX
l o 3 )4.990
B (M
10') 4.993
c1-
I-
5.069 i 0.007
i
4.871 t 0.015 4.945 i
0.001
0.006
5.021
t
0.001 X
0.013
i
Direct potentiometry
5.029
4.971 i 0.008
a The precision in each case is expressed as the average deviation for 2 determinations.
tallochromic indicator methods ( 3 ) often suffer from interference effects in chloride solutions. The curve for the titration of 5 cm3 of a solution containing M total mercury(I1) and 0.2 M total chloride M EDTA is shown in Figure 6. against The iodomercurate electrode could not be used in this way because the formation constants of the anionic iodomercurate(I1) complexes are higher than that for the complex between mercury(I1) and EDTA. Analytical Investigations. The results of the analysis of standards A and B by direct potentiometry and by po-
tentiometric titration are shown in Table I. There is good agreement between the values obtained using the two techniques and the known values. The titration method is simpler (and more precise) because the total chloride concentration does not need to be controlled within the stringent limits necessary for the iodide and chloride concentrations when using the direct potentiometry technique.
ACKNOWLEDGMENT We thank General Mills Inc. for the gift of Aliquat 3369, and G. B. Deacon, Monash University, for directing our thoughts towards the mercury(I1) systems.
LITERATURE CITED (1) R. W. Cattrall and Chin-Poh Pui, Anal. Chem., 47, 93 (1975). (2) G. J. Moody and J. D. R. Thomas, Talanta, 19, 623 (1972). (3) R. Belcher, and A. J. Nutten, "Quantitative Inorganic Analysis", 3rd ed., Butterworths, London, 1970, p 274. (4) H. Freiser and Q. Fernando, "Ionic Equilibria in Analytical Chemistry", John Wiley, New York, N.Y., 1963, pp 310-314.
RECEIVEDfor review June 18, 1975. Accepted September 22,1975. We are grateful to the Australian Research Grants Committee for financial support.
Kinetic Methods of Analysis with Differential Redox Potentiometry at Tubular Carbon Electrodes in Flowing Streams Ralph Ira Porterfield' and Carter L. Olson* College of Pharmacy, The Ohio State University, Columbus, Ohio 432 70
A new differential potentiometric method has been developed for measuring the rate enzyme catalyzed reactions. The electrode cell is a flow stream concentration cell using two tubular carbon electrodes separated by a membrane salt bridge. Nernstian behavior made posslbie the dlrect calculation of enzyme activlty. The potentiometric ranges were normally less than 6 mV which allowed the use of linear calibration plots in place of logarithmic plots. Glucose assays were run on 0.1-ml samples of human blood serum. The results were in agreement with results obtained using standard AutoAnalyzer techniques.
Kinetic methods of analysis have received increasing attention particularly with regard to enzyme systems important in clinical chemistry. A t the present time, the majority of clinical enzyme assays are done spectrophotometrically. The potential advantages for developing electrochemical techniques in addition to, or in lieu of, existing techniques vary depending on the assay but include increased freedom from interferences, increased specificity of detection, increased sensitivity, and substantially lower cost and simpler instrumentation. Enzyme catalyzed reactions have been studied using a variety of potentiometric methods and electrodes. These include potentiometry (at constant current) using platinum electrodes ( I ) , the use of concentration cells (2), the use of Present address Pfizer Diagnostics Division, Groton, Conn. 556
ANALYTICAL CHEMISTRY, VOL. 48, NO. 3, MARCH 1976
immobilized enzyme systems with ion selective electrodes (3-14), and the direct use of ion selective electrodes (1530). The present paper describes a new electrode and cell configuration which is useful for kinetic methods in general and for the analysis of both enzymes and their substrates. The design is essentially a semimicro flow stream concentration cell where the cell compartments are separated by a thin membrane. The cell is operated in either continuous flow steady-state mode or in stop-flow mode. In the present study, the stop-flow mode yielded the lowest noise signals. The utility of the electrode design and methodology is demonstrated by using it for the assay of glucose in human blood serum. Theory. The concentration cell used in these experiments is shown in Figure 1. I t consists of two tubular carbon electrodes separated by a thin dialysis membrane which serves as a salt bridge. The potential a t each electrode is described by the Nernst equation:
where y is the activity coefficient, brackets indicate molar concentration, and all other terms have their usual significance. The potential of the concentration cell, Eceli,is given by the following equation: Ecell
where
E2
and
E1
= E2
- E1 + E j n
(2)
are the single electrode potentials at the
two electrodes as given by Equation 1, and Ejn is the junction potential plus any other asymmetry potentials that may occur. Because the solution is essentially common on both sides of the membrane, the value for Ejn is approximately zero. In general, solution concentration and ionic strengths are such that concentrations of the redox couples can be substituted for activities in the equations. Thus, Equation 2 can be rewritten as:
RT Ecell= E” +-In nF
A
B
flkk
,ELECTRODE
I
[Ox12 - E” - RT [Ox11 - ln-
nF
[Red12
[Red]1
which can be rearranged to the following:
(3) C
The concentration subscripts refer to the electrode where the concentration is present. Electrode 1 is the upstream electrode and electrode 2 is the downstream electrode. T o illustrate, assume that the redox couple measured a t the electrode is directly coupled to a kinetic process, such as an enzyme reaction, that some of the reduced form is converted to oxidized form during the reaction time, and that initial solution concentrations exist a t electrode 1. The concentrations a t electrode 2 will either change as a function of time if the experiment is a stop-flow experiment or be steady-state values dependent on delay time if a continuous flow technique is used. Concentrations a t electrode 2 can be expressed as follows: [Ox], = [Ox11 2
+x
[Red], = [Red112
-Y
(4)
where 2 is a stream splitting factor (0 < 2 i1) depending on flow stream arrangement), X is the increase in concentration observed a t electrode 2 due to production of [Ox] by a chemical reaction or by addition of a calibrating standard, and Y is the loss of [Red] observed a t electrode 2 due to consumption of [Red] by a chemical reaction. For a calibration procedure, Y = 0, and for a chemical reaction Y = W X where W is the stoichiometric ratio of X to Y . The cell potential may be written as:
SIDE
D VIEW
END
VIEW
Figure 1. Potentiometric flow stream concentration cell
The electrode system can be used in either a stop-flow mode where Ecell is measured vs. time or in a continuous flow mode where a steady-state voltage is measured which is proportional to reaction rate and delay time between electrodes. For a continuous flow experiment, steady-state concentrations are found a t the two electrodes. The difference in these concentrations represents the integrated concentration change that occurs as a solution element moves through the delay line between the electrodes. Therefore, although the measurement is a differential measurement, the integrated form of the equation represents the simultaneous two-point kinetic measurement. In some instances, if the reaction prQceeds rapidly or if the initial flow line is long, the redox concentration a t the first electrode cannot be assumed to be the initial concentration found a t the mixing point. The concentration can be calculated a t the two electrodes if the reaction is assumed to proceed a t a constant initial steady state rate. In the experiment, the initial concentration after stream mixing, [Oxlo, can be determined if the flow rates are known. The delay times for the solution to move from the mixing point to the first electrode, t ~and , to the second electrode, t ~can , be measured. Equation 6 can be written as follows:
If [Red] is large with respect to [Ox] for example, [Red11 2 100 [Ox11 and lOOY, then: where [Ox11 = [Oxlo + ht1 and [OX]Z= [Ox10 + kt:!. From Equation 7 , This can be simplified to:
mkz[ENZl[S] K, + [SI Substituting for OX]^, and [Ox]:! in Equation 8 gives
k =
+
RT [Ox112 X Ecell= -In nF [Ox]12 For the case of a monosubstrate enzyme catalyzed reaction where the reaction proceeds a t an essentially initial steadystate rate, X can be described by the equation:
exp
nFE cell [Oxlo + kt, ( 7 = [Oxlo +) htl
which can be rearranged to solve for k , the reaction rate.
(7) where m is the stoichiometric ratio between the measured redox species produced and the substrate consumed, and the rest of the symbols are the standard Michaelis Menten terms. Depending on relative concentrations, the reaction rate can be used to determine either enzyme activity or substrate concentration. If [SI >> KM,X = m J”kp[Enz]d t and X is directly proportional to enzyme activity. If K M >> [SI, X = m J ” { k ~ [ E n z ] ( S ) d t land K ~ )X is directly proportional to the substrate concentrations.
If Ecell is small, the denominator in Equation 10 becomes approximately the time delay between the two electrodes, t z - tl. The reaction rate can be calculated directly if Nernstian behavior is obtained a t the electrode. Otherwise, an experimental slope would be required in place of the term nF/RT. ANALYTICAL CHEMISTRY, VOL. 48, NO. 3, MARCH 1976
557
REFERENCE ELECTRODE
I
rELECTRODE I
1
MEMBRANE
+WASTE
-\
ELECTRODE 2
1
MEMBRANE MIXER
SAMPLE SAMPLE
REAGENT
WASTE
Figure 3. Flow stream arrangement for stop-flow measurements
WASTE
Flgure 2. Flow stream arrangement for continuous flow measurements
For a stop-flow experiment, reagent and sample mixing is done between the electrodes so that a stable reagent stream redox ratio is present a t the upstream electrode. When the pumps are stopped, the reaction takes place in the downstream electrode only and the potential change reflects the concentration change in the second electrode. Two approaches can be used to obtain the value of the reaction rate. The first is to use pairs of data a t specified points in time after the reaction starts. For example, values of Ecella t times t l and t2 after reaction starts can be written as follows:
used, both Equations 15 and 16 give the same value for k . Using Equation 16 is the simpler approach if slopes are directly measured from the data plots. However, Equation 15 should yield the exact values, and averaging multiple calculations is easily implemented using computerized data acquisition and analysis. T o demonstrate the applicability of the approach to enzymatic analysis, the well studied glucose oxidase system was used. The chemistry can be described by the following equations. Glucose 2H+
[Oxlo is the concentration after the mixing point where the reaction starts, and [Ox11 is the stable concentration a t the upstream electrode. Subtracting Equation 11 from Equation 12 yields Equation 13:
+0 2
[Glucose Oxidase]
Gluconic Acid
+ Hz02 + 2Fe(Cn)e4-
[Peroxidase]
+ H202
H2O + 2 F e ( c N ) ~ ~ -
The redox system measured a t the electrodes is the ferroferricyanide redox couple. In the above case, the initial concentration of ferrocyanide is large with respect to both the initial ferricyanide concentration and the ferricyanide ultimately produced by the enzyme reaction. Two moles of ferricyanide are produced for each mole of glucose substrate reacted. Therefore, the stoichiometry must be remembered when calculating the glucose oxidase activity.
EXPERIMENTAL Which can be rearranged to yield Equation 14, which has the same form as Equation 9. (14) The value for k is given by
Alternatively the logarithmic form of Equation 8 can be differentiated
where [Ox11 is a premixing constant.
therefore,
and
k=
NF [Ox],dE/dt RT
At short times, dE/dt is the initial slope of a plot of Eceiivs. time and OX]^ is close to the value of [Oxlo. At longer times, a precise value of [Ox12 is not known and the value of dE/dt gradually falls off. If initial values for dE/dt are 558
ANALYTICAL CHEMISTRY, VOL. 48, NO. 3, MARCH 1976
Electrode Assembly. T h e electrode assembly is shown in Figure 1. The tubular carbon electrodes were prepared from Ceresin wax impregnated spectrographic grade graphite rods. The electrodes, which were 0.155-inch 0.d. and 0.150 inch long were pressfit into a well, drilled into the Kel-F plug, and sealed with epoxy cement. The electrode and capping plug, press-fit over the electrode, were predrilled with undersize holes to permit release of excess epoxy. After drying, the holes were drilled to a final inside diameter of 0.0555 inch. T h e two holes were connected by a 1/3s-inch milled slot on the inside surface of the plug which continued the solution flow line. The cell was assembled by screwing two of the electrode plugs together inside a threaded Lucite block with a disk of dialysis membrane sandwiched between them to isolate the solution flow lines and to provide a salt bridge. Electrical contact was made through a copper wire touching the outside surface of the carbon electrode. Flow System. several^ flow stream arrangements were tried for both continuous flow and stop flow methods. The flow stream configurations finally selected are shown in Figures 2 and 3. Solutions were transported via 22 gauge Teflon tubing which was connected by press-fitting into holes drilled in the flow components (mixer-T and electrode assembly). The Teflon tubing was connected to the peristaltic pumps by means of short Tygon sleeves. Two types of variable speed peristaltic pumps (Scientific Industries, Model 403 and Harvard Apparatus, Model 500-1200) were used throughout the experiments. The Scientific Industries pump gave a smoother flow rate but was restricted to lower flow rates than could be obtained from the Harvard Apparatus pump. The sample stream did not pass through a pump head prior to measurement and contacted only inert Teflon tubing and materials. The sample and reagent streams were mixed in a low holdup volume mixing assembly. The mixer cavity was milled to hold a 7 mm X 2 mm Teflon-coated stirring bar (Cole-Parmer, No. 8545). The mixing bar was vibrated by a water driven magnetic stirrer. The Teflon flow lines were thermostated in Tygon tubing water jackets which were connected to a circulating water bath by means of Teflon adaptors. Measurement System. The cell potential was measured connecting the electrodes directly via shielded cable to a high imped-
ELECTFIODE . , ,ELECTRODE . ; E A
SAMPLE
REAGENT
REAGENT
REFERENCE
Figure 4. Flow stream arrangement for continuous flow calibration
ance potentiometric recorder (Leeds and Northrup, Model XL680). Noise was minimized by placing a capacitor across the recorder leads. The capacitance values varied from 10 t o 60 WFdepending on experimental conditions. Reagents. All solutions were prepared in a pH 6.3 phosphate buffer prepared by dissolving 65.6 g of NaH2P04 and 33.6 g of Na2HP04 in 4 1. of double distilled water. Glucose oxidase stock solutions, used for the determination of glucose were prepared daily by dissolving 0.20 g of crude glucose oxidase (Worthington Biochemical Corp., Catalogue No. 8495, 1.35 units/mg) in buffer, filtering off undissolved protein, and diluting to 50 ml. High purity glucose oxidase (Worthington Biochemical Corp., Catalogue No. 4579, 150 units/mg) was used for the glucose oxidase assays. Peroxidase stock was prepared by dissolving 1.25 mg of purified horseradish peroxidase (Worthington Biochemical Corp., Catalogue No. 6499, 656 units/mg) in 25 ml of buffer. Reagent solutions containing K*Fe(CN)e and KsFe(CN)e were prepared by diluting a 1 mM K3Fe(CN)e stock solution prepared in buffer and a 0.1 M &Fe(CN)e stock solution which was prepared in buffer, stored in a dark container, and kept under nitrogen scrubbed by a vanadous solution. A 1000-ppm D-glucose stock solution was prepared from anhydrous C.P. dextrose approximately 12 h before use. Incubation time ensured mutarotation equilibrium before use. Human blood serum samples, obtained from the Clinical Chemistry Department of T h e Ohio State University Hospital, were used as received except for dilution. Procedure. Electrode Calibration. When using the stop-flow technique, the following calibration procedure was used. For a glucose assay, a deaerated reagent solution containing 30 mM ferrocyanide, 0.2 mM ferricyanide, 10 pprn peroxidase, and 1600 ppm glucose oxidase (crude glucose oxidase) is passed through the reagent line and buffer is passed through the sample line (Figure 3). The pump is then stopped and the potential measured. For a glucose oxidase assay, the reagent solution contained 60 000 ppm glucose in place of the glucose oxidase. A series of calibration solutions normally covering the range from 1 X 10-jM to 5 X lO-jM ferricyanide was introduced through the reagent stream. T h e resulting stop-flow potentials were measured and plotted. The stream splitting factor was calculated using the flow rates of the sample and reagent streams. The flow rate of the reagent stream could be obtained by subtracting the flow rate of the reagent stream from the flow rate of the two waste streams. When using the continuous flow technique, the calibration procedure was run using the modified flow stream arrangement shown in Figure 4.If the assay was for glucose oxidase, the reagent solution contained 20 m M ferrocyanide, 10 ppm peroxidase, and 60 000 ppm glucose stored in the dark under nitrogen. The reference solution contained 0.2 mM ferricyanide and the solution passed through the sample stream typically ranged from 0.20 to 0.24 mM ferricyanide. T h e resulting continuous flow potentials were plotted vs. change in excess sample ferricyanide concentration. T h e calibration plots were used to verify continued Nerstian behavior with old electrodes. Non-Nerstian response indicates need for electrode cleaning or replacement. T h e plot can be used directly to read the assays. Determination of Glucose. Analysis of glucose and human blood serum glucose samples was done using the stop flow differential potentiometric method. The reagent solution was prepared by mixing 5 ml of ferrocyanide stock, 5 ml of peroxidase stock, and 10 ml of glucose oxidase stock solution. The reagent was kept in a dark container through which vanadous scrubbed nitrogen gas was passed. The bubbling action of the nitrogen had no observable effect upon either peroxidase or glucose oxidase activity during the course of the experiments. A typical glucose calibration curve, Figure 5, covered a glucose concentration range of 20 to 100 ppm glu-
10
20
30
40
50 60 QLUCOSE- PPY
70
Flgure 5. Giucose calibration curve-stop-flow
80
SO
I00
measurement
Reagent contains 20 mM ferrocyanide, 0.2 mM ferricyanide, 10 ppm peroxidase, and 1600 ppm glucose oxidase (1.34 unitslmg). T = 24.4 f 0.1 OC, pH 6.3
Table I. Short Range Ferricyanide Calibration
1.05 1.10 1.15 1.20 1.25
1.23 2.40 3.57 4.64
58.1
58.0 58.8 58.6 5.69 58.7 Average value = 58.4 mV u = 0 . 4 mV
cose. Human blood serum assays were performed by diluting 0.1 ml of serum t o 2.0 ml with buffer. Standard addition experiments were done on samples containing 0.1 ml human serum and 0.2 to 1.0 ml of 100 ppm glucose which were diluted to 2.0 ml with buffer. Determination of Glucose Oxidase. Glucose oxidase activity was determined using both stop-flow and continuous flow methodology. In both cases, the reagent solution contained 0.2 mM ferricyanide, 2.0 mM ferrocyanide, 10 ppm peroxidase, and 60000 pprn glucose. Sample solutions were prepared by diluting 1 to 10 ml of approximately 0.4 ppm high purity glucose oxidase stock solution (150 units/mg) to 10 ml with buffer.
R E S U L T S AND DISCUSSION The long range potential behavior was observed to be Nernstian with a 59-mV slope over a concentration range of 0.1 M to 0.05 mM. Short range potential behavior typical of assay conditions is shown in Table I. The flow rate was approximately 1/3 ml/min throughout the experiments. Under continuous flow conditions, the average noise level was about 30 p V . The Scientific Industries pump was used for the continuous flow experiments. Flow rate and stream splitting varied less than 0.5% when checked before and after a series of experiments. The silicone rubber pump tubing was stable for several months of continuous use. The magnitude of the potential response is dependent on the reaction rate and time which are determined by the solution concentrations and flow stream delay time. I t is also dependent on the concentration of the poised redox couple. For example, the relative change in ferricyanide concentration for a fixed rate of ferricyanide production is dependent on the initial concentration of ferricyanide, Le., the lower the initial concentration, the greater the relative concentration change and potential change. The low initial concentration limit for ferricyanide was found to be approximately 0.05 mM if Nernstian behavior was required. However, analytical results could be obtained, using a calibration plot, for initial concentrations as low as 0.01 mM ferricyanide. In the stop-flow mode, the average noise level varied between l to 10 pV. A t a pumping flow rate of ml/min, the time required for the solution to travel from the mixer to the sample electrode was about 5 s.
’&
ANALYTICAL CHEMISTRY, VOL. 48, NO. 3, MARCH 1976
559
240
c
I80'
I20
2
30,000
60,000
sop00
l20,OOO
60
GLUCOSE-PPM
Figure 6. Glucose dependence, stop-flow Reagent contains 20 mM ferrocyanide, 0.2 mM ferricyanide, 10 ppm peroxidase and 0.158 ppm glucose oxidase (150 units/mg). Sample contains 0 to 120 000 ppm glucose. Stream splitting factor (2)= 0.495 for reagent, 0.505 for sample. T = 23.1 O C , pH 6.3
560
ANALYTICAL CHEMISTRY, VOL. 48, NO. 3, MARCH 1976
I60
240
M G % 18)
Figure 7. Correlation between serum glucose values determined by the stop flow potentiometric method ( A ) and by the University Hospital AutoAnalyzer method ( B ) Reagent contains 20 mM ferrocyanide, 0.2 mM ferricyanide, 10 ppm peroxidase, and 1600 ppm glucose oxidase (1.34 units/mg). Reagent contains 5 % blood serum, T = 24.4 OC,pH 6.3 ~~~
Reaction rate dependence on glucose concentration is shown in Figure 6. The ferrocyanide concentration (2.0 mM) and peroxidase concentration (10 ppm) were well above the minimum concentrations where the reaction rate of the peroxidase reaction is no longer limited by either ferrocyanide or peroxidase concentration (31). For the analysis of human serum glucose, the reagent solution contained 1600 ppm glucose oxidase, 20 mM ferrocyanide, 0.2 mM ferricyanide, and 10 ppm peroxidase in p H 6.38 buffer, and the sample contained 5% blood serum prepared by diluting 0.1 ml serum to 2 ml with the same buffer. Blood samples were obtained from the Clinical Chemistry Department of The Ohio State University Hospital. A standard addition experiment was run to determine if the serum affected the analytical results. The standard addition value for the serum glucose was 92 mg % and the value calculated directly using a calibration plot was 93.5 mg % which indicates agreement within experimental error. Figure 7 illustrates the close correlation between results obtained using the stop-flow differential potentiometric method and results obtained by the clinical chemistry laboratory using the standard AutoAnalyzer procedure. The relative deviation for the samples is 4.8%. Glucose oxidase was assayed using both the continuous flow and stop-flow methods. Typical calibration data for the two methods are shown in Tables I1 and 111. The specific activity of the high purity glucose oxidase was determined on several occasions using both stop-flow and continuous flow methodology, and found to be 122.8 f 1.8 units/mg a t 25 "C. The activity was checked using a Gilford Model 240 Spectrophotometer. Ferricyanide generation was monitored a t 420 nm. The specific activity determined using five enzyme concentrations ranging from 3.9 to 39.0 units/l. was 122 f 2 units/mg which indicates excellent agreement and verifies that specific activities can be calculated, assuming Nernstian behavior, from the potential change vs. time. The Michaelis constant for the glucose oxidase reaction was found to be 2.48 X a t pH 6.3. In comparing the stop-flow and continuous flow methods for measuring glucose oxidase activity and glucose concentration, it was felt that the stop-flow method was preferred for the following reasons: the noise level was substantially smaller, the quantity of sample required was smaller, and the assay speed was somewhat faster for the stop-flow method. Normal assay times varied from 30 s to 2 min for the stop-flow method and from 2 to 4 min for the continuous flow method. In both cases, accurate measurement of
120
~~
Table 11. Glucose Oxidase Determination (Continuous Flow) Glucose oxidase, ppma
( K X 108)b
0.01794 0.03584 0.05378 0.07167 0.08961
7.74 15.87 23.64 31.38 39.50
K/[G.O.]ppm X IO6
4.31 4.42 4.40 4.38 4.41 Average = 4.38 u = 0.044 a Concentration in reaction mixture. b Calculated using Equation 10. Reagent contains 20 mM ferrocyanide, 0.2 mkl ferricyanide, 10 ppm peroxidase, and 60 000 ppm glucose.
Table 111. Glucose Oxidase Determination (Stop Flow) Glucose oxidase, ppm'
( K X 10')b
K/[G.O.)ppm X l o 6
3.49 3.44 3.55 3.52 0.1010 3.51 Average = 3.50 u = 0.041 a Concentration in reaction mixture. b Calculated using Equation 15. Reagent contains 20 mM ferrocyanide, 0.2 mM ferrocyanide, 1 0 ppm peroxidase, and 60 000 ppm glucose. 0.0202
0.0404 0.0606 0.0808
7.05 13.91 21.51 28.50 35.50
glucose in human serum was achieved using 0.1 ml of sample. I t should be possible to obtain satisfactory results with substantially smaller samples. The new methods can be summarized as follows. The differential potentiometric method described above is capable of providing excellent analytical results for the glucose and glucose oxidase assays. The analytical sensitivity particularly for the stop-flow method, because of small sample requirements, is good. Enzyme activities as low as 2 units/l. and glucose concentrations as small as 5 ppm were assayed. The instrumentation required is remarkably simple. Since a conventional reference electrode with a fixed potential is not required, the differential potential can be measured directly on high sensitivity recorders with no voltage bucking circuits required. The electrode and cell material are inexpensive enough to be considered expendable items. Good results were obtained on a set of electrodes over a period of several months. Reaction rates can be determined directly
through use of the Nernst equation with a minimum need for calibration and reference standards. The differential method described has been applied to other systems, although these will not be described in detail in this paper. In particular, the assay of serum lactic acid dehydrogenase using the stop-flow method has been done showing excellent correlations with values obtained by the standard Wroblewski method, and the non-enzymatic oxidation of ascorbic acid by ferricyanide has also been measured using the stop flow method.
ACKNOWLEDGMENT We would like to acknowledge the support and cooperation of The Ohio State University Hospital Clinical Chemistry Division in providing clinical samples.
LITERATURE CITED (1) D. N. Kramer, P. L. Cannon, Jr., and G. G. Guilbauit, Anal. Chem., 34, 842 (1962). (2) H. V. Malmstadt and H. L. Pardue, Anal. Chem., 33, 1040 (1961). (3) J. G. Montalvo and G. G. Guilbault, Anal. Chem., 41, 1897 (1969). (4) J. G. Montalvo and G. G. Guilbault, Anal. Chem., 41, 2093 (1969). (5) J. G. Montalvo, Anal. Eiochem., 38, 357 (1970). (6) G. G. Guilbault and J. G. Montalvo, J. Am. Chem. SOC.,92, 2533 (1970). (7) G. G. Guilbault and E. Hrabankova, Anal. Chem., 42, 1779 (1970). (8) G. G. Guilbault and Geza Nagy. Anal. Chem., 45, 417 (1973). (9) G. J. Paparillo. A. K. Mukherji, and C. M. Shearer, Anal. Chem., 45, 790 (1973). (;O) W. J. Biaedei, T. R. Kissel, and R. G. Bogaslaski, Anal. Chem., 44, 2030 (1972).
(11) G. Nagy, H. L. Von Storp, and G. G. Guilbault, Anal. Chim. Acta, 66, 443 (1973). (12) H. E. Booker and John Haslom, Anal. Chem., 46, 1055 (1974). (13) L. F. Culhen, J. F. Rusling, Arthur Schleifer, and G. J. Pagriello, Anal. Chem., 46, 1955 (1974). (14) W. J. Blaedel and T. R. Kissei, Anal. Chem., 47, 1602 (1975). (15) S. A. Katz, Anal. Chem., 36, 2500 (1964). (16) G. G. Guilbault, R. K. Smith, and J. G. Montaivo, Anal. Chem., 41, 600 (19691 (17) George Baum, Anal. Eiochem., 39, 65 (1971). (18) George Baum and Frank 8. Ward, Anal. Eiochem., 42, 487 (1971). (19) George Baum and Frank B. Ward, Anal. Chem., 43, 947 (1971). (20) Bernard F. Erlanger and Robert F. Sach. Anal. Eiochem., 33 318 (1970). (21) G. G. Guilbault, W. F. Guthnecht, S. S. Kuon, and R. Cochran. Anal. Eiochem., 46, 200 (1972). (22) W. R. Hessien, L. H. VonStorD. and G. G. Guilbault. Anal. Chim. Acta, 61, 89 (1972). (23) R. A. Llenado and G. A. Rechnitz, Anal. Chem., 44, 468 (1972). (24) R. A. Llenado and G. A. Rechnitz. Anal. Chem., 44, 1366 (1972). (25) R. A. Lienado and G. A. Rechnitz, Anal. Chem., 45, 826 (1973). (26) R. A. Llenado and G. A. Rechnitz, Anal. Chem., 46, 1109 (1974). (27) G. G. Guilbault and F. R. Shu, Anal. Chem., 44, 2961 (1972). (28) G. H. Zeman, Anal. Eiochem., 52, 63, (1973). (29) L. H. Goodson and William B. Jacobs, Anal. Eiochem., 51, 362 (1973). (30) D. S. Papastathopoulos and G. A. Rechnitz, Anal. Chem., 47, 1792 (1975). (31) W. J. Blaedel and Carter Olson, Anal. Chem., 36,343 (1964). I
- - - I
RECEIVEDfor review October 1, 1973. Resubmitted November 5, 1975. Accepted November 5, 1975. We gratefully acknowledge support by the National Institutes of Health, Grant GM-15821. R.I.P. was also supported in part by a National Science Foundation predoctoral fellowship.
Constant Potential Pulse Polarography Joseph H. Christie,' Larry L. Jackson, and Robert A. Osteryoung" Department of Chemistry, Colorado State University, f o r t Collins, Colo. 80523
The new technique of constant potential pulse polarography, in which all pulses are to be the same potential, is presented theoretically and evaluated experimentally. The response obtained is in the form of a faradaic current wave superimposed on a constant Capacitative component. Results obtained with a computer-controlled system exhibit a capillary response current similar to that observed in normal pulse polarography. Calibration curves for Pb obtained using a modified commercial pulse polarographic instrument are in good accord with theoretical predictions.
drop a t the same time in drop life and a t the same potential. There is no charging current component in this difference since the charging current is a function of potential and time only. The faradaic response is of the same form as in ordinary pulse polarography, but is diminished in magnitude by the diminution factor (1 - .\/76/3(T a)), .where 6 is the pulse width and T is the delay time. In this paper, we present a simpler variant of pulse polarography in which the diminished faradaic response is superimposed on a constant, but non-zero, capacitative component.
+
THEORETICAL We have previously reported on the background capacitative current developed in pulse polarography ( 1 ) . As the drop expands a t constant potential, a charging current must flow to maintain constant surface charge density on the electrode. This charging current is not compensated in the ordinary pulse polarographic experiment and the output current difference contains a term dependent on the difference between the charging currents flowing before and after the potential step is applied to the electrode. This point has been discussed in detail (2). The technique of alternate drop pulse polarography (2) was developed to compensate for charging currents by differencing the current at a pulsed drop and a non-pulsed
The wave-form for this variant pulse polarographic technique is shown in Figure 1. The name-constant potential pulse polarography-derives from the fact that each pulse is to the same potential Ez; the potential El during the delay time is different for each drop. This wave-form may be considered. the complement of the ordinary normal pulse polarographic wave-form. The current is measured only once in the life of each drop: a t time T + 6 while the potential is a t Ea. Using the same assumptions as in our earlier work ( 2 ) , we can write for the current 2
I = Zf(El,E2,7+ 6) - - k m 2 / 3 Q ( E a ) /+ ( ~6)'13 3
Present address, U S . Geological Survey, B r a n c h o f A n a l y t i c a l Laboratories, 345 M i d d l e f i e l d Road, M e n l o P a r k , Calif. 94025.
(1)
where k = 0.8515 cm2/g2l3,m is the rate of flow of mercury, and Q ( E )is the potential dependent charge density on the ANALYTICAL CHEMISTRY, VOL. 48, NO. 3, MARCH 1976
561
