urine was run for a total of 600 minutes, only three additional peaks appeared which did not correspond to those present in the simulated urine containing added ketosteroids. These were all small, and appeared a t 61, 88, and 133 minutes (Figure 1,A). It is not yet known whether these peaks represent ketosteroids or some other substances, b u t infrared microtechniques developed in this laboratory should prove useful in identifying such materials (10). I n Table I, ratios of peak areas for 17-ketosteroids obtained for the synthetic mixture injected directly (Figure 2,B) are compared with those obtained for the same mixture added to simulated urine (Figure 2 , A ) . These data suggest a small relative loss of 1l-hydroxyetiocholanolone and 1l-hydroxyandrosterone during isolation. Ratios of peak areas for 17-ketosteroids found in the normal male urine (Table I) are compatible with data for individual 17ketosteroids reported b y Dobriner (3).
Although these results are very encouraging, quantitative aspects of the procedure require further study. ACKNOWLEDGMENT
The authors gratefully acknowledge the kind help in connection with preparation of the column provided b y B. G. Creech, Texas Medical Center, Houston, Tex. LITERATURE CITED
(1) Brooks, R. V., Biochem. J . 68, 50
(1958).
(2) Cooper, J. A., Creech, B. G., Anal. Biochem. 2,502 (1961). (3) , , Dobriner. K.. J. Clin. Invest. 32. 940 I
,
(1953). (4) Girard, A.! Sandulesco, G., Helv. Chim. Acta. 19,1095 (1936). (5) Haahti, E. 0. .4.,Scund. J . Clin. Lab. Inoest. 13, Supplement 59 (1961). (6) Haahti, E. 0. A,, VandenHeuvel, W. J. A., Horninn, E. C..Anal. Biochem. 2,182 (i96i). -’ (7) Homing, E. C., Moscatelli, E. A.,
Sweeley,
c. C.,
751-2 (lg5’).
Chem. I d . (London)
(8) Peterson, R. E., Pierce, C. E., “Lipids and the Steroid Hormones in Clinical Medicine,” F. W. Sunderman, F. W. Sunderman, Jr., eds., p. 158, J. B. Lippincott Go., Philadelphia, 1960. (9) Preedy, J. R. K., Aitlten, E. H., J . Biol. Chem. 236, 1300 (1961). (10) Sparagana, M., Mason, W. B., ANAL. CHEM.34.242 (1962). (11) Teich, ‘S., Rogers, J., Lieberman, S., Engel, L. L., Davis, J. W., J . A m . Chem. SUC.75,2523 (1953). MARIOSPARAGANA’ W. B. MASON E. H. KEUTMANN Departments of Medicine and Biochemistry School of Medicine and Dentistry The University of Rochester Rochester 20, N. Y. RECEIVED for review May 21, 1962. AcThis investicepted June 18, 1962. gation was supported in part by research grant CY-1003 (C10) from the Yational Cancer Institute, U.S.P.H.S. Post-doctoral Fellow, National Institute of hrthritis and Metabolic Diseases, U.S.P.H.S.
An Impulse (Coulostatic) Relaxation Method for the Study of Rapid Electrode Processes SIR: The step-functional relaxation methods for the study of rapid electrode processesi.e., galvanostatic, potentiostatic, double-pulse galvanostatic, voltostatic, and faradaic rectification techniques-suffer the practical disadvantage that they require observation or control of voltages while large currents are passing through a n electrolytic cell. I n addition, the fact that the relatively low double layer impedance is in parallel with the faradaic impedance obscures features of interest in short time relaxation in some of these methods. I n principle, both problems would be circumvented if the system were perturbed by an impulse rather than a step function and relasation were observed after cessation of the impulse---thus, no net current flows through the cell, and the double layer capacitance discharges through the faradaic impedance so that these elements are in series rather than parallel configuration. Potential, current, and voltage impulses may be conceived, but at very short times, a t which nonfaradaic elements contribute substantially to the current-potential-time relation; only the last two arc practical, and the result is the same whichever is chosen.
from the leadine edge of a 25-volt Dulse from a Tektroiix i63 pulse gen&ator (rise time, 0.2 psec.) coupled to a conventional droDDine mercurv electrode .I mercury pool assembly (reskance, ca. 50 ohms) through a nominal 20 ppf. as observed on a Tektronix 535A oscilloscope with type CA vertical pre-
EXPERIMENTAL
*
simple and convenient mental method of approximating an impulse function is the coupling of a fast rise pulse generator to the electrolytic cell through a small condenser. Figure 1 shows the impulse derived
-
TIME
Figure 1.
Impulse voltage under conditions described in text Major vertical division = 0.5 volt Major horizontal division = 0.5 psec. VOL. 34, NO. 9, AUGUST 1Y62
1159
TlME
amplifier (scope rise time 23 nsec.), with dropping electrode and pool shortcircuited by immersing capillary in pool. The impulse half-width of 0.1 psec. in this arrangement is limited by the rise time of the pulse generator. For studies of cell processes the impulse is applied a t preselected times in drop life with the aid of a capillary rapper and sweep delay circuitry in the oscilloscope. With this relatively crude arrangement, potential measurements can be made within 2 psec. after onset of the impulse, a time limited by the recovery time of the Type D preamplifier used in the measurements. This time is of the same order as the shortest reported times of measurement with step-functional methods. More sophisticated circuitry is under development. RESULTS AND DISCUSSION
When measurements are made a t times after cessation of the impulse, the theory of the method is readily approached by approximating the impulse as a Dirac delta function. For
TlME
Figure 3. Potential-time relaxation of 1 mM mercurous nitrate, 1 .OmM KNOs. Cathodic impulse of Figure 1 applied at 1 .O sec. in drop life Major horizontal division: upper curve 5.0 psec.; lower curve 50 fisec. Maior vertical division = 1.0 mv.
4 Figuire 4.
Potential-time r*elaxatioin of
2M KCI, cathodic impulse of Figur'e 1 aPPdied at 2 sec. in drop lif e Major horizontal division = 50 prec. Major vertical division = 1 mv.
1 160
ANALYTICAL CHEMISTRY
small potential excursions, the theory for diffusion limited charge-transft,r can be obtained through a linearization procedure analogous to that of Berzins and Delahay for the galvanostatic method ( I ) . The potential-time expression for the impulse case is the derivatile of the result given by thcse authors. This result corresponds well with intuition because the systemdisturbing function in the impulse case is the derivative of the disturbing function in the galvanostatic step case. More dctailed discussion of the theory for various relaxation schemes will be given in works in preparation. Delahay and Mohilner ( 2 ) h a r e independently suggested a “coulostatic” method for the study of adsorption
kinetics. The principlp of their method is essentially the same as that of the method herein described, and the term is an a p t one because the system rrlaxes from the effect of rapid transfer of a small amount of charge from one electrode to the other. Qualitative examination of the experimental data of Figurw 2 and 3 shows clearly that relaxation times are much shorter in the mercurous nitrate than in the mercuric-EDTh system. I n the latter case the dccay is resolvable into two components suggesting a two-step relaxation process presumably involving a slow chemical step. Further discussion of these c a m will be given in future works. As anticipated, essentially no relaxation occurs
in solutions containing only supporting electrolytes. A typical example is shown in Figure 4. LITERATURE CITED
(1) Berzins, T., Delahay, P., J . A m . Chem. SOC.,77,6448 (1955). (2) Delahay, P., Mohilner, D. M., Ibid., in
press
W.H. REINMUTH~ C. E. WILSON
Department of Chemistry Columbia University New York 27, N. Y. RECEIVEDfor review June 4, 1962. Accepted June 19, 1962. Fellow of the Alfred P. Sloan Foundation, 1962-64.
Note on “An Impulse (Coulostatic) Relaxation Method for the Study of Rapid Electrode Processes by W. H. Reinmuth and C. E. Wilson” SIR: I n connection with the above communication by Reinmuth and Wilson, I wish to point out that work on the coulostatic method and its application to the study of fast electrode processes (9, 51, adsorption kinetics (4, 7 , 8), and the determination of traces ( I , 2, 6) has been carried out for some time in this laboratory. The principle of the coulostatic method was described in the paper (7) cited by Reinmuth and Wilson, and the expression “coulostatic method” was coined in that paper. Work in progress on application to electrode kinetics and analytical determinations of traces was announced in that paper, and application to sdsorption kinetics was discussed a t some length. .4 detailed investigation of the application to fast electrodc reactions has already been accepted for publication (3, 5 ) . This 1Toi-k is summarized as follows: Part I ( 3 ) . A new method (chargestep or coulostatic) for t h e kinetic study of fast electrode processes is discussed. T h e method involves charging of t h e electrode with a known quantity of electricity b y means of a coulostat t o cause a departure from t h e equilibrium potential, a n d recording of t h e overvoltage-time curve during t h e subsequent discharge of the double layer capacity c d by the electrode reaction. Overvoltage-time
curves are derived for the following cases: constant c d and linearized current-overvoltage ( I - 7 ) characteristic without mass transfer control or with mass transfer controlled by semi-infinite linear diffusion; constant c d and quadratic and cubic approximations of the I-? characteristic in the absence of mass transfer control; and variable double layer capacity. Conditions for pure control by either diffusion or the charge transfer reaction are derived, and it is shown that conditions can be selected for which diffusion need not be considered when the apparent standard rate constant does not exceed 0.2 to 0.3 cm. set.-' The method has about the same potentialities a8 the potentiostatic and single-pulse galvanostatic methods but has the advantage of somewhat greater simplicity of technique and interpretation of results. The coulostatic method also allows the determination of the differential capacity of the double layer even when a fast charge transfer reaction occurs on the electrode. Part I1 (5). Methodology for t h e coulostatic study of electrode kinetics is discussed, and application is made t o the discharge of Zn(I1) on a Znamalgam hanging drop in 1M KC1. Known quantities of electricity were supplied to the Zn-amalgam electrode by discharge of a small capacitor
(-300 ppf.), initially charged a t a known voltage (-10 volts), across the electrochemical cell. Overvoltage-time curves were recorded by means of a cathode-ray oscilloscope in the interval 0 to 40 psec. after charging. The theory of Part I was verified experimentally, and essentially pure control by the charge transfer reaction was achieved. The influence of the cell resistance is treated quantitatively. Kinetic parameters a t 25’ 1’ C.: apparent standard rate constant, 0.0041 cm. sec.-l; transfer coefficient. cy = 0.30.
*
LITERATURE CITED
(1) Delahay, P., ANAL.CHEM.,in press. (2) Delahay, P., Anal. Chim. Acta, in
press.
(3) Delahay, P., J . Phys. Chem., in press. (4) Delahay, P., Technical Report to the
Office of Naval Research, Project NR 051-258, May 1962. (5) Delahay, P., Aramatata,A., J . Phys. Chem., in press. (6) Delahay, P., Ide, Y., unpublished data. ( 7 ) Delahay, P., Mohilner, D. M., J . Am. Chem. SOC.,in press. (8) De!ahay, P., Takemori, Y., unpublished data.
PAULDELAHAY
Coates Chemical Laboratories Louisiana Sta.te University Baton Rouge 3, La. VOL. 34,
NO. 9, AUGUST 1962
1161
