a linear velocity, also increasing the HEPT. This is apparently a reasonable enough conclusion from the usual plot of the van Deemter equation as shown in Figure 1. Furthermore, when the decompression effect is taken into account (1, 3, 4), it is seen that a local plate height contribution made a t high pressure makes a greater _contribution to apparent plate height ( H ) than a similar local plate height contribution made at lower pressure, as shown by the equation
When the pressure gradient is small,
( ~ ; / p 3does ~ not differ significantly from unity anywhere in the column, but when the pressure gradient is large, ( ~ , / f i ) ~large i s a t the head of the column and small at the tail of the column. Thus, the head of the column makes a greater than normal contribution to apparent plate height, while the contribution of the tail of the column is reduced. The net effect of inlet-tooutlet pressure ratio on apparent plate height is, therefore, not significantly large, contrary to the earlier published views. What is significant, however, is the improvement of apparent plate height a t high average column pressure as compared with low average column pressure, although this gain is also nullified if speed of analysis is con-
sidered, since the number of plates obtainable per unit time under otherwise equal conditions varies inversely with pressure. LITERATURE CITED
( 1 ) Giddings, J. C., ANAL. CHEM.35, 353 (1963). (2) Ibjd., 36, 741 (1964). (3) Giddings, J. C., Seager, S. L., Stucki, L. R.. Stewart. G. H.. Zbid.. 32. 867 (1960j. (4) Sternberg, J. C., Poulson, R. E., Zbzd., 36, 58 (1964). I
.
JAMES C. STERNBERQ Beckman Instruments, Inc. Fullerton, Calif. RECEIVED for review December 31, 1963. Accepted February 3, 1964.
Time Dependence of A.C. Polarographic Currents SIR: Considerable interest has attended the study of time dependence of d.c. polarographic currents. Examination of the variation of d.c. currents with mercury column height (varying drop-life) or the more sensitive studies of instantaneous currents over a single drop-life are of considerable use in d.c. polarographic studies of kinetics and mechanisms of electrode processes. Charge transfer, homogeneous chemical reactions, adsorption, depletion, and stirring effects all show characteristic influence on such investigations under suitable conditions (6, 7 , 12). Similar studies of ax. polarographic currents have not been reported. Most likely responsible for this is the fact that, until recently, a x . polarographic and faradaic impedance theory suggested no useful application of such measurements. Early theoretical work on the reversible and quasi-reversible (2) a.c. polarographic impedance indicated no time-dependent terms except for very short-lived transients (1) and the electrode area when the dropping mercury electrode is employed. If such is the case, then the faradaic alternating current amplitude observed at a dropping mercury electrode will be independent of mercury column height and will vary with t213 (t = time) over the life of a single drop. Phase angles between faradaic alternating current and applied alternating potential were predicted to be timeindependent, even with the dropping mercury electrode-i.e. , phase angles are independent of electrode area. These conclusions alone would suggest that little is to be gained from investigations of a.c. polarographic current dependence on mercury column height or a.c. polarographic current-time curves. However, the recent, more rigorous theoretical work of Matsuda 922
e
ANALYTICAL CHEMISTRY
(8) on the a s . polarographic wave with electrode processes controlled by diffusion and charge transfer kinetics (the quasi-reversible case) indicates that the simple behavior predicted by earlier theory is not always t o be expected. Influenced by Matsuda's work, we have undertaken a theoretical and experimental investigation of the time dependence of a x . polarographic currents. This communication deals with some preliminary conclusions. A more detailed account will be given a t a later date. THEORY
Matsuda's equation for the a.c. polarographic wave with a quasireversible electrode process and an applied alternating potential given by
E(t) =
Ed.c.
- AE sin ut
(1)
may be written (for small values of A E and reduced form of redox couple initially absent from solution) (8)
I ( d ) = I(rev.)F(W2) X
sin [ut
+ cot-'
(1
+
e)] (2)
@ = l - a
D = Do@DRa
f
(1.61
+
(1.13 -I-Ati/z)z
(3)
(4)
(7) (8)
and Z(rev.) is the amplitude term for the reversible a.c. polarographic wave given by n2F2ACo*( ~ D o ) ~ / ~ A E I (rev.) = (9) j 4RT cosh2 2 Notation used in this communication is identical to that used in a previous publication (13). These equations predict a time dependence, incorporated in the F(W2) term, not predicted by earlier theory. Matsuda's equations apply to the expanding plane electrode (8),a simplified model for the dropping mercury electrode. However, one should not conclude that the additional time dependence is introduced by drop growth, a factor also not considered by earlier theory. One can show easily, using Matsuda's approach, that for diffusion to a stationary plane electrode the a x . wave equation is identical t o Equation 2 except for the definition of F(XtlI2). For diffusion to-a stationary plane electrode, F(Xt1'2) is given by (16) F(XtlI2) = I (ae-'
+
where
= f08fRQ
(6)
- fl)ehZterfc(Xtllz) (IO)
Thus, time dependence also may occur with a stationary electrode. Drop growth influences the magnitude of the time dependence, but is not its source. The F(W2) term indicates that, with the dropping mercury electrode, a departure from the independence of the alternating current amplitude on mer-
a 0.00.
0.80
.
-0.06
-0.04.
-0.02
E0.c.-
0.02
0.00
El12
0.04
0.06
C V O L T S VS. S.C.E.)
Figure 1. Calculatc:d a.c. polarogram (center portion) a t varying mercury drop-life 1 = 25.0' C., kn = 1.0 X cm. second-', (Y = 0.40 n = 1.0, CO+ = 5.0 X lO-'M, D = 5.0 X cm? second-' cni?, A€ = 5.0 X lo-' volt A = 3.5 X o = 40s radians second-' Shows alternating current at end of drop-life.
----
-_--__
-----
---
T 7 7
= 12.0 seconds = 9 . 0 seconds = 5.0 seconds
cury column height and the t 2 ' 3 variation of the faradaic current-time curve may be observed under proper conditions. Examination of Equations 3 or 10 shows that for W2>50 F(Xt'I2) = 1 (11) and the time dependence disappears, the a.c. wave equation reducing to that given in the earlier theory ( 2 ) . For normal drop-life (3 to 10 seconds), significant deviation from the simple theory is predicted when kn is less than about lo-* cm. set.-', that is, when the charge transfer rate is sufficiently slow that charge transfer kinetically influences the d.c. polarographic process. Thus, the a.c. polarographic wave height and shape is predicted to be independent of mercury column height when the d.c. process is reversible itnd dependent on mercury column height when the d.c. wave is quasi-revertible. The time dependence also disappears when W2 1 cm. second-’ ( 1 1 ) ] and the Ti(IV)/Ti
(111) system in 0.20OM oxalic acid [kA = 4.6 x lo-* cm. second-’ ( I C ) ] show no dependence of alternating current amplitude on mercury column height as would be expected because the heterogeneous charge transfer rate constants exceed 10-2 cm. second-’. However, the V(III)/V(II) system in 1M H2SO4 [ k ~= 1 X cm. second-’ ( l o ) ] shows a definite dependence on mercury column height which varies with d.c. potential as predicted by theory. Some typical results are shown in Figure 2. The cross-over potential, Ed.c, *, is independent of alternating potential frequency in agreement with theory. The value of a calculated from the Ed.?.*potential was 0.46 + 0.03, in excellent agreement with the value reported by Randles (10) for this system based on conventional faradaic impedance and d.c. polarographic measurements. These initial results show promise regarding the validity of the theory and the applicability of a x . polarographic time-dependence studies. Additional, more detailed, experimental investigations will be attempted. Among them will be observations on systems involving chemical kinetic and adsorption effects, quantitative examination of faradaic alternating current-time curves at the dropping mercury electrode, the dependence of phase angles on mercury column height, etc., and similar studies with higher ha,rmonic currents. LITERATURE CITED
(1) Berzins, T., Delahay, P., Z. Elektrochem. 59, 792 (1955). (2) Breyer, B., Bauer, H. H., “Chemical
Analysis,” Vol. 13, P. J. Elving and I. M. Kolthoff, eds., Chap. 2,. Inter. science, New York, 1963. (3) R. P.. J . Electroanal. Chem. . ,5,Buck. 295 11963). ’ (4) Delahay, P., in “Advances in Electrochemistry,, and Electrochemical Engineermg, Vol. I , P. Delahay and C. W. Tobias, eds., Chap. 5, Interscience, New York, 1961. (5) Hung, H. L., Delmastro, J. R., Smith, D. E., J . Eleclroanal. Chem., in press. (6) Kuta, J., Smoler, I., in “Advances in Polarography,” Vol. 1, I. S. Longmuir, ed., pp. 350-8, Pergamon, New York, 1960.
(7) Kuta, J., Smoler, I., in “Progress in Polarography,” Vol. 1, P. Zuman, ed., with collaboration of I. M. Kolthoff, Chap. 3, Interscience, New York, 1962. (8) Matsuda, H., 2. Elektrochem. 62, 977 (1958). (9) Matsuda, H., Ayabe, Y., Bull. Chem. SOC. J a p a n 28, 422 (1955). (10) Randles, J. E. B., Canadian J . Chem. 37, 238 (1959). (11) Randles, J. E. B., Somerton, K. W., Trans. Faraday soc. 48, 937 (1952). (12) Reilley, C. N., Stumy, W., in
“Progress in Polarography, Vol. 1, P. Zuman, ed., with collaboration of I. M. Kolthoff, Chap. 3, Interscience, New
York, 1962. (13) Smith, D. E., ANAL. CHEM.35, 602 (1963). (141 lbid.. D. 610. (15) Zbid.; ‘p. 1811. (16) Smith, D. E., Northwestern Uni-
versity, Evanston, Ill., unpublished work,-1963.
HOYINQ L. HUNQ DONALD E. SMITH
Department of Chemistry Northwestern University Evanston, Ill. RECEIVED for review December 20, 1963. Accepted February 3, 1964. Research supported by the National Science Foundation.
Effect of Metal tons on Nuclear Hyperfine Coupling Constants in EPR Spectra SIR:We have investigated the effects of metal ions on the nuclear hyperfine coupling constants of the electron paramagnetic resonance (.EPR) spectra of a variety of anions of aromatic nitro compounds. The anion radical of p-chloronitrobenzene was selected as a model system since it3 EPR spectrum consists of three well resolved triplets resulting from interaction of the unpaired electron with i,he N14 nucleus, two equivalent (ortho) protons and two more equivalent (meta) protons. The radical anions were generated electrochemically in dinethylformamide (DMF) containing the metal ions to be investigated as suppor ,ing electrolytes. The effect of the metal ion on the W 4 coupling constant (aN)was investigated.
Coupling constants are believed to have better than 1% relative error. The variation of U N is shown in Figure 1 as a function of concentration of the various supporting electrolytes. The figure shows first that the shifts in uN caused by metal ions are considerably greater than those occasioned by interaction with water or other hydrogen-bonding solvents when compared on a concentration basis (4). The shift in a N qualitatively follows the solvation energy and other physical parameters of the various cations in DMF. No metal ion couplings are observed in the E P R spectra and.bhe exact nature of the interaction between the anion radical and the metal cation species is
not known. A rapidly exchanging metal ion system should show a lack of metal ion coupling. Also, since all solutions contain about millimolar water under real experimental conditions, the interaction may be via aquo-metal ion species. The E P R spectra also show a line broadening effect most markedly observed in the odd spin states of the nitrogen. A similar line broadening does not occur in aqueous-dimethylformamide mixtures with tetraethylammonium perchlorate as supporting electrolyte, indicating that this effect is definitely caused by the presence of the metal ions. Metal ion effects are also noted in the cyclic voltammetry of the nitro compounds. The first peak, corresponding VOL. 36, NO. 4, APRIL 1964
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