EXPERIMENTAL
The study was made with apparatus carefully designed for fast analyses. The catharometer is of a new design, having a dead volume of 40 pl. and a response time of less than 0.1 second, the recorder (Graphispot, S.E.F.R.A.M., Paris) has a time constant of 0.25 second. Experiments were made with two columns described in Table 11. Values of H were measured for different values of injection time using several flow rates; the beginning and the end of the injection were recorded on the chromatogram using a margin marker. Typical results for air peaks are shown Figures 1 and 2. From these results i t may be concluded that H is given by the expression: H = H oh + t2R2u2 7
Table 111. Values of X Solute Column 1 Column 2 Air 0.027 n-C6 ... 0: 005 n-Ca ... 0.030 n-C, 0.07 ...
H O being the conventional expression of H.E.T.P. as previously given and discussed ( 1 ) . Table I11 gives the values of h found in our experiments. Some discrepancies may be noted, especially for n-pentane on column 2, but the results do not shorn any trend. These values are consistent with a n injection time equal t o 6 T which gives a of 0.028. This value may of course depend on the manner in which the beginning and end of the injection are appreciated. These experiments are
not sufficient t o ascertain this last point but the dependence of H on the square of t, R, and u,and the inverse of L is supported by the experiments reported here. Two conclusions may be drarrn: careful attention must be paid t o the design of injection system when very fast analyses are sought; when a van Deemter curve is drawn for a column, a constant injection time is used. Thus, for a large flow rate the new term becomes very important and H increases with u2. LITERATURE CITED
(1) Giddings, J. C., "Chromatography," Erich Heftman, ed., pp. 20-31, Reinhold, S e w York, 1961. GEORGES GUIOCHON
Ecole Polytechniyue Paris, France RECEIVEDfor review October 22, l%2. Accepted Ileceniber 12, 1962.
Chronopotentiometry at Rotating Disk Electrodes SIR: Interest in rotating disk electrodes is steadily increasing among students of electrode processes ( 5 ) probably because the theoretical behavior for both reversible and irreversible processes is developed, use of the electrodes is convenient, and results are remarkably reproducible. Attention has been given to experimental studies using constant potential electrolyqis ; although rotating disks have been useful also for constant current processes. For instance, chronopotentiometry a t moving electrodes is possible, but does not appear to have been reported in the literature. A t first glance, such an application may not seem feasible because convection limited processes are not so conveniently controlled a5 diffusion limited processes. Our preliminary data suggest that chronopotentiometry a t rotating disk electrodes is possible, but t h a t reproducibility of transition times is not so great as n a s originally hoped. It has been found, experimentally, that id 2 becomes nearly constant for a given rotation speed a t sufficiently large applied constant currents. The available range of current for constant i+ moveq t o higher values with increasing rotation speeds and the greater double layer charging current produces positive del iations in i+. A mathematical treatment of the transition time can be given and some important results are reported here. When i t is assumed that diffusion prevails n-ithin the boundary layer of thickness 6 (the Levich thickness)
400
ANALYTICAL CHEMISTRY
and convection determines the concentrations outside, the boundary conditions for the reaction 0 ne- + R are :
+
C o ( ~ , t )= Coo
z
b0
t = 0
(la)
It has been shown in slightly different form by Bowers, et al. ( 3 ) that: C,(O,t)
=
where the term on the right side of Equation 3, preceding the bracket, is the fundamental constant of a static chronopotentiometric experiment. This equation predicts that i r 1 I 2 and r increase ivith decreasing values of current for a given value of 6. I3y writing boundary conditions given in Equations ICand Id, we have approximated the actual condition of the boundary layer. Gregory and Riddiford (6) have shown that the boundary layer in fact extends over a distance of twice the Levich thickness from the disk, and that nithin this boundary layer. diffusion gradually predominates over convection such that, a t the surface of the diqk, transport is purely diffusive. It is poisible that a better approximation would be to operate in terms of the thicknes. of the fictitious Nermt layer (-0.8934 6). u
coo - 2 x x
(2b)
Both of these reduce to the semi-iiifinite case nhen 6 -+ m . At the tranii= 0 and tion time, CO(O,r)
II-ith decreasing current. i ~ ' / ? increases rapidly and becomes difficult to meabure n-hen the outer boundary of the depletion layer interzects the Levich thickness a t time T or befcre.
1000
Then we can define a critical current for practical measurements where approximately 6
900
(4)
1/007.=l and
800 In T iew of the Le\-ich rquation relating boundary layer thickness and the angular velocity ( 8 )
cn
E
700
w
a 5
a o 600 for Dc. in sq. em. i)er ,*ecoiid, V , the kineniat,ic viscosity in sq. em. per second and U , the angular velocity in radian* per second, t h r critical current in ampere.< i.q givrn by i, = 0.606 0.62
n
0 5 I +
500
z
W
E
x ~
U
a ~
~
~
*
/
3
~
4; w l / a ~
~
y
-
1(7a) / 6
when concentration is expressed in moles per cubic em. and area in Fq. cm. 1t is clear that
0
400
c3
z -
k 300
5
-
-I
Tliu>, to acliieve transition times in a given experiment using a rotating disk electrode, t,he availahle currents should be greatcr than the criticd value given by Equation i a or i b . A s a test of the t,heory, the reduction of 0.00403F K3Fe(CS)6 in 0.W KCl wi-: studied using a platinum disk of 0.317 sq. cm. area,. T o ensure constant rotation speed and freedom from horizontal wobbl~: limiting current3 were mcviwrcd as R funct'ion of rotation speed a t several applied Iiotentials on thr conr.ection limited plateau. The results are slion-n in Figure 1 along with the tlieoretical curve calcu1at)ed from the Levich equation. The theoretical slope is:
(8)
and as obtained u-irig Yon Stackelberg'-: difl'usion coefticient (10) for fer,ric;-anidc in liotashium chloride, Do = i . 7 X 10-6 q.rm. per wcond. and the kinematic viscosity v = 0.8933 X IO-% sq. cm. prr second ( 7 ) . The experiniental curve.; haye smaller than thtwreticd slopes, and similar results have rccently been obtained by Azim and Ritldif'ord ( 1 ) for the reduction of a ferricyanide solution with a different ionic strength. It is possible that a migratory contribution t o the current exists t o diminish the slope. On the
200
I O 0
0
2
I
3
4
5
(REVOLUTIONS PER SECOND) Figure 1 ,
"*
Limiting currents for potassium ferricyanide reduction Solution: 0.00403F K3Fe(CN)6ond 0.5F KCI Applied potentials: 0 -0.2 volt vs. SCE 0 -0.1 volt VS. SCE X 0.0 volt vs. SCE E o = $0.1 14 volt vs. SCE
other hand, our present rotat'ing disk elect'rode is not the opt,imurn design required for use with Equation 6 hecause it corresponds t o the case of a rotating semi-infinite cylinder. Rather us. i than base calculations of i+ using Equation 3 on 6 values gi\-en by 1,kpation 6, we h a r e used the experimpntal ~ a l u eof 6 given by Equation 9. 6 (experimental) =
0.650 X A'1'2
ciii.
(9)
Calculated curve5 of i+I2 u,c. i and experimental points are shon n in Figure 2. The intercept of S = 0 has the and vas obtained value 303 pa.
from the geometric electrode area and the diffusion coefficient given above. Experimental values of i+* for the static case are from 1 to 6% high at low currents, and this presumably arise. from natural convection. The electrode was oriented horizontally and diffusion occurred in an upward direction. Earlier results of Laitinen and Kolthoff (9) showed that vertical diffusion promoted convection in ferricyanide reduction. I n addition, the rotating electrode could not be shielded which would tend to encourage convection as Bard ( 2 ) has shown. Agreement is fair at low rotation speeds and cleriations at higher rotations probably result from the large uncertainty in chooqing transition times from the VOL. 35, NO. 3, MARCH 1963
401
450
I
0.g3
P lc N= 20
5
4 00
-3 N \
w
9
%
v,
6,
P O
n
I Q 0
5
N= 4 0
350
+\
I
0
(u
>
b .4
300
I
I
I
I
500
1000
1500
2000
I
CURRENT- MICROAMPERES Figure 2.
Plots of
iT1”
vs. i for various rotation speeds N in revolutions/second
Solid curves calculated from Equation 3 using experimental 6, and iecalculated from Equation 5 Static = 3 0 3 rnicroarnp.-sec.’/2 calculated from: Ci = 0.00403F KaFe(CN)e A = 0.317 sq. cm. DO = 7.7 X sq. cm. per second N = O 0 N = 0.15 0 N = 0.93
+
-0-
N = 5 N = 2 0
N =40
the platinum disk was coated with recorded plots. Apparently some natparaffin wax to eliminate chemical ural convection persists at slow rotation speeds. Positive deviations of i ~ ~ ’ * attack. A three-electrode constant current supply using operational amplifiers, from a constant value at high currents patterned after DeFord’s ( 4 ) arrangefor all rotations result from the double ment, was used. Potential-time curves layer charging (2). were recorded with a CEC Model 5-124 Recording Oscillograph. Rotation EXPERIMENTAL speeds were measured with a Strobotac Type 1531-A. The belt driven electrode assembly and electronic controlled variable speed LITERATURE CITED motor were mounted on a rigid support vibration insulated. The rotating elec(1) Azim, S.,Riddiford, A. C., ANAL. trode was a 5-mil. thickness platinum CHEM.34, 1023 (1962). (2) Bard, A. J.,Ibid., 33, 11 (1961). disk sealed with DeKhotinsky cement (3) Bowers, R. C., Ward, G., Wilson, C. t o a l/r-inch diameter thick wall glass M., DeFord, D. D., J . Phys. Chem. 6 5 , capiliary tube. The upper half of the 672 (19611. capillary was encased in a metal tube (4) DeFord,’ D. D., private communicawhich fitted snugly in the bearing astion presented a t 133rd American sembly. The capillary was waxed into Chemical Society Meeting, 8an Franthe metal sheath. Exposed cement near cisco, Calif., April 1958.
402
ANALYTICAL CHEMISTRY
(5) Galus, Z., Olson, C., Lee, H. Y. Adams, R. N., ANAL. CHEM.34, 164
(1962). Many earlier references are given in this citation. (6) Gregory, D. P., Riddiford, A. C., J . Chem. SOC.3756 (1956). ( 7 ) Harned, H. S., and Owen, B. B., “The Physical Chemistry of Electrolytic Solutions,” 2nd ed., Reinhold Publishing Corp., New York, 1950, p. 177. (8) Levich, V. G., Acta Physiocochim. U.R.S.S. 17, 257 (1942). (9) Lingane, J. J., “Polarography,” Interscience, New York, 1952, Vol. I, p. 28. (10) Von Stackelberg, M., Pilgram, M., Toome, V., 2. Elektrochem. 57, 342 (1953). R. P. BUCK H. E. KELLER Bell & Howell Research Center Pasadena, Calif. RECEIVED for review November 23, 1962, Accepted January 15, 1963.
