ROBERTA. OSTERYOUNG AND JOSEPH H. CHRISTIE
1348
tion of the ionic head of -SO4- to the hydration is eliminated. The hydration behavior of the two shortest SDPS values is similar to that of SDS, the presence of the oxyethylene part being less effective. The reason for this is not clear. However the following explanation seems possible: (1) the hydrating water associated with the -SO4- ionic head hinders the oxyethylene part from hydration through its steric effect to make the hydration incomplete or (2) the structure of the micelles formed by these two surfactants is such a structure that the hydration occurs less effectively in the oxyethylene part. Elworthy and Macfarlenes have shown that the hydration of nonionic surfactants such as polyoxyethylene hexadecyl ethers is highly dependent on the geometry of the micelle. With the SDPS having n 2 3, there is a linear relaition between the hydration of the polyoxyethylene chain and the chain length. The number of hy-
drating water molecules per oxyethylene unit, which is estimated from the slope of the linear portion in Figure 5, is approximately 5.0, which is comparable with a value of 4.3 estimated from the data of Kushner.’ The linear relationship would suggest that the shape of the micelles remains unchanged, Le., spherical, in the range of oxyethylene units studied since any change in the shape of the micelles will be reflected in their hydration. It is shown, for example, that the spherical micelles of nonionic surfactants are more hydrated than the rodlike ones.6
Acknowledgments. The authors express their thanks to Dr. H. Kita, Director of Research Laboratories, for his encouragement and permission to publish this paper. They also thank Dr. K. Kakiuchi for his measurements of ultracentrifugal sedimentation and Mr. K. Majima for his help in preparing the samples.
A Quantitative Study of Desorption in the Zinc(I1)-Thiocyanate System
by Robert A. Oeteryoung and Joseph H.Christie North American Aviatwn Scienee C a t e r , Thouand Oaks, California 91360 (Received September SO, 1966)
Potential step chronocoulometric, potential sweep-step chronocoulometric, and chronopotentiometric data indicate that Zn(I1) which is adsorbed at a mercury electrode at -300 mv 218. sce from a thiocyanate solution desorbs rapidly when the potential is changed to -900 mv. A theoretical treatment is carried out for prescribed desorption conditions and the theory is compared with experiment. The error introduced into chronopotentiometric adsorption studies by this “desorption effect” is discussed.
Introduction In a previous publication, we presented qualitative evidence for the desorption, during the double-layer charging region of a chronopotentiogram, of Zn(I1) adsorbed from a thiocyanate solution.’ It wmi pointed out that this “desorption effect” could introduce serious error in the chronopotentiometric study of adsorption. The present work presents further experimental studies of desorption in the ainc (11)-thiocyanate The Journal of Phy&al Chemirtry
system and presents a quantitative treatment of chronocoulometric and chronopotentiometric experiments under the prescribed conditions for desorption. The reduction of Zn(I1) in thiocyanate media appears to be an ideal system for the quantitative study of desorption. Double potential step chronocoulometric (1) J. H. Christie and R. A. Osteryoung. Anal. Chem., 3 8 , 1620 (1966).
DESORPTION IN THE ZINC(II)-THIOCYANATE SYSTEM
1349
experiments indicate that increasing amounts of Zn(I1) are adsorbed as the initial potential is made increasingly anodic from -900 mv. Figure 1 shows n F r as a function of initial potential, obtained from double potential step chronocoulometric experimenb2 Biased chronopotentiometric measurements yield qualitatively similar results.' An initial potential can therefore be chosen at which a large amount of Zn(I1) is adsorbed and complete desorption can be obtained just prior to the Zn(I1) reduction wave (at about -1.0 v).
Theory Chronocoulometry. An electrode, at an initial potential, Eo, at which an oxidant 0 is adsorbed to the extent
of r moles/cm2 or nFP coulombs/cm2, is stepped to a potential El, at which the species 0 desorbs. Only 0 is initially present in the solution and El is such that no faradaic current flows. We assume that the desorption is instantaneous and is complete. After a time, a, the potential is stepped to E2, at which the reaction
-300 -400
-500 -600
E 1,
O+ne+R
-700 -800
-!
)O
mV vs.S.C.E.
(1)
takes place at its diffusion-limited rate.a The chargetime behavior for t > a is given by
Figure 1. nFr as a function of initial potential, obtained from double potential step chronocoulometric experiments.4 1.0 mF Zn(I1) in 0.5 F NaSCN 0.5 F NaNOs.
+
observed.) The resulting i0-r behavior, derived in the Appendix, is given by ?r
a
where *COis the bulk concentration of 0 and Aqo2 is the charge consumed in charging the double layer from Eo to E2. The other symbols have their usual electrochemical significance. A derivation of eq 2 is given in the Appendix. The E-t function and a Q-t response are shown in Figure 2a. If a = 0, eq 2 reduces to the familiar chronocoulometric equation for the presence of a d s ~ r p t i o n . ~ - ~
i o d T a=
nFd&*Co 2
Fr + n---[d~ - dT-1 U
(4) where a is the length of time taken for desorption and T is the time from the start of the experiment to the transition time. If we identify a with the time spent in the double-layer charging region, then a a ) = 0, and using the integral equation for Dirichlet boundary conditions, eq A 2
Q(t > a ) =
2nFflo*Co1/t_a
+
1/; n F I2' ; [ t{ T
-
sin-'$]
(All)
To get the experimentally observed charge, we add the appropriate double-layer contribution and we add +nFF to adapt our result to the nonfaradaic desorption.
&(t> a) = nFI'{ 1
The Journal of Physical Chemistry
+
l/znF1/ao*C nFF -(1/; a
2 n F 1 / Z * C 0 6 .
l/?r
+ ;2 [ &t . l
- t_U sin-'
+
d;]} +
Aqm (A12)
