~~
Table I.
Sample n-Amyl-alcohol
Data Elution time, min
Adsorbent Sterling FT Sterling FT (Hz treated) n-Butyric acid Sterling FT Sterling FT (He-treated) N-Methylaniline Sterling MT Sterling MT (Hdreated) This is the minimum amount to times.
T, "C 160
Minimum sample size, go 1 X lo-'
1.3
160 190
3 X 10-9 1 X lW4
1.3 1.4
190 243
1 X lo-' 1 X lo-'
0.7
0.7
1.4 243 1 X lo-' obtain reproducible retention
lowered, so that treated FT and MT give considerable scope for rapid analysis with columns of high performance. However, the most interesting point arising from this work is the possibility of eliminating bleeding of the stationary phase, which causes serious trouble for gas chromatographymass spectrometry coupling. The use of our columns coupled with mass spectrometry can lead to cleaner and more reliable mass spectra, and, consequently, to easier identification of an extended range of compounds, including the very polar, high-boiling and multifunctional ones, which are contained in very complex mixtures of interest in the fields of biological and biomedical chemistry. ACKNOWLEDGMENT
bonding compounds with hydrogen-treated graphitized carbon blacks is not only competitive with, but in many cases definitely more convenient than, GLC on porous polymers. The range of linearity of GSC is extended so that small amounts of any polar compound can be detected. Column efficiency is enhanced and retention times are considerably
The authors are indebted to A. Liberti for helpful discussions and R. Samperi for technical assistance. Received for review March 30, 1971. Accepted June 22, 1971. This work is supported by the Consiglio Nazionale delle Ricerche.
Electrooxidation of Iodine on Smooth Platinum in Acetic Acid Medium Influence of Adsorption of Electrode Products upon Voltammetric Limiting Currents Roland0 Guidelli and Giovanni Piccardi Institute of Analytical Chemistry, University of Florence, Florence, Italy Iodine in acetic acid gives a single anodic voltammetric curve on smooth platinum. The mean limiting current decreases progressively with the rest time of the electrode at a given constant potential tending to an asymptotic value, owing to the adsorption of electrode products. The use of a normal pulse-polarographic technique applied to a solid platinum microelectrode permitted us to eliminate the inconvenience due to adsorption. I t was thus possible to attribute the anodic wave of iodine to its electrooxidation to I". A plausible rate-determining stage for the overall electrode process l2+ I' is the following: l2+ I 1 lsdsorbed e. Some general considerations about the influence of the adsorption of electrode products upon voltammetric limiting currents are presented.
IN A PRECEDING paper (I) the authors reported that in acetic acid, iodine gives two cathodic waves on a smooth platinum microelectrode, due to its reduction to Ia- and I-, respectively. Tne aim of the present work is to study the behavior of iodine toward electrooxidation on platinum in acetic acid medium. To this end two different polarographic techniques were employed, herein referred to as techniques I and 11, both making use of a platinum microelectrode with periodical renewal of the diffusion layer (DLPRE) described by Cozzi
and coworkers (2). In the cell of the DLPRE a Teflonfinned piston containing an iron nucleus is moved by a magnetic coil, activated by short current pulses, producing a rapid laminar flow of the solution around a hemispherical platinum microelectrode. This flow is interrupted abruptly by a valve about 30 msec (washing period, t,) from its start. With technique I, the cell of the DLPRE is directly connected to a conventional polarograph. In this case the piston is moved at regular intervals of time t l , of the order of 3 to 5 sec. The washing period, t,, is therefore followed by a much t l , during which the solution longer period of time, (tl - t,) is perfectly still. If the potential applied to the DLPRE is such as to allow the Occurrence of a charge-transfer process, then, during the washing period t, the depolarizer reaches the electrode surface both by diffusion and convection. At the end of period t,, the depolarizer moves only by diffusion, so that the instantaneous current decreases with time. At the end of period tl, a new washing sweeps away to a large extent the effect of prior electrolysis ; hence, the instantaneous current increases sharply, reaching a maximum value, ,.,i at the end of the new washing period. The geometry of the cell and the energy of the washing are so adjusted that ,i
(1) R. Guidelli and G. Piccardi, A n d . Lert., 1, 779 (1968).
(2) D. Cozzi, G. Raspi, and L. Nucci, J . Elecrroanal. Chem., 12, 36 (1966).
+
+
-
ANALYTICAL CHEMISTRY, VOL. 43, NO. 12, OCTOBER 1971
1639
T
exchanges charges with the electrode. The applied potential is kept at the’value EJ for a given period t,, during which n o washings are performed. The current flowing during t J is integrated electronically. Upon submitting the electrode to several cycles (ti t,), differing only by the value of E, and recording the amount of electricity Q involved in each single period t / against E,, a charge-potential curve is obtained having the shape of a normal voltammogram. With technique 11, the instantaneous current flowing during tt is followed oscillographically and is measured from the start of period t / , Le., from the instant in which the potential jump is effected. The main difference between technique 11 and technique I consists in the fact that, with technique I, the electrode is constantly held under polarization at the potential E,, whereas, with technique 11, the electrode is continuously pre-treated at the initial potential E, for a given period of time ti, before each single integration of current at the potential El.
+
EXPERIMENTAL
i’
*2
v
Figure 1. Anodic charge-potential curve of 10-3M IZ and 0.3MLiC10, in acetic acid f, =
90 sec; t/ = 3 sec; E,
=
$1.3 V
Voltammograms were recorded using a three-electrode system consisting of a Metrohm Polarecord E 261 polarograph coupled with a Metrohm iR-Compensator E 446. Charge-potential curves were recorded using an apparatus similar to that described in Reference 3. The apparatus employed in the present work, however, unlike that of Reference 3, was driven by a multichannel electronic timer, which permitted us to maintain E, rigorously constant during the period tf and to perform several “washings” of the DLPRE during each single period t,. The potential of the DLPRE was controlled us. a Ag/AgCl, 0.3 LiC1(CH3COOH) reference electrode. The supporting electrolyte employed was 0.3M LiC104. The acetic acid was dried by the method using triacetyl borate ( 4 ) prepared according to Pictet and Galeznoff
(5). is about equal to the current which would have been attained a t the same instant t = t,, had the electrolysis started at time f = 0 in a still solution originally homogeneous up to the electrode surface. Therefore, the diffusion layer thickness at the end of each washing period is about equal to which, for a typical depolarizer with D = 5 X cm2/sec cm. With and for t , = 30 msec, assumes the value 7 X technique I, the instantaneous potentiostatic current flowing between two successive washings is followed oscillographically. In view of the particular cell arrangement, the time is measured from the start of the washing; the choice of the time origin is not critical, provided the current is measured after sufficiently long times (say, for t 2 0.25 sec). The polarograph records the mean current at the DLPRE over the period of electrolysis tl against the applied potential. The voltammetric curve so obtained is analogous to a polarographic wave, the only difference being that here the average current is recorded at a stationary spherical electrode rather than at a growing drop; the period of electrolysis tl is the equivalent of the drop time. With technique 11, the cell of the DLPRE is connected to an electronic apparatus of the pulse-polarographic type as described by the authors (3). In this case the DLPRE is held for a period of time t , a t an “initial” potential E,, a t which no charge-transfer process takes place. During this period of time the electrode is submitted t o one or more “washings,” which sweep away completely the effect of prior electrolysis. At the end of period t, a potential jump is effected from E, to a final potential E , a t which the depolarizer
G,
(3) G. Piccardi
1640
and R. Guidelli, Ric. Sci.,38, 247 (1968).
RESULTS AND DISCUSSION
A solution of IZin acetic acid gives a single anodic wave on the DLPRE. As opposed to the two reduction waves of Iz t o 13- and to I-, respectively, the anodic voltammogram recorded with technique I exhibits a height which depends on the rate at which the potential is applied to the DLPRE. Thus the anodic wave of 12, recorded toward more positive potentials, is about three times higher than the overall reduction wave of I2 to I- for a rate of polarization of 0.47 mV/sec and about four times higher for a rate of polarization of 4.7 mV/sec. The notable influence of the rate of polarization upon the height of the voltammetric anodic wave of II in CH3COOH can be more easily understood when we observe that, upon recording this wave at a given rate of polarization and arresting the applied potential at any point either on the rising portion or on the plateau of the wave, the mean current at constant potential decreases gradually with time, tending to an asymptotic value. The oscillographic investigation of the instantaneous current flowing between two successive washings, carried out along the plateau of the anodic voltammogram, shows that the time dependence of this current does not satisfy the Cottrell equation corrected for sphericity : it112
oc (l/n’/2
+ Dl/2t”2/rO)
(1)
Consequently the instantaneous limiting current is not controlled by spherical diffusion. In Equation 1, i is the instantaneous current, t the time elapsed from the start of the washing, D = 3.5 X 10-6 cm2/sec is the diffusion coefficient (4) W. C . Eichelberger and V. K. La Mer, J . Amer. Chem. SOC.,55, 3633 (1933). ( 5 ) A. Pictet and A. Galeznoff, Chem. Ber., 36, 2219 (1903).
ANALYTICAL CHEMISTRY, VOL. 43, NO. 12, OCTOBER 1971
I
eo
I
lo
I
=:
3 a r r
l - 1
sec
Figure 2. The ratio R = it*/(l/& f D*tf/P) against t as obtained from the potentiostatic current-time curves a, b, and c of Figure 3 of the depolarizer, and P = 0.1 cm is the radius of the spherical electrode. The experimental measurements show ) from that the ratio R = i t 1 ’ p / ( l / + ’ 2 D 1 ’ 2 t 1 / 2 / Pobtained a given current-time curve increases with t rather than remaining constant. The rate of growth of R with t is higher, the longer the time during which the electrode remained within the range of potentials corresponding to the limiting current prior to the recording of the current-time curve under study, i.e., the lower the corresponding mean limiting current. The above experimental facts have been clarified with technique 11. The charge-potential curve of a 10-aM I s solution in acetic acid is shown in Figure 1. It was obtained by keeping the electrode at a potential Ei = +1.3V for a period t , = 90 sec (during which the electrode was subjected to 35 successive washings), and then for a period tl of 3 sec, at a potential E, varying from +1.6 to 4-2.55 ‘V during the whole recording. The height of the chargepotential curve in Figure 1 is with good approximation five times greater than the height of the overall cathodic chargepotential curve corresponding to the electroreduction of the same iodine solution to I-. Furthermore, the time dependence of the instantaneous anodic limiting current of Ip which flows during the period t / at the potential E/ = 2.35 V satisfies the Cottrell equation, therefore denoting control by diffusion. The preceding experimental observations lead to the conclusion that the anodic voltammogram of I p in acetic acid is due to the oxidation of IZ up to the oxidation number
+
+5:
-
IV
+ 5e
(2) The obedience of the instantaneous limiting current as recorded with technique I1 to the Cottrell equation is shown in Figure 2, curve a, in which the ratio R = it1’2/(l/s1’2 D1izt1‘2/r0) is practically constant with t. At the most we may note that curve a exhibits a slight negative slope, not justifiable by the hypothesis of any type of slow chemical reaction antecedent, parallel, or subsequent to the chargetransfer proper. The charge Q d obtained by integrating the potentiostatic instantaneous limiting current flowing during the period I / at the potential E/ = 2.35 V, does not decrease appreciably with the number of cycles ( t i tf) to which the DLPRE has previously been submitted, provided the period t i is sufficiently long (say, 2 50 sec). When, on keeping the period t J constant (e.g., equal to 6 sec), the period ti is progressively decreased, the effect of the pre-treatment of the electrode at the potential E; becomes gradually less appreciable and the conditions realized using technique I are more nearly approached. The oscillogram of Figure 3 shows three current-time curves recorded during a period t , of 6 sec at a potential E/ = 2.35 V. Curve a was recorded after having pretreated the electrode at the potential Ei = 1.3 V for 90 sec: curves b and c were recorded iml/212
+
+
Figure 3. Curve a is the potentiostatic current-time curve given by a solution of 10-3M Iz and 0.3M LiCIOa in acetic acid at the potential E/ = f2.35 V after a pretreatment of the electrode at the potential E, = f1.3 V for 90 sec. Curves b and c were obtained immediately after curve a by interposing between two successive periods of electrolysis t/ of six seconds at the potential Ef a period ti of only three seconds at the potential Ei mediately after curve a by interposing between two S U C C Z S S I ~ ~ periods of electrolysis t/ at the potential Et a period f, of on!‘ three seconds at the potential E,. During each single periot , , the DLPRE was subjected to one “washing” in order K homogenize the concentration of the depolarizer up to the electrode surface. The decrease in the current in passing from the potentiostatic curve a to the successive curve b is notable. The decrease in the current in passing from curve b to curve c i s on the other hand small, although still appreciable. The deviation of curves b and c from the behavior expressed by the Cottrell equation is shown in Figure 2. Here the ratic R as derived from curves a, 6, and c in Figure 3 is plotted against the time t measured from the instant of pulse application. The shape of the current-time curves a, b, and c is practically independent of the particular choice of the initial potential E,. The decrease in the instantaneous limiting current in passing from curve a to curve c of Figure 3, as well as the analogous decrease in the anodic mean limiting current of I:! (as recorded with technique I at a given potential) with increasing rest time of the electrode at that given potential, may be explained by the gradual coverage of the electrode by the products of the electrooxidation of iodine. The accumulation of these products at the electrode surface is controlled by the diffusion of I 2 toward the electrode and also, presumably, by the rate of their desorption. On the basis of the data herein reported, it is impossible to establish whether the oxidation products of I z are physically adsorbed or chemisorbed with formation of some type of platinum compound film. The pulse-polarographic technique eliminates the effects of this adsorption (provided t, is sufficiently long) since, before each single period of electrolysis t f , the potential applied to the electrode is brought back to a value E, at which the products adsorbed are eliminated from the electrode. In order to establish whether the removal of the adsorbed products is mechanical--i.e., occurs as a consequence of the series of “washings” performed during t,, or else is due to the electroreduction of these products at E,, the following experiment was performed. After having electrolyzed the solution at a potential E/ corresponding to the anodic limiting current of I p , the applied potential was switched back to a value E, and the instantaneous current flowing at this latter
ANALYTICAL CHEMISTRY, VOL. 43, NO. 12, OCTOBER 1971
1641
I
I
i
I
-
1
ad
4 0.5
-
-
-
\. e
\
I
I
potential was followed oscillographically. In this experiment no washings were performed at the potential E,. The current flowing a t E; falls rapidly to zero after a few tenths of a millisecond from the instant of the potential jump E/ + E;. This behavior is encountered for any value of E, chosen between the foot of the reduction curve of IZt o 13- and the foot of the oxidation curve of IZ t o I V . Such a behavior is typical of a capacitive current and in fact it is analogous, even quantitatively, to that observed upon applying the potential jump E/ + E, to the DLPRE immersed in a solution containing the supporting electrolyte alone. These experimental observations suggest that the removal of the adsorbed products following the potential jump E/ E, and the subsequent washings during ti with technique I1 is not due to the electroreduction of these products. In fact, if this were the case, the current flowing after the E, -+ E, jump in a still solution would be due to the electroreduction both of the oxidation products of I1 adsorbed on the electrode and of those returning to the electrode from the diffusion layer. Consequently, it should last for a time interval of a few seconds. This is what is actually observed when jumping from the plateau to the foot of a reversible voltammetric curve, such as that due t o Fe(CN)6*- electrooxidation on platinum. Of course, if during electrolysis a t the potential E/ the oxidation products of Iz remain completely adsorbed on the electrode surface without diffusing away from the electrode, then the current following the E, -P Eipotential jump is expected to fall to zero within a few tenths of a millisecond, just as a capacitive current does. In this case, however, the total quantity of electricity involved in the E, 4 E, jump would be much greater than that which is actually observed with the supporting electrolyte alone under otherwise identical conditions. This expectation is at variance with experiment. Furthermore, the El + E, jump followed by a short rest (say, 1 sec) at the potential E, would be sufficient to eliminate the oxidation products of IZ completely. On the contrary, a period t, of at least 50 sec at the potential E, is required in practice for eliminating the effects of prior electrolysis at E, completely. The amount of the oxidation products of IZ adsorbed during the first seconds of electrolysis is relatively small, but nevertheless this amount is able t o produce an appreciable coverage of the electrode, with the consequent decrease in its effective area. It follows that the potentiostatic instantaneous current recorded on an electrode initially free from adsorbate decreases with the time t of electrolysis more than it would in the absence of adsorption phenomena. This explains the negative slope, although slight, of the R os. t plot obtained from curve a, Figure 3, which can be considered to have been recorded on an electrode initially free from oxidation products of iodine adsorbed on its surface. On the other hand the deviation of curve a from the Cottrell equation is so slight that on practical grounds the corresponding potentiostatic current may
-
1642
I
I
1
be considered to be diffusion-controlled. The washing carried out at the potential E, = 1.3 V during the period I, elapsed between the recording of curve a and that of curve bin Figure 3 homogenizes the solution around the electrode, but is not able to remove the oxidation products of Iz adsorbed on the electrode surface to a n appreciable extent, so that the successive electrolysis at the potential E, (curve b) takes place on an electrode partially covered from the beginning of the new period t / . Curve b is therefore lower than curve a from the very beginning of the period t,, and deviates notably from the behavior described by the Cottrell equation. FOI values of 1, as low as 3 sec, the degree of coverage of the electrode by the electrolysis products grows from cycle to cycle, although progressively more slowly, tending to a stationary value. This explains the small difference already existing between curves b and c. The possible causes of the deviation of the current-time curves recorded in the proximity of the asymptotic behavior (e.g., curve c in Figure 3) from the Cottrell equation will be examined in the next section. The attribution of the anodic wave of If in acetic acid to the electrooxidation of Ip to Iv has been confirmed by coulometric measurements carried out by the use of a platinum macroelectrode with an area of 12.5 cm2, immersed in the cell of the DLPRE and maintained at a constant potential E = 2.0 V, which is close to the half-wave potential of the anodic curve. The decrease in the limiting value Q d of the charge flowing at the DLPRE during ti, as obtained from charge-potential curves recorded with technique 11, is shown in Figure 4 as a function of the amount of electricity that has flowed through the macroelectrode. The ratio of the anodic limiting charge Q d to the corresponding initial anodic limiting charge Q d o , as recorded before the start of electrolysis on the platinum macroelectrode, is shown on the ordinates. The ratio p of the number of coulombs that have flowed through the macroelectrode to the number of coulombs theoretically required for the oxidation of the iodine initially contained in the cell up t o the oxidation number +1 is shown on the abscissae. The plot in Figure 4 is linear within the range 1 > Q d / Q d o> 0.3. The extrapolation of the linear portion to the Qd/Qdo= 0 axis points out that the electrooxidation of 1, involves 5 electrons per iodine atom. The deviations from < 0.3 must problinearity which are encountered for Q d / Q d O ably be ascribed to side reactions tending to lower the current efficiency. In fact we must consider that the whole series of measurements reported in Figure 4 required about 24 consecutive hours on account of the time (1.5 hours) spent for the recording of each charge-potential curve. The plot oj Figure 4 does not change appreciably with a change of the initial concentration of iodine within the range from 5 X 10'6MtO 10-2M. From a n analysis of the rising portion of the anodic chargepotential curve of Iz t o IV, it has been possible to draw some
ANALYTICAL CHEMISTRY, VOL. 43, NO. 12, OCTOBER 1971
conclusions about the mechanism by which the overall electrode process L --* IV takes place. In this connection use has been made of a n equation (Eq. 20 of Reference 6) of the type : ;/id
= f(kb,ro,D,fi,tur)
(3)
In Equation 3, i is the mean current at a given potential E along the rising portion of a voltammetric curve recorded on the DLPRE with technique I, whereas i d is the corresponding mean diffusion limiting current. Equation 3 allows the diffusion overpotential to be separated from the chargetransfer overpotential, under the assumption that the flux of the depolarizer at the electrode surface is proportional t o the first power of its volume concentration, C(ro,t ) , at the electrode surface:
(4) where k b is the rate constant for the electrode process proceeding toward oxidation. In the boundary condition, Equation 4, it is assumed that the rate for the electrode process proceeding toward reduction is negligible; in other words the electrode process is considered t o be totally irreversible. It should be noted that the platinum microelectrode employed in this work has a radius of about 1 mm. Consequently, confining ourselves to electrolysis times not exceeding 4 sec, diffusion toward this electrode may be practically taken as linear. In fact, under these conditions, in Equation 1 the term Dli2t1i2/r0,accounting for electrode curvature, is much smaller than 1/7r1j2. Consequently, in the following part of this paper the condition tl (or t , ) 5 4 sec having been constantly satisfied, the diffusion toward the DLPKE will be considered linear for simplicity. If in Equation 20 of Reference 6, valid in the case of spherical diffusion. the value Y for the radius of the electrode is made to tend 13infinirq, then we immediately obtain the equation ~
valid in the case of linear diffusion. In Equation 5 the parameters A and p are defined by the equations: =
kbf11‘2/D1i2,’ p = t,/tl
(6)
Equation 5 may be easily extended to the case in which the DLPRE is employed in connection with technique 11. In ‘act we must note that the ratio j h d between the mean currents and ;d relative to a given period of electrolysis tl is identical o the ratio Q / Q d between the corresponding amounts of :lectricity flowing during the same period of electrolysis. Moreover, when technique 11 is employed, the washing period is zero since the washing of the electrode takes place during he initial period t,, in which the current flowing at the poentia1 E,, although small, is not integrated electronically. Zonsequently the quantity p in Equation 5 vanishes, so that his equation simplifies as follows:
3quation 7, which is analogous to a n equation derived by Zhristie et al. ( E q . 5 , Reference 7), allows X t o be determined is a function of the applied potential E by measuring Q / Q d 6) R . Guidelli and G. Piccardi, Electrochim. Acta, 13,99 (1968). 7 ) J. H. Christie, G. Lauer, and R. A. Osteryoung, J. Electround. Chem., 7,60 (1964).
at the various potentials. It should be noted that in general kb is expressed by the equation (8):
where kbo is the rate constant a t the reference potential Eo,no the number of electrons preceding the rate-determining stage, as calculated with reference to the stoichiometric equation of the overall electrode process, nl the number of electrons involved in the rate-determining stage, v1 the stoichiometric number of this latter stage, and CY the charge-transfer coefficient. Upon substituting k b from Equation 8 into Equation 6, we obtain:
The plot of log X against E is actually linear along the whole rising portion of the charge-potential curve of I p to Iv, in agreement with Equation 9 and, consequently, in agreement with the hypothesis of a totally irreversible electrode process with a first-order kinetics. The slope of this plot is of 5.24 V - l , so that (n,/vl nla)is equal t o 0.31. Since the value of CY is usually near 0.5 and the simultaneous transfer of two electrons (nl = 2 ) is improbable, the experimental value of (n,/vl nla) suggests that we have: no = 0, nl = 1, CY = 0.31. In this case the rate-determining stage of the overali electrode process Iz -t I\’ can be expressed by the equation:
+
+
IS
-P
I’ f ladsorbed f e
(10,
and excludes the possibility of a prior dissociation of molecular iodine into two iodine atoms, as occurs in the case of tht: reduction of I p to I- in aqueous media (9). It is possible thaL the rate-determining stage consists in the asymmetrical stretching of the iodine-iodine bond within a molecule of iodine at the electrode-solution interphase and in the simultaneous tunnelling of one electron from the more negative iodine atom to the electrode. Influence of the Adsorption of Electrolysis Products upon Limiting Currents. The lowering of the anodic mean limiting current of Iz, as recorded with technique I, with increasing rest time of the electrode at constant potential and the simultaneous deviation of the potentiostatic current-time curves from the behavior described by the Cottrell equation may be attributed to two different phenomena, both provoked by the adsorption of the electrolysis products : nonlinear diffusion of the depolarizer toward islets of electrode material left free from adsorbate; and slowing down of some chemical step preceding the charge-transfer proper. The first phenomenon takes place in the case in which the islets left free from adsorbate have average linear dimensions comparable to the diffusion layer thickness. In the case of adsorbed molecules of normal size, the above situation requires that adsorption takes place preferentially at sites contiguous to those already occupied, i.e., that strong dispersion forces are established among adsorbed molecules. In fact the diffusion layer thickness 6, for the case of linear diffusion, is given by : 6 = %hDt (11) cm for the and therefore ranges from 5 X 10-4 t o 1 X periods of electrolysis commonly employed in polarography (0.1 sec < t < 5 sec). We shall assume that the previous requirements are fulfilled and that the electron-transfer does not take place across the adsorbed molecules of the electrolysis product. In this case we can represent schematically the electrode surface as a set of conducting islets free from adsorbate of (8) H. Mauser, 2. Elektrochem., 62, 419 (1958). (9) K. J. Vetter, 2. Physik. Chem. (Leipzig), 199, 285 (1952).
ANALYTICAL CHEMISTRY, VOL. 43, NO, 12, OCTOBER 1971
1643
and of the specific conductivity divided by nF by the diffusion coefficient D of the depolarizer, from Equation 17 of Reference 10 we immediately obtain the following expression for the flux D(dC/bx)t-o of the depolarizer through the electrode surface :
.(E)
DC* r-o 6 K Equation 14 holds in the case that 6 is greater than b. The quantity K is expressed under the form of a series expansion, which is independent of S but depends on a and b. In particular, when a equals I/4b, ‘12b,and J/4b,Kis given by 2.051646, 0.53366, and 0.10606, respectively. It is therefore evident that if, for a given constant value of the ratio a/b, the average linear dimensions of the conducting islets are much lower than the diffusion layer thickness (a
