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The redoxokinetic effect - a simple picture
SHORT
COXIMUNICATIONS
341
1 C.I.T.C.E. Conventions: P. V_\S KYSSELBERGHE (Chairman): Reports of Commission No. 3 C.I.T.C.E. Electrockentical Aromencluttrre and Definitions: 105-1, Buttcrxvorths. London. x955. pp. zo--.+9: (a) Proc. 6th Meefing. Poitiers, (b) Proc. 8th Afeeling. Madrid, 1956. Butterworths. London. r95S. pp. 18-47; (c) Proc. gfh Meetittg. Paris. 1957. Butrcrworths, London, 19~~~. pp. r76-r?rc): and report presented to Physical Chcm&tr)- Section of I.G.P.A.C. (in the press). A large abstract of (c) will be published shortly in J. Elzcfrounal. Chem. 2 I.U.P.X.C. Stockholm conventions of 1953: J. A. CHRISTIASSES ASD M. PouRn.\rs. Corrrpl. vznd. 17118 Couf. I. U. P.--l .C., _Sfockkoltn. 1953, pp. 82-S.): T. S. IaICliT AND .I. J. DE ~3ETHIINE. J. C/rem. Edrccutioar, 34 (1957) 435; J . A. C~imsTI.*xsEs, J. .-I WI. Cltem. Sot.. Sz (1960) 5517. J R. G. B.%TFS AND 1'. E. RO\VER. J. Research Nntl. Bltr. Sfnndurds, 53 (1954) 2S3. -a -5. J. DE ~~T~~uxF., T. S. LICIIT AND h'. SWECC~EMAN. _/. Electrochem. Sot., x06 (1959) GrS; A. J. DE RETHUSE, J. EIectrochcm. SOC., 107 (~9th) 919.
J.
The
redoxokinetic
effect
-
Eicclrounaf.
a simple
Ckct~c.,
2 (1961)
340-341
picture
When an alternating current is impressed on an electrode. its mean electrode potential departs from the equilibrium \:alue. This phenomenon \vas first obscrvcd by Doss AND AGARW.AL~-.I, who described it as the “redosokinetic effect”. The term “faraclaic rectification” has also been used by some later uxxkers5~-7. In rcccnt years, the phenomenon has assumed importance. The: sensitive electroanalytical technique6 of radio-frequency polarography is based on this effect. It has also been utilized to determine kinetic parameters in clcctrodc reactions. The purpose of this brief communication is to prcscnt a simple picture of this effect*_ Consider, for con\rcnience of esposition. that the a-c. leas a square wa\.cfoTm, and that the galvanostatic technique is adopted with the currents i-and i A (in thccathodic and anodic half-cycles) being equal in magnitude. The current driven through the electrode in each half-cycle polarizes the clcctrode. If the polarization is sy,wtzetricnZ of the ovcrpotential during the cathodic and in the half-cycles, i.e., if the magnitude anodic half-cycles is the same, then the mean electrode potential will remain at the equilibrium value. On the other hand, if the clectrodcs are polarized to different extents during the cathodic and anodic half-cycles, then the mean cIcctrode potential potential is called the rcdososhifts from the equilibrium value. The shift in mean kinetic potential \I/. PURE ACTI\-r\l’IOK If i- and i+ arc large enough
to
make
the
POLhHIZ_ATION
activation
ovcrpotentials
This note was prcscntcd Lndia. April. 19Go. l
at the
First
Seminar
in Electrochemistq
f.
Eieclroanat.
held at Karaikudi.
Chem.,
2 (1961)
South
341-343
SHORT
31” then
the Tafel
case of the rate
CON
equation
Al UKICATIONS
can be used*.
IVc
have
and
The
redosokinetic
because Ii+1 = 1 i-1 /9 -= 0.5. th en YJ =
potential
is given
by the difference
between
1 qa.* 1 and 1 +-I.
Thus
7.. 1 iI, and we see that !P depends on /S. the symmetry factor. If will o; and if @ r_” o-5, \I/ + o, in which case the mean potential
depart from the equilibrium value. Let us write (p 0.5) = x. Considering /3 and x as variables, the domains are: o <,!I < rand--0.5 < n -K $-o-5. \Vhcn /3 (and therefore x) incrcascs, 1 qa” 1 increases and 1 qc- 1 decreases for a given io_ But when /? = 0.5 and x = o. Y-’ = o. Hence as p becomes increasingly different from 0.5, i.e., as x deviates from zero, the magnitude can also be seen to increase for a given io. of Y’I7&x+I-l+-) It may be noted that /?, bp determining the differences in the slopes of the cathodic and anodic Tafel lines also determines the symmetry of the polarization curve. The term "synr~dry factor” is therefore most appropriate. It is known that p decides the sJ.mmetry of the encrgv barrier at the cathode-electrolyte interphase. It also governs the distribution of the elcctrodc potential bct\veen the for\vard and backward reactions. Hcncc, the development of a redosokinetic potential implies that the energy barrier is asymmetric and hence that the elcctrodc potential is unequally apportioned between the cathodic and anodic reactions. PURE
In order
to obtain
coKcsswrn_.\rros
a qualitative
picture,
POL~XRIZ_I~I-ION
we shall
concept. The limitations and approsimatc elsewhercg. We have for I vc+l and Irlc-l.
use
the NERNST
“diffusion
layer”
nature of this concept have been discussed and for ifi,,,. the following equations:
and zFD ilh.
=-c(x--cco) d
If i.+~c~. + i-lrm., i-c., if L)nCn (.z -> 00)/a H * DOCO (n --> oo)/d0, then I ++I # I qc-l and Y# 0. A redosokinetic potential will therefore develop if there is any difference in the diffusion coefficients DO and DK or in the bulk concentrations Co (x -P CO) and CR (x-, co) of th e oxidant 0 and reductant R involved in the charge transfer reaction. l The Tafel cm has been considered depends on fl as has been shown by
onI\- for simplicity. Even for [q,,-l and I+,-1 making USC of the full rate cyuationz.7.n. f.
Eiectroanat.
Chon.,
<
o. IZ/Z volts,
2 (196x)
W
341-343
SHOHT COMh¶UNICXTIONS
343
The author is grateful to Prof. PAUL DELMIA\-, Coatcs Chemical Laboratory, Louisiana State University, U.S.A., for his kindness in reading the manuscript and making helpful
suggestions.
Central Electrochemical Karaikudi-3 (Ix&a) 1 K.
S. G.
2 K. S. G.
Doss
ASD AND
H.
P.
H. P.
A. K. N. REDDY
Imtitrcte,
:\C_'IRWAL, _&C.\Rw.U.,
J. Sci. Iwd. Research (India). Proc. Indian =icod. sci., 3.) Yvoc. Zwdiau Acud. Sci., 34 PYOC. Indiarr _-?cad.Sci.. 35
S. C;. Doss AND H. P. _~GARWAL, Doss .\SD H. P. _-\C.ARXVAL, 5 I<. I-3.OLDHAM, Trorzs. Furadny Sot., 53 (~957) 80. a C. C. B.\RKER. Arral. Chinr. .-Zcfa. 18 (1958) I r8. 7 H. MATSUDA ASD PAUL DELAHAY, J. _-lm. Chern. Sot., 82 (19(io) e S. Ii. RASG.\RAJAS. J. El~clroanoZ. Cllzm., I (1960) 396. Q PAUL DELAUAV , _\'eo It~sfrcrme~ttal Methods in EIeclrociremislry. New York. 195.). Chap. g. 3
K.
Doss
Rescarclr
* Ii. S. G.
Q
~SO.
(1~50)
(1951) (1951) (1952)
329.
1’63. 45.
1547. Intersciencc
Received
Publishers.
Inc.,
March moth. 1961
J. Electroatral. Chew..
2 (2961)
341-343
COXIMUNICATIONS
341
1 C.I.T.C.E. Conventions: P. V_\S KYSSELBERGHE (Chairman): Reports of Commission No. 3 C.I.T.C.E. Electrockentical Aromencluttrre and Definitions: 105-1, Buttcrxvorths. London. x955. pp. zo--.+9: (a) Proc. 6th Meefing. Poitiers, (b) Proc. 8th Afeeling. Madrid, 1956. Butterworths. London. r95S. pp. 18-47; (c) Proc. gfh Meetittg. Paris. 1957. Butrcrworths, London, 19~~~. pp. r76-r?rc): and report presented to Physical Chcm&tr)- Section of I.G.P.A.C. (in the press). A large abstract of (c) will be published shortly in J. Elzcfrounal. Chem. 2 I.U.P.X.C. Stockholm conventions of 1953: J. A. CHRISTIASSES ASD M. PouRn.\rs. Corrrpl. vznd. 17118 Couf. I. U. P.--l .C., _Sfockkoltn. 1953, pp. 82-S.): T. S. IaICliT AND .I. J. DE ~3ETHIINE. J. C/rem. Edrccutioar, 34 (1957) 435; J . A. C~imsTI.*xsEs, J. .-I WI. Cltem. Sot.. Sz (1960) 5517. J R. G. B.%TFS AND 1'. E. RO\VER. J. Research Nntl. Bltr. Sfnndurds, 53 (1954) 2S3. -a -5. J. DE ~~T~~uxF., T. S. LICIIT AND h'. SWECC~EMAN. _/. Electrochem. Sot., x06 (1959) GrS; A. J. DE RETHUSE, J. EIectrochcm. SOC., 107 (~9th) 919.
J.
The
redoxokinetic
effect
-
Eicclrounaf.
a simple
Ckct~c.,
2 (1961)
340-341
picture
When an alternating current is impressed on an electrode. its mean electrode potential departs from the equilibrium \:alue. This phenomenon \vas first obscrvcd by Doss AND AGARW.AL~-.I, who described it as the “redosokinetic effect”. The term “faraclaic rectification” has also been used by some later uxxkers5~-7. In rcccnt years, the phenomenon has assumed importance. The: sensitive electroanalytical technique6 of radio-frequency polarography is based on this effect. It has also been utilized to determine kinetic parameters in clcctrodc reactions. The purpose of this brief communication is to prcscnt a simple picture of this effect*_ Consider, for con\rcnience of esposition. that the a-c. leas a square wa\.cfoTm, and that the galvanostatic technique is adopted with the currents i-and i A (in thccathodic and anodic half-cycles) being equal in magnitude. The current driven through the electrode in each half-cycle polarizes the clcctrode. If the polarization is sy,wtzetricnZ of the ovcrpotential during the cathodic and in the half-cycles, i.e., if the magnitude anodic half-cycles is the same, then the mean electrode potential will remain at the equilibrium value. On the other hand, if the clectrodcs are polarized to different extents during the cathodic and anodic half-cycles, then the mean cIcctrode potential potential is called the rcdososhifts from the equilibrium value. The shift in mean kinetic potential \I/. PURE ACTI\-r\l’IOK If i- and i+ arc large enough
to
make
the
POLhHIZ_ATION
activation
ovcrpotentials
This note was prcscntcd Lndia. April. 19Go. l
at the
First
Seminar
in Electrochemistq
f.
Eieclroanat.
held at Karaikudi.
Chem.,
2 (1961)
South
341-343
SHORT
31” then
the Tafel
case of the rate
CON
equation
Al UKICATIONS
can be used*.
IVc
have
and
The
redosokinetic
because Ii+1 = 1 i-1 /9 -= 0.5. th en YJ =
potential
is given
by the difference
between
1 qa.* 1 and 1 +-I.
Thus
7.. 1 iI, and we see that !P depends on /S. the symmetry factor. If will o; and if @ r_” o-5, \I/ + o, in which case the mean potential
depart from the equilibrium value. Let us write (p 0.5) = x. Considering /3 and x as variables, the domains are: o <,!I < rand--0.5 < n -K $-o-5. \Vhcn /3 (and therefore x) incrcascs, 1 qa” 1 increases and 1 qc- 1 decreases for a given io_ But when /? = 0.5 and x = o. Y-’ = o. Hence as p becomes increasingly different from 0.5, i.e., as x deviates from zero, the magnitude can also be seen to increase for a given io. of Y’I7&x+I-l+-) It may be noted that /?, bp determining the differences in the slopes of the cathodic and anodic Tafel lines also determines the symmetry of the polarization curve. The term "synr~dry factor” is therefore most appropriate. It is known that p decides the sJ.mmetry of the encrgv barrier at the cathode-electrolyte interphase. It also governs the distribution of the elcctrodc potential bct\veen the for\vard and backward reactions. Hcncc, the development of a redosokinetic potential implies that the energy barrier is asymmetric and hence that the elcctrodc potential is unequally apportioned between the cathodic and anodic reactions. PURE
In order
to obtain
coKcsswrn_.\rros
a qualitative
picture,
POL~XRIZ_I~I-ION
we shall
concept. The limitations and approsimatc elsewhercg. We have for I vc+l and Irlc-l.
use
the NERNST
“diffusion
layer”
nature of this concept have been discussed and for ifi,,,. the following equations:
and zFD ilh.
=-c(x--cco) d
If i.+~c~. + i-lrm., i-c., if L)nCn (.z -> 00)/a H * DOCO (n --> oo)/d0, then I ++I # I qc-l and Y# 0. A redosokinetic potential will therefore develop if there is any difference in the diffusion coefficients DO and DK or in the bulk concentrations Co (x -P CO) and CR (x-, co) of th e oxidant 0 and reductant R involved in the charge transfer reaction. l The Tafel cm has been considered depends on fl as has been shown by
onI\- for simplicity. Even for [q,,-l and I+,-1 making USC of the full rate cyuationz.7.n. f.
Eiectroanat.
Chon.,
<
o. IZ/Z volts,
2 (196x)
W
341-343
SHOHT COMh¶UNICXTIONS
343
The author is grateful to Prof. PAUL DELMIA\-, Coatcs Chemical Laboratory, Louisiana State University, U.S.A., for his kindness in reading the manuscript and making helpful
suggestions.
Central Electrochemical Karaikudi-3 (Ix&a) 1 K.
S. G.
2 K. S. G.
Doss
ASD AND
H.
P.
H. P.
A. K. N. REDDY
Imtitrcte,
:\C_'IRWAL, _&C.\Rw.U.,
J. Sci. Iwd. Research (India). Proc. Indian =icod. sci., 3.) Yvoc. Zwdiau Acud. Sci., 34 PYOC. Indiarr _-?cad.Sci.. 35
S. C;. Doss AND H. P. _~GARWAL, Doss .\SD H. P. _-\C.ARXVAL, 5 I<. I-3.OLDHAM, Trorzs. Furadny Sot., 53 (~957) 80. a C. C. B.\RKER. Arral. Chinr. .-Zcfa. 18 (1958) I r8. 7 H. MATSUDA ASD PAUL DELAHAY, J. _-lm. Chern. Sot., 82 (19(io) e S. Ii. RASG.\RAJAS. J. El~clroanoZ. Cllzm., I (1960) 396. Q PAUL DELAUAV , _\'eo It~sfrcrme~ttal Methods in EIeclrociremislry. New York. 195.). Chap. g. 3
K.
Doss
Rescarclr
* Ii. S. G.
Q
~SO.
(1~50)
(1951) (1951) (1952)
329.
1’63. 45.
1547. Intersciencc
Received
Publishers.
Inc.,
March moth. 1961
J. Electroatral. Chew..
2 (2961)
341-343