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Reaction layer concept applied to rotating disk electrodes
JOURKAL
248
OF
ELECTROANALYTICAI_
Short Reaction
layer
studied
which
by
canbe
LEVTCH
AND
described
communications applied
concept
The rotating diskelectrode chernicalprocesses coupled
CHEMISTRY
to rotating
disk
electrodes
(RDE)
is veryconvenientforinvestigatin&the kinetics of electrochemicalreactionsr. Several such cases were KOUTECKY~ and suitable equations were given for processes by the relations with
k _!+B+C 1 _a 5
+Ze
(1~)
33 z
ne
c
(2)
k
zl+Bf-X+-A
(3)
We noticedthatusingthereactionlayerconceptitiseasyto obtainforprocess (r) an equationidenticalwiththatgiven by LEVICH AXD KOUTECKY. Because the reaction layer treatment gave results similar to more rigorous treatmentsinthe case of polarography 73 and chronopotentiometry4 for electron transfer followed by chemical reaction:
OS
+
rze +
Red
5
A
(4)
used this method to describe process (4)inthe case of the RIDE. The concentrationCo, canbe calculated approximatelyfromthe equationforthe RIDE1 ; b Cos[o.t) = CCBwe
2,3
(5)
o.62nF_4Do,v-‘w_o~~”
where
Gisthe buLk concentration OS, Cox(o$) is the concentration Ox at the surface of the electrode, uis the kinematic viscosity. o is the angular velocity, A is the surface area ofelectrode_ The other symbols havetheirusual meaning. If the chemical reaction Red 5 A is fast, according to the reaction layer the concentration Red canbe written5
wherepisthereactionlayerthickness_ Introducing (5) and (6)inthe N&nstequationandwiththereactionlhyerthickness given by6:~
concept,
SHORT
COMMU!?ICATIONS
249
one cam obtain
When
i =
because
i&z
the potential
for the rotating
by the formula
is giveI
disk electrode Ehd
El,?
E"
=
RT +
-
?ZF
In
D Redaoxfox
where 6, the thickness of the diffusionlayeris given we have the final equation: Assuming fox = fEea, R
’
El,2
Inthe
same
way
we
RT
Red
El,?
=
cantreatthe
+
-
-1tF
by:
6 =
I.~zD~'~v~'~c-o-~/~.
kl/”
(10)
In -l/6
l/d
-116
process
?-Ox + Butinthis
(9)
Dortkedf~cd
ne +
3- Red
(11) isgivenbytheequations:
casethethicknessofthereactionlayer Bl/'
(=I
P=
The
final
result for
(II)
will be k
El,2
=
E"
+
Rg In
k1/3(Cb)
113
o_g~o'f~~-~I~DIP
(13)
where The
Cbis the bulk concentration of OS. relation (IO) predicts that the half-wave potentialofthekineticprocess (g)is, in the case ofreduction,shiftedtowards more positive potentials withrespectto the potential which would be noticed if, in (q), Red did not undergo transformations. Theshiftishigher.thehigher k andthe smallero and D. Inthe case oftheprocess (rr) the kinetichalf-wavepotentialis also dependentonbulkconcentration Ox-Both relations aretrueif charge transfer is fastItwas notpossibleto check this equation by experiments. Only afewprocesses are knownsofarwhichgo according to equations (q)and(rr)withfastchargetransfer_ Thebestexampleofreaction(g)in polarographyisthe o,xidatjon of ascorbic acid Onrotatingplatinum andcarbonpaste disk electrodes this reaction behaves irreversibly and cannot be treated in the fashion given.
SHORT
250
COlbIi%IUNICA-l-ZONS
ACKNOWLEDGEMENT
This
work
was
supported
(II-I)-6S6
and
Dspartwzen
t of C?zemzstry,-
Unimrsity Laiwvence,
of
this support
by
the
Atomic
is gratefully
Energy
Commissicjn
acknowledged.
through
AT
’
ZGALUS
Kansas,
Kan_ (77.S.A
contract
_)
RALPH
1 V- G- LEVICH, Fiziko-khimicheskaya gidrodixamika (Physico-ChemicaZ darstvennoe, Izdatel’stvo Fizikomatematicheskoi Literatury, Moscow, z V_ G_ LEVICH AND J_ KOUTECKY. Zhzw_ Fiz. IThim_, 32 (rg58) 1565. 3 D. M. H. KERN, J_ Am_ Chem. SOG.. 75 (1953) ‘473; 76 (1954) IOII4 2. GXLUS, Ph.D_ Dissevtalion, Warsaw University, 1960. 5 V_ HANUS, Chem. Zuesti, 8 (1954) 702_ 6 J_ KOUTECKY AND R_ BRDICKX. Collection CzechosZov_ Chem. Communs..
EkcfroanaZ_
ADAMS , Gosu-
Hydrotrydamicsj 1959, p. 348_
IZ
(1947)
Received J-
N.
Chew.,
337_
April +
rqth,
(1962)
rg6z
245-250
248
OF
ELECTROANALYTICAI_
Short Reaction
layer
studied
which
by
canbe
LEVTCH
AND
described
communications applied
concept
The rotating diskelectrode chernicalprocesses coupled
CHEMISTRY
to rotating
disk
electrodes
(RDE)
is veryconvenientforinvestigatin&the kinetics of electrochemicalreactionsr. Several such cases were KOUTECKY~ and suitable equations were given for processes by the relations with
k _!+B+C 1 _a 5
+Ze
(1~)
33 z
ne
c
(2)
k
zl+Bf-X+-A
(3)
We noticedthatusingthereactionlayerconceptitiseasyto obtainforprocess (r) an equationidenticalwiththatgiven by LEVICH AXD KOUTECKY. Because the reaction layer treatment gave results similar to more rigorous treatmentsinthe case of polarography 73 and chronopotentiometry4 for electron transfer followed by chemical reaction:
OS
+
rze +
Red
5
A
(4)
used this method to describe process (4)inthe case of the RIDE. The concentrationCo, canbe calculated approximatelyfromthe equationforthe RIDE1 ; b Cos[o.t) = CCBwe
2,3
(5)
o.62nF_4Do,v-‘w_o~~”
where
Gisthe buLk concentration OS, Cox(o$) is the concentration Ox at the surface of the electrode, uis the kinematic viscosity. o is the angular velocity, A is the surface area ofelectrode_ The other symbols havetheirusual meaning. If the chemical reaction Red 5 A is fast, according to the reaction layer the concentration Red canbe written5
wherepisthereactionlayerthickness_ Introducing (5) and (6)inthe N&nstequationandwiththereactionlhyerthickness given by6:~
concept,
SHORT
COMMU!?ICATIONS
249
one cam obtain
When
i =
because
i&z
the potential
for the rotating
by the formula
is giveI
disk electrode Ehd
El,?
E"
=
RT +
-
?ZF
In
D Redaoxfox
where 6, the thickness of the diffusionlayeris given we have the final equation: Assuming fox = fEea, R
’
El,2
Inthe
same
way
we
RT
Red
El,?
=
cantreatthe
+
-
-1tF
by:
6 =
I.~zD~'~v~'~c-o-~/~.
kl/”
(10)
In -l/6
l/d
-116
process
?-Ox + Butinthis
(9)
Dortkedf~cd
ne +
3- Red
(11) isgivenbytheequations:
casethethicknessofthereactionlayer Bl/'
(=I
P=
The
final
result for
(II)
will be k
El,2
=
E"
+
Rg In
k1/3(Cb)
113
o_g~o'f~~-~I~DIP
(13)
where The
Cbis the bulk concentration of OS. relation (IO) predicts that the half-wave potentialofthekineticprocess (g)is, in the case ofreduction,shiftedtowards more positive potentials withrespectto the potential which would be noticed if, in (q), Red did not undergo transformations. Theshiftishigher.thehigher k andthe smallero and D. Inthe case oftheprocess (rr) the kinetichalf-wavepotentialis also dependentonbulkconcentration Ox-Both relations aretrueif charge transfer is fastItwas notpossibleto check this equation by experiments. Only afewprocesses are knownsofarwhichgo according to equations (q)and(rr)withfastchargetransfer_ Thebestexampleofreaction(g)in polarographyisthe o,xidatjon of ascorbic acid Onrotatingplatinum andcarbonpaste disk electrodes this reaction behaves irreversibly and cannot be treated in the fashion given.
SHORT
250
COlbIi%IUNICA-l-ZONS
ACKNOWLEDGEMENT
This
work
was
supported
(II-I)-6S6
and
Dspartwzen
t of C?zemzstry,-
Unimrsity Laiwvence,
of
this support
by
the
Atomic
is gratefully
Energy
Commissicjn
acknowledged.
through
AT
’
ZGALUS
Kansas,
Kan_ (77.S.A
contract
_)
RALPH
1 V- G- LEVICH, Fiziko-khimicheskaya gidrodixamika (Physico-ChemicaZ darstvennoe, Izdatel’stvo Fizikomatematicheskoi Literatury, Moscow, z V_ G_ LEVICH AND J_ KOUTECKY. Zhzw_ Fiz. IThim_, 32 (rg58) 1565. 3 D. M. H. KERN, J_ Am_ Chem. SOG.. 75 (1953) ‘473; 76 (1954) IOII4 2. GXLUS, Ph.D_ Dissevtalion, Warsaw University, 1960. 5 V_ HANUS, Chem. Zuesti, 8 (1954) 702_ 6 J_ KOUTECKY AND R_ BRDICKX. Collection CzechosZov_ Chem. Communs..
EkcfroanaZ_
ADAMS , Gosu-
Hydrotrydamicsj 1959, p. 348_
IZ
(1947)
Received J-
N.
Chew.,
337_
April +
rqth,
(1962)
rg6z
245-250