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The mechanism of faradaic reactions at the thionine coated electrode
J. Eiecxroanai.
182 (1985)
Chem..
Elsevier Sequoia
S.A..
99
99- I1 1
Lausanne
-
Printed in The Netherlands
THE MECHANISM OF FARADAlC COATED ELECi-RODE
W. JOHN
ALBERY
Deparlmenr
of Chemisrr):
A. ROBERT Deparzmenr BS8
ITS
and MARTYN
AT THE
THlONlNE
G. BOUTELLE College.
London
SIV7
-7A Y (Great
Britain)
HILLMAN of Pnysicol
(Grear
(Received
Imperial
REACTIONS
Chemisrr);
School of Chemislg;
Unicersic.v
a/ Brisrol,
Canrock’s
Close.
Brisrol
Britain)
29th May
1984;
in revised form 16th August
1984)
ABSTRACT Ressul~s are presented modified speed.
electrode.
for the reduction
Systematic
analysis
film thickness and electrode
of
Fe(lil)
and
of the varialion
polential
of
of
estimated located The
from
rate constant
the second
in a block
order
diagram
rate of the Fe(CN)z-
by the transport
rcle
in a thionins
for Fe(ill)
with
which
fi*r the surface
rate constant
for
shows all the possible
is in reasonable
homogsneous mechanisms
reaction is five orders of magnitude
of Fe(CN)i-
through the electrolyte
the
A general equation is derived which inciadcs rakes place in a thin rexlion layer in the rrinl.
rextion the
rota1i.m
reaction between
are shown 10 be distinct and special cases of the general equation.
two parallel processes
the heterogeneous
by leucothionine
proves that the reaction is a “surface”
outermost layer of leucothionine and Fe(lll) in solution. bolh the “surface” reaction and the cast where the reaction These
Fe(CN)zthe reaction
agreement
reaction.
The
The value
with
Fe(Jll)
a vaiur
reaction
for [his type of modified
faster so that the rnle is controlled
or by the transport
This change in the rate limiting process agrees wi:h the position
of eit-Irons
of the system
is
elecctrode.
through
either
the film.
in t1.e block diagram.
INTRODUCTION
Previous
work on the thionine
coated
electrode
[l-3]
has elucidated
the nature of
the coated layer [4,5] and the mechanism of charging and discharging the redox centres in the modified electrode [6]. In this paper we report investigations on the mechanism of Faradaic reactions carried out at the thionine coated electrode. Theoretical analysis by the San.-Lant school [7-91 and by ourselves [13,11] has shown that the reaction zone can be located in different places in the film. We have identified the ten different cases given in Table 1. In this table we have also given the notation proposed by ourselves and by Saveant for the different cases and our expressions
for the observed
electrochemical
rate constant
for
the modified
elec-
of a modified electrode electrode it is trode, AhE. To understand. the operation important to find out to which case a s!lstem belongs. We have proposed a systematic method [IO] for doin g this. In this paper we apply this method to the reduction of Fe(III) and of Fe(CN)z-.
100
HPERIMENTAL
The methods of preparing thionine coated electrodes [l-3] the zpparatus and procedures have been described previously [3]. The rotating disc elektiode was made of platinum with a radius of 0.351 cm. AU water was deionized and then doubly distilled. All chemicals were of AnalaR grade except for thionine which was purified as described previously 161. All experiments were carried out at 25°C. All potentials were measured and are reported with respect to the saturated calomel electrode TABLE The
1
ten different
kinetic
cases
Case ’
Notation
k;,,=
Location
Sk”
-
X-“h 0
St,
E
Wo
Surface reaction at electrolyte layer interface
LSk
SR
LSt,
E
Lk
R
KkLb,
LRZ1.1,
S+E
Uo =+
I(D, L
Narrcw reaction zone in layer
LEk
ER
Kb,(
DCk/>;)‘r-
LEt,
S
my/L
Reaction layer close to electrode
a);’
_
k;
Et;
S
of ref. 7 b
/Us
Reaction layer close 10 electrolyte layer interface
K&/L
Throu.&out layer
the
Direct reaction on electrode
a In our notation the upper case ietter indicates the location (S. surface; L, layer; E. electrode); the lower case letters indiute the cate limiting process. b In Savtit’s notation E is equivalent to I,. S is equivalent to ty and R is equivalent to k. The notation indicates the rate limiting process but not the location. c The following symbols are used: concentration of B at electrode/film interface b, concen!ration of Y in solution at film/electrolyte interface ys K partit+, oxfficient for Y into film L film thickness diffu-;ion c-efficient for Y in. film D, diffusion coefficient for electrons in film 4 k” second order heterogeneous rate constant for reaction of B and Y at film/electrolyte interface. k second order homogeneous rate constant for reaction of B and Y in film. k’E electrochemical rate constant for reaction of Y on the electrode.
101
(SCE). The reduction of Fe(III) was carried out in 0.1 mol dmm3 paratoluene.. sulphonic acid (PTS). The reduction of Fe(CN)zwas carried out in potassiunl sulphate (0.1 mol dmw3) buffered at pH 3.0 with citric acid/potassium citrate. Stopped flow measurements were carried out using a Nortech SF3A stopped flow spectrophotometer, detecting thionine at a wavelength of 599 nm. RESULTS
AND
DISC:JSSION
Analysis
to find the mechanism
for Fe(lI1)
In the anodic solutions used in this work the thionine/leucothionine for free species in the electrolyte would be:
Th
red,>x couple
Leu
Recent work ustng a series of different thiazine dyes [12] and analysis of Raman spectra [S] has shown that the thionine coated electrode consists of a polymer containing three redox moieties. The electrode potential and pH behaviour of the redox s,stem in the coat is similar to that of free species in solution [6]. We start by considering the reduction of Fe(II1) by the Ieucothionine centres in the coat. Our proposed procedure [lo] for mechanistic diagnosis is given in Table 2. The Eouteckjl-Levich equation [13] for the limiting current, i,, at a rotating modified disc electrode is: nFAy,/i,
= L~v-‘/W’~
+ l/&n
(1)
where A is the area of the electrode, y_ is the bulk concentration of the electrolyte species, W is the rotation speed in Hz, and !c;Ma is the heterogeneous rate constant for the modified electrode [lO,ll]. Lev is the Levich constant and is given by Lev = 1_55~‘/3v-‘/6
(21
where D is the diffusion coefficient of Y in the electrolyte and Y is the kinematic viscosity. Typical plots of eqn. (1) for different bulk concentrations of Y are shown in Fig. 1. Within experimental error the data fall on a common line. Following the diagnosis in Table 2 it is clear that the currents do depend on rotation speed and that each plot is reasonably linear. The value of Lev from the gradient of the common line through all the data in Fig. 1 is (1.14 f 0.08) x 10m3 cm s-“~ and this agrees well with the value of 1.04 x 10S3 cm s- l/1_ found by reducing Fc(II1) on ir clean unmodified platinum electrode. Hence we conclude that eqn. (1) is obeyed and we reach the bottom left hand comer of Table 2. Next we examine the behaviour of k;,, found from the intercepts of the
TABLE
2
Diagnosis
tif mechanism
for modified
elec~rodcs
1
Is Kouwckjl-Levich plot linear?
?
1
n Yes
1
i Is gradient I
r
l-
given
by Lev- ‘? 1
Ye5J-
Sk”
LSk
Lk
Order
w.r.1.
h,
1
l/2
1
Order
W.T.I. L
0
0
1
LEI, 0 -1
* Eqn. (A): 2
nFAy% (i-w-‘) =_----+ iL
where
k;,E
B/1/1
= Kh,( D$/,;,)“‘,
and
rhe rer.raining
symbols
are as in eqn.
(I).
Fig. 1. Typical Kouteckjr-Lrvich piots (eqn. 11) for the reduction of Fc(Ili) electrode. The concentrations of Fe(lll) in mmol cm-’ were as follows: (X ) 0.10. 1.00. The broken line shows the Levich gradient obtained from the reduction plaIinum electrode.
a~
1
(0) of
:hionine
modified
0.25. (A) 0 50. (0) Fe(lll) on a bare
103
..
Koutecky-Levich plots which correspond. to infinite rotation speed with negligible concentration polarization in the electrolyte phase. Figure 2 shows values of khE measured for coats of different thicknesses (L). It can be seen that the rate constant for the reaction h.xs no significant variation with respect to L. The gradient is 0.05 + 0.07 and the order of k& with respect to L is zero: Hence from Table 2 the mechanism is ei:her SK” or LSK. To distinguish between these two cases we examine the behaviour of the electrode as the concentration of leucothionine (b,) is varied. This occurs on the rising part of the current vo!tage curve. An advantage of the thionine coat&l electrode is that one can measure the composition of the ccat from its optical density. We have shown [4] that the fraction, f, of the coat which is
the coloured In[f/(l
-J)]
species,
thionine,
= (2ayF/RT)(
is given by a modified
Nemst
equation:
E - Ee)
(3)
where cr = 0.27 and Ee = 0.180 V. In Fig. 3 we show how ki,, obtained from the intercepts of Koutecky-Levich plots varies with (1 - f), the fraction of the coat which is leucothionine (b,,), and which is calculated From eqn (3). The log-log plot is a good straight line with a gradient of 1.02 & 0.02. Henc? the order of the reaction with respect to leucothionine is unity, and completing the diagnosis in Table 2 we conclude that the mechanism is SK”. The reac.tion is not a layer reaction but takes place by electron transfer between leucothionine molecules in the outermost layer of the modified electrode and Fe(fII) species still in the electrolyte place. From the results in Fig. 3 we find that when the layer is fully reduced (f = 0), the value of k’,,, is 1.5 x 10m3 cm s-‘. From the molecular dimensions of a thionine molecule and making allowance for counter ions and solvation we estimate that the molecular volume J/’ of each thionine moiety is 0.4 ~1~. Then 6,, the concentration of leucothionine in the fully layer, is given by (N,vl)-’ where N, is Avogadro’s consLant and the value is approximately 4 mol dmm3. Hence the value of the second
\
1.0;
7
2
t
Y=-’ \ \
,E I ‘, I _. 0.y E
\\
I -
I
I
,/’
I
-a5
\
\
/
/
-/ /v‘_
i QOb
\\
1’
/
/
/
/
/
/is<,
/
/
\
‘Y+\
‘\\ \ I
OD
//
/
I
05
Fig. 2. Plot showing the order of kk,,
lo with
In (L/nm!
respect to L
\
15
the thiclrness of the film_
104
order homogeneous
rate constant for the surface reaction, k”, is
ic” = 4 x 10m4 dm3 mol-’
cm s-i
(4)
Surface reaction us. reacrion layer
In our work we have emphasized that the surface reaction described by k”- is a separate paralIe1 reaction route to any pathway which takes place in the coated layer [lC,ll]. SaGant and co-workers have preferred to regard the surface reaction as a limiting case of the layer reaction when the reaction layer thickness becomes comparable to molecular dimensions [7,9]. We now discuss the relation between homogeneous rate constants such as khE. k” and homogeneous rate constants referring to reaction in either the layer or in the electrolyte. Fi,,tsre 4 shows a schematic view of the redox centres in the outermost layer. In one direction these molecules look towards the “open sea” and can react directly with species in the electrolyte solution. The electrolyte species does not have to enter the layer and the transition state will be somewhere on the electrolyte side of the layer molecules. In the other direction, the “landward” side, the redox centre is part of the layer and hence reaction on this side will be a layer reaction. To react this side the electrolyte species does have to diffuse into the layer. The interface between the electrolyte and the layer can therefore be located along the line of centres of the outermost layer. We first consider the reaction of these molecules with species in the electrolyte. The flux (mol cm-’ s-‘) will be given by flux H,O = k”y,b’/2
Fig. 3. Plot showing variation
(5)
of /cbE with mole fraction of leucothionine
in the coat.
105
where we assume &hat kW is the same as the homogeneous second order rate constant, _ys is rhe concentration of Y in ahe eicctrolyte (allowing for any concentration polarizaticn). 6’ is the surface mncentration of B (mol cm-‘) in rhe outermost layer, and the factor of I/2 arises because the reaction can only take place on the seaward side of the iin% cenires. The surface concentration of B, b’, is related to its bulk concentration in the layer, b,, by 6’ = b,L’
(6)
where L’ is the distance between layers (see Fi g. 4). This process we have called the “surface reaction” and have written flUX n20
(7)
= k”_Q,
From eqns. (5)-(7)
we find tha?
k” = kwL’/2
(8)
Now turning to the layer reactions Y will penetrate a distance x into the layer with an exponential distribution given by ~7= Os exp( -x/X,
>
where the reaction length XL is given by X, = ( D,/kLb,)“’ Here, K is tk:e partition coefficient for Y between electrolyte and layer, D, is the diffusion coe::ficient of Y in the Iayer. and kL is the second order rate constant in the layer. Summing the contributions from successive layer and using eqn. (6), the flux in the layer i:: given by
where the factor of l/2
arises because molecules
Elecholyte
Fig. 4. Model of redox at the electrolyte
layer interface.
in the outermost
layer can only
106
carry out layer obtain flux,
reactions
= Kk,b,ij;L’
We now combine
on their
“landward”
1
-
1 - exp( - L’/X,)
eqns.
(8) and
(9) to give
side.
l/2
1
Summing
the geometric
series
we
(9)
an expression
for AZ’,,! where
flux = k’,,,iJ’s Kk ‘L’
k’,,i
-=kwL’/2+
1 - exp( - L’/X,)
hs
-
Kk ’-L’/2
(10)
This general equation relates the heterogeneous electrochemical rate constant for the second order rate constants kW and k L modified electrode, k’,,,. to the homogeneous in the electrolyte and the layer respecti\.ely. The second term in this equation has two limiting forms. First when L’ -S X,,. corresponding to slow reaction, we find This approximation gives the usual that the second term = KkLXL z+ KkL.5’/2. expression for our LSk case. Y penetrates through several layers (L’ -C XL) and the reaction takes place in a reaction layer close to the electrolyte interface. On the other to fast reaction, Y does not penetrate beyond hand when L’ >> XL, corresponding the outermost layer and the second term = KkLL’. This is the limit discussed by Saveant et al and considered by them to describe the “surface” reaction [7.9]. Under these conditions eqn. (10) reduces to k ;, F,‘b, = L’( k”‘/2
+ Kk ‘/2)
(11)
In ot:r view there are still two parallel routes for reaction even though it may prove diffic ult to find experimental methods for discrimination between the two different contvibutions. in the particular case when K = 1 and kL = kW the first and third terms in eqn. (1C: cancel out and there is then no difference between our for.mulation and that of Saveant et al. However, these are rather peculiar and special conditions. In our view it is much more likely that K will be smaller than 1. Under these conditions the third term of the general equation (10) is likely to be smaller than the first and the second term will only be significant if the denominator is much smaller than one, which arises when L’ > XL. Then we obtain our form of the general equation: 1: &/ho
= k” + Kk LXL
(12)
Here then are the two parallel processes: the electrolyte reaction involving just the outermost layer and the layer reaction involving several layers. Hence our treatment and Saveant’s treatment can be seen to be two special cases of the general equation (10). Connection
beiween homogeneous
and heterogeneo&
rate constants
In the treatment above we have assumed that there is a connection between the heterogeneous rate constant k” and the homogeneous rate constant kW given by eqn.
107
(8). We now examine whether this assumption is justified or not. First order constants found from spectrophotometry are plotted against the concentration Fe(Il1) in Fig. 5. From the gradient we find that dm” mol-’
k” = 650( +-40)
s-’
. value L’, the distance between the layers. will depend upon the thionine molecules. If they are flat then we estimate that there is a between the layers. However if they are oriented edgeways then a would be appropriate. Using these two values we find from eqn.
The the nm nm for
L’ =
for
0.6 nm
k” = 2.0 x 10-j
dm3 mol-’
cm s-’
nm
k” = 4.9 x 10-j
dm3 mol-’
cm s-’
L’ = 1.5
rate of (12a)
orientation of distance of 0.6 distance of 1.5 (8;:
Both values are about an order of magnitude from t~ie value for k” in eqn. (4) of 4 X lo-’ dm3 mol-’ cm s-‘. Considering that no allowance has been made for the roughness of the surface and the inevitable uncertainties in the geometry of the layer, we consider that this agreement is reasonable and supports our analysis and interpretation. Location
We
of Fe(iZZ)
are now also
diagrams
(see
different
diagram
reaction
Fig.
cases
in block
in a position 6).
that
in Table
we
to locate
introduced
1. The
is that one can predict
diagram
advantage
the change
this particular [ll]
to
show
the
system
in the
interrelation
block of the
of locating a system in such a block in the rate limiting step on changing such
0
1.5-L c AT
/
1.0-
d 0
of
/
Yj-/ (1
/
(
0
1
,
2 [Fe(EtjJ/mmd
dmm3
Fig. 5. Results from Ihe first order rate constant. k,. from the homogeneous reaction of Fe(III) leucothionine ploned against [Fe(W)].
Gith
108
variables as the thickness of the layer or the loading in the coat, and hence one can find ‘the effect of these changes on khE_ First we have to consider whether B is greater or less than one where B = k”b,/Kk;
03)
The parameter 8 compares the effectiveness of the two different surface reactions, k”b, for reaction at the surface and Kk’, for reaction at the electrode. An estimate of k; can be obtained from extrapolating Tafel plots for the reduction of Fe(III) on a clean electrode to the potential used in this work. We find that k; - 3 X 10’ cm s-‘. Hence from eqns. (4) and (13) e-5x10-6xK-’ We expect that K the partition
\ \ \ \ \ \ \ \ \
(14) coefficient
for Fe(M)
between
the layer and the
Sh”,
,LEk -_
Fig. 6. Block diagram showing the ten different cases listed in Table 1 for Ieaction at a modified electrode [ll] as a function of Ihe parameters XL/L, X6/L. and ~a defined in eqo 115). (16) and (19) respectively. The location of the Fe(III) reaction is shown by the thick double headed arrow for values of Kc 1.
109
solution is less than one. Equation K it is Iikely that
(14) therefore
shows that for reasonable
values of
B-=1 Hence we use the block diagram illustrated in Fig. 6 of ref. 11 and shown in Fig. 6. The point Q has been located assuming that K= 1, but the analysis will show that the exact location of Q with respect to 0 is not important. From our previous paper [6].we know that the diffusion coefficient D, for an ion in the layer is - lo-l3 cm* s-r and for the charge carriers 0, is - 10-l’ cm’ s-‘. Using the value of the homogeneous rate constant in eqn. (12) we find that the thickness of the two reaction layers XL at the surface and X6 at the electrode xe: XL = ( DY/k&,)““2
- 6 X 10m9
cm
05)
and Xi = ( DJ!cK~~)‘*‘~
- 4 X 10m6 X K-lr-
cm
(16)
The small value of XL arising frcm the small value of D, shows why the layer reaction is inefficient compared to the surface reaction_ Taking a typical value of L of 5 x lo-’ cm we find the foilowing values for the ratios which locate the system on the base of the cube: X;/L
-
lo-’
(17)
and SA/L -_ 19 y- ‘12 The distance Ks =
k”/KkL
up the cube is measured - K-l
(18) by (19)
The parameters ~~ compares the competition for Fe(II1) in the solution between the surface reaction (k”) and the layer reactiqn (KkL). The value of K, as discussed above is likely to be less than 1. In Fig. 6, using the values in eqns. (17)-(19), we locate the system in the cube. It can be seen that in agreement with our diagnosis the system lies in the.SK” zone. Although the point Q was located assuming K = 1, %r lower values of Q the point moves closer to 0 but this makes no difference to OIX conclusion that the system lies in the SK’ zone. Fe(CiV),3 - reaction We have also investigated the reduction of Fe(CN)zon the coated electrode. From stopped flow results we find that the s-and order rate constant for the reaction of Fe(CN)iwith leucothionine is (3.7 f 0.7) X 10’ dd mol-’ s-‘. This rate constant is five orders of magnitude greater than the rate constant for Fe(III). Using eqn. (8) we predict that kkjE would be 11 cm s-‘; this value is so large that at low concentrations of Fe(CN)zthe reaction on the rotating disc electrode would be
2 Fig. 7. Typical
,
4
I
(W/Hzlvz
Levich plot for the reduction
6
of Ft(CN)i-
on a thionine coated electrode.
by the mass transport of the Fe(CN)zto the electrode. Results in Fig. 7 show that this is G-tdeed the case; the value of the diffusion coefficient from the gradient is in excellent agreement with that determined on a bare platinum electrode. More important, the increase in k and the concomitant increase in k” will shift the system In Fig. 6 so that it moves from SK” zone into the St, zone. Hence as one increases the flux of Fe(CN>zfrom the bulk soiution then, if that flux exceeds the supply of electrons from .Ie electrode through the layer to the electrolyte interface, the rate limiting step will shift from the limiting transport of Fe(CN)i to the iimiting transport of the cha;-ge through the layer. Such an effect has indeed been observed by us [6] when the concentration of Fe(CN)iexceeds 0.1 mol dmm3. It is gratifying that the analysis can be applied to fink these two complementary systems in the block diagram describing the different reaction mechanisms. controlled
ACKNOWLEDGEMENTS
We thank ICI, the SERC and the Wolfson Foundation for financial is a contribution from the Wolfson Unit for Modified Electrodes.
support.
This
111 REFERENCES K.J. Hall. A.R. Hillman. R.G. Egdell and A.F. 1 W.J. Albery. W.R. Bowen. F.S. Fisher,. A. W. Foulds, Orchard. J. Electroanal. Chem., 107 (1980) 37. 2 W.J. Albery, A.W. Foulds, KJ. Hall, A.R Hillman. R.G. Egdell and A.F. Orchard, Nature (London). 282 (1979) 793. 3 WJ. Albery, A..W. Foulds. K-J. Hall and A.R. Hillman. J. Electrochem. Sot.. 127 (1980) 654. 4 W.J. Albery. AR. Hillman. R.G. Egdell and H. Nutton, J. Chem. Sot.. Faraday Trans. I, 80 (1984) 111. 5 K. Hutchinson. R.E. Hester. W.J. Albery and A.R. Hillman. J. Chem. Ser.. Faraday Trans. I. 80 (1984) 2053. 6 W.J. Albery. M.G. Boutelle, P.J. Colby and A.R Hillman. J. Elecrrr,anal. Chem.. 133 (1982) 135. 7 C.P. Andrieux, J.M. Dumas-Bouchiat and J.M. Sav&mf J. Electroanal. Chem., 131 (1982) 1. 8 C.P. Andrieux and J.M. Savkant, J. Electroanal. Chem., 1% (1982) 163. 9 F.C. Anson, J.M. Sav&mt and K. Shigehara, J. Phys. Chem.. 87 (1933) 214. 10 W-l. A:bery and A.R. Hillman. R.S.C. Ann. Rep. C, 78 (1981) 377. 11 W.J. Albery and A.R. Hillman, J. Electroanal. Chem., 170 (1984) 27. 12 J.M. Bagldreay and M.D. Archer. Eleclrochim. Acta. 28 (1983) 1515. 13 J. Kouteck? and V.G. Levich. Zh. Fir. Khim., 32 (1956) 1565.
182 (1985)
Chem..
Elsevier Sequoia
S.A..
99
99- I1 1
Lausanne
-
Printed in The Netherlands
THE MECHANISM OF FARADAlC COATED ELECi-RODE
W. JOHN
ALBERY
Deparlmenr
of Chemisrr):
A. ROBERT Deparzmenr BS8
ITS
and MARTYN
AT THE
THlONlNE
G. BOUTELLE College.
London
SIV7
-7A Y (Great
Britain)
HILLMAN of Pnysicol
(Grear
(Received
Imperial
REACTIONS
Chemisrr);
School of Chemislg;
Unicersic.v
a/ Brisrol,
Canrock’s
Close.
Brisrol
Britain)
29th May
1984;
in revised form 16th August
1984)
ABSTRACT Ressul~s are presented modified speed.
electrode.
for the reduction
Systematic
analysis
film thickness and electrode
of
Fe(lil)
and
of the varialion
polential
of
of
estimated located The
from
rate constant
the second
in a block
order
diagram
rate of the Fe(CN)z-
by the transport
rcle
in a thionins
for Fe(ill)
with
which
fi*r the surface
rate constant
for
shows all the possible
is in reasonable
homogsneous mechanisms
reaction is five orders of magnitude
of Fe(CN)i-
through the electrolyte
the
A general equation is derived which inciadcs rakes place in a thin rexlion layer in the rrinl.
rextion the
rota1i.m
reaction between
are shown 10 be distinct and special cases of the general equation.
two parallel processes
the heterogeneous
by leucothionine
proves that the reaction is a “surface”
outermost layer of leucothionine and Fe(lll) in solution. bolh the “surface” reaction and the cast where the reaction These
Fe(CN)zthe reaction
agreement
reaction.
The
The value
with
Fe(Jll)
a vaiur
reaction
for [his type of modified
faster so that the rnle is controlled
or by the transport
This change in the rate limiting process agrees wi:h the position
of eit-Irons
of the system
is
elecctrode.
through
either
the film.
in t1.e block diagram.
INTRODUCTION
Previous
work on the thionine
coated
electrode
[l-3]
has elucidated
the nature of
the coated layer [4,5] and the mechanism of charging and discharging the redox centres in the modified electrode [6]. In this paper we report investigations on the mechanism of Faradaic reactions carried out at the thionine coated electrode. Theoretical analysis by the San.-Lant school [7-91 and by ourselves [13,11] has shown that the reaction zone can be located in different places in the film. We have identified the ten different cases given in Table 1. In this table we have also given the notation proposed by ourselves and by Saveant for the different cases and our expressions
for the observed
electrochemical
rate constant
for
the modified
elec-
of a modified electrode electrode it is trode, AhE. To understand. the operation important to find out to which case a s!lstem belongs. We have proposed a systematic method [IO] for doin g this. In this paper we apply this method to the reduction of Fe(III) and of Fe(CN)z-.
100
HPERIMENTAL
The methods of preparing thionine coated electrodes [l-3] the zpparatus and procedures have been described previously [3]. The rotating disc elektiode was made of platinum with a radius of 0.351 cm. AU water was deionized and then doubly distilled. All chemicals were of AnalaR grade except for thionine which was purified as described previously 161. All experiments were carried out at 25°C. All potentials were measured and are reported with respect to the saturated calomel electrode TABLE The
1
ten different
kinetic
cases
Case ’
Notation
k;,,=
Location
Sk”
-
X-“h 0
St,
E
Wo
Surface reaction at electrolyte layer interface
LSk
SR
LSt,
E
Lk
R
KkLb,
LRZ1.1,
S+E
Uo =+
I(D, L
Narrcw reaction zone in layer
LEk
ER
Kb,(
DCk/>;)‘r-
LEt,
S
my/L
Reaction layer close to electrode
a);’
_
k;
Et;
S
of ref. 7 b
/Us
Reaction layer close 10 electrolyte layer interface
K&/L
Throu.&out layer
the
Direct reaction on electrode
a In our notation the upper case ietter indicates the location (S. surface; L, layer; E. electrode); the lower case letters indiute the cate limiting process. b In Savtit’s notation E is equivalent to I,. S is equivalent to ty and R is equivalent to k. The notation indicates the rate limiting process but not the location. c The following symbols are used: concentration of B at electrode/film interface b, concen!ration of Y in solution at film/electrolyte interface ys K partit+, oxfficient for Y into film L film thickness diffu-;ion c-efficient for Y in. film D, diffusion coefficient for electrons in film 4 k” second order heterogeneous rate constant for reaction of B and Y at film/electrolyte interface. k second order homogeneous rate constant for reaction of B and Y in film. k’E electrochemical rate constant for reaction of Y on the electrode.
101
(SCE). The reduction of Fe(III) was carried out in 0.1 mol dmm3 paratoluene.. sulphonic acid (PTS). The reduction of Fe(CN)zwas carried out in potassiunl sulphate (0.1 mol dmw3) buffered at pH 3.0 with citric acid/potassium citrate. Stopped flow measurements were carried out using a Nortech SF3A stopped flow spectrophotometer, detecting thionine at a wavelength of 599 nm. RESULTS
AND
DISC:JSSION
Analysis
to find the mechanism
for Fe(lI1)
In the anodic solutions used in this work the thionine/leucothionine for free species in the electrolyte would be:
Th
red,>x couple
Leu
Recent work ustng a series of different thiazine dyes [12] and analysis of Raman spectra [S] has shown that the thionine coated electrode consists of a polymer containing three redox moieties. The electrode potential and pH behaviour of the redox s,stem in the coat is similar to that of free species in solution [6]. We start by considering the reduction of Fe(II1) by the Ieucothionine centres in the coat. Our proposed procedure [lo] for mechanistic diagnosis is given in Table 2. The Eouteckjl-Levich equation [13] for the limiting current, i,, at a rotating modified disc electrode is: nFAy,/i,
= L~v-‘/W’~
+ l/&n
(1)
where A is the area of the electrode, y_ is the bulk concentration of the electrolyte species, W is the rotation speed in Hz, and !c;Ma is the heterogeneous rate constant for the modified electrode [lO,ll]. Lev is the Levich constant and is given by Lev = 1_55~‘/3v-‘/6
(21
where D is the diffusion coefficient of Y in the electrolyte and Y is the kinematic viscosity. Typical plots of eqn. (1) for different bulk concentrations of Y are shown in Fig. 1. Within experimental error the data fall on a common line. Following the diagnosis in Table 2 it is clear that the currents do depend on rotation speed and that each plot is reasonably linear. The value of Lev from the gradient of the common line through all the data in Fig. 1 is (1.14 f 0.08) x 10m3 cm s-“~ and this agrees well with the value of 1.04 x 10S3 cm s- l/1_ found by reducing Fc(II1) on ir clean unmodified platinum electrode. Hence we conclude that eqn. (1) is obeyed and we reach the bottom left hand comer of Table 2. Next we examine the behaviour of k;,, found from the intercepts of the
TABLE
2
Diagnosis
tif mechanism
for modified
elec~rodcs
1
Is Kouwckjl-Levich plot linear?
?
1
n Yes
1
i Is gradient I
r
l-
given
by Lev- ‘? 1
Ye5J-
Sk”
LSk
Lk
Order
w.r.1.
h,
1
l/2
1
Order
W.T.I. L
0
0
1
LEI, 0 -1
* Eqn. (A): 2
nFAy% (i-w-‘) =_----+ iL
where
k;,E
B/1/1
= Kh,( D$/,;,)“‘,
and
rhe rer.raining
symbols
are as in eqn.
(I).
Fig. 1. Typical Kouteckjr-Lrvich piots (eqn. 11) for the reduction of Fc(Ili) electrode. The concentrations of Fe(lll) in mmol cm-’ were as follows: (X ) 0.10. 1.00. The broken line shows the Levich gradient obtained from the reduction plaIinum electrode.
a~
1
(0) of
:hionine
modified
0.25. (A) 0 50. (0) Fe(lll) on a bare
103
..
Koutecky-Levich plots which correspond. to infinite rotation speed with negligible concentration polarization in the electrolyte phase. Figure 2 shows values of khE measured for coats of different thicknesses (L). It can be seen that the rate constant for the reaction h.xs no significant variation with respect to L. The gradient is 0.05 + 0.07 and the order of k& with respect to L is zero: Hence from Table 2 the mechanism is ei:her SK” or LSK. To distinguish between these two cases we examine the behaviour of the electrode as the concentration of leucothionine (b,) is varied. This occurs on the rising part of the current vo!tage curve. An advantage of the thionine coat&l electrode is that one can measure the composition of the ccat from its optical density. We have shown [4] that the fraction, f, of the coat which is
the coloured In[f/(l
-J)]
species,
thionine,
= (2ayF/RT)(
is given by a modified
Nemst
equation:
E - Ee)
(3)
where cr = 0.27 and Ee = 0.180 V. In Fig. 3 we show how ki,, obtained from the intercepts of Koutecky-Levich plots varies with (1 - f), the fraction of the coat which is leucothionine (b,,), and which is calculated From eqn (3). The log-log plot is a good straight line with a gradient of 1.02 & 0.02. Henc? the order of the reaction with respect to leucothionine is unity, and completing the diagnosis in Table 2 we conclude that the mechanism is SK”. The reac.tion is not a layer reaction but takes place by electron transfer between leucothionine molecules in the outermost layer of the modified electrode and Fe(fII) species still in the electrolyte place. From the results in Fig. 3 we find that when the layer is fully reduced (f = 0), the value of k’,,, is 1.5 x 10m3 cm s-‘. From the molecular dimensions of a thionine molecule and making allowance for counter ions and solvation we estimate that the molecular volume J/’ of each thionine moiety is 0.4 ~1~. Then 6,, the concentration of leucothionine in the fully layer, is given by (N,vl)-’ where N, is Avogadro’s consLant and the value is approximately 4 mol dmm3. Hence the value of the second
\
1.0;
7
2
t
Y=-’ \ \
,E I ‘, I _. 0.y E
\\
I -
I
I
,/’
I
-a5
\
\
/
/
-/ /v‘_
i QOb
\\
1’
/
/
/
/
/
/is<,
/
/
\
‘Y+\
‘\\ \ I
OD
//
/
I
05
Fig. 2. Plot showing the order of kk,,
lo with
In (L/nm!
respect to L
\
15
the thiclrness of the film_
104
order homogeneous
rate constant for the surface reaction, k”, is
ic” = 4 x 10m4 dm3 mol-’
cm s-i
(4)
Surface reaction us. reacrion layer
In our work we have emphasized that the surface reaction described by k”- is a separate paralIe1 reaction route to any pathway which takes place in the coated layer [lC,ll]. SaGant and co-workers have preferred to regard the surface reaction as a limiting case of the layer reaction when the reaction layer thickness becomes comparable to molecular dimensions [7,9]. We now discuss the relation between homogeneous rate constants such as khE. k” and homogeneous rate constants referring to reaction in either the layer or in the electrolyte. Fi,,tsre 4 shows a schematic view of the redox centres in the outermost layer. In one direction these molecules look towards the “open sea” and can react directly with species in the electrolyte solution. The electrolyte species does not have to enter the layer and the transition state will be somewhere on the electrolyte side of the layer molecules. In the other direction, the “landward” side, the redox centre is part of the layer and hence reaction on this side will be a layer reaction. To react this side the electrolyte species does have to diffuse into the layer. The interface between the electrolyte and the layer can therefore be located along the line of centres of the outermost layer. We first consider the reaction of these molecules with species in the electrolyte. The flux (mol cm-’ s-‘) will be given by flux H,O = k”y,b’/2
Fig. 3. Plot showing variation
(5)
of /cbE with mole fraction of leucothionine
in the coat.
105
where we assume &hat kW is the same as the homogeneous second order rate constant, _ys is rhe concentration of Y in ahe eicctrolyte (allowing for any concentration polarizaticn). 6’ is the surface mncentration of B (mol cm-‘) in rhe outermost layer, and the factor of I/2 arises because the reaction can only take place on the seaward side of the iin% cenires. The surface concentration of B, b’, is related to its bulk concentration in the layer, b,, by 6’ = b,L’
(6)
where L’ is the distance between layers (see Fi g. 4). This process we have called the “surface reaction” and have written flUX n20
(7)
= k”_Q,
From eqns. (5)-(7)
we find tha?
k” = kwL’/2
(8)
Now turning to the layer reactions Y will penetrate a distance x into the layer with an exponential distribution given by ~7= Os exp( -x/X,
>
where the reaction length XL is given by X, = ( D,/kLb,)“’ Here, K is tk:e partition coefficient for Y between electrolyte and layer, D, is the diffusion coe::ficient of Y in the Iayer. and kL is the second order rate constant in the layer. Summing the contributions from successive layer and using eqn. (6), the flux in the layer i:: given by
where the factor of l/2
arises because molecules
Elecholyte
Fig. 4. Model of redox at the electrolyte
layer interface.
in the outermost
layer can only
106
carry out layer obtain flux,
reactions
= Kk,b,ij;L’
We now combine
on their
“landward”
1
-
1 - exp( - L’/X,)
eqns.
(8) and
(9) to give
side.
l/2
1
Summing
the geometric
series
we
(9)
an expression
for AZ’,,! where
flux = k’,,,iJ’s Kk ‘L’
k’,,i
-=kwL’/2+
1 - exp( - L’/X,)
hs
-
Kk ’-L’/2
(10)
This general equation relates the heterogeneous electrochemical rate constant for the second order rate constants kW and k L modified electrode, k’,,,. to the homogeneous in the electrolyte and the layer respecti\.ely. The second term in this equation has two limiting forms. First when L’ -S X,,. corresponding to slow reaction, we find This approximation gives the usual that the second term = KkLXL z+ KkL.5’/2. expression for our LSk case. Y penetrates through several layers (L’ -C XL) and the reaction takes place in a reaction layer close to the electrolyte interface. On the other to fast reaction, Y does not penetrate beyond hand when L’ >> XL, corresponding the outermost layer and the second term = KkLL’. This is the limit discussed by Saveant et al and considered by them to describe the “surface” reaction [7.9]. Under these conditions eqn. (10) reduces to k ;, F,‘b, = L’( k”‘/2
+ Kk ‘/2)
(11)
In ot:r view there are still two parallel routes for reaction even though it may prove diffic ult to find experimental methods for discrimination between the two different contvibutions. in the particular case when K = 1 and kL = kW the first and third terms in eqn. (1C: cancel out and there is then no difference between our for.mulation and that of Saveant et al. However, these are rather peculiar and special conditions. In our view it is much more likely that K will be smaller than 1. Under these conditions the third term of the general equation (10) is likely to be smaller than the first and the second term will only be significant if the denominator is much smaller than one, which arises when L’ > XL. Then we obtain our form of the general equation: 1: &/ho
= k” + Kk LXL
(12)
Here then are the two parallel processes: the electrolyte reaction involving just the outermost layer and the layer reaction involving several layers. Hence our treatment and Saveant’s treatment can be seen to be two special cases of the general equation (10). Connection
beiween homogeneous
and heterogeneo&
rate constants
In the treatment above we have assumed that there is a connection between the heterogeneous rate constant k” and the homogeneous rate constant kW given by eqn.
107
(8). We now examine whether this assumption is justified or not. First order constants found from spectrophotometry are plotted against the concentration Fe(Il1) in Fig. 5. From the gradient we find that dm” mol-’
k” = 650( +-40)
s-’
. value L’, the distance between the layers. will depend upon the thionine molecules. If they are flat then we estimate that there is a between the layers. However if they are oriented edgeways then a would be appropriate. Using these two values we find from eqn.
The the nm nm for
L’ =
for
0.6 nm
k” = 2.0 x 10-j
dm3 mol-’
cm s-’
nm
k” = 4.9 x 10-j
dm3 mol-’
cm s-’
L’ = 1.5
rate of (12a)
orientation of distance of 0.6 distance of 1.5 (8;:
Both values are about an order of magnitude from t~ie value for k” in eqn. (4) of 4 X lo-’ dm3 mol-’ cm s-‘. Considering that no allowance has been made for the roughness of the surface and the inevitable uncertainties in the geometry of the layer, we consider that this agreement is reasonable and supports our analysis and interpretation. Location
We
of Fe(iZZ)
are now also
diagrams
(see
different
diagram
reaction
Fig.
cases
in block
in a position 6).
that
in Table
we
to locate
introduced
1. The
is that one can predict
diagram
advantage
the change
this particular [ll]
to
show
the
system
in the
interrelation
block of the
of locating a system in such a block in the rate limiting step on changing such
0
1.5-L c AT
/
1.0-
d 0
of
/
Yj-/ (1
/
(
0
1
,
2 [Fe(EtjJ/mmd
dmm3
Fig. 5. Results from Ihe first order rate constant. k,. from the homogeneous reaction of Fe(III) leucothionine ploned against [Fe(W)].
Gith
108
variables as the thickness of the layer or the loading in the coat, and hence one can find ‘the effect of these changes on khE_ First we have to consider whether B is greater or less than one where B = k”b,/Kk;
03)
The parameter 8 compares the effectiveness of the two different surface reactions, k”b, for reaction at the surface and Kk’, for reaction at the electrode. An estimate of k; can be obtained from extrapolating Tafel plots for the reduction of Fe(III) on a clean electrode to the potential used in this work. We find that k; - 3 X 10’ cm s-‘. Hence from eqns. (4) and (13) e-5x10-6xK-’ We expect that K the partition
\ \ \ \ \ \ \ \ \
(14) coefficient
for Fe(M)
between
the layer and the
Sh”,
,LEk -_
Fig. 6. Block diagram showing the ten different cases listed in Table 1 for Ieaction at a modified electrode [ll] as a function of Ihe parameters XL/L, X6/L. and ~a defined in eqo 115). (16) and (19) respectively. The location of the Fe(III) reaction is shown by the thick double headed arrow for values of Kc 1.
109
solution is less than one. Equation K it is Iikely that
(14) therefore
shows that for reasonable
values of
B-=1 Hence we use the block diagram illustrated in Fig. 6 of ref. 11 and shown in Fig. 6. The point Q has been located assuming that K= 1, but the analysis will show that the exact location of Q with respect to 0 is not important. From our previous paper [6].we know that the diffusion coefficient D, for an ion in the layer is - lo-l3 cm* s-r and for the charge carriers 0, is - 10-l’ cm’ s-‘. Using the value of the homogeneous rate constant in eqn. (12) we find that the thickness of the two reaction layers XL at the surface and X6 at the electrode xe: XL = ( DY/k&,)““2
- 6 X 10m9
cm
05)
and Xi = ( DJ!cK~~)‘*‘~
- 4 X 10m6 X K-lr-
cm
(16)
The small value of XL arising frcm the small value of D, shows why the layer reaction is inefficient compared to the surface reaction_ Taking a typical value of L of 5 x lo-’ cm we find the foilowing values for the ratios which locate the system on the base of the cube: X;/L
-
lo-’
(17)
and SA/L -_ 19 y- ‘12 The distance Ks =
k”/KkL
up the cube is measured - K-l
(18) by (19)
The parameters ~~ compares the competition for Fe(II1) in the solution between the surface reaction (k”) and the layer reactiqn (KkL). The value of K, as discussed above is likely to be less than 1. In Fig. 6, using the values in eqns. (17)-(19), we locate the system in the cube. It can be seen that in agreement with our diagnosis the system lies in the.SK” zone. Although the point Q was located assuming K = 1, %r lower values of Q the point moves closer to 0 but this makes no difference to OIX conclusion that the system lies in the SK’ zone. Fe(CiV),3 - reaction We have also investigated the reduction of Fe(CN)zon the coated electrode. From stopped flow results we find that the s-and order rate constant for the reaction of Fe(CN)iwith leucothionine is (3.7 f 0.7) X 10’ dd mol-’ s-‘. This rate constant is five orders of magnitude greater than the rate constant for Fe(III). Using eqn. (8) we predict that kkjE would be 11 cm s-‘; this value is so large that at low concentrations of Fe(CN)zthe reaction on the rotating disc electrode would be
2 Fig. 7. Typical
,
4
I
(W/Hzlvz
Levich plot for the reduction
6
of Ft(CN)i-
on a thionine coated electrode.
by the mass transport of the Fe(CN)zto the electrode. Results in Fig. 7 show that this is G-tdeed the case; the value of the diffusion coefficient from the gradient is in excellent agreement with that determined on a bare platinum electrode. More important, the increase in k and the concomitant increase in k” will shift the system In Fig. 6 so that it moves from SK” zone into the St, zone. Hence as one increases the flux of Fe(CN>zfrom the bulk soiution then, if that flux exceeds the supply of electrons from .Ie electrode through the layer to the electrolyte interface, the rate limiting step will shift from the limiting transport of Fe(CN)i to the iimiting transport of the cha;-ge through the layer. Such an effect has indeed been observed by us [6] when the concentration of Fe(CN)iexceeds 0.1 mol dmm3. It is gratifying that the analysis can be applied to fink these two complementary systems in the block diagram describing the different reaction mechanisms. controlled
ACKNOWLEDGEMENTS
We thank ICI, the SERC and the Wolfson Foundation for financial is a contribution from the Wolfson Unit for Modified Electrodes.
support.
This
111 REFERENCES K.J. Hall. A.R. Hillman. R.G. Egdell and A.F. 1 W.J. Albery. W.R. Bowen. F.S. Fisher,. A. W. Foulds, Orchard. J. Electroanal. Chem., 107 (1980) 37. 2 W.J. Albery, A.W. Foulds, KJ. Hall, A.R Hillman. R.G. Egdell and A.F. Orchard, Nature (London). 282 (1979) 793. 3 WJ. Albery, A..W. Foulds. K-J. Hall and A.R. Hillman. J. Electrochem. Sot.. 127 (1980) 654. 4 W.J. Albery. AR. Hillman. R.G. Egdell and H. Nutton, J. Chem. Sot.. Faraday Trans. I, 80 (1984) 111. 5 K. Hutchinson. R.E. Hester. W.J. Albery and A.R. Hillman. J. Chem. Ser.. Faraday Trans. I. 80 (1984) 2053. 6 W.J. Albery. M.G. Boutelle, P.J. Colby and A.R Hillman. J. Elecrrr,anal. Chem.. 133 (1982) 135. 7 C.P. Andrieux, J.M. Dumas-Bouchiat and J.M. Sav&mf J. Electroanal. Chem., 131 (1982) 1. 8 C.P. Andrieux and J.M. Savkant, J. Electroanal. Chem., 1% (1982) 163. 9 F.C. Anson, J.M. Sav&mt and K. Shigehara, J. Phys. Chem.. 87 (1933) 214. 10 W-l. A:bery and A.R. Hillman. R.S.C. Ann. Rep. C, 78 (1981) 377. 11 W.J. Albery and A.R. Hillman, J. Electroanal. Chem., 170 (1984) 27. 12 J.M. Bagldreay and M.D. Archer. Eleclrochim. Acta. 28 (1983) 1515. 13 J. Kouteck? and V.G. Levich. Zh. Fir. Khim., 32 (1956) 1565.