Generation of changing sing spase charge in a diffufion layer
for electrode process with subsequent homogeneous reaction
Yu.I.Kharkats, A.V.Sokirko
The A.N.Frumkin Institute of Electrochemistry,
Academy of Sciences of the USSR, Moscow
It is known that during electric current passing a space
charge region arises in diffusion layer, whose distribution
density decreases non-exponentially as it was in diffuse layer,
but in a sooth fashion [1]. When the current density tends to its
limiting value the space charge density in the vicinity of the
electrode increases abruptly coinciding in sign with that
for electroactive ions.
Here we present the results of investigation of space charge
z+
distribution in diffusion layer for reduction of cations A +
- o - -
2e -` A , and parallel oxygen reduction O + 2H O + 4e --` 4OH
2 2
- +
with subsequent recombination reaction of OH and H ions in
- +
diffusion layer: OH + H --` H O. This reaction scheme was
2
analyzed in detail in ref. [2], in which the mechanism of
migration current exaltation effect in acidic solutions was
theoretically investigated.
The set of electrodiffusion equations describing the
distributions of component's concentrations and the potential in
diffusion layer may be written as
dc dJ i L dc dJ
1 1 2
--- + c ---- = -----, --- - c ---- = 0, (1)
1 0 2
dx dx FD c dx dx
1
dc dJ dc dJ i L
3 4 2
D (--- - c ---- ) - D ( --- + c ---- ) = - ---- = - D j , (2)
3 3 4 4 0 3 2
dx dx dx dx Fc
c c = K , c + c = c + c . (3)
3 4 0 2 3 1 4
Here c , c , c and c - are dimensionless concentrations of
1 2 3 4
+ - +
cations A , anions, OH ions and H ions, c is the dimensional
0
+
concentration of A ions in the solution bulk, J = Fv/RT is the
dimensionless electric potential, x is dimensionless coordinate
(0<x<1), L is the thickness of Nernst diffusion layer, i and i
1 2
are current densities for cation's discharge and oxygen
reduction, K - the ionic product for water, the boundary
0
conditions at x=1 can be written as c (1)=1, c (1)=1+k, c (1)=0,
1 2 3
c (1)=k, J(1)=0.
4
Taking into account that recombination reaction for water is
very fast and the equilibrium constant satisfies to inequality
-
K , 1, we can suppose that in the diffusion layer either ions OH
0
+
or H ions can exist simultaneously. Correspondingly the
recombination reaction plane x=q splits the diffusion layer into
two regions 0<x<q and q<x<1. We can put c >0 and c ~0 in the
4 3
region spaced to the right of the point x=q and c >0 and c ~0 in
3 4
the region spaced to the left of the point x=0. These
approximations make it possible to determine the potential
distribution J(x) and then using Poisson equation to find space
charge distribution r = - e RT J"/F.
Calculated r(x) distributions for series of parameters j ,
1
and fixed j and k values are shown in Figure.
2
Fig. Space charge distribution for D /D = 0.56; k = 0.8; j =4,
3 4 2
0 2
and j : 1 - 2; 2 - 2.5; 3 - 2.7. r = 2 e c ( l /L) , l is the
1 0 D D
Debuy length.
The analysis shows that as a result of recombination
reaction inside the the diffusion layer some interesting
peculiarities in space charge distribution arise. At the point of
homogeneous reaction localization x=q and under the condition
D j > kD j the abrupt charge of the sign and absolute value of
3 2 4 1
r(x) takes place. In the discussed model due to high value of
rate constant of recombination reaction its reaction layer had
practically zero thickness. In more general case of moderate
reaction rates there must exist some transition region in which
space charge varies from positive to negative values.
Qualitatively the obtained result can be explained as follows. We
can present the plane of recombination reaction localization as
+
some electrode plane at x=q which is from fervor one side with H
-
ions and from the other side with OH ions. Then in the region
+
q<x<1 where H ions exist we have as in usual electrolyte
positive space charge distribution. And in the region 0<x<q where
-
OH exist we have correspondingly negative space charge
distribution.
We note in conclusion that the peak in space charge
distributions including also changing the sign of space charge
was earlier predicted in refs.[3,4] for the systems in which
besides movable carriers of charge also fixed charges exist.
References.
1. V.G.Levich. Physic-chemical Hydrodynamics.M.: 1959.
2. A.V.Sokirko, Yu.I.Kharkats, Electrokhimija, 25 (1989) 232.
3. Yu.I.Kharkats, Electrokhimija, 20 (1984) 248.
4. Yu.Ya.Gurevich, A.V.Noskov, Yu.I.Kharkats, Elekrokhimiya,
Proc. Acad. Sci. USSR, 298 (1988) 383.
