koff - LEPA
koff - LEPA
koff - LEPA
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and<br />
c 2 = 0 A2.34<br />
c1 = c / exp ! a2<br />
3 z3<br />
" %<br />
$ '<br />
# &<br />
dz<br />
(<br />
) A2.35<br />
0<br />
Equation (1.120) becomes<br />
F(!) = c<br />
(<br />
(<br />
!<br />
0<br />
)<br />
0<br />
exp ! a2 "<br />
$<br />
#<br />
exp ! a2 "<br />
$<br />
#<br />
3 z3<br />
3 z3<br />
%<br />
'<br />
&<br />
dz<br />
%<br />
'<br />
&<br />
dz<br />
The normalising integral is finite and equal to<br />
exp ! a2<br />
3 z3<br />
" %<br />
$ '<br />
# &<br />
dz<br />
(<br />
) =<br />
0<br />
2 3<br />
9<br />
5/6<br />
a 2/3 * 2 " %<br />
#<br />
$<br />
3&<br />
'<br />
The concentration profiles are therefore given by<br />
! y $<br />
c(x, y) = F<br />
"<br />
#<br />
! (x) %<br />
&<br />
= F(") =<br />
To calculate the thickness of the diffusion layer, we can write<br />
and<br />
" !c%<br />
#<br />
$<br />
!y&<br />
'<br />
y=0<br />
! dF $<br />
"<br />
#<br />
d! %<br />
& !=0<br />
= !! " dF %<br />
!y #<br />
$<br />
d! &<br />
'<br />
!=0<br />
=<br />
3 1/6 a 2/3 ' 2 ! $<br />
"<br />
#<br />
3%<br />
& c b<br />
2<br />
= 1 " dF %<br />
" #<br />
$<br />
d! &<br />
'<br />
!=0<br />
This equation allows us to calculate a= 0.87116.<br />
By integration of eq.(1.118), we have<br />
! =<br />
∫<br />
l<br />
3<br />
0<br />
3a 2 Dx<br />
dx<br />
!<br />
0<br />
l<br />
∫ dx<br />
=<br />
A2.36<br />
A2.37<br />
3 1/6 a 2/3 c' 2 ! $<br />
"<br />
#<br />
3%<br />
&<br />
exp (<br />
2<br />
a2<br />
3 z3<br />
! $<br />
# &<br />
" %<br />
dz<br />
"<br />
) A2.38<br />
0<br />
= (c<br />
"<br />
= cb<br />
"<br />
A2.39<br />
= 0.8131 a 2/3 c b = c b A2.40<br />
∫<br />
l<br />
3<br />
0<br />
0.759Dhx<br />
dx<br />
< v ><br />
l<br />
∫ dx<br />
0<br />
=<br />
3<br />
4<br />
0.759Dh<br />
< v ><br />
l<br />
3 l 4/3<br />
The limiting current on the band electrode is then for the case illustrated in figure 13<br />
I = nFDLc b l dx<br />
0 ! (x)<br />
! = nFDLc b l<br />
!<br />
0<br />
dx<br />
3<br />
3a 2 Dx<br />
"<br />
= 3 –1/3 a "2/3 nFc b LD 2/3 " 1/3 l 2/3<br />
A2.41<br />
32
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