XII Iberian Meeting of Electrochemistry XVI Meeting of the ...

XII Iberian Meeting of Electrochemistry & XVI Meeting of the Portuguese Electrochemical Society O C 02
Convolutive modelling with Mathematica ® using Oldham-
Mahon-Myland h i (t) functions. C r E q mechanism in C V.
M. J. Barrera-Niebla 1 , M.J. González Morín 1 , M. R. García Hernández 2 ,
D.M. Grandoso Medina 1 , L.C. Fernández Mérida 1
1 Physical Chemistry Department. University of La Laguna. La Laguna. 2 Consejería de Presidencia,
Justicia y Seguridad. Gobierno de Canarias.TENERIFE. CANARY ISLANDS. SPAIN.
mbarnie@ull.es
Convolutive Modelling is an important methodology of Semiintegral and Convolution
Electrochemistry [1]. We model with Mathematica ® software, in order to overcome the
advanced mathematics, the I E curves for a C r Eq
mechanism at planar electrodes.
The mentioned methodology employs the universal convolution algorithm of Oldham
and the extended semiintegrals M R (t)
and M P (t)
. The mechanism represented by
k
k
f
S(
soln)
R(
soln)
R(
soln)
ne P(
soln)
(1)
k'
kb
allows us to infer for k k'
the following expression for h R (t)
, namely
2k
k'
1
2exp ( k k')
t
h R ( t)
2( k k')
t
2
2 k t
k'
exp
k k'
Erfi
3/ 2
( k k')
k'
t
Erfi
k k'
k t
k k'
required to calculate, with Mathematica ® , the single integral of equation (2) needed in
the convolutive modelling. When k k'
an easier equation is obtained.. These
methodologies let us to obtain the files: M R (t)
, M P (t)
, and in duplicate, I (E)
. A very
basic program written for Mathematica ® is reported to model I E curves. We check
these files with those obtained by convolutive modelling with Oldham-Mahon-Myland
g(t)
functions and by digital simulation with DigiSim ® and DigiElch ® . This comparison
was made with the assistance of SigmaPlot ® software. The agreement is excellent. The
methodologies employed are based in the following convolutions
dh t
I t M t i ( )
( ) i ( )* i R,
P
(3)
dt
The extended semiintegrals M R (t)
and M P (t)
are connected with electrode surface
concentrations by a linear relation with known parameters. Hence the C R ( 0, t)
and
C P ( 0, t)
files are obtained in a straightforward procedure and are complementary with
the concentration profiles C R ( x,
1 t ) and C P ( x,
1 t ) determined by digital simulation.
(2)
Acknowledgements: To Professor Keith B. Oldham, Peter J. Mahon and Jan C. Myland.
References
[1] Barrera-Niebla, M.J.. Semiintegral and Convolution Electrochemistry. Research line.
Department of Physical Chemistry. (2010). La Laguna University. Tenerife. Canary Islands.
September, 811, 2010. ISEL - Lisbon 41