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<strong>XII</strong> <strong>Iberian</strong> <strong>Meeting</strong> <strong>of</strong> <strong>Electrochemistry</strong> & <strong>XVI</strong> <strong>Meeting</strong> <strong>of</strong> <strong>the</strong> Portuguese Electrochemical Society O C 05<br />

Convolutive modelling with universal master equation <strong>of</strong><br />

Oldham-Mahon-Myland by using Ma<strong>the</strong>matica ® s<strong>of</strong>tware.<br />

E q C i mechanism in C V at spherical electrodes.<br />

M. J. Barrera-Niebla 1 , M. R. García Hernández 2 , M. J. González Morín 1 ,<br />

L.C. Fernández Mérida 1 , D.M. Grandoso Medina 1<br />

1 Physical Chemistry Department. University <strong>of</strong> La Laguna. La Laguna<br />

2 Consejería de Presidencia, Justicia y Seguridad. Gobierno de Canarias<br />

TENERIFE. CANARY ISLANDS. SPAIN.<br />

mbarnie@ull.es<br />

Convolutive Modelling is an important methodology <strong>of</strong> Semiintegral and Convolution<br />

<strong>Electrochemistry</strong> [1]. We model with Ma<strong>the</strong>matica ® s<strong>of</strong>tware, to overcome <strong>the</strong> advanced<br />

ma<strong>the</strong>matics, I E curves for E q C i mechanism at spherical electrodes. The mechanism<br />

represented by<br />

k f<br />

<br />

<br />

k<br />

S( so ln) ne P(<br />

so ln) P(<br />

so ln) Q(<br />

so ln)<br />

(1)<br />

kb<br />

allows us to infer <strong>the</strong> following expressions for S (t)<br />

and P (t)<br />

, namely<br />

S(<br />

t)<br />

<br />

1 1 DSt<br />

<br />

<br />

exp<br />

erfc<br />

DSt<br />

a 2<br />

a <br />

<br />

P(<br />

t)<br />

exp<br />

kt<br />

<br />

<br />

Figure 1. Modelled<br />

voltammograms.<br />

DSt<br />

<br />

<br />

<br />

a <br />

1 1 D t <br />

exp P<br />

erfc<br />

DPt<br />

a 2<br />

a <br />

a electrode radius<br />

D <br />

<br />

Pt<br />

<br />

a <br />

required to apply <strong>the</strong> algorithm used to implement <strong>the</strong> master equation. A very basic<br />

program written for Ma<strong>the</strong>matica ® is reported to model I E curves. We check, with<br />

SigmaPlot , <strong>the</strong>se files with those obtained by digital simulation with DigiElch ® .<br />

The next figure display <strong>the</strong> comparison<br />

between convolutive modelling and digital<br />

simulation. The agreement is excellent. The<br />

60<br />

40<br />

20<br />

0<br />

-20<br />

-40<br />

-60<br />

-80<br />

-100<br />

-120<br />

10 6 I/A<br />

E/V<br />

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6<br />

(2)<br />

parameters employed were: T 298. 15K<br />

;<br />

a 10 3<br />

9<br />

2 1<br />

m ;<br />

DS DP<br />

10<br />

m s ;<br />

3<br />

CS b 1mol<br />

m<br />

0. 5<br />

0 4<br />

1<br />

k 10<br />

m s ;<br />

E reverse 0. 5V ;<br />

(3)<br />

; n 1<br />

;<br />

k 1s<br />

1 ;<br />

0<br />

E 0. 0V<br />

;<br />

1<br />

v 1V<br />

s ; t reverse 1s<br />

;<br />

3<br />

( sampling time)<br />

10<br />

s . DigiSim ® results<br />

also agree with previous files.<br />

Acknowledgements: To Pr<strong>of</strong>essor Keith B. Oldham, Peter J. Mahon and Jan C. Myland.<br />

References<br />

[1] Barrera-Niebla, M.J.; Semiintegral and Convolution <strong>Electrochemistry</strong>. Research line.<br />

Department <strong>of</strong> Physical Chemistry. (2010). La Laguna University. Tenerife. Canary Islands.<br />

September, 811, 2010. ISEL - Lisbon 44

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