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Citation: Liu Xiaoping*, Cha Chuansin. SOLUTION OF THREE DIMENSIONAL DIFFUSION EQUATIONS BY STANDARD ELECTRODE RESPONSE TO SINGLE-SHOT TRANSIENT PERTURBATION[J]. Acta Physico-Chimica Sinica, ;1988, 4(01): 1-3. doi: 10.3866/PKU.WHXB19880101 shu

SOLUTION OF THREE DIMENSIONAL DIFFUSION EQUATIONS BY STANDARD ELECTRODE RESPONSE TO SINGLE-SHOT TRANSIENT PERTURBATION

1.
Department of Chemistry; Wuhan University; Wuhan; China

Received Date: 8 September 1987
Available Online: 15 February 1988

An idea and theory of finding the general solution of three dimensional diffusion equation by using the the experimental electrode response to single-shot transient perturbation are presented. The following formulas were derived for the electrode reaction O+ne<=>R at an electrode of any shape or array of electrodes:
∫∫cds=Ac~*_O/P+A_0(P,D_0,Ω)exp{-PL[I(t,D_0,Ω)]z/FAD_0c′_0}
0≤z<δ
∫∫c_Rds=Ac~*_R/P+A_R(P,D_R,Ω)exp{-PL[I(t,D_R,Ω)/FD_Rc′_0}
When I(t,D'_O,Ω) is the expression for experimental current response of a standard system of n=1 to large amplitude potential step, then I(t,D_O,Ω)and I(t,D_R,Ω) could be obtained by substitution of D_0 and D_R of system studied for D′_0 in I(t,D′_0,Ω) respectively. A=∫∫ds is the total surface area of electrode or array of electrodes. While Ω is the domain of all points on surface of electrodes. δ is a very small value. c′_0 is the bulk concentration of electroactive specie in the standard samples, c~*_0 and c~*_R are bulk concentrations of elecroactive specie in any sample to be studied. L is the operator of the Laplace trasformation, P is the variable of the Laplace transfrmation. c_0 and c_R are the Laplace trasformation of c_0 and c_r respectively. A_0(P,D_0,Ω) and A_R(P,D_R,Ω) depend on experimental method employed in investigating studied system.
【DOI】 cnki:ISSN:1000-6818.0.1988-
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