用单次电化学实验求电极邻近区域三维扩散方程的通解

电化学问题中的三维扩散方程一般都很难求解,即使是微园盘电极,也多采用数值计算或近似方法来处理。若电极形状不规则,严格求解将更困难,即便借助计算机也是件耗时而麻烦的工作。为解决这一困难,本文提出用单次电化学实验求电极邻近区域三维扩散方程通解的设想:

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

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-