Abstract:

For a RDE system not to be coupled with homogeneous chemical reactions, the Laplace transform of the general convective diffusion equation is
s~-c_j(x, s)-c_j~*=D_l ~2~c_j(x, s)/ ~2x-V_x c_j(x, s)/ x
in which, s is the Laplace transformation variable complementary to time t, c_j~* is the bulk concentration of species j, ~-c_j(x, s) is the Laplace transform of concentration c_j(x, t), D_j is the diffusion coefficient, x is the axle center of RDE, V_x is the solution velocity at x direction, we solve this equation with a canonical perturbation method for small variables |vs/D_(jω)| and |D_(jω)/vs|, here v is the. kinetical viscosity of the electrolyte solution, and ω is the rotation speed of RDE. We get two equations
~c_j(0, s)/ x=[c_j~*/s-c_j(0, s)][(s/D_j)~1/2+1/δ_j exp(-1.05δ_j(d/D_j)~1/2]
or (0.7% relative error)
~-c_j(0, s)/ x=((s/D_j)~1/2[c_j~*/s-~-c_j(0, s)])/(1-[1+1.07δ_j(d/D_j)~1/2]exp[-2.07δ_j(s/D_j)~1/2])
(1% relative error)
in which δ_j is the limiting diffusion layer thickness of the steady state at RDE.
Upon the last two Laplace, we are able to deal with nonstationary processes in a RDE system with Laplace transformation procedure.
For the large-amplitude potential step process, the current equation obtained is
i(t)/i_1=(π(D_Ot)/δ_O~2)~-1/2+erfc[0.525((D_Ot)/δ_O~2)~-1/2
where i_1 is the limiting current of the steady state at the RDE. The calculated value is closed to the theoretical results of Siver and Bruckenstein et al.
For the pulsed current process, we obtain the limiting pulsed current equation
i_1/i_(p1)=T_1/T+0.830((D_OT)/δ_O~2)~1/2(1-T_1/T)~1.011(0.9>T_1/T>0.01, ((D_OT)/δ_O~2)<0.34)
in which, i_(p1) is the limiting pulsed current, T is the cycle time of the pulsed current, T_1 is the pulsed time. The calculated value is closed to the theoretical and experimental results of Viswanathan et al.