Jochen Kieninger
Electrochemical Methods for the Micro- and Nanoscale
www.electrochemical-methods.org

Task 6.1 (Rotating ring disk electrode - collection efficiency)

The collection efficiency of an RRDE depends on geometrical parameters only, assuming stable reaction products. The radii are $r_1$ for the disk, $r_2$ the inner and $r_3$ the outer of the ring.

import numpy as np

r1 = 2.5  # mm (disk radius)
r2 = 3  # mm (inner ring radius)
r3 = 4  # mm (outer ring radius)

• For the collection efficiency $N$, Albery and Bruckenstein (https://dx.doi.org/10.1039/tf9666201920) proposed a generally accepted solution:

a = (r2/r1)**3 -1
b = (r3/r1)**3 - (r2/r1)**3

def FF(x):
    result = np.sqrt(3)/4/np.pi
    result *= np.log((1+x**(1/3))**3/(1+x))
    result += 3/2/np.pi*np.arctan((2*x**(1/3)-1)/np.sqrt(3))
    result += 0.25
    return result

N = 1-FF(a/b) + b**(2/3)*(1-FF(a))
N = N - (1+a+b)**(2/3)*(1-FF(a/b*(1+a+b)))
round(N, 2)

0.4