A Rotating Ring-Disk Electrode (RRDE) is a special type of working electrode used for analytical purposes in an electrochemical cell. Spinning a disk at high speed in an electrolyte solution sets up a well-defined mass transport flow condition. Material is initially transported by the solution flow to the disk electrode and then subsequently past the ring electrode.

Collection Efficiency

The theoretical collection efficiency can be computed from the three principle diameters describing the RRDE geometry: the disk outer diameter ( d_1 ), the ring inner diameter ( d_2 ), and the ring outer diameter ( d_3 ). This somewhat tedious computation is made easier by normalizing the ring diameters with respect to the disk diameter

{\sigma}_{OD} = \frac{d_3}{d_1}

{\sigma}_{ID} = \frac{d_2}{d_1}

and by defining three additional quantities in terms of the normalized diameters

{\sigma}_{A} = {\sigma}_{ID}^3 - 1

{\sigma}_{B} = {\sigma}_{OD}^3 - {\sigma}_{ID}^3

{\sigma}_{C} = \frac{{\sigma}_{A}}{{\sigma}_{B}}

and by defining a complex function,  G(x) , as follows:

G(x) = \frac{1}{4} + \left(\frac{\sqrt{3}}{4{\pi}}\right) ln \left[{\frac{(x^{1/3} + 1)^3}{x+1}}\right] + \frac{3}{2{\pi}} {\arctan}\left[{\frac{2x^{1/3}-1}{\sqrt{3}}}\right]

In terms of the normalized quantities and complex function above, the theoretical collection efficiency ( N_{theoretical} ) for a rotating ring disk electrode is given by the following equation:

N_{theoretical} = 1-{\sigma}_{OD}^2+{\sigma}_B^{2/3}-G({\sigma}_C)-{\sigma}_B^{2/3}G({\sigma}_A)+{{\sigma}_{OD}^2}G({\sigma}_C{\sigma}_{OD}^3)


Allen J. Bard and Larry R. Faulkner, Electrochemical Methods: Fundamentals and Applications, New York: Wiley, 2001, 2nd ed., Chapter 9.