When a sinusoidal modulation is superimposed on the rotation speed of a rotating disk electrode, the corresponding modulated current follows the Levich equation closely for sufficiently low ratios of the modulation frequency to the constant center rotational frequency. In this work, the frequency response of the modulated current (amplitude and phase) is derived for the general case and the results experimentally confirmed over a wide range of Schmidt numbers (230-2100 Sc) and modulation to rotational frequency ratios for the reduction of Fe +3 to Fe +2 in 1.0M H2SO4 over the temperature range 2'5~176 Tables are given of the phase and amplitude factors which would be encountered for the normal range of both modulation and solution parameters.In recent papers (1-6), we have considered various theoretical and experimental aspects of hydrodynamic voltammetry at the rotating disk (RDE) and ring-disk electrodes (RRDE). In these studies, the angular velocity of the RDE, ~, was programmed as a function of time, t, or current, i. With the exception of one study (4) involving step speed change, this work dealt with conditions for which the Levich equation always applied, i.e., a quasi-steady state existed in which the concentration gradients adjacent to the RDE could be described adequately using the instantaneous angular ve]ocity, ~, of the electrode and the von K~rm~n (7)-Cochran (8) approach. Recently, using the results of Benton (9), we considered the current transient produced by a step change in angular velocity, A~, of a RDE held at a limiting current. After such a step change in ~,, the fluid velocities in the region adjacent to the RDE adjust very rapidly from values characteristic of the initial velocity, ~o, to those characteristic of the final velocity, ~o % A~, while the concentration profiles adjust somewhat more slowly.We consider here the problem of describing the limiting, convective-diffusion controlled current at a disk subjected to a rotational velocity program of the form ~1/2 = ~ol/S(1 _[_ e cos ~t)[1] In Eq. [1]
= A~I/~/~ol/~ [2]and ~ is the modulation frequency in radians/sec. In this paper, we refer to this class of techniques as sinusoidal hydrodynamic voltammetry (SHM) to distinguish it from other uses now being made of the term "hydrodynamic voltammetry (10)." Equation [1] will describe the experimental situation for all values of ~o, e, and r including those for which the angular acceleration, d~,/dt, is too high for the quasi-steady state assumptions used in our previous studies of a sinusoidal modulation of ~ to apply. These broader experimental conditions will produce current responses deviating from those (5, 6) found for Levich-type conditions (~ small), i.e., the current is not given by i = i~o + Ai cos ct [3] where 9 Electrochemical Society Active Member.
