Hydrodynamic modulation

The technique of hydrodynamic modulation voltammetry (HMV), in which the rate of stirring is pulsed between high and low values, is demonstrated in this experiment. The application of HMV for the quantitative analysis of ascorbic acid in vitamin C tablets using the method of standard additions also is outlined. 

Heterogeneous rate constants, 12, 113 Hofmeister sequence, 153 Hybridization, 183, 185 Hydrodynamic boundary layer, 10 Hydrodynamic modulation, 113 Hydrodynamic voltammetry, 90 Hydrodynamic voltammogram, 88 Hydrogen evolution, 117 Hydrogen overvoltage, 110, 117 Hydrogen peroxide, 123, 176... 

The aforementioned experiments at rotating electrodes concerned merely steady-state conditions so-called transients123 at these electrodes, e.g., with potential or current steps, as well as with hydrodynamic modulation, i.e., variation of co with time, are, as a consequence of their non-steady-state conditions, less important in analysis and therefore will not be treated here. 

Cooper EL, Coury LA jr (1998) Mass transport in sonovoltammetry with evidence of hydrodynamic modulation from ultrasound. J Electrochem Soc 145 1994—1999... 

Dewald HD, Peterson BA (1990) Ultrasonic hydrodynamic modulation voltammetry. Anal Chem 62 779-782... 

The use of hydrodynamic modulation voltammetry was reported [155] and modified [156]. A simple treatment of the data transforms the voltammetric current-voltage waves into peak shaped curves, which gave improved resolution in the analysis of mixtures. 

All the electrode kinetic methodology described until now has assumed a steady state (or quasi-steady state in the case of the DME). Many techniques at stationary electrodes involve perturbation of the potential or current in combination with forced convection, this offers new possibilities in the evaluation of a wider range of kinetic parameters. Additionally, we have the possibility of modulating the material flux, the technique of hydrodynamic modulation which has been applied at rotating electrodes. Unfortunately, the mathematical solution of the convective-diffusion equation is considerably more complex and usually has to be performed numerically. 

Hydrodynamic modulation has been performed almost exclusively at the rotating disc electrode. It has found use for analytical purposes at rotating and tubular electrodes owing to the fact that non-convectively dependent electrode processes are unaffected by the modulation [236]. 

We will first briefly consider some of the treatments of potential step and current step techniques at hydrodynamic electrodes. One should bear in mind, however, that this division is somewhat artificial owing to the implicit dependence of one on the other. We then treat a.c. voltammetric techniques, LSV, and finally consider hydrodynamic modulation. 

This technique was proposed by Bruckenstein and co-workers [280, 281] and is useful in that the current due to the modulation of the fluid flow is essentially free of any electrode surface-controlled contributions in most cases. Thus, it can be used as an analytical tool to increase sensitivity [282]. Step changes were originally considered but this was later extended to sinusoidal hydrodynamic modulation (SHM) in the limiting current region and then to the region of mixed convective-diffusion/kinetic control [283—287]. If the modulation frequency is o, then the modulation, which is small, can be described by... 

The fact of modulating the square root of Q was naturally supported by the results of the Levich theory in steady-state conditions [8]. With the increasing development of impedance techniques, aided by a sophisticated instrumentation [2], the authors of the present work promoted the use of impedance concept for this type of perturbation and introduced the so-called electrohydrodynamic (EHD) impedance [9, 10]. A parallel approach has been also investigated by use of velocity steps in both theoretical and experimental studies [5, 11, 12]. More recently, Schwartz et al. considered the case of hydrodynamic modulations of large amplitude for increasing the sensitivity of the current response and also for studying additional terms arisen with non linearities [13-15],... 

HMRDE hydrodynamically modulated rotating disc electrode... 

In the following, a theoretical background is given with a view to providing a Arm qualitative understanding of the factors which affect the hydrodynamically modulated signal. Reference should be made to the original literature cited for a more extensive treatment. 

Fig. 10.4. Equivalent circuit for the electrode with hydrodynamic modulation R. denotes the solution resistance, C0/. the double layer capacitance, RF the faradaic resistance and Z the impedance contributed by diffusional transport of the reactants to the surface. Hydrodynamic modulation is represented by the modulated current, JD and the resultant current in the external circuit represented by I,.

Miller and Bruckenstein [27,28] introduced the hydrodynamically modulated rotating disc electrode (HMRDE) in 1974. The steady-state current density at a rotating disc electrode is well-defined, given by the Levich equation (equation (10.15)) ... 

Vibration of an electrode is an experimentally simple way of producing hydrodynamic modulation. Whilst the advantage is experimental simplicity, the disadvantage is that the hydrodynamic regime is difficult to describe accurately (see Section 10.3.6.3). 

---