Mass Transport to the Electrode Surface

The great advantage of the RDE over other teclmiques, such as cyclic voltannnetry or potential-step, is the possibility of varying the rate of mass transport to the electrode surface over a large range and in a controlled way, without the need for rapid changes in electrode potential, which lead to double-layer charging current contributions. 

While thin-layer cells have most commonly been used with flow parallel to the electrode surface as described earlier, several detectors have employed a radial-flow geometry and operate with flow entering from a jet perpendicular to and centered on the electrode surface as illustrated in Figure 27.7. This is intended to reduce dead volume and provide more effective mass transport to the electrode surface. The cell illustrated acts as an end fitting for a microbore LC column. Thin-layer cells with a radial-flow (vs. cross-flow) geometry give superior performance at lower flow rates [13]. While conventional LC columns operate at 1 mL/min, it is not uncommon to use microbore columns at 10 pL/ min, a hundredfold lower flow. It is important not to confuse these cells with the wall-jet concept. Here the orifice is very small and close to the working electrode. The cell is very thin and the wall-jet hydrodynamics are blocked since there are two walls. 

Hydrodynamic and stirred-solution electrodes. Certain advantages result when the electrode is moved past the solution or vice versa. The increased mass transport increases the current and often increases the sensitivity (although not necessarily the signal-to-noise ratio). In addition, hydrodynamic electrodes such as the rotated platinum electrode and rotated-disk electrode exhibit a current-potential behavior similar to that of the DME. That is, they give the familiar plateau when the current is limited by mass transport to the electrode surface and the current is proportional to the solution concentration of the electroactive species. 

In seeking to understand those processes that contribute to the dynamics of monolayer formation, it is important to consider the role of mass transport to the electrode surface. Assuming linear diffusion conditions for micromolar concentrations in solution, a monolayer in which the surface coverage is 1.1 x 10-10 mol cm-2 will require a layer approximately 0.01 cm thick within the solution to be depleted of [Os(bpy)2 (p3p)2]2+- The characteristic time, t, for this diffusion process is given by the following equation ... 

However, SAMs are rarely structurally perfect and typically contain defects where crystalline domains meet, at step-edges, and where the electrode is not coated with the SAM. Defects of this kind all facilitate mass transport to the electrode surface where efficient electron transfer can take place. A key objective in characterizing SAMs is to map out the nature, size and distribution of the pinholes and other defects. Undoubtedly, scanning probe microscopy, such as the AFM and STM techniques discussed earlier in Chapter 3, play important roles in this area. However, voltammetry is an extremely powerful approach for detecting defects in SAMs when in contact with solution. This extraordinary sensitivity arises from the ability to routinely detect currents at the nanoamp and picoamp levels which... 

Thus the steps in the reaction scheme are Mass transport to the electrode surface... 

The effect of altering the rate of mass transport to the electrode surface was also studied (see Fig. 2.20). At low rotation rates, the reaction is mass transport-controlled but as the rotation speed is increased, the current tends to a rotation speed-independent value indicating that the current becomes limited by some other process. 

Hydrodynamic electrodes — are electrodes where a forced convection ensures a -> steady state -> mass transport to the electrode surface, and a -> finite diffusion (subentry of -> diffusion) regime applies. The most frequently used hydrodynamic electrodes are the -> rotating disk electrode, -> rotating ring disk electrode, -> wall-jet electrode, wall-tube electrode, channel electrode, etc. See also - flow-cells, -> hydrodynamic voltammetry, -> detectors. 

In cyclic voltammetric experiments, the sole form of mass transport to the electrode surface is diffusion, and in the case of large (millimetre dimensions) electrodes the diffusion of material to the electrode occurs in the single dimension perpendicular to the electrode surface. As will be discussed in Section 5 the situation is more complex for electrodes of smaller dimensions. 

We started this book with a schematic presentation (Fig. lA) of the current-potential relationship in an electrolytic cell from the region where no current is flowing, in spite of the applied potential, to the region where the current rises exponentially with potential, following an equation such as Eq. 8D and through the limiting current region, where the current has a constant value, determined only by the rate of mass transport to the electrode surface or away from it. 

These examples are based on both electrodes operating in the activation polarization regime, in which the logarithm of the current is proportional to the overpotential. However, there are situations - particularly at low concentrations - in which the electrochemical reaction is limited by mass transport to the electrode surface. This is referred to as concentration polarization, and is illustrated in Figure 13.2d. In this case, above a critical overpotential the current becomes constant, which appears as a vertical line in the plot. A new mixed potential is established at the intersection of this vertical line and the cathode polarization for the oxygen reduction. This potential depends on the gas concentration, and thus can be used for the chemical sensor signal. 

The membrane has two purposes. Firstly it separates the internal components of the sensor from the external working environment. This is useful in that the electrolyte composition may be maintained and that fouling of the electrode by components of the analyte mixture may be prevented. Secondly, the membrane forms a well defined diffusion barrier for the analyte to pass through. The steady state current observed under potentiostatic control is a function of the kinetics of electron transfer at the electrode and of mass transport to the electrode surface. At high potentials when electron transfer is fast the current is solely a function of mass transfer. This may be controlled by changing the thickness of the membrane and changing the membrane material. The sensitivity and selectivity of the sensor may therefore be controlled to some extent by judicious choice of the membrane material. 

Most of the initial practical and theoretical work in cyclic voltammetry was based on the use of macroscopic-sized inlaid disc electrodes. For this type of electrode, planar diffusion dominates mass transport to the electrode surface (see Fig. II. 1.13a). However, reducing the radius of the disc electrode to produce a micro disc electrode leads to a situation in which the diffusion layer thickness is of the same dimension as the electrode diameter, and hence the diffusion layer becomes non-planar. This non-linear or radial effect is often referred to as the edge effect or edge diffusion . 

Usual conditions for LSV or CV experiments require a quiet solution in order to allow undisturbed development of the diffusion layer at the electrode. Some groups, however, have purposely used the interplay between diffusion and convection in electrolytes flowing in a channel or similar devices [23]. In these experiments (see also Chapter 2.4), mass transport to the electrode surface is dramatically enhanced. A steady state develops [54] with a diffusion layer of constant thickness. Thus, such conditions are in some way similar to the use of ultramicroelectrodes. Hydro-dynamic voltammetry is advantageous in studying processes (heterogeneous electron transfer, homogeneous kinetics) that are faster than mass transport under usual CV or LSV conditions. A recent review provides several examples [22]. 

This result implies that the diffusion layer thickness is controlled by both diffusion and convection. By comparison with experimental results for hydrodynamic electrodes such as the rotating disc electrode [33], it can be shown that at stationary electrodes with convective mass transport to the electrode surface exhibits a dependence. In the case of the insonated electrode, acoustic streaming contributes significantly to this convective flux [31]. 

Mercury electrodeposition is a model system for experimental studies of electrochemical phase formation. On the one hand, the product obtained is a liquid drop, corresponding very well with the liquid drop model of classical nucleation theory. Besides, electron transfer is fast [61] and therefore the growth of nuclei is controlled by mass transport to the electrode surface [44]. On the other hand, the properties of the mercuryjaqueous solution interface have been the object of study for over a century and hence are fairly well understood. The high overpotential for proton reduction onto both mercury and vitreous carbon favor the study of the process over a wide range of overpotentials. In spite of the complications introduced by the equilibrium between the Hg +, Hg2 " ", and Hg species, this system offers an excellent opportunity to verily the fundamental postulates of the electrochemical nucleation theory. In fact, the dependence of the nucleation rate on the oxidation state of the electrodepositing species is fiiUy consistent with theory critical nuclei appear with similar sizes and onto similar number densities of active sites... 

If we consider an electrochemical experiment which is conducted in a solution that has supporting electrolyte and in stagnant solutions (non-hydrodynamic conditions, see later) such that migration and convection can be neglected from Eq. (2.25), this is thus reduced to consider the only relevant mode of mass transport to the electrode surface on the experimental time scale, which is difliision. 

In Fig. 2.10 it is evident that as the standard electrochemical rate constant, kf, is either fast or slow, termed electrochemically reversible or electrochemicaUy irreversible respectively, changes in the observed voltammetry are striking. It is important to note that these are relative terms and that they are in relation to the rate of mass transport to the electrode surface. The mass transport coefficient, mj-, is given by ... 

When high electrochemical conversion efficiency of dilute solution species is required (e.g., electrochemical detection), a working electrode design common in coulometric flow cells is a porous flow-through electrode. Recently, this type of emitter electrode was implemented into an ES emitter system (Figure 3.9). This electrode design, because of the very small pore size, provided for efficient mass transport to the electrode surface even at flow rates of several hundred microliters per minute. 

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