Mass transport reaction layer thickness

In these electrode processes, the use of macroelectrodes is recommended when the homogeneous kinetics is slow in order to achieve a commitment between the diffusive and chemical rates. When the chemical kinetics is very fast with respect to the mass transport and macroelectrodes are employed, the electrochemical response is insensitive to the homogeneous kinetics of the chemical reactions—except for first-order catalytic reactions and irreversible chemical reactions follow up the electron transfer—because the reaction layer becomes negligible compared with the diffusion layer. Under the above conditions, the equilibria behave as fully labile and it can be supposed that they are maintained at any point in the solution at any time and at any applied potential pulse. This means an independent of time (stationary) response cannot be obtained at planar electrodes except in the case of a first-order catalytic mechanism. Under these conditions, the use of microelectrodes is recommended to determine large rate constants. However, there is a range of microelectrode radii with which a kinetic-dependent stationary response is obtained beyond the upper limit, a transient response is recorded, whereas beyond the lower limit, the steady-state response is insensitive to the chemical kinetics because the kinetic contribution is masked by the diffusion mass transport. In the case of spherical microelectrodes, the lower limit corresponds to the situation where the reaction layer thickness does not exceed 80 % of the diffusion layer thickness. 

For optical transducers, the measured signals are directly proportional to [P], so that, once again, reaction layer thickness and mass-transport kinetics determine the sensitivity of the biosensor, and signals are directly proportional to analyte concentration. For potentiometric transducers, signals are proportional to log[P], and therefore to log[S]. ... 

The metal ion in electroless solutions may be significantly complexed as discussed earlier. Not all of the metal ion species in solution will be active for electroless deposition, possibly only the uncomplexed, or aquo-ions hexaquo in the case of Ni2+, and perhaps the ML or M2L2 type complexes. Hence, the concentration of active metal ions may be much less than the overall concentration of metal ions. This raises the possibility that diffusion of metal ions active for the reduction reaction could be a significant factor in the electroless reaction in cases where the patterned elements undergoing deposition are smaller than the linear, or planar, diffusion layer thickness of these ions. In such instances, due to nonlinear diffusion, there is more efficient mass transport of metal ion to the smaller features than to large area (relative to the diffusion layer thickness) features. Thus, neglecting for the moment the opposite effects of additives and dissolved 02, the deposit thickness will tend to be greater on the smaller features, and deposit composition may be nonuniform in the case of alloy deposition. 

In contrast to the rotating disc electrode, mass transport to the ring is nonuniform. Nevertheless, the thickness of the diffusion layer Spj, which depends on the coordinate x in the direction of flow, and the rate of mass transport can be calculated. We consider a simple redox reaction, and rewrite Eq. (14.5) in the form ... 

As suggested before, the role of the interphasial double layer is insignificant in many transport processes that are involved with the supply of components from the bulk of the medium towards the biosurface. The thickness of the electric double layer is so small compared with that of the diffusion layer 8 that the very local deformation of the concentration profiles does not really alter the flux. Hence, in most analyses of diffusive mass transport one does not find any electric double layer terms. For the kinetics of the interphasial processes, this is completely different. Rate constants for chemical reactions or permeation steps are usually heavily dependent on the local conditions. Like in electrochemical processes, two elements are of great importance the local electric field which affects rates of transfer of charged species (the actual potential comes into play in the case of redox reactions), and the local activities... 

For a triphasic reaction to work, reactants from a solid phase and two immiscible liquid phases must come together. The rates of reactions conducted under triphasic conditions are therefore very sensitive to mass transport effects. Fast mixing reduces the thickness of the thin, slow moving liquid layer at the surface of the solid (known as the quiet film or Nemst layer), so there is little difference in the concentration between the bulk liquid and the catalyst surface. When the intrinsic reaction rate is so high (or diffusion so slow) that the reaction is mass transport limited, the reaction will occur only at the catalyst surface, and the rate of diffusion into the polymeric matrix becomes irrelevant. Figure 5.17 shows schematic representations of the effect of mixing on the substrate concentration. 

In a typical spectroelectrochemical measurement, an optically transparent electrode (OTE) is used and the UV/vis absorption spectrum (or absorbance) of the substance participating in the reaction is measured. Various types of OTE exist, for example (i) a plate (glass, quartz or plastic) coated either with an optically transparent vapor-deposited metal (Pt or Au) film or with an optically transparent conductive tin oxide film (Fig. 5.26), and (ii) a fine micromesh (40-800 wires/cm) of electrically conductive material (Pt or Au). The electrochemical cell may be either a thin-layer cell with a solution-layer thickness of less than 0.2 mm (Fig. 9.2(a)) or a cell with a solution layer of conventional thickness ( 1 cm, Fig. 9.2(b)). The advantage of the thin-layer cell is that the electrolysis is complete within a short time ( 30 s). On the other hand, the cell with conventional solution thickness has the advantage that mass transport in the solution near the electrode surface can be treated mathematically by the theory of semi-infinite linear diffusion. 

Here, t is time and x is the distance traveled within a layer of thickness L. Di is the effective diffusion constant of the species i. The first term represents the mass transport, and the second is the pH-dependent reaction term. This equation has to be written for every participating species, with the appropriate sign in front of the reaction term. 

A general mathematical formulation and a detailed analysis of the dynamic behavior of this mass-transport induced N-NDR oscillations were given by Koper and Sluyters [8, 65]. The concentration of the electroactive species at the electrode decreases owing to the electron-transfer reaction and increases due to diffusion. For the mathematical description of diffusion, Koper and Sluyters [65] invoke a linear diffusion layer approximation, that is, it is assumed that there is a diffusion layer of constant thickness, and the concentration profile across the diffusion layer adjusts instantaneously to a linear profile. Thus, they arrive at the following dimensionless set of equations for the double layer potential, [Pg.117]

Further increase in anode potential gets into limiting current plateau range (El in Fig. 10.6). In this region, the potential is so high that the electrochemical reaction is faster than mass transport that is, Cu ions produced on the anode surface in a unit time are more than those that mass transport can remove from the anode surface into the bulk solution. As a result, a Cu ion concentrated layer is developed inside the Prandtl boundary layer [4]. The concentrated Cu layer is called Nernst layer or diffusion layer, which has a thickness of [13]... 

In this highly exothermic reaction, kinetic control is a function of the catalyst characteristics and surface temperature, and the mass transport control and boundary layer thickness is based on the catalyst bed geometry and flow velocity. Both the gauze and ceramic foam have tortuous flow paths, but the extruded cordierite monolith has microchan-... 

The main hypotheses for developing the EHD impedance theory are that the electrode interface is uniformly accessible and the electrode surface has uniform reactivity. However, in many cases, real interfaces deviate from this ideal picture due, for example, either to incomplete monolayer adsorption leading to the concept of partial blocking (2-D adsorption) or to the formation of layers of finite thickness (3-D phenomena). These effects do not involve the interfacial kinetics on bare portions of the metal, which, for simplification, will be assumed to be inherently fast. The changes will affect only the local mass transport toward the reaction sites. Before presenting an application of practical interest, the theoretical EHD impedance for partially blocked electrodes and for electrodes coated by a porous layer will be analyzed. 

For disk-type electrodes, usually with a radius of O.l-l.O cm the thickness of the diffusion layer that is depleted of reactant is much smaller than the electrode size so that mass transport can be described in terms of planar diffusion of the electroactive species from the bulk solution to the electrode surface as schematized in Figure 1.2a, where semi-infinite diffusion conditions apply. The thickness of the diffusion layer can be estimated as for a time electrolysis t and usually ranges between 0.01 and 0.1 mm (Bard et al., 2008). For an electrochemically reversible -electron transfer process in the absence of parallel chemical reactions, the variation of the faradaic current with time is then given by the Cottrell equation ... 

As can be easily derived from the concentration pattern, the reaction takes place either mainly in the bulk of the well-mixed liquid phase or in the liquid-phase boundary layer. In reactions which occur in the bulk of the liquid phase, the concentration of gaseous educts decreases only within the interfacial layer (thickness d) to the concentration cAj by physical diffusion processes. Only in the case of mass transport processes that are fast relative to the reaction rate is the latter proportional to the cAl j in the liquid phase. If the catalytic reaction is fast enough a reaction surface may develop within the boundary layer which may even move into the interface itself and, thus, neither the bulk of the liquid nor the liquid-phase boundary layer is utilized any more for the reaction. A simple approach in order to determine the regime of the overall reaction rate can be performed by comparison of the intrinsic kinetics with the rate of mass transfer according to Table 2 [22],... 

---