Mass transport diffusion layer, thickness

Rigorous calibration is a requirement for the use of the side-by-side membrane diffusion cell for its intended purpose. The diffusion layer thickness, h, is dependent on hydrodynamic conditions, the system geometry, the spatial configuration of the stirrer apparatus relative to the plane of diffusion, the viscosity of the medium, and temperature. Failure to understand the effects of these factors on the mass transport rate confounds the interpretation of the data resulting from the mass transport experiments. 

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 a simple model, one assumes that convective mass transport keeps the concentration constant at some fixed distance 5 from the solid wall. Thus, the diffusion layer thickness is constant. 

In the solution of mass transport problems, several dimensionless groups are used in order to reduce the number of variables. Diffusion layer thicknesses etc. are expressed in much of the literature in terms of these dimensionless variables. 

The mass transport coefficient is, in general, a complex time and potential-dependent function through the linear diffusion layer thickness, <% ,. Only under certain conditions does this dependence disappear (as, for example, for nemstian... 

The mass transport limiting current is the maximum current (or rate) that the process can achieve. In order to increase its value, an increase of the electrode area, bulk concentration, or mass transport coefficient is needed. In the last case, this means a decrease of the diffusion layer thickness which can be done, for example, by forced convection. 

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. 

Thin-layer cell — An electrochemical cell with the reactant solution confined to a thin layer. -> mass transport can be neglected as long as the layer thickness / is smaller than the diffusion layer thickness / (2 Dtf 2 for a given experimental time t. Thin-layer cells are frequently employed in spectroelectrochemical experiments and in - cyclic voltammetry. 

We alluded to the Nernst diffusion layer thickness 5, in the first chapter. It relates to the mass-transport limited current density through the equation... 

The concept of the diffusion layer thickness can also be applied, however, when the main mode of mass transport is convection. In such cases one assumes that there is a thin layer of liquid at the surface... 

The peak current increases (tends towards the value obtained for a bare electrode) with decreasing scan rates, as the mass transport will not be hindered by small sphere sizes. With increasing scan rates, the diffusion layer thickness decreases, and minimizes the effects of mass transport on the voltammetric response. Eventually, numerical simulations of cyclic voltammograms as a function of scan rate will provide information on the microparticle sphere radius. 

The relation between the interfacial and bulk concentrations depends on mass transport, most often by diffusion (i.e., thermal motion) and/or convection (mechanical stirring). Often a stationary state is reached, in which the concentrations near the electrode can be described approximately by a diffusion layer of thickness 8. For a constant diffusion layer thickness the Nernst equation takes the form... 

Mass transport in MREF is a combination of steady state and non-steady state diffusion processes. The mass transfer limited current density (i,) is related to the reactant concentration gradient (Cb-Cs) and to the diffusion layer thickness (8) by Nemst using the following equation ... 

Therefore, the model of mass transport in a MREF waveform can be illustrated using a simple model of duplex diffusion layer , which was developed by Ibl 111121 for pulse plating. As shown in Figure 2, the diffusion layer may be divided into two parts, a pulsating diffusion layer of thickness 8p and a stationary diffusion layer. At the end of a pulse, the pulsating diffusion layer thickness 8p (under low duty cycle) is given by ... 

Amperometric electrodes made on a microscale, on the order of 5 to 30 /rm diameter possess a number of advantages. The electrode is smaller than the diffusion layer thickness. This results in enhanced mass transport that is independent of flow, and an increased signal-to-noise ratio, and electrochemical measurements can be made in high-resistance media, such as nonaqueous solvents. An S-shaped sigmoid current-voltage curve is recorded in a quiet solution instead of a peak shaped curve because of the independence on the diffusion layer. The hmiting current, q, of such microelectrodes is given by... 

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