Interfaces, diffuse examples

Very often, the electrode-solution interface can be represented by an equivalent circuit, as shown in Fig. 5.10, where Rs denotes the ohmic resistance of the electrolyte solution, Cdl, the double layer capacitance, Rct the charge (or electron) transfer resistance that exists if a redox probe is present in the electrolyte solution, and Zw the Warburg impedance arising from the diffusion of redox probe ions from the bulk electrolyte to the electrode interface. Note that both Rs and Zw represent bulk properties and are not expected to be affected by an immunocomplex structure on an electrode surface. On the other hand, Cdl and Rct depend on the dielectric and insulating properties of the electrode-electrolyte solution interface. For example, for an electrode surface immobilized with an immunocomplex, the double layer capacitance would consist of a constant capacitance of the bare electrode (Cbare) and a variable capacitance arising from the immunocomplex structure (Cimmun), expressed as in Eq. (4). 

The concentration boundary layer is rarely at steady state. The only transport mechanism away from the interface is diffusion, and diffusion is a slow process. We will practice dealing with unsteady diffusion away from an interface with Example 8.5. 

Now, this quantity impedance (Z) turns out upon detailed analysis to contain within the characteristics of its variation with frequency,48 properties of the reaction occurring at the electrode/solution interface. For example, if a reaction occurring there has as its rale-determining step the electron transfer, then the variation of the impedance with frequency will have certain characteristics different from those shown in the Z — log to plot if the rate-determining step involves instead diffusion in the solution. So, by working out how Z varies with log CD according to a chosen mechanism... 

Table 6.3 Interfacial compositions and rates of interface diffusion at the bottom of the column in Example 6.4...

The surface recombination of a-Si H is greatly enhanced in multilayer structures which constrain the electron-hole pair to be near an interface. For example a thin a-Si H film sandwiched between a-Sig N4 layers, has a luminescence intensity which drops rapidly when the layer thickness is less than 200 A. These results are discussed further in the next chapter (Section 9.4.1) and show that surface recombination effects extend 100-200 A into the film, and that electron-hole pairs created farther from the surface are not influenced by the surface at low temperature. As the carriers become more mobile at higher temperatures, the diffusion length increases and surface recombination is more significant. 

For flows with almost uniform transport coefficients, a simple approximation of the grid cell interface diffusivity for example, may be obtained... 

What makes mass transfer between phases more complex than heat transfer is the discontinuity at the interface, which occurs because the concentration or mole fraction of diffusing solute is hardly ever the same on opposite sides of the interface. For example, in distillation of a binary mixture, is greater than and the gradients near the surface of a bubble might be as shown in Fig. 21,7a. For the absorption of a very soluble gas, the mole fraction in the liquid at the interface would be greater than that in the gas, as shown in Fig, 2lJb. 

The adsorption kinetics of interfacial active molecules at liquid interfaces, for example surfactants at the aqueous solution/air or solution/organic solvent interface, can be described by quantitative models. The first physically founded model for interfaces with time invariant area was derived by Ward Tordai (1946). It is based on the assumption that the time dependence of interfacial tension, which is directly correlated to the interfacial concentration T of the adsorbing molecules, is caused by a transport of molecules to the interface. In the absence of any external influences this transport is controlled by diffusion and the result, the so-called diffusion controlled adsorption kinetics model, has the following form... 

In the absence of convective mass transfer and chemical reaction, calculate the steady-state liquid-phase mass transfer coefficient that accounts for curvature in the interfacial region for cylindrical liquid-solid interfaces. An example is cylindrical pellets that dissolve and diffuse into a quiescent liquid that surrounds each solid pellet. The appropriate starting point is provided by equation (B) in Table 18.2-2 on page 559 in Bird et al. (1960). For one-dimensional diffusion radially outward, the mass transfer equation in cylindrical coordinates reduces to... 

Wetlands exhibit distinct redox gradients between the soil and overlying water column and in the root zone (Chapter 4), resulting in aerobic interfaces. For example, the aerobic layer at the soil-floodwater interface is created by a slow diffusion of oxygen and the rapid consumption at the interface. The thin aerobic layer at the soil-floodwater interface and around roots functions as an effective zone for aerobic oxidation of Fe(ll) and Mn(II). Below this aerobic layer there exists the zone of anaerobic oxidation of Fe(ll) and Mn(ll) and reduction of Fe(III) and Mn(IV). The juxtaposition of aerobic and anaerobic zones creates conditions of intense cycling of iron and manganese mediated by both biotic and abiotic reactions. 

Although describing properties of the bulk liquids, in surfactant solutions the value of K strongly influences the adsorption dynamics at the liquid-liquid interface. For example, in adsorption and diffusion processes in water-oil systems, knowledge of the K value is fundamental in interpreting the experimental data (114, 115, 164, 169). 

It would be interesting to compare these results with the findings of Ericsson et al. who measured diffusion of this peptide in the aqueous channels of the cubic phase [53]. According to these investigators, the self-diffusion data indicated that desmopressin interacted significantly with the monoolein-water interface. For example, the desmopressin diffusion coefficients in the cubic phase at 40 °C was about a factor 9 smaller than in H20 solution, a difference that is larger than what... 

There should be some caution in broadly applying (9.1) to all types of carrier transport at interfaces. For example, the relationship does not accurately model the transit time of ballistic transport because the calculation of Xt depends on the mobility, which is only accurate in so far as it measures a diffusive process, i.e., one that involves multiple scattering events [9]. Because the small polaron conductors have transport mediated by lattice vibrations, numerous scattering events will occur as the carriers cross the space charge layer. Therefore, the transit times as calculated by (9.1) should be representative of the behavior for this class of materials [10]. 

Reflection spectroscopy has also been carried out successfully by reflection off a water/immiscible liquid interface. Total internal reflection at a liquid-liquid interface can be used to monitor ion-transfer across the interface. For example, the kinetics of the reduction of TCNQ and the oxidation of l,l -dime-thylferrocene by [Fe(CN)g] in the aqueous phase have been considered. The kinetics of these reactions were studied by chronoabsorptometry, assuming diffusion control. Ion-transfer kinetics across interfaces have been treated theoretically and applied to the study of indicator transfer. 

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