Transport across interfaces

Fig 29. A simple equivalent circuit for the artificial permeable membrane. Physical meaning of the elements C, membrane capacitance (dielectric charge displaceme-ment) R, membrane resistance (ion transport across membrane) f pt, Phase transfer resistance (ion transport across interface) Zw, Warburg impedance (diffusion through aqueous phase) Ctt, adsorption capacitance (ion adsorption at membrane side of interface) Cwa, aqueous adsorption capacitance (ion adsorption at water side of interface). From ref. 109. 

We have discussed transport in the bulk and transport across interfaces and phase boundaries (i.e., discontinuities). In this section, we shall mainly treat an intermediate transport situation, the so-called junction. At junctions, the atomistic processes that occur under a load have much in common with interface processes, such as the relaxation behavior of the SE s which are swept across them. 

There is need to distinguish more generally between those processes in which charge transport across interfaces is driven by electron exchange and those in which ions and charge-bearing particles are transferred. 

An interesting result is that the absolute rate of desorption for the desorbing protein is the same in the mixed film as in the pure monolayer providing the area occupied is over 30% of the total surface area ( ). Under these conditions, the concentration of protein in the sub-surface layer is evidently determined by the surface pressure and not the surface density. This result has implications for systems where proteins are transported across Interfaces or membranes. 

Finally, considering what was discussed previously, when dealing with nanosized materials and nanostructured electrodes for electrochemistry, it is important to separate the different effects of interface on the electronic and ionic transport the kinetics and mechanisms of transport along and across interfaces. The literature commonly considers transport along interfaces as grain boundary transport, corresponding to diffusion parallel to interfaces, as in grain boundaries of polycrystalUne materials or in nanoscale materials, as across nanostructures limited to a thin layer of nanometric thickness. In contrast, transport across interfaces involves transport perpendicular to the interface. 

Gradients in surface (or interfacial) tension can accelerate the spreading of fluids, enhance the stability of surfactant-laden films of liquid, emulsions, and foams, and increase rates of mass transport across interfaces. The motion of fluid driven by a gradient in surface tension is referred to as a Marangoni flow . We have demonstrated that electrochemical reduction of IF to IF at an electrode that... 

In contrast to the transport along interfaces, little is known about the transport across interfaces. This transport involves diffusion perpendicular to the interface, across the segregation-induced chemical potential gradients and related electric fields. This transport plays an important role in heterogeneous gas/solid and solid/solid processes. 

Losego MD, Grady ME, Sottos NR, Cahill DG, Braun PV. Effects of chemical bonding on heat transport across interfaces. Nat Mater 2012 11 502-6. 

The applications of this simple measure of surface adsorbate coverage have been quite widespread and diverse. It has been possible, for example, to measure adsorption isothemis in many systems. From these measurements, one may obtain important infomiation such as the adsorption free energy, A G° = -RTln(K ) [21]. One can also monitor tire kinetics of adsorption and desorption to obtain rates. In conjunction with temperature-dependent data, one may frirther infer activation energies and pre-exponential factors [73, 74]. Knowledge of such kinetic parameters is useful for teclmological applications, such as semiconductor growth and synthesis of chemical compounds [75]. Second-order nonlinear optics may also play a role in the investigation of physical kinetics, such as the rates and mechanisms of transport processes across interfaces [76]. 

The above discussion relates to diffusion-controlled transport of material to and from a carrier gas. There will be some circumstances where the transfer of material is determined by a chemical reaction rate at the solid/gas interface. If this process determines the flux of matter between the phases, the rate of transport across the gas/solid interface can be represented by using a rate constant, h, so that... 

One can, nevertheless, conclude that (i) there is only a very small barrier for hole injection from ITO to PTV, if any barrier at all, (ii) a finite energy should exist for hole transport across the PTVIDASMB interface, and (iii) PBD should act as an efficient internal blockade for hole transport towards the cathode. 

Two product barrier layers are formed and the continuation of reaction requires that A is transported across CB and C across AD, assuming that the (usually smaller) cations are the mobile species. The interface reactions involved and the mechanisms of ion migration are similar to those already described for other systems. (It is also possible that solid solutions will be formed.) As Welch [111] has pointed out, reaction between solids, however complex they may be, can (usually) be resolved into a series of interactions between two phases. In complicated processes an increased number of phases, interfaces, and migrant entities must be characterized and this requires an appropriate increase in the number of variables measured, with all the attendant difficulties and limitations. However, the careful selection of components of the reactant mixture (e.g. the use of a common ion) or the imaginative design of reactant disposition can sometimes result in a significant simplification of the problems of interpretation, as is seen in some of the examples cited below. 

Theoretical aspects of mediation and electrocatalysis by polymer-coated electrodes have most recently been reviewed by Lyons.12 In order for electrochemistry of the solution species (substrate) to occur, it must either diffuse through the polymer film to the underlying electrode, or there must be some mechanism for electron transport across the film (Fig. 20). Depending on the relative rates of these processes, the mediated reaction can occur at the polymer/electrode interface (a), at the poly-mer/solution interface (b), or in a zone within the polymer film (c). The equations governing the reaction depend on its location,12 which is therefore an important issue. Studies of mediation also provide information on the rate and mechanism of electron transport in the film, and on its permeability. 

Interfaces between two different media provide a place for conversion of energy and materials. Heterogeneous catalysts and photocatalysts act in vapor or liquid environments. Selective conversion and transport of materials occurs at membranes of biological tissues in water. Electron transport across solid/solid interfaces determines the efficiency of dye-sensitized solar cells or organic electroluminescence devices. There is hence an increasing need to apply molecular science to buried interfaces. 

Note that Eqs. (4) and (5) implicitly consider the transfer across the interface as the rate-determining step in the ion transfer processes [51], and neglect other steps involved in the process such as the ion transport across the diffusion boundary layers [55] and across the diffuse electrical double layer [50]. 

Volatilization. Transfer of chemicals across the air/water interface can result in either a net gain or loss of chemical, although in many cases the bulk concentration in the air above a contaminated water body is low enough to be neglected (20). When the atmosphere is the primary source of the contaminant, as for example polychlorinated biphenyls in some parts of the Laurentian Great Lakes, atmospheric concentrations obviously cannot be neglected. The Whitman two-film or two-resistance approach (21) has been applied to a number of environmental situations (20, 22, 23). Transport across the air/water interface is viewed as a two-stage process, in which both phases of the interface can offer resistance to transport of the chemical. The rate of transfer depends on turbulence in the water body and in the atmosphere, the... 

In most circumstances, it can be assumed that the gas-solid reaction proceeds more rapidly than the gaseous transport, and therefore that local equilibrium exists between the solid and gaseous components at the source and sink. This implies that the extent and direction of the transport reaction at each end of the temperature gradient may be assessed solely from thermodynamic data, and that the rate of transport across the interface between the gas and the solid phases, at both reactant and product sites, is not rate-determining. Transport of the gaseous species between the source of atoms and the sink where deposition takes place is the rate-determining process. 

When only one phase is forming eddy currents, as when a gas is blown across the surface of a liquid, material is transported from the bulk of the metal phase to the interface and this may reside there for a short period of time before being submerged again in the bulk. During this residence time fr, a quantity of matter, qr will be transported across the interface according to the equation... 

The simple kinetics for uptake of soluble substrate of the bacteria in a biofilm is traditionally described by a combination of mass transport across the water/biofilm interface, transport in the biofilm itself and the corresponding relevant biotransformations. Transport through the stagnant water layer at the biofilm surface is described by Fick s first law of diffusion. Fick s second law of diffusion and Michaelis-Menten (Monod) kinetics are used for describing the combined transport and transformations in the biofilm itself (Williamson... 

Although mass transfer across the water-air interface is difficult in terms of its application in a sewer system, it is important to understand the concept theoretically. The resistance to the transport of mass is mainly expected to reside in the thin water and gas layers located at the interface, i.e., the two films where the gradients are indicated (Figure 4.3). The resistance to the mass transfer in the interface itself is assumed to be negligible. From a theoretical point of view, equilibrium conditions exist at the interface. Because of this conceptual understanding of the transport across the air-water boundary, the theory for the mass transport is often referred to as the two-film theory (Lewis and Whitman, 1924). 

Mass fluxes of alkali elements transported across the solid-solution interfaces were calculated from measured decreases in solution and from known surface areas and mineral-to-solution weight-to-volume ratios. Relative rates of Cs uptake by feldspar and obsidian in the batch experiments are illustrated in Figure 1. After initial uptake due to surface sorption, little additional Cs is removed from solution in contact with the feldspars. In contrast, parabolic uptake of Cs by obsidian continues throughout the reaction period indicating a lack of sorption equilibrium and the possibility of Cs penetration into the glass surface. 

Chang-Lin JE, Kim KJ, Lee VH. Characterization of active ion transport across primary rabbit corneal epithelial cell layers (RCrECL) cultured at an air-interface. Exp Eye Res 80 827-836 (2005). 

Setups Allowing to Measure Drug Transport Across Pulmonary Epithelia Interfacing Air... 

The major ions are transported across the air-sea interface by the ejection of water droplets from the sea surfece. These droplets result from water turbulence at the sea surface that causes microscopic bubbling. Some of these bubbles burst, ejecting seawater into the atmosphere. Since not all of the salt ions are ejected to the same degree, bursting bubbles can alter the ion ratios in the remaining water. 

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