Transport across an interface

Fig. 10-22. Overvoltages in an anodic hole transfer (a) at a photoexcited n-type electrode and (b) at a p-type electrode of the same semiconductor iih = overvoltage for hole transfer across an interface = inverse overvoltage due to generation and transport of photoexcited holes in an n>type electrode.

Interfacial transfer is the transport of a chemical across an interface. The most studied form of interfacial transfer is absorption and volatilization, or condensation and evaporation, which is the transport of a chemical across the air-water interface. Another form of interfacial transfer would be adsorption and desorption, generally from water or air to the surface of a particle of soil, sediment, or dust. Illustration of both of these forms of interfacial transfer will be given in Section l.D. 

Y. Oren and A. Litan, The state of the solution-membrane interface during ion transport across an ion-exchanger membrane, 3. Phys. Chem., 78 (1974), p. 1805. 

A fixed amount of condensed phase enclosed by an interface will undergo essentially the same process, except that the time scales may differ greatly. For solid phases, the interfaces will reduce gradients in curvature by diffusional processes such as interface diffusion, crystal diffusion, and vapor transport. At similar time scales (in the case of crystal diffusion) interfaces will move because atoms will experience differences in diffusion potential across an interface arising from differences in the curvature according to Eq. 3.76. 

Other Mechanisms. We acknowledge that numerous other processes (such as detritivore activity and microbial transformations) may affect transport across the interface, but our techniques could evaluate only the processes previously discussed. An obvious area for future research is microbial degradation and release of methylmercury from sediments. The assessment of factors regulating this transformation and release is essential for predictive models on Hg transport and bioaccumulation. 

In this section the important cases for food packaging are treated. These cases differ from the previous examples in that mass transfer takes place across an interface between two different media with different characteristics, e.g. with different diffusion coefficients. If the value of a quantity is desired, for example the concentration of the substance transported across the interface in one of the two media, then a mass balance must be considered that takes into account the ratio of the contact surface area and the volume of the corresponding medium. 

The possible development of gradients in the components of the interfacial stress tensor due to flow of an adjacent fluid implies that the momentum flux caused by the the flow of liquid at one side of the interface does not have to be completely transported across the interface to the second fluid but may (partly or completely) be compensated in the interface. The extent to which this is possible depends on the rheological properties of the interface. For small shear stresses the interface may behave elastically or viscoelastically. For an elastic interfacial layer the structure remains coherent the layer will only deform, while for a viscoelastic one it may or may not start to flow. The latter case has been observed for elastic networks (e.g. for proteins) that remciln intact, but inside the meshes of which liquid can flow leading to energy dissipation. At large stresses the structure may yield or fracture (collapse), leading to an increased flow. 

K.B. Eisenthal, Photochemistry and Photophysics of Liquid Interfaces by Second Harmonic Spectroscopy, J. Phys. Chem. 100 (1996) 12997. (Article among the topics discussed are dynamics of photo-induced structure changes, transport of charge across an interface, the rotational motions of interfacial molecules, intermolecular energy transfer within the interface, interfacial photopol5mieriza-tion, and photoprocesses at a semiconductor/liquid interface,)... 

Saylor JR, Handler RA (1997) Gas transport across an air/water interface populated with capillary waves. Phys Fluids 9 2529-2541... 

Diffusion across an interface. Consider a pond containing pure water. If the air above it is dry, water will evaporate from the surface, especially if the wind is blowing. The air flow will readily be turbulent, so that water vapor can be transported from the pond surface by convection. Now a surfactant is added, enough to produce a monomolecular layer on the pond, and the evaporation rate is markedly reduced. It is often assumed that the surfactant layer provides resistance to evaporation because water cannot readily diffuse through it. However, the layer is very thin (a few nanometers) and can only cause a small resistance to diffusion (see Section 5.3.3). The main explanation of the reduced evaporation must be that the wind over the surface causes a y-gradient, so that the surface can now withstand a tangential stress hence a laminar boundary layer of air will be formed near the surface, and the diffusion of water vapor through the boundary layer (which may be about a millimeter thick) will cause a considerable decrease in transport rate. 

From the principle governing current-potential response of liquid-liquid electrochemistry, it follows that the interface between the two immiscible electrolytes can be treated in a manner similar to solid electrodes. It must be stressed again that it is ion transport across the interface, and not an electrode redox process, that determines the potential and current character-... 

The charges that we are concerned with here are the electronic charges (electrons and holes). For charges of this type to be transported across the interface, electrochemical reactions must take place. In the presence of a membrane that is impermeable to ions, what will happen then Here, the membrane must serve at least two functions (i) a pathway for electronic charges and (ii) an electrode surface for chemical transformation (reduction and oxidation or redox reactions). 

Crawford M J, Frey J G, VanderNoot T J and Zhao Y G 1996 Investigation of transport across an immiscible liquid/liquid interface—electrochemical and second harmonic generation studies J. Chem. Soc. Faraday Trans. 92 1369-73... 

When no external electrical current is supplied to the system, the mass-transfer process across an interface is basically by extraction, including both the transport in the bulk of solutions and the interfacial kinetic steps. As mentioned in Section I, when thermodynamic equilibrium in the system is established, the Galvani potential difference reaches a certain value in accordance with the distribution equilibrium. The theoretical calculation for interfacial potential and equilibrium distribution presented in previous sections can be... 

Mass transfer, an important phenomenon in science and engineering, refers to the motion of molecules driven by some form of potential. In a majority of industrial applications, an activity or concentration gradient serves to drive the mass transfer between two phases across an interface. This is of particular importance in most separation processes and phase transfer catalyzed reactions. The flux equations are analogous to Ohm s law and the ratio of the chemical potential to the flux represents a resistance. Based on the stagnant-film model. Whitman and Lewis [25,26] first proposed the two-film theory, which stated that the overall resistance was the sum of the two individual resistances on the two sides. It was assumed in this theory that there was no resistance to transport at the actual interface, i.e., within the distance corresponding to molecular mean free paths in the two phases on either side of the interface. This argument was equivalent to assuming that two phases were in equilibrium at the actual points of contact at the interface. Two individual mass transfer coefficients (Ld and L(-n) and an overall mass transfer coefficient (k. ) could be defined by the steady-state flux equations ... 

An example of a polarizable interface is that between a mereury electrode and liquid water, since the concentration of mercury ions in the aqueous phase is quite negligible. In this case, it is common to assume a a practical convention that equilibrium at the interface exists when the emf of the mercury electrode-reference electrode pair vanishes, since a Galvani potential difference between mercury and water cannot be measured. An example of a reversible interface is that between a hydrous oxide solid and liquid water. In this case, and OH ions can cross the interface freely and are potential-determining. Equilibrium at the interface is established when the net ion transport across the interface vanishes, i.e., when there is no change in the pH value of the aqueous phase. Note that the interface between a soil particle and the soil solution is in general reversible. Any charged species that is adsorbed by the particle and found in the soil solution is potential-determining. 

On the other hand, the synthetic organic chemist, who has often to deal with immiscible or sparingly miscible fluids, has to contend with the problem of transport of a desired species across an interface such as gas-liquid, liquid-liquid, or fluid-solid. In such a situation, one has to fall back on the concept of mass transfer coefficient by defining a hypothetical film across which transport occurs—an approach to which the chemist is unaccustomed. Although the two models (one based on diffusion and the other on mass transfer coefficient) are related, we shall largely be concerned (more as chemical engineers now) with the latter in dealing with interfacial phenomena (e.g., in Chapters 7 and 14-17). 

Immiscible polymers caimot produce molecularly homogeneous mixtures due to finite and often high values of interfadal tension. Consequently, a mixed state in an immiscible polymer system may consist of polymer domains with sharp or diffuse interfaces depending upon how the local properties, such as concentration, viscosity, and density, vary on both sides of the interfaces [138]. A sharp interface results if the properties are discontinuous and there is no mass transport across the interface. In contrast, a diffused interface is obtained when the properties vary gradually and continuously across the interface. A material parameter, the interfadal tension, o, characterizes immiscible polymer systems and is defined as ... 

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