Space charge boundary layer

From a similar viewpoint, Clark (93) attempts to give an interpretation of the catalytic activity of oxides of the transition metals using the simplified band model of semiconductors. The important mechanism of the electron transfer in a space-charge boundary layer is not discussed in Clark s publication. 

Space Charge Boundary Layers In Electrochemical Equilibrium with the Gas Phase Chemisorption... 

Fig. 6. Concentration variation of defects n and p or nM and nlM 1 respective1 in an n and P type oxidewlth a space charge boundary layer.

Since space charge boundary layers make quantitative treatment quite difficult, Cabrera and Mott (37) have attempted to circumvent this difficulty in their well-known theory of metal oxidation by making the following two simplifications, whose applicability should first be discussed since they are not always justified (1) It is assumed that the space charge effects can be neglected in layers which are not thicker than several hundred A. (2) The assumption Is implied, although not explicitly stated, that the concentration of defects within the thin oxide layer is constant. Simplification (1) is justified to a first approximation in the formation of poorly conducting n-type oxide layers but not in other cases. 

The question has been considered (44) as to whether or not a cubic rate law can also be achieved by transport phenomena in p-type space charge boundary layers. These considerations were based on the assumption that the entire oxide layer constitutes a space charge boundary layer. In order to simplify the derivation of the rate law, we assume in the formation of p- and p-n type boundary layers that the electric field established in the surface layer is caused to a first approxi mation only by the distribution of holes, i. e., p >>nj ej an< p n. Under these assumptions, the derivation of the nole current leads to the following expression ... 

To evaluate the contribution of the SHG active oriented cation complexes to the ISE potential, the SHG responses were analyzed on the basis of a space-charge model [30,31]. This model, which was proposed to explain the permselectivity behavior of electrically neutral ionophore-based liquid membranes, assumes that a space charge region exists at the membrane boundary the primary function of lipophilic ionophores is to solubilize cations in the boundary region of the membrane, whereas hydrophilic counteranions are excluded from the membrane phase. Theoretical treatments of this model reported so far were essentially based on the assumption of a double-diffuse layer at the organic-aqueous solution interface and used a description of the diffuse double layer based on the classical Gouy-Chapman theory [31,34]. 

Since the electro-osinotic flow is induced by the interaction of the externally applied electric field with the space charge of the diffuse electric double layers at the channel walls, we shall concentrate in our further analysis on one of these 0 1 2) thick boundary layers, say, for definiteness, at... 

In contrast to this, with a homogeneous membrane corresponding to Problem 3, the motion in a symmetry cell of the liquid boundary layer, adjacent to an electrically inhomogeneous membrane, is induced by the electric field interaction with an essentially nonequilibrium space charge, formed only in the course of the ionic transport itself. 

A similar expression is to be expected for the distribution of electrons in exhaustion boundary layers. The evaluation of these equations is not easy. Therefore, it is desirable to simplify our assumptions concerning the distribution of the electrons and holes in the boundary layer. This simplification is illustrated by Fig. 3. With a suitable choice of the thickness I of the boundary layer, the simplification will satisfactorily approximate the real case. The distribution of space charge in an inundation boundary layer can be similarly calculated, and will be shown below in parentheses. 

This form of an isotherm is characteristic for a chemisorption process on an n-type catalyst forming a boundary layer with a space charge. It is evident that this mechanism is quite different from the mechanism of physical or van der Waals adsorption, which is represented by the Langmuir equation. 

Finally, we must consider the contribution of the electrostatic work required to transfer one electron into free space. After overcoming the short range chemical forces, the electron must be moved a certain distance against the electric field in the surface. Under the assumption that the lines of force of the electric field are located between the ion defects in the boundary layer and the surface charges represented by the chemisorbed gas atom, we obtain the expression afi for this electrostatic work term. is the boundary field strength represented in Equation (11), and a is the distance between the surface of the oxide and the centers of charge of the chemisorbed atoms in the a-phase. 

An important consideration for the electronics of semiconductor/metal supported catalysts is that the work function of metals as a rule is smaller than that of semiconductors. As a consequence, before contact the Fermi level in the metal is higher than that in the semiconductor. After contact electrons pass from the metal to the semiconductor, and the semiconductor s bands are bent downward in a thin boundary layer, the space charge region. In this region the conduction band approaches the Fermi level this situation tends to favor acceptor reactions and slow down donor reactions. This concept can be tested by two methods. One is the variation of the thickness of a catalyst layer. Since the bands are bent only within a boundary layer of perhaps 10-5 to 10 6 cm in width, a variation of the catalyst layer thickness or particle size should result in variations of the activation energy and the rate of the catalyzed reaction. A second test consists in a variation of the work function of the metallic support, which is easily possible by preparing homogeneous alloys with additive metals that are either electron-rich or electron-poor relative to the main support metal. 

As the skin is relatively thick compared to the space-charge layers at its boundaries, the bulk of the membrane may be expected to be electroneutral [56,57], The Nernst-Planck equation can be solved, therefore, by imposing the electroneutrality condition C,/C= C. /C, where the subscripts j and k refer to positive and negative ions, respectively, and C is the average total ion concentration in the membrane. In the case of a homogenous and uncharged membrane bathed by a 1 1 electrolyte, the total ion concentration profile across the membrane is linear and the resulting steady-state flux is described by... 

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