Space charge concept

Pejovnik 1991 SOCl2/LiAlCl4 Space charge concept 98... 

So far the ionic space charge concepts have been mainly applied to transport and storage. An area that is not adequately addressed but expected to be greatly influenced by such effects is the area of interfacial transfer and reactions including reaction kinetics, catalysis, or in particular the electrochemical transfer reaction. In many of these processes, defect concentrations are involved in the rate determining steps and not only will space charge considerations help understand them but more importantly lead to a targeted improvement of electrochemical performance. 

Often, the concept of (two-dimensional) surface or (three-dimensional) space charge is employed. Here it is assumed that the charge is distributed in a continuous fashion (smeared out) over the surface S or volume V. Surface and space charge can be described in terms of surface-charge density = dQldS or space-charge density Qy = dQldV, which may either be constant or vary between points. 

Examples of p(r) are energy density, charge density, current density (see Section 4.6), difference density (difference between a final density and an initial density), electric moment density, magnetic moment density, local reactivity functions (see Section 4.5.2), force density, etc. Note that, for ensuring the stability of matter, the net force density must vanish everywhere in space. The concept of a PDF has generated many significant developments in interpretative quantum chemistry. 

An electric field in the semiconductor may also produce passivation, as depicted in Fig. 6.1c. In semiconductors the concentration of free charge carriers is smaller by orders of magnitude than in metals. This permits the existence of extended space charges. The concept of pore formation due to an SCR as a passivating layer is supported by the fact that n-type, as well as p-type, silicon electrodes are under depletion in the pore formation regime [Ro3]. In addition a correlation between SCR width and pore density in the macroporous and the mesoporous regime is observed, as shown in Fig. 6.10 [Thl, Th2, Zh3, Le8]. 

The present chapter is devoted mainly to one of these new theories, in particular to its possible applications to photon physics and optics. This theory is based on the hypothesis of a nonzero divergence of the electric field in vacuo, in combination with the condition of Lorentz invariance. The nonzero electric field divergence, with an associated space-charge current density, introduces an extra degree of freedom that leads to new possible states of the electromagnetic field. This concept originated from some ideas by the author in the late 1960s, the first of which was published in a series of separate papers [10,12], and later in more complete forms and in reviews [13-20]. 

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. 

In the above analysis, we used the concept of space charge layer, to be more precise, a depletion layer that would form in a doped, wide-gap semiconductor contacting another phase (a metal, an electrolyte solution, or vacuum). The poly crystalline diamond/metal junctions (where metal is Au, Pt, Pd, etc.) often show rectifying properties [67, 68] and their capacitance characteristics resemble those of a diamond/electrolyte solution junction. 

Understanding of the electrostatics across nanocrystalline semiconductor film-electrolyte junctions presents interesting challenges, particularly from a theoretical perspective. Concepts related to space-charge layers, band-bending, flat-band potential and the like (Section 1.3) are not really applicable here because the crystallite dimensions comprising these layers are comparable to (or even smaller than) nominal depletion layer widths. 

Following Debye-Huckel, the distribution of ions can be calculated via the Boltzmann energy distribution. The application of this law is based on the concept that the ion cloud represents a space charge which is most dense in the vicinity of the central ion and decreases with growing distance to the central ion. A number of simplifying assumptions concerning the state of ions is made ... 

The presence of organic ions or (hydrolyzed) multivalent metal ions requires an even more sophisticated approach to the EIL, and the modelling is usually more speculative. Common practice usually leaves open the problem of the point charge concept, in contrast to the homogeneous charge. Another problem which is not considered in practical applications is the structure of water in the interfacial region, which is connected to the homogeneity of the available space and the choice of the value of the relevant permittivity. The use of bulk permittivity results in an apparent value of all the space parameters of the EIL. 

Thus, since the time interval between and on the one hand, and on the other hand, is sufficiently large (from to 10 s), the time characteristics of many electrode processes satisfy conditions (43). Therefore, the concept of quasi-Fermi levels has a rather wide range of application. At the same time, quantitative description (see, e.g.. Ref. 67) requires that certain additional conditions should be satisfied. It is necessary, in particular, that the quasi-level behavior in the space-charge region be sufficiently smooth the latter condition holds true if a and reco/nbina-... 

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