Chemical potentials schematic representation

A more effective carrier confinement is offered by a double heterostmcture in which a thin layer of a low band gap material (the active layer) is sandwiched between larger band gap layers. The physical junction between two materials of different band gaps, and chemical compositions, is called a heterointerface. A schematic representation of the band diagram of such a stmcture is shown in Figure 4. Electrons injected under forward bias across the p—N junction into the lower band gap material encounter a potential barrier, AE at thep—P junction which inhibits their motion away from the junction. The holes see a potential barrier of AE at the N—p heterointerface which prevents their injection into the N region. The result is that the injected minority... 

Fig. 19.15 Schematic representation of range of corrosion potentials expected from various chemical tests for sensitisation in relation to the anodic dissolution kinetics of the matrix (Fe-l8Cr-IONi stainless steel) and grain boundary alloy (assumed to be Fe-lOCr-lONi) owing to depletion of Cr by precipitation of Cr carbides of a sensitised steel in a hot reducing acid (after Cowan and Tedmon )...

Figure 5.7. Schematic representation of the definitions of work function O, chemical potential of electrons i, electrochemical potential of electrons or Fermi level p = EF, surface potential %, Galvani (or inner) potential

Figure 7.14. Schematic representation of the spatial variation of electrode potential, chemical potential of oxygen and electrochemical potential of O2 for the cell 02, M1YSZ1M, 02 (=1 atm).

Figure 8.8 Series of iniiared spectra during (a) CO2 production and (b) progressive oxidation of COaj[ on Pt3Sn(l 11) in 0.5 M H2SO4 saturated with CO each spectrum was accumulated ftom 50 interferometers at the potential indicated, (c, d) LEED pattern and schematic representation of the p(4 X 4) structure observed on PtsSnflll) after exposing the surface to O2 and electrolyte. The gray dicles are Pt surface atoms, the black circles are Sn atoms covered with OH, and the dotted circles are Sn atoms that are chemically different from Sn atoms modified with OH. (Reprinted with permission from Stamenkovic et al. [2003]. Copyright 1999. The American Chemical Society.)...

Figure 17.17 Schematic representation of a single-compartment glucose/02 enzyme fuel cell built from carbon fiber electrodes modified with Os -containing polymers that incorporate glucose oxidase at the anode and bilirubin oxidase at the cathode. The inset shows power density versus cell potential curves for this fuel cell operating in a quiescent solution in air at pH 7.2, 0.14 M NaCl, 20 mM phosphate, and 15 mM glucose. Parts of this figure are reprinted with permission from Mano et al. [2003]. Copyright (2003) American Chemical Society.

Figure 2.47 (a) 1RRAS spectra of CO adsorbed on Pt in 1.0 M HCI04 saturated with CO. The electrode potential was held constant at (i) 50 mV vs. NHE, (ii) 250 mV, (iii) 450 mV and (iv) 650 mV. (b) Difference spectra resulting from subtraction of the IRRAS spectra (iii) and (i). (c) EMIRS spectrum of Pt electrode in CO-saturated 1 M HCIO modulated between + 50mV and 450mV. (d) A schematic representation of spectra at two potentials which could produce an EMIRS spectrum similar to that shown in (c). The IRRAS spectra in (a) rule out this possibility. After Russell et al, (1982). Copyright 1982 American Chemical Society,... 

Figure 2.5 Schematic representation of the Au/MPS/PAH-Os/solution interface modeled in Refs. [118-120] using the molecular theory for modified polyelectrolyte electrodes described in Section 2.5. The red arrows indicate the chemical equilibria considered by the theory. The redox polymer, PAH-Os (see Figure 2.4), is divided into the poly(allyl-amine) backbone (depicted as blue and light blue solid lines) and the pyridine-bipyridine osmium complexes. Each osmium complex is in redox equilibrium with the gold substrate and, dependingon its potential, can be in an oxidized Os(lll) (red spheres) or in a reduced Os(ll) (blue sphere) state. The allyl-amine units can be in a positively charged protonated state (plus signs on the polymer...

Fig. 20 Schematic representation of a two-terminal device. The scattering region (enclosed in the dashed-line frame) with transmission probability T(E) is connected to semi-infinite left (L) and right (R) leads which end in electronic reservoirs (not shown) at chemical potentials Eu and r, kept fixed at the same value p for linear transport. By applying a small potential difference electronic transport will occur. The scattering region or molecule may include in general parts of the leads (shaded areas) (adapted from [105] with permission Copyright 2002 by Springer)...

Fig. 32. Schematic representation of the isomers of cyclen-based complexes, with chirality and potential exchange mechanisms between them. From (Dickins et al., 1998), reproduced with permission of the Royal Chemical Society (RSC) on behalf of the Centre National de la Recherche Scientifique (CNRS).

The effects of the crystallographic face and the difference between metals are evidence of the incorrectness of the classical representations of the interface with all the potential decay within the solution (Fig. 3.13a). In fact a discontinuity is physically improbable and experimental evidence mentioned above confirms that it is incorrect, the schematic representation of Fig. 3.136 being more correct. This corresponds to the chemical models (Section 3.3) and reflects the fact that the electrons from the solid penetrate a tiny distance into the solution (due to wave properties of the electron). In this treatment the Galvani (or inner electric) potential, (p, (associated with EF) and the Volta (or outer electric) potential, ip, that is the potential outside the electrode s electronic distribution (approximately at the IHP, 10 5cm from the surface) are distinguished from each other. The difference between these potentials is the surface potential x (see Fig. 3.14 and Section 4.6). 

FIGURE 6 Schematic representation of an oxide catalyst with its functional compartments in various structural states for high (back) and low (front) chemical potentials of oxygen. The arrows and the question mark indicate the complex distribution of oxygen in its dual role as a reactant at the surface and as a constituent of the catalyst material in the bulk. Its abundance is controlled by the presence of reducing species in the gas phase leading to a dependence of the results of XRD structural analysis on the availability of reducing gas-phase species. For details and references, see the text. 

Figure 8. Schematic representation of chemical potential energy surfaces. Counting of states below reaction barrier for both reactants and products gives a minimal estimate of numbers of coupled equations to be solved.

Fig. 4.4. A schematic representation of the work M/done in transporting a mole of species / from an equiconcentration surface where its concentration and chemical potential are c, and fif to a surface where its concentration and chemical potential are Cp and fip.

Fig. 9. Schematic representation of double layer structure and potential profiles of the interface between a nitrobenzene (NB) solution of 0.1 M Pn4Ph4B and an aqueous (w) solution of 0.05 M LiCl in the presence (solid line) and absence (broken line) of a saturated DLPC monolayer at the potential of zero charge, where the surface potential was assumed to be negligible. (Reprinted from [98] with permission. Copyright The Chemical Society of Japan).

Figure 1 Chemical structures of GC (panel A) and AT (panel B) base pairs with schematic representation of potential hydration sites. The diagram specifies those functional groups of DNA, in the vicinity of which waters are observed frequently in X-ray crystallographic structures. The diagram does not reflect the relative occupancies and precise localizations of individual water molecules.

Figure 3. Schematic representation of the variation of k upon A " and potential applications in the determination of "rx/r.x (k represents the standard rate for A "" = 0) [27]. Reproduced by pennission of American Chemical Society.

Figure 7. Schematic representation of growth mechanism of PEDOT nanostructures for high oxidation potential (1.4 V) (a) slow reaction rate at high monomer concentration and (b) fast reaction rate at low monomer concentration. Courtesy of II Cho et al. Reprinted with permission from II Cho and Lee.216 Copyright 2008 American Chemical Society.

Fig. 6.4 Schematic representation of the division of the electrochemical potential of species i in phase a into chemical and electrical...

Figure 18.2.6 Schematic representation of the variation of electron-transfer rate, and transfer coefficient, a, with electrode potential for an ideal semiconductor electrode. The current is is equivalent to that defined in (18.2.9) or (18.2.10). At sufficiently extreme potentials (not shown) mass transfer would lead to a limiting current on the right side of the diagram. [Reprinted with permission from B. R. Horrocks, M. V. Mirkin, and A. J. Bard, 7. Phys. Chem., 98, 9106 (1994). Copyright 1994, American Chemical Society.]...

Fig. 12.14. Schematic representation of the potential energy surface for S2 and Sq of stilbene including the photocyclization reaction. Approximate branching ratios and quantum yields are indicated. Reproduced from J. Phys. Chem., 98, 6291 (1993), by permission of the American Chemical Society.

A schematic representation of the inner region of the double layer model is shown in Fig. 1. Figure lb describes the distribution of counterions and the potential profile /(a ) from a positively charged surface. The potential decay is caused by the presence of counterions in the solution side (mobile phase) of the double layer. The inner Helmholtz plane (IHP) or the inner Stem plane (ISP) is the plane through the centers of ions that are chemically adsorbed (if any) on the solid surface. The outer Helmholtz plane (OHP) or the outer Stem plane (OSP) is the plane of closest approach of hydrated ions (which do not adsorb chemically) in the diffuse layer. Therefore, the plane that corresponds to x = 0 in Eq. (4) coincides with the OHP in the GCSG model. The doublelayer charge and potential are defined in such a way that ao and /o, op and Tp, and <5d and /rf are the charge densities and mean potentials of the surface plane, the Stem layer (IHP), and the diffuse layer, respectively (Fig. 1). 

Fig. 4.9 Schematic representation of the liquid/liquid interface featuring two adsorption planes. The various equilibria are affected by the distribution of the Galvani potential difference (A" ) across the interface. Reprinted with permission from Ref. [23]. Copyright (2001) American Chemical Society.

FIGURE 15.1 Schematic representation of a microchip used for high-speed electrophoretic separations. Narrow channels were etched in the injection and separation areas, while wide channels were fabricated for all other sections. These differential channel widths ensured the majority of the potential was apphed across the narrow channels. Owing to the high separation field strengths (up to 6.1 V cm per volt of applied potential), suhsecond separations were possible. (Reproduced from Jacobson, S. C. et al. Anal. Chem., 70, 3476, 1998. With permission from American Chemical Society.)... 

Fig. 2 Schematic representation of the potential energy landscape of ground and excited states. Because of its nonequilibrium nature, the excited state structure evolves into radiative and radiationless channels. The radiationless transitions can result from bifurcation into reactive chemical processes and nonreactive physical pathways (internal conversion/intersystem crossing). Reproduced with permission from ref. 14. AAAS 2007.

Fig. 4 Schematic representation of (a) twisted intramolecular charge transfer process and (b) the potential energy surfaces. Reproduced with permission from ref. 25. 2010, American Chemical Society.

FIGURE 21.3 Schematic representation of quantities related to the reference level problem. (Adapted from Brazovskii, S.A., and Kirova, N.N. 1981. JEPT Lett., 33, 4, 1981.) The relevant quantities are the Fermi level p, the vacuum level the work function , the internal (bulk) chemical potential /zi, the chemical potential /Zch. the electrostatic potential as a function of the distance to the surface the volume average of x) inside the surface <(> > the volume average of (f> x) outside the surface outer> and the surface electrostatic potential... 

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