Electron between two metals

The qualitative elements of Marcus theory are readily demonstrated. For example, the process of transferring an electron between two metal ions, Fe2+ and Fe3 +, may be described schematically by Fig. 33 (Eberson, 1982 Albery and Kreevoy, 1978). The reaction may be separated into three discrete stages. In the first stage the solvation shell of both ions distorts so that the energy of the reacting species before electron transfer will be identical to that after electron transfer. For the self-exchange process this of course means that the solvation shell about Fe2+ and Fe3+ in the transition state must be the same if electron transfer is not to affect the energy of the system. In the second phase, at the transition state, the electron is transferred without... 

Fig. XXVIII-2.—Potential energy of an electron between two metals, in equilibrium.

Figure 20. Elastic tunneling of an electron between two metal phases separated by vacuum (rectangular barrier). Shown are the wave functions of a free electron propagating in a direction perpendicular to the interface. The wave function decays exponentially in the vacuum. The tunneling probability is related to the amplitude of the free electron wave functions (see section 6).

Figure 5.19 The tunneling of a single electron between two metal electrodes through an intermediate island can be blocked if the electrostatic energy of a single excess electron on the central island is large compared to the energy of thermal fluctuation.

In these equations the electrostatic potential i might be thought to be the potential at the actual electrodes, the platinum on the left and the silver on the right. However, electrons are not the hypothetical test particles of physics, and the electrostatic potential difference at a junction between two metals is nnmeasurable. Wliat is measurable is the difference in the electrochemical potential p of the electron, which at equilibrium must be the same in any two wires that are in electrical contact. One assumes that the electrochemical potential can be written as the combination of two tenns, a chemical potential minus the electrical potential (- / because of the negative charge on the electron). Wlien two copper wires are connected to the two electrodes, the... 

Wlien an electrical coimection is made between two metal surfaces, a contact potential difference arises from the transfer of electrons from the metal of lower work function to the second metal until their Femii levels line up. The difference in contact potential between the two metals is just equal to the difference in their respective work fiinctions. In the absence of an applied emf, there is electric field between two parallel metal plates arranged as a capacitor. If a potential is applied, the field can be eliminated and at this point tire potential equals the contact potential difference of tlie two metal plates. If one plate of known work fiinction is used as a reference electrode, the work function of the second plate can be detennined by measuring tliis applied potential between the plates [ ]. One can detemiine the zero-electric-field condition between the two parallel plates by measuring directly the tendency for charge to flow through the external circuit. This is called the static capacitor method [59]. 

Application of an electric field between two metal electrodes causes a few ions and electrons to be desorbed and is surface or thermal emission (see Chapter 7 for more information on thermal ionization). Unless the electrodes are heated strongly, the number of electrons emitted is very small, but, even at normal temperatures, this emission does add to the small number of electrons caused by cosmic radiation and is continuous. 

Another common type of reaction in aqueous solution involves a transfer of electrons between two species. Such a reaction is called an oxidation-reduction or redox reaction. Many familiar reactions fit into this category, including the reaction of metals with acid. 

The area of contact between two different types of conductors is a special place in any circuit. The character of current flow in this region depends on the phases in contact. The simplest case is that of contact between two metals. In both conductors the conduction is due to the same species (i.e., electrons). When current crosses the interface, the flow of electrons is not arrested aU electrons, which come from one of the phases freely, cross over to the other phase on their arrival at the interface. No accumulation or depletion of electrons is observed. In addition, current flow at such a junction will not produce any chemical change. 

It is typical that in Eq. (3.23) for the EMF, all terms containing the chemical potential of electrons in the electrodes cancel in pairs, since they are contained in the expressions for the Galvani potentials, both at the interface with the electrolyte and at the interface with the other electrode. This is due to the fact that the overall current-producing reaction comprises the transfer of electrons across the interface between two metals in addition to the electrode reactions. 

The Volta potential between two metals is related directly to the electron work functions of these metals. Taking into account that for two metals in contact at equilibrium we have = p, and that = 1, we obtain from Eq. (9.2) ... 

The results discussed in Sections 3.1-3.3 turned out as very valuable with respect to the knowledge about the transition from bulk metal to molecule. The most important method, however, to gain direct information from individual metal nanoparticles on their inner electronic life is the tunnelling spectroscopy. The method is based on the single-electron tunnelling (SET) through an intermediate island between two metal electrodes as is indicated in Figure 10. 

The Schottky-Mott theory predicts a current / = (4 7t e m kB2/h3) T2 exp (—e A/kB 7) exp (e n V/kB T)— 1], where e is the electronic charge, m is the effective mass of the carrier, kB is Boltzmann s constant, T is the absolute temperature, n is a filling factor, A is the Schottky barrier height (see Fig. 1), and V is the applied voltage [31]. In Schottky-Mott theory, A should be the difference between the Fermi level of the metal and the conduction band minimum (for an n-type semiconductor-to-metal interface) or the valence band maximum (for a p-type semiconductor-metal interface) [32, 33]. Certain experimentally observed variations of A were for decades ascribed to pinning of states, but can now be attributed to local inhomogeneities of the interface, so the Schottky-Mott theory is secure. The opposite of a Schottky barrier is an ohmic contact, where there is only an added electrical resistance at the junction, typically between two metals. 

Fig. 10 Aviram-Ratner rectification via HOMO and LUMO. (a) A D-o-A molecule is sandwiched between two metal electrodes. MD is the electrode proximal to the donor, MA is the electrode proximal to the acceptor, is the electrode metal work function, IPD is the ionization potential of the donor, EAa is the electron affinity of the acceptor, (b) No pathway for current exists when a voltage is applied in the reverse bias direction, (c) Under a comparable voltage to (b) but in the forward bias direction, rectification results from electrons flowing from MA to LUMO to HOMO to MD...

Charge-transfer transitions, involving the transfer of an electron between two orbitals one of which is associated predominantly with the ligand and the other with the metal. 

Figure 7.19 Principle of tunneling between two metals with a potential difference V, separated by a gap s. Electrons tunnel horizontally in energy from occupied states of the metal to unoccupied states of the tip.

The benzene molecule is attached as a phenyl group, between two metal centers (structure I), and as a "benzene four-electron donor, three-center coordinating group in structures II, VI, and X. The C-C distance in all these molecules is 1.42 A, and the dihedral angle between the planes containing the osmium atoms and the mean plane of the benzyne in the three complexes is remarkably constant at 69 3°. 

Covalent bond A bond formed by the sharing of electrons between two non-metal atoms. 

Mechanical processing (e.g., abrasion) of metallic surfaces causes the emission of electrons this is known as the Kramer effect (Kramer 1950). The effect has been shown by the measurement of selfgenerated voltages between two metallic surfaces under boundary lubrication (Anderson et al. 1969, Adams and Foley 1975). The exoelectrons have a kinetic energy from 1 to 4 eV (Kobzev 1962) and they may initiate some chemical reactions. For instance, if the metal (whose surface has been worked) is placed in an aqueous solution of acrylonitrile, the latter forms an abundant amount of an insoluble... 

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