Electron rates

It is now well established that in lithium batteries (including lithium-ion batteries) containing either liquid or polymer electrolytes, the anode is always covered by a passivating layer called the SEI. However, the chemical and electrochemical formation reactions and properties of this layer are as yet not well understood. In this section we discuss the electrode surface and SEI characterizations, film formation reactions (chemical and electrochemical), and other phenomena taking place at the lithium or lithium-alloy anode, and at the Li. C6 anode/electrolyte interface in both liquid and polymer-electrolyte batteries. We focus on the lithium anode but the theoretical considerations are common to all alkali-metal anodes. We address also the initial electrochemical formation steps of the SEI, the role of the solvated-electron rate constant in the selection of SEI-building materials (precursors), and the correlation between SEI properties and battery quality and performance. 

According to the Marcus theory [64] for outer-sphere reactions, there is good correlation between the heterogeneous (electrode) and homogeneous (solution) rate constants. This is the theoretical basis for the proposed use of hydrated-electron rate constants (ke) as a criterion for the reactivity of an electrolyte component towards lithium or any electrode at lithium potential. Table 1 shows rate-constant values for selected materials that are relevant to SE1 formation and to lithium batteries. Although many important materials are missing (such as PC, EC, diethyl carbonate (DEC), LiPF6, etc.), much can be learned from a careful study of this table (and its sources). 

In the first part of the reaction scheme (Eq. 30) the generation (g) of holes (h ) in the valence band and of the surface radical S is described. The holes can also be consumed by recombination with electrons (rate v J or by direct hole transfer to the redox system (v, i). The surface radical can react with an electron from the conduction band (v ,2) or with the redox system (v, 2), processes by which the radical disappears. Accordingly, the original bond is repaired as illustrated in Fig. 7b. 

Electron rate constant, intramolecular, 40 175 Electron relaxation times, iron-sulfiir proteins, 47 252-257... 

Scheme 15 The initial one-electron rate-limiting step in the oxidation of NADH by the ROMs studied in this work (taken from Ref. 174).

Oxidative reactions of 2AP(-H) have been studied in oxygen-saturated solutions because 2AP(-H) radicals do not exhibit observable reactivities towards O2 [10]. In contrast, O2 rapidly reacts with hydrated electrons (rate constant of 1.9x10 ° s ) [51] and hydrated electrons do not interfere in... 

Figure 18 Dependence of back-electron rate constant on pH for Ru bpyElphosbpy)1" covalently bound to SnC>2. The observed small reactivity variations (ca. factor of 3) are consistent with a residual zeta-potential-based driving-force effect.

ZnO Parravano Addition of cations with valence greater than 2 Increases the number of electrons Rate increased... 

MoOa, WO, UO CraOa, NiO, FeO, ZnO A. Clark O2 at 500°C Decreases the number of electrons Rate decreased... 

Figure 2.3 Evidence for the Marcus inverted region from intramolecular electron rate constants as a function of AG° in methyltetrahydrofuran solution at 206 K. Reprinted with permission from G.L. Closs, L.T. Calcaterra, H.J. Green, K.W. Penfield and J.R. Miller, ]. Phys. Chem., 90,3673 (1986). Copyright (1986) American Chemical Society...

Long-distance intramolecular electron transfer can be described in the framework of the Marcus theory 175). In the formulation of Lieber et al. 177), the intramolecular electron rate constant, can be written as... 

Photoexcited hot electrons may further be emitted from metals into electrolyte solutions [6.119]. Once electrons have been emitted into the solvent, they can diffuse back to the emitter and be recaptured by the electrode, or they are scavenged by redox acceptor species within the picosecond time range. Protons appeared to be a very effective scavenger [6.120]. Particularly, subpicosecond laser-induced nonequilibrium hot electrons lead to high emission electron rates which can react with acceptors to form intermediates. This is followed by localized metal nucleation [6.121]. 

In general, many kinetics data are accumulated prior to proposing a reaction mechanism. In our case, we will simply use the stoichiometry information obtained in Experiment 5.4 along with intuition based on past work in the field. The following is an interactive pre-lab exercise for proposing the rate law for the electron transfer between [Co(en)3)]2+ and [Co(ox)2(en)]. The kinetics will then be investigated using conventional visible spectroscopy. Experimental data, in combination with the rate law, will be used to determine the outer-sphere electron rate constant. 

The reactivity of the transition metal ions depends on the availability of an orbital and the gain in energy on addition of the electron. Rate coefficients for the reaction of some dispositive ions are shown in Table 3. 

For barium azide, on the other hand, Torkar et al. found the activation energy for thermal decomposition to be much greater than that for ionic conductivity and proposed an electronic rate-controlling mechanism [97] ... 

Both Forster and electron exchange rate constants depend on the spectral overlap integral J between the emission spectrum of the donor and the absorption spectrum of the acceptor. A high value of J induces a high electron rate The rate constant of the electron exchange (kt) is equal to... 

Piqueria trinervia possible herbicidal activity has been thoroughly studied. It was first demonstrated that piquerol A (26a) inhibited the germination and plant growth of several weeds, therefore it was proposed as responsible of P. trinervia allelopathic activity [52]. The mechanism of action of piquerol A was next studied [53]. This compound inhibited ATP synthesis and phosphorylating electron rate in pea chloroplasts. On the... 

The optical phase of the carrier wave in a linearly polarized femtosecond pulse can be measured by the photoelectron rate (Fig. 6.59). If the electrons are produced by the nth harmonic of the visible femtosecond pulse, the rate is proportional to the 2nth power of the visible field amplimde. The amplitude depends strongly on the phase of the optical wave relative to the envelope maximum of the pulse. Measurements of this photo-electron rate as a function of the phase shift of the field amplitude against the pulse maximum allows the determination of the phase and the pulse width of the high-harmonic attosecond pulse [754]. There are many more applications of attosecond pulses these can be found, for example, in the publications of the groups of P. Corkum at the NRC in Ottawa [753] and F. Krausz at the MPI for Quantum Optics in Garching, who have pioneered this field [754]. 

This has been used for two-level tunnelling systems in insulating glasses. The coupling coefficient Fip from the phonon deformation potential should be independent of T and A, because the density of phonon modes in the Debye model is proportional to co up to the maximum frequency cod and this co-dependence counteracts the smaller overlap for larger A. The electron rate Re may therefore dominate the total rate at small values of A, while Rip may be faster for large A up to the Debye energy k T. ... 

As for the second parameters, the electric field strength Emax, we have found more sensible to employ the electron temperature instead. In fact it was simpler to express the electron rate constants, calculated from their cross-sections and evaluated assuming a Maxwellian energy distribution function for electrons, described by a single parameter, their temperature Te. 

Assuming a one-electron rate-determining charge transfer step, b /f at the lower potential is approximately 1 + a. From Table 3.5 we see that this is true if the second step is rate-determining. Considering the possibility that adsorption should be taken into account because of change in the Tafel slope, we suspect that mechanism (5) in Table 3.6 could be appropriate. 

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