Rate constants electrons

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). 

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

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.

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... 

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. 

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. 

We see for both the fluorine and chlorine based laser mixtures that densities of order 2-3 x 10 " electrons per cm are observed in steady state. This was at some variance with the commonly accepted computer models at the time. In the course of readjusting electron rate constants it was found that laser energy output was not terribly sensitive to (or a very good measure of) the electron density. Towards the end of the pulse (or sooner for dilute halogen mixtures) we see that the electron density increases rapidly. This is due to... 

Electron Rate Constants and Quenching Rate Constants 11 / 177 TABLE 6. ELECTRON TRANSFER RATE CONSTANTS (k.) BETWEEN PHOTOSENSITIZERS AND CATIONIC PHOTOINITIATORS AND... 

---