Kinetics of Energy Storage

defect chemistry can be exploited to give the voltage-capacity relation. Here, however, electroneutrality has to be replaced by Poisson s equation (for details, the reader is referred to the references [50-51]). 

Naturally, also the very core of the interfaces might store Li at potentials still higher than metallic lithium. The same can happen at dislocation cores, pores, or frozen-in point defects (cf. Li-storage in carbon vacancies [52]). 

The aptitude of a given storage mechanism is mainly determined by the cell voltage connected with it (positive electrodes are typically in the range of 2-5 V vs. Li/Li+ negative electrodes in the range of 0-1.5 V), the respective storage capacity connected with it, and its reversibility. 

In contrast to Section 3.5.4, where equilibrium thermodynamics (i.e. a current-less state was discussed), this section deals with losses that occur while current is flowing. A nonzero current leads to losses (overpotentials) that can be translated into resistances. These kinetic contributions lead to U E (U terminal voltage, / current) for discharge (/ 0) and to U E for the charge process (1 0). 

In other words, under realistic conditions (/ 0), entropy is produced, with the positive entropy production being given by fluxes and forces related to the process j. Equation (5) assumes that all these processes are in series, which is mostly correct. The most obvious contributions are transport resistances, due to the finite conductivities of Li+ and e in electrolyte and electrodes. For usual geometries, these resistances are constant to a good approximation, while for resistances stemming from impeded charge transfer and phase boundaries, the dependence on current can be severe. 

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