Lithium batteries are considered the key storage devices for most emerging green technologies such as wind and solar technologies or hybrid and plug-in electric vehicles. Despite the tremendous recent advances in battery research, surprisingly, several fundamental issues of increasing practical importance have not been adequately tackled. One such issue concerns the energy efficiency. Generally, charging of 10(10)-10(17) electrode particles constituting a modern battery electrode proceeds at (much) higher voltages than discharging. Most importantly, the hysteresis between the charge and discharge voltage seems not to disappear as the charging/discharging current vanishes. Herein we present, for the first time, a general explanation of the occurrence of inherent hysteretic behaviour in insertion storage systems containing multiple particles. In a broader sense, the model also predicts the existence of apparent equilibria in battery electrodes, the sequential particle-by-particle charging/discharging mechanism and the disappearance of two-phase behaviour at special experimental conditions.
We consider viscous, heat conducting mixtures of molecularly miscible
chemical species forming a fluid in which the constituents can undergo chemical
reactions. Assuming a common temperature for all components, we derive a closed
system of partial mass and partial momentum balances plus a mixture balance of
internal energy. This is achieved by careful exploitation of the entropy
principle and requires appropriate definitions of absolute temperature and
chemical potentials, based on an adequate definition of thermal energy
excluding diffusive contributions. The resulting interaction forces split into
a thermo-mechanical and a chemical part, where the former turns out to be
symmetric in case of binary interactions. For chemically reacting systems and
as a new result, the chemical interaction force is a contribution being
non-symmetric outside of chemical equilibrium. The theory also provides a
rigorous derivation of the so-called generalized thermodynamic driving forces,
avoiding the use of approximate solutions to the Boltzmann equations. Moreover,
using an appropriately extended version of the entropy principle and
introducing cross-effects already before closure as entropy invariant couplings
between principal dissipative mechanisms, the Onsager symmetry relations become
a strict consequence. With a classification of the factors in the binary
products of the entropy production according to their parity--instead of the
classical partition into so-called fluxes and driving forces--the apparent
anti-symmetry of certain couplings is thereby also revealed. If the diffusion
velocities are small compared to the speed of sound, the Maxwell-Stefan
equations follow in the case without chemistry, thereby neglecting wave
phenomena in the diffusive motion. This results in a reduced model with only
mass being balanced individually. In the reactive case ..
This is a study on electrolytes that takes a thermodynamically consistent coupling between mechanics and diffusion into account. It removes some inherent deficiencies of the popular Nernst-Planck model. A boundary problem for equilibrium processes is used to illustrate the features of the new model.
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