A Double-Layer Model for Describing the Effect of Solvation and Adsorption of Ions on Electrode Surfaces in Batteries
Authors: Lück Jessica , Latz Arnulf 
Published: February 2020

The commercial launch of lithium-ion batteries by Sony took place a quarter of a century ago, but the scientific interest in this technology still did not decrease. This is due to the challenging demands for energy storage in different applications like electro-mobility or for mid-term storage of renewable energy sources. Considering the intrinsic limitations of lithium-intercalation batteries in terms of energy density, taking conversion batteries into account is equally reasonable, when searching for improved battery systems.
For both types, conversion and insertion batteries, electronic and ionic conductors are in contact with each other. At the interface between these conductors a electrochemical double layer emerges to compensate potential differences. Since 1913 with the work of Gouy and Chapman [1,2] this is well-known in literature. While a lot had been done regarding modeling the transport in insertion batteries, the exchange reaction occurring between bulk electrode and the interface between electrode and electrolyte were mostly treated with a simple Butler-Volmer approach. Following this ansatz processes at the electrolyte/electrode interface, like adsorption and solvation on electrode surfaces, or the influence of the double-layer are not accounted.
In 1991 Bruce and Saidi [3] showed that electrointercalation has to be understood as a two-step process and proposed their so called adatom model according to the growth mechanism for metal deposition. Figure 1 shows this model: the intercalation reaction consists of a adsorption step with partially desolvation, followed by an insertion step. During the later one the adion loses its remaining solvation shell and gets incorporated in the lattice of the electrode. This has been confirmed for different insertion materials [4-6], which proves these interface effects to be relevant in electrochemical systems based on intercalation reactions. To derive predictive models of batteries it is crucial to obtain a comprehensive understanding of the reaction mechanism taking place at the electrochemical interface.
Therefore we formulate a model for a consistent accumulation of charges at the interface between a concentrated electrolyte and some active material from thermodynamic and electrostatic considerations. In this way electrosorption, that is adsorption with partial desolvation, and the electrochemical double-layer are covered. Our developed model applies in particular to both intercalation and conversion reactions in batteries. Within a thermodynamic consistent reaction-transport model for Li-ion batteries [7] we use these derived equations to couple the transport in the electrolyte with the transport in the solid phase. Here the time-dependent calculation of the underlying equation leads to a charging of the double-layer in the beginning of discharge. Surface charges accumulate with a reasonable concentration on the electrode surface while transport properties of the cell are maintained. Mirror charges in the electrolyte and in the border area of the electrode are generated consistently to compensate the surface charges.
[1] L.G. Gouy, J. Phys. Theor. Appl. 9, 457-468, (1910).
[2] D.L. Chapman, Philos. Mag. 25, 475-481, (1913).
[3] P.G. Bruce, et al., J. Electroanal. Chem. 322, 93-105, (1992).
[4] S. Kobayashi, et al., J. Phys. Chem. B 109,13322-13326, (2005).
[5] M. Nakayama, et al., J. Phys. Chem. C 118, 27245-27251, (2014).
[6] M. Nakayama, et al., J. Phys. Chem. B 107, 10603-10607,(2003).
[7] A. Latz, et al., J. Pow. Sour. 196, 3296-3302, (2011).

Figure 1.
Schematic diagram of the lithium intercalation reaction at electrolyte – electrode interface

Figure 1