In this contribution discrete modeling of space charge zones in solids is presented, which is a sensible approach for handling pronounced space charge potentials as well as non-idealities in realistic solid state system¹. At interfaces in charge-carrier containing systems, individual charge carriers redistribute, which leads to transport but also storage anomalies². Such space charge zones are usually described by a continuum picture based on classic Gouy-Chapman (or Mott-Schottky) models. In addition to issues of internal consistency, this continuum approach is questionable if extremely steep profiles close to the interface occur, and analytical corrections are not very helpful. We show how discretization remedies a variety of such short-comings, allows for a straightforward taking account of non-idealities, and even provides surprising insight into double layer capacitance and conductance effects. Combining discrete modeling with the continuum description provides a particularly powerful method with the help of which non-idealities in the first layers (variation in structure, elastic effects, saturation effects, changes in dielectric constant) can be directly addressed. Various examples of practical value for functional ceramics and batteries are discussed. We believe that such discretization represents a substantial progress in the field of space charge theory being advantageous over introducing corrections into the already overstrained Gouy-Chapman function.

References

1. C. Xiao; C.-C. Chen; J. Maier, Discrete modeling of ionic space charge zones in solids, submitted.
2. C.-C. Chen, J. Maier, Decoupling electron and ion storage and the path from interfacial storage to artificial electrodes, Nature Energy 2018, 3 (2), 102-108.