Page 349 - High Temperature Solid Oxide Fuel Cells Fundamentals, Design and Applications

Cell, Stack and Sustern Modelling 32 5

eventually the results will be integrated with both macro- and molecular
modelIing [64-691.

7 1.8.4.3 Models of Mixed lonic and Electronic Conducting (MIEC) Electrodes
These specialised electrode models usually consider the MIEC electrode in
combination with the electroIyte and focus on correlating performance with
the semiconductor characteristics of the electrode (and sometimes electrolyte)
[70-721. Recent modelling of oxygen reduction and oxygen permeation at
perovskite electrodes includes both MIEC effects and classical diffusion-type
analysis [73-751.

11.9 Molecular-Level Models

Molecular-Ievel SOFC models aim to understand (i) the kinetics of the reaction at
the interface between electrode and electrolyte, (ii) the conduction process in the
electrolyte, and (iii) the conduction process in the electrodes. Catalytic activity at
TPB, activation energy for oxygen ion transport, and surface exchange current
are application examples for such models.
Within the last two decades, enormous progress has been achieved in the
ability to calculate the structures, the properties (e.g., thermodynamic,
mechanical, transportation properties), and the reactivity of solids starting from
atomistic approaches. The molecular-level models can be classified into three
categories.

0 Empirical interatomic potential models. Such simulations start from a
given effective potentia1 that describes the interatomic forces in a
system of atoms using essentialIy classical techniques. The simulation
algorithms are based on static minimisation methods to calculate the
structural configuration of the lowest potential energy. One popular
approach is the molecular dynamics method. Classical molecular
dynamics can use the simple interatomic potential as well as kinetic
energy to simulate fast diffusion and high-temperature properties as
well as other material properties. Molecular dynamics has been
performed to investigate the grain boundary phenomena in cubic
zirconia at constant temperatures up to 2673 K with a system of 1920
atoms [76]. Simulations indicate that the interfaces between perfect
zirconia crystals are sources of resistance in these ionic conducting
systems. Another approach is Monte Carlo methods, computing
random changes in the structure with results accepted or rejected on
the energy criterion. Monte CarIo methods are suitabIe to treat
disordered systems and, for example, the vacancy distribution and ion
motions in heavily doped, fast ionic conducting fluorite oxides such as
CeOz [77].
0 Quantum mechanical electronic structure calculations, or the ab initio
methods. Ab initio methods are based, at some level of simplification, on the