Theoretical model for surface diffusion driven Ni-particle agglomeration in anode of solid oxide fuel cell

•An analytical model capable of explaining experiments is derived in a natural way.•Mechanism and limiting factor for Ni particle growth are discussed and quantified.•Only one adjustable parameter describing electrode morphology is used in the model.•The model is in very good agreements with the available experimental data sets.

The agglomeration of Ni particles in nickel–yttria stabilized zirconia (YSZ) anode is an important degradation mechanism for the solid oxide fuel cell and is widely believed to be driven by surface diffusion. This work aims to develop a quantitative model to describe the agglomeration kinetics. The model treats the anode as a system of random packing Ni and YSZ particles. Surface diffusion occurs between the connected Ni particles of different sizes characterized by two representative radii, but is influenced by the YSZ network. The Fick's law for diffusion, the Gibbs–Thomson relation for vacancy concentration and the coordination number theory for percolating Ni network are employed in the mathematical derivation. The growth kinetics is expressed as an analytical function consisting of two model parameters, one for the Ni-particle size distribution and the other for the influence of the YSZ backbone. The model is in excellent agreement with the available experiments. The influence of the YSZ backbone is further considered to obtain a model with just one fitting parameter. The one-parameter model is also in good agreement with the experiments and the fundamental physics for the Ni-particle growth is therefore believed to be well characterized.