**1.2 Basic justification of classical MD**

344 Molecular Dynamics – Theoretical Developments and Applications in Nanotechnology and Energy

Fig. 2. Computational methods at different length and time scales to model a SOFC material adopted from Cheng et.al. 2011. (Adapted figure reproduced from Cheng et.al. 2011.

(Gatewood et al., 2011; Lau et al., 2008, 2009; Pornprasertsuk et al., 2007; Turner et al., 2010; Wang et al., 2010, 2011). Specifically, KMC can probe SOFC performance by simultaneously capturing various reaction pathways of electrochemical and physicochemical reactions in the electrolyte and at the three-phase boundary (TPB), i.e. the interface where the gas reactants, electrolyte, and electrode meet. The electrical current through the YSZ is simulated in direct current (dc) and alternating current (ac), as electrochemical impedance spectra under various operating conditions using a minimal set of uniform chemical reaction rates on an assumed cubic YSZ lattice via KMC (Gatewood et al., 2011; Lau et al., 2008, 2009; Pornprasertsuk et al., 2007; Turner et al., 2010; Wang et al., 2010, 2011). Despite the robustness of KMC simulation, this approach is based on a rigid lattice gas model and can not predict the experimentally observed ionic conductivity maximum as a function of Y2O3 dopant concentration (Hull, 2009). Beyond the kinetics driven atomic motion as implemented in minimal KMC models, the complex dynamics of real lattices and the realtime multi-particle ion-vacancy interactions at a finite temperature can be computed 'on-thefly' in simulation. However simple or complex, the ionic conductivity of any atomistic model of solid YSZ is, the conductivity can accurately be derived from standard equilibrium classical MD simulation (Frenkel & Smit, 1996). Thus to explore and understand the nature of unique ionic conductivity in the solid electrolytes of SOFC's, YSZ solids have been

Copyright 2011 RSC Publishing.)

In crystalline solids, ionic conductivity is fundamentally different from electronic conductivity. Electronic conduction in a metal, for example, occurs on a three-dimensional array of ion cores whose excess valence electrons have dissociated to form a continuous "sea of free electrons" partially filling the electronic bands around the Fermi-level. Because the electron has a small mass, its de Broglie wavelength is large and therefore quantum mechanical effects force the electrons into those bands. As ions are much heavier than electrons, their motion is far less governed by quantum mechanics. Below the typical atomic vibrational frequencies (< 100 GHz), ionic motion is best described by thermally activated hopping between (usually) charge-compensating sites (Dyre et al., 2009).

The dynamics of mobile ions in a disordered inorganic ionic conductor (e.g. amorphous YSZ) is clearly a complex multi-particle problem. Unlike a perfect crystal, the potentialenergy landscape experienced by an ion in a disordered solid is irregular and contains a distribution of depths and barrier heights. The ions' interaction with the dynamic atomic lattice network is fundamental: first, because the lattice supplies a persistent disordered potential energy landscape for the mobile anions and second, because the local fluctuations of the lattice atoms promote anionic jumps. Additional multi-particle behavior stems from the interaction among the mobile ions and vacancies. All these distinct coupled interactions contribute to the complete theoretical description of ionic conductivity in amorphous solids (Dyre et al., 2009; Lammert et al., 2010). A complete analytical microscopic theory is not available by now and, due to the complexity of the problem, would be extremely difficult to formulate without some basic understanding at the atomistic level. The direct approach to ionic conduction in the YSZ electrolyte of the SOFC is via molecular dynamics (MD) simulations. From the time-evolved atomic trajectories detailed microscopic information about the underlying mechanisms is available. Understanding them would make theoretical prediction possible.
