Modeling and evaluation of sintered microstructure and its properties for rSOFC fuel electrodes by coarse-grained molecular dynamics

Coarse-grained molecular dynamics modeling and analysis of graded porous electrodes of reversible solid oxide cells sintered in two steps

“…Instead, the interactions between CG particles are considered to predict the physical process. The physical equivalence between the all-atom and coarse-grained systems is modeled by using the constitutive equation as follows: 25 where the overall energy of the coarse-grained system E CG is equivalent to the average energy of the canonical ensemble 〈 H MD 〉 for the constrained all-atom system; x I and u I are the displacement and velocity for the CG particle I , p i and x i are the momentum and displacement of the atom i , Z is the partition function, k B is the Boltzmann constant, and f Ji is the weighting function depending on the aforementioned CG mapping scheme; Δ in eqn (1) is a three dimensional delta function expressed as follows: 1 …”

“…For the CG particles system, E CG in eqn (1) is expressed as follows: 1 where U int = 3( N MD − N CG ) k B T is the equipartition theorem related to thermal energy (here N MD and N CG are the number of atoms and CG particles, respectively); the second and third terms on the right side of eqn (5) are the kinetic and potential energy of the CG system, which is similar to the all-atom system addressed in eqn (3); M IJ is the mass matrix for CG particles expressed as follows: 25 …”

“…The potential term (the last term in eqn (5)) is calculated as follows: 25 which indicates that the potential energy between all-atom and CG particle systems is equivalent.…”

“…However, fitting of the potential function for crystal materials is also hard to implement due to the oscillatory manner and divergences of the RDF for the crystal phase in the numerical iterative method. 28–30 Therefore, a parameterization approach was developed in our previous study, 1,25 for fitting the coarse-grained potential and force field of the crystal materials as addressed in eqn (7). The Born–Mayer–Buckingham potential is commonly used to describe the interactions for LSCM and YSZ materials concerned in this study, which are parameterized as follows: 25 where V IJ is the potential energy for the CG particle in eqn (7); q I and q J are the charges of the CG particles I and J , and ε 0 and ε r are the vacuum and relative permittivity coefficients, respectively, which denote the coulombic potential; the last two terms denote the effects of exclusion ( A and ρ are Pauli exclusion parameters) and attraction ( C IJ is the van der Waals coefficient), respectively.…”

“…More details of the coarse-grained mapping scheme are illustrated in our previous study. 1,25 The physical process of the all-atom system is also coarsegrained to t the CG particles system. Atoms are integrated into CG particles with both mass and charges, and the interactions between atoms inside CG particles are neglected.…”