Analysis of the dependence of spinodal decomposition in nanoparticles on boundary reaction rate and free energy of mixing

The mathematical model for intercalation dynamics in phase-separating materials (Singh et al., 2008) is a powerful tool for the investigation of the spinodal decomposition in nanoparticles. By means of this model, we conduct a careful mathematical analysis of the intercalation dynamics in nanoparticles to study the dependence of spinodal gap on the boundary reaction rate and the particle size, which can be used for LiFePO 4 battery material application. Consistent with previous investigations, we found that for some range of the boundary reaction rate and the particle size the concentration spinodal gap is not continuous, but it has stable “islands” where no spinodal decomposition is expected. The new important observation is that the presence of an infinitesimally small boundary reaction rate will destabilize nanoparticles even for infinitesimal length. In particular for nanoparticles having the size of order or less than interphase width λ , the spontaneous charge or discharge will occur at the reaction rate of order 0.1 D / λ . The further raise of the intercalation rate will stabilize the system until some size limit of order two diffusion length. The intercalation effects are proven by means of numerical simulations. We also show that the increasing enthalpy of the spinodal mixture as well as increasing elastic energy due to the lattice misfit can destabilize the particles and increase the spinodal gap.