  Using mathematical model for intercalation dynamics in phase-separating
materials proposed in (Singh, G. K.; Ceder, G.; Bazant, M. Z. Electrochimica
Acta 2008, 53, 7599) and developed further in (Burch, D.; Bazant, M. Z. Nano
Letters 2009, 9, 3795) we found that the spinodal gap generally shrinks as the
particle size decreases. We also got that for some range of boundary reaction
rate parameter and particle size the concentration spinodal gap is not
continuous but it has stable "islands" where no spinodal decomposition is
expected. In fact the presence of infinitesimally small boundary reaction rate
parameter will destabilize nano particle even for infinitesimal length of
particle. But then further continuous raise of this parameter will stabilize
the system till some limit. We made careful analysis to study the dependence of
spinodal decomposition on boundary reaction rate and size parameters which can
be used for LiFePO4 battery material application. Our model predicted that for
nanoparticles having size less than diffusion length and enough small boundary
reaction rate spontanious charge or discharge will occur.
