Spinodal Gap Dependence on Size and Boundary Reaction Rate for Intercalation in Nanoparticles

TL;DR

This study models how nanoparticle size and boundary reaction rates influence spinodal decomposition, revealing size-dependent stability and potential for spontaneous charge/discharge in battery materials.

Contribution

It provides a detailed analysis of spinodal gap dependence on size and boundary reaction rate, including the discovery of stable 'islands' where decomposition is suppressed.

Findings

Spinodal gap shrinks with decreasing particle size.

Existence of stable 'islands' where no spinodal decomposition occurs.

Nanoparticles smaller than diffusion length with low boundary reaction rates can spontaneously charge or discharge.

Abstract

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.