Phase transition kinetics in lattice models of intercalation compounds

► Differential-difference equation for concentration evolution is formulated. ► Phase transition kinetics is studied in quasichemical and diagram approximations. ► Uphill diffusion and number of particle conservation lead to nanostructuring. ► Wave-like spreading of nanostructuring in lattice fluids is observed. ► Phase transition front velocity during deintercalation is not constant.