Landau theory of ferroelectric transition in long cylindrical nanoparticles

Using a phenomenological Landau theory, the size dependence on ferroelectric transition for free-standing long cylindrical nanoparticles is discussed. We derive the size dependence of the transition temperature, polarization profile as well as the static susceptibility. The transition temperature vanishes below a critical size where the static susceptibility shows divergence obeying Curie-Weiss law. In order to make this result compared with experiments, the average polarization and the susceptibility is computed with a Gaussian particle size distribution. The average polarization in such a case shows smearing with respect to the particle size whereas the divergence in the susceptibilty gets rounded. This might correspond to a size dependent soft mode which can be observed in Raman measurement