Phase transitions in fractal clusters in the presence of electric fields

Abstract

It is shown that if the size distribution of the nuclei formed during phase transition is a fractal cluster, then the spatial distribution of the electric field in the cluster is highly inhomogeneous. Electric field is accumulated in small scales, and its strength grows according to the power law from larger scales to smaller scales. When the dielectric permeability of the nuclei is much larger than that of the surrounding medium, the electric field grows as $E\ensuremath{\propto}{3}^{k},$ where k is a number of the nucleus in the fractal cluster with the sizes ${a}_{1}\ensuremath{\gg}{a}_{2}\ensuremath{\gg}{a}_{3}\ensuremath{\gg}\ensuremath{\cdots}\ensuremath{\gg}{a}_{k}.$ We determined the work of formation of the nuclei in the fractal cluster taking into account the change of the configuration of electric field E. It is demonstrated that the formation of fractal clusters leads to the dynamics of a phase transition with bifurcations, whereby the growth of a nucleus causes the formation of the new nuclei.