Structural Transition Models for a class of Irreversible Aggregates

TL;DR

This paper reviews two theoretical models that explain the structural transition in irreversible fractal aggregates, highlighting how growth velocity minima relate to changes in fractal dimension and the influence of environmental factors.

Contribution

Introduces and compares two novel theoretical approaches using Poisson and Biharmonic equations to model structural transitions in fractal aggregates.

Findings

Transition correlates with minimum growth velocity.

Structural transition involves a decrease in fractal dimension.

Environmental effects influence aggregate structure.

Abstract

A progress report on two recent theoretical approaches proposed to understand the physics of irreversible fractal aggregates showing up a structural transition from a rather dense to a more multibranched growth is presented. In the first approach the transition is understood by solving the Poisson equation on a squared lattice. The second approach is based on the discretization of the Biharmonic equation. Within these models the transition appears when the growth velocity at the fractal surface presents a minimum. The effects of the surrounding medium and geometrical constraints for the seed particles are considered. By using the optical diffraction method, the structural transition is further characterized by a decrease in the fractal dimension for this peculiar class of aggregates.