The Branched Polymer Growth Model Revisited

TL;DR

This paper revisits the Branched Polymer Growth Model, introduces an adapted version (ABPGM) with improved realism, and analyzes its phase diagram showing reentrant behavior in the presence of impurities.

Contribution

The paper proposes a modified version of the BPGM, called ABPGM, which better reflects experimental conditions and preserves monomer functionalities.

Findings

ABPGM retains monomer functionalities and branching probability as input.

The phase diagram of ABPGM shows a reentrant transition.

Critical locus in (b,c) space delineates growth regimes.

Abstract

The Branched Polymer Growth Model (BPGM) has been employed to study the kinetic growth of ramified polymers in the presence of impurities. In this article, the BPGM is revisited on the square lattice and a subtle modification in its dynamics is proposed in order to adapt it to a scenario closer to reality and experimentation. This new version of the model is denominated the Adapted Branched Polymer Growth Model (ABPGM). It is shown that the ABPGM preserves the functionalities of the monomers and so recovers the branching probability b as an input parameter which effectively controls the relative incidence of bifurcations. The critical locus separating infinite from finite growth regimes of the ABPGM is obtained in the (b,c) space (where c is the impurity concentration). Unlike the original model, the phase diagram of the ABPGM exhibits a peculiar reentrance.