The branched polymer growth model revisited

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.

Errors and Error Tolerance in Irreversible Multistep Growth of Nanostructures

“…While a large number of models have been offered to describe single-step (or one-pot) growth processes such as crystallization, polymerization, and self-assembly, ,− we are unaware of any simple model that generally describes irreversible stepwise growth of discrete structures. The model we propose does not purport to accurately describe the molecular behavior of a specific system but rather aims to capture the general features of irreversible stepwise growth and synthesis processes, similar to the way in which some of the self-assembly, crystallization, and polymerization models capture the basic features of such growth processes. ,− The model focuses on the growth of a single structure in each simulation, where growth is performed by binding monomers to specific sites on the face of a structure (Figure , panel C). In each growth step a different type of monomers is added and bound to the structure.…”