From particle condensation to polymer aggregation

Abstract

We draw an analogy between droplet formation in dilute particle and polymer systems. Our arguments are based on finite-size scaling results from studies of a two-dimensional lattice gas to three-dimensional bead-spring polymers. To set the results in perspective, we compare with in part rigorous theoretical scaling laws for canonical condensation in a supersaturated gas at fixed temperature, and derive corresponding scaling predictions for an undercooled gas at fixed density. The latter allows one to efficiently employ parallel multicanonical simulations and to reach previously not accessible scaling regimes. While the asymptotic scaling can not be observed for the comparably small polymer system sizes, they demonstrate an intermediate scaling regime also observable for particle condensation. Altogether, our extensive results from computer simulations provide clear evidence for the close analogy between particle condensation and polymer aggregation in dilute systems.

Microcanonical characterization of first-order phase transitions in a generalized model for aggregation

“…Refs. 33,[56][57][58][59]62,63,67 ), but also on the recently developed kinetic approaches which use the microcanonical entropies to estimate temperature-dependent rate constants 60,61 .…”

“…Although this model was introduced in the 70s, it has gained renewed interest due to its non-additive properties caused by its longe-range interactions 54,55 . Another important feature of such model is that it displays an aggregation transition that is independent of the shape of the forming aggregate, so that it is an appealing candidate to describe (at least qualitatively) the microcanonical properties of the aggregation transitions observed, for instance, in disordered systems under confinement [56][57][58] .…”