Cluster phases of penetrable rods on a line

TL;DR

This paper investigates the phase behavior of one-dimensional penetrable rods modeled by the GEM4 potential, revealing a sequence of cluster fluid phases with critical points and slow nucleation dynamics, challenging traditional expectations for 1D systems.

Contribution

It reconstructs the phase diagram of the 1D GEM4 system, identifying cluster fluid phases and their critical points, which is novel for one-dimensional penetrable particle models.

Findings

Sequence of cluster fluid phases with increasing pressure.

Critical points at the coexistence lines between phases.

Slow growth of the 2-cluster phase from metastable fluid.

Abstract

Phase transitions are uncommon among homogenous one-dimensional fluids of classical particles owing to a general non-existence result due to van Hove. A way to circumvent van Hove's theorem is to consider an interparticle potential that is finite everywhere. Of this type is the generalized exponential model of index 4 (GEM4 potential), a model interaction which in three dimensions provides an accurate description of the effective pair repulsion between dissolved soft macromolecules (e.g., flexible dendrimers). Using specialized free-energy methods, I reconstruct the equilibrium phase diagram of the one-dimensional GEM4 system, showing that, apart from the usual fluid phase at low densities, it consists of an endless sequence of {\em cluster fluid phases} of increasing pressure, having a sharp crystal appearance for low temperatures. The coexistence line between successive phases in the sequence invariably terminates at a critical point. Focussing on the first of such transitions, I show that the growth of the 2-cluster phase from the metastable ordinary fluid is extremely slow, even for large supersaturations. Finally, I clarify the apparent paradox of the observation of an activation barrier to nucleation in a system where, due to the dimensionality of the hosting space, the critical radius is expected to vanish.