Cluster phases of penetrable rods on a line

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.

arXiv comment24 pages, 17 figures

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Cited by in corpus (10)

• Hexatic phase and cluster crystals of two-dimensional GEM4 spheres
• Ground state of weakly repulsive soft-core bosons on a sphere
• Freezing of soft-core bosons at zero temperature: A variational theory
• Quantum Critical Behavior of One-Dimensional Soft Bosons in the Continuum
• Probing the existence of phase transitions in one-dimensional fluids of penetrable particles
• Clusterization of weakly-interacting bosons in one dimension: an analytic study at zero temperature
• Soft-particle lattice-gas in 1d: one- and two-component cases
• Emergence of an Ising critical regime in the clustering of 1D soft matter revealed through string variables
• Static density response of one-dimensional soft bosons across the clustering transition
• Evolution of static and dynamical density correlations in a one-dimensional soft-core gas from the Tonks-Girardeau limit to a clustering fluid