Identification of a polymer growth process with an equilibrium multi-critical collapse phase transition: the meeting point of swollen, collapsed and crystalline polymers

Abstract

We have investigated a polymer growth process on the triangular lattice where the configurations produced are self-avoiding trails. We show that the scaling behaviour of this process is similar to the analogous process on the square lattice. However, while the square lattice process maps to the collapse transition of the canonical interacting self-avoiding trail model (ISAT) on that lattice, the process on the triangular lattice model does not map to the canonical equilibrium model. On the other hand, we show that the collapse transition of the canonical ISAT model on the triangular lattice behaves in a way reminiscent of the $\theta$-point of the interacting self-avoiding walk model (ISAW), which is the standard model of polymer collapse. This implies an unusual lattice dependency of the ISAT collapse transition in two dimensions. By studying an extended ISAT model, we demonstrate that the growth process maps to a multi-critical point in a larger parameter space. In this extended parameter space the collapse phase transition may be either $\theta$-point-like (second-order) or first-order, and these two are separated by a multi-critical point. It is this multi-critical point to which the growth process maps. Furthermore, we provide evidence that in addition to the high-temperature gas-like swollen polymer phase (coil) and the low-temperature liquid drop-like collapse phase (globule) there is also a maximally dense crystal-like phase (crystal) at low temperatures dependent on the parameter values. The multi-critical point is the meeting point of these three phases. Our hypothesised phase diagram resolves the mystery of the seemingly differing behaviours of the ISAW and ISAT models in two dimensions as well as the behaviour of the trail growth process.

References in corpus (4)

• Phase Transitions of Single Semi-stiff Polymer Chains
• Collapse transition of self-avoiding trails on the square lattice
• Semi-flexible hydrogen-bonded and non-hydrogen bonded lattice polymers
• Universality of collapsing two-dimensional self-avoiding trails

Cited by in corpus (13)

• Loop models with crossings
• Weighting of topologically different interactions in a model of two-dimensional polymer collapse
• Generalised interacting self-avoiding trails on the square lattice: phase diagram and critical behaviour
• Self-avoiding trails with nearest neighbour interactions on the square lattice
• Nature of the collapse transition in interacting self-avoiding trails
• Anomalous critical behaviour in the polymer collapse transition of three-dimensional lattice trails
• Semi-flexible interacting self-avoiding trails on the square lattice
• Polymer collapse of a self-avoiding trail model on a two-dimensional inhomogeneous lattice
• Solution of semi-flexible self-avoiding trails on a Husimi lattice built with squares
• Lattice polymers with two competing collapse interactions
• Adsorption of 2d polymers with two- and three-body self-interactions
• The role of three-body interactions in two-dimensional polymer collapse
• Anomalous polymer collapse winding angle distributions