Identification of a polymer growth process with an equilibrium multicritical 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 behavior 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 (ISAT) model 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 θ point of the interacting self-avoiding walk (ISAW) model, 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 multicritical point in a larger parameter space. In this extended parameter space the collapse phase transition may be either θ-point-like (second order) or first order, and these two are separated by a multicritical point. It is this multicritical point to which the growth process maps. Furthermore, we provide evidence that in addition to the high-temperature gaslike 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 multicritical point is the meeting point of these three phases. Our hypothesized phase diagram resolves the mystery of the seemingly differing behaviors of the ISAW and ISAT models in two dimensions as well as the behavior of the trail growth process.

Anomalous critical behavior in the polymer collapse transition of three-dimensional lattice trails

“…Interestingly, all these models k = 1,2,3 have been seen [14] to behave in the same way on the triangular lattice and, as we shall see, seem to behave in the same way on the simple cubic lattice (though the two-and three-dimensional models differ from each other in behavior).…”

“…The equivalent static model is an eISAT with a particular value of k = k G 4.15 at one particular temperature T = T G . It was demonstrated [14] that this value of k = k G separates models where the collapse transition is first order (k > k G ) from models where the collapse transition is second order (k < k G ). It was shown that for k < k G the second-order transition was most likely in a single universality class, which was the same as the one in the (two-dimensional) ISAW θ -point collapse transition.…”

Lattice polymers with two competing collapse interactions

“…Again, this is quite different to the exponent ν = 4/7 for the ISAW. Another important difference that has been recently observed [29,30] is that the low temperature phase is maximally dense. On the square lattice this implies that if one considers the proportion of the sites on the trail that are at lattice sites which are not doubly occupied via…”

Polymer collapse of a self-avoiding trail model on a two-dimensional inhomogeneous lattice

“…By considering the trails on the triangular lattice we can assign different energies to doubly-or triply-visited sites, which induces another collapsed phase in two dimensions. The homogeneous lattice case of this model has been studied previously [20], showing that the collapse transition to the globule phase is θ-like and the other collapsed phase is characterised by maximally dense configurations whose interior is dominated by triply-visited sites. The important difference to the third phase of the semi-stiff ISAW model is that this maximally dense phase is not ordered in a real crystalline sense as so may behave differently to the introduction of disorder.…”