Semi-flexible hydrogen-bonded and non-hydrogen bonded lattice polymers

TL;DR

This study explores how adding stiffness affects lattice models of hydrogen-bonded polymers, revealing that the collapse transition remains unchanged and identifying a novel second-order phase transition in two dimensions.

Contribution

It demonstrates that stiffness does not alter the collapse transition in hydrogen-bonded lattice polymers and characterizes a new second-order phase transition in two dimensions.

Findings

Collapse transition unaffected by stiffness.

Disappearance of crystal phase at high bending energies.

Second-order globule-crystal transition in 2D with divergent specific heat.

Abstract

We investigate the addition of stiffness to the lattice model of hydrogen-bonded polymers in two and three dimensions. We find that, in contrast to polymers that interact via a homogeneous short-range interaction, the collapse transition is unchanged by any amount of stiffness: this supports the physical argument that hydrogen bonding already introduces an effective stiffness. Contrary to possible physical arguments, favouring bends in the polymer does not return the model's behaviour to that comparable to the semi-flexible homogeneous interaction model, where the canonical $\theta$-point occurs for a range of parameter values. In fact, for sufficiently large bending energies the crystal phase disappears altogether, and no phase transition of any type occurs. We also compare the order-disorder transition from the globule phase to crystalline phase in the semi-flexible homogeneous interaction model to that for the fully-flexible hybrid model with both hydrogen and non-hydrogen like interactions. We show that these phase transitions are of the same type and are a novel polymer critical phenomena in two dimensions. That is, it is confirmed that in two dimensions this transition is second-order, unlike in three dimensions where it is known to be first order. We also estimate the crossover exponent and show that there is a divergent specific heat, finding $\phi=0.7(1)$ or equivalently $\alpha=0.6(2)$. This is therefore different from the $\theta$ transition, for which $\alpha=-1/3$.