Mechanical unfolding of directed polymers in a poor solvent: novel critical exponents

TL;DR

This paper analyzes a solvable model of directed polymers in a poor solvent under force, revealing a second-order unfolding transition with novel critical exponents close to 2/3.

Contribution

It provides an exact solution for the critical force and introduces new critical exponents characterizing the phase transition.

Findings

Critical force depends on temperature below the $ heta$-transition.

Transition is second order with unique critical exponents.

Critical exponents $ u$ and $ ilde{ u}$ are approximately 2/3.

Abstract

We study the thermodynamics of an exactly solvable model of a self-interacting partially directed self-avoiding walk (DSAW) in two dimensions, when a force is applied on one end of the chain. The critical force for the unfolding is determined exactly, as a function of the temperature, below the $\Theta$-transition. The transition is second order and characterized by new critical exponents which are determined by a careful numerical analysis. The usual polymer critical index $\nu$ on the critical line, and another one, which we call $\zeta$, take a non-trivial value which is numerically close to 2/3.