Polymer glass transition occurs at the marginal rigidity point with connectivity z*=4

TL;DR

This paper demonstrates that the polymer glass transition occurs at a critical connectivity of z*=4, where the system's rigidity and arrested dynamics emerge, confirmed through simulations distinguishing liquid and glassy states.

Contribution

The study identifies the marginal rigidity point at z*=4 as the key criterion for polymer glass transition, combining theoretical analysis with Brownian dynamics simulations.

Findings

Polymer systems become solid when average contacts per monomer exceed 4.

Simulations show a clear shape and dynamics difference at the z*=4 threshold.

The criterion effectively distinguishes liquid from glassy polymer states.

Abstract

We re-examine the physical origin of the polymer glass transition from the point of view of marginal rigidity, which is achieved above a certain number of intermolecular contacts. In the case of polymer chains in a melt / poor solvent, each monomer has two neighbors bound by covalent bonds and also a number of central-force contacts modelled by the Lennard-Jones (LJ) potential. We find that when the average number of contacts per monomer (covalent and non-covalent) exceeds the critical value z*=4, the system becomes solid and the dynamics arrested - a state that we declare the glass. Coarse-grained Brownian dynamics simulations show that at sufficient strength of LJ attraction (which effectively represents the depth of quenching, or the quality of solvent) the polymer globule indeed crosses the threshold of z*=4, and does become a glass. We verify this by showing the distinction between the `liquid' polymer droplet at z<z*, which changes shape and adopts the spherical conformation in equilibrium, and the `glassy' droplet at z>z*, which retains its shape frozen at the moment of z* crossover. These results provide a robust working criterion to tell the liquid apart from the glass for the linear polymers.