Phase Transition with Non-Thermodynamic States in Reversible Polymerization

TL;DR

This paper explores a reversible polymerization process that exhibits a nonequilibrium phase transition, with distinct steady states characterized by different polymer length distributions and growth behaviors depending on fragmentation strength.

Contribution

It reveals a novel nonequilibrium phase transition in a reversible polymerization system, showing how steady states change with fragmentation rate and identifying non-thermodynamic states.

Findings

Above critical fragmentation, steady state with exponential tail and linear polymer number.

Below critical fragmentation, non-thermodynamic steady state with algebraic tail.

Characteristic exponent of length distribution varies continuously with fragmentation rate.

Abstract

We investigate a reversible polymerization process in which individual polymers aggregate and fragment at a rate proportional to their molecular weight. We find a nonequilibrium phase transition despite the fact that the dynamics are perfectly reversible. When the strength of the fragmentation process exceeds a critical threshold, the system reaches a thermodynamic steady state where the total number of polymers is proportional to the system size. The polymer length distribution has a sharp exponential tail in this case. When the strength of the fragmentation process falls below the critical threshold, the steady state becomes non-thermodynamic as the total number of polymers grows sub-linearly with the system size. Moreover, the length distribution has an algebraic tail and the characteristic exponent varies continuously with the fragmentation rate.