Conformational properties of strictly two-dimensional equilibrium polymers

TL;DR

This study uses Monte Carlo simulations to analyze the conformational properties of two-dimensional equilibrium polymers, revealing universal scaling behaviors, polydispersity characteristics, and fractal perimeter dimensions.

Contribution

It demonstrates that polydisperse equilibrium polymers share universal exponents with monodisperse ones and characterizes their size distribution and scattering properties.

Findings

Polydisperse equilibrium polymers have the same universal exponents as monodisperse polymers.

The average chain length increases exponentially with scission energy and surface fraction.

The form factor exhibits generalized Porod scattering indicating a fractal perimeter.

Abstract

Two-dimensional monodisperse linear polymer chains are known to adopt for sufficiently large chain lengths $N$ and surface fractions $\phi$ compact configurations with fractal perimeters. We show here by means of Monte Carlo simulations of reversibly connected hard disks (without branching, ring formation and chain intersection) that polydisperse self-assembled equilibrium polymers with a finite scission energy $E$ are characterized by the same universal exponents as their monodisperse peers. Consistently with a Flory-Huggins mean-field approximation, the polydispersity is characterized by a Schulz-Zimm distribution with a susceptibility exponent $\gamma=19/16$ for all not dilute systems and the average chain length $<N> \propto \exp(\delta E) \phi^{\alpha}$ thus increases with an exponent $\delta = 16/35$. Moreover, it is shown that $\alpha=3/5$ for semidilute solutions and $\alpha \approx 1$ for larger densities. The intermolecular form factor $F(q)$ reveals for sufficiently large $<N>$ a generalized Porod scattering with $F(q) \propto 1/q^{11/4}$ for intermediate wavenumbers $q$ consistently with a fractal perimeter dimension $d_s=5/4$.