Conformational properties of strictly two-dimensional equilibrium polymers

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 \(\left<N \right>\propto \exp (\delta E) \phi ^{\alpha }\) 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 \(\left<N \right>\) a generalized Porod scattering with \(F(q) \propto 1/q^{11/4}\) for intermediate wavenumbers q consistently with a fractal perimeter dimension \(d_s=5/4\).

Snapshot of a subvolume of a much larger configuration of strictly two-dimensional equilibrium polymers as considered in this study for a broad range of surface fractions and scission energies. Despite the low dimensionality and the strong polydispersity of the annealed chain systems, the same univeral scaling relations and asymptotic exponents as for their monodisperse quenched peers are found as suggested by a simple Flory-Huggins type mean-field approximation. This holds especially for semidilute solutions and dense melts where the chains are demonstrated to adopt compact configurations of a fractal perimeter dimension 5/4. The intermolecular form factor F(q) thus reveals a generalized Porod scattering with \(F(q) \propto 1/q^{11/4}\) for intermediate wavenumbers q Snapshot of a subvolume of a much larger configuration of strictly two-dimensional equilibrium polymers as considered in this study for a broad range of surface fractions and scission energies. Despite the low dimensionality and the strong polydispersity of the annealed chain systems, the same univeral scaling relations and asymptotic exponents as for their monodisperse quenched peers are found as suggested by a simple Flory-Huggins type mean-field approximation. This holds especially for semidilute solutions and dense melts where the chains are demonstrated to adopt compact configurations of a fractal perimeter dimension 5/4. The intermolecular form factor F(q) thus reveals a generalized Porod scattering with \(F(q) \propto 1/q^{11/4}\) for intermediate wavenumbers q