2025/07/01 by Wittmer, J. P., Cavallo, A., Johner, A.
#FOS: Physical sciences #Soft Condensed Matter (cond-mat.soft) #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.2507.00649
Two-dimensional monodisperse linear polymer chains are known to adopt for sufficiently large chain lengths N and surface fractions ϕ 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 γ=19/16 for all not dilute systems and the average chain length ∝ exp(δE) ϕα thus increases with an exponent δ= 16/35. Moreover, it is shown that α=3/5 for semidilute solutions and α≈ 1 for larger densities. The intermolecular form factor F(q) reveals for sufficiently large a generalized Porod scattering with F(q) ∝ 1/q11/4 for intermediate wavenumbers q consistently with a fractal perimeter dimension ds=5/4.