Conformational properties of strictly two-dimensional equilibrium polymers
Résumé
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 ⟨N ⟩ ∝ 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 ⟨N ⟩ a generalized Porod scattering with F (q) ∝ 1/q11/4 for intermediate wavenumbers q consistently with a fractal perimeter dimension ds = 5/4.
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