Interchain Monomer Contact Probability in Two-Dimensional Polymer Solutions

Using molecular dynamics simulations of a standard bead–spring model, we investigate the density crossover scaling of strictly two-dimensional (d = 2) self-avoiding polymer chains without chain crossings focusing on properties related to the contact exponent θ2 set by the intrachain subchain size distribution. With R ∼ Nν being the size of chains of length N, the number nint of interchain monomer contacts per monomer is found to scale as nint ∼ 1/Nνθ2 with ν = 3/4 and θ2 = 19/12 for dilute solutions and ν = 1/d and θ2 = 3/4 for N ≫ g(ρ) ≈ 1/ρ2. Irrespective of the density ρ, sufficiently long chains are thus found to consist of compact packings of blobs of fractal perimeter dimension dp = d – θ2 = 5/4. In agreement with the generalized Porod scattering of compact objects with fractal contour, the Kratky representation of the intramolecular form factor F(q) reveals a strong nonmonotonous behavior approaching with increasing density a limiting power-law slope F(q)qd/ρ ≈ 1/(qR)θ2 in the intermediate regime o...