Structure and dynamics of dilute two-dimensional ring polymer solutions

Structure and Dynamics of dilute two-dimensional (2D) ring polymer solutions are investigated by using discontinuous molecular dynamics simulations. A ring polymer and solvent molecules are modeled as a tangent-hard disc chain and hard discs, respectively. Some of solvent molecules are confined inside the 2D ring polymer unlike in 2D linear polymer solutions or three-dimensional polymer solutions. The structure and the dynamics of the 2D ring polymers change significantly with the number (N _in) of such solvent molecules inside the 2D ring polymers. The mean-squared radius of gyration (R ²) increases with N _in and scales as R ∼ N ^v with the scaling exponent v that depends on N _in. When N _in is large enough, v ≈ 1, which is consistent with experiments. Meanwhile, for a small Ni _n ≈ 0.66 and the 2D ring polymers show unexpected structure. The diffusion coefficient (D) and the rotational relaxation time (x _rot) are also sensitive to Ni _n: D decreases and τ increases sharply with Nin. D of 2D ring polymers shows a strong size-dependency, i.e., D ∼ ln(L), where L is the simulation cell dimension. But the rotational diffusion and its relaxation time (τ _rot) are not-size dependent. More interestingly, the scaling behavior of τ _rot also changes with N _in; for a large Ni _n τ _rot ∼ N ^2.46 but for a small N _in τ _rot ∼ N ^1.43.