Structure and Dynamics of Dilute Two-Dimensional Ring Polymer Solutions

Abstract

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 (Nin) of such solvent molecules inside the 2D ring polymers. The mean-squared radius of gyration (R 2 ) increases with Nin and scales as R ~ N ν with the scaling exponent ν that depends on Nin. When Nin is large enough, ν ≈ 1, which is consistent with experiments. Meanwhile, for a small Nin ≈ 0.66 and the 2D ring polymers show unexpected structure. The diffusion coefficient (D) and the rotational relaxation time (τrot) are also sensitive to Nin: 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 (τrot) are not-size dependent. More interestingly, the scaling behavior of τrot also changes with Nin; for a large Nin τrot ~ N 2.46 but for a small Nin τrot ~ N 1.43 .

Dynamic Properties of Linear and Cyclic Chains in Two Dimensions. Computer Simulation Studies

“…Recent computer simulations of a similar model founded this exponent located between 1.30 and 1.04 for similar model of rings of longer (consisting of up to N = 512 segments) at the polymer concentration φ = 0.05 and 1.0 respectively . Discontinuous molecular dynamics of two-dimensional rings with solvent molecules (at low solvent concentration φ = 0.16) showed that the exponent 2ν changes from 2.0148 (the maximum possible number of solvent molecules inside the chain contour) to 1.330 (no solvent molecules inside the chain contour); the latter value is quite close to our findings. It is worth mentioning that experiments on single circular DNA adsorbed on mica also founded the exponent 2 v = 1.5 …”

“…These macromolecules can now be precisely synthesized and characterized. − The structure of cyclic chains and their dynamics properties were the subjects of numerous experimental, − theoretical, − and simulation studies − although the discussion about their properties is not closed yet. The two-dimensional polymer systems containing cyclic macromolecules were also a subject of experiments − and theoretical considerations. , Computer simulations of strictly two-dimensional cyclic macromolecules and of strongly adsorbed three-dimensional rings were not so numerous. ,− They mainly showed that the adsorption of rings is considerably higher than that of linear and star-branched chains. The mobility of rings confined to a thin film was found to slow down during the annealing (or when the strength of the adsorption increases) and they were always slower than linear chains. , …”

Circular Kardar-Parisi-Zhang equation as an inflating, self-avoiding ring polymer

“…In general, the conformation and dynamics of circular polymers is still a subject of considerable interest [36]. Current experimental capabilities reach even down to single molecule experiments [1], so that one might speculate on the possibility to observe a dynamical transition of the type elucidated here in appropriate non-equilibrium, 2D constrained settings [37].…”