Dynamics And Conformations Of Confined Ring Polymer

DNA is under confinement in the nucleus. A typical physical model to describe this phenomenon is DNA confined in a nanotube. Related studies deepen our understanding of the conformational properties of macromoleclues, and also reveal the potential to realize DNA separation, detection and even sequencing in experiments. Ring polymer is an important topology of macromolecules. Investigations of confined ring polymers are not only meaningful to understand the biological processes, bur also provide a new direction for the development of theory about polymers under confinement. In this dissertation, we study the conformational properties and the dynamic behaviors of ring polymers under a nanotube and adsorbed on a plane.First, we study the conformational properties of ring chains confined in a cylindrical nanotube by theoretical analysis and Langevin dynamics simulations, and make a comparison with the linear counterparts. The scaling relationships of the occupied length in nanotube with the diameter of the nanotube D and the chain length N of ring polymers obtained from the scaling theory, the blob theory and the Flory theory are the same as that of linear polymers. Theoretical derivations based on the blob theory assume that a ring chain confined in the nanotube consist of two blob strings with the blob size being half the diameter of the nanotube. Geometric analysis shows that the chain is the most stable as a helical structure between the two blob strings is formed. Then it gets that the ratio of the occupied length in the nanotube of ring chains and linear chains R‖r/R‖,l is0.575. Flory theory also shows that the ratio R‖r/R‖,l is0.630. These two ratios are very close to that obtained from our simulations0.584. It implies that at a same diameter the nanotube, a ring chain has a higher elongation to16.8%than a linear chain, which has been confirmed by other experiments and our simulations. With increasing the chain rigidity, R‖r/R‖,l gets smaller and approaches to1/2at large chain rigidities. There is a transition regime of confined polymers between the de Gennes regime and the Odijk regime. For ring chains the transition regime is less obvious.We then investigate the dynamics of a ring chain ejection from the nanotube. When the chain length N is larger than the critical length N*, the ejection is purely a entropy driven process.Due to the smaller blob size of a ring chain confined in the nanotube, its ejection is faster than a linear chain. However, as N<N*, the chain must diffuse to the nanotube exit at first and then the entropic force drives the ejection process. It indicates that compared with a linear chain, a ring chain need diffuse a longer distance to get the nanotube exit. The diffusion is much slower than the entropy driven ejection so that the total ejection time of a ring chain is longer that of a linear one.Finally, we investigate the adsorption of ring chains with one segment fixed at the attractive plane by3-dimensional Langevin dynamics simulations, and make a comparison with the linear counterparts. The critical adsorption point (CAP) of a ring chain is the same as that of a linear chain. Namely, the critical attractive strength under the thermodynamic limit is εc(Nâ†'∞)=0.30. The scaling relationship of the number of adsorbed segments with the chain length at the CAP is identical for a ring chain and a linear chain. The scaling exponent is0.50. The number of adsorbed segments of a ring chain is always larger than that of a linear chain with a ratio1.25-1.30. For weak attraction, the number of adsorbed segments of a ring chain is larger than a linear chain with the same chain length. The number is identical for strong attraction. For strong adsorption, the number of adsorbed monomers scales with the time as n(t)～tNβ with the scaling exponent β=0.62. Thus, the scaling relationship of the adsorption time with chain length is τ～N1/β with the scaling exponent1/β being quite close to1.56and1.57obtained from our simulations for ring and linear chains, respectively. These values are in good line with the theoretical prediction1+v3d=1.588. The adsorption of ring polymers follows the zipping mechanism. However, the adsorption process is much more complex. The stem-flower model describing the adsorption of a linear chain is not adoptable for the ring chain. A ring polymer has only loops and trains in its adsorbed conformation. We find that the loop size is comparable to the chain length at first and then gets smaller before the disappear of the loop. The adsorbed ring chains are always more compact than linear chains and being close to sphere, which are reflected from the form factor and intersections for the chain conformations projected onto the attractive plane.