We investigate the effect of chain topology on conformation and adsorption transition on an attractive surface of a ring polymer in a dilute solution in a good solvent. Based on Flory theory, we find that the ratio of the mean squared radii of gyration of a ring polymer and a linear chain of identical length is 0.574, which is in good agreement with the results from renormalization theory, previous simulations and experiments. Using three-dimensional Langevin dynamics simulations, we examine the adsorption transition of a flexible ring polymer chain with one bead grafted to a flat solid surface and the conformation of the adsorbed chain. Compared with the linear chain, the ring polymer has the same critical adsorption point (CAP). At the CAP, the crossover exponent of the number of adsorbed beads with chain length is about 0.50 for both ring and linear chains. At the CAP, ring polymers are adsorbed on the surface more than linear chains, which agrees with experiments. In addition, we further observe that, compared with linear chains, the adsorption of ring polymers is faster. Under strong attractions, we observe that the exponent of the adsorption time as a function of the chain length is 1 + v3D, where v3D = 0.588 is the Flory exponent in three dimensions.

Using 3-dimensional Langevin dynamics simulations, we investigated the dynamics of loop formation of chains with excluded volume interactions, and the stability of the formed loop. The mean looping time τl scales with chain length N and corresponding scaling exponent α increases linearly with the capture radius scaled by the Kuhn length a/l due to the effect of finite chain length. We also showed that the probability density function of the looping time is well fitted by a single exponential. Finally, we found that the mean unlooping time τu hardly depends on chain length N for a given a/l and that the stability of a formed loop is enhanced with increasing a/l.

Using Langevin dynamics simulations, we investigate the dynamics of the translocation of a flexible polymer into a confined area under a driving force through a nanopore. We choose an ellipsoidal shape for the confinement and consider the dependence of the asymmetry of the ellipsoid measured by the aspect ratio on the translocation time. Compared with an isotropic confinement (sphere), an anisotropic confinement (ellipsoid) with the same volume slows down the translocation, and the translocation time increases with increasing the aspect ratio of the ellipsoid. We further find that it takes different lengths of time for polymer translocation into the same ellipsoid through the major axis and minor axis directions, depending on the average density of the whole chain in the ellipsoid, ϕ. For ϕ lower than a critical value ϕc, the translocation through the minor axis is faster, and vice versa. These complicated behaviors are interpreted by the degree of the confinement and the anisotropic confinement induced folding of the translocated chain.

We investigate the ejection dynamics of a ring polymer out of a cylindrical nanochannel using both theoretical analysis and three dimensional Langevin dynamics simulations. The ejection dynamics for ring polymers show two regimes, like for linear polymers, depending on the relative length of the chain compared with the channel. For long chains with length N larger than the critical chain length Nc, at which point the chain just fully occupies the nanochannel, the ejection for ring polymers is faster compared to linear chains of identical length due to a larger entropic pulling force; while for short chains (N < Nc), it takes a longer time for ring polymers to eject out of the channel due to a longer diffusion distance to reach the exit of the channel before experiencing the entropic pulling force. These results can help us to understand many biological processes, such as bacterial chromosome segregation.

Using analytical techniques and Langevin dynamics simulations, we investigate the dynamics of polymer translocation through a nanochannel embedded in two dimensions under an applied external field. We examine the translocation time for various ratio of the channel length L to the polymer length N. For short channels L ≪ N, the translocation time τ ∼ N1+ν under weak driving force F, while τ ∼ F−1L for long channels L ≫ N, independent of the chain length N. Moreover, we observe a minimum of translocation time as a function of L/N for different driving forces and channel widths. These results are interpreted by the waiting time of a single segment.

Using Langevin dynamics simulations, we investigate the dynamics of chaperone-assisted translocation of a flexible polymer through a nanopore. We find that increasing the binding energy ε between the chaperone and the chain and the chaperone concentration Nc can greatly improve the translocation probability. Particularly, with increasing the chaperone concentration a maximum translocation probability is observed for weak binding. For a fixed chaperone concentration, the histogram of translocation time τ has a transition from a long-tailed distribution to a Gaussian distribution with increasing ε. τ rapidly decreases and then almost saturates with increasing binding energy for a short chain; however, it has a minimum for longer chains at a lower chaperone concentration. We also show that τ has a minimum as a function of the chaperone concentration. For different ε, a nonuniversal dependence of τ on the chain length N is also observed. These results can be interpreted by characteristic entropic effects for flexible polymers induced by either the crowding effect from a high chaperone concentration or the intersegmental binding for the high binding energy.