Monte Carlo simulation of a single ring among linear chains: Structural and dynamic heterogeneity

Abstract

We perform lattice Monte Carlo simulation using the bond-fluctuation model to examine the conformation and dynamic properties of a single small flexible ring polymer in the matrix of linear chains as functions of the degree of polymerization of the linear chains. The average conformation properties as gauged by the mean-square radius of gyration and asphericity parameter are insensitive to the chain length for all the chain lengths examined ͑30, 100, 300, and 1000͒. However, in the longer chain ͑300 and 1000͒ samples, there is an increased spread in the distribution of the value of these quantities, suggesting structural heterogeneity. The center-of-mass diffusion of the ring shows a rapid decrease with increasing chain length followed by a more gradual change for the two longer chain systems. In these longer chain systems, a wide spread in the value of the apparent self-diffusion coefficient is also observed, as well as qualitatively different square displacement trajectories among the different samples, suggesting heterogeneity in the dynamics. A primitive path analysis reveals that in these long chain systems, the ring can exist in topologically distinct states with respect to threading by the linear chains. Threading by the linear chain can dramatically slow down and in some cases stall the diffusive motion of the ring. We argue that the life times for these topological conformers can be longer than the disentanglement time of the linear chain matrix, so that the ring exhibits nonergodic behavior on time scales less or comparable to the life time of these conformers. Our results suggest a picture of the ring diffusion as one where the diffusion path consists of distinctive segments, each corresponding to a different conformer, with slow interconversion between the different conformers.

A Study of the Morphology, Dynamics, and Folding Pathways of Ring Polymers with Supramolecular Topological Constraints Using Molecular Simulation and Nonlinear Manifold Learning

“…21,22 Yang et al studied the diffusion of 30-ring polymer in a matrix of linear chains using Monte Carlo simulation, where they find that the threading of a linear polymer into the ring would significantly slows the diffusion of the ring. 20 Recent molecular dynamics simulation study by Jung and co-workers also show that the threading between the rings can underlie the slowing down in diffusivity as ring size increases.…”

“…4 Synthetic ring polymers are useful components in the engineering of artificial micro-devices and molecular machines, such as catenane nanoswitches made up of two interlocked ring polymers. [5][6][7][8][9][10][11] Due to the absence of free ends, the topology of ring polymers gives rise to significant structural and dynamic differences compared to their linear counterparts, and the structure and rheological properties of ring polymers have been subject to extensive theoretical, [12][13][14][15] experimental, [16][17][18] and simulation [19][20][21][22] investigations.…”

Density functional theory for inhomogeneous ring polymeric fluids

“…However, it is fairly difficult to ensure the concatenation or nonconcatenation of two different rings. Here, both CBMC simulations and DFT calculations ignore these topological constraints such as "concatenation," "chain crossing," or "no chain crossing" [9]. After equilibrating the system, we calculated the ensemble averages for the density distribution of the beads.…”

“…Roovers and Tanaka observed a depression of the Flory theta temperature by 6 • C in the ring polymer solutions, compared to chain ones [7,8]. Moreover, rings cannot "reptate" like linear chain molecules or "retract" like branched polymers [9]. Owing to the unique topology, the microstructure and thermodynamic properties of ring polymers have attracted much attention in the last few decades.…”

“…They found that the rings exhibit several different threaded states, and each state corresponds to a distinct diffusion mechanism [9]. Halverson et al carried out a molecular dynamics simulation on the statics and dynamics properties of nonconcatenated ring polymers in a melt.…”