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Published August 14, 2010 | Published
Journal Article Open

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


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 1000). However, in the longer chain (300 and 1000) 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.

Additional Information

© 2010 American Institute of Physics. Received 23 November 2009; accepted 30 June 2010; published online 10 August 2010. This work is supported by the National Natural Science Foundation of China (NSFC) (Grant Nos. 50873098, 50930001, and 20734003) programs and the Fund for Creative Research Groups (Grant No. 50921062). L.J.A. and Z.G.W. acknowledge the financial support of NSFC (Grant No. 20620120105). Z.Y.S. acknowledges the financial support of JLSTP (Grant No. 20070113).

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