Ring polymer dynamics

Consider the dynamics of an entangled ring polymer in an array of fixed obstacles [Fig. 9.40(a)]. The ring is not permanently trapped by the obstacles, but is able to diffuse. The ring does not have free ends and, therefore, classical snake-like reptation is not expected for it. An ideal untrapped ring polymer in an array of fixed topological obstacles is an unentangled loop formed by double-folded strands of Ne monomers each, similar to an arm of a star at the moment of complete retraction. 

Cyclization is much more sensitive to excluded volume effects than other properties of polymer chains. These effects operate both to retard ring-closure dynamics and to accelerate the ring-opening step of cyclized chains. 

A theory for the dynamic properties of ring polymers was proposed by Bloomfield and Zimm (54). This theory is another application of the method of the original Zimm theory (29) to a different geometry. Therefore, Eq. (2.1)—(2.10) are used again with a slight modification. Suppose the ring model consists of (N +1) beads. The (1, l)-element... 

Imai (56) constructed a theory fear the intrinsic viscosity and sedimentation constant of ring polymers using the Fixman method shown in 2.3.2 for a model similar to the Hearst-Harris model which will be described in 4.2.2. This model reduces to the Rouse model in a limiting case. The excluded volume potential is included in the form of Eq. (2.26) and the same type of calculation as described in 2.3.2 was performed for a steady shear flow. Dynamic mechanical properties were not treated, although the extension to include this case is only a matter of tedious calculations. 

Obukhov SP, Rubinstein M, Duke T (1994) Dynamics of a ring polymer in a gel. Phys Rev... 

Chen WD, Chen JZ, Liu LJ, Xu XL, An LJ (2013) Effects of chain stiffness on conformational and dynamical properties of individual ring polymers in shear flow. Macromolecules 46 7542-7549... 

Cifre JGH, Pamies R, Martinez MCL, de la Torre JG (2005) Steady-state behavior of ring polymers in dilute flowing solutions via Brownian dynamics. Polymer 46 267-274... 

We have just begun to understand the dynamic behavior of ring polymers in the condensed state. This situation will motivate theoretical and experimental work needed for clarification of the mechanism in which rings within rings can relax and diffuse. 

Brown, S., and Szamel, G., 1998a. Computer simulation study of the structure and dynamics of ring polymers,. Chem. Phys., 109 6184-6192. 

Collepardo-Guevara, R. Suleimanov, Y. V. Manolopoulos, D. E., Bimolecular Reaction Rates from Ring Polymer Molecular Dynamics. J. Chem. Phys. 2009, 130,174713. 

Perez, A. Tuckerman, M. E. Muser, M. H., A Comparative Study of the Centroid and Ring-Polymer Molecular Dynamics Methods for Approximating Quantum Time Correlation Eunctions from Path Integrals. J. Chem. Phys. 2009,130,184105. 

Rosa, A. Orlandini, E. Tubiana, L. Micheletti, C., Structure and Dynamics of Ring Polymers Entanglement Effects Because of Solution Density and Ring Topology. Macromolecides 2011,44,8668-8680. 

Hegde, G. A. Chang, J.-F. Chen, Y.-L. Khare, R., Conformation and Diffusion Behavior of Ring Polymers in Solution A Comparison Between Molecular Dynamics, Multiparticle Collision Dynamics, and Lattice Boltzmann Simulations. J. Chem. Phys. 2011,135,184901. 

Despite the extensive literature which is available on the behaviour of cyclic polymers in solution, the static properties and indeed the dynamic properties of ring polymers in the melt remain largely unexplored. As recently points out by Mdller, Wittmer and Cates [75] no experimental study of the radius of gyration of rings in the melt appears to have been made. A good understanding of the static properties of the system is of course an indispensable starting point for a reasonable description of the dynamics, so this is unfortunate. ... 

Suleimanov YV, Perez de Tudela R, Jambrina PG, Castillo JF, Saez-Rabanos V, Manolopoulos DE, Aoiz FJ (2013) A ring polymer molecular dynamics study of the isotopologues of the H + H2 reaction. Phys Chem Chem Phys 15 3655... 

The dynamics of linear or branched polymers is known to follow the reptation mechanism, in which the chain ends of polymer molecules play a critically important role. On the contrary, ring polymers are unique in the absence of the chain ends and therefore their non-reptation dynamics has been a fundamental issue in both theory and practice in polymer materials science. 

Crystallization Dynamics Using a Defect-Free Ring Polymer... 

Pochan, D.J., Chen, Z.Y., Cui, H.G. et al. (2(X)4) Toroidal triblock copolymer assembUes. Science, 306,94-97. Rubinstein, M. (1986) Dynamics of ring polymers in the presence of fixed obstacles. Physical Review Letters, 57,3023-3026. 

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