%0 Book Section %1 statphys23_0488 %A Iyer, B.V.S. %A Lele, A.K. %A Juvekar, V.A. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K blend dynamics polymers pom-pom ring ring-linear statics statphys23 topic-7 viscoelasticity %T Dynamics of Ring Polymers in Melt Environment %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=488 %X Dynamics of ring polymers and the resulting viscoelastic response of a melt of ring chains and melt of ring-linear blends is an interesting puzzle in the theory of polymer dynamics. It was conjectured by Cates & Deutsch 1 that ring polymers in a melt of rings have a compact self-similar Cayley-tree structure with $R_g N^2/5$ due to the presence of the topological constraint of non-concatenation. Addition of linear chains is expected to cause dilution of this constraint and consequently alter the static structure of the ring and the dynamic response of the polymeric system. Experiments by Roovers 2 indicate that the viscosity of a ring polymer melt is about 10 times lower than that of a linear polymer melt of about the same molecular weight. It is also observed that monodisperse rings show a power law dependence of gain modulus after crossover unlike for monodisperse linear chains, which show a plateau modulus 2. Further, presence of small amounts of linear chains in a melt of rings was shown to alter the viscoelastic response of the system drastically. Ring-linear blends in fact show a non-monotonic increase in zero-shear viscosity with maximum in viscosity of magnitude twice that of the linear melt at a volume fraction of 50\% linear chains 2. The understanding of the underlying molecular mechanisms responsible for the above mentioned varied viscoelastic response of ring polymeric systems is approached in two steps. In the first step we present the influence of the environment (ring chain neighbors/linear chain neighbors) on the static structure. Secondly we study the mechanism of relaxation in a given melt environment based on a coarse grained mean-field tube model (Pom-Pom Ring) and its modifications. We present scaling arguments for influence of concentration of linear chains on static structure of a ring starting with the Cayley-tree structure for a ring in a melt of pure rings. The linear viscoelastic response predictions of Pom-Pom Ring (PPR) model for the case of pure ring melt is shown to be in semi-quantitative agreement with the experiments of Roovers 2. Modifications for capturing self-similar dynamics are incorporated to the first order PPR model and shown to be effective in improving the predictions of the first-order PPR model. Finally we present some plausible approaches to understanding the response of ring-linear blends based on the influence of linear chains on ring static structure, regimes of entanglement in a ring-linear blend and the role of constraint release. 1) Cates, M. E.; Deutsch, J. M., J. Phys. (Paris) 1986, 47, 2121-2128.\\ 2) Roovers, J., Macromolecules 1988, 21, 1517-1521.

@incollection{statphys23_0488, abstract = {Dynamics of ring polymers and the resulting viscoelastic response of a melt of ring chains and melt of ring-linear blends is an interesting puzzle in the theory of polymer dynamics. It was conjectured by Cates \& Deutsch [1] that ring polymers in a melt of rings have a compact self-similar Cayley-tree structure with $R_g \sim N^{2/5}$ due to the presence of the topological constraint of non-concatenation. Addition of linear chains is expected to cause dilution of this constraint and consequently alter the static structure of the ring and the dynamic response of the polymeric system. Experiments by Roovers [2] indicate that the viscosity of a ring polymer melt is about 10 times lower than that of a linear polymer melt of about the same molecular weight. It is also observed that monodisperse rings show a power law dependence of gain modulus after crossover unlike for monodisperse linear chains, which show a plateau modulus [2]. Further, presence of small amounts of linear chains in a melt of rings was shown to alter the viscoelastic response of the system drastically. Ring-linear blends in fact show a non-monotonic increase in zero-shear viscosity with maximum in viscosity of magnitude twice that of the linear melt at a volume fraction of 50\% linear chains [2]. The understanding of the underlying molecular mechanisms responsible for the above mentioned varied viscoelastic response of ring polymeric systems is approached in two steps. In the first step we present the influence of the environment (ring chain neighbors/linear chain neighbors) on the static structure. Secondly we study the mechanism of relaxation in a given melt environment based on a coarse grained mean-field tube model (Pom-Pom Ring) and its modifications. We present scaling arguments for influence of concentration of linear chains on static structure of a ring starting with the Cayley-tree structure for a ring in a melt of pure rings. The linear viscoelastic response predictions of Pom-Pom Ring (PPR) model for the case of pure ring melt is shown to be in semi-quantitative agreement with the experiments of Roovers [2]. Modifications for capturing self-similar dynamics are incorporated to the first order PPR model and shown to be effective in improving the predictions of the first-order PPR model. Finally we present some plausible approaches to understanding the response of ring-linear blends based on the influence of linear chains on ring static structure, regimes of entanglement in a ring-linear blend and the role of constraint release. 1) Cates, M. E.; Deutsch, J. M., J. Phys. (Paris) 1986, 47, 2121-2128.\\ 2) Roovers, J., Macromolecules 1988, 21, 1517-1521.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Iyer, B.V.S. and Lele, A.K. and Juvekar, V.A.}, biburl = {https://www.bibsonomy.org/bibtex/22c18fc8096d673e14d2fb96b7fef3229/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {b22b4526222d322342a8876bc3befea9}, intrahash = {2c18fc8096d673e14d2fb96b7fef3229}, keywords = {blend dynamics polymers pom-pom ring ring-linear statics statphys23 topic-7 viscoelasticity}, month = {9-13 July}, timestamp = {2007-06-20T10:16:21.000+0200}, title = {Dynamics of Ring Polymers in Melt Environment}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=488}, year = 2007 }