Structure and Dynamics of Ring Polymers: Entanglement Effects Because of Solution Density and Ring Topology

The effects of entanglement in solutions and melts of unknotted ring polymers have been addressed by several theoretical and numerical studies. The system properties have been typically profiled as a function of ring contour length at fixed solution density. Here, we use a different approach to investigate numerically the equilibrium and kinetic properties of solutions of model ring polymers. Specifically, the ring contour length is maintained fixed, while the interplay of inter- and intrachain entanglement is modulated by varying both solution density (from infinite dilution up to ≈40% volume occupancy) and ring topology (by considering unknotted and trefoil-knotted chains). The equilibrium metric properties of rings with either topology are found to be only weakly affected by the increase of solution density. Even at the highest density, the average ring size, shape anisotropy and length of the knotted region differ at most by 40% from those of isolated rings. Conversely, kinetics are strongly affected ...

[1]  Kurt Kremer,et al.  Statistics of polymer rings in the melt: a numerical simulation study , 2009, Physical biology.

[2]  D. Theodorou,et al.  Onset of Entanglements Revisited. Dynamical Analysis , 2009 .

[3]  Average size of random polygons with fixed knot topology. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Ralf Everaers,et al.  Structure and Dynamics of Interphase Chromosomes , 2008, PLoS Comput. Biol..

[5]  P. De Los Rios,et al.  Numerical simulation of gel electrophoresis of DNA knots in weak and strong electric fields. , 2006, Biophysical journal.

[6]  Steve Plimpton,et al.  Fast parallel algorithms for short-range molecular dynamics , 1993 .

[7]  Kurt Kremer,et al.  Rheology and Microscopic Topology of Entangled Polymeric Liquids , 2004, Science.

[8]  A. Grosberg,et al.  Topologically driven swelling of a polymer loop. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[9]  Doros N. Theodorou,et al.  Topological Analysis of Linear Polymer Melts: A Statistical Approach , 2006 .

[10]  Shlomo Havlin,et al.  Crumpled globule model of the three-dimensional structure of DNA , 1993 .

[11]  J. D. Cloizeaux.  Ring polymers in solution : topological effects , 1981 .

[12]  A. Stella,et al.  Slow topological time scale of knotted polymers , 2008 .

[13]  Erwin Frey,et al.  Excluded volume effects on semiflexible ring polymers. , 2009, Nano letters.

[14]  L. Willner,et al.  Direct observation of the transition from free to constrained single-segment motion in entangled polymer melts. , 2003, Physical review letters.

[15]  M. Rubinstein,et al.  Dynamics of ring polymers in the presence of fixed obstacles. , 1986, Physical review letters.

[16]  Wittmer,et al.  Topological effects in ring polymers: A computer simulation study. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[17]  Pavlos S. Stephanou,et al.  Melt Structure and Dynamics of Unentangled Polyethylene Rings: Rouse Theory, Atomistic Molecular Dynamics Simulation, and Comparison with the Linear Analogues , 2010 .

[18]  P. Gennes.  Reptation of a Polymer Chain in the Presence of Fixed Obstacles , 1971 .

[19]  M. Baiesi,et al.  Topological signatures of globular polymers. , 2011, Physical review letters.

[20]  Davide Marenduzzo,et al.  DNA–DNA interactions in bacteriophage capsids are responsible for the observed DNA knotting , 2009, Proceedings of the National Academy of Sciences.

[21]  Peter Virnau,et al.  Knots in globule and coil phases of a model polyethylene. , 2005, Journal of the American Chemical Society.

[22]  Chris Sander,et al.  The double cubic lattice method: Efficient approaches to numerical integration of surface area and volume and to dot surface contouring of molecular assemblies , 1995, J. Comput. Chem..

[23]  Davide Marenduzzo,et al.  Polymers with spatial or topological constraints: Theoretical and computational results , 2011, 1103.4222.

[24]  Akos Dobay,et al.  Linear Random Knots and Their Scaling Behavior , 2005 .

[25]  David C. Morse,et al.  Viscoelasticity of Concentrated Isotropic Solutions of Semiflexible Polymers. 1. Model and Stress Tensor , 1998 .

[26]  J. Dubochet,et al.  Tightness of random knotting. , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[27]  Carsten Kutzner,et al.  GROMACS 4:  Algorithms for Highly Efficient, Load-Balanced, and Scalable Molecular Simulation. , 2008, Journal of chemical theory and computation.

[28]  Ralf Everaers,et al.  Viscoelasticity and primitive path analysis of entangled polymer liquids: from F-actin to polyethylene. , 2007, The Journal of chemical physics.

[29]  Kurt Binder,et al.  Anomalous structure and scaling of ring polymer brushes , 2011, 1104.4943.

[30]  D. Y. Yoon,et al.  Chain Dynamics of Ring and Linear Polyethylene Melts from Molecular Dynamics Simulations , 2011 .

[31]  Stephen R Quake,et al.  Behavior of complex knots in single DNA molecules. , 2003, Physical review letters.

[32]  Erwin Frey,et al.  Shapes of semiflexible polymer rings. , 2007, Physical review letters.

[33]  S G Whittington,et al.  Statistical topology of closed curves: Some applications in polymer physics , 2007 .

[34]  Alexander Y. Grosberg,et al.  A few notes about polymer knots , 2009 .

[35]  P. Lai.  Dynamics of polymer knots at equilibrium. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  G. Grest,et al.  Dynamics of entangled linear polymer melts: A molecular‐dynamics simulation , 1990 .

[37]  A. Stella,et al.  Size of knots in ring polymers. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[38]  J. Rudnick,et al.  The Shapes of Random Walks , 1987, Science.

[39]  Kurt Kremer,et al.  Molecular dynamics simulation study of nonconcatenated ring polymers in a melt. I. Statics. , 2011, The Journal of chemical physics.

[40]  Steven J. Plimpton,et al.  Equilibration of long chain polymer melts in computer simulations , 2003, cond-mat/0306026.

[41]  Arnulf B. A. Graf,et al.  Dynamics of a rigid body in a Stokes fluid , 2004, Journal of Fluid Mechanics.

[42]  Bruno H. Zimm,et al.  The Dimensions of Chain Molecules Containing Branches and Rings , 1949 .

[43]  Alexander Vologodskii,et al.  Brownian dynamics simulation of knot diffusion along a stretched DNA molecule. , 2006, Biophysical journal.

[44]  Quake,et al.  Topological effects of knots in polymers. , 1994, Physical review letters.

[45]  Wittmer,et al.  Topological effects in ring polymers. II. Influence Of persistence length , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[46]  D. Y. Yoon,et al.  Comparison of ring and linear polyethylene from molecular dynamics simulations , 2006 .

[47]  D Richter,et al.  Unexpected power-law stress relaxation of entangled ring polymers. , 2008, Nature materials.