Molecular dynamics simulation study of nonconcatenated ring polymers in a melt. I. Statics.

Molecular dynamics simulations were conducted to investigate the structural properties of melts of nonconcatenated ring polymers and compared to melts of linear polymers. The longest rings were composed of N = 1600 monomers per chain which corresponds to roughly 57 entanglement lengths for comparable linear polymers. For the rings, the radius of gyration squared, [linear span]R(g)(2)[linear span], was found to scale as N(4/5) for an intermediate regime and N(2/3) for the larger rings indicating an overall conformation of a crumpled globule. However, almost all beads of the rings are "surface beads" interacting with beads of other rings, a result also in agreement with a primitive path analysis performed in the next paper [J. D. Halverson, W. Lee, G. S. Grest, A. Y. Grosberg, and K. Kremer, J. Chem. Phys. 134, 204905 (2011)]. Details of the internal conformational properties of the ring and linear polymers as well as their packing are analyzed and compared to current theoretical models.

[1]  Hyunjung Lee,et al.  Fractionation of Cyclic Polystyrene from Linear Precursor by HPLC at the Chromatographic Critical Condition , 2000 .

[2]  J. Sikorav,et al.  Kinetics of chromosome condensation in the presence of topoisomerases: a phantom chain model. , 1994, Biophysical journal.

[3]  Christophe Zimmer,et al.  Chromosome arm length and nuclear constraints determine the dynamic relationship of yeast subtelomeres , 2010, Proceedings of the National Academy of Sciences.

[4]  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.

[5]  Thomas Cremer,et al.  Chromosome territories--a functional nuclear landscape. , 2006, Current opinion in cell biology.

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

[7]  B. Duplantier,et al.  Statistical mechanics of polymer networks of any topology , 1989 .

[8]  D. Heermann,et al.  On the Influence of Topological Catenation and Bonding Constraints on Ring Polymers , 2010 .

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

[10]  Jiro Suzuki,et al.  Dimension of ring polymers in bulk studied by Monte-Carlo simulation and self-consistent theory. , 2009, The Journal of chemical physics.

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

[12]  Thomas Cremer,et al.  Spatial preservation of nuclear chromatin architecture during three-dimensional fluorescence in situ hybridization (3D-FISH). , 2002, Experimental cell research.

[13]  T. McLeish.  Tube theory of entangled polymer dynamics , 2002 .

[14]  E. Shakhnovich,et al.  The role of topological constraints in the kinetics of collapse of macromolecules , 1988 .

[15]  G. Hadziioannou,et al.  Dilute solution characterization of cyclic polystyrene molecules and their zero-shear viscosity in the melt , 1987 .

[16]  B. Steensel,et al.  Nuclear organization of active and inactive chromatin domains uncovered by chromosome conformation capture–on-chip (4C) , 2006, Nature Genetics.

[17]  C. Strazielle,et al.  Cyclic macromolecules. Synthesis and characterization of ring-shaped polystyrenes , 1983 .

[18]  Hans-Jörg Limbach,et al.  ESPResSo - an extensible simulation package for research on soft matter systems , 2006, Comput. Phys. Commun..

[19]  J. Ferry.  Viscoelastic properties of polymers , 1961 .

[20]  T. Schneider,et al.  Molecular-dynamics study of a three-dimensional one-component model for distortive phase transitions , 1978 .

[21]  K. Binder.  Monte Carlo and molecular dynamics simulations in polymer science , 1995 .

[22]  M. Antonietti,et al.  Polymer topology and diffusion: a comparison of diffusion in linear and cyclic macromolecules , 1992 .

[23]  Kurt Kremer,et al.  Structure of many arm star polymers: a molecular dynamics simulation , 1987 .

[24]  J. M. Deutsch,et al.  Conjectures on the statistics of ring polymers , 1986 .

[25]  Arthur Victor Tobolsky.  Properties and Structure of Polymers. , 1960 .

[26]  S. Shanbhag,et al.  What Is the Size of a Ring Polymer in a Ring−Linear Blend? , 2007 .

[27]  Kurt Kremer,et al.  The bond fluctuation method: a new effective algorithm for the dynamics of polymers in all spatial dimensions , 1988 .

[28]  S. Edwards,et al.  The Theory of Polymer Dynamics , 1986 .

[29]  On two intrinsic length scales in polymer physics: Topological constraints vs. entanglement length , 2000, cond-mat/0006464.

[30]  T. Lodge.  Reconciliation of the Molecular Weight Dependence of Diffusion and Viscosity in Entangled Polymers , 1999 .

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

[32]  G. Szamel,et al.  Structure and dynamics of ring polymers , 1998 .

[33]  Y. Matsushita,et al.  Topological effect in ring polymers investigated with Monte Carlo simulation. , 2008, The Journal of chemical physics.

[34]  V. Breedveld,et al.  Melt Dynamics of Blended Poly(oxyethylene) Chains and Rings , 2009 .

[35]  J. Roovers,et al.  Synthesis of high molecular weight ring polystyrenes , 1983 .

[36]  Kurt Kremer,et al.  Static and dynamic properties of two-dimensional polymer melts , 1990 .

[37]  S. Hess,et al.  Rheological evidence for a dynamical crossover in polymer melts via nonequilibrium molecular dynamics , 2000, Physical review letters.

[38]  J. Roovers,et al.  Synthesis and characterization of ring polybutadienes , 1988 .

[39]  J. Arsuaga,et al.  Modeling of chromosome intermingling by partially overlapping uniform random polygons , 2011, Journal of mathematical biology.

[40]  I. Amit,et al.  Comprehensive mapping of long range interactions reveals folding principles of the human genome , 2011 .

[41]  S. Nechaev,et al.  Dynamics of a polymer chain in an array of obstacles , 1987 .

[42]  T. Cremer,et al.  Chromosome territories, nuclear architecture and gene regulation in mammalian cells , 2001, Nature Reviews Genetics.

[43]  P. Gennes.  Scaling Concepts in Polymer Physics , 1979 .

[44]  D. Y. Yoon,et al.  Monte-carlo method for simulations of ring polymers in the melt. , 2009, Macromolecular rapid communications.

[45]  Julien Dorier,et al.  Topological origins of chromosomal territories , 2009, Nucleic acids research.

[46]  Scott T. Milner,et al.  Relaxation of self-entangled many-arm star polymers , 1989 .

[47]  S. Milner,et al.  Stress relaxation in entangled melts of unlinked ring polymers. , 2010, Physical review letters.

[48]  Nils B Becker,et al.  Looping probabilities in model interphase chromosomes. , 2010, Biophysical journal.

[49]  K. Kremer,et al.  Dissipative particle dynamics: a useful thermostat for equilibrium and nonequilibrium molecular dynamics simulations. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[50]  Tom Misteli,et al.  Cell biology: Chromosome territories , 2007, Nature.

[51]  William Stafford Noble,et al.  A Three-Dimensional Model of the Yeast Genome , 2010, Nature.

[52]  S. Onogi,et al.  Rheological Properties of Anionic Polystyrenes. II. Dynamic Viscoelasticity of Blends of Narrow-Distribution Polystyrenes , 1970 .

[53]  J. Wittmer,et al.  Algebraic displacement correlation in two-dimensional polymer melts. , 2010, Physical review letters.

[54]  Won Bo Lee,et al.  Entangled Polymer Melts: Relation between Plateau Modulus and Stress Autocorrelation Function , 2009 .

[55]  G. Szamel,et al.  Computer simulation study of the structure and dynamics of ring polymers , 1998 .

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

[57]  Pavel G. Khalatur,et al.  Molecular Dynamics Simulations in Polymer Science: Methods and Main Results , 2012 .

[58]  M. Klein,et al.  Modified nonequilibrium molecular dynamics for fluid flows with energy conservation , 1997 .

[59]  R. Porter,et al.  Dependence of Flow Properties of Polystyrene on Molecular Weight, Temperature, and Shear , 1971 .

[60]  G. Szamel,et al.  Influence of topological constraints on the statics and dynamics of ring polymers. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[62]  J. Wittmer,et al.  Static properties of polymer melts in two dimensions , 2010, 1004.4123.

[63]  Kurt Kremer,et al.  Identifying the primitive path mesh in entangled polymer liquids , 2004 .

[64]  Obukhov,et al.  Dynamics of a ring polymer in a gel. , 1994, Physical review letters.

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

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

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

[68]  Long range bond-bond correlations in dense polymer solutions. , 2004, Physical review letters.

[69]  P. Español,et al.  Statistical Mechanics of Dissipative Particle Dynamics. , 1995 .

[70]  J. Dekker,et al.  Capturing Chromosome Conformation , 2002, Science.

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

[72]  Rhonald Lua,et al.  Fractal and statistical properties of large compact polymers: a computational study , 2003 .

[73]  Kurt Kremer,et al.  Reply to the Comment on: “What is the Entanglement Length in a Polymer Melt ?“ , 2000 .

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

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

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

[77]  B. Trathnigg,et al.  Hplc of Polymers , 1998 .

[78]  J. Banavar,et al.  Computer Simulation of Liquids , 1988 .

[79]  J. Wittmer,et al.  Intramolecular long-range correlations in polymer melts: the segmental size distribution and its moments. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[80]  A. Khokhlov,et al.  Polymer chain in an array of obstacles , 1985 .

[81]  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 .

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

[83]  J. Koelman,et al.  Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics , 1992 .