Topologically driven swelling of a polymer loop.

Numerical studies of the average size of trivially knotted polymer loops with no excluded volume were undertaken. Topology was identified by Alexander and Vassiliev degree 2 invariants. Probability of a trivial knot, average gyration radius, and probability density distributions as functions of gyration radius were generated for loops of up to N = 3,000 segments. Gyration radii of trivially knotted loops were found to follow a power law similar to that of self-avoiding walks consistent with earlier theoretical predictions.

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

[2]  Tetsuo Deguchi,et al.  Universality of random knotting , 1997 .

[3]  Muthukumar,et al.  Knottedness in ring polymers. , 1991, Physical review letters.

[4]  M. Kardar,et al.  Equilibrium shapes of flat knots. , 2001, Physical review letters.

[5]  Y. Diao,et al.  The Average Crossing Number of Equilateral Random Polygons , 2003 .

[6]  H. Stanley,et al.  Statistical physics of macromolecules , 1995 .

[7]  S. Whittington,et al.  Asymptotics of knotted lattice polygons , 1998 .

[8]  T. Mansour,et al.  Involutions avoiding the class of permutations in Sk with prefix 12 , 2007 .

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

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

[11]  Pierre-Edouard Sottas,et al.  Scaling behavior of random knots , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[12]  Rabin,et al.  Flory-type theory of a knotted ring polymer. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[13]  Ronald C. Read,et al.  The knot book: An elementary introduction to the mathematical theory of knots , 1997, Complex..

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

[15]  Grosberg.  Critical exponents for random knots , 1999, Physical review letters.

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

[17]  M. Fixman.  Radius of Gyration of Polymer Chains , 1962 .

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