Advertisement

Threading Rings

  • Davide MichielettoEmail author
Chapter
  • 262 Downloads
Part of the Springer Theses book series (Springer Theses)

Abstract

Understanding the dynamical and rheological properties of solutions of long ring polymers is of primary importance in several areas of soft matter, material science and biophysics (Cremer and Cremer 2001; Kapnistos et al. 2008; Halverson et al. 2011b, 2013). As mentioned in Chap.  2, ring polymers do not follow the standard reptation theory and in order to make progress it seems that the scientific community will require innovative and unconventional approaches to analyse their properties.

Keywords

Linear Polymer Black Ring Free Diffusion Dense Solution Topological Constraint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Adam, G., Gibbs, J.H.: On the temperature dependence of cooperative relaxation properties in glass-forming liquids. J. Chem. Phys. 43(1), 139 (1965)ADSCrossRefGoogle Scholar
  2. Adams, C.C.: The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots. W H Freeman and Company, New York (1994)zbMATHGoogle Scholar
  3. Aichele, M., Baschnagel, J.: Glassy dynamics of simulated polymer melts: coherent scattering and van Hove correlation functions. Eur. Phys. J. E 5(2), 229 (2001)CrossRefGoogle Scholar
  4. Berthier, L., Biroli, G.: Theoretical perspective on the glass transition and amorphous materials. Rev. Mod. Phys. 83(2), 587 (2011)ADSCrossRefGoogle Scholar
  5. Biroli, G., Bouchaud, J.-P., Cavagna, A., Grigera, T.S., Verrocchio, P.: Thermodynamic signature of growing amorphous order in glass-forming liquids. Nat. Phys. 4(10), 771 (2008)CrossRefGoogle Scholar
  6. Bouchaud, J.-P., Biroli, G.: On the Adam-Gibbs-Kirkpatrick-Thirumalai-Wolynes scenario for the viscosity increase in glasses. J. Chem. Phys. 121(15), 7347 (2004)ADSCrossRefGoogle Scholar
  7. Cammarota, C.: Ph.D. thesis, La Sapienza (Roma) (2009)Google Scholar
  8. Cammarota, C.: A general approach to systems with randomly pinned particles: unfolding and clarifying the random pinning glass transition. Europhys. Lett. 101(5), 56001 (2013)ADSCrossRefGoogle Scholar
  9. Cammarota, C., Biroli, G.: Ideal glass transitions by random pinning. Proc. Natl. Acad. Sci. USA 109(23), 8850 (2012)ADSCrossRefGoogle Scholar
  10. Cates, M., Deutsch, J.: Conjectures on the statistics of ring polymers. J. Phys. Paris 47, 2121 (1986)CrossRefGoogle Scholar
  11. Cremer, T., Cremer, C.: Chromosome territories, nuclear architecture and gene regulation in mammalian cells. Nat. Rev. Genet. 2(4), 292 (2001)CrossRefGoogle Scholar
  12. Doi, M., Edwards, S.: The Theory of Polymer Dynamics. Oxford University Press, Oxford (1988)Google Scholar
  13. Gokhale, S., Nagamanasa, K.H., Ganapathy, R., Sood, A.K.: Growing dynamical facilitation on approaching the random pinning colloidal glass transition. Nat. Commun. 5, 1 (2014)CrossRefGoogle Scholar
  14. Grosberg, A.: Annealed lattice animal model and Flory theory for the melt of non-concatenated rings: towards the physics of crumpling. Soft Matter 10, 560 (2014)ADSCrossRefGoogle Scholar
  15. Grosberg, A.Y., Rabin, Y., Havlin, S., Neer, A.: Crumpled globule model of the three-dimensional structure of DNA. Europhys. Lett. 23(5), 373 (1993)ADSCrossRefGoogle Scholar
  16. Halverson, J.D., Lee, W.B., Grest, G.S., Grosberg, A.Y., Kremer, K.: Molecular dynamics simulation study of nonconcatenated ring polymers in a melt. I. Statics. J. Chem. Phys. 134(20), 204904 (2011a)Google Scholar
  17. Halverson, J.D., Lee, W.B., Grest, G.S., Grosberg, A.Y., Kremer, K.: Molecular dynamics simulation study of nonconcatenated ring polymers in a melt. II. Dynamics. J. Chem. Phys. 134(20), 204905 (2011b)Google Scholar
  18. Halverson, J.D., Grest, G., Grosberg, A.Y., Kremer, K.: Rheology of ring polymer melts: from linear contaminants to ring-linear blends. Phys. Rev. Lett. 108(3), 038301 (2012)ADSCrossRefGoogle Scholar
  19. Halverson, J.D., Kremer, K., Grosberg, A.Y.: Comparing the results of lattice and off-lattice simulations for the melt of nonconcatenated rings. J. Phys. A 46(6), 065002 (2013)ADSCrossRefGoogle Scholar
  20. Halverson, J.D., Smrek, J., Kremer, K., Grosberg, A.: From a melt of rings to chromosome territories: the role of topological constraints in genome folding. Rep. Prog. Phys. 77, 022601 (2014)ADSMathSciNetCrossRefGoogle Scholar
  21. Kane, C.L., Lubensky, T.C.: Topological boundary modes in isostatic lattices. Nat. Phys. 10(1), 39 (2013)CrossRefGoogle Scholar
  22. Kapnistos, M., Lang, M., Vlassopoulos, D., Pyckhout-Hintzen, W., Richter, D., Cho, D., Chang, T., Rubinstein, M.: Unexpected power-law stress relaxation of entangled ring polymers. Nat. Mater. 7(12), 997 (2008)ADSCrossRefGoogle Scholar
  23. Karmakar, S., Parisi, G.: Random pinning glass model. Proc. Natl. Acad. Sci. USA 110(8), 1 (2013)CrossRefGoogle Scholar
  24. Klein, J.: Dynamics of entangled linear, branched, and cyclic polymers. Macromolecules 118(33), 105 (1986)ADSCrossRefGoogle Scholar
  25. Kob, W., Donati, C., Plimpton, S., Poole, P., Glotzer, S.: Dynamical heterogeneities in a supercooled Lennard-Jones liquid. Phys. Rev. Lett. 79(15), 2827 (1997)ADSCrossRefGoogle Scholar
  26. Kremer, K., Grest, G.S.: Dynamics of entangled linear polymer melts: a molecular-dynamics simulation. J. Chem. Phys. 92(8), 5057 (1990)ADSCrossRefGoogle Scholar
  27. Lee, E., Kim, S., Jung, Y.: Slowing down of ring polymer diffusion caused by inter-ring threading. Macromol. Rapid Commun. 36, 1115–1121 (2015)CrossRefGoogle Scholar
  28. Likos, C.N., Narros, A., Moreno, A., Capone, B.: Multi-blob coarse graining for ring polymer solutions. Soft Matter 10, 9601 (2014)ADSCrossRefGoogle Scholar
  29. Lo, W.-C., Turner, M.S.: The topological glass in ring polymers. Europhys. Lett. 102(5), 58005 (2013)ADSCrossRefGoogle Scholar
  30. Maxwell, J.C.: L. On the calculation of the equilibrium and stiffness of frames. Phil. Mag. 27, 294 (1864)Google Scholar
  31. Mézard, M., Parisi, G.: The Bethe lattice spin glass revisited. Eur. Phys. J. B 20, 217 (2001)ADSMathSciNetCrossRefGoogle Scholar
  32. Milner, S., Newhall, J.: Stress relaxation in entangled melts of unlinked ring polymers. Phys. Rev. Lett. 105(20), 208302 (2010)ADSCrossRefGoogle Scholar
  33. Nagamanasa, K.H., Gokhale, S., Sood, A.K., Ganapathy, R.: Direct measurements of growing amorphous order and non-monotonic dynamic correlations in a colloidal glass-former. Nat. Phys. 11(May), 403 (2015)CrossRefGoogle Scholar
  34. Obukhov, S., Rubinstein, M.: Dynamics of a ring polymer in a gel. Phys. Rev. Lett. 73(9), 1263 (1994)ADSCrossRefGoogle Scholar
  35. Orlandini, E., Whittington, S.G.: Entangled polymers in condensed phases. J. Chem. Phys. 121(23), 12094 (2004)ADSCrossRefGoogle Scholar
  36. Ozawa, M., Kob, W., Ikeda, A., Miyazaki, K.: Equilibrium phase diagram of a randomly pinned glass-former. Proc. Natl. Acad. Sci. USA 112(22), 6914 (2015)ADSCrossRefGoogle Scholar
  37. Palmer, R.G., Stein, D.L., Abrahams, E., Anderson, P.W.: Models of hierarchically constrained dynamics for glassy relaxation. Phys. Rev. Lett. 53(10), 958 (1984)ADSCrossRefGoogle Scholar
  38. Parisi, G., Sourlas, N.: Critical behavior of branched polymers and the Lee-Yang edge singularity. Phys. Rev. Lett. 46(14), 871 (1981)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  39. Pasquino, R., Vasilakopoulos, T., Jeong, C., Lee, H., Rogers, S., Sakellariou, G., Allgaier, J., Takano, A., Bras, A., Chang, T., Goossen, S., Pyckhout-Hintzen, W., Wischnewski, A., Hadjichristidis, N., Richter, D., Rubinstein, M., Vlassopoulos, D.: Viscosity of ring polymer melts. ACS Macro Lett. 2, 874 (2013)CrossRefGoogle Scholar
  40. Rosa, A., Everaers, R.: Ring polymers in the melt state: the physics of crumpling. Phys. Rev. Lett. 112, 118302 (2014)ADSCrossRefGoogle Scholar
  41. Rubinstein, M.: Dynamics of ring polymers in the presence of fixed obstacles. Phys. Rev. Lett. 57(24), 3023 (1986)ADSCrossRefGoogle Scholar
  42. Rubinstein, M.: Discretized model of entangled-polymer dynamics. Phys. Rev. Lett. 59(17), 1946 (1987)ADSCrossRefGoogle Scholar
  43. Rubinstein, M., Colby, H.R.: Polymer Physics. Oxford University Press, Oxford (2003)Google Scholar
  44. Smrek, J., Grosberg, A.Y.: Understanding the dynamics of rings in the melt in terms of annealed tree model. J. Phys.: Condens. Matter 27, 064117 (2015)ADSGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.School of Physics and AstronomyUniversity of EdinburghEdinburghUK

Personalised recommendations