Topological Interactions in Ring Polymers
Ring polymers are one of the last big mysteries in polymer physics, and this thesis tackles the problem of describing their behaviour when interacting in dense solutions and with complex environments and reports key findings that help shed light on these complex issues. The systems investigated are not restricted to artificial polymer systems, but also cover biologically inspired ensembles, contributing to the broad applicability and interest of the conclusions reached. One of the most remarkable findings is the unambiguous evidence that rings inter-penetrate when in dense solutions; here this behaviour is shown to lead to the emergence of a glassy state solely driven by the topology of the constituents. This novel glassy state is unconventional in its nature and, thanks to its universal properties inherited from polymer physics, will attract the attention of a wide range of physicists in the years to come.
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algorithm atoms average beads behaviour Biol Biroli cell centre of mass chains Chap Chem coils complex knots computed configurations contour correlations dangling ends defined dense solutions diffusion disentanglement display DNA knots DNA network dynamics of rings entanglement equilibrated exponent fact fraction gel electrophoresis experiments gel structure genetic material Gennes glass transition glass-forming Grosberg Halverson impalements Kapnistos Kremer Kuhn length lattice animal length-scales Lett linear polymers linking number loops melt of rings Michieletto mini-circles mitochondrial mobility Molecular Dynamics molecules monomers motion non-monotonic observed parameter persistence length Phys physical potential probe properties quantity radius of gyration relaxation replication reptation ring polymers Rubinstein scaling scattering function segments simulation Soft Matter solution of rings Stasiak stress strongly connected component supercoiling Thesis threadings time-scale topoisomerase topoisomerase II topological constraints topological interactions Trigueros un-knotted unlinked V/cm Viovy