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Statistical Mechanics of Catenatedand Knotted Polymer Structures

Ahmadian Dehaghani, Zahra | 2020

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 53887 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Ejtehadi, Mohammad Reza
  7. Abstract:
  8. In this thesis, we investigate the effects of topological constraints in catenanes composed of interlinked ring polymers on their size in a good solvent as well as on the location of their θ-point when the solvent quality is worsened. We mainly focus on poly[n]catenanes consisting of n ring polymers each of length m interlocked in a linear fashion. We study the scaling of the poly[n]catenane’s radius of gyration assuming that R ~ m^μ n^ν with µ = 16/25 and ν = 3/5 in a good solvent, with these values of µ and ν obtained by means of a Flory-like theory and further confirmed by numerical simulations. We show that individual rings within catenanes feature a surplus swelling due to the presence of N_L topological links and using Flory theory, we find η ~ n^(1/5) as swelling ratio. Furthermore, we consider poly[n]catenanes in solvents of varying quality and we demonstrate that the presence of topological links leads to an increase of its θ-temperature in comparison to isolated linear and ring chains with the following ordering: T_Catenane^θ> T_linear^θ>T_ring^θ. We also show that the presence of links similarly raises the θ-temperature of a single linked ring in comparison to an unlinked one, bringing its θ-temperature close to the one of a poly[n]catenane. Thereafter, we investigate the impact of confinement on [2]catenane topological behavior and show that in strong confinement, the effect of topology is negligible. Finally, we investigate a knotted polymer with varying stiffness in elongational flow. By studying knot size in different strain rate and stiffness, we observe three scenarios for untying process
  9. Keywords:
  10. Confinement ; Elongational Flow ; Flory Theory ; Polycatenane ; Knotted Polymer ; Topological Constraint

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