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Title: Knotted polymers and filaments
Author: Matthews, Richard James
ISNI:       0000 0004 2701 1076
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2010
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The behaviour of knotted polymers and non-Brownian knotted filaments is investigated using bead-spring models, simulated using three different dynamical methods. We focus on knotted polymers under confinement, and on the dynamics of knotted polymers and filaments. Langevin Dynamics is applied to study polymers confined in a slit. We find that, for relatively wide slits, knots decrease the force exerted by the polymer on the walls, whilst for narrower slits, they increase it. We interpret the results in terms of the effect of knots on the ability of polymers to spread out as the width is decreased. We simulate knotted polymers migrating through a designed channel with sections of two different depths under an electric field. Trends in the mobility as a function of knot type depend on the depth of the narrower section. We discuss possible links to experimentally important knot electrophoresis. We employ a Stochastic Rotation Dynamics algorithm to investigate knots diffusing in polymers under tension. We focus on two knot groups to demonstrate the effect of topology on effective friction coeffcients and length relaxation. The latter is controlled by a breathing mode. We use the Rotne-Prager tensor in simulations of knotted filaments under shear in the non-Brownian regime. We discover rich dynamical modes, which we classify into families. The modes show regular and chaotic motion with migration in the vorticity direction. We propose that, as filament deformability is varied, the onset of knot-tightening is determined by a dimensionless knot deformation number. We study the effect of knotting on the ejection of flexible and semi-flexible polymers from a spherical, virus-like capsid. The polymer ejection rate is primarily controlled by the knot, which moves to the hole in the capsid and then acts as a ratchet. More complex knots lead to slower ejection. Finally, we show preliminary results that indicate an interesting interplay between persistence length and tension in determining the location of a knot in a polymer of non-uniform flexibility. For lower tensions, the knot may be more likely to be found in a stiffer part of the polymer.
Supervisor: Yeomans, Julia ; Louis, Ard Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available