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Threaded Network of Ring Polymers
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Noodee, Nart (2021) Threaded Network of Ring Polymers. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b3520293~S15
Abstract
A system of highly entangled ring polymers embedded in a gel was studied using Monte Carlo simulation and analytic approaches using the techniques of statistical mechanics. The rings are assumed to be flexible, unlinked and unknotted at synthesis. The gel confines the ring polymers to adopt “duplex” structures in which any mesh volume of the gel occupied by the polymer contains both an outgoing and returning segment of the ring. These duplex structures are further assumed to be unbranched for simplicity. The emergence of effective “ends” on these linear duplex configurations offers the possibility of utilising the standard tube model and reptation dynamics, developed for linear polymers. This helps to simplify the dynamics of the rings, that can then be treated as reptating linear chains. Inter-ring threadings have been confirmed to exist in recent molecular dynamics (MD) simulations. These can be incorporated in the present work by the process of one end of a duplex chain threading through (between the two strands of) a second duplex ring. This generates a pair of threadings, an “active” one on the threading ring and a partner “passive” threading on the threaded ring. Threadings are included in our Monte Carlo simulations and are shown to have very different properties. The main advantage of this approach is that we can access a regime in which there are many threadings per ring, a regime that remains inaccessible to brute force MD or, indeed, any other technique. The simulation results suggests that threadings play a vital role in reducing the ring polymer mobilities, resulting in an increase in the stress relaxation time that is exponential in the number of threadings per polymer. Several other novel features are identified, including a heavy tailed distribution of stress relaxation times and a sub-diffusive plateau in the mean squared curvilinear displacement of the polymers as a function of time. The data presented in this thesis supports the hypothesis that the fundamental mechanism behind the slowing down of ring dynamics is pinning provided by passive threadings. The distribution of the active penetrations reveals the previously unexplored role of an entropy associated with the network of inter-ring threadings. Some threading configurations are topologically inaccessible and bias the positions of the active threadings on their corresponding chain contours, enriching them near the chain ends. We explore an analytic approach to understand the driven diffusion of polymers relative to the active threading sites. In one limit, where the network entropy is small, we recover threading lifetimes consistent with Doi-Edwards theory of linear polymer. In the limit where the network entropy plays an important role the agreement is less good. This may indicate that mean-field approaches are fundamentally inadequate to study this problem and motivates possible future studies, e.g. based on retaining information at the level of distribution functions.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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Library of Congress Subject Headings (LCSH): | Threads (Computer programs), Polymers, Monte Carlo method, Statistical mechanics | ||||
Official Date: | April 2021 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Department of Physics | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Turner, Matthew | ||||
Sponsors: | Royal Government of Thailand. Development and Promotion of Science and Technology | ||||
Format of File: | |||||
Extent: | vi, 97 leaves: illustrations, plates, charts. | ||||
Language: | eng |
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