UBC Theses and Dissertations
Modelling a tethered polymer loop : shape and thickness compressibility Wong, Wesley Philip
A Monte Carlo simulation was used to investigate the thickness compressibility and shape properties of a tethered polymer loop. Specifically, the dependence on chain length, bending stiffness (i.e. persistence length) and excluded volume interactions was examined. Power law relationships were determined when appropriate. For a flexible phantom chain of 90 segments, reasonably good agreement was found with the predictions of an analytical random flight model based on the diffusion equation. By examining the transition from flexible to semi-flexible, rough bounds were placed on the domain in which a worm-like chain can be well described by an equivalent freely jointed chain. As the bending stiffness was increased but the contour length held fixed, the polymer loop crossed over into the "stiff elastic rod" regime. This was marked by a change in the relationship between force and gap distance, as well as an alteration of shape properties. Finally, the single polymer loop model was compared to a simulation of the red blood cell spectrin network by Boal . Many of the features of network geometry and elastic thickness compliance could be well approximated by the single chain model.
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