Modelling a single polymer entanglement

The slip-spring model introduced by Likhtman (Macromolecules 38, 6128-6139 (2005)) simulates a single chain entangled within a polymer melt. Single-chain models such as the slip-spring model allow the rheology of polymers to be studied without requiring the use of expensive multiple-chain molecular dynamics simulations. This study investigates the slip-spring model in the context of a single entanglement and compares it to a two-chain entanglement model. A better understanding of the mechanisms involved in an entanglement is obtained, through the properties of stress relaxation and mean squared displacement, but also through analysis of the bead positions and bond vectors involved. Flaws are identified within the slip-spring model, for which modifications to the model are suggested, including the addition of a non-isotropic spring-constant and the replacement of the slip-spring by a slip-chain. This examination of the simple case is carried out, so that the knowledge gained may be later applied to the multiple-entanglement slip-spring model. During the course of this study, the generic polymer simulation (GPS) package was con- structed by the Reading Theoretical Polymer Physics Group. GPS provides an object-orientated simulation framework, designed to keep simulations organised and make new simulations faster to create. An overview of the concepts involved is included in this thesis. Another tool encountered within this study is maximum likelihood estimation, a statistical technique that, when applied to polymer models such as the slip-spring model, allows the estimation of model parameters. Such a fitting is not only useful for finding the best parameters, but also prevents the model flaws from being obscured by incorrect parameter fitting.EThOS - Electronic Theses Online ServiceGBUnited Kingdo