Abstract/Summary

Polymer melts generally demonstrate complicated dynamic and stress relaxation behaviours, which are usually difficult to be described by theoretical models and typically involve many parameters. The thesis specifically centers on developing novel models to study entangled polymer melts with the help of Monte Carlo methods. We commence by providing a brief description of the problems and prior knowledge for polymer and Bayesian statistics in Chapter 1. In Chapter 2, we develop a multi-bead coarse-grained model based on singleparticle dynamics at the level of the individual molecule. Next, we show how to embed Kalman filter into Markov chain Monte Carlo (MCMC) paradigm to draw inferences on the model parameters. Then the estimates of parameters can be used to reproduce the dynamics of the center of mass of single chains in molecular dynamics (MD) simulations. We explore the performance of coarse-grained models for linear chains with different hidden beads and find that the multi-bead model is preferable to have Rouse-like structure rather than asymmetric star structure. The next part of the thesis investigates two different models dealing with nonlinear systems. The first model is the extension of the multi-bead model for dealing with nonlinear interactions and the second model is described by the generalized Langevin equation with memory kernel. The MCMC method fails for the first model due to the fact that the particle MCMC using for parameter estimation ends up with noisy likelihood and is unable to explore the parameter space sufficiently. Laplace transform and numerical approximation are applied to get the estimates of unknown parameters for the second model. Comparing the linear multi-bead model and the model with memory kernel, we find that the former is more promising to describe the dynamics of entanglement polymers. In Chapter 4, we introduce Monte Carlo methods in combination with the slipspring model, which was originally developed for describing dynamics of entangled polymers, for detecting entanglements in the polymer melts obtained from MD simulations. The total number, the effective lengths and the locations of the anchor points of the slip-springs will be well decided by Bayesian statistical methods. The Bayesian alternative can also compute the posterior distribution of different models and provide uncertainty analysis on the estimation of model parameters. Finally, in Chapter 5, we provide concluding remarks and discuss the limitations of our methodologies, and point out possible future research directions.