Abstract/Summary

In this thesis, we investigate two problems of entangled branched polymers, i.e., the numerical solutions of the arm-retraction problem for well-entangled star arms and the relaxation behaviours of branched polymers with different architectures. For the first problem, the arm retraction dynamics is studied using both the onedimensional Rouse chain model and the slip-spring model by an advanced numerical method for the first-passage time problems, namely the forward flux sampling (FFS) method. In the one-dimensional Rouse chain model, we measured the first-passage time that the arm free end extends to a distance away from the origin, showing that the mean first-passage time is getting shorter if the Rouse chain is represented by more beads. The simulation results validate the prediction of an asymptotic solution for the multi-dimensional first-passage problem, which suggests the arm retraction time is much shorter than the prediction of the Milner-McLeish theory without constraint release. Then, we implement the FFS method to the slip-spring model and get the relaxation spectra for different arm lengths, ranging from mildly entangled to well-entangled star arms. We also proposed an algorithm to extract the dynamic observables, i.e., the end-to-end vector and stress relaxation functions, from the FFS simulation results. For the second problem, we conduct a series of molecular dynamics (MD) simulations using high-performance GPU methods on the mildly entangled branched polymers of different architectures, including 3-arm symmetric and asymmetric stars, and H-shaped polymers. The slip-spring model, whose parameters are carefully calibrated according to the MD results of linear chains, is also implemented to predict the relaxation behaviours of the branched polymers. We present a detailed analysis of the arm end-to-end vector relaxation functions and the monomer mean-squared displacements. By comparing the MD and slipspring model simulation results, we propose a slip-link “hopping” mechanism, which accounts for the behaviour that the entanglements can pass through the branch point when the third arm is disentangled