RELAXATION DYNAMICS OF BRANCHED POLYMERS

Open Access
Author:
Ghosh, Arnav
Graduate Program:
Materials Science and Engineering
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
October 04, 2007
Committee Members:
  • Ralph H Colby, Committee Chair
  • Qing Wang, Committee Member
  • Ronald Hedden, Committee Member
  • Janna Kay Maranas, Committee Member
Keywords:
  • dynamics
  • relaxation
  • rouse
  • star
  • branched
  • polymers
  • entangled
Abstract:
The Rouse model for star polymers was successfully derived by solving the differential equations governing the net force acting on each bead in a star polymer chain. As opposed to a linear polymer, where we have N unique roots for N beads, in the case of star polymers, there are only 2Na+1 unique roots and all odd unique roots (except the last root corresponding to the branch point) starting with the first root have a multiplicity of f −1. The relaxation time of the pth unique Rouse mode of a star polymer varies as (2Na + 1)2/p2. Since alternate Rouse modes in a star polymer have a multiplicity of f − 1, they add to the terminal modulus of the star polymers and the terminal modulus, G( ) ends up being proportional to f −1 (besides being inversely proportional to N, which is also the case with linear polymers). A self-consistent theory for the relaxation of entangled star polymers was developed based on the work done by Colby and Rubinstein on linear blends. This theory considers the duality of relaxation dynamics (direct stress relaxation and indirect relaxation by release of constraints) and models the relaxation due to constraint release R(t) based on Dean’s approach in solving the vibration frequencies of glassy chains with random spring constants. In our case, the mobilities of beads were considered to be random and based on the relative weight of the prefactor of a Maxwell function, a group of which was fitted to the stress relaxation function μ(t) of a star polymer (proposed and derived by Doi). The tube dilation model for star and comb polymers was investigated in detail and predictions compared to rheological data from polypropylene, polybutadiene and polystyrene comb polymers along with PEP star polymers. The relaxation time from the Tube Dilation Model was compared with the classical Tube Model and was shown to have an extra power dependence on the fraction of the comb backbone.