Branch point dynamics of Polymer Stars
(2013) British Applied Mathematics Colloquium — Location: Leeds, UK
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- Abstract
- (en) The Rouse model [1] and the tube model [2] are the basic models for the description of polymer dynamics (of linear chains) in the unentangled and entangled regime, respectively. In the melt state, a polymer chain is mutually entangled with other chains experiencing topological constraints. The tube model represents these entanglements as an effective tube, in which the chain is confined. Here, we extend the Rouse model to chains with symmetric star-like architecture. To account for confinement effects in the entangled regime, we locasise each segment of the Rouse chain in its own harmonic potential [3]. For both regimes unentangled and entangled, we derive analytical expressions for the mean square displacement (MSD). These expressions account only for internal Rouse modes and are valid for segments in the close vicinity of the branch point only. We test the validity of our theoretical expressions, in the entangled regime, against Molecular Dynamics (MD) simulations. For this reason we perform a simulation on a melt of entangled symmetric polymer stars, in which chain ends are fixed (i.e. all other relaxation mechanisms except internal Rouse modes are suppressed) . The simulations reveal that localisation of the branch point is weaker compared to our model predictions, suggesting the presence of an early tube dilation process not included in current tube models. When early tube dilation is accounted for, our model predictions are in accordance with the simulation results. Furthermore, we perform a simulation on the same melt of symmetric stars, in which the chain ends are now free. We find that our theoretical expressions provide a very good description of the MD data when the model parameters are rescaled on the basis of the “dynamic dilution” hypothesis [4]. [1] P.E. Rouse, J. Chem. Phys. 21, 1972 (1953) [2] M. Doi and S. F. Edwards. The Theory of Polymer Dynamics. Oxford University Press, 1986 [3] D.J. Read, K. Jagannathan, and A.E. Likhtman, Macromolecules, 41, 6843 (2008) [4] T.C.B. McLeish, Advances in Physics, 51, 1379 (2002)
- Affiliations
Department of Applied Mathematics University of Leeds
Citations
Hawke, L. G. D., & Read, D. J. (2013). Branch point dynamics of Polymer Stars. British Applied Mathematics Colloquium, Leeds, UK. https://hdl.handle.net/2078.5/180849