Effects of Nematic Ordering on the Relaxation Spectrum of a Polymer Network with Included rod-like Particles: Mean-Field Approximation
✍ Scribed by Yuli Y. Gotlib; Isaak A. Torchinskii; Vladimir P. Toshchevikov
- Publisher
- John Wiley and Sons
- Year
- 2004
- Tongue
- English
- Weight
- 293 KB
- Volume
- 13
- Category
- Article
- ISSN
- 1022-1344
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
Summary: Equilibrium and local dynamic properties of ordered polymer networks with included rod‐like particles are considered using a simplified network model. Lagrange multipliers in the equations of motion of rigid rods are replaced by their averaged values. This approximation corresponds to modelling rod‐like particles by elastic Gaussian springs with mean‐square lengths independent of the orientational order. Nematic‐like interactions between network segments and rods are taken into account in terms of the Maier‐Saupe mean‐field approximation. Nematic ordering of rods induces network segments ordering and changes the relaxation spectrum of the network. The relaxation spectrum of the ordered network splits into two main branches for parallel and perpendicular components of chain segments with respect to the director. Relaxation times of a polymer network are calculated as functions of the wave number for the corresponding normal mode and of the order parameter taking into account both the dynamic factor (determined by friction effects) and the statistical factor (related to mean‐square fluctuations of segment projections). We compare the relaxation spectra of ordered unstretched polymer networks with fixed boundaries with those for polymer networks at free boundaries. A polymer network with free boundaries is stretched along the director. This produces additional fine structure of the two main branches in the relaxation spectrum.
Cell of a three‐chain network model with included rods.
imageCell of a three‐chain network model with included rods.