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Effects of Nematic Ordering on the Relaxation Spectrum of a Polymer Network with Included rod‐like Particles: Mean‐Field Approximation
Author(s) -
Gotlib Yuli Y.,
Torchinskii Isaak A.,
Toshchevikov Vladimir P.
Publication year - 2004
Publication title -
macromolecular theory and simulations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.37
H-Index - 56
eISSN - 1521-3919
pISSN - 1022-1344
DOI - 10.1002/mats.200300044
Subject(s) - rod , liquid crystal , relaxation (psychology) , mean field theory , perpendicular , condensed matter physics , statistical physics , gaussian , field (mathematics) , polymer , materials science , physics , mathematics , geometry , quantum mechanics , nuclear magnetic resonance , medicine , psychology , social psychology , alternative medicine , pathology , pure mathematics
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.