The Mesoscopic Theory of the Slow Relaxation of Linear Macromolecules

The Mesoscopic Theory of the Slow Relaxation of Linear Macromolecules

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The review is devoted to the description of the relaxation behaviour of very concentrated solutions or melts of linear polymers. A mesoscopic approach, which deals with the dy- namics of a single macromolecule among others and is based on some statements of a general kind, is used. From a strictly phenomenological point of view, the mesoscopic approach is a microscopic macromolecular approach. It reveals the internal connection between phenomena and gives more details than the phenomenological approach. From a strictly microscopic point of view, it is a phenomenological one. It needs some meso- scopic parameters to be introduced and determined empirically. However, the mesoscopic approach permits us to explain the different phenomena of the dynamic behaviour of polymer melts ± diffusion, neutron scattering, viscoelasticity, birefringence and others ± from a macromolecular point of view and without any specific hypotheses. The meso- scopic approach constitutes a phenomenological frame within which the results of inves- tigations of behaviour of weakly-coupled macromolecules can be considered. The resul- tant picture of the thermal motion of a macromolecule in the system appears to be con- sistent with the common ideas about the localisation of a macromolecule: one can intro- duce an intermediate length which has the sense of a tube diameter and/or the length of a macromolecule between adjacent entanglements. In fact, it appears to be the most impor- tant parameter of the theory, as it was envisaged by Edwards and by de Gennes. Keywords. Birefringence, Localisation of macromolecule, Polymer dynamics, Viscoelasti- city, Weakly-coupled chains 1 Introduction ............................... 145 2 Macromolecules in Equilibrium ................... 146 2.1 Macromolecular Coil. ......................... 2.2 Bead-and-Spring Model 148 2.3 Normal Co-ordinates. 150 2.4 Excluded-Volume Effects. ....................... 151 2.5 Macromolecules in Solvent 154 2.6 Weakly-Coupled Macromolecules. .................. 155 3 Dynamics of a Tagged Macromolecule ................ 157 3.1 A Macromolecule in a Dilute Solution. ............... The Mesoscopic Theory of the Slow Relaxation of Linear Macromolecules Vladimir N. Pokrovskii Department of Physics, University of Malta, Msida, MSD 06, Malta e-mail: vpok@isaac.phys.um.edu.mt Advances in Polymer Science, Vol. 154 # Springer-Verlag Berlin Heidelberg 2001
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3.1.1 Equation of Macromolecular Dynamics . .............. 157 3.1.2 Linear Modes. .............................. 159 3.2 A Macromolecule in an Entangled System. ............. 160 3.2.1 Many-Chain Problem. ......................... 3.2.2 Linear Equation for a Probe Macromolecule 162 3.3 Heuristic Speculations for Memory Functions ............ 165 3.4 Dynamics of a Reptating Macromolecule ............... 167 4 Low-Frequency Modes for Weakly-Coupled macromolecules ... 169 4.1 Modes of Motion in Linear Approximation. 169 4.2 Correlation Functions. 171 4.2.1 Equilibrium Correlation Functions. ................. 4.2.2 One-point Non-Equilibrium Correlation Functions ......... 172 4.2.3 Two-point Non-Equilibrium Correlation Functions 173 4.3 Relaxation Times of the Macromolecular Coil 5 The Localisation Effect 175 5.1 Mobility of a Macromolecule ......................
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The Mesoscopic Theory of the Slow Relaxation of Linear Macromolecules

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