Numéro |
J. Phys. II France
Volume 7, Numéro 10, October 1997
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Page(s) | 1469 - 1487 | |
DOI | https://doi.org/10.1051/jp2:1997196 |
J. Phys. II France 7 (1997) 1469-1487
Dynamics of a Polymer Test Chain in a Glass Forming Matrix: The Hartree Approximation
M. Rehkopf1, V.G. Rostiashvili1, 2 and T.A. Vilgis11 Max-Planck-Institut für Polymerforschung, Postfach 3148, 55021 Mainz, Germany
2 Institute of Chemical Physics, Russian Academy of Science, 142432, Chernogolovka, Moscow region, Russia
(Received 7 January 1997, received in final form 2 June 1997, accepted 6 June 1997)
Abstract
We consider the Langevin dynamics of a Gaussian test polymer chain coupled with a surrounding matrix which can undergo the
glass transition. The Martin-Siggia-Rose generating functional method and the nonpertubative Hartree approximation are used
to derive the generalized Rouse equation for the test chain. It is shown that the interaction of the test chain with the surrounding
matrix renormalizes the bare friction and the spring constants of the test chain in such a way that the memory function as
well as the bending dependent elastic modulus appear. We find that below the glass transition temperature
of the matrix the Rouse modes of the test chain can be frozen and moreover the freezing temperatures (or the ergodicity-nonergodicity
transition temperature)
depends from the Rouse mode index
p.
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