https://doi.org/10.1140/epjb/e2003-00142-3
Polymer chain in a quenched random medium: slow dynamics and ergodicity breaking
1
Max Planck Institute for Polymer Research 10 Ackermannweg, 55128 Mainz, Germany
2
Laboratoire Européen Associé, Institut Charles Sadron 6 rue Boussingault, 67083 Strasbourg Cedex, France
Corresponding author: a vilgis@mpip-mainz.mpg.de
Received:
17
December
2002
Published online:
23
May
2003
The Langevin dynamics of a self-interacting chain embedded in a quenched
random medium is investigated by making use of the generating functional
method and one-loop (Hartree) approximation. We have shown how this
intrinsic disorder causes different dynamical regimes. Namely, within the
Rouse characteristic time interval the anomalous diffusion shows up. The
corresponding subdiffusional dynamical exponents have been explicitly
calculated and thoroughly discussed. For the larger time interval the
disorder drives the center of mass of the chain to a trap or frozen state
provided that the Harris parameter, ,
where Δ is a disorder strength, b is a Kuhnian segment length, N
is a chain length and ν is the Flory exponent. We have derived the
general equation for the non-ergodicity function f(p) which
characterizes the amplitude of frozen Rouse modes with an index
. The numerical solution of this equation has been implemented and shown
that the different Rouse modes freeze up at the same critical disorder
strength
where the exponent
and does not depend from the solvent quality.
PACS: 61.25.Hq – Macromolecular and polymer solutions; polymer melts; swelling / 78.55.Qr – Amorphous materials; glasses and other disordered solids / 66.90.+r – Other topics in nonelectronic transport properties of condensed matter
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2003