Eur. Phys. J. E 5, 133-148
Glassy effects in the swelling/collapse dynamics of homogeneous polymers
E. Pitard1 and J.-P. Bouchaud21 Harvard University, USA, and Laboratoire de Physique Mathématique et Théorique, Université Montpellier II, UMR 5825, France
2 SPEC-CEA Saclay, l'Orme des Merisiers, 91191 Gif-sur-Yvette Cedex, France
estelle@lpm.univ-montp2.fr
bouchau@spec.saclay.cea.fr
(Received 23 October 2000)
Abstract
We investigate, using numerical simulations and analytical
arguments, a simple one-dimensional model for the swelling or the
collapse of a closed polymer chain of size N, representing the
dynamical evolution of a polymer in a 
-solvent that is rapidly
changed into a good solvent (swelling) or a bad solvent (collapse).
In the case of swelling, the density profile for intermediate times is
parabolic and expands in space as t1/3, as predicted by a
Flory-like continuum theory. The dynamics slows down after a time
when the chain becomes stretched, and the polymer gets
stuck in metastable "zig-zag"configurations, from which it escapes
through thermal activation. The size of the polymer in the final
stages is found to grow as
. In the case of collapse,
the chain very quickly (after a time of order unity) breaks up into
clusters of monomers ("pearls"). The evolution of the chain then
proceeds through a slow growth of the size of these metastable
clusters, again evolving as the logarithm of time. We enumerate the
total number of metastable states as a function of the extension of
the chain, and deduce from this computation that the radius of the
chain should decrease as
. We compute the total number
of metastable states with a given value of the energy, and find that
the complexity is non-zero for arbitrary low energies. We also obtain
the distribution of cluster sizes, that we compare to simple
"cut-in-two"coalescence models. Finally, we determine the aging
properties of the dynamical structure. The subaging behaviour that we
find is attributed to the tail of the distribution at small cluster
sizes, corresponding to anomalously "fast"clusters (as compared to
the average). We argue that this mechanism for subaging might hold in
other slowly coarsening systems.
61.25.Hq - Macromolecular and polymer solutions; polymer melts; swelling.
05.20.Dd - Kinetic theory.
64.70.Pf - Glass transitions.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2001
