Eur. Phys. J. E 4, 371-387
Heterogeneous dynamics at the glass transition in van der Waals liquids, in the bulk and in thin films
D. Long1 and F. Lequeux21 Laboratoire de Physique des Solides, Université de Paris XI, Bât. 510, 91405 Orsay Cédex, France
2 Laboratoire de Physico-Chimie Macromoléculaire, École Supérieure de Physique et de Chimie Industrielles de la Ville de Paris, 10 rue Vauquelin, F-75231 Paris Cédex 05, France
(Received 21 March 2000 and Received in final form 4 December 2000)
Abstract
It has been shown over the last few years that
the dynamics close to the glass transition is strongly heterogeneous, both
by measuring the diffusion coefficient of tagged particles or by NMR
studies.
Recent experiments have also demonstrated that
the glass transition temperature
of thin polymer films can be shifted as compared to the same
polymer in the bulk.
We propose here first a thermodynamical
model for van der Waals liquids, which accounts for experimental
results regarding the bulk modulus of polymer melts and the evolution
of the density with temperature. This model allows us
to describe the density fluctuations in such van der Waals liquids.
Then, by considering the thermally induced density fluctuations in the bulk,
we propose that the 3D glass transition
is controlled by the percolation of small domains of slow
dynamics, which allows to explain the heterogeneous dynamics close
to 
.
We show then that these domains percolate
at a lower temperature in the quasi-2D case of thin suspended
polymer films and
we calculate the corresponding glass transition
temperature reduction, in quantitative agreement
with experimental results of Jones and co-workers.
In the case of strongly adsorbed films, we show that the strong adsorption
amounts to enhance the slow domains percolation. This effect
leads to 1) a broadening of the glass transition and 2) an increase of
in quantitative agreement with experimental results. For both strongly
and weakly adsorbed films, the shift in is given by a power
law, the exponent being the inverse of that of the correlation length
of 3D percolation.
64.70.Pf - Glass transitions.
68.15.+e - Liquid thin films.
61.41.+e - Polymers, elastomers and plastics.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2001
