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Soft Matter and Biological Physics

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. Lequeux2

1  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)

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 $T_{\rm g}$. 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 $T_{\rm g}$ in quantitative agreement with experimental results. For both strongly and weakly adsorbed films, the shift in $T_{\rm g}$ 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