Finite-Size Effect in the Dynamics Near the Glass Transition

Abstract

The dynamics near the glass transition in a two-dimensional lattice model of polymer melt is studied by Monte Carlo simulation. Mean-square displacements of the individual monomers as well as of the centres of mass of the polymers are observed for over seven decades of time which provide quite reliable equilibrated values (corresponding to the results from a quasi-static cooling measurement) of the diffusion constant. The diffusion constants are determined as a function of temperature and size of the lattice (keeping the density of the monomers and the degree of polymerization fixed). A striking size dependence is shown by the diffusion constant at low temperatures, which suggests the possibility of the existence of strongly cooperatively rearranging regions in the system, as was postulated by Adam and Gibbs. Our results indicate the increase of the mean size of such regions as the temperature is lowered.