THE INFLUENCE OF THE COOLING RATE ON THE GLASS-TRANSITION AND THE GLASSY STATE IN 3-DIMENSIONAL DENSE POLYMER MELTS - A MONTE-CARLO STUDY

In this Monte Carlo simulation we study the glass transition of a dense three-dimensional polymer melt using a lattice model (a bond-fluctuation model on a simple cubic lattice) that was highly optimized for a vector supercomputer. Long bonds are symmetrically favoured to create a competition between bond energy and packing constraints, which prevents the melt from crystallizing when it freezes. The onset of this freezing can be monitored by the temperature variation of various static quantities that probe both the length scale of a bond vector, such as the mean bond length and mean energy per bond, and that of the whole chain, such as the radius of gyration. As the melt vitrifies, these quantities gradually become independent of temperature in a narrow range around T almost-equal-to 0.2 (the temperature is measured in units of an energy parameter, epsilon, introduced in the model Hamiltonian) and their value at low temperatures is strongly influenced by the cooling rate. It is thus possible to infer from these curves the cooling-rate dependence of the freezing temperature T(g). This analysis, which was done for fourteen different cooling rates covering two decades, shows that T(g) does not necessarily vary linearly with the logarithm of the cooling rate, but can also be well described by a 'Vogel-Fulcher' type of equation, giving a freezing temperature of T(K) almost-equal-to 0.17 at an infinitely slow cooling rate. The type of cooling-rate dependence of T(g) that is found depends upon the physical quantity from which it is derived and upon the size of the studied temperature and cooling-rate interval. Despite the difference in the detailed dependence of T(g) on the cooling rate, the extrapolated value T(K) coincides with the Vogel-Fulcher temperature T0, obtained from the temperature variation of the diffusion coefficient, within the error bars.