A Model for Relaxation in Supercooled Liquids and Polymer Melts
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ABSTRACT A new model for molecular rearrangements in liquids is proposed. The liquids are regarded as dense ensembles of vibrating molecules satisfying the excluded volume condition. A continuity condition is applied on the molecular scale of such systems and is regarded as controlling rearrangements leading to translations of molecules beyond the range of their vibration amplitude. It results in cooperative rearrangements which are considered as taking place in systems with fluctuating density. Rates of rearrangements are considered as being controlled by thermal activation with activation energy barriers dependent on local density. Various dependencies of the activation energy barriers on local density are examined. It is shown, that the model is able to reproduce the extremal cases of temperature dependencies of relaxation times represented on one edge by the Arrhenius relation and on the other edge by the Vogel-Fulcher-Tamman relation. The model can, however, provide a broad spectrum of other dependencies filling the gap between these extremes. All cases are based on the uniform microscopic picture of cooperative molecular rearrangements resulting from system continuity. The model is implemented as a simulation algorithm (Dynamic Lattice Liquid - DLL algorithm) which is used to simulate dynamic properties of liquids and polymer melts. Simulation results obtained for polymers are compared with experimental results obtained by means of the dynamic mechanical measurements on polyisobutylene samples with various molecular weights. INTRODUCTION Due to a dense packing of molecules, the dynamic properties of liquids become complex and the relaxations extend over various, usually well distinguishable, time scales [e.g. 1-3]. On the short time scale, Tv, the molecules oscillate around some quasi-fixed positions being temporarily "caged" by neighbors. It is believed that more extensive translational motions of molecules take place on a much longer time scale, %o,due to breaking down of cages by cooperative processes. Trajectories of molecules consist, therefore, both of oscillatory components and of occasional longer range translational movements between subsequent quasi-fixed states, as illustrated in Figure 1.The macroscopic flow of the liquid is related to the longer time scale ('rT), in which the arrangement of molecules becomes unstable because each molecule wanders through the material changing neighbors during the translational motion steps. Fig. 1. Schematic illustration of a trajectory of a molecule in a liquid as composed of vibrational and translational parts.
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translation 211 Mat. Res. Soc. Symp. Proc. Vol. 455 01997 Materials Research Society
Although the picture of motion in a liquid shown above is commonly accepted and partially documented by computer simulations of dense Lennard-Jones systems [4,5], it is not quite clear under which conditions single diffusion steps can occur. Theories of transport phenomena in liquids do not consider this problem explicitly. In theories based on the picture
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