Physical aging relaxation time scales

This chapter relates to some recent developments concerning the physics of out-of-equilibrium, slowly relaxing systems. In many complex systems such as glasses, polymers, proteins, and so on, temporal evolutions differ from standard laws and are often much slower. Very slowly relaxing systems display aging effects [1]. This means in particular that the time scale of the response to an external perturbation, and/or of the associated correlation function, increases with the age of the system (i.e., the waiting time, which is the time elapsed since the preparation). In such situations, time-invariance properties are lost, and the fluctuation-dissipation theorem (FDT) does not hold. 

Monte Carlo simulation results for the non-equilibrium and equilibrium d3oiamics of a glassy polymer melt are presented. When the melt is rapidly quenched into the supercooled state, it freezes on the time scale of the simulation in a non-equilibrium structure that ages physically in a fashion similar to experiments during subsequent relaxation. At moderately low temperatures these non-equilibrium effects can be removed completely. The structural relaxation of the resulting equilibrated supercooled melt is strongly stretched on all (polymeric) length scales and provides evidence for the time-temperature superposition property. 

A systematic study of the relaxation of rubbing induced birefringence in PS has been conducted. Extensive and clear experimental evidence have been foimd that show the absence of the physical aging effects in the relaxation of RIB, and the relaxation of RIB involves very small length scales. The RIB relaxation is then modeled by a relaxation times distribution function that depends only on temperature but not on thermal or strain history. An individual birefringence elements model has been proposed and a systematic way has been devised to extract the parameters in the model from specifically designed experiments, namely the Temperature Lag measurements and the Continuous Curve measurements. The results predicted by the model agree well with experiments. 

As the annealing temperatures T drop further away from Tg, the aging process slows down and the time scales involved become quite long. Consequently many studies are carried out under thermally accelerated conditions. The relaxation of the enthalpy and volume of the glass are convenient parameters to follow when monitoring the physical aging process, as are the time-dependent small strain mechanical properties. Spectroscopic and scattering methods can also be employed... 

Equation (7) is also only valid for a short-term creep experiment in which the time of creep is short relative to the time scale of aging such that the characteristic relaxation time is constant. It is noted that the relaxation function of equation (7) has the correct limits and differs from the Kohlrausch compliance function J = Js ) which was suggested initially by Struik (14) and which is not physically meaningful at long times (28). 

When structural-rheological simplicity does not hold and, for example, fi in equation (7) changes with physical aging, exact reduction of the creep or stress relaxation cnrves cannot be accomplished. However, it is estimated by the author that a change in the KWW parameter of approximately 5-10% would result in a deviation of the logarithm of the aging time shift factor (log ate) of 0.05 over two decades in time scale. Scatter in reduced curves of this order of magnitude is often observed because of the scatter in the creep or stress relaxation data (23,39,40). Researchers have not systematically looked for such small deviations in their rednced curves. 

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