Out-of-equilibrium dynamics

The aim of this chapter is to show how the concepts of FDT violation and effective temperature can be illustrated in the framework of the above quoted system, as done experimentally in Ref. 12 and theoretically in Refs. 15-19. We do not discuss here the vast general domain of aging effects in glassy systems, which are reviewed in Refs. 2-4. Since the present contribution should be understood by beginners in the field, some relevant fundamental topics of equilibrium statistical physics—namely, on the one hand, the statistical description of a system coupled to an environment and, on the other hand, the fluctuation-dissipation theorem (in a time domain formulation)—are first recalled. Then, questions specifically related to out-of-equilibrium dynamics, such as the description of aging effects by means of an effective temperature, are taken up in the framework of the above-quoted model system. 

When out-of-equilibrium dynamic variables are concerned, as will be the case in the following sections of this chapter, the equilibrium fluctuation-dissipation theorem is not applicable. In order to discuss properties such as the aging effects which manifest themselves by the loss of time translational invariance in... 

The time-domain formulation constitutes a proper framework for the necessary modifications of the fluctuation-dissipation formulas when the frequency-dependent quantities cannot be properly defined, as may be the case when out-of-equilibrium dynamic variables are concerned. 

Therefore, the maximum of Cp °° occurs where the correlation length associated with the tetrahedral order is maximum, i.e. along the Widom line associated with the LL phase transition." In MF we may compare Cp calculated for the LLCP scenario J(j > 0) with Cp calculated for the SF scenario J(j = 0) [Fig. 7(b)]. We see that the sharper maximum is present only in the LLCP scenario, while the less sharp maximum occurs at the same T in both scenarios. We conclude that the sharper maximum is due to the fluctuations of the tetrahedral order, critical at the LLCP, while the less sharp maximum is due to fluctuations in bond formation. The similarity of our results with the experiments in nanopores is striking. Data in ref. [ °] show two maxima in Cp. They have been interpreted as an out-of-equilibrium dynamic effect in [ °], but more recent experiments show that they are a feature of equilibrated confined water. Therefore, our interpretation of the two maxima is of considerable interest. 

Concerning confined polymers exhibiting slowing-down of both the equilibrium and the out-of-equilibrium dynamics, the obvious conclusion is that there exists full interdependence between the two aspects of glassy dynamics in confinement. This agrees with findings on bulk glass former, which, as shown by several studies, display the same interdependence [20, 41, 74, 87, 153, 163, 180]. 

The critical analysis of recently published experimental results allows concluding that, dififerentiy firom bulk glass formers [41, 74, 86, 180], the equilibrium and out-of-equilibrium dynamics are decoupled in confinement [16, 23]. In other words, it is not possible to describe the Tg and the kinetics of equilibrium recovery... 

Free Interface and Out-of-Equilibrium Dynamics in Confined Polymers... 

A concern in the application of the model originates from the fact that, above a confinement length scale of the order of microns, the out-of-equilibrium dynamics exhibit no dependence on such length scale. Hence, on increasing the confinement... 

In recognizing that arguments based on the rate of spontaneous fluctuations fail to describe the out-of-equilibrium dynamics and in view of recent activity on the influence of adsorption on the glassy dynamics in confinement, we identify the free interfacial surface as the main parameter determining the magnitude of negative deviations from bulk behaviour. In doing so, we emphasize how a suitable model for the description of the out-of-equilibrium dynamics in confinement must account for the presence of dominant bulk linear dynamics and the amount of free interface. We show how there exists solid indications that the FVHD model nicely fits in the idea that the free interface is the key parameter to describe the out-of-equilibrium dynamics in confinement. 

---