Structural-relaxation time universal dependence

One theory that describes the temperature dependence of relaxation time and structural recovery is the Tool-Narayanaswamy-Moynihan (TNM) model developed to describe the often nonlinear relationship between heating rate and Tg. In this model, the structural relaxation time, x, is referenced as a function of temperature (T), activation enthalpy (Ah ), universal gas constant (R), hctive temperature (7)), and nonlinearity factor (x) (Tool, 1946 Narayanaswamy, 1971 Moynihan et al., 1976) ... 

It is noteworthy that the neutron work in the merging region, which demonstrated the statistical independence of a- and j8-relaxations, also opened a new approach for a better understanding of results from dielectric spectroscopy on polymers. For the dielectric response such an approach was in fact proposed by G. Wilhams a long time ago [200] and only recently has been quantitatively tested [133,201-203]. As for the density fluctuations that are seen by the neutrons, it is assumed that the polarization is partially relaxed via local motions, which conform to the jS-relaxation. While the dipoles are participating in these motions, they are surrounded by temporary local environments. The decaying from these local environments is what we call the a-process. This causes the subsequent total relaxation of the polarization. Note that as the atoms in the density fluctuations, all dipoles participate at the same time in both relaxation processes. An important success of this attempt was its application to PB dielectric results [133] allowing the isolation of the a-relaxation contribution from that of the j0-processes in the dielectric response. Only in this way could the universality of the a-process be proven for dielectric results - the deduced temperature dependence of the timescale for the a-relaxation follows that observed for the structural relaxation (dynamic structure factor at Q ax) and also for the timescale associated with the viscosity (see Fig. 4.8). This feature remains masked if one identifies the main peak of the dielectric susceptibility with the a-relaxation. 

Processes during a cell cycle are evidenced to be closely controlled cooperative events, including synchronisation within the ensemble. This caused us to describe relaxation within each cell by a Debye process, the relaxation time of which should increase with the size of the cell involved ( finite-size effect ). In that way ensemble structure and relaxation processes of cell ensembles are strictly interrelated. The universal energy density distribution and the universal relaxation mode distribution turn out to be copies of each other. Consequently, the spectrum depends only on the universal properties of the ensemble structure, i.e. on the value of p. Since all the cell populations studied here belong to the / = 3 class, the linear relaxation behaviour should show the same features. 

We have emphasized relaxation, regulation, and feed-down in this analysis to account for the remarkable universality, persistence, and specihcity of biochemical processes, and at the same time for the robustness and resilience of life as a whole. We expect that many universal pathways depend sensitively on the hne structure of chemistry and that these pathways would no longer be used by life if that structure were changed, perhaps even slightly. However, that does not lead us to conclude that some other structures would not arise in their place to fulfill similar functions. Thus, we try to avoid the hrst fallacy in a sensitivity analysis confusing adaptation to the environment with singularity o/the environment. 

The local dynamics is naturally strongly dependent on the exact chemical nature and structure of the polymer one studies. The large scale dynamics, however, is largely universal and is described with the Rouse model whereas for longer chains the tube model and reptation concept is believed to describe the chain dynamics [2]. It is easy to see that no single simulation method can capture the physics of polymer dynamics on all these length and time scales [3]. For situations where we can ignore quantum effects (which can, however, be important in polymer crystals [4]) MD simulations with chemically realistic force fields are the method of choice to study local relaxation. 

For the simulation of more complex flows, one needs a constitutive equation or a rheological equation of state. Nearly all of the many equations that have been proposed over the past fifty years are basically empirical in nature, and only in the last twenty-five years have such models been developed on the basis of mean field molecular theories, e.g., tube models. Although the early models were often developed with a molecular viewpoint in mind, it is best to think of them as continuum models or semi-empirical models. The relaxation mechanisms invoked were crude, involving concepts such as network rupture or anisotropic friction without the molecular detail required to predict a priori the dependence of viscoelastic behavior on molecular structure. While these lack a firm molecular basis and thus do not have universal validity or predictive capability, they have been useful in the interpretation of experimental data. In more recent times, constitutive equations have been derived from mean field models of molecular behavior, and these are described in Chapter 11. We describe in this section a few constitutive equations that have proven useful in one or another way. More complete treatments of this subject are given by Larson [7] and by Bird et al. [8]. 

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