Relaxation rate, free volume model

After describing and justifying the underlying assumptions of the free-volume model, we apply it to calculate all the thermodynamic quantities of interest. We also include in our model the effects of slow relaxation rates, so that our results can be compared directly to experiment. We still do not have many rigorous results. Instead, we have a simple picture of a quite complex set of phenomena. We have built a single, unified theory from which one can continue to study all aspects of the transition. Although the theory has its weaknesses, which principally result from the necessity to make approximations along the way, it has the desired robustness from which to proceed further. 

Here we wish to describe how the effect of these strongly temperature-dependent structural relaxation rates near Tg can be incorporated into the free-volume model. Our analysis differs significantly from that described above because we have at our disposal an equilibrium theory of the heat capacity and volume to begin our discussion. By starting from a concrete... 

The free-volume model was originally derived to explain the temperature dependence of the viscosity. We have shown that it has a much broader application and can explain many of the outstanding experimental observations. This includes the existence of an entropy catastrophe at 7 and the approximate equality of Tj, and 7], first observed by Angell and coworkers.The relation between ln and 7, measured by Moynihan et al., also follows naturally and quantitatively from the notion that the liquidlike cell fraction p is the important variable that ceases to reach equilibrium when the relaxation rates become longer than the time scale for the measurement. 

Here, only the athermal version of the DLL model has been described. It has been shown elsewhere [11 13] that the model is able to represent the temperature dependent dynamics of systems as well. This, however, requires additional assumptions concerning free volume distribution and related potential barriers for displacements of individual elements. It has been demonstrated [11-13] that in such a version the model can describe a broad class of temperature dependencies of relaxation rates in supercooled liquids with the variety of behavior ranging between the extremes described by the free volume model on one side and the Arrhenius model on the other side. 

Experimental data on nitrogen obtained from spin-lattice relaxation time (Ti) in [71] also show that tj is monotonically reduced with condensation. Furthermore, when a gas turns into a liquid or when a liquid changes to the solid state, no breaks occur (Fig. 1.17). The change in density within the temperature interval under analysis is also shown in Fig. 1.17 for comparison. It cannot be ruled out that condensation of the medium results in increase in rotational relaxation rate primarily due to decrease in free volume. In the rigid sphere model used in [72] for nitrogen, this phenomenon is taken into account by introducing the factor g(ri) into the angular momentum relaxation rate... 

Steady-state behavior and lifetime dynamics can be expected to be different because molecular rotors normally exhibit multiexponential decay dynamics, and the quantum yield that determines steady-state intensity reflects the average decay. Vogel and Rettig [73] found decay dynamics of triphenylamine molecular rotors that fitted a double-exponential model and explained the two different decay times by contributions from Stokes diffusion and free volume diffusion where the orientational relaxation rate kOI is determined by two Arrhenius-type terms ... 

Relaxation times for water filling the pores of an NaX specimen have been fitted to a model with the following assumptions (a) coupling, as above, of molecular diffusion and rotation (b) the median jump time r is governed by a free volume law (allows the curvature in the plots of jump rate, (3r) x vs. 10S/T in Figure 5), and (c) a broad distribution of correlation times (allows a better fit to the data, accounts for an apparent two-phase behavior in T2 (31, 39), and is reasonable in terms of the previous discussion of Pi(f) and r). 

This time-dependent behavior v ould be expected based on the model that as the network chains lose mobility during the aging process (due to the decrease in free volume), the ability to dissipate stress is reduced. The decrease in stress relaxation rate can therefore be explained on the basis of free volume collapse during physical aging. 

The cylinder stretching protocol appears to work very well for simple solvent-free membrane models [111, 113, 114], but with more refined models this method suffers from two drawbacks, both related to the equifibration of a chemical potential. First, the cylinder separates the simulation volume into an inside and an outside. If solvent is present, its chemical potential must be the same in these two regions, but for more highly resolved models the solvent permeability through the bilayer is usually too low to ensure automatic relaxation. Second, the chemical potential of lipids also has to be the same in the two bilayer leaflets, and again for more refined models the lipid flip-flop rate tends to be too low for this to happen spontaneously. 

Gravity is an important parameter which affects the relaxation process following sudden cooling. To take the gravity into account in the RSC model, we further assume that the downward transition rate is proportional to the free volume in a given region, i.e., (l+otck). Here k is the index of the... 

Understanding the mechanisms of polar order decay is crucial for the tailoring of new exploitable active materials. In contrast with crystals, polymers containing oriented molecules tend to evolve towards a randomization of dipole orientation when the field is removed. Relaxation in such poled systems, following the molecular statistical model, arises from thermal reorientation whose rate is governed by the mobility of the molecules in the matrix. The mobility is in turn determined by a number of parameters including, in particular, glass transition temperature (Tg) and the amount of free volume in the polymer. 

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