Relaxation time primitive

The whole concept of symmetry and law becomes more palatable against the backdrop of approximate symmetries. Inviolate laws that militate against the scientific spirit, are then prevented by broken symmetries and developments in science amount to relaxing the primitive laws, so as to describe more general situations around the special cases dictated by exact symmetries, i.e. by maximizing the parameter e. Any law that reflects a symmetry must then be considered as a useful starting point rather than a final result and conclusions based on perceived symmetries of space and time must be revisited to identify the effects of broken symmetry on the laws of Nature. 

If both ends of the molecule are free to move, and so the chain can reptate, segments in the interior of the chain will relax faster by reptation than by primitive-path fluctuations, and so reptation will control the longest relaxation time of the chain. However, because primitive-path fluctuations are so much faster for the chain ends than for the chain center, the chain ends will still relax by primitive-path fluctuations. Only for very high molecular weights (MfMg 100) are the contributions of fluctuations confined to small enough portions of the chain ends that these effects can be neglected. 

In the above, X is the chain stretch, which is greater than unity when the flow is fast enough (i.e., y T, > 1) that the retraction process is not complete, and the chain s primitive path therefore becomes stretched. This magnifies the stress, as shown by the multiplier X in the equation for the stress tensor a, Eq. (3-78d). The tensor Q is defined as Q/5, where Q is defined by Eq. (3-70). Convective constraint release is responsible for the last terms in Eqns. (A3-29a) and (A3-29c) these cause the orientation relaxation time r to be shorter than the reptation time Zti and reduce the chain stretch X. Derive the predicted dependence of the dimensionless shear stress On/G and the first normal stress difference M/G on the dimensionless shear rate y for rd/r, = 50 and compare your results with those plotted in Fig. 3-35. 

Si, S2, S3 T V numerical coefficients of order unity obtains from summations temperature unit tangent vector for a primitive 0 T context) a, fi component of the stress tensor relaxation time... 

Different relaxation functions are derived assuming that the real (physical) ensemble of relaxation times is confined between the upper and lower limits of self-similarity. It is predicted that at times, shorter than the relaxation time at the lowest (primitive) self-similarity level the relaxation should be of classical, Debye-like type, whatever the pattern of nonclassical relaxation at longer times. The analysis of diffusion for a Brownian particle, where the assumption that the... 

In like manner, it becomes easy to predict the pattern of anomalous, nonexponential relaxation at times, shorter than the relaxation time X at the lowest (i.e., 1-st) self-similarity level. This level may be considered as the primitive one (in a sense that it cannot be further tesselated into subclusters) hence, the relaxation should be of a classical, Debye-like type,... 

The fractional exponent KWW can be rewritten as (1 — n), where n is the coupling parameter of the CM. The breadth of the dispersion is reflected in the magnitude of n and increases with the strength of the intermolecular constraints. The dispersion and the structural relaxation time are simultaneous consequences of the many-molecule dynamics, and hence they are related to each other. The intermolecularly cooperative dynamics are built upon the local independent (primitive) relaxation, and thus a relation between the primitive relaxation time To and Ta is expected to exist. The CM does not solve the many-body relaxation problem but uses a physical principle to derive a relation between Ta and To that involves the dispersion parameter, n. This defining relation of the CM... 

From the view that the a-relaxation is the product of the cooperative dynamics originating from the JG or primitive relaxation, it is natural to expect that the properties of the JG relaxation will mimic those of the structural relaxation. We consider the relaxation time as well as the relaxation strength of the JG relaxation. 

In the previous subsection, we have provided conceptually the rationale and experimentally some data to justify the expectation that the primitive relaxation time To of the CM should correspond to the characteristic relaxation time of the Johari-Go Id stein (JG) secondary relaxation Xjg- Furthermore, it is clear from the CM relation, Ta = ( "to)1 1- , given before by Eq. 6 that To mimics Ta in behavior or vice versa. Thus, the same is expected to hold between Xjg and Ta. This expectation is confirmed in Section V from the properties of tjg- The JG relaxation exists in many glass-formers and hence there are plenty of experimental data to test the prediction, xjG T,P) xo(T,P). Broadband dielectric relaxation data collected over many decades of frequencies are best for carrying out the test. The fit of the a-loss peak by the one-sided Fourier transform of a Kohlrausch function [Eq. (1)] determines n and Ta, and together with tc 2 ps, To is calculated from Eq. 6... 

Figure 46. Relaxation map of PET showing the primary relaxation and three secondary relaxations. The calculated primitive relaxation time are represented by stars. [A. Sanz, A. Nogales, and T. Ezquerra, paper presented at the 5th International Discussion Meeting on Relaxation in Complex Systems, July 7-13, 2005 and to be published in J. Non-Cryst. Solids 2006.]...

In the previous section, at temperatures above 7g, the Johari-Goldstein relaxation time has been shown to correspond well to the primitive relaxation time, and both are related to the structural a-relaxation time by Eq. (10). This equation should continue to hold at temperatures below T,. However, testing this relation in the glassy state is difficult because of either the scarcity or the unspecified thermal history of the data on the a-relaxation time xa. In fact, a reliable characterization of the structural relaxation can be acquired only at equilibrium, and such condition is rarely satisfied below Tg. Glassy systems are nonergodic, and their properties can depend on aging time and thermal history. Anyway, for glasses in isostructural state with a constant Active temperature Tf, both ra and To as well as Xjg should have Arrhenius dependences with activation enthalpies Ea, Eq, and Ejg respectively. Eq. (10) leads us to the relation... 

Figure 50. Temperature dependencies of the various relaxation times of OTP. Filled circles are a-relaxation times of bulk OTP obtained by photon correlation spectroscopy open diamonds are JG relaxation times obtained by dielectric spectroscopy open circles are the primitive relaxation times x0 of bulk OTP calculated by Eq. (10). The photon correlation spectroscopy relaxation times of OTP confined in 7.5-nm pores (A) 5.0-nm pores ( ) 2.5-nm pores ( ).

---