Relaxation process, definition

A phenomenon closely related to electronic relaxation is the existence of diffuseness in the absorption spectra of the higher excited electronic states of molecules. It has been known for some time that very fast electronic relaxation processes occur when the higher excited states of molecules are caused to interact with radiation. It is remarkable then that only in relatively recent work has the association between these fast processes and spectral diffuseness been clearly focused upon. These spectral results provide some of the most definitive features that may be associated with the electronic relaxation mechanisms. First, the results from solid-state spectra 62 ... 

The final possibility, a uniformly interesting movie, would have to depict a process with thousands or millions of critical steps occuring in a definite order, each step necessary to understand the next, as in an industrial process, the functioning of a digital computer, or the development of an embryo. Enzymes, having been optimized by natural selection, may be expected to have somewhat complex mechanisms of action, perhaps with several equally important critical steps, but not with thousands of them. There is reason to believe that processes with thousands of reproducible non-trivial steps usually occur only in systems that are held away from thermal equilibrium by an external driving force. They thus belong to the realm of complex behavior in continuously dissipative open systems, rather than to the realm of relaxation processes in closed systems. 

The density matrix method is useful in treating relaxation processes, linear and non-linear laser spectroscopies and non-equilibrium statistical mechanics. In this chapter, the definition of density matrix and the equation of motion (EOM) it follows are introduced. The projection operator technique, which makes the density matrix method a very powerful tool in non-equilibrium statistical mechanics, is presented. 

In such a case, no conclusion about the mechanisms can be reached from the form of 4(t) and the observed rate will be determined primarily by the fastest process. By extension of the argument, one easily sees that marked deviation of any of the parallel processes from exponential decay will be reflected in the overall rate with possible change in the functional form. Thus, if the rotation is described by exp(-2D t) as in Debye-Perrin theory, and the ion displacements by a non-exponential V(t), one finds from eq 5 that 4(t) = exp(-2D t)V(t) and the frequency response function c(iw) = L4(t) = (iai + 2D ) where iKiw) = LV(t). This kind of argument can be developed further, but suffices to show the difficulties in unambiguous interpretation of observed relaxation processes. Unfortunately, our present knowledge of counterion mobilities and our ability to assess cooperative aspects of their motion are both too meagre to permit any very definitive conclusions for DNA and polypeptides. 

If the symmetry increases or decreases drastically, the spin-lattice relaxation process is fast, or the optical pumping is not successful in producing large spin alignment, the above rules would not be as definite. 

The free-volume concept is by no means rigorous, but it can be the basis of a useful empirical method of analyzing relaxation processes near the glass transition. We should also remark that other ways of defining free volume have been postulated (Ferry 1980 Miller 1978), but the definition presented here is perhaps the most accepted. 

In general, the most comprehensive and accurate information concerning various relaxation processes typical of a given polymer and determining its characteristic IMM can be obtained by studyii polymers that contain liuninescent grou (luminescent markers, LM or reporters ) purposely covalently bonded to definite parts of the macromolecules. Usually, the LM content in the polymer does not exceed 0.1 mol% (i.e., 1 LM per 1000 units of the polymer of the main structure). An increase in the LM content can obscure the properties of the macromolecule. 

A definitive step in extending the CM is to include the relaxation processes occurring before the a-relaxation and to establish the existence of the primitive... 

In the extended CM, the JG relaxation is just part of the continuous evolution of the dynamics. The JG relaxation should not be represented by a Cole-Cole or Havriliak-Negami distribution, as customarily assumed in the literature, and considered as an additive contribution to the distribution obtained from the Kohlrausch a-relaxation. Nevertheless, the JG relaxation may be broadly defined to include all the relaxation processes that have transpired with time up until the onset of the Kohlrausch a-relaxation. Within this definition of the JG relaxation, experiments performed to probe it will find that essentially all molecules contribute to the JG relaxation and the motions are dynamically and spatially heterogeneous as found by dielectric hole burning [180,283] and deuteron NMR [284] experiments. This coupling model description of the JG relaxation may help to resolve the different points of view of its nature between Johari [285] and others [180,226,227,280,281,283,284],... 

A recently developed modification of the pendent drop method gives definite area changes of the drop surface, which can be used to initiate transient relaxation processes (Miller et al. 1993a, b). A metering system consisting of two syringes (cf Fig. 6.7) is used to form a drop... 

By definition irreversible electronic relaxation processes cannot occur in isolated small and too-many level small (intermediate) case molecules because of the insufficient density of final levels. For long times the molecule senses the presence of a finite number of possible final levels instead of the effective continuum that is required to drive irreversible electron relaxation. When collisional processes are appended, it is clear that the continuous density of states of the colliding pair can provide the necessary driving force for irreversible relaxation. The observed magnitudes of electronic relaxation rates as well as dependencies on the initial state, perturbing molecules, temperature, and so on, are the aspects of the processes that are of central interest. 

Here, the internal viscosity is defined as the contribution of the glassy-relaxation process to the zero-shear viscosity. This definition is different from the common understanding of the term used in literature/ although both have similar notions as to the existence of an effect of fast sub-Rouse-segmental motions on polymer viscoelasticity. In the literature the term internal viscosity generally refers to the effect that would lead to a plateau value of the intrinsic viscosity at high frequencies. 

According to the present author the applicability of this definition depends on the patience of the experimentalist if he allows himself more time, then he might conclude that a relaxation process starts at low frequ cies (as depicted by the presence of a minimum in the loss modulus at low fiequencies) or after a long time in creep experiments. Another, more philosophical definition (or a complaint) could be ... 

There are two hypothetical limiting cases of interest. In one, an infinitely slow cooling rate maintains thermodynamic equilibrium to the ideal glass, and the equilibrium formalism is applicable. In the other a fluid in equilibrium (at its fictive temperature) is quenched infinitely fast to a temperature low enough so that no molecular transport occurs. In this case, what were dynamic fluctuations in time becomes static fluctuations in space. The most elementary treatment of this glass is then as a thermodynamic system with one additional parameter, the fictive temperature. In an actual experiment, of course, relaxations take place and the state of the system is dependent upon its entire thermal history and requires many parameters for its definition. Detailed discussion of the use of irreversible thermodynamics for the study of relaxation processes in liquids and glasses is contained in reviews by Davies (1956, 1960). 

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