Physical Relaxation

The equilibrium mechanical properties of soft polymeric networks (gels, elastomers) are described in some detail in Chapter 6. Ideally elastomers and covalently crosslinked gels are perfect solids that have no time dependence. The reality is quite different, in that there may be significant dissipation in the network due to a number of mechanisms, the most of important of which are retraction of loose network ends and the chemical scission of the network 

5 It should be emphasized that data of good precision covering a broad temperature range are needed to distinguish between the Arrhenius and WLF relationships. 

Early experiments with elastomers showed that the relaxation toward equilibrium was sharply dependent on crosslink density. It was found that tightly crosslinked networks relaxed very quickly, whereas networks with low crosslink density exhibited relaxation that covered an extremely broad time scale. These early experiments were correlated in terms of the expression for the tensile relaxation modulus E(t)  

---

Time-temperature superposition is frequently applied to the creep of thermoplastics. As mentioned above, a simple power law equation has proved to be useful in the modelling of the creep of thermoplastics. However, for many polymers the early stages of creep are associated with a physical relaxation process in which the compliance (D t)) changes progressively from a lower limit (Du) to an upper limit (DR). The rate of change in compliance is related to a characteristic relaxation time (x) by the equation ... 

In this chapter we shall concentrate on an overview of the physical relaxation processes relating to organic molecules, along with a simple kinetic analysis of these processes. More detailed accounts of the processes themselves will be covered in subsequent chapters. 

The observations of complex dynamics associated with electron-stimulated desorption or desorption driven by resonant excitation to repulsive electronic states are not unexpected. Their similarity to the dynamics observed in the visible and near-infrared LID illustrate the need for a closer investigation of the physical relaxation mechanisms of low energy electron/hole pairs in metals. When the time frame for reaction has been compressed to that of the 10 s laser pulse, many thermal processes will not effectively compete with the effects of transient low energy electrons or nonthermal phonons. It is these relaxation channels which might both play an important role in the physical or chemical processes driven by laser irradiation of surfaces, and provide dramatic insight into subtle details of molecule-surface dynamics. 

Assuming that (13.11) makes sense in the context of the system under investigation (i.e., that physical relaxation times are in the appropriate range for the condition of local equilibrium to be satisfactorily approximated), we seek the field-type differential equation that describes asymptotic (-evolution of fields Rfx, y, z, t) toward the known metric geometrical limit. Solutions of this equation are expected to describe a wide variety of thermal, acoustic, and diffusion phenomena in nonequilibrium conditions where local thermodynamic variables retain experimental meaning. 

When purely physical relaxation is of interest, there is advantage in making tests at very short times. To this end, Birley and Ahmad23 devised a... 

The first step, relaxation, involved achieving not only deep physical relaxation but also deep mental relaxation. The induction of such a relaxed state often required a considerable length of time, especially in the beginning it was not unusual for percipients to spend five to ten minutes on this step alone, even after they had learned it well. Modem systematic techniques for relaxing the body, such as Jacobson s progressive relaxation [38], autogenic training [119], or biofeedback procedures would probably work well. Comfortable meditative postures would probably also be effective. 

The third effect, a feeling of "peacefulness," also increases from the beginning of the hypnotic state through approximately 60. william reports that he is extremely peaceful at this point. Beyond 60, he says, that peacefulness is not a meaningful concept, as was the case with physical relaxation. As described later in connection with the plots of william s identity, there is no longer a self to be peaceful or not peaceful beyond this point. 

We can now define the connection between the physical relaxation processes and the internal structure of the direct self-energy diagram in Fig. 11a ... 

New qualities to taste Enjoy eating and eat very much More in the here-and-now Time passes more slowly Distance in walking changed Sexual orgasm has new, pleasurable qualities New qualities to touch Movements exceptionally smooth Get physically relaxed, don t want to move... 

These systems involve the irradiation of areas in a sheet of organic polymer, made by a vinyl polymerization reaction, to produce a change in refractive index. The effect is attributed to photopolymerization of residual monomer to yield a local increase in density. Diffusion of the monomer in the high-viscosity matrix is slow, as is the physical relaxation of the matrix it-itself, and the full index change takes some time to develop. 

The first effect, "physical relaxation," is not plotted beyond 20. According to... 

William his relaxation increases markedly as he is hypnotized and quickly reaches a value of extremely relaxed. However, he reports that after a depth of 50 it does not make sense to ask him about physical relaxation because he is no longer identified with his body his body is "just a thing, something I ve left behind." One does not rate the relaxation of things. 

In actual long term applications of polymers, however, it is well known that chemical reactions occur which actually change the viscoelastic properties of the material while it is in use. In addition, environmental factors such as exposure to solvents or even water, while not always chemically modifying a material, can have a profound influence on its viscoelastic properties in much the same way as a true chemical transformation. If predictions based exclusively on time-temperature correspondence were to be successful, the rates of all of these processes would have to vary with temperature in exactly the same m inner as does the viscoelastic spectrum. While this might be approximately true in certain special cases, it is usually not so. Thus, a more general theoretical framework is necessary to predict the properties of simultaneously chemically reacting and physically relaxing networks. 

---