Relaxation molecular motion

Regardless of the types of molecular motion, relaxation occurs only if there is some specific interaction between the nucleus and its environment that can result in energy exchange. We now describe the six interactions that have been mentioned, beginning with the one that is always present—the interaction between nuclear magnetic dipoles. In the following treatment of each of these relaxation mechanisms, we shall focus on the relaxation rate R.x = 1/Tb as the overall relaxation rate is the sum of the rates produced by each mechanism. 

The influence of temperature and strain rate can be well represented by Eyring s law physical aging leads to an increase of the yield stress and a decrease of ductility the yield stress increases with hydrostatic pressure, and decreases with plasticization effect. Furthermore, it has been demonstrated that strain rate. Strueture property relationships display similar trends e.g., Oy increases with the ehain stiffness through a Tg increase and yielding is favored by the existence of mechanically active relaxations due to local molecular motions ( relaxation). 

We begm tliis section by looking at the Solomon equations, which are the simplest fomuilation of the essential aspects of relaxation as studied by NMR spectroscopy of today. A more general Redfield theory is introduced in the next section, followed by the discussion of the coimections between the relaxation and molecular motions and of physical mechanisms behind the nuclear relaxation. 

Another aspect of plasticity is the time dependent progressive deformation under constant load, known as creep. This process occurs when a fiber is loaded above the yield value and continues over several logarithmic decades of time. The extension under fixed load, or creep, is analogous to the relaxation of stress under fixed extension. Stress relaxation is the process whereby the stress that is generated as a result of a deformation is dissipated as a function of time. Both of these time dependent processes are reflections of plastic flow resulting from various molecular motions in the fiber. As a direct consequence of creep and stress relaxation, the shape of a stress—strain curve is in many cases strongly dependent on the rate of deformation, as is illustrated in Figure 6. 

The stress—relaxation process is governed by a number of different molecular motions. To resolve them, the thermally stimulated creep (TSCr) method was developed, which consists of the following steps. (/) The specimen is subjected to a given stress at a temperature T for a time /, both chosen to allow complete orientation of the mobile units that one wishes to consider. (2) The temperature is then lowered to Tq T, where any molecular motion is completely hindered then the stress is removed. (3) The specimen is subsequendy heated at a controlled rate. The mobile units reorient according to the available relaxation modes. The strain, its time derivative, and the temperature are recorded versus time. By mnning a series of experiments at different orientation temperatures and plotting the time derivative of the strain rate observed on heating versus the temperature, various relaxational processes are revealed as peaks (243). 

Anisotropy of molecular motion monosubstituted benzene rings, e.g. phenyl benzoate (44), show a very typical characteristic in the para position to the substituents the CH nuclei relax considerably more rapidly than in the ortho and meta positions. The reason for this is the anisotropy... 

Both spin-lattice and spin-spin relaxation depend on rates of molecular motion, for relaxation results from the interaction of fluctuating magnetic fields set up by nuclei in the spin system and in the lattice. A quantitative theory of this dependence was given by Bloembergen et al., who obtained... 

Turning from chemical exchange to nuclear relaxation time measurements, the field of NMR offers many good examples of chemical information from T, measurements. Recall from Fig. 4-7 that Ti is reciprocally related to Tc, the correlation time, for high-frequency relaxation modes. For small- to medium-size molecules in the liquid phase, T, lies to the left side of the minimum in Fig. 4-7. A larger value of T, is, therefore, associated with a smaller Tc, hence, with a more rapid rate of molecular motion. It is possible to measure Ti for individual carbon atoms in a molecule, and such results provide detailed information on the local motion of atoms or groups of atoms. Levy and Nelson " have reviewed these observations. A few examples are shown here. T, values (in seconds) are noted for individual carbon atoms. 

Nuclear dipole-dipole interaction is a veiy important relaxation mechanism, and this is reflected in the relationship between 7, and the number of protons bonded to a carbon. The motional effect is nicely shown by tbe 7 values for n-decanol, which suggest that the polar end of the molecule is less mobile than the hydrocarbon tail. Comparison of iso-octane with n-decanol shows that the entire iso-octane molecule is subject to more rapid molecular motion than is n-decanol—compare the methyl group T values in these molecules. 

The relaxation modulus (or any other viscoelastic function) thus obtained is a mean s of characterizing a material. In fact relaxation spectra have been found very useful in understanding molecular motions of plastics. Much of the relation between the molecular structure and the overall behavior of amorphous plastics is now known. 

Up to now it has been tacitly assumed that each molecular motion can be described by a single correlation time. On the other hand, it is well-known, e.g., from dielectric and mechanical relaxation studies as well as from photon correlation spectroscopy and NMR relaxation times that in polymers one often deals with a distribution of correlation times60 65), in particular in glassy systems. Although the phenomenon as such is well established, little is known about the nature of this distribution. In particular, most techniques employed in this area do not allow a distinction of a heterogeneous distribution, where spatially separed groups move with different time constants and a homogeneous distribution, where each monomer unit shows essentially the same non-exponential relaxation. Even worse, relaxation... 

Molecular Motion in amorphous atactic polystyrene (PS) is more complicated and a number of relaxation processes, a through 5 have been detected by various techniques as reviewed recently by Sillescu74). Of course, motions above and below the glass transition temperature Tg have to be treated separately, as well as chain and side group mobility, respectively. Motion well above Tg as well as phenyl motion in the glassy state, involving rapid 180° jumps around their axes to the backbone has been discussed in detail in Ref.17). Here we will concentrate on chain mobility in the vicinity of the glass transition. 

The accessibility of chitin, mono-O-acetylchitin, and di-O-acetylchitin to lysozyme, as determined by the weight loss as a function of time, has been found to increase in the order chitin < mono-O-acetylchitin < di-O-acetylchitin [120]. The molecular motion and dielectric relaxation behavior of chitin and 0-acetyl-, 0-butyryl-, 0-hexanoyl and 0-decanoylchitin have been studied [121,122]. Chitin and 0-acetylchitin showed only one peak in the plot of the temperature dependence of the loss permittivity, whereas those derivatives having longer 0-acyl groups showed two peaks. 

The dramatic slowing down of molecular motions is seen explicitly in a vast area of different probes of liquid local structures. Slow motion is evident in viscosity, dielectric relaxation, frequency-dependent ionic conductance, and in the speed of crystallization itself. In all cases, the temperature dependence of the generic relaxation time obeys to a reasonable, but not perfect, approximation the empirical Vogel-Fulcher law ... 

One further point needs to be mentioned when probing the feasibility of a particular experiment. Apart from its dependence on temperature and concentration (for instance of ions, solutes, impurities, isotopes), relaxation times - in particular the longitudinal relaxation time Tj - depend on the field strength. This can be understood from the concept that energy exchange is most efficient if the timescale of molecular motion is equal to the Larmor frequency. Often, molecular motion takes place over a wide range of frequencies, so that the func-... 

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