Transition relaxation process

Another example of an application of Eq. (145) is on microcomposite polymer materials. We have performed dielectric measurements of the glass transition relaxation process in a nylon-6,6 sample quenched in amorphous (QN), a crystalline nylon-6,6 sample (CN), and a microcomposite sample (MCN), which is the same crystalline nylon-6,6 but with incorporated kevlar fibers [275,276],... 

Over the past two decades, DMA has proven to be a useful technique for the characterisation of biomaterials since it not only gives a quantitative assessment of material properties such as stiffness and damping, but also provides structural information. This is because the dynamic mechanical properties of materials are sensitive to aU kinds of transitions, relaxation processes, structural heterogeneity and morphology of multi-phase systems such as crystalline polymers, polyblends and composites. DMA can also pinpoint thermal transitions for example, typical output of tan 8 versus temperature will display a peak at Tg. Above 7, peaks correspond to the crystalline regions and eventually Tm. As a technique, DMA is also sensitive for the characterisation of polymers of similar chemical compositions, as well as detecting the presence of moderate quantities of additives such as plasticisers or leachable materials. For example, PVC is very stiff, however, with the addition of plasticisers it can be made more flexible. 

Voth G A and Hochstrasser R M 1996 Transition state dynamics and relaxation processes in solutions a frontier of physical chemistry 100 13034M9... 

Determination of the glass-transition temperature, T, for HDPE is not straightforward due to its high crystallinity (16—18). The glass point is usually associated with one of the relaxation processes in HDPE, the y-relaxation, which occurs at a temperature between —100 and —140° C. The brittle point of HDPE is also close to its y-transition. 

T. Hashimoto, T. Miyoshi and H. Ohtsuka, Investigation of the relaxation process in the Cu3Au-alloy order-disorder phase transition near the transition point, Phys. Rev. B 13.1119 (1976). 

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. 

Because non-adiabatic collisions induce transitions between rotational levels, these levels do not participate in the relaxation process independently as in (1.11), but are correlated with each other. The degree of correlation is determined by the kernel of Eq. (1.3). A one-parameter model for such a kernel adopted in Eq. (1.6) meets the requirement formulated in (1.2). Mathematically it is suitable to solve integral equation (1.2) in a general way. The form of the kernel in Eq. (1.6) was first proposed by Keilson and Storer to describe the relaxation of the translational velocity [10]. Later it was employed in a number of other problems [24, 25], including the one under discussion [26, 27]. 

In the oxidized form, the weak coupling of the high-spin Fe(III) ion to its surroundings amd the very large ligand-field energy of about 10,000 cm (12) are not liable to give rise to very efficient relaxation processes (see Appendix). However, the S = 5/2 manifold provides a set of transitions for multiple direct processes that may be efficient... 

The transitions between energy levels in an AX spin system are shown in Fig. 1.44. There are four single-quantum transitions (these are the normal transitions A, A, Xi, and X2 in which changes in quantum number of 1 occur), one double-quantum transition 1% between the aa and j8 8 states involving a change in quantum number of 2, and a zero-quantum transition 1% between the a)3 and fia states in which no change in quantum number occurs. The double-quantum and zero-quantum transitions are not allowed as excitation processes under the quantum mechanical selection rules, but their involvement may be considered in relaxation processes. 

If only single-quantum transitions (h, I2, S], and S ) were active as relaxation pathways, saturating S would not affect the intensity of I in other words, there will be no nOe at I due to S. This is fairly easy to understand with reference to Fig. 4.2. After saturation of S, the fMjpula-tion difference between levels 1 and 3 and that between levels 2 and 4 will be the same as at thermal equilibrium. At this point or relaxation processes act as the predominant relaxation pathways to restore somewhat the equilibrium population difference between levels 2 and 3 and between levels 1 and 4 leading to a negative or positive nOe respectively. 

For a reUable extraction of distances, it is important that dipolar relaxation is strongly dominating other relaxation processes. Hence, it is important to avoid paramagnetic ions or molecules such as transition metals or (paramagnetic) oxygen. Especially solution of small molecules therefore have to be carefully degased. 

Several types of spin-lattice relaxation processes have been described in the literature [31]. Here a brief overview of some of the most important ones is given. The simplest spin-lattice process is the direct process in which a spin transition is accompanied by the creation or annihilation of a single phonon such that the electronic spin transition energy, A, is exchanged by the phonon energy, hcoq. Using the Debye model for the phonon spectrum, one finds for k T A that... 

Ammonium alums undergo phase transitions at Tc 80 K. The phase transitions result in critical lattice fluctuations which are very slow close to Tc. The contribution to the relaxation frequency, shown by the dotted line in Fig. 6.7, was calculated using a model for direct spin-lattice relaxation processes due to interaction between the low-energy critical phonon modes and electronic spins. 

Spin-spin relaxation is primarily induced by magnetic dipole interactions between paramagnetic ions. Usually, the most important spin-spin relaxation process is the so-called cross-relaxation process in which a transition of an ion / from the state K) to toe state is accompanied by a transition of another ion j from the... 

Fig. 6.9 Schematic illustration of a cross-relaxation process by which the ion i performs a transition a, accompanied by a transition of a neighboring ion, j. (Reprinted with permission from [38] copyright 1979 by Elsevier)...

Fig. 8.10 Schematic illustration of LIES ST and reverse LIESST oidicf complex. Spin allowed d-d transitions are denoted by arrows and the radiationless relaxation processes by wavy lines (from [21])...

A major limitation of CW double resonance methods is the sensitivity of the intensities of the transitions to the relative rates of spin relaxation processes. For that reason the peak intensities often convey little quantitative information about the numbers of spins involved and, in extreme cases, may be undetectable. This limitation can be especially severe for liquid samples where several relaxation pathways may have about the same rates. The situation is somewhat better in solids, especially at low temperatures, where some pathways are effectively frozen out. Fortunately, fewer limitations occur when pulsed radio and microwave fields are employed. In that case one can better adapt the excitation and detection timing to the rates of relaxation that are intrinsic to the sample.50 There are now several versions of pulsed ENDOR and other double resonance methods. Some of these methods also make it possible to separate in the time domain overlapping transitions that have different relaxation behavior, thereby improving the resolution of the spectrum. 

In the theory of deuteron spin-lattice relaxation we apply a simple model to describe the relaxation of the magnetizations T and (A+E), for symmetry species of four coupled deuterons in CD4 free rotators. Expressions are derived for their direct relaxation rate via the intra and external quadrupole couplings. The jump motion between the equilibrium positions averages the relaxation rate within the same symmetry species. Spin conversion transitions couple the relaxation of T and (A+E). This mixing is included in the calculations by reapplying the simple model under somewhat different conditions. The results compare favorably with the experimental data for the zeolites HY, NaA and NaMordenite [6] and NaY presented here. Incoherent tunnelling is believed to dominate the relaxation process at lowest temperatures as soon as CD4 molecules become localized. 

If the applied shear stress varies during the experiment, e.g. in a tensile test at a constant strain rate, the relaxation time of the activated transitions changes during the test. This is analogous to the concept of a reduced time, which has been introduced to model the acceleration of the relaxation processes due to the deformation. It is proposed that the reduced time is related to the transition rate of an Eyring process [58]. The differential Eq. 123 for the transition rate is rewritten as... 

---