Relaxation processes localized motions

It is noteworthy that the neutron work in the merging region, which demonstrated the statistical independence of a- and j8-relaxations, also opened a new approach for a better understanding of results from dielectric spectroscopy on polymers. For the dielectric response such an approach was in fact proposed by G. Wilhams a long time ago [200] and only recently has been quantitatively tested [133,201-203]. As for the density fluctuations that are seen by the neutrons, it is assumed that the polarization is partially relaxed via local motions, which conform to the jS-relaxation. While the dipoles are participating in these motions, they are surrounded by temporary local environments. The decaying from these local environments is what we call the a-process. This causes the subsequent total relaxation of the polarization. Note that as the atoms in the density fluctuations, all dipoles participate at the same time in both relaxation processes. An important success of this attempt was its application to PB dielectric results [133] allowing the isolation of the a-relaxation contribution from that of the j0-processes in the dielectric response. Only in this way could the universality of the a-process be proven for dielectric results - the deduced temperature dependence of the timescale for the a-relaxation follows that observed for the structural relaxation (dynamic structure factor at Q ax) and also for the timescale associated with the viscosity (see Fig. 4.8). This feature remains masked if one identifies the main peak of the dielectric susceptibility with the a-relaxation. 

Photophysical and photochemical processes in polymer solids are extremely important in that they relate directly to the functions of photoresists and other molecular functional devices. These processes are influenced significantly by the molecular structure of the polymer matrix and its motion. As already discussed in Section 2.1.3, the reactivity of functional groups in polymer solids changes markedly at the glass transition temperature (Tg) of the matrix. Their reactivity is also affected by the / transition temperature, Tp, which corresponds to the relaxation of local motion modes of the main chain and by Ty, the temperature corresponding to the onset of side chain rotation. These transition temperatures can be detected also by other experimental techniques, such as dynamic viscoelasticity measurements, dielectric dispersion, and NMR spectroscopy. The values obtained depend on the frequency of the measurement. Since photochemical and photophysical parameters are measures of the motion of a polymer chain, they provide means to estimate experimentally the values of Tp and Tr. In homogeneous solids, reactions are related to the free volume distribution. This important theoretical parameter can be discussed on the basis of photophysical processes. 

We shall consider a simple model for the a, P and (aj8) processes. We assume that a reference dipole at any instant t = 0) finds itself in a local environment r, and let V be the probability of obtaining this environnient. We assume that as time develops the dipole may partially relax via local motions in this environment r, and characterized by a decay function (pp t). If []r is the average moment observed for a time scale long compared with the local motions (Pr process), but short compared with the time scale for the microbrownian motions (a process), then the P. process has a magnitude —[] . We assume that the a process breaks down the environment r and relaxes the remainder of completely. The correlation function for this scheme is... 

Thus the mean moment that is not relaxed by local motions (p process) is relaxed by the a process, which is an alternative statement of the conservation rule. Quite recendy. Smith and Boyd [40] used a theory to describe the P process (in vinyl acetate copolymers) that is formally equivalent to that described above. The single dipole theory that leads to Equation (10) has been extended by Williams [12] to include cross-correlation terms in the general expression for r) in Equation (8). 

A qualitative theoretical interpretation of the experimental findings on the basis of the dipole correlation function has been proposed by Williams and Watts. They assumed that a reference dipole may find itself in a number of different environments and, consequently, the fraction of relaxed by local motions will depend on the particular environment. The environments may, in turn, be changed by micro-Brownian motions. Let the probability of finding the dipole in an environment / be p(l). If the fraction of the mean square dipole moment relaxed by the j -process is = //, then (1 —(5m ) of the mean square dipole moment is left unrelaxed by this... 

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. 

Relaxation dispersion data for water on Cab-O-Sil, which is a monodis-perse silica fine particulate, are shown in Fig. 2 (45). The data are analyzed in terms of the model summarized schematically in Fig. 3. The y process characterizes the high frequency local motions of the liquid in the surface phase and defines the high field relaxation dispersion. There is little field dependence because the local motions are rapid. The p process defines the power-law region of the relaxation dispersion in this model and characterizes the molecular reorientations mediated by translational displacements on the length scale of the order of the monomer size, or the particle size. The a process represents averaging of molecular orientations by translational displacements on the order of the particle cluster size, which is limited to the long time or low frequency end by exchange with bulk or free water. This model has been discussed in a number of contexts and extended studies have been conducted (34,41,43). 

The lattice models provide useful interpretations of spin relaxation in dissolved polymers and rubbery or amorphous bulk polymers. Very large data bases are required to distinguish the interpretive ability of lattice models from other models, but as yet no important distinction between the lattice models is apparent. In solution, the spectral density at several frequencies can be determined by observing both carbon-13 and proton relaxation processes. However, all the frequencies are rather hl unless T2 data are also included which then involves the prospect of systematic errors. It should be mentioned that only effective rotational motions of either very local or very long range nature are required to account for solution observations. The local... 

Tanaka et al. have studied the surface molecular motions of PS films coated on a solid substrate by lateral force microscopy and revealed that the Tg at the surface was much lower than the corresponding bulk one [148]. Possible reasons for this included an excess free volume induced by localized chain ends, a reduced cooperativity for of-relaxation process, a reduced entanglement, and a unique chain conformation at the surface. For comparison, they examined surface relaxation behavior of high-density PMMA brushes. 

Now we consider an experiment in which a static electric field is suddenly applied to a dilute polypeptide solution. If the rates of interconversions between helix and random-coil units are much faster than those of rotational motions of the entire dissolved polymer molecule as well as of local segments of it, there will be an increase in the dielectric constant which approaches a constant value (ds)ch with time t. This relaxation process is a kind of chemical relaxation, because the helix-coil interconversions responsible for it may be regarded as chemical reactions. Its detailed study should provide information about such elementary processes as those illustrated in Eqs. (E-13) and (E-15). This is Schwarz s basic idea. 

After the formulation of defect thermodynamics, it is necessary to understand the nature of rate constants and transport coefficients in order to make practical use of irreversible thermodynamics in solid state kinetics. Even the individual jump of a vacancy is a complicated many-body problem involving, in principle, the lattice dynamics of the whole crystal and the coupling with the motion of all other atomic structure elements. Predictions can be made by simulations, but the relevant methods (e.g., molecular dynamics, MD, calculations) can still be applied only in very simple situations. What are the limits of linear transport theory and under what conditions do the (local) rate constants and transport coefficients cease to be functions of state When do they begin to depend not only on local thermodynamic parameters, but on driving forces (potential gradients) as well Various relaxation processes give the answer to these questions and are treated in depth later. 

In the case of polycarbonates, it has been observed that by adding miscible low molecular weight additives, with specific chemical structures, it is possible to increase the yield stress of the polymer, as well as to reduce the local molecular motions that are responsible for the secondary relaxation processes... 

However, the situation becomes already more complicated for ternary single crystals like lanthanum-aluminate (LaAlC>3, er = 23.4). The temperature dependence of the loss tangent depicted in Figure 5.3 exhibits a pronounced peak at about 70 K, which cannot be explained by phonon absorption. Typically, such peaks, which have also been observed at lower frequencies for quartz, can be explained by defect dipole relaxation. The most important relaxation processes with relevance for microwave absorption are local motion of ions on interstitial lattice positions giving rise to double well potentials with activation energies in the 50 to 100 meV range and color-center dipole relaxation with activation energies of about 5 meV. 

The P zone extend over a large temperature range. This is a characteristic of a secondary process which involve local motions of the lateral groups [155], They are more diversified movements with a large spectrum of relaxation times. Therefore, thermal cleaning of the t.s.c. global spectra is used to study the broad relaxation peaks of the low temperature secondary relaxation [42], This is effective because it allows one to excite only the specific transition of interest [155],... 

The initial hypothesis is that the ft -relaxation process of the PDMP involved local and independent motions of the side chains, taking into account the broadness... 

Fully deuterated linear poly(ethylene) (PE) has been investigated also via various 2H NMR techniques below Tm, i.e. in the semi crystalline state [83, 84]. The crystallinity ratio was measured as a function of temperature and it was shown that the motions are highly restricted in the amorphous regions of PE. It was shown that the onset of 3 and a transitions (at which mobility appears in the crystalline phase) may be observed by 2H NMR on raising the temperature. This onset of local motions in the crystalline phase is related to the chain relaxation process quoted previously. 

The conversion of the initially formed Si np state to the Si ct state by intramolecular electron transfer is very fast and varies in a way that parallels but does not exactly correspond to the dielectric relaxation time for the solvent used. This is because the local environment around the excited-state molecule is different from that surrounding a solvent molecule [120, 340]. That is, the ICT process is to a large extent determined by the dielectric relaxation processes of the solvent surrounding the ANS molecule. Thus, solvent motion seems to be the controlling factor in the formation and decay of the ICT excited state of ANS and other organic fluorophores [120, 340]. A detailed mechanism for fast intramolecular electron-transfer reactions of ANS and 4-(dimethylamino)benzonitrile, using two simplified molecular-microscopic models for the role of the solvent molecules, has been given by Kosower [340] see also reference [116]. 

The experimental observation that viscoelastic behavior can be shifted and superimposed, at least to a first approximation, means that all the relaxation processes involved have the same (or nearly the same) temperature dependence. Because the relaxation processes that occur in polymers involve a whole range of length scales, by which we mean they involve coupled motions that range from local rearrangements of just a few chain segments to motions of the chain as a whole, this implies that frictional forces encountered by a chain act in the same or a very similar manner on all the segments. This is important if you intend to be in the business of developing theories of polymer dynamics, but concerns us no further here. 

According to this model, the temperature dependence of molecular motions for adsorbed and non-adsorbed chain units in filled PDMS containing hydrophilic Aerosil is shown in Fig. 9 [9]. The lowest temperature motion is a C3 rotation of the CH3 groups around the Si-C bond (line 1 in Fig. 9). The rate of the a-relaxation (points 2 in Fig. 9) in filled PDMS is close to that for unfilled sample (line 2 in Fig. 9). It has been proposed that independence of the mean average frequency of a-relaxation process on the filler content in filled PDMS is due to defects in the chain packing in the proximity of primarily filler particles [7]. Furthermore, the chain adsorption does not restrict significantly the local chain motion, which is due to high flexibility of the siloxane main chain as well as due to fast adsorption-desorption processes at temperatures well above Tg. 

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