Slow relaxation experiments

Harmonic and transient relaxation experiments for dodecyl dimethyl phosphine oxide solutions were performed with the elastic ring method by Loglio [240]. This methods allows oscillation experiments in the frequency range from about 0.5 to 0.001 Hz and is suitable for comparatively slow relaxing systems. Slow oscillation experiments can be performed much easier now with the pendent drop apparatus [186]. Both techniques are also able to perform transient relaxation experiments. The two types of experiments have a characteristic frequency defined in the same way by Eq. (4.110). 

In the drop shape technique sinusoidal area changes can be easily generated via changes of the drop volume in a very accurate way. The Fourier analysis of the surface tension response however shows that besides the main mode with the period T of the generated oscillation there are also modes with periods of 3T/2, T/2, T/4 and T/8. The origin of these modes is not yet fully understood but certainly caused by deviation of the area changes from harmonicity and surface layer compression/expansion beyond the limits of a linear theory. 

A particular way of presenting harmonic relaxation data is the plot of surface tension changes versus the corresponding area changes. As one can see in Fig. 4.45 an ellipse results the tilt angle and the thickness of which contain the rheological information. 

While the tilt is a measure of the dilational elasticity, the thickness is proportional to the exchange of matter rate, sometimes named dilational viscosity. The ellipse thickness corresponds to the phase shift between the generated area oscillation and the surface tension response. With increasing frequencies the thickness decreases while the tilt angle increases up to a final value of representing the dilational elasticity modulus So. 

The general application of tensiometry was shown in [241] and it was impressively demonstrated how large the capacity of interfacial studies for medical research is. For example, selected dynamic surface tension values of serum or urine correlate with the health state of patients suffering from various diseases. In the course of a medical treatment these values then change from a pathological level back to the normal values determined as standard for a certain group of people (age and sex). 

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We want to give only two examples of interfacial relaxation methods. The whole field of interfacial relaxations and rheology is so broad and of strong practical relevance that this topic deserves a whole book. At first, two examples, a harmonic and a transient experiment will be shown as example for slow relaxation experiments, while as second we will present results of experiments performed under ground and microgravity conditions, respectively, based on the principle of oscillating bubbles. 

The tenn slow in this case means that the exchange rate is much smaller than the frequency differences in the spectrum, so the lines in the spectrum are not significantly broadened. Flowever, the exchange rate is still comparable with the spin-lattice relaxation times in the system. Exchange, which has many mathematical similarities to dipolar relaxation, can be observed in a NOESY-type experiment (sometimes called EXSY). The rates are measured from a series of EXSY spectra, or by perfonning modified spin-lattice relaxation experiments, such as those pioneered by Floflfman and Eorsen [20]. 

Plasticization and Other Time Effects Most data from the literature, including those presented above are taken from experiments where one gas at a time is tested, with Ot calculated as a ratio of the two permeabihties. If either gas permeates because of a high-sorption coefficient rather than a high diffusivity, there may be an increase in the permeabihty of all gases in contact with the membrane. Thus, the Ot actually found in a real separation may be much lower than that calculated by the simple ratio of permeabilities. The data in the hterature do not rehably include the plasticization effect. If present, it results in the sometimes slow relaxation of polymer structure giving a rise in permeabihty and a dramatic dechne in selectivity. 

Liquid lubricant confined in molecularly thin films would experience dramatic changes in its physical properties, such as increased viscosity, slow relaxation, and solidihcation. Progress in studies of thin film rheology has greatly improved our understanding of boundary lubrication, which is the subject to be discussed in this section and in the next. 

Figure 2.7.3 illustrates an example of a T -T2 experiment showing the raw data for %2 decays for several values of tj. The existence of fast and slow relaxations is... 

Other viscoelastic experiments can be performed but often the slow relaxation processes make it difficult to achieve an equilibrium response. 

Mechanistic Ideas. The ordinary-extraordinary transition has also been observed in solutions of dinucleosomal DNA fragments (350 bp) by Schmitz and Lu (12.). Fast and slow relaxation times have been observed as functions of polymer concentration in solutions of single-stranded poly(adenylic acid) (13 14), but these experiments were conducted at relatively high salt and are interpreted as a transition between dilute and semidilute regimes. The ordinary-extraordinary transition has also been observed in low-salt solutions of poly(L-lysine) (15). and poly(styrene sulfonate) (16,17). In poly(L-lysine), which is the best-studied case, the transition is detected only by QLS, which measures the mutual diffusion coefficient. The tracer diffusion coefficient (12), electrical conductivity (12.) / electrophoretic mobility (18.20.21) and intrinsic viscosity (22) do not show the same profound change. It appears that the transition is a manifestation of collective particle dynamics mediated by long-range forces but the mechanistic details of the phenomenon are quite obscure. 

From comparison of Table 8.2 with Table 7.1 (or of Eq. (7.20) with Eq. (7.10)), i.e. of transient NOE or NOESY vs. steady state NOE intensities, it appears that the latter are superior under any circumstance. This superiority is striking if the intrinsic asymmetry of the steady state NOE with respect to the symmetry of transient NOE and NOESY experiments (Section 7.4) can be exploited, as in the case of irradiation of fast relaxing nuclei to detect NOE to slow relaxing nuclei. Of course, NOE experiments are advantageous over NOESY experiments if one is looking for dipolar connectivities from only a few specific signals. 

A detailed study of model (16) for CO oxidation on polycrystalline platinum was carried out by Makhotkin et al. [139]. Numerical experiments revealed that the bulk diffusion effect on the character of reaction dynamics is rather different and controlled by the following factors (1) the initial composition of catalyst surface and bulk, (2) the steady state of its surface and bulk, and (3) the position of the region for slow relaxations of kinetic origin (see ref. 139). As a rule, diffusion retards the establishment of steady states, but the case in which the attainment of this state is accelerated by diffusion is possible. 

In several experiments, in particular the study by Temkin and co-workers [224] of the kinetics in ethylene oxidation, slow relaxations, i.e. the extremely slow achievement of a steady-state reaction rate, were found. As a rule, the existence of such slow relaxations is ascribed to some "side reasons rather than to the purely kinetic ("proper ) factors. The terms "proper and "side were first introduced by Temkin [225], As usual, we classify as slow "side processes variations in the chemical or phase composition of the surface under the effect of reaction media, catalyst deactivation, substance diffusion into its bulk, etc. These processes are usually considered to require significantly longer times to achieve a steady state compared with those characterizing the performance of chemical reactions. The above numerical experiment, however, shows that, when the system parameters attain their bifurcation values, the time to achieve a steady state, tr, sharply increases. 

The results of the numerical experiment for system (20) necessitated a general mathematical investigation of slow relaxations in chemical kinetic equations. This study was performed by Gorban et al. [226-228] who obtained several theorems permitting them to associate the existence of slow relaxations in a system of chemical kinetic equations (and, in general, in dynamic systems) with the qualitative changes in the phase portrait with its parameters (see Chap. 7). 

In numerical experiments, slow relaxation is distinctly observed if the trajectory approaches the unstable steady state. The system rapidly enters its neighbourhood (after 1 s) and then relatively slowly (during 100 s) moves toward its stable steady state. This phenomenon has been described for the three-step adsorption mechanism. 

The conditions of kinetic experiments can essentially affect the observed steady- and unsteady-state dependences. For example, in real experiments the observation time is always limited. Hence, in the region of slow relaxations, it can lead to the fact that hysteresis will also be observed in the case when the steady state is unique. 

Numerical experiments show that the effect of diffusion on the unsteady-state behaviour can be quite different. This effect depends on various factors, in particular the initial composition of catalyst surface and bulk, their steady states and the position of the region for slow relaxations that are of kinetic origin. 

If the time of a slow relaxation process observed for kinetic curves [77] with decreasing temperature are calculated using the diffusion model, we will obtain a value that is close to that measured by experiment ( 50 min). 

A frequency dependence of complex dielectric permittivity of polar polymer reveals two sets or two branches of relaxation processes (Adachi and Kotaka 1993), which correspond to the two branches of conformational relaxation, described in Section 4.2.4. The available empirical data on the molecular-weight dependencies are consistent with formulae (4.41) and (4.42). It was revealed for undiluted polyisoprene and poly(d, /-lactic acid) that the terminal (slow) dielectric relaxation time depends strongly on molecular weight of polymers (Adachi and Kotaka 1993 Ren et al. 2003). Two relaxation branches were discovered for i.s-polyisoprene melts in experiments by Imanishi et al. (1988) and Fodor and Hill (1994). The fast relaxation times do not depend on the length of the macromolecule, while the slow relaxation times do. For the latter, Imanishi et al. (1988) have found... 

As in all correlation experiments, the experiments require measurable coupling between nuclei X and Y and sufficiently slow relaxation so that non-equilibrium magnetizations survive for the duration of the sequence. 

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