Relaxation processes measurement

Peak of a-process at Tg, post-Tg signal from rigid amorphous fraction Higher scatter of TW-TSDC peaks under a global peak indicates higher compositional heterogeneity Non-Debye decay functions (e.g., KWW) is inappropriate to describe the TSDC relaxation process measured in temperature scanning mode... 

A detailed description of the molecular motions in the Maier-Saupe potential disturbed by the electric probe field has been done by Martin and co-workers. These authors obtained the numerical solutions for the relaxation times T and Tj and for polarization. They found that the relaxation process measured at nUE geometry is slowed down with respect to the Debye-type motion in the isotropic phase, whereas the second relaxation process connected with the molecular reorientations around the long axes (nlE geometry) becomes faster in the presence of the nematic potential, that is, gn > 1 and < 1. 

Figure 4.4 Temperature dependence of the relaxation time (a) and relaxation amplitude (b) of the second and postulated third relaxation processes measured for a 2.5 wt% L64 solution. The effect of impurities can be seen by comparing the results for the relaxation times for a purified L64 ( , A) an industrial L64 ( , A) and a mixture of L64 and L61 (0.25 wt%) (+,0). Adapted and reproduced from Reference 42 with permission of the American Chemical Society.

Nevertheless, the present physical models on liquid phases are far from reaching a comprehensive picture of the dynamical scenario. Focusing on complex liquids, even the single dynamic process has been, very often, only partially elucidated. Here we recall some of the typically exploited models to describe and to address the relaxation processes measured in an optical scattering experiment, both OKE and LS. According to a simplified scheme, these models can be classified into two main groups. 

Ultrasonic absorption is used in the investigation of fast reactions in solution. If a system is at equilibrium and the equilibrium is disturbed in a very short time (of the order of 10"seconds) then it takes a finite time for the system to recover its equilibrium condition. This is called a relaxation process. When a system in solution is caused to relax using ultrasonics, the relaxation lime of the equilibrium can be related to the attenuation of the sound wave. Relaxation times of 10" to 10 seconds have been measured using this method and the rates of formation of many mono-, di-and tripositive metal complexes with a range of anions have been determined. 

Relaxation kinetics may be monitored in transient studies tlirough a variety of metliods, usually involving some fonn of spectroscopy. Transient teclmiques and spectrophotometry are combined in time resolved spectroscopy to provide botli tire stmctural infonnation from spectral measurements and tire dynamical infonnation from kinetic measurements that are generally needed to characterize tire mechanisms of relaxation processes. The presence and nature of kinetic intennediates, metastable chemical or physical states not present at equilibrium, may be directly examined in tliis way. 

We examined the role of vector percolation in the fracture of model nets at constant strain and subjected to random bond scission, as shown in Fig. 11 [1,2]. In this experiment, a metal net of modulus Eo containing No = 10" bonds was stressed and held at constant strain (ca. 2%) on a tensile tester. A computer randomly selected a bond, which was manually cut, and the relaxation of the net modulus was measured. The initial relaxation process as a function of the number of bonds cut N, could be well described by the effective medium theory (EMT) via... 

Wilkes, G. L. The Measurement of Molecular Orientation in Polymeric Solids. Vol. 8, pp. 91-136. Williams, G. Molecular Aspects of Multiple Dielectric Relaxation Processes in Solid Polymers. Vol. 33, pp. 59-92. 

Luminescence lifetime spectroscopy. In addition to the nanosecond lifetime measurements that are now rather routine, lifetime measurements on a femtosecond time scale are being attained with the intensity correlation method (124), which is an indirect technique for investigating the dynamics of excited states in the time frame of the laser pulse itself. The sample is excited with two laser pulse trains of equal amplitude and frequencies nl and n2 and the time-integrated luminescence at the difference frequency (nl - n2 ) is measured as a function of the relative pulse delay. Hochstrasser (125) has measured inertial motions of rotating molecules in condensed phases on time scales shorter than the collision time, allowing insight into relaxation processes following molecular collisions. 

Investigation of water motion in AOT reverse micelles determining the solvent correlation function, C i), was first reported by Sarkar et al. [29]. They obtained time-resolved fluorescence measurements of C480 in an AOT reverse micellar solution with time resolution of > 50 ps and observed solvent relaxation rates with time constants ranging from 1.7 to 12 ns. They also attributed these dynamical changes to relaxation processes of water molecules in various environments of the water pool. In a similar study investigating the deuterium isotope effect on solvent motion in AOT reverse micelles. Das et al. [37] reported that the solvation dynamics of D2O is 1.5 times slower than H2O motion. 

Several commercial companies now offer process compatible NMR systems. These systems are either low resolution based on relaxation time measurements or high resolution Fourier Transform spectral measurements. The low resolution systems are manufactured by Process Control Technologies (www.pctnmr.com) and Progression, Inc. (www.progression-systems.com). Progression s systems... 

Effectiveness of a crude oil demulsifier is correlated with the lowering of shear viscosity and dynamic tension gradient of the oil-water interface. Using the pulsed drop technique, the interfacial dilational modulii with different demulsifiers have been measured. The interfacial tension relaxation occurs faster with an effective demulsifier. Electron spin resonance with labeled demulsifiers indicate that the demulsifiers form reverse micelle like clusters in bulk oil. The slow unclustering of the demulsifier at the interface appears to be the rate determining step in the tension relaxation process. 

Although relaxation measurements have been widely used in nuclear magnetic resonance studies of solid catalysts and adsorbed molecules, they have not found such favor in similar ESR work. Relaxation phenomena, however, do play a very important role in any magnetic resonance experiment, whether or not this aspect of the problem is studied. In fact, the temperature at which most ESR experiments are conducted is dictated by the relaxation process. Furthermore, even qualitative data on relaxation times can be used as supporting evidence in the identification of a paramagnetic species. 

Reorientations produce characteristic maxima in the relaxation rate, which may be different for the various symmetry species of CD4. The measured relaxation rates exhibit dependence on two time constants at low temperatures, but also double maxima for both relaxation rates. We assume that molecules may move over some places (adsorption sites) on the cage walls and experience different local potentials. Under the assumption of large tunnelling splittings the T and (A+E) sub-systems relax at different rates. In the first step of calculation the effect of exchange between the different places was considered. Comparison with experimental data led to the conclusion that we have to include also a new relaxation process, namely the contribution from an external electric field gradient. It is finally quite understandable to expect that such effect appears when CD4 moves in the vicinity of a Na+ ion. 

Molecular Motions and Dynamic Structures. Molecular motions are of quite general occurrence in the solid state for molecules of high symmetry (22,23). If the motion does not introduce disorder into the crystal lattice (as, for example, the in-plane reorientation of benzene which occurs by 60° jumps between equivalent sites) it is not detected by diffraction measurements which will find a seemingly static lattice. Such molecular motions may be detected by wide-line proton NMR spectroscopy and quantified by relaxation-time measurements which yield activation barriers for the reorientation process. In addition, in some cases, the molecular reorientation may be coupled with a chemical exchange process as, for example, in the case of many fluxional organometallic molecules. ... 

Kinetic schemes involving sequential and coupled reactions, where the reactions are either first-order or pseudo-first order, lead to expressions for concentration changes with time that can be modeled as a sum of exponential functions where each of the exponential functions has a specific relaxation time. More complex equations have to be derived for bimolecular reactions where the concentrations of reactants are similar.19,20 However, the rate law is always related to the association and dissociation processes, and these processes cannot be uncoupled when measuring a relaxation process. 

The sound absorption coefficient, a, is increased when the dynamics of the chemical system are of the same order of magnitude as the frequency of the sound wave,41 and experimentally this quantity is measured as a function of frequency of the ultrasonic sound wave (Fig. 4). When the frequency of the sound wave is of the same order as the frequency for the relaxation process, effects due to relaxation of the equilibrium give rise to characteristic changes in the quantity a//2, where a is the sound absorption coefficient measured at frequency /40 The variation of a with frequency, /, has an inflection point at the relaxation frequency of the system, fr, which is related to 1/t, where r is the relaxation time (1/t = 27i/r).40,41 The expression relating the quantity... 

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