Relaxation frequencies, determination

The full lines indicate the approximate temperature dependence of the a, / , and y relaxation frequencies determined by dynamic mechanical and dielectric measurements... 

The aim of this work is to analyze the changes in the relevant thermal behavior of the crosslinked EVA encapsulant material due to outdoor exposure in Mediterranean climate by TSC and DSC thermal analysis. The changes in thermal properties should be discussed and special interest will be focused on the specific TSC relaxation parameters like activation energy and relaxation frequency determination by using the initial rise method. 

In paramagnetic materials, the relaxation frequency is in general determined by contributions from both spin-lattice relaxation and spin-spin relaxation. Spin-lattice relaxation processes can conveniently be studied in samples with low concentrations of paramagnetic ions because this results in slow spin-spin relaxation. Spin-spin relaxation processes can be investigated at low temperatures where the spin-lattice relaxation is negligible. Paramagnetic relaxation processes have... 

As discussed in Sect. 6.2, the electronic states of a paramagnetic ion are determined by the spin Hamiltonian, (6.1). At finite temperamres, the crystal field is modulated because of thermal oscillations of the ligands. This results in spin-lattice relaxation, i.e. transitions between the electronic eigenstates induced by interactions between the ionic spin and the phonons [10, 11, 31, 32]. The spin-lattice relaxation frequency increases with increasing temperature because of the temperature dependence of the population of the phonon states. For high-spin Fe ", the coupling between the spin and the lattice is weak because of the spherical symmetry of the ground state. This... 

For polyatomic gases in porous media, however, the relaxation rate commonly decreases as the pore size decreases [18-19]. Given that the relaxation mechanism is entirely different, this result is not surprising. If collision frequency determines the Ti, then in pores whose dimensions are in the order of the typical mean free path of a gas, the additional gas-wall collisions should drastically alter the T,. For typical laboratory conditions, an increase in pressure (or collision frequency) causes a proportional lengthening of T1 so the change in T, from additional wall collisions should be a good measure of pore size. 

A more complex but faster and more sensitive approach is polarization modulation (PM) IRLD. For such experiments, a photoelastic modulator is used to modulate the polarization state of the incident radiation at about 100 kHz. The detected signal is the sum of the low-frequency intensity modulation with a high-frequency modulation that depends on the orientation of the sample. After appropriate signal filtering, demodulation, and calibration [41], a dichroic difference spectrum can be directly obtained in a single scan. This improves the time resolution to 400 ms, prevents artifacts due to relaxation between measurements, and improves sensitivity for weakly oriented samples. However, structural information can be lost since individual polarized spectra are not recorded. Pezolet and coworkers have used this approach to study the deformation and relaxation in various homopolymers, copolymers, and polymer blends [15,42,43]. For instance, Figure 7 shows the relaxation curves determined in situ for miscible blends of PS and PVME [42]. The (P2) values were determined... 

The ultrasonic absorption spectrum for a series of inorganic salts with /i-CD showed one relaxation process.166 No absorption was observed for solutions only containing /i-CD. The equilibrium constants determined from competitive binding isotherms were relatively low (2-30 M-1). The relaxation frequency (/, ) was related to the observed relaxation rate constant, which is equal to the sum of the association and dissociation processes. The association rate constants for all salts with the exception of perchlorate were similar and this result was interpreted to mean that... 

The equilibrium constant and dissociation rate constant were determined simultaneously by non-linear least-squares fitting, unless the absorption signal was too low157 or no dependence of relaxation frequency on concentration was observed.159,161,162 The association rate constant was then calculated from the definition of the equilibrium constant. The equilibrium constants determined from the dynamics in this manner agree fairly well with equilibrium constants determined independently. 

Simulations were made for all three frequencies, determining the g-values principally at 94 GHz, and showing transferability of parameters between frequencies. It was demonstrated (from the model compounds) that interfering signals from Mn(II) at 94 GHz could be eliminated using field-swept echo spectra and making use of the different 7) or r2 relaxation times for the components of the spectra. 

Correlation frequencies determined from T1 Tle and T2 relaxation times were plotted against reciprocal temperature and activation energies calculated. The methyl group had a comparatively high activation energy (4.7 kcal/mole) which was attributed to steric hindrance from the reorientation of the two methyls bound to the same carbon and steric hindrance arising from the two phenyl groups on the carbon atom. 

One of the standard methods of analysis in PCS is to determine the average relaxation frequency a>) = (1/r). This is obtained by measuring the initial slope of the relaxation function. This can easily be seen from... 

As revealed from Eqs. (1) and (2), or their candid forms (4) and (5), the longitudinal relaxation is determined by the spectral densities in the order of o>h toc, whereas the transverse relaxation involves the contribution from the zero frequency component Jo(0). In the case of solid matter, tc is generally very long. Hence, the transverse relaxation is predominantly determined by the zero frequency component Jo(0). In Eq. (5), for example, the zero frequency term (the first term) dominates the other terms that are reciprocally proportional to Tc for co2x2 1. Tic increases as xc increases (i.e. as the material under consideration becomes solider), whereas T2c decreases infinitely as xc increases. For example, Tic is generally in an order of several tens several hundreds of seconds for the crystalline component and in an order of a few tenths of a second for rubbery components of polymers. On the other hand, T2c is of an order of a few tens of microseconds for the crystalline or glassy component and a few milliseconds for the rubbery component of polymers. In this work, Tic and T2c are used for characterizing different components in crystalline polymers. 

Characteristic frequencies may be found from dielectric permittivity data or, even better, from conductivity data. The earlier data by Herrick et al. (6) suggest that there is no apparent difference between the relaxation frequency of tissue water and that of the pure liquid (7). However, these data extend only to 8.5 GHz, one-third the relaxation frequency of pure water at 37°C (25 GHz), so small discrepancies might not have been uncovered. We have recently completed measurements on muscle at 37°C and 1°C (where the pure water relaxation frequency is 9 GHz), up to 17 GHz. The dielectric properties of the tissue above 1 GHz show a Debye relaxation at the expected frequency of 9 GHz (8 ) (Figure 3). The static dielectric constant of tissue water as determined at 100 MHz compares with that of free water if allowance is made for the fraction occupied by biological macromolecules and their small amount of bound water (1, 9). 

As already mentioned before, if one could localize a core hole on a given nucleus it would oscillate with a hopping frequency determined by the level splitting Wa, and the n-charge would have a relax in the presence of a moving hole, i.e. dynamic relaxation. However, for a deep core hole the hopping frequency would be practically zero and we would then have static relaxation (cf. Sect. 3). We shall now discuss these two cases in some detail. 

Hence the relaxation frequency of the bulk semicircle (Rm Cspr ) equals cbuik/fibuik and is again geometry-independent. However, stray capacitances can impede the quantitative determination of local permeabilities, and therefore also of bulk relaxation frequencies (Sec. 5). 

In the EHD impedance method, modulation of the flow velocity causes a modulation of the velocity gradient at the interface which, in turn, causes a modulation in the concentration boundary layer thickness. As demonstrated previously in Section 10.3.3 and Fig. 10.3 the experiment shows a relaxation time determined solely by the time for diffusion across the concentration boundary layer. Although there is a characteristic penetration depth, 8hm, of the velocity oscillation above the surface, and at sufficiently high modulation frequencies this is smaller than the concentration boundary layer thickness, any information associated with the variation of hm with w is generally lost, unless the solution is very viscous. The reason is simply that, at sufficiently high modulation frequencies, the amplitude of the transfer function between flow modulation and current density is small. So, in contrast to the AC impedance experiment, the depth into the solution probed by the EHD experiment is not a function... 

The dynamic window of a given NMR technique is in many cases rather narrow, but combining several techniques allows one to almost completely cover the glass transition time scale. Figure 6 shows time windows of the major NMR techniques, as applied to the study of molecular reorientation dynamics, in the most often utilized case of the 2H nucleus. Two important reference frequencies exist The Larmor frequency determines the sensitivity of spin-lattice relaxation experiments, while the coupling constant 8q determines the time window of line-shape experiments. 2H NMR, as well as 31P and 13C NMR, in most cases determines single-particle reorientational dynamics. This is an important difference from DS and LS, which access collective molecular properties. 

Figure 3.89. The two relaxations for a colloidal particle. The low-frequency relaxation is determined by diffusion in the far field, that at high frequency by Maxwell conduction in the double layer. The imaginary part "(fl)) has peaks at the two relaxations. Molecular relaxations, as considered in figs. 1.4,7 and 1.4.8 come on top of these and are observable at higher frequencies.

Freezing of a dipolar liquid is accompanied by a rapid decrease in its electric permittivity [8-10]. Following solidification, dipole rotation ceases and the electric permittivity is almost equal to n, where n is refractive index, as it arises from deformation polarisation only. Investigation of the dynamics of a confined liquid is possible from the frequency dependences of dielectric properties, which allows both the determination of the phase transition temperature of the adsorbed substance and characteristic relaxation frequencies related to molecular motion in particular phases. 

The acenaphthylene label, being incapable of motion independent of the polymer chain, is expected to monitor segmental relaxation of the macromolecule. The relaxation data adhere well to an Arrhenius relationship over the relatively restricted frequency-temperature range sampled. This behaviour is similar to that observed for the PMA relaxation as determined by phosphorescence depolarization(9,10) but contrasts with that of PMMA in which backbone motion of lesser activation energy was sensible at temperatures inferior to T (11),... 

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