Bulk relaxation

De Pristo A. E., Rabitz H. Scaling theoretic deconvolution of bulk relaxation data state-to-state rates from pressure-broadening linewidths,... 

Here m(r, t) is the relative difference of the longitudinal magnetization M and its equilibrium value Mo m = (M — Mo)/Mo, D is the bulk diffusion coefficient and p is the bulk relaxation rate. The general solution to the Torrey-Bloch equation can be written as... 

Polymer-Specific Effects of Bulk Relaxation and Stringlike Correlated Motion in the Dynamics of a Supercooled Polymer Melt. 

The coating chamber was equipped with a set of independently controlled stainless steel boats and a shutter system to enable the fabrication of multilayer structures. Pure selenium pellets were loaded into one boat and As Sei alloys into another. The two sources were evaporated sequentially (without breaking the vacuum) at boat temperatures of about 450 K. Typical coating rates were l j,m/min. After evaporation, they were allowed to anneal over several weeks in the dark at room temperature. During this period, due to structural bulk relaxation, most physical properties of the photoconductor film become stabilized. The compositions of the deposited films were determined by electron probe microanalysis, and the compositions quoted (0 < X < 0.20) are accurate to within 0.5 at.%. By shuttering the beginning and the end of the evaporation, a uniform arsenic composition across the film thickness can be obtained. In all experiments, a transparent gold electrode ( 300 jm thick) was used as the top contact. 

The processes observed in the depolarized Rayleigh spectrum correspond to internal modes of motion. Thus, they may have relaxation times which substantially exceed those obtained from the longitudinal or bulk relaxation alone. Nevertheless they are a part of the a relaxation process as it is normally observed in the creep compliance. All processes with the same shift factors make up the full a relaxation. In liquids with substantial depolarized Rayleigh scattering the slowly relaxing part of the W scattering is also dominated by the orientation fluctuations associated with the internal modes of motion. Each internal mode contributes some intensity, but it is believed that fairly short wavelength modes dominate the scattered intensity. 

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). 

Section III deals with the surface excitations of the anthracene crystal, confined in the first (SJ, second (S2) and third (S3) (001) lattice planes. The experimental observations are briefly summarized. A simple model shows how the fast radiative decay arises and how the underlying bulk reflection modulates this superradiant emission, as well as why gas condensation on the crystal surface strongly narrows this emission, thus accounting for the observed structures. An intrinsic process is proposed to explain the surface-to-bulk relaxation at low temperatures, observed in spite of the very weak surface-to-bulk coupling for k 0 states. 

As to the relaxation of the excitons in surfaces II and III by the bulk effect, a consistent discussion is as follows The bulk relaxation probability at the energy level s, PV(ES2), has been evaluated, at low temperatures, as few reciprocal centimeters and attributed to acoustical phonons (cf. Section II). With JSK 2cm"1, the direct probability (3.29) is evaluated as 0.2 cm"1, compatible with the observed value,141 while the phonon-assisted process (3.30) is drastically depressed and becomes comparable to direct transfer. 

The position and the width of this dip, at about I Ocm"1 above the Raman peak, indicate the energy gap above which the intrasurface relaxation, assisted by acoustical-phonon creation, competes with the surface-to-bulk relaxation. If we figure 3 to 4cm -1 for the relaxation rate to the bulk (for K 0 wave vectors cf. Section 1II.A.3), we conclude that the intrasurface relaxation, at 10cm 1 above the emitting state, is comparable. This conclusion on the acoustical-phonon relaxation is consistent with the theoretical estimates121127 (cf. Section III.A.4) and the experimental values derived by KK analysis of the bulk reflectivity (Section II.C.3b). 

Shablakh et al. (1984) investigated the dielectric properties of bovine serum albumin and lysozyme at different hydration levels, at low frequency. Besides a relaxation attributed to the electrode—sample interface, they detected a further bulk relaxation that can be confused with a d.c. conduction effect. The latter relaxation was explained by a model of nonconductive long-range charge displacement within a partially connected water structure adsorbed on the protein surface. This model has nonconventional features that differ from the assumptions of other more widely accepted models based on Debye relaxations. 

This expression indicates that a decrease in the thickness d produces an increase in S, with the consequent repercussion on the bulk relaxation modulus [Eq. (3.50)] and the rigidity under compression [Eq. (3.48)]. Figure 3.24 shows the stress-strain curves under compression for elastomer blocks of different shapes. It can be seen that as S increases the curves lose the linearity displayed in a large interval of extensions when S has a low... 

This equation indicates that the tensile modulus does not show an explicit dependence on both the shear and the bulk relaxation moduli. It can easily be seen that for K t) G t), E t) 3G t). 

In the same way, the response to a sinusoidal change of volume yields the complex bulk relaxation modulus. 

As Eqs. (5.84) and (5.87) indicate, the tensile modulus and the Poisson ratio are related to the shear and bulk relaxation moduh by the formulae... 

J. R. Macdonald, "Power-Law Exponents and Hidden Bulk Relaxation in the Impedance Spectroscopy of Solids," Journal of Electroanalytical Chemistry, 378 (1994) 17-29. 

An analysis of the maximum bubble pressure method including all known theoretical approaches was given only recently so that data from literature are only of approximate character [160]. Therefore, the current level of kinetic theories of adsorption from micellar solutions and the corresponding experimental technique is still insufficient for investigations of the micellisation kinetics with a precision comparable to that of bulk relaxation methods. This pessimistic conclusion, however, relates to a less extent to methods based on small (mainly periodic) perturbations of the adsorption equilibrium. 

The spin-spin relaxation times Tje were obtained from the decay of the echo amplitude in a qudn )ole echo sequence (see Fig. 6). Since a unique decomposition into two ejqmnentials was impossible the given Tj data present bulk relaxation times and refer to both mobile and immobile deuterons. One sees that Tj first decreases with decreasing tenqierature, then passes through a minimum and finally increases again. 

Figure 17.8. Semilog plot ofnormalizedreorientational time-correlation fimction of the unit vector along the O-H bond of the water molecules in different layers. Layers are represented as follows bulk water, double dotted dashed Une central layer, single dotted dashed line intermediate layer, dashed line surface layer, solid line. The faster than bulk relaxation of the surface and intermediate layers is evident in the reverse micelle. At intermediate times a crossover is observed and the surfece layer has a pronounced long-time decay component The faster long-time decay for the intermediate layer compared with the central water layer is also observed. Figure adapted with permission from/. Chem. Phys., 137 (2012), 014515-1-9. Copyright (2012) American Institute of Physics.

This expression yields a surface relaxation time (Ys/ s the bulk, the second derivative of orientation with respect to z replaces the simple direction orientation difference In the surface term. Ignoring flow, the bulk relaxation has a characteristic time where h Is the liquid crystal film... 

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