Rate of relaxation

FIGURE 2.17 Differential efficiency of receptor coupling for cardiac function, (a) Guinea pig left atrial force of contraction (inotropy, open circles) and rate of relaxation (lusitropy, filled circles) as a function (ordinates) of elevated intracellular cyclic AMP concentration (abscissae). Redrawn from [6]. 

Thus a strong bond is not always desirable. We can see this from Table 7 and 8. The authors of [100] interpreted their experimental data as follows the rigidity of specimens increases with increasing PVC-filler interaction as a result the rate of relaxation of stresses arising at interphases in the course of deformation decreases. The overstressed states at the interphases may, in the authors opinion, promote separation of the polymer from the filler surface. That is, it is more desirable that the matrix-filler bond is not rigid but labile. 

Linear polymers may exhibit elastic behavior with good recovery if the molecular weight is very high (10 or more), owing to the slow rate of relaxation of very long chains. 

Chandra and his coworkers have developed analytical theories to predict and explain the interfacial solvation dynamics. For example, Chandra et al. [61] have developed a time-dependent density functional theory to predict polarization relaxation at the solid-liquid interface. They find that the interfacial molecules relax more slowly than does the bulk and that the rate of relaxation changes nonmonotonically with distance from the interface They attribute the changing relaxation rate to the presence of distinct solvent layers at the interface. Senapati and Chandra have applied theories of solvents at interfaces to a range of model systems [62-64]. 

Another approach to determining the contribution being made by each of the possible com-pression/decompression mechanisms involves monitoring the degree and rate of relaxation in tablets immediately after the point of maximum applied force has been reached. Once a powder bed exceeds a certain yield stress, it behaves as a fluid and exhibits plastic flow [121,122], Certain investigators [122] have studied plastic flow in terms of viscous and elastic elements and have derived the following equation ... 

A major limitation of CW double resonance methods is the sensitivity of the intensities of the transitions to the relative rates of spin relaxation processes. For that reason the peak intensities often convey little quantitative information about the numbers of spins involved and, in extreme cases, may be undetectable. This limitation can be especially severe for liquid samples where several relaxation pathways may have about the same rates. The situation is somewhat better in solids, especially at low temperatures, where some pathways are effectively frozen out. Fortunately, fewer limitations occur when pulsed radio and microwave fields are employed. In that case one can better adapt the excitation and detection timing to the rates of relaxation that are intrinsic to the sample.50 There are now several versions of pulsed ENDOR and other double resonance methods. Some of these methods also make it possible to separate in the time domain overlapping transitions that have different relaxation behavior, thereby improving the resolution of the spectrum. 

The rate of relaxation caused by desorption or readsorption is assumed to follow a simple first order function with a rate constant a (8)... 

For systems close to equilibrium the non-equilibrium behaviour of macroscopic systems is described by linear response theory, which is based on the fluctuation-dissipation theorem. This theorem defines a relationship between rates of relaxation and absorption and the correlation of fluctuations that occur spontaneously at different times in equilibrium systems. 

In the right-hand part of Figure 10 are shown simulation results obtained by using the above kinetic equations and the rectangular cell model which divides the air/water interface into one hundred cells. In this simulation, the relative magnitudes of the rate of relaxation processes and the rate of compression were set up as follows. ... 

Selective inversion experiments for the determination of slow exchange rates are analogous to the saturation-transfer method in that they involve selective manipulation of one of the exchanging sites, while observing the subsequent effect on the second site as a function of time [48, 69, 70]. Chemical exchange, if present, will provide an alternative route to normal spin relaxation processes which a spin system undergoes, if perturbed at the start of an experiment. The rate of relaxation will depend on both the exchange rate k and the spin-lattice relaxation rate (Ti) (fig. 5). 

The actual rate of relaxation dependsonthe mode of masstransport operative. The three basic modes are ... 

Before discussing individual results for spin orbit relaxation, a general framework for the kinetic treatment will be given. The rate of relaxation in a system involving only two states,... 

The homogeneous quenching of I(5 %) generated in the photolysis of CF3I is sufficiently slow so that the dominant term in Eq. (49) is apparently that due to diffusion to the walls of the reaction vessel (followed by efficient deactivation). Thus it is observed that as the total pressure of inert gas present is lowered, the rate of relaxation increases, showing an inverse first power relation27 (Fig. 11). The rate of diffusion to the vessel walls is given by the diffusion equation ... 

Accordingly, plots of a t)/a(0) vs t from different shear rates should superimpose. Experimentally the curves do not superimpose when the shear rate is in the non-Newtonian region, the initial rate of relaxation being increasingly more rapid for higher shear rates. The normal stress decays more slowly than shear stress, but behaves similarly with respect to the effect of previous shearing flow in the non-Newtonian region. 

It has recently been pointed out by Gordon1 that the root-mean-square fluctuations in the sampled values of the autocorrelation function of a dynamical variable do not necessarily relax to their equilibrium values at the same rate as the autocorrelation function itself relaxes. It is the purpose of this paper to investigate the relative rates of relaxation of autocorrelation functions and their fluctuations in certain systems that can be described by Smoluchowski equations,2 i.e., Fokker-Planck equations in coordinate space. We exhibit the fluctuation and autocorrelation functions for several simple systems, and show that they usually relax at different rates. 

Comparison of Rates of Relaxation of Scaled rms Fluctuation Functions U(f t) and Autocorrelation Functions p(f t) at Short, Intermediate, and Long Times, for the Functions /Shown and the Systems Described in Table I... 

We can also see in Tables I and II the effects of a change in the origin of /upon the relaxation of U. The difference between the Ws for cos Sand for 1 — cos S in the case of the plane rotor (and the analogous case of the particle in a box) is perhaps especially striking. At intermediate times, the translation is seen to change the relative rate of relaxation of U from 0.73 to 1.14, but at short and long times, it changes the nature of the relaxation behavior completely. We can readily show from Eq. (4), in fact, that for... 

The flow of energy from the ground state can also be calculated when it is assumed that the rate of electronic dephasing is small (i.e., L%Pg = 0) and/or the rate of pure vibrational dephasing is small (i.e., L%Hg = 0). These conditions apply when the rate of relaxation to equilibrium is small relative to the rate of loss of phase coherence. Under these conditions... 

Einstein A coefficient in its (001-000) transition at 2349 cm -1 than that for the corresponding band at 2223 cm -1 in NzO, appears always to be the minor triatomic product emitting in this range. Although these results are presently preliminary (and their interpretation may need to be revised if, for example, rates of relaxation of the excited products are distorting the partially relaxed vibrational distributions), they seem incompatible with the diode laser observations unless reaction (18) produces C02 substantially in vibrational levels with v3 = 0. Further experiments are in progress. 

The rate of relaxation by nonradiative pathways can be increased by addition of quenchers. Quenching of fluorescence occurs by several mechanisms, many of which involve collision of the excited chro-mophore with the quenching molecule. Some substances such as iodide ion are especially effective quenchers. The fluorescence efficiency of a substance in the absence of a quencher can be expressed (Eq. 23-lb) in terms of the rate constants for fluorescence (fcf), for nonradiative decay (km), and for phosphorescence ( r )=... 

The rate of relaxation at constant temperature51,52 is generally proportional to the magnitude of displacement from the equilibrium and is characterized by a relaxation time r. 

In the systems under consideration the ions exchange between different binding sites rapidly compared with the rate of relaxation, and the observed linewidth is given by ... 

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