Static decay rate

Static decay rates of carbon or metal-filled versus metal-painted or neat polycarbonate are shown in Table 18.6. All the filled polycarbonates performed similarly, a charge of 5 kV decayed in less than 0.06 s compared to more than 100 s for neat PC [63]. Metal-filled composites may show ohmic behavior in the interior but appear nonohmic overall due to surface depletion of the conductive species [68]. 

In the limit when the rates of interconversion kAB and kaA are much slower than the individual state decay rates KA and Kb, Eq. (9.39) reduces to the static case discussed above and the lifetime ratio of Eq. (9.37) provides useful information on the value of [Parameter]. However, in the most general case such lifetime ratio is a complex function of [Parameter] as given by Eq. (9.39). 

Fig. 6.16 NSE relaxation curves obtained from a 16% volume fraction poly(fluorosilicone) gel in acetone using tbe bigb resolution NSE spectrometer INI5 at tbe ILL, Grenoble. Tbe existence of plateaus that represent tbe level of excess scattering from static inhomogenieties at low wave vector Q is clearly visible. Tbe decay rates times of tbe dynamic parts yield tbe collective diffusion coefficient of tbe gel. (Reprinted with permission from [291]. Copyright 2002 American Chemical Society)...

The electron-spin time-correlation functions of Eq. (56) were evaluated numerically by constructing an ensemble of trajectories containing the time dependence of the spin operators and spatial functions, in a manner independent of the validity of the Redfield limit for the rotational modulation of the static ZFS. Before inserting thus obtained electron-spin time-correlation functions into an equation closely related to Eq. (38), Abernathy and Sharp also discussed the effect of distortional/vibrational processes on the electron spin relaxation. They suggested that the electron spin relaxation could be described in terms of simple exponential decay rate constant Ts, expressed as a sum of a rotational and a distortional contribution ... 

The so-called static dephasing regime (SDR) predicts a linear dependence of I/T2 on the magnetic moment of the particles in solution (22, 25). This regime describes the transverse relaxation of homogeneously distributed static protons in the presence of static, randomly distributed point dipoles. The free induction decay rate, I/T2, is then proportional to the part of the sample magnetization due to the dipoles (p), M = rap, where ra is the concentration... 

Calibration of FAGE1 from a static reactor (a Teflon film bag that collapses as sample is withdrawn) has been reported (78). In static decay, HO reacts with a tracer T that has a loss that can be measured by an independent technique T necessarily has no sinks other than HO reaction (see Table I) and no sources within the reactor. From equation 17, the instantaneous HO concentration is calculated from the instantaneous slope of a plot of ln[T] versus time. The presence of other reagents may be necessary to ensure sufficient HO however, the mechanisms by which HO is generated and lost are of no concern, because the loss of the tracer by reaction with whatever HO is present is what is observed. Turbulent transport must keep the reactor s contents well mixed so that the analytically measured HO concentration is representative of the volume-averaged HO concentration reflected by the tracer consumption. If the HO concentration is constant, the random error in [HO] calculated from the tracer decay slope can be obtained from the slope uncertainty of a least squares fit. Systematic error would arise from uncertainties in the rate constant for the T + HO reaction, but several tracers may be employed concurrently. In general, HO may be nonconstant in the reactor, so its concentration variation must be separated from noise associated with the [T] measurement, which must therefore be determined separately. 

A rather simple interpretation of the behaviour of vibrating electrodes can be obtained by considering the response to a square-wave motion, to which a sinusoid rather crudely approximates [33]. Here, it is considered that the concentration boundary layer is periodically renewed by the instantaneous rapid motion and that in the intervals between the square-wave steps the solution is at rest. This is a reasonable approximation for most practical purposes because the hydrodynamic boundary layer relaxation time is short, (Section 10.3.3). In this simple model, the waveform would instantaneously rise to a limit during the motion, decaying as a function of t m during the static phase. This decay rate will obviously be dependent on the size and geometry of the electrode wire, microwire, band or microband. If the delay time between steps were r then the mean current would vary as (l/r,)/o f 1/2df, i.e., as t, i/2 or as fm. 

The static experiments show that there is a complex between TBP and PNP at the dodecane/water interface. Even by simply mixing the two solutions it was clear that this interaction was time-dependent. However, the decay rate was sufficiently fast so that given the need to ensure uniform mixing in the bulk phases and the time required to accumulate a reasonable S/N, only the long time tail of the decay curve could be measured. No accurate estimate of the decay rate could be made in the Petri-dish. The solution was to construct a flow cell to measure the kinetics of the TBP and PNP interaction at the dodecane/water interface [48]. 

Although the energy level of surface electrons becomes independent of the material beyond roughly 20 nm, the surface state is not totally independent of the bulk phase. This situation can be demonstrated by the influence of the bulk phase on the decay rate of static charge. Figure 24.5 depicts the influence of the bulk phase... 

Ring, et al., (1998 and 1999) have used a time-dependent magnetic field and the combination of a static magnetic field in a direction perpendicular to that of a time-dependent field to create and manipulate novel coherences and to monitor the quantum beats associated with specifiable details of the time evolution of these coherences. The frequencies and decay rates of different classes of coherence (AMj = 2 and 1 polarization beats, AMj = 0 singlet triplet population beats) may be sampled and modified selectively. 

When the predissociation rate is so much larger than the radiative decay rate that the fluorescence quantum yield is too low to measure a radiative decay rate directly, it is possible to infer the decay rate of the parent molecule from the effect of a static magnetic field on the polarization of a photofragment (Buijsse and van der Zande, 1997). 

Form An antistat in liquid form may provide more immediate and lower static decay and resistivity properties than the same chemical composition used in powder form, likely because of differences in migration rate or dispersion. PO film forms also matter for instance, winding a film into a roll using high tension delays the migration of the antistat to the film surface, compared with an unwound film. 

Table 18.6 Static charge decay rate of selected polycarbonate-based plastics.

An accurate knowledge of the individual rates of vacancy decay is interesting in several fields. Firstly, transition rates present a sensitive tool to investigate details of atomic structure since they probe static properties (atomic wave functions) as well as dynamic properties (electron correlation and relaxation). Secondly, an accurate knowledge of relative decay rates is important in practical applications In experimental studies of ion-atom collisions either fluorescence or electron emission is detected and the ionization cross sections are derived. In the L-shell case uncertainties of fluorescence and Coster-Kronig yields are a limiting factor upon deriving ionization cross sections. ... 

More precise data on both energy levels and decay rates, plus additional theoretical work, will be needed to get more information about the short-distance behaviour of the static potential. Experimental studies of the 66 system, being the heaviest observed so far, and therefore the most non-relativistic, can play an important role in giving us this information. 

The formulas for the radiative and non-radiative decays rate in the quasi-static approximation were also derived by Gersten and Nitzan (GN) [48] who extended the quasi-static treatment to spheroids based on an expansion in terms of an orthogonal set of eigenfunctions, so that shape-induced shifts of radiative and non-radiative decay rates can be described. The accuracy of the GN decay rates versus the exact electrodynamic theory has been described in literature [47, 49, 50] for spherical nanoparticles, while no exact anal3d ic solution exists for spheroids [51]. 

The typical limitation of light scattering experiments "" " is that they cannot measure all quantities independently in order thoroughly to test the theory. For example, eq. (3.9) relates a dynamic quantity, the diffusion constant D, to a static quantity, the hydrodynamic radius Rh. D is usually measured by determining the initial decay rate of the dynamic structure factor S k, t) in the low-k limit. However, Rh is not measured independently, but rather determined indirectly using eq. (3.9). Of course, an independent measurement of Rh is easily possible in a simulation. 

Fig. 3.6 D k) (cf. eq. [3.14]) obtained from the dynamical data for Nd, = 30 (filled circles), 40 (filled triangles) and 60 (filled diamonds). Instead of trying to perform the limit r 0 the maximum value of D k, t) (see eq. [3.17]) was taken. Hence, the data should be viewed as an upper limit to the actual initial decay rate. For comparison, the data resulting from the static evaluation with Ewald sums are also included with corresponding open symbob (from Ref. 61).

In Ref. 61 the analysis of the initial decay rate of S k, t) was also done for A 76 0, studying the Ewald generalization of eq. (3.15). For the monomeric diffusion coefficient Do Dtinweg and Kremer used the value which was obtained from the diffusion constant D. In that sense the procedure can be viewed as fitted to A = 0 however, it should be noted that the value is physically very reasonable. In Fig. 3.6 these static values are compared to the data extracted from the actual dynamics. An accurate determination of D k) is not easy. In Ref. 61 the following procedure was adopted inspired by eq. 3.14, one can define... 

As was mentioned before, a static average over a dynamical operator yields the short-time behavior (i.e., the initial decay rate of the correlation functions). Eqs (3.9) and (3.15) are based on this reasoning. Moreover, as discussed in the previous section, there are reasons to believe that in the long chain limit the approach gives good results even for long times. 

---