Characteristics lifetime

In principle, FCS can also measure very slow processes. In this limit the measurements are constrained by the stability of the system and the patience of the investigator. Because FCS requires the statistical analysis of many fluctuations to yield an accurate estimation of rate parameters, the slower the typical fluctuation, the longer the time required for the measurement. The fractional error of an FCS measurement, expressed as the root mean square of fluorescence fluctuations divided by the mean fluorescence, varies as 1V-1/2, where N is the number of fluctuations that are measured. If the characteristic lifetime of a fluctuation is r, the duration of a measurement to achieve a fractional error of E = N l,/- is T = Nr. Suppose, for example, that r = 1 s. If 1% accuracy is desired, N = 104 and so T = 104 s. 

The resulting overall picture of liquid water is that of a very dynamical macromolecular system, where clusters of different size and structure coexist in different subvolumes of the liquid and each has characteristic lifetimes and specific temperature dependences. In our opinion, if we would... 

The conventional analysis of fluorescence decay is described in terms of a sum of one or more exponential terms, each with a characteristic lifetime... 

For long-term heat ageing, property retention depends on the property and grades considered. Impact strength and elongation at break are especially heat-sensitive characteristics. Lifetimes based on a 50% decay of elongation at break are evaluated at ... 

In Eqs. (S) and (T), [gas] and [ref] represent the time-dependent concentrations of the gas of interest and the reference gas, respectively, which are assumed to decay with characteristic lifetimes or response times after the instantaneous injection of the pulse, and ax (units of W m-2 per ppb or ppm) is the radiative forcing of the gas or reference per unit increase in their atmospheric concentrations. The value of ax is assumed to be time-independent. 

An excited state has a characteristic lifetime under given conditions of temperature, solvent and concentration of substrate, and of other species in the solution. These lifetimes are short, varying from more than 10 s at liquid-nitrogen temperature for some of the longest-lived triplets to less than 10-l- s for some of the shortest-lived singlets. A small number of representative values are shown in Table 1.3. 

Hydrogen atom transfer from anthracene, excited into its lowest excited singlet state, to anthraquinone impurity molecules creates a radical pair that strongly quenches the fluorescence from anthracene crystals. The reverse transfer rate constant, found from measurements of fluorescence intensity and its characteristic lifetime at different moments after the creation of the radical pair, varies from 106 to 10s s 1 in the range 110-65 K, kc = 4 x 104 s 1, TC = 60K. The kc values drops to 102 s 1 in the deuteroanthracene crystal [Lavrushko and Benderskii, 1978]. 

When one metal ion is used as a donor for sensitizing the emission of a second accepting metal ion, the characteristic lifetimes r of their excited states, which are related to their deactivation rates by r = k l, are affected by the metal-to-metal communication process. This situation can be simply modeled for the special case of an isolated d-f pair, in which the d-block chromophore (M) sensitizes the neighboring lanthanide ion (Ln) thanks to an energy transfer process described by the rate constant k 1 ". In absence of energy transfer, excited states of the two isolated chromophores decay with their intrinsic deactivation rates kxl and kLn, respectively, which provides eqs. (32) and (33) yielding eqs. (34) and (35) after integration ... 

The resonance illustrated in fig. 4.5 has a width 0.008 91 eV, corresponding to a lifetime of 7.39 x 10 s. This is much longer than the direct lifetime, justifying the concept of a resonance as a compound state with a characteristic lifetime. The physical constants that enable these calculations to be done easily are... 

Every study of liquid water at a molecular level must take into account three properties that together characterize the microscopic behavior and the thermodynamic qualities. These are the tetrahedral symmetry of the molecule, the large number of hydrogen bonds formed between near-neighbor molecules, and the very short characteristic lifetime of these bonds. 

However—and this is the third aspect—the characteristic lifetime of a hydrogen bond is very short (between 10 and 10 s) and this is why viscoelastic properties of a gel structure will never be observed even in short characteristic time experiments. The explanation of such a short time is that hydrogen bond lifetimes are determined by the proton dynamics [3,8]. In particular, large-amplitude librational movements take easily the proton from the region, between two oxygens, where the energy of the bond is sufficiently large. 

The formation of most of the heavy elements occurs in one of two processes of neutron capture the s-process or the r-process. These two broad divisions are distinguished on the basis of the relative lifetimes for neutron captures (Xn) and electron decays (t ). The condition that t > where Tp is a characteristic lifetime for /3-unstable nuclei near the valley of /3-stability, ensures that as captures proceed the neutron-capture path will itself remain close to the valley of /3-stability. This defines the s-process. In contrast, when it follows that successive neutron captures will proceed into the neutron-rich regions off the /3-stable valley. Following the exhaustion of the neutron flux, the capture products approach the position of the valley of /3-stability by /3-decay, forming the r-process nuclei. The s-process and r-process patterns in solar system matter are those shown in Figure 2. 

MD simulations are used to further test the new effective force fields. The main features observed are given by changes in the dynamic behavior. The new functions yield shorter characteristic lifetimes for water molecules in the first ionic shell than those found when the 12-6 function is used to represent the short-range interactions. Although more studies are required, these simulations indicate that combinations of short-range interaction exponents such as those proposed here may be more suitable for the representation of aqueous electrolyte solutions at high temperatures. 

The radionuclides which can be fabricated together with their characteristics (lifetime energies of emitting radiation) are shown in Table 4.9. 

A collection of fluorescing molecules in a particular homogeneous environment has a characteristic lifetime. In a different environment, the same molecules may have a different lifetime. A collection of two species, either different molecules or similar molecules in different microenvironments, may exhibit a fluorescent decay with a time course that contains contributions fi-om both species. Thus we would observe a biexponential decay with two distinct lifetimes. 

Of course, it is possible to have more than two fluorescing species in solution, in which case F(t) is multiexponential, with each species having a characteristic lifetime. In practice, one assumes that the decay law with the fewest terms that adequately fits the experimental data is indicative of the number of distinct fluorescent species. In other words, if no monoexponential decay can be found to fit... 

An original use of lanthanide metals in the field of ionic liquid crystals was proposed by Biinzli and coworkers [78, 79]. They doped ionic liquid crystals with europium ions, and exploited their photophysical properties. They showed that emission characteristics, lifetime of the excited state, and intensity of the hypersensitive... 

In Fig. 20 we portray the results of model calculations for the time dependence of /(f), based on Eqs. (86), (92) and (93), for superfluid ( He)jy clusters with Af = 1.88 X 10 at r = 0.4 K. These calculations were performed for d = 39 A, which falls well in the physically acceptable region of d. This /(f) versus f curve exhibits a near exponential decay with time, with the characteristic lifetime Ttun for electron tunneling. Using the simple relation /(T-ruN)/f(0) = we obtained from Fig. 20 that ttun — 8 x lO s for Ai= 1.88 x 10, which is included in Table VII. 

The goals of a quantitative description of reliability are determination of the failure rate during the working lifetime and prediction of the characteristic lifetime of a system or component. 

When the probability density function fit) is known (or R(t) or F(t)), the mean time to failure MTTF, which is the characteristic lifetime, can easily be calculated as... 

This rather simple kinetic model is getting obscured by the fact that we cannot measure the protons but the fluorescence of OH and 4>0-, each decaying to its ground state with a characteristic lifetime (t and t, respectively). It should also be remembered that the lifetime is affected by radiative and nonradiative transition and the rate of the nonradiative transition may vary with the conditions prevailing in the microspace (Kosower et al., 1975 and 1978 Kosower and Dodiuk, 1978 Dodiuk et al., 1979). 

Kinetics of Electron Scavenging. If a single characteristic lifetime, t = l/ku could be ascribed to the geminate recombination process... 

These equations can be further simplified by defining r- and q-liniited characteristic lifetimes r < and ry of Rv Let ty he l/(y. the average lifetime of R- as limited by q. Let xK iy when (Q) -(RMgX). Also, define the r-limited characteristic diffusion distance oK oK - (I)ruf . Then (from equation 7.26)... 

The characteristic lifetime of RX is tk, l-. i and that of li is homogeneous-reaction limited lifetimes rh are lO /fi.. which is at least one order of magnitude less than r, (t, 5 10 - s) when A. > 10 M s. Thus, the minimum value of the rate constant for a reaction that can exhibit reaction-mixing effects is well below the diffusion-control limit. Reactions of Me, with RX might well fall into the range for these effects. 

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