Static lifetime

To measure the lifetime of hydrocarbon reserves, often the static lifetime of reserves (also called the reserve production ratio) is calculated as the ratio between reserves and the annual production of the current year. A criticism of this approach is that it seems unrealistic to assume that the production of, e.g., crude oil will remain constant in future at today s level, and then suddenly fall from a high level down to zero it can rather be expected that there will be an increase to a peak production and then a gradual decline in production. 

Table 3.9 shows the distribution of world hard coal reserves and resources in 2005. Total reserves amounted to 728 Gt (626 Gtce), of which the vast majority are located in the USA and China, followed by India and Russia. The top ten countries represent 85% of total reserves. Considering the production of 2005, the static lifetime of hard coal can be calculated at around 150 years however, we should acknowledge the simplicity of this approach, as coal use is expected to increase significantly in the future. As for hard coal resources, whose quantification is more uncertain, Russia is leading, followed by China and the United States. Figure 3.22 shows the geographical distribution of cumulative production, reserves and resources of hard coal. 

A comparison of the global ciunulative production of tungsten, the reserves, and the static lifetime presented in Fig. 2.5 is very informative. From this comparison, it can be seen that the reserves increased from 700.0001 in 1951 to 2.3 million t in 1978, in spite of considerable production growth rates. This increases the static lifetime of the reserves from 38 to 49 years. 

FIGURE 2.5. Cumulative mine production, reserves, and static lifetime of tungsten (1.1.1946-1.1.1978) [2.19]. 

The question is often asked. How often should calibration be carried out Is it sufficient to do it once, or should it be repeated The answer to this question depends on the instrument type. A very simple instrument that is robust and stable may require calibrating only once during its lifetime. Some fundamental meters do not need calibration at all. A Pitot-static tube or a liquid U-tube manometer are examples of such simple instruments. On the other hand, complicated instruments with many components or sensitive components may need calibration at short intervals. Also fouling and wearing are reasons not only for maintenance but also calibration. Thus the proper calibration interval depends on the instrument itself and its use. The manufacturers recommendations as well as past experience are often the only guidelines. 

Most Mossbauer spectra are split because of the hyperfine interaction of the absorber (or source) nuclei with their electron shell and chemical environment which lifts the degeneracy of the nuclear states. If the hyperfine interaction is static with respect to the nuclear lifetime, the Mossbauer spectrum is a superposition of separate lines (i), according to the number of possible transitions. Each line has its own effective thickness t i), which is a fraction of the total thickness, determined by the relative intensity W of the lines, such that t i) = Wit. 

Static SIMS, used for sub-monolayer elemental analysis. At the lowest current densities and hence the lowest rates of erosion, a monolayer on the surface has a lifetime of many hours. The surface is essentially unchanging during the experiment, but a vacuum system at a pressure of 10 10mbar is needed to allow adequate time to complete the analysis. In favourable cases, as little as 0.1% of a monolayer of material can be detected. 

The commercialization of inexpensive robust LED and laser diode sources down to the uv region (370 nm) and cheaper fast electronics has boosted the application of luminescence lifetime-based sensors, using both the pump-and-probe and phase-sensitive techniques. The latter has found wider application in marketed optosensors since cheaper and more simple acquisition and data processing electronics are required due to the limited bandwidth of the sinusoidal tone(s) used for the luminophore excitation. Advantages of luminescence lifetime sensing also include the linearity of the Stem-Volmer plot, regardless the static or dynamic nature of the quenching mechanism (equation 10) ... 

The time necessary for removing one monolayer during a SIMS experiment depends not only on the sputter yield, but also on the type of sample under study. We will make an estimate for two extremes. First, the surface of a metal contains about 1015 atoms/cm2. If we use an ion beam with a current density of 1 nA/cm2, then we need some 150 000 s - about 40 h - to remove one monolayer if the sputter yield is 1, and 4 h if the sputter rate is 10. However, if we are working with polymers we need significantly lower ion doses to remove a monolayer. It is believed [4] that one impact of a primary ion affects an area of about 10 nm2, which is equivalent to a circle of about 3.5 nm diameter. Hence if the sample consists, for example, of a monolayer film of polymer material, a dose of 10n ions/cm2 could in principle be sufficient to remove or alter all material on the surface. With a current density of 1 nA this takes about 1500 s or 25 min only. For adsorbates such as CO adsorbed on a metal surface, we estimate that the monolayer lifetime is at least a factor of 10 higher than that for polymer samples. Thus for static SIMS, one needs primary ion current densities on the order of 1 nA/cm2 or less, and one should be able to collect all spectra of one sample within a quarter of an hour. 

There is a linear relationship between tq/t and the concentration of the quencher. In these sensors, the static fluorescence quenching has no effect on the lifetimes. 

Fluorescence quenching is described in terms of two mechanisms that show different dependencies on quencher concentration. In dynamic quenching, the quencher can diffuse at least a few nanometers on the time scale of the excited state lifetime (nanoseconds). In static quenching, mass diffusion is suppressed. Only those dye molecules which are accidentally close to a quencher will be affected. Those far from a quencher will fluoresce normally, unaware of the presence of quenchers in the system. These processes are described below for the specific case of PMMA-Phe quenched by MEK. 

Creep leads ultimately to rupture, referred to as creep-rupture, stress-rupture or static fatigue. Creep-rupture of thermoplastics can take three different forms brittle failure at low temperatures and high strain rates ductile failure at intermediate loads and temperatures and slow, low energy brittle failure at long lifetimes. It is this transition back to brittle failure that is critical in the prediction of lifetime, and it is always prudent to assume that such a transition will occur [1], A notch or stress concentration will help to initiate failure. 

Finally, it should be noted that homo-FRET, which is just the exchange of energies between the same dyes, is undetected by common spectroscopic or lifetime measurements and needs the hetero-FRET probing for its detection. The Red-Edge effect allows the easy distinguishing of the decrease of anisotropy due to FRET (static effect) from that occurring due to rotational freedom of fluorophores (dynamic effect), which does not depend on excitation wavelength. 

Following an external perturbation, the fluorescence quantum yield can remain proportional to the lifetime of the excited state (e.g. in the case of dynamic quenching (see Chapter 4), variation in temperature, etc.). However, such a proportionality may not be valid if de-excitation pathways - different from those described above - result from interactions with other molecules. A typical case where the fluorescence quantum yield is affected without any change in excited-state lifetime is the formation of a ground-state complex that is non-fluorescent (static quenching see Chapter 4). 

Case C Q is not in large excess and mutual approach of M and Q is possible during the excited-state lifetime. The bimolecular excited-state process is then diffusion-controlled. This type of quenching is called dynamic quenching (see Section 4.2.2). At high concentrations of Q, static quenching may occur in addition to dynamic quenching (see Section 4.2.4). 

The excited-state lifetime of the uncomplexed fluorophore M is unaffected, in contrast to dynamic quenching. The fluorescence intensity of the solution decreases upon addition of Q, but the fluorescence decay after pulse excitation is unaffected. Quinones, hydroquinones, purines and pyrimidines are well-known examples of molecules responsible for static quenching. 

A linear relationship is thus obtained, as in the case of the Stern-Volmer plot (Eq. 4.10), but there is no change in excited-state lifetime for static quenching, whereas in the case of dynamic quenching the ratio I0/I is proportional to the ratio to/t of the lifetimes. 

Figure B8.2.1 shows the fluorescence spectra of DIPHANT in a polybutadiene matrix. The h/lu ratios turned out to be significantly lower than in solution, which means that the internal rotation of the probe is restricted in such a relatively rigid polymer matrix. The fluorescence intensity of the monomer is approximately constant at temperatures ranging from —100 to —20 °C, which indicates that the probe motions are hindered, and then decreases with a concomitant increase in the excimer fluorescence. The onset of probe mobility, detected by the start of the decrease in the monomer intensity and lifetime occurs at about —20 °C, i.e. well above the low-frequency static reference temperature Tg (glass transition temperature) of the polybutadiene sample, which is —91 °C (measured at 1 Hz). This temperature shift shows the strong dependence of the apparent polymer flexibility on the characteristic frequency of the experimental technique. This frequency is the reciprocal of the monomer excited-state...

Dr / r2 1 the donor and acceptor cannot significantly diffuse during the excited-state lifetime of the donor. This case is called the static limit. Distinction according to the mechanism of tranfer should be made. 

It should be emphasized that, because small molecules in usual solvents have diffusion coefficients <10 cm2 s-1, the rapid diffusion limit can be attained only for donors with lifetimes of 1 ms. This is the case for lanthanide ions for instance, the lifetime of Tb3+ chelated to dipicolinate is 2.2 ms. Stryer and coworkers (1978) showed that using Tb3+ as a donor and rhodamine B as an acceptor, the concentration of rhodamine B resulting in 50% transfer was 6.7 x 10 6 M, which is three orders of magnitude less than the concentration corresponding to 50% transfer in the static limit. 

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). 

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