Birks constant

Here G ° (E) denotes the yield for minimum ionizing particles or low LET radiation (for instance, 1 MeV electrons or y-rays) Kgi (E) is the field-dependent Birks constant. This formula is equivalent to the theoretical descriptions by Jaffe or Kramers (see Section 5.5). For a given field strength. Equation 43 should describe the apparent charge carrier yield as a function of the ionization density of the different particles. In Figure 20 data obtained by Ochsenbein for different particles are compared to Equation 43. The solid line was obtained with Kbi = 0.0295 cm/MeV. A more detailed consideration requires that the angle between the particle track and the electric field is to be taken into account (Aubert et al., 1990). 

Fig. 7.40 The temperature dependence of the linear rate constant for reaction of nickel with SO2 at temperatures in the range 500-1 000°C and at pressures from 0 013 to 1 atm (after Kofstad , Wotton and Birks , Kofstad and Akesson , Luthra and Worrell , Nakai and Takasawi and Seiersten and Kofstad )...

The effect of the substitution of a heavy-atom directly onto the nucleus of aromatic compounds (internal heavy-atom effect) on intercombinational radiative and nonradiative processes can be seen by examination of experimental data obtained for naphthalene and its derivatives. The data obtained by Ermolaev and Svitashev<104) and analyzed by Birks(24) to obtain individual rate constants for the various processes are collected in Table 5.9. 

In this case, chemiluminescence was monitored using a red-sensitive PMT to detect emissions from HFf. A factor-of-six enhancement in sensitivity to 1.1 parts per billion (ppbv) DMS was obtained. This is consistent with the fact that, based on the rate constant for the H + F2 rate determining step [Reaction (28)], the reaction can cycle approximately 7 times during the cell residence time and confirms the observation by Turnipseed and Birks [7] that F atoms are produced in the F2 + DMS reaction. 

Rate constants for the various processes follow the nomenclature of Birks et al.1 insofar as this is possible however, in view of the possible participation... 

The introduction of reversible photoassociation at higher fluor (or quencher) concentrations invalidates the analysis of fluorescence decay curves of either emitting species in terms of a single decay constant since these species do not relax independently accordingly the decay curves each represent the sum of two exponential components and the corresponding decay constants Ax and A2 are related to the photoassociation rate constants kDM and kMD and to the lifetimes rp and t of both emitting species. The treatment given below follows that of Birks, Dyson, and Munro.1... 

The rate constant kTD for fluorescence of the pyrene intermolecular solution excimer has been found to follow the relation kFD = n2(kFD)n=I, where n is the the refractive index of the solvent69 . The values of kTO for the 1-methylnaphthalene excimer in ethanol at various temperatures are also consistent with the above relation 76). The fact that (kFD)n=I is independent of solvent and temperature indicates that the excimer has a specific structure, according to Birks 69,71). Experimentally, it was observed much earlier that kFM = n2(kFM)n=i for the polycyclic aromatic hydrocarbons, and that k /kp is independent of solvent and temperature. Table 5 shows that agreement between independent investigators of the excimers of naphthalene compounds is not always good, as in the case of 1-methylnaphthalene. 

There have been many experimental studies of the quenching of fluorescence from aromatic molecules by such species as CC14, CBr4,02. The ratio between fluorescence intensity and (constant) photostimulation intensity is proportional to the fluorescence quenching quantum efficiency. Alternatively, the inverse fluorescence intensity should be linearly related to the quencher concentration the Stern—Volmer law [47]. Birks [6] has... 

SFTI-1 is a 14 amino acid cyclic peptide expressed in the seeds of sunflowers.91 As its name suggests, it is a potent trypsin inhibitor, and indeed is the most potent Bowman-Birk inhibitor (BBI) known, with a subnanomolar inhibition constant for trypsin. Although not strictly a toxin, since its natural function is not yet known, we include it here because of our focus on cyclic peptides from plants, and because other trypsin inhibitors from plants are regarded as toxins because of their toxic effects on insect pests. 

Figure 5.5. Relationship between the energy gap AE(T, - Sg) and the logarithm of the rate constant kj of intersystem crossing in aromatic hydrocarbons (data from Birks. 1970).

Thus, typical rate constants for the two nonradiative processes S S, and Sj-v So differ by a factor of 10 -10 (Birks, 1970). 

For the polystyrene matrices it is clear that k2 values on the order of 10 to 10 seem to be typical. Values of qD were calculated from these rate constants using as encounter radii either the 15 A suggested by Birks or the average intermolecular separation distance calculated from the equation derived by Chandrasekhar (13), whichever was smaller. The results are presented in Table II. Again very little individuality among the dopant molecules is noted. 

The photophysical behaviour of polystyrene in solution can be explained by a Birks-type scheme in which k[)M is an average rotational constant whereby a 1 3 intramolecular excimer is formed. On this basis. 

Figure 4.2 Birks scheme [1] of excitation and deactivation by bimolecular processes k M nd the rate constants of excimer association and dissociation,...

It should be anphasized that the development of the expressions for charge transfer kinetics given here is not completely general. It rests on the assumptions of absolute rate theory. More general treatments have been given in the literature where no a priori assumption of the form of the dependence of the rate constants on potential is made (Birke [1971], Holub et al. [1967]). A point which arises from these more general treatments is worth pursuing here. For the case of semiinfinite diffusion to a planar interface, the faradic impedance may be written in the form... 

R. L. Birke [1971] Operational Admittance of an Electrode Process where an a priori Dependence of Rate Constant on Potential Is Not Assumed, J. Electroanal. Chem. 33, 201-207. 

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