Decay slope

Quantitative data on local structure can be obtained via an analysis of the decaying slope next to the absorption edge. The absorption of an X-ray photon boosts a core electron up into an unoccupied band of the material which, in a metal, is the conduction band above the Fermi level. Electrons in such a band behave as if nearly free and no fine structure would be expected on the absorption tail . However, fine structure is observed up to 500 to 1000eV above the edge (see Figure 2.73(b)). The ripples are known as the Kronig fine structure or extended X-ray absorption fine structure (EX AFS). 

Calibration of FAGE1 from a static reactor (a Teflon film bag that collapses as sample is withdrawn) has been reported (78).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. 

An alternative theoretical treatment of a,a -dipyridylpolyene complexes was proposed in 1990 by Reimers and Hush [41], in which the quantum calculation is performed at the CNDO level with an empirical adjustment of the d levels of ruthenium with respect to the bridging ligand orbitals. This calculation gave a higher decay slope of —0.13 A . In more recent work, the explicit treatment of the solvent allowed reproduction of experimental coupling within 25 /) of experimental data, with a decay slope of -0.127 A [60]. 

Bisporphyrin compounds linked by one to three phenylene spacers have been used by McLendon et al. to probe electron transfer between excited zinc porphyrin and Fe(III)(bisimidazole) porphyrin as acceptor site [76]. Electron transfer rates were deduced from the decrease in the lifetime of the first excited singlet state of the zinc porphyrin. The variation with the edge-to-edge distance between porphyrins gave a decay slope of —0.4A. This dependence was attributed by the authors to the poor conjugation between adjacent phenylene rings twisted by 55° from each other. 

Table 2. Parameters of the intervalence bands. Fab values from Hush s formula, and decay slope for compounds constituting a series. ... 

The comparison with theoretical estimations on metal/molecule/metal nanojunctions could be fruitful since, in both approaches, one tries to optimize the preexponential term and the decay slope. A recent systematic theoretical study by Joachim and Magoga has ranked a large number of bridge structures, made of several repeat units [91]. They were characterized by the value of the conductance, and its rate of decay with distance. The comparison with the compounds of the... 

Vlll. Relations between Tafel and Potential-Decay Slopes... 

We have remarked earlier that the treatment given above is based on an assumption for the case of that is, they are in an effective parallel combination. This is not strictly correct for a number of conditions, so the logarithmic potential-decay slopes in relation to Tafel slopes must be worked out from the full kinetic equations of Harrington and Conway (104) referred to earlier, based on the relevant mechanism of the electrode reaction. Numerical solution procedures, using computer simulation calculations, are then usually necessary for comparison with observed experimental behavior. 

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