Exponential distance dependence

Composilion has a marked effect on p. Dilution can cause (i to drop by orders of magnitude. The functional dependence is often expressed in terms of an exponential dependence on intersite distance R=at m as suggested by the homogeneous lattice gas model, p c)percolation threshold for transport. 

St /G AG-0.14 V fluorescence quenching stilbene radical anion detected in transient absorption no Gs near injection site or in intervening sequence k = 1012-108 s 1 for 0-4 intervening A-T base-pairs (-3.4-17 A) exponential distance dependence of CT rate constant (3 0.6-0.7 A"1 small variations in k depending on whether G is in the A or T arm of the hairpin... 

Eng MP, Albinsson B (2006) Non-exponential distance dependence of bridge-mediated electronic coupling. Angew Chem Int Ed 45 5626—5629... 

On the other hand, it is known that PET is essentially a contact process described by an exponential distance dependence, which functions effectively at a donor-acceptor distance considerably shorter than that for FRET processes [72]. Thus, it is also feasible to increase donor-acceptor distance to reduce PET. A poly(fluorene-alt-1,4-phenylene) derivative with spiroanthracenyl groups (12) was synthesized... 

Cases of distance-dependent rate constants 1. Exponential distance dependence... 

Here Psa is the transfer probability. Esa represents the resonance condition (in practise the spectral overlap of the emission of S and the relevant absorption of A) and occurs in both formulas. The quantity gsA comprises the optical strengths of the relevant transitions and a distance-dependence of the type rsA n=6,8, etc.). The quantity /sa, however, is proportional to the wave function overlap of S and A and comprises an exponential distance-dependence. 

Using this apparatus, Binnig et al. demonstrated the exponential distance dependence of tunneling current over four orders of magnitude. Their first results are summarized in Fig. 1.6. The value of the work function was found to depend sharply on the condition of the surfaces. Initially, the measured values were around 0.6 - 0.7 eV. After repeated cleaning, the slope became much steeper. A value of 3.2 eV was obtained, which can last for several minutes. Being still lower than the value for clean surfaces, 4 — 5 eV, it was... 

It should be emphasized that the linearity of the plot in Figure 3 is merely a consequence of the rates of both charge transfer and triplet excitation transfer being exponentially distance dependent. It is the slope of the resulting line that contains the information about the relationship between the respective electronic coupling elements. In Figure 3, the slope is, within experimental error, equal to one, confirming that, indeed, 0 = + 0. ... 

ET rates have been measured in eight different Ru(bpy)2(im)(HisX) + derivatives of wild-type and mutant cytochromes c [16, 32, 68, 83]. Maximum ET rates do not correlate well with a simple exponential distance dependence (Figure 7). Two modified proteins, for example, have comparable ET rates (Ru(His72), 9.0 x 10 s ... 

This study, together with other experiments on 23(n) (vide infra) provided the first definitive experimental evidence for the exponential distance dependence of long-range ET processes which was predicted on the basis of an exponential decay behavior of the electronic coupling element, V i, with increasing donor-acceptor separation (Eq. 3). 

In some bridged A-br-D systems, in which the donor and acceptor are rigidly linked by a norbornylogous bridge (Ref. [39], pp. 623 626), it was found that the rate of electron transfer could be fitted to an exponential distance-dependent form ... 

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