Orientation factors

A fi nal factor in the an alysis of the energy-transfer efBcien-cies is the orientation fiuxor K, which is given by 

In these equations, Or is the angle between the emission transition dipole of the donor and the absorption transition 

Dependence of the Transfer Rate on Distance (r), the Overlap Integral (/), and 

The linear dependence offc on the overlap integral 7 has also been experimentally proven. This was accomplished using a D-A pair linted by a rigid steroid spacer. The 

Another important characteristic of RET is that the transfer rate is proportional to the decay rate of the fluoro-phore (Eq. [13.1]). This means that for a D-A pair spaced by the value, the rate of transfer will be kjsx ) whether the decay time is 10 ns or 10 ms. Hence, long-lived lanthanides are expected to display RET over distances comparable to those for the nanosecond-decay-time fluorophores, as demonstrated by transfer from Tb to Co in thermolysin. This fortunate result occurs because the transfer rate is proportional to the emission rate of the donor. The proportionality to the emissive rate is due to the term Qq/ d in Eq. [13.2]. It is interesting to speculate what would happen if the transfer rate were independent of the decay rate. In this case, a longer-lived donor would allow more time for energy transfer. Then energy transfer would occur over longer distances where the smaller rate of transfer would still be comparable to the donor decay rate. 

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The K factors in (C3.4.1) represent another very important facet of tire energy transfer [4, H]. These factors depend on tire orientations of tire donor and acceptor. For certain orientations tliey can reduce tire rate of energy transfer to zero—for otliers tliey effect an enhancement of tire energy transfer to its maximum possible rate. Figure C3.4.1 exhibits tire angles which define tire mutual orientation of a donor and acceptor pair in tenns of Arose angles the orientation factors and are given by [6, 7]... 

Fig. 9. Tangent modulus (T), tenacity (° ), and elongation (A ) as a function of (a) bitefiingence and (b) t-axis ciystaUine orientation factor for nylon-6. To...

The Bowyer and Bader [96] methodology can be used to predict stress-strain response of short fiber-rein-forced plastics. The stress on the composite (cT( ) at a given strain can be computed by fitting the response to a form of Eq. (4) with two parameters, the fiber orientation factor (Cfl) and interfacial shear strength (t,). 

Biefer, GJ Mason, SG, Electrokinetic Streaming, Viscous Flow and Electrical Conduction in Inter-Fiber Networks, The Pore Orientation Factor, Transactions of the Faraday Society 55, 1239, 1959. 

FIGURE 8.4 Orientation factor for the card-pack and head-to-tail dimers. 

IR dichroism has also been particularly helpful in this regard. Of predominant interest is the orientation factor S=( 1/2)(3—1) (see Chapter 8), which can be obtained experimentally from the ratio of absorbances of a chosen peak parallel and perpendicular to the direction in which an elastomer is stretched [5,249]. One representation of such results is the effect of network chain length on the reduced orientation factor [S]=S/(72—2 1), where X is the elongation. A comparison is made among typical theoretical results in which the affine model assumes the chain dimensions to change linearly with the imposed macroscopic strain, and the phantom model allows for junction fluctuations that make the relationship nonlinear. The experimental results were found to be close to the phantom relationship. Combined techniques, such as Fourier-transform infrared (FTIR) spectroscopy combined with rheometry (see Chapter 8), are also of increasing interest [250]. 

Dale, R., Eisinger, J. and Blumberg, W. (1979). The orientational freedom of molecular probes. The orientation factor in intramolecular energy transfer. Biophys. J. 26, 161-94. 

Importantly, in most applications the measured (change in) FRET efficiency cannot be translated directly into an average distance between donor and acceptor fluorophore because the fraction of donor molecules involved in FRET is unknown (i.e., all molecules display 25% FRET or 50% of the molecules display 50% FRET), and the orientation factor (k2) is unknown (see also Chapter 7). 

Thus, E is defined as the product of the energy transfer rate constant, ku and the fluorescence lifetime, xDA, of the donor experiencing quenching by the acceptor. The other quantities in Eq. (12.1) are the DA separation, rDA the DA overlap integral, / the refractive index of the transfer medium, n the orientation factor, k2 the normalized (to unit area) donor emission spectrum, (2) the acceptor extinction coefficient, eA(k) and the unperturbed donor quantum yield, QD. 

The localized product-NBO view also makes clear the importance of the non-planarity of the TS in achieving favorable hyperconjugative stabilizations, because interactions of 7t-planar geometry. Indeed, one can see that favorable vicinal n-a or a-7r overlap should primarily involve one end (hybrid) of each NBO, oriented, if possible, in the anti conformation for maximum stabilization. This viewpoint allows one to recognize the importance of angular and orientational factors that would not be evident in a purely topological framework. 

Both parts (a) and (b) of Example 6-1 illustrate that rates of molecular collisions are extremely large. If collision were the only factor involved in chemical reaction, the rates of all reactions would be virtually instantaneous (the rate of N2-02 collisions in air calculated in Example 6-l(a) corresponds to 4.5 X107 mol L-1 s-1 ). Evidently, the energy and orientation factors indicated in equation 6.4-2 are important, and we now turn attention to them. 

The way of using the index is flexible. Comparisons can be made at the level of process, subprocess, subsystem, or considering only part of the factors (e.g. only process oriented factors). Different process alternatives can be compared with each other on the basis of the ISI. Also the designs of process sections can be compared in terms of their indices in order to find the most vulnerable point in the design. Sometimes a comparison based on only one or two criteria is interesting. E.g. a toxicity hazard study can be done by considering only the toxic exposure subindex. Because its flexibility the total inherent safety index is quite easily integrated to simulation and optimization tools. 

Rate = Collision frequency x Energy factor x Orientation factor 4.4.1 Collision Frequency... 

Fig. 4.17. Angles involved in the definition of the orientation factor k2 (left) and examples of values of tc2 (right).

This section deals with a single donor-acceptor distance. Let us consider first the case where the donor and acceptor can freely rotate at a rate higher than the energy transfer rate, so that the orientation factor k2 can be taken as 2/3 (isotropic dynamic average). The donor-acceptor distance can then be determined by steady-state measurements via the value of the transfer efficiency (Eq. 9.3) ... 

Dale R. E., Eisinger J. and Blumberg W. E. (1975) The Orientational Freedom of Molecular Probes. The Orientation Factor in Intramolecular Energy Transfer, Biophys. J. 26, 161-194. 

Wu P. and Brand L. (1992) Orientation Factor in Steady-State and Time-Resolved Resonance Energy Transfer Measurements, Biochemistry 31, 7939-7947. 

Figure 1.20. (a) Angles 0 0y, and y, describing the relative orientation of the electronic transition dipole moments s between two dye molecules, (b) Relative orientations of the electronic transition dipole moments between two equal dye molecules in the channels of zeolite L. (c) Angular dependence of the orientation factor k2 under the anisotropic conditions (b) and averaged over y. 

It can be assumed that the orientation of the amorphous regions is a result of the deformation of a rubber-elastic network. Therefore, it can be expected that crystallization during spinning occurs at the neck, where the deformation is maximal. The amorphous phase develops into a load-bearing factor which is related to its orientation, as expressed by Hermans orientation factor. 

Figure 13.3 Crystalline (fc) and amorphous (fa) orientation factors as a function of take-up speed for the three PET samples described in Table 13.1 , branched , linear (IV, 0.66) A, linear (IV, 0.61) [13]. From Some effects of the rheological properties of PET on spinning line profile and structure developed in high-speed spinning, Perez, G., in High-Speed Fiber Spinning, Ziabicki, A. and Kawai, H. (Eds), 1985, pp. 333-362, copyright (1985 John Wiley Sons, Inc.). Reprinted by permission of John Wiley Sons, Inc.

Figure 13.3 also shows the orientation factors of the crystalline and amorphous regions as a function of take-up speed, which is pronounced in the case of a branched PET polymer. The shift towards increased freezing temperatures in branched polymer samples seems to be an indicator of higher elasticity (Figure 13.4). 

The goal of the current investigation was to achieve further insight into the nature of these interactions and to understand the stereoselectivity of biological systems, partially a result of orientation factors. It has been observed for a number of enzymes that the environment of the active site is relatively... 

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