Rate of energy transfer

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]... 

The measurement of fluorescence intensity from a compound containing cliromophores of two spectral types is an example of a system for which it is reasonable to operate witli tire average rates of energy transfer between spectral pools of molecules. Let us consider tire simple case of two spectral pools of donor and acceptor molecules, as illustrated in figure C3.4.2 [18]. The average rate of energy transfer can be calculated as... 

The product of the collision energy E(L) and collision frequency f L) is integrated over all crystals in the distribution to obtain the total rate of energy transfer. Different approaches have been used to estimate E(L) and f L), both for particle impacts and turbulent fluid induced attrition. 

A substance (usually liquid) employed to remove surface metal oxides in preparation for soldering, brazing or other metal fusion techniques. Also, the rate of energy transfer across a given surface area. 

The formation of activated species during mechanoehemieal degradation is, in general, not sufficiently documented both experimentally and with respect to the proposed mechanisms to give a definite proof of their existence. In the dilute state, the rate of energy transfer is high and it is reasonable to assume that any activated species, if present, will be thermalized well before the occurrence of a chemical reaction. 

If a mass Gl of liquid is raised through a net height hr by a mass GA of air in unit time, the net rate of energy transfer to the liquid is Gighr. If the pressure of the entering air is P. the work done by the air in expanding isothermally to atmospheric pressure Pa is given by ... 

Rate of energy gain / Rate of energy transfer by coolant flow / from the reactor to the jacket/... 

Inasmuch as the interaction energy can be related to the transition moments, Forster has been able to develop a quantitative expression for the rate of energy transfer due to dipole-dipole interactions in terms of experimental parameters<4 aB-30) ... 

The efficiency of resonance transfer is often given in terms of a critical radius R0. If R0 is the distance such that the rate of energy transfer is equal to the sum of all other donor deactivation rates... 

However, cfc-stilbene does not behave as a classical triplet energy acceptor inasmuch as the rate of energy transfer is much larger than would be predicted from Eq. (9.7) for donors with triplet energies less than 57 kcal/mole. This is then additional information consistent with Eq. (9.5). 

The saturation behavior of a spectrum - the variation of integrated intensity with microwave power - is related to the spin-lattice relaxation time, a measure of the rate of energy transfer between the electron spin and its surroundings. Saturation often depends on the same structural and dynamic properties as line widths. 

Post-Forster Subsequent derivations of the rate of energy transfer... 

The efficiency of energy transfer (E) is the ratio of the number of energy transfer occurrences from D to A divided by the total number of excitations of a donor molecule. This is the same as the ratio of the rate of energy transfer to the total rate of deactivation of the excited donor. The rate of energy transfer between single donor and acceptor molecules is proportional to 1 /r6DA (Eq. (1.1)) this is a very... 

The important conclusion is that we can measure the rate of energy transfer without ever measuring the energy transfer directly, provided we could measure the total rate constant of decay from the excited state in both cases. In the case of fluorescence, this total rate is the reciprocal of the measured fluorescence lifetime the... 

The rate of energy transfer is simply the difference in the reciprocal fluorescence lifetimes of the donor, measured in the presence and absence of acceptor. Of course, if we measure the fluorescence lifetime of the donor, we do not have to keep track of the number of donors that have been excited this is a great advantage of measuring lifetimes. 

The probability per unit time for photodestruction of the donor ( pb,z>) is always the same, in the presence and absence of the acceptor. However, in the presence of the competing process of energy transfer the overall rate of photobleaching is less. Therefore, we can use the rate of photobleaching to measure the rate of energy transfer. This method uses measurements recorded in the second to minute range in order to measure rates in the nanosecond range. 

We now focus our attention on the presence of the unperturbed donor quantum yield, Qd, in the definition of R60 [Eq. (12.1)]. We have pointed out previously [1, 2] that xd appears both in the numerator and denominator of kt and, therefore, cancels out. In fact, xo is absent from the more fundamental expression representing the essence of the Forster relationship, namely the ratio of the rate of energy transfer, kt, to the radiative rate constant, kf [Eq. (12.3)]. Thus, this quantity can be expressed in the form of a simplified Forster constant we denote as rc. We propose that ro is better suited to FRET measurements based on acceptor ( donor) properties in that it avoids the arbitrary introduction into the definition of Ra of a quantity (i />) that can vary from one position to another in an unknown and indeterminate manner (for example due to changes in refractive index, [3]), and thereby bypasses the requirement for an estimation of E [Eq. (12.1)]. 

The rate of energy transfer at a very short donor-acceptor separation R by the exchange mechanism has been given by Dexter (1953) as follows ... 

It was concluded, therefore, that intramolecular energy transfer is involved in the chemiluminescence of 58. The rate of energy transfer was calculated to be 2.3 X 107 sec-1 12 ). 

Classically, a circularly polarized light beam with angular frequency w(= 2nv) transfers angular momentum at a rate of E/w, where E is the rate of energy transfer. Considered as a beam of photons, E = Nhui/2-n, so that the angular momentum of each photon is h/2n = h. 

Energy transfer Because the species are continually in collision, the rate of energy transfer is never considered to be the rate-limiting step, unlike in unimolec-ular gas-phase reactions. 

How many of the reactions in this mechanism might be influenced by the rate of energy transfer One of them is the termination step, which can be thought of as a three-step process (reactions (7) to (9) below). As described in Section 6.4.3, there are possible further complications, since two other product channels are possible (reactions (10) and (11)). 

As discussed in Section 2.1, in high-Reynolds-number turbulent flows the scalar dissipation rate is equal to the rate of energy transfer through the inertial range of the turbulence energy spectrum. The usual modeling approach is thus to use a transport equation for the transfer rate instead of the detailed balance equation for the dissipation rate derived from (1.27). Nevertheless, in order to understand better the small-scale physical phenomena that determine e, we will derive its transport equation starting from (2.99). 

In a subsequent study, Agrawal, Raff and Thompson showed that the sticking probability for the molecule was independent of the interactions used for the substrate atoms. The mobility of the H atoms and the rate of energy transfer between the H atoms and the substrate, however, were reported to depend somewhat on the lattice. Despite the small dependence on the substrate model, the major results of the initial study remained unchanged. 

Two important factors determine the efficiency with which energy is transferred from the donor to the acceptor the extent of spectral overlap and the distance that separates the donor-acceptor pair (Fig. 2A). The spectral overlap for any particular pair (e.g., FITC-TRITC or FITC-PE) is constant. However, the rate of energy transfer is extremely sensitive to changes in distance because it is inversely proportional to the sixth power of the distance separating the two fluorochromes. By using the same donor-acceptor pair, FRET is useful for studying relative changes in either molecular conformation or intermolecular interactions. 

It is convenient initially to classify elementary reactions either as energy-transfer-limited or chemical reaction-rate-limited processes. In the former class, the observed rate corresponds to the rate of energy transfer to or from a species either by intermolecular collisions or by radiation, or intramolecular-ly due to energy transfer between different degrees of freedom of a species. All thermally activated unimolecular reactions become energy-transfer-limited at high temperatures and low pressures, because the reactant can receive the necessary activation energy only by intennolecular collisions. 

Chemical processes, in contrast, are processes that are not limited by rates of energy transfer. In thermal processes, chemical reactions occur under conditions in which the statistical distribution of molecular energies obey the Maxwell-Boltzmann form, i.e., the fraction of species that have an energy E or larger is proportional to e p(—E/RT). In other words, the rates of intermolecular collisions are rapid enough that all the species become thermalized with respect to the bulk gas mixture (Golden and Larson, 1984 Benson, 1976). 

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