Energy transfer distance dependence

The energy transfer distance depends on the quenching mechanism. Different mechanisms to transfer the energy are known ... 

N. Koga, K. Sameshima, K. Morokuma, Ab initio MO calculations of electronic coupling matrix elements on model systems for intramolecular electron transfer, hole transfer, and triplet energy transfer distance dependence and pathway in electron transfer and relationship of triplet energy transfer with electron and hole transfer, J. Phys. Chem., 1993, 97, 13117-13125. 

The first term is due to spontaneous radiative relaxation and nonradiative phonon relaxation as described in eq. (13), where / , is the probability of ion i in the excited state. The second term is due to energy transfer induced by ion-ion interaction, where W es and W A are rates of resonant and phonon-assistant energy transfer, which depend on distance between donor and acceptor RtJ. For resonant energy transfer... 

It is clear from eq. (15) that a modification of the density of phonon states in nanocrystals influences the efficiency of energy transfer. Because the energy transfer rate depends also on the distance between the donor and acceptor, the transfer in very small nanocrystals is restricted. This restriction may be understood based on the fact that the hopping length and the transfer probability are restricted for a donor to find a matching acceptor in the neighborhood of the nanoparticle. 

A simple theoretical approach has been developed to simulate the decay of a donor excited state in the presence of electronic energy transfer in polymer coils with arbitrary degrees of non-nearest neighbour, cross-chain transfer and transfer distance dependencies Excimer fluorescence from pyrene end groups... 

Smitha. M.A. Prasad, E. Gopidas. K.R. Photoinduced electron transfer in hydrogen bonded donor-acceptor sys- 31. terns. Free energy and distance dependence studies and an analysis of the role of diffusion. J. Am. Chem. Soc. 2001,... 

Figure 3. Fluorescence Resonance Energy Transfer in pH sensing. The energy transfer is dependent upon the distance between donor and acceptor molecules, the extent of spectral overlap between donor emission and acceptor absorbance, the quantum yield of the donor and extinction coefficient of the acceptor.

Coloration efficiency, defined as the magnitude of the absorbance from C at 600 nm, was also found to depend on DA (X = C H5) concentration, and saturation (i.e., nonhnear response) was noted at 25 wt% at a total dose of 1000 Gy. From a plot of coloration intensity versus DA concentration in PS films of constant thickness, an energy transfer distance, R = 14 A, from an aromatic group of PS to a molecule of DA could be calculated using a modified Perrin expression (Equation 3.36). A.,.,and Ap are absorbances extrapolated to infinite concentration and at known concentrations of DA, respectively. N is Avogadro s number and V is the reaction volume, assumed to be 4/3 n where R is the distance at which 50% of the PS transfer their excitation energy to molecules of DA... 

Deniz A A, Dahan M, Grunwell J R, Ha T, Faulhaber A E, Chemla D S, Weiss S and Schultz P G 1999 Single-pair fluorescence resonance energy transfer on freely diffusing molecules observation of Forster distance dependence and subpopulations Proc. Natl Acad. Sc/. USA 96 3670-5... 

In (C3.4.I) we find tliree major fonns of dependence on distance RT°,R intennediate and radiative types of energy transfer. The intennediate part usually makes a significant contribution at distances of about a hundred or a few hundred nanometres, where all tliree components Wp, Wj and are comparable in magnitude. At shorter distances Wp dominates, whereas at larger distances dominates. It is... 

Wlien a temperature difference exists in or across a body, an energy transfer occurs from the high-tem-perature region to the low-temperature region. This heat transfer, q, which can occur in gases, liquids, and solids, depends on a change m temperature, AT, over a distance. Ax (i.e., AT/z)ix) and a positive constant, k, which is called the thermal conductivity of the material. In equation form, the rate of conductive heat transfer per unit area is written as... 

The occurrence of energy transfer requires electronic interactions and therefore its rate decreases with increasing distance. Depending on the interaction mechanism, the distance dependence may follow a 1/r (resonance (Forster) mechanism) or e (exchange (Dexter) mechanisms) [ 1 ]. In both cases, energy transfer is favored by overlap between the emission spectrum of the donor and the absorption spectrum of the acceptor. 

Et /ZG AG -0.2 V fluorescence quenching correlates with CT driving force no spectral overlap for energy transfer no Zs in injection site or intervening sequence k = 2 x 1011 s 1 observed up to 20 A in time-resolved and steady-state experiments shallow dependence of CT yield between 6-24 A (y = 0.2-0.3) no dependence of kci between 10-17 A strong efficiency and distance dependence of CT yield vary with Z flanking sequence and intervening mismatches... 

Figure 6.8. Dependence of the energy transfer efficiency (E = etin the figure) on distance. The slope of 5.9 is in excellent agreement with the r e dependence for Forster-type transfer. From Stryer and Haugh-land.(45) Reprinted by permission of Proc. Nat. Acad. Sci. U.S.

As the pressure increases from low values, the pressure-dependent term in the denominator of Eq. (101) becomes significant, and the heat transfer is reduced from what is predicted from the free molecular flow heat transfer equation. Physically, this reduction in heat flow is a result of gas-gas collisions interfering with direct energy transfer between the gas molecules and the surfaces. If we use the heat conductivity parameters for water vapor and assume that the energy accommodation coefficient is unity, (aA0/X)dP — 150 I d cm- Thus, at a typical pressure for freeze drying of 0.1 torr, this term is unity at d 0.7 mm. Thus, gas-gas collisions reduce free molecular flow heat transfer by at least a factor of 2 for surfaces separated by less than 1 mm. Most heat transfer processes in freeze drying involve separation distances of at least a few tenths of a millimeter, so transition flow heat transfer is the most important mode of heat transfer through the gas. 

First calculations of the optimum distance between the reactants, R, taking into account the dependence of the probability of proton transfer between the unexcited vibrational energy levels on the transfer distance have been performed in Ref. 42 assuming classical character of the reactant motion. Effects of this type were considered also in Ref. 43 in another model. It was shown that R depends on the temperature and this dependence leads to a distortion of the Arrhenius temperature dependence of the transition probability. 

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