Collisional energy transfer

In this chapter we shall first outline the basic concepts of the various mechanisms for energy redistribution, followed by a very brief overview of collisional intennoleciilar energy transfer in chemical reaction systems. The main part of this chapter deals with true intramolecular energy transfer in polyatomic molecules, which is a topic of particular current importance. Stress is placed on basic ideas and concepts. It is not the aim of this chapter to review in detail the vast literature on this topic we refer to some of the key reviews and books [U, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, and 32] and the literature cited therein. These cover a variety of aspects of tire topic and fiirther, more detailed references will be given tliroiighoiit this review. We should mention here the energy transfer processes, which are of fiindamental importance but are beyond the scope of this review, such as electronic energy transfer by mechanisms of the Forster type [33, 34] and related processes. 

Figure A3.13.1. Schematic energy level diagram and relationship between mtemiolecular (collisional or radiative) and intramolecular energy transfer between states of isolated molecules. The fat horizontal bars indicate diin energy shells of nearly degenerate states.

The fimdamental kinetic master equations for collisional energy redistribution follow the rules of the kinetic equations for all elementary reactions. Indeed an energy transfer process by inelastic collision, equation (A3.13.5). can be considered as a somewhat special reaction . The kinetic differential equations for these processes have been discussed in the general context of chapter A3.4 on gas kmetics. We discuss here some special aspects related to collisional energy transfer in reactive systems. The general master equation for relaxation and reaction is of the type [H, 12 and 13, 15, 25, 40, 4T ] ... 

Collisional energy transfer in molecules is a field in itself and is of relevance for kinetic theory (chapter A3.1). gas phase kmetics (chapter A3.4). RRKM theory (chapter A3.12). the theory of unimolecular reactions in general,... 

The standard mechanisms of collisional energy transfer for both small and large molecules have been treated extensively and a variety of scaling laws have been proposed to simplify the complicated body of data [58, 59, 75]. To conclude, one of the most efficient special mechanisms for energy transfer is the quasi-reactive process involving chemically bound intennediates, as in the example of the reaction ... 

Lenzer T, Luther K, Troe J, Gilbert R G and Urn K F 1995 Trajectory simulations of collisional energy transfer in highly excited benzene and hexafluorobenzene J. Chem. Phys. 103 626-41... 

Grigoleit U, Lenzer T and Luther K 2000 Temperature dependence of collisional energy transfer in highly excited aromatics studied by classical trajectory calculations Z. Phys. Chem., A/F214 1065-85... 

Hold U, Lenzer T, Luther K, Reihs K and Symonds A C 2000 Collisional energy transfer probabilities of highly excited molecules from kinetically controlled selective ionization (KCSI). I. The KCSI technique experimental approach for the determination of P(E, E) in the quasicontinuous energy ranged. Chem. Phys. 112 4076-89... 

Michaels C A, Lin Z, Mullin A S, Tapalian H C and Flynn G W 1997 Translational and rotational excitation of the C02(00°0) vibrationless state in the collisional quenching of highly vibrationally excited perfluorobenzene evidence for impulsive collisions accompanied by large energy transfers J. Chem. Phys. 106 7055-71... 

Brown N J and Miller J A 1984 Collisional energy transfer in the low-pressure-limit unimoleoular dissooiation of FIO2 J. Chem. Rhys. 80 5568-80... 

The states arising from the. .. Ip Ss configuration of Ne have very nearly the same energy as that of the 2 Sq state of He so that collisional energy transfer results in efficient population of these Ne states. Similarly, the states arising from the. .. configuration... 

Quenching is the reduction in fluorescence intensity and can be caused by various processes. It occurs either during the lifetime of the excited state or in the ground state. Quenching processes that happen in the excited state are collisional quenching, charge transfer reactions, or energy transfer. The latter is the basis for FRET probes but the other events happen as well under certain conditions and it is important to consider them. 

Energy transfer, as described by Forster [78], requires a long range dipole-dipole interaction between the donor and the acceptor fluorophore. This energy transfer is possible at distances between 2 and 10 nm. Contrary to what happens in collisional quenching, there is no need for physical contact between the two molecules. 

Before proceeding, an important note must be made. In literature, two different but fully equivalent approaches have been taken in s.e. The first approach considers a cell that contains (unknown) numbers of donors and acceptors No and NA. When energy transfer takes place (be it from collisional encounters or because a stable population of FRET pairs exist with FRET efficiency E) this diminishes the effective number of emitting donors with Ns [3] that is, the FRET efficiency for this population is unity. Thus, the residual donor emission results from (No — Ns) unquenched donor molecules, and the Ns population emits only sensitized emission. This approach is intuitive in case no assumptions are being made on the presence of a stable population of FRET pairs or on the magnitude of E in a donor-acceptor complex. 

Forster (1959) classifies the qualitative features based on which one can distinguish the various modes of energy transfer. Mainly, only collisional transfer depends on solvent viscosity (vide infra), whereas complexing between the donor and acceptor changes the absorption spectrum. On the other hand, the sensitizer lifetime decreases for the long-range resonant transfer process, whereas it should be unchanged for the trivial process. 

In liquids, collisional energy transfer takes place by multistep diffusion (the rate determining step) followed by an exchange interaction when the pair is very close. The bimolecular-diffusion-controlled rate constant is obtained from Smoluchowski s theory the result, including the time-dependent part, may be written as... 

In atmospheric pressure discharges, where concentrations of N atoms are greatly reduced and possibly absent, the discrimination between alkanes and alkenes is not observed and an alternative means of initiating the reaction is required. In the absence of significant concentrations of N, the mechanism may consist of collisional energy transfer from N2(A32 +), which lies 593 kJ mor1... 

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