Average rotational energy transfer

The average rotational energy transfer (ARET) is then given by... 

Fig. 2. Average rotational energy transfer (ARET) for different collision energies. Solid line quantum mechanical wave packet propagation using the MCTDH method (from Ref. [22]) dashed line MQCB method (equation (47)) dotted line classical dynamics.

The energy relaxation time, Eq. [50], as a function of the magnitude of the solute s dipole and its location exhibits an opposite trend." The increased collision rate (which slows down reorientation) enhances the rotational energy transfer to the solvent molecules. Thus, for a solute with a small dipole, the energy relaxation at the interface is much slower than in the bulk. However, the difference between the bulk and surface energy relaxation rates decreases as the dipole is increased because preserving the solute hydration shell makes the interfacial friction similar to that of the bulk, despite the fact that the average solvent density just outside the solute hydration shell is smaller than in the bulk. 

Measuring Doppler widths of rotational lines by laser-probe techniques gives velocity distributions in just the same way as measuring Doppler widths of atomic lines by conventional means. In this method a laser beam with a very narrow band width is tuned over the spectral line to determine the profile of the Doppler broadened line. The line shape can be interpreted to give the average velocity of the product. As yet, this method has been applied only to rotational energy transfer studies however, with the availability of mode-locked lasers providing narrow band widths, this procedure may become more widely used. 

The rotation of the fluorophores is a factor that affects the energy transfer. Only maximal rotational freedom will permit tda estimation. There is no way to predict this factor. Therefore the dynamic averaged value of k2 is considered 2/3. This prediction induces a certain error in the calculation of distances (see Chap. 1). 

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) ... 

Triplet—triplet energy transfer from benzophenone to phenanthrene in polymethylmethacrylate at 77 and 298 K was studied by steady-state phosphorescence depolarisation techniques [182], They were unable to see any clear evidence for the orientational dependence of the transfer probability [eqn. (92)]. This may be due to the relative magnitude of the phosphorescence lifetime of benzophenone ( 5 ms) and the much shorter rotational relaxation time of benzophenone implied by the observation by Rice and Kenney-Wallace [250] that coumarin-2 and pyrene have rotational times of < 1 ns, and rhodamine 6G of 5.7 ns in polymethyl methacrylate at room temperature. Indeed, the latter system of rhodamine 6G in polymethyl methacrylate could provide an interesting donor (to rose bengal or some such acceptor) where the rotational time is comparable with the fluorescence time and hence to the dipole—dipole energy transfer time. In this case, the definition of R0 in eqn. (77) is incorrect, since k cannot now be averaged over all orientations. 

It appears, for example, that rotational energy is relatively easily transferred and that most collisions are in fact effective in the exchange of such energy. Frequencies associated with typical molecular rotations are of the order of 1011 or 1012 cycles, or rotations, per second. Alternatively, we say that it takes about 10-11 or 10"12 sec for one rotation of a molecule. We see, therefore, that in gases at pressures lower than 1 atm many rotations occur between collisions, and deactivation, but that in liquids the molecules generally will not be able to complete a rotation in the short time of 10"13 sec that exists on the average between collisions. We conclude, therefore, that in liquids the molecules are not free to rotate, and this conclusion is consistent with our observations that vibrational absorption bands generally show rotational fine structure only when the sample is a gas. 

By now we have a fairly detailed understanding of the mechanism of CET between highly excited molecules and a bath atom. We turn next to understanding of the relative contribution of rotation and vibration to the CET process. We performed clasical trajectory calculations of the average energy transferred per collision, , between an exited benzene molecule and an argon atom [11] in which three cases were investigated, a) collisions with unconstrained normal initial conditions, b) collisions where the rotations of the benzene molecule are initially frozen , c) eollisions where... 

We can also see the slow energy transfer between rotational and translational subsystems by tracing how an equipartition of both modes is achieved. In Fig. 12, we present the temporal behavior of averaged rotational and translational energies. In this sample, after very large fluctuations in the initial stage, it takes quite a long time to reach an equipartitioned state. Similarly, it sometimes happens that equipartition is not realized even within several nanoseconds. 

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