Measurements rotational relaxation

Another, purely experimental possibility to obtain a better estimate of the friction coefficient for rotational motion in chemical reactions consists of measuring rotational relaxation times of reactants and calculating it according to equation (A3,6,35) as y. =... 

Again, it is a prerequisite for such measurements that the fluorescence decays at a rate similar to that of the motion under investigation. Measurable rotational relaxation times are in the range 1 ns to 1 ps, corresponding to the rotation of species with molar masses up to 10 g moP in aqueous solution. 

Figure 78 shows the dependence of experimentally measured rotational relaxation times (tJ of AP, PRODAN, and anthracene on rjIT in four morpholinium ILs. The calculated (upper solid line) and (lower dashed line) values from the SED theory are also shown. 

Spectroscopic detemiination of the HE rotational distribution is another story. In both the chemical laser and infrared chemiluminescence experiments, rotational relaxation due to collisions is faster or at least comparable to the time scale of the measurements, so that accurate detemiination of the nascent rotational distribution was not feasible. However, Nesbitt [40, 41] has recently carried out direct infrared absorption experiments on the HE product under single-collision conditions, thereby obtaining a fiill vibration-rotation distribution for the nascent products. 

Storer model used in this theory enables us to describe classically the spectral collapse of the Q-branch for any strength of collisions. The theory generates the canonical relation between the width of the Raman spectrum and the rate of rotational relaxation measured by NMR or acoustic methods. At medium pressures the impact theory overlaps with the non-model perturbation theory which extends the relation to the region where the binary approximation is invalid. The employment of this relation has become a routine procedure which puts in order numerous experimental data from different methods. At low densities it permits us to estimate, roughly, the strength of collisions. 

Fig. 1.25. Temperature-dependence of rotational relaxation cross-section from [81], For the lowest temperature point the experimental uncertainty is indicated, the latter being the biggest one over the whole set of measurements.

The value of the magnetic hyperfine interaction constant C = 22.00 kHz is supposed to be reliably measured in the molecular beam method [71]. Experimental data for 15N2 are shown in Fig. 1.24, which depicts the density-dependence of T2 = (27tAv1/2)-1 at several temperatures. The fact that the dependences T2(p) are linear until 200 amagat proves that binary estimation of the rotational relaxation rate is valid within these limits and that Eq. (1.124) may be used to estimate cross-section oj from... 

Winter T. G., Hill G. L. High-temperature ultrasonic measurements of rotational relaxation in hydrogen, deuterium, nitrogen and oxygen, J. Acoust. Soc. Am. 42, 848-58 (1967). 

This simple relaxation theory becomes invalid, however, if motional anisotropy, or internal motions, or both, are involved. Then, the rotational correlation-time in Eq. 30 is an effective correlation-time, containing contributions from reorientation about the principal axes of the rotational-diffusion tensor. In order to separate these contributions, a physical model to describe the manner by which a molecule tumbles is required. Complete expressions for intramolecular, dipolar relaxation-rates for the three classes of spherical, axially symmetric, and asymmetric top molecules have been evaluated by Werbelow and Grant, in order to incorporate into the relaxation theory the appropriate rotational-diffusion model developed by Woess-ner. Methyl internal motion has been treated in a few instances, by using the equations of Woessner and coworkers to describe internal rotation superimposed on the overall, molecular tumbling. Nevertheless, if motional anisotropy is present, it is wiser not to attempt a quantitative determination of interproton distances from measured, proton relaxation-rates, although semiquantitative conclusions are probably justified by neglecting motional anisotropy, as will be seen in the following Section. 

Molecular rotors are useful as reporters of their microenvironment, because their fluorescence emission allows to probe TICT formation and solvent interaction. Measurements are possible through steady-state spectroscopy and time-resolved spectroscopy. Three primary effects were identified in Sect. 2, namely, the solvent-dependent reorientation rate, the solvent-dependent quantum yield (which directly links to the reorientation rate), and the solvatochromic shift. Most commonly, molecular rotors exhibit a change in quantum yield as a consequence of nonradia-tive relaxation. Therefore, the fluorophore s quantum yield needs to be determined as accurately as possible. In steady-state spectroscopy, emission intensity can be calibrated with quantum yield standards. Alternatively, relative changes in emission intensity can be used, because the ratio of two intensities is identical to the ratio of the corresponding quantum yields if the fluid optical properties remain constant. For molecular rotors with nonradiative relaxation, the calibrated measurement of the quantum yield allows to approximately compute the rotational relaxation rate kor from the measured quantum yield [Pg.284]

T2 measurements usually employ either Carr-Purcell-Meiboom-Gill (CPMG) [7, 8] spin-echo pulse sequences or experiments that measure spin relaxation (Tlp) in the rotating frame. The time delay between successive 180° pulses in the CPMG pulse sequence is typically set to 1 ms or shorter to minimize the effects of evolution under the heteronuc-lear scalar coupling between 1H and 15N spins [3]. 

The rotational relaxation of DNA from 1 to 150 ns is due mainly to Brownian torsional (twisting) deformations of the elastic filament. Partial relaxation of the FPA on a 30-ns time scale was observed and qualitatively attributed to torsional deformations already in 1970.(15) However, our quantitative understanding of DNA motions in the 0- to 150-ns time range has come from more accurate time-resolved measurements of the FPA in conjunction with new theory and has developed entirely since 1979. In that year, the first theoretical treatments of FPA relaxation by spontaneous torsional deformations appeared. 16 171 and the first commercial synch-pump dye laser systems were delivered. Experimental confirmation of the predicted FPA decay function and determination of the torsional rigidity of DNA were first reported in 1980.(18) Other labs 19 21" subsequently reported similar results, although their anisotropy formulas were not entirely correct, and they did not so rigorously test the predicted decay function or attempt to fit likely alternatives. The development of new instrumentation, new data analysis techniques, and new theory and their application to different DNAs in various circumstances have continued to advance this field up to the present time. 

The rotational relaxation time zK can be combined with time-dependent nuclear Overhauser effect (NOE) measurements to determine interproton... 

The effects of Nj and He on the rotational relaxation rate in the CO2 00° 1 upper laser level have been measured by Abrams and Cheo 379), who used the output of a g-switched CO2 laser (1 Kw peak power, 20 nsec) to selectively deplete the population of one rotational level in a flowing CO2, CO2 + He and CO2 + N2 laser amplifier. The relaxation from neighbouring rotational levels into this depleted state showed up as a recovery of the amplifier gain at the corresponding line which was detected as a function of time with a third cw single-frequency CO2 laser. 

One can employ linearly polarized light to excite selectively those fluorophores that are in a particular orientation. The difference between excitation and emitted light polarization changes whenever fluorophores rotate during the period of time between excitation and emission. The magnitude of depolarization can be measured, and one can therefore deduce the fluorophore s rotational relaxation kinetics. Extrinsic fluorescence probes are especially useful here, because the proper choice of their fluorescence lifetime will greatly improve the measurement of rotational relaxation rates. One can also determine the freedom of motion of the probe relative to the rotational diffusion properties of the macromolecule to which it is attached. When held rigidly by the macromolecule, the depolarization of a probe s fluorescence is dominated by the the motion of the macromolecule. 

We have not measured fluorescence depolarization with fluorophors and our polymers, but such measurements have been made by others, particularly with proteins and, as you indicate, it is possible to determine rotational relaxation times for the macromolecule and thus to obtain some insight into its behavior in solution. 

Chapter E is devoted to the mean-square dipole moment and mean rotational relaxation time derived from dielectric dispersion measurements. Typical data, both in helieogenic solvents and in the helix-coil transition region, are presented and interpreted in terms of existing theories. At thermodynamic equilibrium, helical and randomly coiled sequences in a polypeptide chain are fluctuating from moment to moment about certain averages. These fluctuations involve local interconversions of helix and random-coil residues. Recently, it has been shown that certain mean relaxation times of such local processes can be estimated by dielectric dispersion experiment. Chapter E also discusses the underlying theory of this possibility. 

Dielectric dispersion measurements also provide a means of determining rotational diffusion coefficients or mean rotational relaxation times of solute molecules. In principle, data for these hydrodynamic quantities can be used for a... 

Bauer et al. [237] and Alms et al. [238] have studied a wide range of organic molecules (benzene, mesitylene, methyl iodide, nitrobenzene, etc.) in solution. They have compared the measured long-time rotational relaxation times with both Perrin s ellipsoid rotational times with stick boundary conditions [223] and with those from Hu and Zwanzig s similar calculation based on slip boundary conditions [227]. There is close agreement between experiment and the slip boundary condition model of Hu and Zwanzig. Typical rotational times could be expressed as... 

Samson and Deutch [258] and Hess [259a] have also discussed the reaction of anisotropic molecules, though only Hess considered rotational relaxation effects. No studies have used the experimentally measured values of rotational relaxation times, which may be 1.5—10 times faster than the Debye equation, eqn. (108), predicts. The theory of Sole and Stockmayer [256] will underestimate the rate of chemical reactions when rotational relaxation is faster than they assumed. 

The rotational relaxation times of these nitrocompounds have not been measured. Comparison with the studies of perylene by Klein and Haar [253] suggests that most of these nitrocompounds have rotational times 10—20 ps in cyclohexane. For rotational effects to modify chemical reaction rates, significant reaction must occur during 10ps. This requires that electron oxidant separations should be <(6 x 10-7x 10-11)J/2 2 nm. Admittedly, with the electron—dipole interaction, both the rotational relaxation and translational diffusion will be enhanced, but to approximately comparable degrees. If electrons and oxidant have to be separated by < 2 nm, this requires a concentration of > 0.1 mol dm-3 of the nitrocompound. With rate coefficients 5 x 1012 dm3 mol-1 s 1, this implies solvated electron decay times of a few picoseconds. Certainly, rotational effects could be important on chemical reaction rates, but extremely fast resolution would be required and only mode-locked lasers currently provide < 10 ps resolution. Alternatively, careful selection of a much more viscous solvent could enable reactions to show both translational and rotational diffusion sufficiently to allow the use of more conventional techniques. 

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