Magic-angle condition

Let Ix, Iy and Iz be the intensity components of the fluorescence, respectively (Figure 6.3). If no polarizer is placed between the sample and the emission monochromator, the light intensity viewed by the monochromator is Iz + Iy, which is not proportional to the total fluorescence intensity (Ix + Iy + Iz). Moreover, the transmission efficiency of the monochromator depends on the polarization of the incident light and is thus not the same for Iz and Iy. To get a response proportional to the total fluorescence intensity, independently of the fluorescence polarization, polarizers must be used under magic angle conditions (see appendix, p. 196) a polarizer is introduced between the excitation monochromator and the sample and... 

Sample preparation was given elsewhere [2]. Femtosecond fluorescence upconversion and picosecond time-correlated single-photon-counting set-ups were employed for the measurement of the fluorescence transients. The system response (FWHM) of the femtosecond fluorescence up-conversion and time-correlated single-photon-counting setups are 280 fs and 16 ps, respectively [3] The measured transients were fitted to multiexponential functions convoluted with the system response function. After deconvolution the time resolution was 100 fs. In the upconversion experiments, excitation was at 350 nm, the transients were measured from 420 nm upto 680 nm. Experiments were performed under magic angle conditions (to remove the fluorescence intensity effects of rotational motions of the probed molecules), as well as under polarization conditions in order to obtain the time evolution of the fluorescence anisotropy. 

Figure 2a shows a few fluorescence upconversion transients as measured for 1 dissolved in n-heptane, under magic angle conditions. The transients show multi-exponential decay behavior... 

It should be noted that the activation energies for motional processes in the same crosslinked polymer gel calculated from line widths in 13C NMR spectra are higher than those calculated from 1H NMR spectra under the magic angle conditions (residual line width). These findings indicate that 13C line widths (which are of the order of 10 Hz) are probably more affected by sample inhomogeneity and by relatively small residual chemical shift anisotropies 162). 

In order to examine the properties of the fluorescent states for the dendrimers more closely, fluorescence decay times for all first generation dendrimers were determined in toluene by single-photon timing detecting the emission under magic angle condition. 

This equation is sometimes called the magic-angle condition, because when it fulfilled, the spins precess about the cube diagonal which is at the magic angle with respect to Bo. Therefore, the WAHUHA pulse sequence decouples the homonuclear dipole-dipole interaction in first order (cf. Section 3.4.3). 

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