Correlation time systems

In spin relaxation theory (see, e.g., Zweers and Brom[1977]) this quantity is equal to the correlation time of two-level Zeeman system (r,). The states A and E have total spins of protons f and 2, respectively. The diagram of Zeeman splitting of the lowest tunneling AE octet n = 0 is shown in fig. 51. Since the spin wavefunction belongs to the same symmetry group as that of the hindered rotation, the spin and rotational states are fully correlated, and the transitions observed in the NMR spectra Am = + 1 and Am = 2 include, aside from the Zeeman frequencies, sidebands shifted by A. The special technique of dipole-dipole driven low-field NMR in the time and frequency domain [Weitenkamp et al. 1983 Clough et al. 1985] has allowed one to detect these sidebands directly. 

Just as in phase transitions in statistical mechanical systems, observable quantities in PCA systems display singularities obeying simple power laws with universal critical exponents at the transition point. For example, letting ni be the number of sites with correlation length, and t be the correlation time, Kinzel [kinz85b] finds that for p ... 

Up to now it has been tacitly assumed that each molecular motion can be described by a single correlation time. On the other hand, it is well-known, e.g., from dielectric and mechanical relaxation studies as well as from photon correlation spectroscopy and NMR relaxation times that in polymers one often deals with a distribution of correlation times60 65), in particular in glassy systems. Although the phenomenon as such is well established, little is known about the nature of this distribution. In particular, most techniques employed in this area do not allow a distinction of a heterogeneous distribution, where spatially separed groups move with different time constants and a homogeneous distribution, where each monomer unit shows essentially the same non-exponential relaxation. Even worse, relaxation... 

Fig. 29. Observed and calculated 2H NMR spectra for the mesogenic groups of a) the nematic (m = 2), b) the smectic (m = 6) liquid crystalline polymer in the glassy state, showing the line shape changes due to the freezing of the jump motion of the labelled phenyl ring. The exchange frequency corresponds to the centre of the distribution of correlation times. Note that the order parameters are different, S = 0.65 in the frozen nematic, and S = 0.85 in the frozen smectic system, respectively...

The second separation method involves n.O.e. experiments in combination with non-selective relaxation-rate measurements. One example concerns the orientation of the anomeric hydroxyl group of molecule 2 in Me2SO solution. By measuring nonselective spin-lattice relaxation-rat s and n.0.e. values for OH-1, H-1, H-2, H-3, and H-4, and solving the system of Eq. 13, the various py values were calculated. Using these and the correlation time, t, obtained by C relaxation measurements, the various interproton distances were calculated. The distances between the ring protons of 2, as well as the computer-simulated values for the H-l,OH and H-2,OH distances was commensurate with a dihedral angle of 60 30° for the H-l-C-l-OH array, as had also been deduced by the deuterium-substitution method mentioned earlier. 

One of the most commonly studied systems involves the adsorption of polynuclear aromatic compounds on amorphous or certain crystalline silica-alumina catalysts. The aromatic compounds such as anthracene, perylene, and naphthalene are characterized by low ionization potentials, and upon adsorption they form paramagnetic species which are generally attributed to the appropriate cation radical (69, 70). An analysis of the well-resolved spectrum of perylene on silica-alumina shows that the proton hyperfine coupling constants are shifted by about four percent from the corresponding values obtained when the radical cation is prepared in H2SO4 (71). The linewidth and symmetry require that the motion is appreciable and that the correlation times are comparable to those found in solution. 

We should note that the use of the Lipari-Szabo analysis implies that relaxation data are available at multiple magnetic fields. It provides a phenomenological description of the rotational motion that can be very useful for comparing systems with similar structure. Nevertheless, one should be aware of the limits of this approach and avoid direct comparison of local or global rotational correlation times for structurally very different compounds. 

Lindenberg and West conclude, after analysis of Eq.(59) at low temperatures where kTccIly, that the correlation function decays on a time scale li/ kT rather than 1/y. Thus, the bath can dissipate excitations whose energies lie in the range (0/fi.y), while the spontaneous fluctuations occur only in the range (0,kT) if kTcorrelation time of the fluctuations is therefore the longer of fi/ kT and 1/y. The idea advanced by these authors is that fluctuations and dissipation can have quite distinct time scales [133], This is important if the two quantum states of the system of interest correspond to chemical interconverting states [139, 144, 145],... 

LIG. 22 A schematic illustration of the dependence of NMR relaxation times T and T2 on the molecular correlation time, xc, characterizing molecular mobility in a singlecomponent system. Both slow and fast motions are effective for T2 relaxation, but only fast motions near w0 are effective in Tx relaxation. 

TEMPERATURE DEPENDENCE OF WATER AND SUCROSE CORRELATION TIMES IN A 90.1% (WAV) SUCROSE-WATER SYSTEM (Te = 261.5 K)... 

Figure 5.2. Simulated fluorescence anisotropy decays for (a) an isotropic system, (b) a system such as a lipid bilayer with short and long rotational correlation times, and (c) a system in which one of the rotational correlation times is infinite, and there is therefore a residual anisotropy or r .

There has been considerable interest in using fluorescence anisotropy to detect multiple environments in membranes as with fluorescence lifetimes (see above). For example, if a fluorophore is located in two environments with long and short lifetimes, then the fluorescence anisotropy decay process at longer times after excitation will be dominated by the long-lived fluorescent species. This occurs with parinaric acids, and this situation has been explored for a number of theoretical cases. 60 A similar situation has been found for DPH in two-phase lipid systems by collecting anisotropy decay-associated spectra at early and late times after excitation. 61 Evidence was found for more than one rotational environment in vesicles of a single lipid of it is at the phase transition temperature. It is important to identify systems showing associated anisotropy decays with more than one correlation time, each of... 

Its special properties offer the possibility of reducing the so-called correlation noise, caused by a limited correlation time. CC is essentially statistical by nature. The system noise (detector noise) is not correlated with the input PRBS the noise in the correlogram, resulting from the detector noise, is converging to zero with increasing correlation time. 

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