Inverse rotational correlation time

Rotational diffusion rates of 2,2,6,6-tetramethyl-4-piperidinol-l-oxyl, bound to 2% cross-linked polystyrene with DF 0.02, arc slower than those of the soluble nit-roxyl (331. The rates (as the inverse rotational correlation time v ) increase with increased swelling of the polymer, from 3 x 10 s with no solvent or with the nonsolvents ethanol and 2-propanol, to 3 x 10 s i with benzene, to >10 s for a benzene solution of the corresponding soluble polystyrene. Increased cross-linking (4% and 12% DVB) gives decreased swelling a decreased rotational diffusion rates. 

In order to visualize the effects of water exchange, rotation and electronic relaxation as well as of magnetic field on proton relaxivity, we have calculated proton relaxivities as a function of these parameters (Fig. 2). The relaxivity maximum is attained when the correlation time, tc1, equals the inverse proton Lar-mor frequency (l/rcl = l/rR + l/rm + l/Tle = a>j). The most important message of Fig. 2 is that the rotational correlation time, proton exchange and electronic relaxation rates have to be optimized simultaneously in order to attain maximum relaxivities. If one or two of them have already an optimal value, the remaining parameter starts to become more limitative. The marketed contrast agents have relaxivities around 4-5 mM1 s 1 contrary to the theoretically attainable values over 100 mM 1 s1, which is mainly due to their fast rotation and slow water exchange. 

The nuclear Overhauser effect (NOE) is a consequence of the modulation of the dipole-dipole interactions (through space) between different nuclei and is correlated with the inverse sixth power of the internuclear distance. Experimentally, the NOE is the fractional change in intensity of one resonance when another resonance is irradiated in a double-irradiation experiment. The NOE phenomenon is intimately related to spin relaxation. The NOE varies as a function of the product of the Larmor frequency, co0, and the rotational correlation time, tc. In small molecules, tc is short relative to uo"1. In this extreme motional narrowing situation, the frequency... 

Referring to transverse relaxation processes that give rise to loss of phase coherence, three motional domains can be defined fast tumbling, where the intrinsic linewidth is Lorentzian in character slow tumbling, where the rotational correlation time is comparable to the inverse of the anisotropy of the magnetic interaction very slow tumbling, where the intrinsic linewidth is once again Lorentzian, but the observed linewidth is simply a powder pattern. 

Line Shape Analysis for Nitroxide Spin Probes. Nitroxide radicals as spin probes and labels are useful for the determination of the motional mechanism, rotational correlation time, to, and local polarity. Figure 2a demonstrates that the relative line widths and line heights depend on the rotational correlation time to, which is inversely proportional to the diffusion constant of rotational diffusion. 

The ESR spectra of nitroxides can be characterised by the rotational correlation time T , which is inversely proportional to the rate or frequency of rotation of the radical. The correlation times for nitroxides can be divided into three distinct regions, designated fast (10 10 s), slow (10 " 10 " s) and very slow (10 "... 

The nature of the lipid-protein interactions can be further studied by the use of ST-ESR techniques. ST-ESR extends the useful timescale of ESR to > 10" S and can be used for the analysis of the amplitude and rate of the rotation of spin-labelled lipids. The rotational correlation time (Tq) which can readily be deduced from ST-ESR spectra, is inversely proportional to the rate of rotation of the spin probe. In the case of the PSII preparations the values for T are given in Table 1. In general all of these rotation rates are very slow indeed. 

Fig. 15. Schematic of polar and alignment disorder as measured by XRD and NMR. Upper line polar disorder with random up or down orientations of the direction of the molecules with equal probabilities to restore the inversion symmetry for X-ray, the two directions are possible with equal probabilities on each site NMR cannot measure polar disorder, all sites are equivalent. Lower line alignment disorder of the molecules characterized by a long correlation time as compared to the inverse Larmor frequency coL, and librational disorder represented by ellipses of thermal-induced rotations (with angular amplitude possibly larger than the corresponding disalignment) around the mean alignment direction of the molecules. The frequencies of librations 1 jx is much larger than the Larmor frequency. For X-ray, both orientational disorders are mixed up with a preponderant contribution of the high-frequency librations for NMR, only alignment disorder remains.

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