Internuclear dipolar relaxation

For heteronuclear dipolar relaxation, the dipole-dipole coupling between two unlike spin- nuclei / and S (e.g., 13C-H pair) separated by an internuclear distance rIS is considered. The Zeeman spin-lattice (7jz) and spin-spin (T2) relaxation times for the / spin are given, respectively, by... 

The photoinduced absorbance anisotropy in a TPD experiment relaxes according to the same correlation function as in Eq. (4.16).(29) Effects of spatial variations in the excitation and probe beams, and chromophore concentration, have been treated and shown not to alter the final result.(29) NMR dipolar relaxation rates are expressed in terms of Fourier transforms of the correlation functions, 4ji< T2m[fi(0)] T2m[i2(f)]>> where fl(f) denotes the orientation of a particular internuclear vector. In view of Eq. (4.7), these correlation functions are independent of the index m, hence formally the same as in Eq. (4.16). For the analysis of NMR relaxation data, it is necessary also to evaluate Fourier transforms of the correlation functions. Methods to accomplish this in the case of deformable DNAs have been developed and applied to analyze a variety of data.(81 83)... 

While the rate of change of dipolar interaction depends on t its magnitude depends only on the internuclear distance and is independent of t,. Thus the dipole-dipole relaxation depends on the molecular correlation time T the internuclear distance r, and the gyromagnetic ratios of the two nuclei, y and js -... 

Transient nOe represents the rate of nOe buildup. The nOe effect (so-called equilibrium value) itself depends only on the competing balance between various complex relaxation pathways. But the initial rate at which the nOe grows (so-called transient nOe) depends only on the rate of cross-relaxation t, between the relevant dipolarly coupled nuclei, which in turn depends on their internuclear distance (r). 

Quantitative evaluation of NOE magnitudes in terms of internuclear distance is problematic and often questionable, since there are influences (experimental and structural) in addition to distance. In particular, if a third NMR active nucleus X is close to nucleus I, reduced enhancements of the 1 signal may be observed because the dipolar cross relaxation of I is dominated by X and no longer by the irradiated S. Indeed, negative NOEs (signal intensity decreases) may occur212. 

One of the important ways in which magnetic nuclei may relax from their upper to their lower energy levels is through a dipolar spin-spin interaction with another magnetic nucleus. This process takes place through space, and its efficiency is inversely proportional to the sixth power of the internuclear distance involved. It follows that the most efficient relaxation by that route can take place when two magnetic nuclei are in close spatial proximity in the same molecule. 

Temperature Dependence of Spin-Lattice Relaxation. The spin-lattice relaxation rate T ) is comprised of various contributions to the relaxation process, including homo- and heteronuclear dipolar interactions, quadrupolar interactions, chemical shift anisotropy, spin-rotation, and others (10). When the relaxation mechanism is dominated by inter- and intramolecular dipole-dipole interactions, the will increase with temperature, pass through a maximum, and decrease with increasing temperature. Since the relaxation rate is the inverse of the relaxation time, the Ti will decrease, pass through a minimum (Timin), and then increase with increasing temperature (77). The T lmin values are proportional to the internuclear distances. 

One of the cross-polarization pulse sequences used to measure is shown in Figure 6.9. During the evolution time, At, of this pulse sequence, the magnetization is spin-locked along Any reorientation of the internuclear vectors induces fluctuations of the dipolar local fields, and the COcomponent of these fluctuating fields participates in the relaxation of the spins. This is a spin-lattice relaxation mechanism which is related... 

Investigation of nitrogen relaxation may also be of interest, in deriving information about anisotropic molecular motion. In fact the determination of a single value cannot be considered as a proof of isotropic motion, if independent internuclear vectors have not been examined. In this respect, results derived from N H dipolar interactions may provide determining complementary information about eventual motional anisotropy. 

Treatment of spin-lattice relaxation of an isolated spin- pair by intramolec-ular dipole-dipole interaction is identical to that for a one spin-1 system. Two like spin- nuclei separated by an internuclear distance r are considered. The Zeeman spin-lattice relaxation time Tiz is given by Eq. (5.40), but with a different multiplicative constant Kd which reflects the dipolar interaction strength. To find the off-diagonal Redfield s element jRi2 may be calculated for the case of dipole-dipole interaction ... 

Rotational resonance (RR) is a MAS NMR technique which selectively restores the dipolar interaction between a homonuclear spin pair, thus allowing the determination of the dipolar coupling constant, and hence, the internuclear distance. Historically, the RR phenomenon was discovered by Andrew and co-workers in a NMR study of phosphorus pentachloride, which consists of PCl4 and PCl " units in the solid state. This group noticed that when the rate of sample spinning matched the difference in resonance frequencies of the nonequivalent phosphorus centres, their peaks broadened and the rate of cross-relaxation was enhanced. 

Reff = observed dipolar coupling constant t = time T20 = spin term in the spherical tensor representation of the dipolar Hamiltonian = zero-quantum relaxation time constant U = propagator = magne-togyric ratio of spin / A/ = anisotropy of the indirect spin-spin interaction 0 = angle between the applied field and the internuclear vector A = dephasing parameter /Uq = permeability of free space Vj. = rotor frequency in Hz 1/, = isotropic resonant frequen-... 

Detailed information on molecular dynamics can be obtained from the determination of the magnetic relaxation times Tu T, and T2. The magnetic relaxation in organic materials usually originates from modulation of dipolar proton-proton couplings, and therefore reflects the dynamics of the internuclear proton-proton vectors. To make an eflTective... 

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