Correlation times electrical

Solid state 2H NMR parameters are almost exclusively governed by the quadrupole interaction with the electric field gradient (EFG) tensor at the deuteron site.1 8 The EFG is entirely intramolecular in nature. Thus molecular order and mobility are monitored through the orientation of individual C-2H bond directions. Therefore, 2H NMR is a powerful technique for studying local molecular motions. It enables us to discriminate different types of motions and their correlation times over a wide frequency range. Dynamics of numerous polymers has been examined by solid state 2H NMR.1 3,7,9 Dynamic information on polypeptides by NMR is however limited,10 26 although the main-chain secondary structures of polypeptides in the solid have been extensively evaluated by 13C and 15N CP/MAS NMR.27,28... 

While the nuclei 3H and 13C relax predominantly by the DD mechanism, relaxation of a quadrupole nucleus such as deuterium essentially involves fluctuating fields arising from interaction between the quadrupole moment and the electrical field gradient at the quadrupole nucleus [16]. If the molecular motion is sufficiently fast (decreasing branch of the correlation function, Fig. 3.20), the 2H spin-lattice relaxation time is inversely proportional to the square of the quadrupole coupling constant e2q Q/H of deuterium and the effective correlation time [16] ... 

Yi and Ys - gyromagnetic ratio of spin 1 and spin S nuclear spin, rJS = intemuclear distance, tr= rotational correlation time, x< = reorientation correlation time, xj = angular momentum correlation time, Cs = concentration of spin S, Cq = e2qzzQ/h = quadrupole coupling constant, qzz = the electric field gradient, Q = nuclear electric quadrupole moment in 10 24 cm2, Ceff = effective spin-rotational coupling constant, a = closest distance of appropriate of spin 1 and spin S, D = (DA+DB)/2 = mutual translational self diffusion coefficient of the molecules containing I and S, Ij = moment of inertia of the molecule, Ao = a// - ol-... 

The microscopic origin of the collective modes has been identified since a long time. They are reported here with the corresponding typical correlation times (CT) reorientation modes (this is the so-called Debye region, CT > 10-12s), libration modes (rotations impeded by collisions, CT = 10 13s), atomic motions (vibrations, CT = 10-14s), electronic motions (CT = 10 16s). When the frequency of the external field increases, the various components of the polarization we have introduced here become progressively no longer active, because the corresponding motions of the solute lag behind the variation of the electric field. 

The determination of correlation times requires particular attention and is not a problem that can be easily resolved. It is necessary to consider not only the overall molecular tumbling, but also internal rotation motions, which can modulate the interaction between the nuclear quadrupole moment and the electric field gradient. In any case, it must be considered that % depends on the square root of and, even if in most cases it is not possible to measure or calculate precise values of t , the uncertainties introduced in the values of x may often be accepted. 

S nuclear quadrupole coupling constants have been determined from line width values in some 3- and 4-substituted sodium benzenesulphonates33 63 and in 2-substituted sodium ethanesulphonates.35 Reasonably, in sulphonates R — SO3, (i) t] is near zero due to the tetrahedral symmetry of the electronic distribution at the 33S nucleus, and (ii) qzz is the component of the electric field gradient along the C-S axis. In the benzenesulphonate anion, the correlation time has been obtained from 13C spin-lattice relaxation time and NOE measurements. In substituted benzenesulphonates, it has been obtained by the Debye-Stokes-Einstein relationship, corrected by an empirically determined microviscosity factor. In 2-substituted ethanesulphonates, the molecular correlation time of the sphere having a volume equal to the molecular volume has been considered. 

As emphasized elsewhere in this text, the physical act constituting an electrodynamic force is the correlated time-varying fluctuation of all component electric charges and electromagnetic fields in each material composing a system. Charge fluctuations at each point are either spontaneous or are in response to electric fields set up by fluctuations elsewhere. The dielectric permittivity is an experimental quantity that codifies not only the response of a material to an applied electric field but also the magnitude of spontaneous fluctuations. 

Hexamethylenetetramine has been extensively studied in this respect30 , and it has been shown that for temperatures ranging above room temperature, reorientational motions are responsible for the strong relaxation. More exactly, hindered rotations interchange the tetrahedron apexes and the nuclei are thus subjected to a sudden reorientation of the electric field gradient. The correlation time of such motions can be derived from the observed signals and experimental results may be depicted by the relation... 

As mentioned above, the frequency of rotational or translational motion of magnetic and electric fields in the lattice nuclei is critical to the effectiveness of spin-lattice relaxation. It cannot be too fast or too slow. It is common to express the frequencies of these types of molecular motion in terms of a so-called correlation time xc. If the angular rotation frequency is to (in radians per second), the rotational correlation time is 1/co, the time required for a molecule (or part of a molecule) to rotate 1 rad. Similarly, the translational correla-... 

It is generally accepted that if electric field gradients occur at the nucleus site, the quadrupole relaxation times, and T, of nuclei with nuclear spin / > 1/2 are related to the reorientational correlation time at the extreme-narrowing limit as given below." " 7rAvi/2 = l/T i = 1/7 2 = Stt /IOX (2/ + 3)/ (2/ - 1) X Qq / (4)... 

Fig. 19. Plots of the decay time of the 515-nm field-indicating absorption change (A) and the rate of ATP formation (B) in chloroplasts as a function of gramicidin concentration the corresponding gramicidin-to-chlorophyll ratios are indicated in the top scaie sampie chioro-phyll concentration=2x10 M. GMCD stands for gramicidin. Figure source Boeck and Witt (1972) Correlation between electrical events and ATP-generation in the functional membrane of photosynthesis. In G Forti, M Avron and A Melandri (eds) Proc II. Intern Congr of Photosynthesis Research, Stresa (1971) p 910.

Here, T2 is the spin-spin relaxation time Av is the linewidth eq is the electric held gradient at the nucleus eQ is the nuclear quadrupole moment and /(rR, rex) is some function of the correlation times rR and rex, for rotational motion and exchange of the ions, respectively. An asymmetry parameter of zero is assumed (18). 

The quantity (e2 qQ) is the known quadrupole coupling constant and is made up of the electronic charge e, electric field gradient q and nuclear quadrupole moment Q. ra is a correlation time for molecular motion, rj is an asymmetry parameter and I is the nuclear spin quantum number. 

---