Narrowing, extreme

Small molecules in low viscosity solutions have, typically, rotational correlation times of a few tens of picoseconds, which means that the extreme narrowing conditions usually prevail. As a consequence, the interpretation of certain relaxation parameters, such as carbon-13 and NOE for proton-bearing carbons, is very simple. Basically, tlie DCC for a directly bonded CH pair can be assumed to be known and the experiments yield a value of the correlation time, t. One interesting application of the measurement of is to follow its variation with the site in the molecule (motional anisotropy), with temperature (the correlation... 

Kovacs H, Bagley S and Kowalewski J 1989 Motional properties of two disaccharides in solutions as studied by carbon-13 relaxation and NOE outside of the extreme narrowing region J. Magn. Reson. 85 530 1... 

For extremely narrow openings (cracks) with deep flow paths (such as mortar joints and tight-fitting components) the flow is laminar and the flow rate, Q (mVs), can be described by the Couette flow equation - ... 

Major groove proportions Extremely narrow but very Wide and with Elattened out on helix... 

Minor groove proportions Very broad but shallow Narrow and with Extremely narrow but very... 

Usually, nuclear relaxation data for the study of reorientational motions of molecules and molecular segments are obtained for non-viscous liquids in the extreme narrowing region where the product of the resonance frequency and the reorientational correlation time is much less than unity [1, 3, 5]. The dipolar spin-lattice relaxation rate of nucleus i is then directly proportional to the reorientational correlation time p... 

Ionic liquids, however, are often quite viscous, and the measurements are thus beyond the extreme narrowing region. The relaxation rates hence become frequency-dependent. Under these conditions, the equation for the spin-lattice relaxation rate becomes more complex ... 

The measurement of correlation times in molten salts and ionic liquids has recently been reviewed [11] (for more recent references refer to Carper et al. [12]). We have measured the spin-lattice relaxation rates l/Tj and nuclear Overhauser factors p in temperature ranges in and outside the extreme narrowing region for the neat ionic liquid [BMIM][PFg], in order to observe the temperature dependence of the spectral density. Subsequently, the models for the description of the reorientation-al dynamics introduced in the theoretical section (Section 4.5.3) were fitted to the experimental relaxation data. The nuclei of the aliphatic chains can be assumed to relax only through the dipolar mechanism. This is in contrast to the aromatic nuclei, which can also relax to some extent through the chemical-shift anisotropy mechanism. The latter mechanism has to be taken into account to fit the models to the experimental relaxation data (cf [1] or [3] for more details). Preliminary results are shown in Figures 4.5-1 and 4.5-2, together with the curves for the fitted functions. 

In both models the rotational shift of the line 5co is the same either in the static limit, where it is equal to zero, or in the case of extreme narrowing where it reaches its maximum value coq. A slight difference in its dependence on tE is observed in the intermediate region only. The experimentally observed density dependence of the shift shown in Fig. 3.5 is in qualitative agreement with theory. 

Landau LD, Lifshitz EM (1959) Fluid mechanics, 2nd edn. Pergamon, London Landerman CS (1994) Micro-channel flow boiling mechanisms leading to Burnout. J Heat Transfer Electron Syst ASME HTD-292 124-136 Levich VG (1962) Physicochemical hydrodynamics. Prentice HaU, London Morijama K, Inoue A (1992) The thermohydraulic characteristics of two-phase flow in extremely narrow channels (the frictional pressure drop and heat transfer of boiling two-phase flow, analytical model). Heat Transfer Jpn Res 21 838-856... 

Anionic pol5Tnerizations make the molecular weight standards that are used to calibrate size-exclusion chromatographs. Equation (13.38) predicts PD = 1.001 at In = 1000. Actual measurements give about 1.05. The difference is attributed to impurities in the feed that cause terminations and thus short chains. Also, the chromatograph has internal dispersion so that a truly monodisperse sample would show some spread. Even so, a PD of E05 is extremely narrow by pol5Tner standards. This does not mean it is narrow in an... 

Furthermore, as will be seen later, under the extreme, narrowing condition, and for isotropic motion, the following simple relationships hold. 

Given the specific, internuclear dipole-dipole contribution terms, p,y, or the cross-relaxation terms, determined by the methods just described, internuclear distances, r , can be calculated according to Eq. 30, assuming isotropic motion in the extreme narrowing region. The values for T<.(y) can be readily estimated from carbon-13 or deuterium spin-lattice relaxation-times. For most organic molecules in solution, carbon-13 / , values conveniently provide the motional information necessary, and, hence, the type of relaxation model to be used, for a pertinent description of molecular reorientations. A prerequisite to this treatment is the assumption that interproton vectors and C- H vectors are characterized by the same rotational correlation-time. For rotational isotropic motion, internuclear distances can be compared according to... 

If we assume that the extreme narrowing condition exists, then the following simpler expression applies ... 

As stated earlier, since tt]/ = yff2yr and since the gyromagnetic ratio of proton is about fourfold greater than that of carbon, then if C is observed and H is irradiated (expressed as C H ), at the extreme narrowing limit Ti, = 198.8% i.e., the C signal appears with a threefold enhancement of intensity due to the nOe effect. This is a very useful feature. For instance, in noise-decoupled C spectra in which C-H couplings are removed, the C signals appear with enhanced intensities due to nOe effects. 

An important by-product of the development of this approach is that Orthogonal Chromatography provides a direct method of estimating the shape of the chromatogram for extremely narrow molecular weight distributions. This shape function is fundamental information for axial dispersion evaluation and is not otherwise easily obtained. Even commercially available monodisperse standards synthesized by anionic polymerization are too polydisperse. 

Fe which have full width 2r at 0.2 mm s . Other isotopes are less demanding, e.g., Au, for which the lines are ten times wider. Most spectrometers are equipped with electromechanical Mossbauer velocity transducers of the loudspeaker type. This technique is suitable for velocity variations ranging from less than 1 mm s full scale up to several cm s and covers the whole reach of hyperfine splitting for most of the common isotopes. Kalvius, Kankeleit, Cranshaw, and others [1-5] have been pioneers in the field, who laid foundations for the development of high-precision drives with feedback amplifiers for proper linear velocity scales with high stability and low hum. Other techniques for Doppler modulation have been developed for isotopes with extremely narrow hyperfine lines, e.g., Zn. For such isotopes, piezoelectric transducers are mostly used [6, 7], more details of which are found in Sect. 7.2.1. 

To minimize experiment time, the highest possible source activity is desirable, with the constraint that the source line width should not increase sigiuficantly (maximum by a factor of 2-3) over the 9-12 months duration of the mission. Calculations and tests indicate an optimum specific activity for Co at 1 Ci per cm [42, 43], Sources of 350 mCi Co/Rh with a specific activity close to this value and extremely narrow source fine width (<0.13 mm s at room temperature), given... 

The small natural width of 2E = 0.0065 mm s implies an extremely narrow relative line width of r/ y = 1.1 lO, which is about 30 times narrower than that for the 14.4 keV state of Fe. 

The ground state as well as the 6.2 keV excited state of Ta possesses sizeable electric quadrupole and magnetic dipole moments (cf. Table 7.1 at the end of the book) which, in cooperation with the extremely narrow line width, generally yield well-resolved Mossbauer spectra even in cases with relatively weak interactions. 

There is a second relaxation process, called spin-spin (or transverse) relaxation, at a rate controlled by the spin-spin relaxation time T2. It governs the evolution of the xy magnetisation toward its equilibrium value, which is zero. In the fluid state with fast motion and extreme narrowing 7) and T2 are equal in the solid state with slow motion and full line broadening T2 becomes much shorter than 7). The so-called 180° pulse which inverts the spin population present immediately prior to the pulse is important for the accurate determination of T and the true T2 value. The spin-spin relaxation time calculated from the experimental line widths is called T2 the ideal NMR line shape is Lorentzian and its FWHH is controlled by T2. Unlike chemical shifts and spin-spin coupling constants, relaxation times are not directly related to molecular structure, but depend on molecular mobility. 

The combination of cross polarization (basically a pulse sequence) and MAS is sufficient to drastically reduce the linewidths of spin-Vi nuclei. Liquid-state proton NMR spectra, as we have seen, are characterized by extremely narrow lines and complex multiplets due to spin-spin coupling in addition, the normal chemical shift range is only around 10 ppm. 

In the case of extreme narrowing in which fast isotropic molecular motions dominate as in the solution state, the spectral density is written by a single correlation time,... 

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