Fast motion regime

Its dynamical range covers both the slow and the fast motion regime (lO -lQii Hz)... 

For a fixed value of Tc, the frequency dependence of either term is a Lorentzian centred at zero frequency. In the tc dependence two regimes are distinguished In the fast motion regime (coiTc spectral density is proportional to tc and does not depend on the measuring frequency a>i, whereas in the slow motion regime (a>iTc > l) it is proportional to ( Tc) i.e. the relaxation rate exhibits dispersion. 

They can serve therefore as a test for Ti dispersion. In Fig. 12 the relaxation results are shown for D-RADP-15. The solid lines are a fit of the theory [19] to the data. Above Tc the lit is excellent, whereas below Tc it probably suffers from the fact that the phase transition is already diffuse and only nearly of second order. This proves that a soft mode component is needed to explain the data. Furthermore, the fact that the ratio ti/t2 remains unchanged above and below Tc proves that the order parameter fluctuations are in the fast motion regime on both sides of the transition. 

Fig. 13 Comparison of the inverse relaxation rates ti and T2 versus 1/T at vi = 98.163 MHz for D-RADP-25 and D-RADP-50. Whereas D-RADP-50 exhibits a pure thermally activated behaviour, in D-RADP-25 a soft mode contribution to the relaxation rate can be observed in the fast motion regime [17]...

In addition to the semiquantitative approach, more quantitative analytical approaches have been reported. For example, in the fast motion regime (t 10 11—10 9 s at X-band), one can compute the nitroxide rotational correlation time based on the measured line-widths and amplitudes (Marsh, 1981 Qin et al., 2001 Xi et al., 2008). Furthermore, it is possible to simulate a nitroxide spectrum based on quantum mechanics and specific motional models (Columbus et al., 2001 Grant et al., 2009 Hustedt et al., 1993 Liang et al., 2000 Qin et al., 2006 Schneider and Freed, 1989). The details of these advanced analysis techniques are not discussed here, interested readers are instead referred to a recent review (Sowa and Qin, 2008) and the relevant literatures. 

Since the pulse sequence is the same for EXSY and NOESY, NOESY (or ROESY) cross peaks might be mistaken for EXSY cross peaks. They can be distinguished in the phase-sensitive experiment, since EXSY and ROESY peaks have opposite phases, as do EXSY and NOESY peaks in the fast motion regime. For example, two resolved OH or NH resonances may exhibit EXSY cross peaks from slow proton exchange. These peaks could be mistakenly taken to be NOESY peaks and interpreted incorrectly in terms of stereochemistry. 

Fig. 7.1.3 [Blii2] NMR-timescale of molecular motion and filter transfer functions of pulse sequences which can be utilized for selecting magnetization according to the timescale of molecular motion. The concept of transfer functions provides an approximative description of the filters. A more detailed description needs to take into account magnetic-field dependences and spectral densities of motion. The transfer functions shown for the saturation recovery and the stimulated-echo filter apply in the fast motion regime.

Mean interaction tensor in the fast-motion regime 147... 

Of particular importance for detection of chemical or physical change in polymer materials are mobility filters, which are sensitive to differences in the numbers of molecules within a given window of correlation times. Within reasonable approximation such filters are relaxation filters. Here, Tj filters are sensitive to differences in the fast motion regime while T2 and Tip filters are sensitive to the slow motion regime. Which time window is of importance can be seen from Fig. 5.7 [101]. It shows a double-logarithmic plot of the mechanical relaxation strengths Hi(t) for two carbon-black filled styrene-butadiene rubber (SBR) samples as a function of the mechanical relaxation time T. They have been measured by dynamic mechanical relaxation spectroscopy. In terms of NMR, the curves correspond to spectral densities of motion. But the spectral densities relevant to NMR are mainly those referring... 

Extreme nar- The fast motion regime where molerowing cular motion is sufficiently rapid that... 

The expressions used to calculate the curves shown in Fig. 14 are obtained as follows. First, the value of logio R corresponding to the onset of the fast-motion regime is approximated as logio ,max = 8.40 + 0.(X)745v, where v is the frequency in gigahertz (GHz). Above this value, = 2 is sufficient to calculate the spectrum. For lowCT values of R, the plotted curves are calculated for v = 9, 94, and 140 using Eq. 6,... 

The ESR working window in which the ESR line shapes are sensitive to rotational reorientation depends on the anisotropy of the A- and g-tensors of the radical for nitroxides, the range for Xp, is 10 -10 s, which means that the technique is applicable to polymer solutions, polymer gels, and solid polymers at temperatures close to or above Tg. At the X-band ESR frequency ( 9 GHz), the rotational dynamics in most liquids is usually sufficiently fast, that is, Xp,Aco 1 [where Am is a measure of the magnitude of the orientation-dependent part of the spin Hamiltonian ffj(t)] such motions (Xjj < lO s) fall within the motional narrowing (fast-motional) regime. For slower dynamics (Xp,Am > 1), more complicated slow-motional spectra are observed. ... 

Pioneering applications of ESR to the study of dynamics of nitroxides attached to polymers was described by Cameron and Bullock,who analyzed fast-motional solntion ESR spectra of simple nitroxides attached to polystyrene. The ESR spectroscopy of nitroxides in the fast-motional regime based on even simplified versions of Eq. 2 has been widely used for solving various problems mainly in the fields of biochemistry and medicine. Unfortunately, critical assessment of the model, and the accnracy and validity of results is frequently missing. 

For an isolated spin-1 system, it is convenient to define sum and difference magnetizations [Eqs. (2.84)-(2.85)] in the J-B experiment. The decay of the difference (quadrupolar order) proceeds exponentially at a rate T q, while the sum (Zeeman order) recovers exponentially towards equilibrium at a different rate. The J-B experiment allows simulataneous determination of these rates from which Ji uJo) and J2 2ujo) can be separated. Table 5.1 briefly summarizes thermotropic liquid crystals in which spectral density measurements were reported. Figure 5.4 illustrates the temperature and frequency dependences of spectral densities of motion (in s by including the interaction strength Kq factor) for 5CB-di5. The result is fairly typical for rod-like thermotropic liquid crystals. The spectral densities increase with decreasing temperature in the nematic phase of 5CB. The frequency dependence of Ji uJo) and J2(2a o) indicate that molecular reorientation is likely not in the fast motion regime. However, the observed temperature dependence of the relaxation rates is opposite to what is expected for simple liquids. This must be due to the anisotropic properties (e.g., viscosity) of liquid crystals. 

A second example is a 220 GHz EPR study of an oligonucleotide with a newly synthesized cytosine spin-label. The spectrum from a monomer in an aqueous solution exhibited a three-line pattern characteristic of a nitroxide in a fast motion regime. The anisotropic diffusion tensor estimated from this fast motion spectrum was consistent with the expected rapid motion of the probe molecule around its tether. 

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