Time shift value, relaxation

The time shift value This moves the curve along the log time axis, which is equivalent to finding a value for t. (When a time shift is used and t is kept as 1, K becomes the ratio of the ionic to segmental relaxation rate constants.)... 

TABLE 30. 13C NMR chemical shift values (8), spin-lattice relaxation times (T ) and nuclear Overhauser effects (NOE) for /1-carotene (78) in CDCI3 at various magnetic field strengths ... 

TABLE 31. I3C NMR chemical shift values (5), observed and calculated spin-lattice relaxation times (7i ) and observed nuclear Overhauser effects (NOE) for zinc me.vo-tetrapheny I porphyri n (79) in CDCI3 solution at 9.4 T... 

FIGURE 31. Typical data set for measurement of the spin-lattice relaxation times of the sp2-hybridized carbon atoms of, 6-carotene at 11.7 T. The chemical shift values are shown across the bottom of the figure. The t-value for each spectrum is the delay time in the inversion-recovery pulse sequence. Reprinted with permission from Reference 49. Copyright (1995) American Chemical Society... 

For transport in amorphous systems, the temperature dependence of a number of relaxation and transport processes in the vicinity of the glass transition temperature can be described by the Williams-Landel-Ferry (WLF) equation (Williams, Landel and Ferry, 1955). This relationship was originally derived by fitting observed data for a number of different liquid systems. It expresses a characteristic property, e.g. reciprocal dielectric relaxation time, magnetic resonance relaxation rate, in terms of shift factors, aj, which are the ratios of any mechanical relaxation process at temperature T, to its value at a reference temperature 7, and is defined by... 

When the temperature is lowered and/or the viscosity of the solution is increased by using glycerol-water mixtures as solvent, the reorientational correlation time increases. Since the reorientational time is the correlation time for nuclear relaxation, the effects on the NMRD profile (Pig. 27) are (i) higher relaxivity values at low frequencies (ii) a shift toward lower... 

The relaxation dynamics (W7 in Fig. 38) is the response of the environment around Trp7 to its sudden shift in charge distribution from the ground state to the excited state. Under this perturbation, the response can result from both the surrounding water molecules and the protein. We separately calculated the linear-response correlation functions of indole-water, indole-protein, and the sum of the two. The results for isomer 1, relative to the time-zero values, are shown in Fig. 42a. The linear response correlation function is accumulated from a 6-ns interval indicated in Fig. 41a during which the protein was clearly in the isomer 1 substate. All three correlation functions show a significant ultrafast component 63% for the total response, 50% for indole-water, and nearly 100% for indole-protein. A fit to the total correlation function beyond the ultrafast inertial decrease requires two exponential decays 1.4 ps (3.6kJ/mol) and 23 ps (2.0kJ/mol). Despite the 6-ns simulation window for isomer 1, the 23-ps long component is not well determined on account of the noise apparent in the linear response correlation function (Fig. 42a) between 30 and 140 ps. The slow dynamics are mainly observed in the indole-water relaxation and the overall indole-protein interactions apparently make nearly no contributions to the slowest relaxation component. 

The concentration of the sample in a particular solvent has little effect on chemical-shift values and, because of the inherently low sensitivity of 13C-n.m.r. spectroscopy, it is advantageous to use as concentrated solutions as possible when measuring these spectra. However, increased concentration, and consequently increased viscosity, causes line broadening due to decreased, spin-lattice relaxation-times (Tj values),18 and thus, poorer resolution. Certain solvents that tend to give viscous solutions (for example, Me2SO-d6) may also give decreased resolution. 

Therefore, Or = 0.0012. This means that the longest relaxation time r of the polyisoprene at 100°C is 0.0012 times its value at 25°C. The viscosity tj changes roughly in proportion to the relaxation time if the small vertical shift factor is neglected. Thus, ... 

TABLE 29. NMR chemical shift values (3), observed and calculated" spin-lattice relaxation times (Ti) and observed nuclear Oveihauser effects (NOE) for squalane (81) and squalene (82) in CIXT3 solution at 11.7 T... 

TABLE 30. NMR chemical shift values (S), spin-lattice relaxation times (Ti) and nuclear ... 

The relaxation modulus is also a function of the strain, and according to the above it is expected that the model should be capable of treatment by means of a temperature-time shift as well as a strain-time shift. Thus, it is the product ede J /KT which defines Nit and the value of the ratio of the modulus to the absolute temperature should be constant for a constant value of the triple poduct. For any fixed temperature, the modulus at a time dj after application of a strain e2, should equal the modulus at a time d2 after application of a strain e2 provided... 

C Spin lattice relaxation times, Tj, spin-spin relaxation times, T2, and nuclear Overhauser enhancements, NOE, for the a-carbons of PBLG of various molecular weights have been used to study transitions from rigid to flexible forms of this polymer (Allerhand and Oldfield, 1973). Effective rotational correlation times, reff, calculated from 7 - and NOE-values, for the a-carbons were 24-32 nanoseconds for the helical form and approximately 0-8 nanoseconds for the random coil (Allerhand and Oldfield, 1973). The transition from the a-helix to the random-coil of PLM causes the resonances of the a- and carbonyl carbons to move upfield 2-3 and 3-4 ppm respectively (Tadokoro et al., 1973), which is consistent with results obtained for PBLG and PCBO. Further work is required before the reasons for the chemical shift differences between the corresponding carbons in the helical and random-coil forms in deuterochloroform-TFA systems can be elucidated. Plots of chemical shifts and relaxation times vs. pH have been used to study the helix-coil transition of poly-L-lysine hydrochloride in aqueous solution (Saito and Smith,... 

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