Correlation time representative

The fast motions described by the spectral density function jf((oo) are expected to occur on a similar time scale (xf 10 " s) as in the corresponding liquid alkane. Thus this motion is in extreme narrowing (t/ 1/too) in the accessible frequency range, and we may assume j/ 2co()) jj(coo) jf 0) = 2xf, where t/ should be considered an effective correlation time, representing the integral over a nonexponential correlation function. 

NMR relaxation parameters are useful probes of molecular motions in polymers. Each correlation time represents the average value of the system, with some distribution around that average. NMR imaging permits the determination of the spatial distribution of NMR relaxation times. This distribution provides information concerning the local motions of the system. In this case, the polymer is partiaUy swollen with solvent, and the spatial distributions of relaxation times reveal the interactions between the solvent and the polymer in the diffusion process. 

Anisotropy describes the rotational dynamics of reporter molecules or of any sensor segments to which the reporter is rigidly fixed. In the simplest case when both the rotation and the fluorescence decay can be represented by single-exponential functions, the range of variation of anisotropy (r) is determined by variation of the ratio of fluorescence lifetime (xF) and rotational correlation time ([Pg.9]

The reciprocal of the frequency can be defined as the rotational correlation time, tc, which represents the approximate time required for reorientation by random thermal tumbling. For values of tc < 5 x 10"9 s, an approximate theoretical solution for the linewidths of the three nitroxide ESR lines is given by (17) ... 

This level provides the most information-rich correlation. It represents a point-to-point relationship between in vitro dissolution and the in vivo input rate of the drug from the dosage form. A linear regression of dissolution and absorption at common time point is established. In such a correlation, the linear relationship of absorption vs. dissolution with a slope of one, an intercept of zero, and a coefficient of determination of... 

Chemists pay much less attention to the NMR relaxation rates than to the coupling constants and chemical shifts. From the point of view of the NMR spectroscopist, however, the relaxation characteristics are far more basic, and may mean the difference between the observation or not of a signal. For the quadrupolar nucleides such as 14N the relaxation characteristics are dominated by the quadrupole relaxation. This is shown by the absence of any nuclear Overhauser effect for the 14N ammonium ion despite its high symmetry, which ensures that the quadrupole relaxation is minimized. Relaxation properties are governed by motional characteristics normally represented by a correlation time, or several translational, overall rotational and internal rotational, and thus are very different for solids, liquids and solutions. 

Figure 2.4. Schematic representation of processes which lead to fluorescence depolarization in proteins rotation of the protein molecule as a whole with correlation time rotation of the fluorophore with correlation time d, and excitation energy transfer, represented by the wavy arrow.

The rotational mobility of human low-density (LDL) and very-low-density (VLDL) lipoproteins was studied as a function of viscosity and temperature in the range of —90 to — 50°C.(86)The rotational behavior for LDL is represented by a single correlation time, consistent with the overall rotation of a spherical rigid particle as the source of the phosphorescence depolarization. For VLDL, internal peptide motions dominate the depolarization profile. 

See Figure 8. HPLC equipment using reversed phase separation with fluorometric detection was used. Injection for correlation HPLC was accomplished with a newly developed device ( 4 ). The total range of phenol measured was five decades of concentration 0.01 -100 jug/L. The two higher concentrations (10 - 100 /i-g/L) were determined solely by conventional methods. The two lower concentrations (0.01 - 0.1 /xg/L) were determined by correlation HPLC with 16 and 3 sequences correlation time, respectively. Measurements at the 1 /xg/L level were carried out both by conventional and by correlation HPLC (1 sequence). The bars indicated on the calibration graph represent the peak area +3 (arbitrary units), where is the standard deviation... 

Fig. 6. Global structural characterization of mPrP(23-231). Dots represent the 98 residues of the N-terminal segment 23-120, which shows features of a flexible, random coil-like polypeptide with rotational correlation times for the groups of Tc

The dependence of (20 MHz and 25° C) on is graphically represented in Pig. 3 for monoaqua Gd(III) complexes with different values of the rotational correlation times. The limiting effect of the residence lifetime is small for low molecular weight complexes (xf> = 50 100 ps) and detectable only when On the other hand, for slowly tumbling... 

The molecular reorientational correlation time tends to dominate the overall correlation time of low molecular weight Gd(III) chelates, particularly in the high field region, and therefore represents a key parameter in governing their relaxivity. The effect of the increase in x on the shape and amplitude of the NMRD profiles was understood in detail early on and, as a consequence, the attempts at optimizing the relaxivity were primarily focused on slowing down the rotation by increasing the size of the... 

Figure 2.4 Carboxylic acid dimer in the potential energy minima with local vibrational states. OV represents the correlation time for a thermally activated proton transfer, and TU, the correlation time for tunneling transfer. (Reproduced with permission from ref. 29.)...

Fig. 6. Normalized cross-peak volumes of five representative spin pairs from NOESY spectra of cyclo(Pro-Gly) at different temperatures, recorded with Tm = 300 ms. Circles, crossrelaxation rates calculated from eq. (27a) using only the linear term. Dashed lines were drawn according to eqs (la) and (2a) using uiol2n = 500 MHz (actual resonance frequency) and interproton distances, r, from the model (table 1). Solid lines connect the points of one spin pair at different temperatures. Experimental temperatures indicated at the top are superimposed on the correlation time axis according to eq. (5) logTc 1/T. Reciprocal temperature axis is scaled and shifted to produce the best visual overlap of the theoretical curves and experimental data points. Inset represents the indicated region around the crossrelaxation rate maximum in the extreme-narrowing regime, magnified 14 times.

Fig. 10. Calibration graph for phenol with fluorimetric detection for 5 concentrations (I0" to lO" gl ) s indicates single injection and c indicates correlation chromatography. The numbers below the data points indicate the correlation time (minutes) (ppt = ng 1" ). The bars represent 3 x standard deviation of the integrated noise (confidence interval).

There is a close analogy with the problem of the validity of the kinetic description of many-body systems. The role of the initial correlations is represented in Eq. (36) by Once the initial state is chosen such as to satisfy Eq. (37) for times longer than some characteristic time, tc, then we have... 

Fig. 3.51. Logarithmic plot of the normalized induced dipole moment correlation function, C(t), for hydrogen-argon mixtures at 165 K. Measurements at 90 amagat ( ) 450 amagat ( ) and 650 amagat (o). The broken lines at small times represents the portion of C(t) affected by the smoothing of the wings of the spectral profiles. Reproduced with permission by the National Research Council of Canada from [109].

Fig. 54 shows some first systematic measurements by Bantle et al.207,209), who changed the delay time by factors of 1 2 4 8 the suggested optimum condition for a recording of the full correlation time corresponds to a value of 4, i.e. the TCF has decayed here to e 2 of the original value at channel 80220. Evidently, the qz dependence can in these four cases be represented by... 

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