Mean correlation time

Fig. 24. Calculated 2H quadrupole echo and MAS NMR spectra for a two-site reorientation35 such that the 2H quadrupole coupling tensor unique principal axis moves through 106°, i.e. the motion appropriate for the two-site motion of the methyl groups in deuterated DMS. The simulations assume an inhomogeneous symmetric log-Gaussian distribution of correlation times with a mean correlation time of 5 x 10 5s and a standard deviation ranging from 0 to 3 decades, (a) Quadrupole echo spectra with echo delay time t = 30 /is. (b) MAS spectra.

With increasing concentration, the mean correlation time increased gradually from 0.10 ns (2%) to 0.22 ns (30%). These are within the values typical of a random coil polymer, 0.1-1.0 ns at 30-40°C. Moreover, the width parameter, / , in the log distribution model was relatively small 10-14, indicating broad distribution of the correlation time. This is also typical of a random coil polymer.- ... 

Fig. 7. Concentration dependence of the mean correlation times for the segmental motion of B. mori silk fibroin determined from NTi and NOE values averaged over Gly C , Ala C , and Ser C assuming the log distribution model. The width parameters in the model were 10-14. The NOE value for the liquid silk in the B. mori silk gland was assumed to be 2.2.

Hiraoki et al. investigated the phenyl ring dynamics of poly(L-phenylalanine) using H-NMR, showing that it is characterized by a fairly broad distribution of correlation times. The mean correlation time of this distribution was 1.2 x 10 Hz at 25°C, which is close to that of the fast motional component of the B. mori and S.c. ricini silk fibroins. The Tyr ring flip in the pentapeptide [Leu ] enkephalin was reported to be 5.6 x 10 Hz at 25°C, which is close to that of the slow motional component observed here for silk fibroin. On the other hand, the ring motion in crystalline N-acetyl-L-Asp-L-Pro-L-Tyr-N -methylamide was found to be 1.1 X 10 Hz at 27°C, close to that of the fast motional component of the silk fibroins. 

There were two reasons for using the mean correlation time, Tmean, rather than relaxation times of individual modes, T, (a) experimental data were analyzed in the same way, (b) individual components, T reflect different types of the real motion, but they have no clear physical meaning in the coarse-grained model. 

This expression is sometimes used with liP) in piece of re. For a nonsphetical molecule, the initial slope of the anisotropy decay is determined by the hannonic mean correlation time."... 

Also shown in Table 12.2 is the harmonic mean correlation time (Bh). Calculation of B/r is somewhat complicated because it depends on the value of ro and the orientation of the transition moments relative to the ellipsoid axis. The values in Thble 12.2 were calculated uang... 

The behavior of methine-labeled poIy(ethyl acrylate)-di (PEA-di), poly(wo-propyl acrylate)-di (PIPA-di), and poly(n-butyl aciylate)-di (PNBA-di) has been studied with deuterium NMR relaxation time measurements in concentrated solutions with chloroform. PEA-di and PNBA-di behaved similarly in terms of solution dynamics, but PIPA-di was found to reorient significantly faster at similar concentrations. The relaxation times were fitted to a log-normal distribution of correlation times and the resulting mean correlation times fit to Arrhenius behavior. The energies of activation were found to increase with increasing concentration from about 6 kJ/mol at lower concentrations to 10-20 kJ/mol from about 40 to 80 wt % polymer. 

The results of fitting the relaxation times to the log-normal distribution of correlation times are shown in Figures 4-6. Since PEA-di and PNBA-di had similar relaxation times, we shall examine their behavior first. For PEA-di and PNBA-di, the behavior of the mean correlation times (To) shown in Figures 4 and 5 were quite similar in terms of both the correlation times and, consequently, the temperature dependence. In all cases, the temperature dependence is reasonably well described with an exponential fimction. For PEA-di a different behavior can be seen from 60 to 70 wt % polymer. Above 60 wt%, the apparent energies of activation increase. The values for the width parameter (not shown), a, were between 2 and 4 for these polymers. 

The log-normal distribution of correlation times can be used to fit the relaxation data from concentrated polymer solutions. The data provide reasonable variations of the mean correlation times with concentration and temperature. Of the systems studied, PIPA-di was found to reorient much more rapidly than either PEA-di or PNBA-di. Relatively low energies of activation were found for PIPA-di in semi-dilute solution. These energies of activation increased with concentration and were similar for all three polymers until the highest concentration where the apparent energies of activation scaled with the glass transition temperature of the bulk polymers. 

Fig. 19 Left 2H relaxation times for PMA-d in toluene solution (open symbols) and in swollen adsorption layers (filled symbols), squares TI, circles T2. Right Mean correlation times for PMA-d in toluene solution (circles) and in swollen adsorption layers (squares) as evaluated fix>m a log-normal distribution of Tj. Both figures taken from [14] with permission.

The mesoscopic structure of ionomers based on diblock copolymers is detemuned by two effects microphase separation of the diblock copolymer and clustering of the ions. For the a,0)-zwitterionic diblock copolymers, this leads to the confinement of the ion clusters to the interface between the two nucrophases. Within the two microphases, polymer dynanucs is different If the fuzziness of this interface extends to lengths significantly beyond the diameter of the ion clusters, a broad distribution of rotational correlation times is expected for a spin probe attached to the cluster surface. In contrast, if the interface were infinitely sharp, a bimodal distribution is expected, with the two sharply defined mean correlation times corresponding... 

As the first point, the dynamics of the phenyl group in the poly-formal can be considered. Motional descriptions from the two segmental models can be compared as they have been before for the polycarbonates ( 5). In the three bond jump model the primary parameter is the harmonic mean correlation time, and in the... 

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