Time Scale of Motions

NMR studies in polymer systems often present some difficulties, because polymer chains may have motions at various spatial scales, with correlation times ranging in very large domains. A model based on different correlation times in various parts of the networks has 

In polymer networks, slow motions, which may occur at larger spatial scales, are frozen. This has been demonstrated in the PDMS model networks described in Section 15.3.1, by measuring the relaxation of the so-called quadrupolar magnetic order in the 2H spin system [29]. This relaxation (observed with an appropriate pulse sequence) is sensitive 

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The dependence of k on viscosity becomes even more puzzling when the time scale of motion along the reaction coordinate becomes comparable to that of solvent dipole reorientation around the changing charge distribution... 

Figure 12.4. Hierarchy of length scales of structure and time scales of motion in polymers. Tg denotes the glass transition temperature. After Uhlherr and Theodorou (1998) (courtesy Elsevier...

Figure 3 Time scale of motions detected by a variety of NMR measurements including relaxation parameters, and analyses of line shape, SLF and exchanges.

We now make two simplifications. One is that the rate of O2 production is uniform over the curved part of the Pt surface, and we ignore the contribution from the end of the rod because it is small in surface area when compared to the rest of the rod. Second, the rod is permeable to O2, with the same diffusion coefficient as in water because the rod is small with respect to the diffusion length in the volume of the solution for the time scale of motion. With these approximations, the problem can be solved by integrating the contributions of a continuum of point sources spread on the cylindrical Pt surface (Eq. (3))... 

In conclusion, common diffraction techniques are typically unable to refer to subunits and sequences of significant dynamics, but are usually able to identify the dominant conformers/conformations. More specific approaches can report on events (e.g. series of reaction(s) and allosteric conformational changes) happening in the crystal state at slower (s-h) or even faster (ms-fis) time scale of motion. However, even the latter approaches are "blind" to highly flexible regions of proteins structures with many conformation possibilities appearing at ms-ns time scale of motion. 

From the simpler resonance line-shape and H/D-exchange analysis to the more complex studies of inherent dynamics, occurring on various time scale of motion, NMR remains a good choice to investigate protein flexibility and plasticity. If linebroadening due to exchange and inhomogeneity is minimized (or completely eliminated), then half-width, Aom, of a line becomes proportional to R, the transverse relaxation rate constant. 

Molecular motion in the polar organic solvent nitrobenzene, induced by both continuous and pulsed electronic fields, was studied by magnetic resonance imaging. The resultant image correlation spectra indicate that the time scale of motion in a 9.6 kV cm electric field is tens of milliseconds. The data were analyzed by the Fokker-Planck probability function for one-dimensional bounded diffusion. 

Fluorescence depolarization measurements of aromatic residues and other probes in proteins can provide information on the amplitudes and time scales of motions in the picosecond-to-nanosecond range. As for NMR relaxation, the parameters of interest are related to time correlation functions whose decay is determined by reorientation of certain vectors associated with the probe (i.e., vectors between nuclei for NMR relaxation and transition moment vectors for fluorescence depolarization). Because the contributions of the various types of motions to the NMR relaxation rates depend on the Fourier transform of the appropriate correlation functions, it is difficult to obtain a unique result from the measurements. As described above, most experimental estimates of the time scales and magnitudes of the motions generally depend on the particular choice of model used for their interpretation. Fluorescence depolarization, although more limited in the sense that only a few protein residues (i.e., tryptophans and tyrosines) can be studied with present techniques, has the distinct advantage that the measured quantity is directly related to the decay of the correlation function. 

Atomic motions cause the energies of scattered neutrons to be changed. Depending on the time scale of motion, one needs to cover an energy range from 10 neV-1 eV and to span wave vectors from 0.01-10 A . This wide time scale of analysis is covered by different classes of instruments. The phase space region ( ,Q) accessible to the various types of neutron spectrometers is schematized in Fig. 1. 

Figure 1.1 Time scale of motions as a function of correlation time Tc or fluctuation frequency p, as detected by solution and solid state NMR.

As was discussed in previous section, NMR is a very useful tool for the study of local molecular motion. The measurements of the relaxation times and line-shape analysis provide information about the dynamics and are sensitive to the amplitude, geometry and time scale of motion. However, this methodology also has some drawbacks. First, the necessity of deuteration, which sometimes is challenging especially for complex peptides and proteins. Second, in the case of bigger molecules with multisite labelling, NMR does not provide a desired resolution, which requires employing 2D MAS NMR techniques for extracting dynamic information with appropriate site resolution. 

A small change in the thermodynamic properties of the solution, as represented by A2, leads to a shift in the dynamics, typically the time scale of motion and dependence on the concentration and the molecular weight. It ofteu happeus that the shift in the dynamic properties is more pronounced compared with the shift in the static properties. Thus, how the time scale depends on the polymer concentration, the molecular weight, and the temperature gives us an important piece of information on the state of the polymer molecules, especially their interactions with the solvent molecules. 

The osmotic pressure and the time scale of motion depend heavily on concentration and molecular weight. The dependence is universal for a certain class of solutions each class, however, exhibits a characteristic dependence. For many years, we had not had a good understanding of those characteristics until the blob concept, the scaling theory, and the reptation model were introduced in 1970s. With simple ideas and simple mathematics, these concepts elegantly explained the observed complicated dependence. 

The time scale of motional averaging at W-band is moved toward slower motion bringing the whole spectrum essentially into a rigid limit under the conditions of the experiment. 

Residue-specific generalized order parameters, S, mapped on the TcSb miniprotein represented by Its ribbon structure. Mobility Is color-coded brown (S < 0.4) stands for high, while yellow (S > 0.5] for lower backbone NH mobility occurring on thel ps4- 10 ns time scale of motion. Orange represents 0.4-0.5values (Pohl et al. unpublished)... 

Hansen et al. used ssNMR to describe the function of synthetic and natural macromolecular systems. These critically depend on the packing and dynamics of the individual components of a given system. ssNMR provides structural information with atomic resolution, but it can also provide a way to characterise the amplitude and time scales of motions over broad ranges of length and time. These movements include molecular dynamics, rotational and translational motions of the building blocks, and also the motion of the functional species themselves, such as protons or ions. °... 

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