Relaxation methyl group rotation

Fig. 1.3 Relaxation map of polyisoprene results from dielectric spectroscopy (inverse of maximum loss frequency/w// symbols), rheological shift factors (solid line) [7], and neutron scattering pair correlation ((r(Q=1.44 A )) empty square) [8] and self correlation ((t(Q=0.88 A" )) empty circle) [9],methyl group rotation (empty triangle) [10]. The shadowed area indicates the time scales corresponding to the so-called fast dynamics [11]...

At low temperature the material is in the glassy state and only small ampU-tude motions hke vibrations, short range rotations or secondary relaxations are possible. Below the glass transition temperature Tg the secondary /J-re-laxation as observed by dielectric spectroscopy and the methyl group rotations maybe observed. In addition, at high frequencies the vibrational dynamics, in particular the so called Boson peak, characterizes the dynamic behaviour of amorphous polyisoprene. The secondary relaxations cause the first small step in the dynamic modulus of such a polymer system. 

This result suggests, if it is assumed that a C-H heteronuclear dipolar relaxation mechanism is operative, that methyl protons dominate the relaxation behavior of these carbons over much of the temperature range studied despite the 1/r dependence of the mechanism. The shorter T] for the CH as compared to the CH2 then arises from the shorter C-H distances. Apparently, the contributions to spectral density in the MHz region of the frequency spectrum due to backbone motions is minor relative to the sidegroup motion. The T p data for the CH and CH2 carbons also give an indication of methyl group rotational frequencies. 

Another study used H T, T2 and 13C T, T p measurements to assess the molecular dynamics in dry and wet solid proteins bacterial RNAase, lysozyme and bovine serum albumin.115 All relaxation time data were analysed assuming three components for the molecular motion methyl group rotation and slow and fast oscillations of all atoms. An inhomogeneous distribution of correlation times was found for all samples, not surprisingly given the inhomogeneous nature of the samples. Interestingly, it was found that dehydration affected only the slow internal motions of the proteins and that the fast ones remained unaltered. 

Possible intramolecular motional modes that might in principle affect the magnetic parameters and relaxation times are (1) methyl group rotation (2) interconversion of axial and equatorial methyls (3) inversion of the NO bond with respect to the CNC plane (4) interconversion of five-membered rings between twisted and planar conformations and (5) other ring motions that may exist. 

The electronic contribution to the relaxation rate of protons in TMQ has been arrived at after a careful sustrac-tion of the methyl group rotation contribution, Fig. 5. The pressure dependence of the room temperature T in TQ and TMQ is shown in Fig. 6. A log-log plot of ( TiTV,t versus reveals a phenomenological relation (T,T) %, with an... 

The present study has provided a critical test of the importance of cross relaxation involving both water and protein protons in hydrated protein systems. In addition it has successfully demonstrated that the temperature dependence of both the water and protein relaxation is dominated by motions in the water phase and not by motions in the solid phase such as methyl group rotations. While a detailed analysis has not yet been attempted, it appears that a picture of water in the interfacial regions around a protein that is consistent with the NMR relaxation data is one characterized by fast if slightly anisotropic motion. Structural models for water-protein interactions must be consistent with this very fluid character of water in this interfacial region-, however, it is also important to recognize that the time scale appropriate to the present experiments is still long when compared to the rotational correlation times or diffusion times usually associated with water in the pure liquid state. 

Fig. 7 Methyl-group rotational barriers (in kcal mol ) from relaxation data.

For the most part, the timescales for the aforementioned kinetic processes are well beyond the accessible timescale for fuUy atomistic MD simulations. Local dynamics such as rotation of a methyl group or a polymer side chain can certainly be explored. For example, in a polymer melt at a temperature of lOOK above the T, the timescale for methyl-group rotations is about Ips and approximately 1-lOns for segmental a-relaxation in a polymer [4b]. Diffusion for even a small molecule such as water in... 

A representative study of relaxation times as a function of temperature for poly(vinyl acetate) is presented in Figure 7.4 [3] where the effects of methyl group rotation and main-chain motion (glass-transition) can easily be distinguished. Correlation times are derived from the minima of or... 

Properties.—Carbon-13 and field-dependent proton spin-lattice relaxation times have been measured as a function of temperature and molecular weight for solutions of polycarbonates in CDCI3. The spin-lattice relaxation times were interpreted in terms of segmental motion, characterized by the sharp cut-off model of Jones and Stockmayer, for phenyl group rotation and methyl group rotation. ... 

Figure 8 Relaxation rates vp vs. inverse temperature for the dynamic glass transition of PMPS as obtained by the different techniques , dielectric spectroscopy , thermal spectroscopy , neutron spectroscopy. The data obtained from neutron scattering depend on the momentum transfer 0. In addition to the dynamic glass transition, the relaxation rates for the methyl group rotation for 0=1.8A ( ) are given. The line is a fit of the Arrhenius equation to the data of the methyl group rotation ( A=8.3kJmoL, log(L = 12.5 Hz). The inset gives dielectric loss vs. frequency for PMPS at different temperatures 212.2 K o, 215.2 K ), 219.2 K A, 225.2 K 0, 235.2 K V, 241.2 K +, 257.41 K , 283.1 K. The errors of the measurements are smaller than the size of the symbols. Lines are guides to the eyes.

It is tempting to identify the break point in Figure 8 as a characteristic temperature of the system. Guillet, in his chapter (18), makes such assignments in several hcmiopolyiiier systons. Indeed one finds in the literatures a maximum at -35 corresponding to the a-methyl group rotation in an nmr relaxation experiment. In this instance the temperature correspondence between the two sets of experiments must be. accidental. 

The relaxation temperature is frequency dependent. In the nmr experiment the maximum corresponds to a methyl group rotational frequ cy of 10 Hz. In the phosphorescence quenching experiment, the triplet lifetimes are on the order of seconds. Impurity diffusion is coupled in an yet unknown way to the methyl group rotation. From a kinetic point of view, -35 is the temperature where the rate of impurity quenching exceeds that of other processes in limiting the phosphorescence decay time. 

The story is even more complicated than we have suggested, because carbon can relax by more than one mechanism. Protons rely on dipole-dipole relaxation, which also works well for protonated carbons but badly for non-proton-ated carbons. But carbon also for example makes use of spin-rotation relaxation, which is particularly active for methyl groups. And the magnetic field dependence of the various mechanisms also differs. We realize that relaxation is a very difficult subject, and if you want to know more then there are plenty of textbooks available ... 

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