Relaxation time shift correlation

To is known as the Vogel-Fulcher temperature and is located about 30 K below Tg. r is the asymptotic value of the relaxation time of the correlator 4> for T—>oo. Also the rheological shift factors a (T) mentioned above approximately follow such temperature dependences [34] ... 

Fig. 5.25 Result of applying shift factors corresponding to an activation energy of 0.43 eV to the relaxation times observed for the collective dynamics (empty symbol) and the self-correlation (full symbol) of PIB 335 K (circle), 365 K (square), and 390 K (triangles) (reference temperature 365 K). The dotted line through the self-correlation data shows the dependence implying Gaussian behaviour (Reprinted with permission from [147]. Copyright 2002 The American Physical Society)...

Thus, larger-scale cooperative chain motions can be observed using this technique. A Tj vs. temperature plot is generally analogous to a curve with the lower time values and minima shifted to lower temperatures (Fig. 4). In the case of rapid motions (to2i 4 1), Tj is identical to Tt and, assuming a single correlation time, both relaxation times are equal to 1/5 Ctc (Eqs. (15) and (19)). 

Fig. 3.20. Relation between the relaxation times T1 and T2 and the effective correlation time zc. In stronger magnetic fields the Tt minimum shifts towards smaller correlation times, i.e. higher "frequencies of molecular motion.

Spin-lattice relaxation times and 13C chemical shifts were used to study conformational changes of poly-L-lysine, which undergoes a coil-helix transition in a pH range from 9 to 11. In order to adopt a stable helical structure, a minimum number of residues for the formation of hydrogen bonds between the C = 0 and NH backbone groups is necessary therefore for the polypeptide dodecalysine no helix formation was observed. Comparison of the pH-dependences of the 13C chemical shifts of the carbons of poly-L-lysine and (L-Lys)12 shows very similar values for both compounds therefore downfield shifts of the a, / and peptide carbonyl carbons can only be correlated with caution with helix formation and are mainly due to deprotonation effects. On the other hand, a sharp decrease of the 7] values of the carbonyl and some of the side chain carbons is indicative for helix formation [854]. 

Hereafter we put /ig = 1. Below we express our results in terms of the statistical properties (correlators) of the environment s noise, X(t). Depending on the physical situation at hand, one can choose to model the environment via a bath of harmonic oscillators [6, 3]. In this case the generalized coordinate of the reservoir is defined as X = ]T)Awhere xi are the coordinate operators of the oscillators and Aj are the respective couplings. Eq. 2 is then referred to as the spin-boson Hamiltonian [8]. Another example of a reservoir could be a spin bath [11] 5. However, in our analysis below we do not specify the type of the environment. We will only assume that the reservoir gives rise to markovian evolution on the time scales of interest. More specifically, the evolution is markovian at time scales longer than a certain characteristic time rc, determined by the environment 6. We assume that rc is shorter than the dissipative time scales introduced by the environment, such as the dephasing or relaxation times and the inverse Lamb shift (the scale of the shortest of which we denote as Tdiss, tc [Pg.14]

In 2D experiments, the precision of the measured values is determined by the precision with which peak positions can be determined in a 2D spectrum. The precision of the values measured along the F2 axis is determined by the acquisition time (as in ID spectra), but the precision of the values measured along the FI axis (i.e. indirectly detected) is determined by the maximum evolution time used in the experiment (assuming it is shorter than the 7V relaxation time of the signal). Hence, if a heteronuclear coupling [e.g. 2/(Si—H)] has to be determined with a precision of 0.1 Hz, it would require a maximum evolution time of the order of 10 s, that is, some 40,000 increments if the spectral width along FI were 4 kHz (in a correlation experiment), which is not very realistic. On the other hand, chemical shifts can be easily determined with the needed precision of 1 Hz along FI. 

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