Partial relaxation

Spectral resolution enhancement can be achieved by partial relaxation, which capitalizes on the different relaxation times, T, of the protons in a molecule (324). The partial relaxation experiment usually employs the inversion recovery pulse sequence [180°- r-90°-acquisition] (390), though progressive saturation (106) can also be employed. 

A series of partially relaxed spectra obtained by the inversion recovery pulse sequence with increasing delay time t (in seconds) is shown as stack runs in Fig. 2.31 (282). At first, all peaks are negative they then gradually become positive with T, protons with shorter Tj becoming positive earlier than those with longer 

Ti values. From plots such as the one shown, the T relaxation times of protons can be readily measured. The relaxation times of various protons in organic molecules usually increase in the order of methylene, methine, methyl, and quaternary. This is seen in the relaxation time of the protons in yff-ionone. 

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Figure 4-6. Representation of the magnetization components A/, A/., and A/,. (A) In presence of field without field H. (B) Immediately after absorption of energy from field Hi. (C) After partial relaxation back to the equilibrium position shown in A.

Electronic absorption spectra are produced when electromagnetic radiation promotes the ions from their ground state to excited states. For the lanthanides the most common of such transitions involve excited states which are either components of the ground term or else belong to excited terms which arise from the same 4f" configuration as the ground term. In either case the transitions therefore involve only a redistribution of electrons within the 4f orbitals (i.e. f—>f transitions) and so are orbitally forbidden just like d—>d transitions. In the case of the latter the rule is partially relaxed by a mechanism which depends on the effect of the crystal field in distorting the symmetry of the metal ion. However, it has already been pointed out that crystal field effects are very much smaller in the case of ions and they... 

Fig. 10. Various stages in the expulsion of a chain that has been tethered to an interface. Left Block copolymer straddling interface. Center Initiation of expulsion process. Right Chain partially expelled, and therefore partially relaxed from the deformation induced by tethering...

Fig. 13. Calculated 2H solid echo spectra for log-Gaussian distributions of correlation times of different widths. Note the differences of the line shapes for fully relaxed and partially relaxed spectra. The centre of the distribution of correlation times is given as a normalized exchange rate a0 = 1/3tc. For deuterons in aliphatic C—H bonds the conversion factor is approximately 4.10s sec-1...

Fig. 21. Deuteron NMR spectra for the phenyl groups in polycarbonate (amorphous film, drawn from solution at room temperature, Mw 30000, Mw/M = 1 -8). Left column fully relaxed spectra. Right column partially relaxed spectra corresponding to the mobile groups only...

Fig. 24. Fully and partially relaxed methyl-deuteron spectra of polycarbonate, proving the heterogeneous nature of the distribution of correlation times...

Figure 2. Muscle stimulation, a) a single nerve impulse (stimulus) causes a single contraction (a twitch). There is a small delay following the stimulus before force rises called the latent period, b) A train of stimuli at a low frequency causes an unfused tetanus. Force increases after each progressive stimulus towards a maximum, as calcium levels in the myofibrillar space increase. But there is enough time between each stimulus for calcium to be partially taken back up into the sarcoplasmic reticulum allowing partial relaxation before the next stimulus occurs, c) A train of stimuli at a higher frequency causes a fused tetanus, and force is maximum. There is not enough time for force to relax between stimuli. In the contractions shown here, the ends of the muscle are held fixed the contractions are isometric.

The most popular, and also a very accurate, experimental method for measuring nonselective spin-lattice relaxation-rates is the inversion recovery (180°-r-90°-AT-PD)NT pulse sequence. Here, t is the variable parameter, the little t between pulses, AT is the acquisition time, PD is the pulse delay, set such that AT-I- PD s 5 x T, and NT is the total number of transients required for an acceptable signal-to-noise ratio. Sequential application of a series of two-pulse sequences, each using a different pulsespacing, t, gives a series of partially relaxed spectra. Values of Rj can... 

The application of partial relaxation FTNMR in the determination of unreacted monomers, solvent, water, and additives in polymers, polymer degradation, and functional group and chain structure characterisation has been reviewed [255]. Hummel [95] underestimates the contribution of NMR to polymer/additive analysis. 

Obviously, the partly inverted Legendre-transformed representations for reactive systems would similarly generate descriptors of the partially relaxed (electronically or geometrically) reactive systems. 

The rotational relaxation of DNA from 1 to 150 ns is due mainly to Brownian torsional (twisting) deformations of the elastic filament. Partial relaxation of the FPA on a 30-ns time scale was observed and qualitatively attributed to torsional deformations already in 1970.(15) However, our quantitative understanding of DNA motions in the 0- to 150-ns time range has come from more accurate time-resolved measurements of the FPA in conjunction with new theory and has developed entirely since 1979. In that year, the first theoretical treatments of FPA relaxation by spontaneous torsional deformations appeared. 16 171 and the first commercial synch-pump dye laser systems were delivered. Experimental confirmation of the predicted FPA decay function and determination of the torsional rigidity of DNA were first reported in 1980.(18) Other labs 19 21" subsequently reported similar results, although their anisotropy formulas were not entirely correct, and they did not so rigorously test the predicted decay function or attempt to fit likely alternatives. The development of new instrumentation, new data analysis techniques, and new theory and their application to different DNAs in various circumstances have continued to advance this field up to the present time. 

The low torsion constant at a = —0.025 is very similar to that observed in a supercoiled pBR322 that was partially relaxed by saturation binding of Escherichia coli single-strand binding (ssb) protein, and which persisted for over a month.(56) It is also similar to that recently inferred from an in vivo assay based on variation in repression efficiency with size of a putative DNA loop.(234) Indeed, it appears that anomalously low torsion constants may be universally encountered in the course of either partial or complete relaxation of supercoiled DNAs, regardless of whether the superhelix density is reduced by action of topoisomerase I, binding of ssb protein, binding of intercalated... 

Rasmussen s efforts to adopt CFF to saccharides merit special attention (32). His latest version (34), which virtually eliminated the torsional term, awaits critical examination. Tvaroska and Bleha (183) performed partial relaxation MM calculations on dimethoxymethane... 

There is considerable activity in the area of MM calculations on small polypeptides. A preliminary amide force field based on the CFF (231,232) and a partial relaxation force field (233) has been reported. Interested readers are referred to review articles cited in ref. 232. 

The analysis in the last paragraph has shown that the incommensurate Xe layer on Pt(lll) at misfits of about 6% is a striped phase with fully relaxed domain walls, i.e. a uniaxially compressed layer. For only partially relaxed domain walls and depending on the extent of the wall relaxation and on the nature of the walls (light, heavy or superheavy) additional statellites in the (n, n) diffraction patterns should appear. Indeed, closer to the beginning of the C-I transition, i.e. in the case of a weakly incommensurate layer (misfits below 4%) we observe an additional on-axis peak at Qcimm + e/2 in the (2,2) diffraction pattern. In order to determine the nature of the domain walls we have calculated the structure factor for the different domain wall types as a function of the domain wall relaxation following the analysis of Stephens et al. The observed additional on-axis satellite is consistent with the occurrence of superheavy striped domain wails the observed peak intensities indicate a domain wall width of A=i3-5Xe inter-row distances. With... 

Simpson RT, Thoma F, Brubaker JM (1985) Chromatin reconstituted from tandemly repeated cloned DNA fragments and core histones a model system for study of higher order structure. Cell 42 799-808 Sugiyama S, Yoshino T, Kanahara H, Kobori T, Ohtani T (2003) Atomic force microscopic imaging of 30 nm chromatin fiber from partially relaxed plant chromosomes. Scanning 25 132-136 Sugiyama S, Yoshino T, Kanahara H, Shichiri M, Fukushi D, Ohtani T (2004) Effects of acetic acid treatment on plant chromosome structures analyzed by atomic force microscopy. Anal Biochem 324 39 4... 

Figure 3.6 A side view of (a) coherent and (b) partially relaxed epilayers. The relaxation process changes both the interplanar spacings of the epilayer and the angles between the reflecting planes and the surface. (Courtesy K.M.Matney)...

It is noteworthy that the neutron work in the merging region, which demonstrated the statistical independence of a- and j8-relaxations, also opened a new approach for a better understanding of results from dielectric spectroscopy on polymers. For the dielectric response such an approach was in fact proposed by G. Wilhams a long time ago [200] and only recently has been quantitatively tested [133,201-203]. As for the density fluctuations that are seen by the neutrons, it is assumed that the polarization is partially relaxed via local motions, which conform to the jS-relaxation. While the dipoles are participating in these motions, they are surrounded by temporary local environments. The decaying from these local environments is what we call the a-process. This causes the subsequent total relaxation of the polarization. Note that as the atoms in the density fluctuations, all dipoles participate at the same time in both relaxation processes. An important success of this attempt was its application to PB dielectric results [133] allowing the isolation of the a-relaxation contribution from that of the j0-processes in the dielectric response. Only in this way could the universality of the a-process be proven for dielectric results - the deduced temperature dependence of the timescale for the a-relaxation follows that observed for the structural relaxation (dynamic structure factor at Q ax) and also for the timescale associated with the viscosity (see Fig. 4.8). This feature remains masked if one identifies the main peak of the dielectric susceptibility with the a-relaxation. 

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