Spin-lattice relaxation dispersion

T. Zavada, R. Kimmich 1999, (Surface fractal probed by adsorbate spin-lattice relaxation dispersion), Phys. Rev. E 59, 5848. 

Fig. 2. Water proton spin-lattice relaxation dispersion in Cab-O-Sil M- samples with two different degrees of compression. The solid lines were computed using the model as in Ref. (45).

Fatkullin, N., and Kimmich, R. (1994). Nuclear spin-lattice relaxation dispersion and segmental diffusion in entagled polymers. Renormalized Rouse formalism. J. Chem. Phys. 101, 822-832. 

The proton spin-lattice relaxation dispersion data (Fig. 9) in MBBA at 18°C [ 135] obtained by the field cycling technique clear-... 

Typical spin-lattice relaxation dispersion curves... 

Spin-lattice relaxation dispersions according to Eq. 30 can be recorded over several decades of the frequency with the aid of field-cycling NMR relaxometry [18-21]. Combined with ordinary high-field NMR relaxometry, the accessible ranges for protons and deuterons are... 

Incrementing the relaxation interval t thus permits one to record the relaxation curve for a given relaxation flux density The spin-lattice relaxation dispersion is then scanned point by point by stepping B through a series of discrete values spread over the desired flux density (or frequency) range. 

Figure 16 shows typical proton spin-lattice relaxation dispersion data for polyethylene melts as an illustration of the three-component behavior of polymer melts. For comparison with model theories the chain-mode regime represented by component B is suited best and will be discussed in detail. It will be shown that the NMR relaxometry frequency window of typically 10 Hz< V <10 Hz (for proton resonance) almost exclusively probes the influence of chain modes represented by component B (compare Fig. 5). That is, the correlation function experimentally relevant for spin-lattice relaxation dispersion may be identified with component B according to...

Rouse dynamics is expected to apply to molecular weights below the critical value where entanglement effects are not yet effective. Experimental data sets for the proton spin-lattice relaxation dispersion [47, 49, 153] are shown in Fig. 27 in comparison to the theoretical frequency dependence predicted by Eq. 64. Very interestingly, the values for the segment fluctuation time Tj fitted to the Ti data coincide with those derived from the Ti minima (see Fig. 14) corrected for the temperature of the field-cycling measurements. That is, the two independent determination methods lead to consistent results. 

Fig. 27a-c. Proton spin-lattice relaxation dispersion under conditions where Rouse dynamics is expected to apply. The theoretical curves have been calculated with the aid of Eq. 64. The validity of this model is restricted to (0 Ts. The positions on the frequency axes where the condition q)Ts=1 apphes are indicated by arrows for the segment fluctuation time Ts fitted to the experimental data. The Tj values are in accord with those derived from the Ti minimum data (see Fig. 14) where applicable, a Polyisobutylene (Mm =4,700 < 15,000), melt at 357 K [49]. b Polydimethylsiloxane (M, =5,200... 

Figures 28, 29, 30, 31, 32, 33, and 34 show a series of typical spin-lattice relaxation dispersion curves. The technique has been applied to melts, solutions, and networks of numerous polymer species. As experimental parameters, the temperature, the molecular weight, the concentration, and the cross-link density were varied. For control and comparison, the studies are partly supplemented by rotating-frame spin-lattice relaxation data and, of course, by high-field data of the ordinary spin-lattice relaxation time. Furthermore, the deuteron spin-lattice relaxation was employed for identifying the role different spin interactions are playing for relaxation dispersion.

Figure 32 shows spin-lattice relaxation dispersion data for PDES (having -CH2CH3 as side groups) both in the isotropic and in the mesomorphic phases [155]. The dispersion of the isotropic melt is governed by the same empirical power laws for regions I and II as stated before (Eq. 168) and in particular as measured in PDMS melts (side groups -CH3). 

These results for the ordered mesophase are to be compared with the spin-lattice relaxation dispersion expected for nematic liquid crystals where a power law... 

It is concluded that the modified power laws for spin-lattice relaxation dispersion in the mesophase reflect a modified behavior of chain modes rather than collective fluctuations of ensembles of molecules in ordered domains. This conclusion is corroborated by the identical frequency dispersion of the spin-lattice relaxation times Ti and Tip in the laboratory and in the rotating frames, respectively. If the order in the PDFS mesophase would be of a nematic nature and the fluctuations causing dispersion region II consequently would be of the ODF type, the frequency dispersion of Tip should vanish while that of Ti is retained [22]. 

Permanent or thermoreversible cross-links mediate the opposite effect on chain dynamics compared with dilution by a solvent instead of releasing topological constraints by dilution, additional hindrances to chain modes are established by the network. With respect to NMR measurands relatively large cross-link densities are needed to affect chain modes visible in the experimental time/frequency window, as demonstrated with proton spin-lattice relaxation dispersion of polyethylene cross-Unked by 10-Mrad irradiation with electron beams [123] and with styrene-butadiene rubbers [29]. However, there is a very strong effect on the dipolar correlation effect which probes much slower motions and can therefore be used favorably for the determination of the cross-Hnk density [29, 176, 177]. 

In the plot shown in Fig. 31e, spin-lattice relaxation dispersion curves of permanently cross-linked PDMS are shown. With decreasing mesh length, the chain modes appear to be shifted to lower frequencies. This is indicated by lower values of the relaxation times while the dispersion slopes of regions I and II are retained. On the other hand, the effect on the crossover frequency is minor. 

The spin-lattice relaxation dispersion was derived with the same sort of theory. Figure 47 shows data obtained under the same conditions as assumed for the mean squared displacement data in Fig. 46. Again the dispersion most specific for the tube/reptation model, namely Ticxco - which is predicted for limit (II)de> was perfectly reproduced at low frequencies. 

Fig. 47. Spin-lattice relaxation dispersion for a chain of 1 =1,600 Kuhn segments (of length b) confined to a randomly coiled tube with a harmonic radial potential with varying effective diameters d. The data were calculated with the aid of the harmonic radial potential theory [70]. c is a constant. At low frequencies the curves visualize the crossover from Rouse dynamics depending on the effective tube diameter. The latter case is described by a Tj dispersion proportional to characteristic for limit (II)de of the tube/ reptation model...

Based on the generalized Langevin equation, the renormalized Rouse models suggest dynamic high- and low-mode-number limits as an implicit structural feature of this equation of motion. This is a stand-alone prediction of paramount importance independent of any absolute values of power law exponents that arise and are measured in the formalism and in experiment, respectively. The two limits manifesting themselves as power law spin-lattice relaxation dispersions were clearly identified in bulk melts of entangled polymers of diverse chemical species. 

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