Two site jump motion

Fig. 6. Theoretical integrated reduction factor of the powder spectrum (amplitude at the top of solid echo) for a two-site jump motion (Pa=Pb) as the function of jump frequency 1/Tc and for different jump angles 2/ . (Reprinted with permission from Ref. 112. Copyright 1990 American Chemical Society.)...

Figure 8 (a) Static spectra of the carbonyl carbon in poly(ethyl methacrylate) (PEMA) accessible by selective isotope enrichment, at different temperatures. The changes in the CSA tensor arise from a two-site jump motion even below the Tg of 378 K, and additional reorientations at higher temperatu res. (b) Above the Tg, the residual width of the still anisotropic spectrum is interpreted in terms of an order parameter S= side chain. Reproduced with permission from Kulik, A. S. Radloff, D. Spiess, H. W. Macromolecules 27, 3111. Copyright (1994) American Chemical Society. 

The motional process is anisotropic, but by coincidence, the PAS orientation relative to the C(CH3)-COO bond is such that the resulting fast-limit spectmm corresponds to an axially symmetric tensor. The resulting line shapes are discussed in the early literature and can conveniently be obtained by computer simulation on the web. Note that usually two-site jump motions do not lead to axially symmetric fast-limit tensors (at least three symmetrically arranged sites or frill rotation around a given axis are required to generally obtain an axially symmetric fast-limit spectmm). See Figure 11(a) for an illustration of the more common case of an anisotropic fast-limit tensor for a two-site jump in a molecular crystal. 

Figure 8 a shows the motionally averaged quadrupole coupling constant, (Cq)/Cq, and asymmetry parameter, ( ), for a two-site jump between axially symmetric equivalent sites. At jump angles of 70° and 109° the principal components (V, Vyy, Vzz) have to be rearranged in order, which leads to the discontinuities in the curve shapes of Fig. 8a. 

The temperature dependent T data are shown in Fig. 9. 7j values decrease from 28 ms at 21°C with increasing temperature, and show a minimum of 6.4 ms at 80° C. These results indicate the presence of the motion with a Larmor frequency of 30 MHz at this temperature. This minimum was found to be attributed to the flipping motion of a phenyl ring from the result of our other experiments discussed in later section.13 The jump rates of the flipping motion were estimated with a two-site jump model that a C-2H bond jumps between two equivalent sites separated by 180°, and that the angle made by the C-2H bond and the rotational axis is 60°. The quadrupole coupling constant of 180 kHz and the asymmetry parameter approximated to zero were used in the calculation. The calculated values for fitting with the... 

The line shapes were calculated for the flipping motion with the two-site jump model described above, and the calculated spectra are shown in Fig. 11 for the higher temperature region. The experimental line shapes at 20 and 30° C are well reproduced showing the motional mode and rates obtained by T analysis are reasonable at least around these temperatures. Above 40°C the calculated line shapes are invariable and remain in the powder pattern undergoing a rapid flipping motion, while the experimental ones... 

Valuable information on the geometry of the proton motion is offered by the Q-dependence of the elastic incoherent intensity (EISF) (see Fig. 4.34). For two site jumps this intensity is described by ... 

Selective inversion recovery experiments i.e. only select frequencies within the powder pattern are excited, have also been performed on 2H for the purposes of studying molecular motion. Initial experiments were performed on deuterated dimethylsulfone (DMS) to demonstrate the utility of the experiment.46 Selective inversion recovery curves were fitted to a suitable motional model, a two-site jump model in the case of DMS, to yield the motional rates as a function of temperature. A significant feature of this work is that the activation energy for the motion so obtained differs markedly from that obtained from earlier 13C chemical shift anisotropy lineshape studies. 

Fig. 15. (a) Normalized pure-exchange CODEX intensities E(tm) as a function of tm for the aromatic ternary CH and the quaternary Cquat in Td-G2(-Me),6 dendrimer (T=363K). The fit curve for the ternary carbons is a stretched exponential cxp[—(rln/rcyi with /I = 0.51 and tc = 401 ms. The dotted line indicates the final CODEX exchange intensities, (b) Motional model of the localized, cooperative dynamics in polyphenylene dendrimers, including two-site jumps of all phenyl substituents of a pentaphenyl benzene building block. As indicated by X-ray analysis and computer simulations, the peripheral aromatic rings are inclined by 30° with respect to an axis normal to the face of the central benzene ring. For details, see ref. 44. 

Fig. 6.2.2. Left Simulated NMR lineshapes that are averaged by various characteristic segmental motions. In the case of fast rotation, y represents the angle between the rotation axis and the C—bond. For a two-site jump, j3 denotes the angle between the C—bond in the two configurations, and the effective asymmetry parameter becomes 17 7 0. Right Calculated 2D exchange spectra for a two-site jump with /3 = 120° (top), and for continuous diffusion (bottom). The distribution functions P(/3) of the reorientation angle are shown, together with the contour maps of the corresponding spectra. All data are displayed on the reduced frequency scale in units of Cq, and mixing times are set equal to the motional correlation time r,..

F 7. Dependence of calculated NMR powder spectra on type and timescale of various motions a) Two-site jumps, 6k = 60°, b) two-site jumps, 6k = 109°, c) tteee-site jumps, = 109°, d) planar rotational (fusion, 6k = 109°, e) tetrahedral jumps, I) isotropic spherical diffusion. 6r = angle between rotation axis and C-D bond direction... 

The sensitivity of typical NMR experiments to the type and time scale of various motions is illustrated in Fig. 7. For simplicity, we have chosen equal correlation times for all motions, namely = 1 x 10 s, = 1 x 10 s and Xg = 5 x 10 s. The powder spectra refer to quadrupole echo sequences [57], and characterize two-site jumps (a, b), three-site jumps (c), planar rotational diffusion (d), tetrahedral jumps (e) and isotropic spherical diffusion (f), respectively. The significant differences of the lineshapes arise from the different motional anisotropies. Evidently, quadrupole echo spectra [57] contain valuable information on the type of motion [10,48,49, 58]. 

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