Pulse sequence used in the 1D PUREX experiments with cross polarization (CP), chemical-shift evolution and refocusing times , mixing time , and -storage period . Standard dipolar decoupling of protons (DD) is applied during evolution and detection of transverse magnetization. pulses are shown in black. In the absence of exchange, the phase cycle yields a pure stimulated echo after the second period; the signals obtained in the absence of exchange (full stimulated echo) are outlined in the figure. After acquiring the signal with exchange, and are interchanged and the reference signal without exchange is recorded. The normalized pure-exchange intensity is obtained as .
Reorientation-angle distributions for isotropic rotational diffusion and the corresponding doubly normalized 1D PUREX intensities as a function of the mixing time, calculated in the slow-motion regime. (a) Reorientation-angle distribution at selected mixing times; (b) vs at selected evolution times.
One-dimensional PUREX spectra as a function of the reorientation angle for . (a) . Full lines: Non-normalized spectra for reorientation angles varying from 10° to 90°. Dashed lines: Point-by-point normalized spectra for reorientation angles varying from 10° to 90°. (b) Same as (a) for .
Calculated 1D PUREX spectra as a function of the rotation axis for a fixed rotation angle of . The CSA principal values used in the calculations are typical for the carbonyl carbons in the backbone of peptides and proteins, . (a) Full powder spectrum for reference. (b) Rotation of around the principal axis of the chemical-shift tensor. (c) Rotation of around the axis. (e) Rotation of around the C–C backbone bond in a glycine residue of a poly-Gly -helix peptide (Ref. 31). The Euler angles relating the CSA principal axes with a molecular frame where the axis is parallel to the C–C bond are . (f) Rotation of around C–N bond in a glycine residue of a poly-Gly -helix peptide (Ref. 31). The Euler angles relating the CSA principal axes with a molecular frame where the axis is parallel to the C–N bond are .
Normalized 1D PUREX intensities plotted as a function of and in the intermediate motional regime for two-site jumps, with CSA parameters of and . (a) vs for various values of the correlation time , with and ; (b) vs for values ranging from 0.2 to 50 ms, with and ; (c) vs for values between 0.2 and 10 ms, with and a reorientation angle . (d) vs with and for several values, considering a two-site jump with a log-Gaussian distribution of correlation times (Refs. 9 and 15). (e) Curves of as a function of , plotted for different KWW distributions of correlation times with of 1, 0.4, and 0.3 and the corresponding fitting using KWW (stretched-exponential) correlation functions. (f) Simulations of vs for different mean correlation times and values. Corresponding fits using KWW correlation functions and the mean correlation times extracted from these fits are also shown.
One-dimensional PUREX intensity curves as a function of temperature, calculated for a two-site jump with a single correlation time following the Arrhenius behavior. (a) Normalized exchange intensity calculated for different activation energies based on the slow-exchange approximation according to Eq. (9), with and ; (b) same as (a) but with and different ; (c) linearized plot for independently determining the activation energy, and ; (d) full curves calculated according to Eq. (10) for several activation energies with . (e) for varying mixing times with fixed and . (f) Exchange intensity (without normalization by ) for several mixing times and . The CSA parameters used in all the calculations were and .
Distributions of correlation times and corresponding normalized exchange intensities : (a) Log-Gaussian distributions of correlation times; (b) curves for two-site jumps calculated for the distributions shown in (a) with ; (c) KWW distributions of correlation times; (d) curves for two-site jumps calculated for the distributions shown in (c) with . (e) curves for random jumps, , and log-Gaussian distributions of correlation times. (f) curves for random jumps, , and KWW distributions of correlation times. The Arrhenius parameters used to perform the linear conversion from to temperature are calculated with and .
One-dimensional PUREX spectra for DMS at 20 °C with a mixing time of 50 ms. Left: reference spectrum. Right: Point-by-point normalized spectrum. Simulations with a reorientation angle of are represented by dotted lines. The measuring time of each pair of spectra was about 1 h.
Experimental 1D PUREX intensities for DMS and corresponding fit curves, in the intermediate motional regime. (a) dependence of the normalized exchange intensity at , 308, 318, and 325 K; (b) dependence of at , 308, 318, 325, and 333 K; (c) Arrhenius plot of the correlation times determined in (a) and (b). The measuring time per spectrum was 20 min.
Experimental 1D PUREX intensity vs temperature for DMS. (a) Normalized exchange intensity for and . Calculated curves using the slow-motion approximation and the general formula are shown as full and dashed curves, respectively; (b) plot of vs on the low-temperature side of . The linear fit based on Eq. (10) provides the Arrhenius parameters.
Experimental 1D PUREX intensities for amorphous atactic polypropylene (aPP) and polyisobutylene (PIB), measured with and . Simulated curves with isotropic rotational diffusion model are also shown. The fits were obtained using KWW distributions of correlation times with for PIB and for aPP. In both cases, the temperature dependencies of the correlation times were assumed to be WLF functions with the parameters given in the text. The experimental data were corrected for spin-diffusion effect by subtracting a constant background measured at low temperatures.
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