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Understanding two-pulse phase-modulated decoupling in solid-state NMR
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10.1063/1.3086936
/content/aip/journal/jcp/130/11/10.1063/1.3086936
http://aip.metastore.ingenta.com/content/aip/journal/jcp/130/11/10.1063/1.3086936

Figures

Image of FIG. 1.
FIG. 1.

Schematic representation of the TPPM sequence.

Image of FIG. 2.
FIG. 2.

Experimental peak height (peak height after Fourier transformation without an apodization function) of the group in -glycine ethylester under TPPM decoupling as a function of the pulse length and the phase angle at different experimental conditions: (a) , , (b) , , (c) , , and (d) , . The experiments were run on a Varian with a proton Larmor frequency of using a 1.8 or a double-resonance MAS probe. The phase resolution of the measurements was 0.25° and the time resolution was . The rf-field amplitudes were determined using a proton nutation experiment. The position of the highest intensity is marked by a white +. Numerical values for the parameters at the peak maxima can be found in Table I.

Image of FIG. 3.
FIG. 3.

Plot of the complex phase and the magnitude of the Fourier coefficients for , , and for a rf field amplitude of for two different pulse lengths ((a)–(c)) and ((d)–(f)) and three different phase angles ((a) and (d)), 20° ((b) and (e)), and 30° ((c) and (f)). The diameter of the circles indicates the magnitude and the color the sign and complex phase of the Fourier coefficients. Blue indicates that the Fourier coefficient is positive and real, red that it is negative and real, black that it is positive and imaginary, and green that it is negative and imaginary.

Image of FIG. 4.
FIG. 4.

(a) Experimental peak height (peak height after Fourier transformation without apodization) of the group in -glycine ethylester under TPPM decoupling as a function of the pulse length and the phase angle at and . The experiments were run on a Varian with a proton Larmor frequency of using a double-resonance MAS probe. The phase resolution of the measurements was 0.25° and the time resolution was . The rf-field amplitude was determined using a proton nutation experiment. Numerical simulations of the peak height as a function of the pulse length and the phase angle using (b) a five-spin system and (c) three-spin -type spin system. The simulations were carried out using the PNMRSIM simulation package. The spinning frequency in all simulations was set to and the rf amplitude was set to . The phase resolution of the simulation was 0.25° and the time resolution was . All dipolar couplings were included in the simulations as well as isotropic and anisotropic chemical shifts. The peak height was simulated for a powder average of 1000 crystallite orientations.

Image of FIG. 5.
FIG. 5.

Numerical simulations of the peak height as a function of the pulse length and the phase angle using a three-spin system as used in Fig. 4(b) but with an extended range of parameters. (a) Full simulation including all interactions. (b) Simulation without the proton chemical-shift tensor. (c) Simulation without the proton homonuclear dipolar coupling. Otherwise, in all simulations the same parameters were used as for the simulation shown in Fig. 4(b), except that the phase resolution of the simulation was 0.5° and the time resolution was .

Image of FIG. 6.
FIG. 6.

Contour plots (blue and red lines) of the coefficients for (a) , ; (b) , ; (c) , ; and (d) , . These contour plots are superimposed on a grayscale density plot of the numerical simulations of a spin system shown in Fig. 5(a). In addition, the resonance conditions (straight lines) and (curved lines) are shown using green lines.

Image of FIG. 7.
FIG. 7.

Contour plot of the sum of the heteronuclear coefficients for (a) and (c) and the sum of the homonuclear coefficients for (b) and (d) . These plots are superimposed on a grayscale density plot of the numerical simulations of a spin system shown in Fig. 5(a). In addition, the resonance conditions and are shown using green lines.

Image of FIG. 8.
FIG. 8.

Plots of the resonance conditions encountered in TPPM decoupling. The location of the resonance conditions are plotted as lines (blue or color coded: zeroth-order resonance conditions: green: second-order or third-order resonance conditions) superimposed on a grayscale density plot of the numerical simulations of a spin system shown in Fig. 5(a). (a) Straight lines correspond to the resonance conditions which recouple heteronuclear dipolar couplings; curved lines correspond to resonance conditions which also recouple heteronuclear dipolar coupling. The strength of the resonance condition is given by the magnitude of the and Fourier coefficient, respectively. The magnitude of some of the zeroth-order resonance conditions has been color coded on the lines. (b) resonance conditions which result in zeroth order ( and 2) in a purely homonuclear dipolar Hamiltonian. Again, the magnitude of the resonance terms has been color coded on the line. (c) resonance condition. (d) resonance condition.

Image of FIG. 9.
FIG. 9.

Contour plots of the decoupling efficiency shown in Fig. 2 ((a) , , (b) , , (c) , , and (d) , ) with the location of the theoretical minimum of the second-order cross terms plotted as a white dotted line. The resonance conditions are shown as white lines for purely homonuclear resonance conditions and as black line for heteronuclear and homonuclear resonance conditions.

Image of FIG. 10.
FIG. 10.

Comparison of TPPM and CM decoupling for direct observation [(a) and (c)] and the spin-echo experiment [(b) and (d)]. The plots show the experimental peak height (peak height after Fourier transformation without an apodization function) of the group in -glycine ethylester under TPPM or CM decoupling as a function of the pulse length and the phase angle at a spinning frequency of and a rf-field amplitude of : (a) peak height under TPPM decoupling , (c) peak height under CM decoupling , (b) peak height after a spin-echo sequence with and TPPM decoupling , (d) peak height after a spin-echo sequence with and CM decoupling . The experiments were run on a Varian Infinity+ spectrometer with a proton Larmor frequency of using a double-resonance MAS probe. The phase resolution of the measurements was 0.25° and the time resolution was . The rf-field amplitudes were determined using a proton nutation experiment. The position of the highest intensity is marked by a white +.

Tables

Generic image for table
Table I.

Experimental parameters of Fig. 2.

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/content/aip/journal/jcp/130/11/10.1063/1.3086936
2009-03-20
2014-04-17
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Understanding two-pulse phase-modulated decoupling in solid-state NMR
http://aip.metastore.ingenta.com/content/aip/journal/jcp/130/11/10.1063/1.3086936
10.1063/1.3086936
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