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Herausgeber: Wiley-VCH GmbH
Kategorie: Wissenschaft und neue Technologien
Sprache: Englisch
Veröffentlichungsjahr: 2021

Beschreibung

In one didactically uniform volume, this book covers experimental equipment and methodological concepts while providing numerous examples in biomaterials, polymers and inorganic substances. The topics covered range from theoretical background knowledge to practical applications and solutions. The whole is rounded off by a glossary, literature and a summary at the end of the chapters, making this a handy textbook for postgraduate courses.

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Leseprobe

Cover

Title Page

Dedication

Foreword

Preface

Introduction

List of Tables

Chapter 1

Table 1.1 Nuclear spin of the fundamental configuration depending on the numb...

Table 1.2 Main nuclear properties of principal isotopes with non‐null spin.

Table 1.3 Typical substances used as chemical shift references in liquid‐stat...

Chapter 3

Table 3.1 External and internal interactions experienced by nuclear spins.

Chapter 4

Table 4.1 Maximum relative line intensities achievable for selective (

/...

Table 4.2 Total and allowed Solomon echoes for semi‐integer quadrupolar spins...

Table 4.3 Solomon echo positions for spins 3/2 and 5/2, corresponding transit...

Chapter 5

Table 5.1 Values of the ratio between the linewidths of the ST and CT signals...

Table 5.2 Values of the ratios between the second‐order quadrupolar shifts of...

Chapter 7

Table 7.1 Nuclear spin observables sensitive to dynamics, experimental condi...

Chapter 8

Table 8.1 Main properties that can be studied by SSNMR for the three categori...

List of Illustrations

Chapter 1

Figure 1.1 The electromagnetic spectrum and expansion of the NMR radio‐frequ...

Figure 1.2 Periodic table containing the most abundant and important isotope...

Figure 1.3 Charge distribution for non‐quadrupolar (

= 1/2) and quadrupolar...

Figure 1.4 Energy separation of the spin states caused by the external magne...

Figure 1.5 Representation of torque (

) and angular velocity (

) vectors ari...

Figure 1.6 Schematic representation of the populations of the two states of ...

Figure 1.7 The basic NMR experiment: (a) the equilibrium magnetization is fl...

Figure 1.8 The two counter‐rotating components of

represented in the labor...

Figure 1.9 Representation of the {

} laboratory and {

} rotat...

Figure 1.10 Evolution of the magnetization in the laboratory (left) and rota...

Figure 1.11 The effective magnetic field

eff

in the laboratory frame (a) an...

Figure 1.12 Time evolution of the magnetization under the effect of the RF f...

Figure 1.13 Time evolution of the magnetization under the effect of the RF f...

Figure 1.14 Time evolution of the magnetization and its components

, a...

Figure 1.15 Quadrature signals

(

) and

(

) as a function of time.

Figure 1.16 FIDs and corresponding frequency spectra obtained for (a) Δ

...

Figure 1.17 Quadrature signals

and

(see Eq. (1.51)) as a function of fre...

Figure 1.18 Orientation of the single magnetic moments and their sum at the ...

Figure 1.19 The local field

ind

induced by electrons in the presence of

,...

Figure 1.20 Chemical shift

or “ppm” scale and trends of shielding and...

Figure 1.21 Example of the dependence of

C chemical shift on the electrone...

Figure 1.22 Shielding and deshielding effects (indicated with signs + and −,...

Figure 1.23 Trend of

H chemical shift of the hydroxyl proton in ethanol as ...

Figure 1.24 Typical

H (a),

C (b), and

Si (c) chemical shift ranges for ...

Figure 1.25 (a) Scheme of the transitions among energy levels for two spin‐1...

Figure 1.26 (a) Examples of line splitting arising from

coupling in system...

Figure 1.27 Spectra arising from

coupling between two like spin‐1/2 system...

Figure 1.28 Dependence of the scalar coupling constant

from the dihedra...

Figure 1.29 Simulated spectra of the A nucleus in an AX system as a function...

Figure 1.30 Fluctuation of

, and

components of the magnetic field a...

Figure 1.31 Representation of a random reorientational motion:

can b...

Figure 1.32 Schematic representation of

(

), and

(

) in th...

Figure 1.33 Scheme of the spin states and the possible zero‐, single‐, and d...

Figure 1.34 Logarithmic plot of the theoretical trends of

, and

1ρ

...

Figure 1.35 Schematic representation of the NOE experiment for a dipolar cou...

Figure 1.36 Trends of NOE enhancement

the correlation time of the ...

Figure 1.37 Inversion recovery pulse sequence and the corresponding evolutio...

Figure 1.38 Saturation recovery pulse sequence and the corresponding evoluti...

Figure 1.39 Pulse sequence for the standard spin‐echo experiment. The corres...

Figure 1.40 Refocusing effect of a 180°

−

pulse on three different mag...

Figure 1.41 Effect of the standard spin‐echo experiments on the magnetizatio...

Figure 1.42 Standard spin‐echo experiment modified in order to remove the re...

Figure 1.43 Carr–Purcell–Meiboom–Gill (CPMG) pulse sequence and trend of the...

Figure 1.44 (a) Spin–lock pulse sequence and the corresponding evolution of ...

Figure 1.45 Pulse sequence of the basic double resonance INEPT experiment an...

Figure 1.46 Scheme of the INEPT experiment for a

‐coupled AX spin system. (...

Figure 1.47 General schemes of pulse sequences for 2D experiments, (a) witho...

Figure 1.48 Effects of the double Fourier transformations applied to

(

Figure 1.49 COSY experiment: pulse sequence and scheme of a 2D spectrum high...

Figure 1.50 A‐X HETCOR experiments. (a) Pulse sequence for direct X acquisit...

Figure 1.51 NOESY experiment: pulse sequence and example of 2D spectrum high...

Figure 1.52 INADEQUATE experiment: pulse sequence and example of 2D spectrum...

Figure 1.53 Examples of chemical exchange. (a) Nuclei moving between two dif...

Figure 1.54 Typical lineshapes due to a spin‐1/2 exchanging between two diff...

Figure 1.55 Basic EXSY experiment: (a) pulse sequence, (b) example of 2D spe...

Chapter 2

Figure 2.1 Representation of the Euler angles used to describe the rotation ...

Chapter 3

Figure 3.1 Representation of an interaction tensor in the principal axis fra...

Figure 3.2 Dependence of shielding on molecular orientation with respect to ...

Figure 3.3 Effect of the shielding interaction on the ½ ↔ −½ transition of a...

Figure 3.4 Effect of the quadrupolar interaction, limited to first‐order cor...

Figure 3.5 Effect of the heteronuclear dipolar interaction on the ½ ↔ −½ tra...

Figure 3.6 Effect of the homonuclear dipolar interaction on the transitions ...

Chapter 4

Figure 4.1 (a) Schematic representation of the isotropic translational and r...

Figure 4.2 Typical behavior of rod‐like molecules in a fluid, e.g. nematic, ...

Figure 4.3 (a) Coordinate systems necessary for the theoretical description ...

Figure 4.4 Alignment of the molecules in domains: (a) maximum (crystalline) ...

Figure 4.5 (a) Distribution function of the molecules as a function of the a...

Figure 4.6 Dependence on sample orientation of the NMR spectrum (here assume...

Figure 4.7 Effect of static disorder on NMR spectra of partially oriented so...

Figure 4.8 (a)

113

Cd NMR spectrum of a single crystal of [Cd(Se‐2,4,6‐

‐Pr

‐...

Figure 4.9 (a) Nuclear spin energy levels determined by the shielding correc...

Figure 4.10 Representative FID and corresponding spectrum of one spin‐1/2 nu...

Figure 4.11 Excitation profiles of RF pulses. (a) For

/2 pulses of dif...

Figure 4.12 Theoretical broadline powder spectra due to the first order quad...

Figure 4.13 Magnetization trajectories for the composite pulse (

/2)

(

...

Figure 4.14 Scheme of a stepped‐frequency experiment performed acquiring a s...

Figure 4.15 Schematic comparison of (a) sudden and (b) adiabatic inversion o...

Figure 4.16 Representation of the spin energy levels for an isolated nucleus...

Figure 4.17 (a) Homogeneously broadened lines: the contribution of the singl...

Figure 4.18 (a) Example of powder lineshape obtained for the shielding inter...

Figure 4.19 Powder lineshapes obtained for the shielding interaction for dif...

Figure 4.20 Orientation of the shielding PAS for a carbonyl carbon nucleus w...

Figure 4.21 Examples of NMR spectra resulting from the presence of (from top...

Figure 4.22 Lineshapes produced by the two‐spin transitions of a spin‐1/2 nu...

Figure 4.23 Lineshapes arising from the dipolar coupling of a spin‐1/2

nuc...

Figure 4.24 Lineshapes arising from the dipolar coupling of a spin‐1/2

nuc...

Figure 4.25 Lineshapes of a spin‐1/2

nucleus from the combined effects of ...

Figure 4.26 Lineshapes of a spin‐1/2

nucleus from the combined effect of s...

Figure 4.27 Scheme of the axes frames necessary to interpret NMR spectra in ...

Figure 4.28 (a) Basic cross‐polarization pulse sequence. SL, Dec., and

...

Figure 4.29 (a) Zeeman energy levels of

and

spin states in the laborator...

Figure 4.30 The different frame transformations involved in CP and heteronuc...

Figure 4.31 The three heat reservoirs involved in the CP process: abundant

Figure 4.32 Scheme of the cross‐polarization process explained by the thermo...

Figure 4.33 CP kinetic curves (signal intensity

contact time), obtained o...

Figure 4.34 (a) Amplitude of the

C signal obtained in adamantane by CP, ca...

Figure 4.35 Examples of CP dynamics curves calculated by Eqs. (4.70) and (4....

Figure 4.36 The heat reservoirs involved in the CP process as the basis of t...

Figure 4.37 Pulse sequence for adiabatic CP in the rotating frame. After the...

Figure 4.38 Pulse sequence for adiabatic CP in the laboratory frame (ADLF/AR...

Figure 4.39 Schemes of the pulse sequences: (a) BRAIN‐CP, a cross‐polarizati...

Figure 4.40 Dependence of

C linewidth at half‐height on

H decoupling freq...

Figure 4.41 Excess linewidth (solid lines) of the

109

Ag resonance recorded f...

Figure 4.42 Effect of the decoupler offset on carbon linewidths for CW (dash...

Figure 4.43 Various spin echo sequences: (a) standard spin echo, (b) solid e...

Figure 4.44 CPMG pulse sequences obtained by adding a train of

...

Figure 4.45 (a) Total FID acquired by the standard CPMG pulse sequence by jo...

Figure 4.46 Acquistion of a Pake powder pattern for an isolated pair of dipo...

Figure 4.47 Theoretical broadline powder spectra due to the first order quad...

Figure 4.48 Theoretical broadline powder spectra due to the first order quad...

Figure 4.49 Diagram of the energy levels of the spin states generated in a s...

Figure 4.50 Energy levels obtained for two dipolar coupled spin‐1/2 nuclei d...

Figure 4.51 Theoretical spectra due to

coupled

H spins in polycrystalline...

Figure 4.52 (a) flip‐flop mechanism, (b) scheme of mono‐dimensional diffusio...

Figure 4.53 Goldman–Shen pulse sequence: M and R indicate the components of ...

Figure 4.54 (a) evolution of the longitudinal magnetization during the secon...

Figure 4.55 Simulations of powder spectra obtained: (a) after the applicatio...

Figure 4.56 Magic‐sandwich echo pulse sequences: (a) refocusing only the hom...

Figure 4.57 Examples of spectra of

= 1 (a) and

= 3/2 (b) nuclei in, from...

Figure 4.58 (a) Example of powder lineshape obtained for the quadrupolar int...

Figure 4.59 Examples of powder spectra of an

= 1 nucleus arising from only...

Figure 4.60 (a) Example of powder spectrum for an

= 5/2 nucleus arising fr...

Figure 4.61 Simulation of spectra for the central transition of a half‐integ...

Figure 4.62 (a) Simulation of the central transition spectra of an

= 3/2 n...

Figure 4.63 Central transition signal intensity for an

= 3/2 (a) and an

...

Figure 4.64 Positions, expressed in units of the delay

, of the allow...

Figure 4.65

Solomon echo amplitudes for a spin 3/2 (a) and...

Figure 4.66

Hahn echo amplitudes for half‐integer quadrupo...

Figure 4.67 Schematic representation of the nuclear spin energy levels and t...

Figure 4.68 Schematic representation of the application of single (a) and do...

Figure 4.69 Hyperbolic secant pulses: change of (a) RF amplitude and (b) RF ...

Figure 4.70 Eigenstate diagrams of a rotating frame Hamiltonian consisting o...

Chapter 5

Figure 5.1 Coordinate transformations from the principal axis system (PAS) (...

Figure 5.2 Formation of echoes in the FID due to MAS and corresponding spect...

Figure 5.3 Intensity ratio between (a) the order 1, (b) the order 2 sideband...

Figure 5.4 Experimental and simulated spectra of 1,3,5‐trimethoxybenzene for...

Figure 5.5 Simulated spectra for a spin‐1/2 nucleus (e.g.

C) at two differ...

Figure 5.6 Rotor‐synchronized detection of the FID: only one point per rotor...

Figure 5.7 Spin packet trajectories in the rotating frame, relative to two d...

Figure 5.8 Scheme of rotational echo trains (under on resonance conditions) ...

Figure 5.9 (a) Use of PASS to separate spinning sidebands of different order...

Figure 5.10 TOSS pulse sequence. One of the sets of parameters originally pr...

Figure 5.11

C MAS spectra of (a) [2‐

C]alanine and (b) [2‐

C]glycine, at...

Figure 5.12 Linewidth (full width at half height) of the lines in Figure 5.1...

Figure 5.13 Parabolic trends of linewidths (full widths at half height)

r...

Figure 5.14 Trends of linewidths

MAS frequency obtained from

C MAS spec...

Figure 5.15

C MAS spectra of polycrystalline 2‐

C‐alanine as a function o...

Figure 5.16 Rotating frame spin diffusion rate constants measured in 8% labe...

Figure 5.17 Simulated

) powder lineshapes for a two‐spin

I–S

sy...

Figure 5.18

C spectra of 8% labeled [2‐

C]alanine at different MAS freque...

Figure 5.19 Peak height of the C

resonance of alanine

C MAS ...

Figure 5.20 Expansions of the regions, corresponding to CH

, CH, and CH

gro...

Figure 5.21 Scheme showing the best decoupling sequences as a function of de...

Figure 5.22 Hartmann–Hahn matching profile for a model system under static (...

Figure 5.23 (a) and (b)

H–

C Hartmann–Hahn matching profiles for adamantan...

Figure 5.24 Depolarization pulse sequence and trends of the

signal intensi...

Figure 5.25 Depolarization curves (

C signal intensity

depolarization ti...

Figure 5.26 (a) Standard CP pulse sequence; (b) RAMP‐CP pulse sequence, wher...

Figure 5.27

H–

C Hartmann–Hahn matching profiles obtained for the carbonyl...

Figure 5.28 Signal intensity in

H–

C conventional CP (solid line) and APHH...

Figure 5.29 One version of the SADIS CP pulse sequence. Note that high‐power...

Figure 5.30 Pulse sequences for the determination of (a) the 90° pulse durat...

Figure 5.31 Pulse sequences for the determination of (a)

nuclei thro...

Figure 5.32 Delayed‐CP pulse sequence for the selection of signals of

nucl...

Figure 5.33 (a) SS‐APT pulse sequence proposed by Lesage et al. (1998), desc...

Figure 5.35

H MAS spectra of

‐acetyl‐

‐

N‐valyl‐

‐

N‐leucine recorded at...

Figure 5.34

H MAS spectra of benzoxazine ethyl dimer as a function of the M...

Figure 5.36 The angle of 54.74°, the root of the second‐order Legendre polyn...

Figure 5.37 WAHUHA pulse sequence. The (passive) rotations in the rotating f...

Figure 5.38 Examples of

H CRAMPS spectra of small organic molecules: (a) ma...

Figure 5.39

H CRAMPS spectra of

‐alanine acquired at different MAS frequen...

Figure 5.40 Synchronization of the WAHUHA decoupling pulse sequence with MAS...

Figure 5.41 Schematic representations of LG (left) and FSLG (right) irradiat...

Figure 5.42 Windowed

H CRAMPS pulse sequence employing the (a) PMLG3, (b) D...

Figure 5.43 Plots of the second‐ and fourth‐order Legendre polynomials.

Figure 5.44 Simulated fast‐VAS lineshapes for the CT of

Na (

= 3/2), broa...

Figure 5.45 Comparison of simulated powder patterns for the CT of a nucleus ...

Figure 5.46 Trend of the linewidth (defined as the distance between the oute...

Figure 5.47 Scheme of the DOR experimental setup, consisting in an outer “MA...

Figure 5.48

O CT spectra of a 41%

O enriched sample of wollastonite (CaS...

Figure 5.49 Simulations of MAS (at infinite frequency) spectra for an

= 5/...

Figure 5.50 Eigenstate diagrams of a rotating frame Hamiltonian consisting o...

Chapter 6

Figure 6.1 (a) General scheme for 2D NMR experiments: the second dimension i...

Figure 6.2 Modulations of an anisotropic interaction Hamiltonian under MAS t...

Figure 6.3 Scheme of a pulse sequence and the corresponding coherence transf...

Figure 6.4 2D magic angle hopping pulse sequence (only one of the four exper...

Figure 6.5 2D 5‐

pulse sequence.

is the evolution variable, whi...

Figure 6.6 (Top) 2D pulse sequence used in STAG, S

, and SASS experiments, a...

Figure 6.7 (a) TOSS–reverseTOSS pulse sequence. Due to the symmetry of the p...

Figure 6.8 2D‐PASS pulse sequence in the “constant‐time” version proposed by...

Figure 6.9 (a) CSA amplification pulse sequence based on the Antzutkin versi...

Figure 6.10 (a) 2D

H anisotropic–isotropic chemical shift correlation spect...

Figure 6.11 (a) Rotary resonance pulse sequence; (b) rotary resonance matchi...

Figure 6.12 Simulations of rotary resonance spectra obtained with different ...

Figure 6.13 Examples of pulse sequences for 2D HETCOR experiments: (a) homon...

Figure 6.14 Basic 2D‐SLF pulse sequence. In the original version reported by...

Figure 6.15 DIPSHIFT pulse sequence. The

increment corresponds to an MREV...

Figure 6.16 (a)

H–

N 2D‐SLF spectrum of

N‐labeled glycylglycine hydrochl...

Figure 6.17 PISEMA pulse sequence: an integer number of LG blocks is applied...

Figure 6.18 2D‐SLF pulse sequence exploiting LG‐CP, developed by van Rossum ...

Figure 6.19 (a)

H–

C 2D LG‐CP build‐up curves recorded for

C‐uniformly l...

Figure 6.20 Pulse sequence for the rotational resonance recoupling (R

) expe...

Figure 6.21

H‐decoupled

P spectrum of

N‐labeled

‐methyldiphenylphospho...

Figure 6.22 Three common REDOR pulse sequences: the scheme of the

channel ...

Figure 6.23 Simplified explanation of a basic block of the REDOR technique. ...

Figure 6.24 The two experiments ((a) “control” and (b) “recoupling”) constit...

Figure 6.25 Typical trends of

(a) and Δ

(b) as a function of

for ...

Figure 6.26 REDOR curves calculated for a

(

)

spin system: (a) with

an...

Figure 6.27 Numerical simulations for the Δ

trend

dip

in a REDOR...

Figure 6.28 Plot of

(

)

for different selected orientations of...

Figure 6.29 Calculated fractions of spins

having undergone 0, 1, 2, 3, or...

Figure 6.30 TRAPDOR pulse sequence. The first 90° pulse on the

channel ca...

Figure 6.31 Scheme of the TEDOR pulse sequence in its 1D version. In the fig...

Figure 6.32 (a) example of a TEDOR curve, built by sampling the signal of

Figure 6.33 (a) Standard 2D‐WISE pulse sequence. (b) 2D‐WISE pulse sequence ...

Figure 6.34 Effect of rotational resonance on the

C NMR lineshapes of the ...

Figure 6.35 Pulse sequence used to observe rotor‐driven magnetization transf...

Figure 6.36 (a)

C spectra obtained at a Larmor frequency of 79.9 MHz for d...

Figure 6.37 (a) Basic DRAMA pulse scheme, with a duration of four MAS period...

Figure 6.38 Simulated dipolar powder pattern spectra obtained for the DRAMA ...

Figure 6.39 Pulse sequence including the windowless MELODRAMA recoupling sch...

Figure 6.40 (a) SEDRA and (b) RFDR pulse sequences. The scheme of the

chan...

Figure 6.41 Normalized difference of intensity between the signals of two co...

Figure 6.42 1D experiment exploiting the 2Q‐HORROR condition (

= 1/2

Figure 6.43 Pulse sequences for (a) the 2D DREAM correlation experiment and ...

Figure 6.44 One of the basic schemes proposed for the broadband BABA recoupl...

Figure 6.45 (a) C7 and POST‐C7 recoupling schemes. The basic elements

for...

Figure 6.46 Homonuclear correlation experiments via dipolar coupling: scheme...

Figure 6.47 Pulse sequences for the 2D (a) MAS‐

‐HMQC and (b) INEPT‐HSQC het...

Figure 6.48 (a) Pulse sequence for the solid‐state 2D refocused INADEQUATE e...

Figure 6.49 (a) Pulse sequence of the 2D nutation NMR experiment; (b) 1D nut...

Figure 6.50 Calculated on resonance nutation spectra for a spin

= 3/2 with...

Figure 6.51 DAS experiment: RF pulse sequence and rotor axis orientation wit...

Figure 6.52 (a) 2D DAS pulse sequence and 1D spectra that would be obtained ...

Figure 6.53 Example of 2D MQMAS time domain data set for a nucleus with

= ...

Figure 6.54 Basic scheme of the MQMAS pulse sequence (top) and example of 2D...

Figure 6.55 Examples of (a) unsheared and (b) sheared 3QMAS spectra.

Figure 6.56 (top) Pulse sequence and coherence transfer pathways of the whol...

Figure 6.57 Pulse sequence for

‐filter MQMAS: the coherence transfer pathwa...

Figure 6.58 (a) and (b): Sketch of STMAS time‐domain data as a function of

Figure 6.59

‐filtered STMAS pulse sequence and corresponding coherence tran...

Chapter 7

Figure 7.1 Example of the effects of chemical exchange on a high‐resolution ...

Figure 7.2 Example of the effects of a motion on the linewidth of an NMR res...

Figure 7.3 Examples of the effects of a motion on an anisotropic lineshape a...

Figure 7.4 Example of the trends of spin–lattice relaxation times (

1ρ

...

Figure 7.5 Example of trends of spin–lattice relaxation times

...

Figure 7.6 Example of trends of spin–lattice relaxation times (

1ρ

...

Figure 7.7 Typical trends of spin–spin and spin–lattice relaxation times (

Figure 7.8 Typical trends of the spin–spin relaxation time

and ...

Figure 7.9 Scheme of the thermodynamic model describing

relaxation ...

Figure 7.10 Spin energy levels originated by quadrupolar order for nuclei wi...

Figure 7.11 Typical ranges of values of the reference frequencies for differ...

Figure 7.12 Examples of spectral density

trends characterizing di...

Figure 7.13 Examples of FID functions commonly used in the discrete fitting ...

Figure 7.14 (a) Example of pulse sequence used in a double‐quantum experimen...

Figure 7.15 Pulse sequences devised to measure spin–lattice relaxation times...

Figure 7.16 (a) Scheme of the PP (full line) and NP (dashed line) techniques...

Figure 7.17 Jeener–Broekaert pulse sequence, used to measure

Figure 7.18 Typical 2D exchange powder patterns obtained for (a) shielding (

Figure 7.19 (a) Basic CODEX pulse sequence, synchronized as shown with sampl...

Chapter 8

Figure 8.1 (a) Molecular structure of barbital and labeling of the atoms. (b...

Figure 8.2 (a) Molecular structure of phenobarbital and labeling of the atom...

Figure 8.3 (a) Structure of a nicotinamide–palmitic acid unit, with atom lab...

Figure 8.4 (a)

F DE‐MAS recorded at 248 K, at a Larmor frequency of 470.6 ...

Figure 8.5 Spin–lattice relaxation times in the laboratory frame of ibuprofe...

Figure 8.6

C CPMAS spectra of (a) α crystalline nifedipine, (b) β crystall...

Figure 8.7

C CPMAS spectra of ibuprofen loaded into MCM‐41 (1 : 1 by weigh...

Figure 8.8

C CPMAS spectra of isotactic and syndiotactic polypropylene and...

Figure 8.9

C CPMAS spectra of three forms of isotactic polypropylene: (a) ...

Figure 8.10 (a)

C CPMAS spectra of four crystalline forms of isotactic pol...

Figure 8.11 (a)

C CP spectrum recorded at room temperature with a contact ...

Figure 8.12

F MAS spectra of a heterophasic sample of polyvinylidene fluor...

Figure 8.13 Example of an on‐resonance

H FID, recorded for a sample of semi...

Figure 8.14

H−

C HETCOR spectra of complexes between PMMA (

C labeled on ...

Figure 8.15 Examples of standardized spin diffusion plots for a lamellar two...

Figure 8.16 (a) Experimental (left) and simulated (right)

C 2D exchange sp...

Figure 8.17 Various experiments and measurements carried out on samples of a...

Figure 8.18 Typical ranges of

Si isotropic chemical shifts of

and

(

A...

Figure 8.19 (a) 2D

O STMAS spectrum of β‐Mg

SiO

(wadsleyite), recorded on...

Figure 8.20

Al MQMAS (a) and 1D MAS (b) spectra of USY zeolite recorded at...

Figure 8.21 (a)

Si 1D MAS (top) and 2D DQ‐MAS (bottom) spectra of a highly...

Figure 8.22 (a) Structure of one SBU‐F (or SBU‐OH) (left) and of six unit ce...

Figure 8.23 (Left) Examples of

Si MAS spectra of Portland cement hydrated ...

Figure 8.24 (a)

B DOR spectrum of Pyrex® recorded at 14.1 T with an outer ...

Figure 8.25 (a) Structures of the following copper(I) complexes: (top left) ...

Figure 8.26 (a)

Sc MAS spectra of (from top to bottom) Sc

BDC

, Sc

(NH

–BD...

Figure 8.27 Quantitative

Si DE‐MAS spectra of (top) silica and (bottom) si...

Figure 8.28 Sketched organization of the molecules in representative mesopha...

Figure 8.29 Orientational order study carried out in the nematic and smectic...

Figure 8.30 Orientational order study carried out in the

phase of 1,...

Figure 8.31 (a) Molecular structure and phase transitions of (−)‐(S)‐[4‐(2‐m...

Figure 8.32 Typical

P static spectra of a rigid phosphodiester group (a); ...

Guide

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Table of Contents

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Solid State NMR

Principles, Methods, and Applications

Klaus Müller

Marco Geppi

Figures edited by Beatrice Omiecienski

Authors

Professor Klaus Müller†

Univ. degli Studi di Trento

Facoltà di Ingeneria

Via Mesiano 77

Facoltà di Ingeneria

38100 Trento

Italy

Professor Marco Geppi

Università di Pisa

Dipartimento di Chimica e Chimica Industriale

v. G. Moruzzi 13

56124 Pisa

Italy

Cover Images: background: Blue interior

@Gettyimages #174765643/sbayram;

main motive: books with handwritten

notes from Prof. Müller @Beatrice

Omiecienski

All books published by WILEY‐VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.

Library of Congress Card No.:applied for

British Library Cataloguing‐in‐Publication Data

A catalogue record for this book is available from the British Library.

Bibliographic information published by the Deutsche Nationalbibliothek

The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at <http://dnb.d-nb.de>.

All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form – by photoprinting, microfilm, or any other means – nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law.

Print ISBN: 978‐3‐527‐31816‐2

ePDF ISBN: 978‐3‐527‐69010‐7

ePub ISBN: 978‐3‐527‐69011‐4

oBook ISBN: 978‐3‐527‐69009‐1

to Klaus

Foreword

Klaus Müller studied Chemistry at the University of Freiburg (1975–1981) and received his doctorate degree in December 1985 with Prof. Kothe at the University of Stuttgart and his postdoctoral lecture qualification in 1993. From 1999 to 2009, he taught as a Professor at the Institute of Physical Chemistry at the same university. As he committed himself to the promotion of research and teaching with great dedication, in these 10 years, he supervised 16 PhD theses, 4 postdocs, and several dissertations within his own research group, as well as the German‐French Double Diploma (a study course in Chemistry). For the postgraduate course of lectures “Magnetic Resonance” (1998–2007), he was seen as a tower of strength.

Müller was both an expert and internationally sought‐after cooperation partner in the area of solid‐state NMR, where he examined both bio‐membranes and host–guest compounds, ceramics, and materials of any kind. For his multiple, often groundbreaking ideas, he was invariably an asset and motivation.

He accepted a Professorship at the University of Trento on 1 January 2009. At this particular time, he was already writing this textbook. From the very beginning, I was permitted to produce the figures for this project and could therefore continually follow the developments. He had the gift to awaken a very special curiosity and his enthusiasm for this project captured me too.

As Klaus Müller – incomprehensibly for all of us – totally unexpectedly passed away on 1 April 2011 at the age of only 55 years, he left behind his manuscript. From the initial, unimaginable idea to complete this book, as already so much time and energy had been put into these pages, a time‐consuming task developed. It took me a long time to find an adequate coauthor.

Therefore I extend my very special thanks to Dr. Marco Geppi, who met the challenge and intensely inspected the existing manuscript. He brought a lot of time and effort in creating the missing chapters and completed this book in the spirit of Klaus Müller.

We also want to thank Silvia Gross as well as Philipp, Oliver, and Giulia Müller for allowing both of us to be contributors and Wiley‐VCH as publisher the rights to continue Klaus Müller's work and to finish the book.

Beatrice Omiecienski

Stuttgart 2020

Preface

Writing this book was one of the most difficult (and long) tasks of my professional life, and writing this preface is probably even more difficult than the rest of the book.

This book was conceived and partially written by Klaus Müller, a very good friend of mine, several years ago. It was his project. I was told after he passed away that he used to put a special love in teaching, and I could clearly find such a love in the parts of the book he developed. A few years after Klaus departure, Silvia told me about this book and asked me if I was willing to complete it. I could not refuse, for Silvia and the little Giulia, and especially for Klaus. And I couldn't for myself, too.

Klaus and I always told each other, “We have to do something together.” We were sharing research subjects, approaches to research, views, and values. In addition, it was a pleasure to stay together. After he moved to Trento, and especially during WWMR 2010 in Florence, we drafted together common projects involving GIDRM and, in particular, the small Italian solid‐state NMR community. However, none of our projects had the time to start, and we never effectively did anything together before his passing on 1 April 2011. This was a few days after a phone call during which we agreed on the title of his talk to a workshop supposedly in Pisa a couple of months later.

Completing his book, transforming it in our book, was an unexpected chance to do something, and something very important, together for the first time.

Now, after the huge effort done to understand, develop, integrate, and complete this book, I am very happy to see our names together, knowing that I did my best to honor and remember him and to value his work. I hope that Silvia and Beatrice will also be happy for the completion of this work, although it took much longer than they probably expected.

I also hope that Klaus will forgive me for the many parts of the book that possibly came out different from his initial idea or from how he could have realized them. But I am sure that he would be happy that finally we were able to do “something together.”

Marco Geppi

Pisa 2020

Marco Geppi obtained his degree in Chemistry in 1991 at the University of Pisa, Italy, working on 2H NMR studies of molecular dynamics in liquid crystals, and his PhD in Chemistry in 1997 at the Scuola Normale of Pisa, working on solid‐state NMR of polymeric materials, with professors C.A. Veracini and F. Ciardelli as supervisors. Part of his PhD research was carried out at the University of Durham, United Kingdom, under the supervision of Prof. R.K. Harris. In 2001 he became a researcher and, in 2014, associate professor in Physical Chemistry at the Department of Chemistry and Industrial Chemistry of the University of Pisa, where he is now leader of the solid‐state NMR spectroscopy group and laboratory, and teacher of Physical Chemistry, Spectroscopy, and solid‐state NMR. In 2015 he was awarded the GIDRM/GIRM gold medal. Since 2017 he has been president of the Italian Discussion Group on Magnetic Resonances (GIDRM). His research interests mainly concern the application of NMR techniques to a variety of solid materials, including polymers, biopolymers, pharmaceuticals, inorganics, organic–inorganic hybrids and composites, and soft matter (e.g. liquid crystals, gels, model membranes). He is also involved in the development of experimental and data analysis NMR techniques, as well as of NMR softwares, mainly devoted to studies on nuclear spin relaxation and molecular dynamics. He has been scientific manager of several contracts with chemical industries and of Italian and international scientific projects. He has coauthored over 140 research articles on NMR spectroscopy.

Introduction

Beyond the horizon of the place we lived when we were young

In a world of magnets and miracles

Our thoughts strayed constantly and without boundary

….

Running before times took our dreams away

Leaving the myriad small creatures trying to tie us to the ground

To a life consumed by slow decay

(High Hopes – Pink Floyd)

Discovered by physicists and widely applied in chemistry, Nuclear Magnetic Resonance (NMR) is a phenomenon that nowadays finds a crucial importance in most fields of natural science (chemistry, biology, physics, pharmacy, agriculture, materials, earth, and environmental science) as well as in medicine and engineering. Common basic principles concerning the spin of atomic nuclei and its interaction with radio waves originated three main, equally important, experimental techniques, which through the years became more and more specialized: solution‐state NMR spectroscopy, solid‐state NMR spectroscopy (to which this book is devoted), and magnetic resonance imaging. The latter finds its main field of application in medicine, where it is nowadays of extraordinary importance. Solution‐state and solid‐state NMR spectroscopies obviously differ on the physical state of the sample under investigation. Although they are both strikingly important in the same fields, they have different applications and can be complementary. Solution‐state NMR spectroscopy is generally unrivalled in the determination of unknown chemical structures, representing a vital tool for chemists, although its applications are not restricted to this field. The role of solid‐state NMR spectroscopy is beyond determining chemical structures of insoluble samples: it also provides precious and detailed information on conformations, molecular packing, intermolecular interactions, polymorphism, structural order/disorder, molecular dynamics, and average phase domain dimensions, i.e. on “microscopic” properties that are crucial in defining the macroscopic behavior of a material. Moreover, it shows virtually no limits on the type of anisotropic phase to be investigated, which can either be crystalline or amorphous, solid or soft. For these reasons, solid‐state NMR spectroscopy is one of the most powerful and versatile techniques for the characterization of materials.

As a physicochemist, my main interest in NMR in general, and solid‐state NMR spectroscopy in particular, stems from its natural position between theory and experiments as these continuously superimpose and apply in NMR and throughout this book. However, as it was for Klaus, my approach to NMR spectroscopy is mostly experimental. In this book the theoretical description of the concepts is always directed to a better understanding of the techniques, their applications, and, finally, the interpretation of the experimental results.

Solid‐state NMR spectroscopy is a field too large and varied to be exhaustively covered in a single book. Here we aimed at giving the essential tools to graduate and PhD students and to novice researchers in the field. Moreover, we wanted to present the possible applications of solid‐state NMR spectroscopy to researchers of other fields, who could find them useful to exploit this technique for their studies.

The book is permeated by the concepts of anisotropy of the internal nuclear interactions and of peculiar linebroadening mechanisms and relaxation behavior occurring in solids and, more in general, in anisotropic phases, also including soft matter. On one hand, these concepts are treated in contrast to solution‐state NMR, determining why and how in comparison solid‐state NMR is theoretically and experimentally more complex, but, potentially, a richer source of information. On the other hand, the implications of such concepts on both low‐ and high‐resolution solid‐state NMR experiments and on their applications are dealt with in detail. Furthermore, we presented and described many useful pulse sequences (both 1D and 2D), and we tackled the crucial aspect of molecular dynamics, in attempts to describe their influence on nuclear properties and to provide a complete survey of the NMR techniques that allow their close investigation. Several subjects, which are certainly very important in the current research, could not be treated here, concerning theoretical aspects (e.g. Floquet theory), techniques (e.g. Dynamic Nuclear Polarization, DNP), and applications (e.g. structural biology studies), for which the reader should refer to more specialized books or scientific literature.

This book consists of eight chapters. Chapter 1 is both a summary of the main concepts at the basis of solution‐state NMR and an introduction to the world of solid‐state NMR. In Chapter 2, the main mathematical and quantum‐mechanical tools necessary to understand the following subjects are briefly treated. Chapter 3 contains the formal description of the main external and internal nuclear spin interactions and their effects on nuclear energy spin levels. Chapters 4 and 5 are devoted to one‐dimensional static and Magic Angle Spinning (MAS) approaches, respectively: in each chapter the main concepts are dealt with from both theoretical and experimental standpoints and a description of the most important experimental techniques is present, following a division among dilute spin ½, abundant spin ½, and quadrupolar nuclei. Chapter 6 treats two‐dimensional solid‐state NMR spectroscopy, providing a description of the main concepts and the main experiments, divided by type of exploited interaction: chemical shift, hetero‐ and homonuclear dipolar, indirect spin–spin, and quadrupolar. Chapter 7 is entirely dedicated to molecular dynamics: theoretical and experimental aspects of the many NMR quantities useful in this field are discussed, highlighting in particular the different motional timescales involved and the procedures to extract motional parameters. Finally, Chapter 8 deals with the application of solid‐state NMR to several important classes of materials: pharmaceuticals, polymers, inorganics, organo metallic complexes and organic–inorganic hybrids and composites, and soft matter.

Many people have to be acknowledged for their contributions to this book. First of all, Beatrice Omiecienski, who was the only person who took part in all the phases of this work, representing, both ideally and in practice, the best possible bridge between Klaus and me. Without her extraordinary and tireless commitment throughout these years, and without her fierce determination in doing everything she could to complete Klaus's original project, this book would not exist. She constantly applied her skills and patience, supporting both Klaus and me in many aspects and, in particular, by editing, revising, and adapting all the many figures of this book.

I owe my special friend Alan Kenwright for the rest of my life for his dedication to greatly improve both the scientific content and English language of the whole book.

I am deeply grateful to Lucia Calucci, Silvia Borsacchi, Elisa Carignani, Francesca Martini, and Federica Balzano, who provided extensive and crucial contributions as well as precious suggestions to several parts of the book. Francesca Nardelli, Noemi Landi, and Elena Maurina are also acknowledged for their help in proof corrections.

I'm in debt with Giovanni Granucci, Giulia Mollica, and Giacomo Parigi, for their help and suggestions on selected subjects, for which my trust in them was much bigger than in myself.

I must acknowledge the authors of earlier and very important books on NMR and, in particular, solid‐state NMR, which are listed in the following as further readings.

I also want to thank my many graduate students, who through the years have been giving me the stimulus and strength to learn more: I wish they could realize how important for me was and is every small piece of knowledge transferred to each of them.

In the end, I thank from the bottom of my heart my research group and my family, who suffered in several ways the consequences of my commitment to this book and supported me for several years.

Marco Geppi

General Text on NMR

Freeman, R. (1997).

Spin Choreography

. Oxford: Spektrum Academic Publishers.

Günther, H. (2013).

NMR Spectroscopy

. Weinheim: Wiley.

Keeler, J. (2010).

Understanding NMR Spectroscopy

. Chichester: Wiley.

Levitt, M.H. (2008).

Spin Dynamics

. Chichester: Wiley.

Slichter, C.P. (1990).

Principles of Magnetic Resonance

. Berlin: Springer‐Verlag.

Texts on Solid‐State NMR

Apperley, D.C., Harris, R.K., and Hodgkinson, P. (2012).

Solid‐State NMR: Basic Principles & Practice

. New York: Momentum Press.

Duer, M.J. (2002).

Solid‐State NMR Spectroscopy: Principles and Applications

. Oxford: Blackwell Science.

Haeberlen, U. (1976).

High Resolution NMR in Solids. Selective Averaging

. New York: Academic Press.

MacKenzie, K.J.D. and Smith, M.E. (2002).

Multinuclear Solid‐State NMR of Inorganic Materials

. Oxford: Pergamon.

McBrierty, V.J. and Packer, K.J. (1993).

Nuclear Magnetic Resonance in Solid Polymers

. Cambridge: Cambridge University Press.

Mehring, M. (1983).

Principles of High Resolution NMR in Solids

. Berlin: Springer‐Verlag.

Saito, H., Ando, I., and Naito, A. (2006).

Solid State NMR Spectroscopy for Biopolymers: Principles and Applications

. Dordrecht: Springer.

Schmidt‐Rohr, K. and Spiess, H.W. (1994).

Multidimensional Solid‐State NMR and Polymers

. London: Academic Press.

Stejskal, E.O. and Memory, J.D. (1994).

High Resolution NMR in the Solid State

. Oxford: Oxford University Press.

1Introductory NMR Concepts

1.1 Historical Aspects

Several reviews discussing the historic evolution of nuclear magnetic resonance (NMR) spectroscopy have been published (see, for instance, Emsley and Feeney (1995)), but the most comprehensive analysis can be found in various articles of the “Encyclopedia of Nuclear Magnetic Resonance,” edited by Wiley (see, for instance, Becker and Fisk (2007)). Here, we only highlight a very short outline of the most important developments, with a particular focus on the field of solid‐state NMR (SSNMR).

The discovery of NMR can be attributed to Isidor I. Rabi (Nobel Prize in physics in 1944) and coworkers, who performed in 1938 the very first NMR experiment on a molecular beam of LiCl (Rabi et al. 1938). However, the first successful NMR experiments on solids and liquids were reported in early 1946 by two independent research groups at Stanford (Bloch, Hansen, Packard) and Harvard (Purcell, Torrey, Pound). Actually, the Harvard group led by Edward M. Purcell at MIT submitted a letter about their discovery to Physical Review on 24 December 1945, more than one month before the submission by the Stanford group to the same journal. However, it was established that the two researches were conducted independently and, for this reason, the 1952 Nobel Prize in Physics was awarded jointly to Bloch and Purcell. In particular, the group at Harvard discovered the phenomenon by studying solid paraffin in their very first experiment, and therefore, we can really say that solids were studied since the beginning of NMR.

The different behaviors between liquids and solids, as well as the anisotropic character of the nuclear interactions, were soon discovered by Bloembergen, Purcell, and Pound working on a CaF2 crystal (Purcell et al. 1946). This was later explained in more detail by Purcell's doctoral student, George Pake, who, through his studies on di‐hydrated CaSO4 crystals, first found the resonance signal that was a doublet and the typical pattern, now carrying his name, given by the homonuclear dipolar coupling between the two water protons in the case of single‐crystal and powder samples, respectively. In the very first years of its life, NMR was mostly applied to solids and its study was rooted firmly in the physics community, for instance, to investigate molecular motions as a function of temperature from changes in a lineshape.

In 1950, Proctor and Yu (1950a, 1950b) fortuitously discovered chemical shift, i.e. how the local chemical environment surrounding a nucleus influences the frequency at which it resonates, by looking at the 14N spectrum of NH4NO3 in water, and spin–spin indirect coupling, observing the 121Sb resonance of NaSbF6 in solution. Implications in NMR spectra became apparent, and most of the efforts moved to the study of liquids, characterized by much narrower lines. In the 1950s, tremendous strides were made in the development of the instrumentation. In 1952, the first high‐resolution commercial spectrometer, working at a proton Larmor frequency of 30 MHz, was introduced by Varian and sold to Exxon in Baytown, TX, and at the end of the 1950s, a 60 MHz spectrometer was available. Great improvements have been made in the stability and homogeneity of the magnetic fields following the introduction of field stabilizers, shim coils, and sample spinning. Moreover, principal advances progressed the development of experiments (e.g. Carr–Purcell spin echoes, 13C spectra at natural abundance) and theory (e.g. Bloch equations, effect of exchange on spectra, nuclear Overhauser effect (NOE), relaxation in the rotating frame, Solomon equations, Redfield theory of relaxation, spin temperature theory, Karplus theory for the dependence of three‐bond J coupling on a dihedral angle, dependence of 1H chemical shift on hydrogen bond strength). In 1958, Andrew observed that the broad 23Na line in NaCl single crystals, arising from dipolar interactions, could be significantly narrowed by spinning the sample sufficiently fast. Moreover, he showed a dependence of the linewidth under spinning on |0.5(3cos2β − 1)|, with β the angle between the axis of rotation and the external magnetic field. Indeed, for β = 54°44′, the dipolar interaction effect on the linewidth was predicted to vanish as demonstrated experimentally in 1959 by Andrew himself (Andrew et al. 1959) and by Lowe (1959). As Andrew writes, “When we reported our first sample rotation results at the AMPERE Congress in Pisa in 1960, Professor Gorter of Leiden found the removal of the dipolar broadening of the NMR lines quite remarkable and referred to it as ‘magic,’ so we called the technique ‘magic angle spinning’ after that.” (Andrew 2007). The 1950s also saw a substantial passage of NMR from the hands of physicists to those of chemists, since the pioneering developments started to be successfully exploited in applications of NMR, mostly as a novel tool for chemical structure determination, especially thanks to the development of correlation charts between chemical shift and molecular functional groups and of the first theories trying to explain these correlations.

In the 1960s, spectrometers were further developed with the introduction of field‐frequency lock (1961), superconducting magnets (1962), and time averaging (1963). Hartmann and Hahn (1962) suggested a method (and developed the corresponding theory) for transferring polarization between two different nuclear species (cross‐polarization [CP]), which would reveal its extraordinary importance for the study of rare nuclei in solids only about 15 years later. Powles and Mansfield (1962) devised a simple two‐pulse “solid echo” technique, able to refocus the quadrupolar and (to a good extent) the dipolar interaction in solids. Moreover, Goldburg and Lee (1963) showed how line narrowing in solids could be achieved not only by sample spinning as shown by Andrew a few years before but also by rotating radio‐frequency (RF) fields, still at the magic angle. Stejskal and Tanner (1965) introduced pulsed field gradients (PFG), opening entirely new perspectives for diffusion measurements. A few years later (1968), Waugh, Huber, and Haeberlen developed the WAHUHA pulse sequence, showing that it was able to remove homonuclear dipolar coupling by using a non‐symmetrized combination of Hamiltonian states (Waugh et al. 1968), and at the same time, Waugh and Haeberlen also proposed the average Hamiltonian theory (AHT) (Haeberlen and Waugh 1968). All this considered, the biggest breakthrough of that decade was represented by the development of Fourier transform (FT) and pulsed methods: the first results, obtained by Ernst and Anderson at Varian Associates, were presented at the Experimental NMR Conference in Pittsburgh in 1965 and published in 1966 in the journal “Review of Scientific Instruments” (Ernst and Anderson 1966) after the same paper had been rejected twice by the Journal of Chemical Physics for being not sufficiently original. FT applied to NMR (FT NMR as we know it today), the main reason for the Nobel Prize in Chemistry awarded to Richard Ernst in 1991, quickly encountered widespread success due to the development, in the same years, of computers and software. In 1965, a new algorithm was developed at Bell Laboratories able to perform a FT of 4096 data points in approximately only 20 minutes!

During the 1970s, there was a huge increase in magnetic field strengths, and a 1H Larmor frequency of 600 MHz was reached in 1977 in a non‐superconducting magnet developed at Carnegie Mellon University. In 1973, the first paper concerning the use of NMR to obtain images by exploiting magnetic field gradients was published by Lauterbur (1973), who expanded the one‐dimensional technique already proposed by Herman Carr in his PhD thesis more than 20 years before. In 2003, Lauterbur was awarded, together with Mansfield (who further contributed to the development of magnetic resonance imaging [MRI] soon after), the Nobel Prize in Medicine.1 Another significant development made in the 1970s was the introduction of bidimensional techniques. Ernst developed an idea of Jeener, presented at an Ampère summer school in 1971 (and never transformed into a published paper), and published his first results in 1975. Due to the almost simultaneous development of MRI, the very first paper dealing with 2D techniques concerned their applications to imaging rather than spectroscopy (Kumar et al. 1975), but spectroscopic applications followed soon (Müller et al. 1975). On the solid's front, first Mansfield, Rhim, Elleman, and Vaughan (Mansfield 1970; Rhim et al. 1973) and then Burum and Rhim (1979) improved the WAHUHA pulse sequence developing the MREV‐8 and BR‐24 pulse sequences for homonuclear dipolar decoupling. Moreover, separated local field (SLF) techniques, separately measuring correlated 13C chemical shifts and dipolar interactions and representing a basis for the development of 2D techniques in solids, were first introduced by Waugh and coworkers in 1976 (Hester et al. 1976). All in all, the 1970s can claim the birth of “high‐resolution SSNMR”: this can be considered coincident with the first experiments where the previously developed magic angle spinning (MAS), CP (based on the Hartmann–Hahn method), and heteronuclear dipolar decoupling techniques were combined together by Schaefer and Stejskal to obtain resolved spectra of rare nuclei, the first of which was the 13C spectrum of poly(methyl methacrylate) (Schaefer and Stejskal 1976