Solid State Nuclear Magnetic Resonance 72 (2015) 41–49

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Solid State Nuclear Magnetic Resonance

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Probing structural and motional features of organic and inorganicsolids through extended family of cross-polarization experiments

Piotr TekelyÉcole Normale Supérieure-PSL Research University, Sorbonne Universités-UPMC University, CNRS, UMR 7203 LBM, Paris, France

a r t i c l e i n f o

Article history:Received 18 June 2015Received in revised form21 July 2015Accepted 19 August 2015Available online 20 August 2015

Keywords:Solid-state NMRCross-polarizationMagic-angle spinningConstant-time cross-polarizationCross-polarization inversionMagnetization transfer

x.doi.org/10.1016/j.ssnmr.2015.08.00240/& 2015 Elsevier Inc. All rights reserved.

ail address: Piotr.Tekely@ens.fr

a b s t r a c t

Combined use of cross-polarization and magic-angle spinning in the middle of the seventies has openeda new era of high-resolution solid-state NMR spectroscopy. Cross-polarization procedure is commonlyused to obtain a shorter measuring time and to investigate or exploit one nucleous by means of the othernucleous involved in the polarization transfer. An extended family of cross-polarization experimentsincluding constant time cross-polarization approach, cross-polarization inversion and indirect observa-tion of proton spin system is reviewed and illustrated with applications to a large range of solids.

& 2015 Elsevier Inc. All rights reserved.

1. Introduction

Cross-polarization (CP) transfer of magnetization [1] betweentwo spin systems I and S is routinely used in magic-angle spinning(MAS) NMR [2] to reduce the measuring time. This reduction isdue to a gain of sensitivity through signal enhancement of lowgamma S spins by abundant I spins and a potentially shorter spin-lattice relaxation of I spins (usually protons). The commonly usedCP method [1] is based on the spin-locking procedure of I spinmagnetization along the radio-frequency field B1. When employedto probe the CP dynamics during the variable contact time, therecorded build up curves may suffer from a simultaneous decaywith a time constant TI1ρ, usually much shorter than TS1ρ. This maycomplicate the access to subtle details of cross-polarization dy-namics containing structural and motional fingerprints of mole-cular systems and lead to a false structural and dynamic image ofinvestigated materials when the cross-polarization transfer timeTIS is longer than the relaxation time in the rotating frame ofprotons, as frequently encountered in inorganic solids. Thisdrawback can be circumvented by using constant time CP ex-periment which will be described in the second part along with itsapplications in inorganic materials.

Part 3 will review the potential of cross-polarization inversionin probing the molecular geometry and motional features of or-ganic and inorganic systems through one- and two-dimensional

experiments.The last part will focus on the experiments devoted to indirect

observation of proton system via cross-polarization and their ap-plications in a large range of organic solids.

This review was written from the perspective of author’s re-search group studies. All relevant contributions from other groupswhich are not included in the references were quoted in the ori-ginal papers.

2. Constant time cross-polarization experiment

2.1. TORQUE pulse sequence

The CP transfer of magnetization between the abundant I andthe rare S spins can be described by the simplified thermodynamicmodel [3] when the average I–I homonuclear dipolar interaction islarger than the I–S heteronuclear dipolar interaction. Assumingnegligible rotating-frame relaxation of the S spins, the dependenceof their NMR signal as a function of contact time tCP, can be de-scribed by the well-known relationship [1]

⎜ ⎟⎛⎝⎜⎜

⎛⎝⎜⎜

⎞⎠⎟⎟

⎛⎝

⎞⎠

⎞⎠⎟⎟M t M

tT

tT

1

1exp exp

1

S CP SI

S T

T

CPI

CPIS

1IS

I1

( ) αγγ

=−

− − −

( )ρ

∞

ρ

where MS∞ is the equilibrium magnetization of spins S;

H H/ /I S I I S S1 1 1 1α ω ω γ γ= = ( ) ( ) is the ratio of the radio-frequency fieldsat the I and S frequencies (the Hartman–Hahn mismatch

P. Tekely / Solid State Nuclear Magnetic Resonance 72 (2015) 41–4942

parameter);T

1ISis the cross-polarization rate, which not only relies

on the strength of the heteronuclear I–S dipolar interaction butalso depends in a complex way on the strength of the homo-nuclear I–I dipolar interaction, on the correlation time and am-plitude of molecular motions and the experimental parameters;TI1ρ is the relaxation time in the rotating frame of the I spins. Ac-cording to Eq. (1), the CP build up curves are inherently sensitiveto internuclear distances via TIS and the presence of mid-kHzmotions via TI1ρ.

It is important to realize that the Eq. (1) is valid not only whenTISoTI1ρ , the usual condition (fast CP regime), but also holdswhatever the ratio TIS/TI1ρ. NMR cross-polarization measurementsare usually analyzed assuming that the cross-polarization time TIS

of magnetization transfer is shorter than the relaxation time TI1ρ.However, the reverse situation (i.e. TIS4TI1ρ , slow CP regime) canbe frequently encountered (vide infra), especially in inorganic so-lids where protons are more remote from rare nuclei than in or-ganic systems. In this case, the S spin magnetization will as wellbegin to rise but this increase cannot proceed further when the Ispin system is rapidly depleted by the TI1ρ relaxation. Conse-quently, the transfer of magnetization is stopped at a time close toTI1ρ and there is a reverse flow from the S to I spin system whichremains depleted by the faster TI1ρ relaxation. This reverse flowfrom the S to I reservoir occurs, as does the forward one, at thecross-polarization rate 1/TIS. In such a situation, when analyzingthe experimental data under the usual fast CP assumption, an in-terpretation of both dynamic parameters will be strongly in error.In fact, it is impossible to know from the cross-polarization curvealone, whether TISoTI1ρ , or TIS4TI1ρ. This is the consequence ofthe fact, that apart from the intensity factor, Eq. (1) is fully sym-metrical with respect to the interchange of TIS and TI1ρ.

Contrary to the standard variable-contact CP experiment, adirect visualization of the ratio TIS/TI1ρ is easily accessible by usingthe TORQUE pulse sequence [4]. This experiment has been ori-ginally designed with the aim of quenching the I spin TI1ρ depen-dence (T One Rho QUEnching) when studying polarization trans-fer in organic solids with TISoTI1ρ. It uses a spin lock period onspin I of duration tSL followed by the cross polarization of variableduration tCP, the total time tconst¼tCPþtSL being kept constant (seeFig. 1 left). The TORQUE signal grows as a function of tCP accordingto

⎛⎝⎜⎜

⎞⎠⎟⎟M t T T

t Texp /

1 exp 1 /1 2

STORQUE

CP TORQUEI CP

IS

1λ

λ( ) = ( − )

− ( − ( − )( ))( − ) ( )

ρ

with λ¼TIS/TI1ρ. Fig. 1 (right) shows the temporal evolution of Sspin magnetization calculated for a standard CP experiment and

x y y

tSL tCP

tconst

I

S

Fig. 1. (left) Scheme of TORQUE pulse sequence [4]. (right) Magnetization transfer time dBottom: TIS¼3.0 ms, TI1ρ¼1.5 ms. Note the change in the curvature of TORQUE graphs.

the TORQUE experiment, both in two different scenarios: (i)TISoTI1ρ ; (ii) TIS4TI1ρ.

As expected, in the standard CP experiment, apart from thedifferences in the absolute intensity, which is not known a priori,identical temporal evolution of magnetization is observed in eachcase. In contrast, the difference in outwards and inwards curvingof the TORQUE temporal evolution is immediately visible. Thisallows, as exemplified below, unambiguous determination of theTIS/TI1ρ ratio and assures proper interpretation of dynamic CPparameters in terms of structural and/or motional features.

2.2. Pitfalls of 1H–29Si cross-polarization dynamics

High-resolution solid state 29Si NMR spectroscopy is frequentlyused in structural studies of inorganic materials including zeolites,minerals, glasses, and cement-based systems. Its important place instructure determination of these materials relies on the fact that 29SiNMR spectra permit a precise determination of the 29Si isotropicchemical shift in different silicon environments of powdered sam-ples. Although the easiest way to record the quantitative 29Si NMRspectrum is a direct excitation by a single pulse, this cannot bereasonably applied in most cases due to extremely long 29Si long-itudinal relaxation times. To avoid this inconvenience, one can takeadvantage of magnetization transfer from protons to 29Si spins.Although when using cross-polarization procedure, the quantitativeproportions of chemically or crystallographically inequivalent sitescannot be reached as with single pulse excitation, an extremelyvaluable structural and dynamic information can be obtained in thismanner. For this, some basic precautions have to be taken. Com-monly encountered complication arises indeed from the fact, thatthe cross-polarization transfer time may be quite long and is fre-quently longer than the relaxation time in the rotating frame ofprotons. This fact must be clearly recognized to avoid a falsestructural and dynamic image of investigated materials. This is il-lustrated below in two classes of inorganic materials.

2.2.1. Silica gelsSilica gels are highly porous materials which play an important

role in numerous applications such as catalysis or chromato-graphic separation and have been the subject of much NMR in-vestigations for several years. The high-resolution solid state 29SiCP/MAS NMR spectra of silica gel show three peaks at –91.5 ppm, –101 ppm and –110 ppm assigned respectively to three Q(2), Q(3)

and Q(4) types of silicon environments. The results from the CP andTORQUE experiments on a Fisher S-157 silica gel sample are pre-sented in Fig. 2.

tcp (ms)

Inte

nsity

(a.u

.) TIS

< T1

I

TIS

> T1

I

ρ

ρ

ependence in standard CP and TORQUE experiments. Top: TIS¼1.5 ms, TI1ρ¼3.0 ms.

P. Tekely / Solid State Nuclear Magnetic Resonance 72 (2015) 41–49 43

Assuming a simple monoexponential polarization transfer, theresults of a fit of three CP curves using Eq. (1) are TUP¼[2.3, 2.6,10.3] ms and TDOWN¼[10.3, 13.4, 30.0] ms, for [Q(2), Q(3), Q(4)] si-licons, respectively. Independent T H1

1( )ρ relaxation measurements

revealed the unique value T H11( )ρ ¼10.370.5 ms [5]. The value of

10.3 ms is equal to TDOWN for Q(2) and to TUP for Q(4). This revealsthat T TIS I

1< ρ for Q(2) whereas T TIS I1> ρ holds for Q(4). For Q(2) and

Q(4) silicons, these two diametrically opposite situations are vi-sualized immediately by the opposite curvatures of the TORQUEtemporal dependence (Fig. 2 bottom). For Q(3) site, the shape of theTORQUE curve proves the existence of at least two different Q(3)

species, first one having T TIS I1< ρ, the second one with T TIS I

1> ρ.

2.2.2. Layered sodium hydrous silicatesThis class of materials, available only in microcrystalline form,

has a two-dimensional layered structure, the negative charge ofthe silicate layer being compensated by sodium ions that are

Fig. 2. Time dependence of 29Si magnetization for three different sites of a silica gelin the standard cross-polarization experiment (top) and TORQUE experiment witha total constant time equal to 18.0 ms (bottom) [5].

Fig. 3. Temporal evolution of 29Si and 23Na magnetization in the standard cross-polarizamagadiite with a total constant time equal respectively to 3.0 and 4.0 ms [6].

coordinated by the oxygen atoms of the intercalated water mole-cules. Magadiite, the most frequently researched, has the idealizedformula Na2Si14O29 �nH2O (n¼8–10). 29Si MAS NMR studies showthe presence of Q(3) and Q(4) silicons in its basic layer structure.The experimental build up curves obtained from standard CP andTORQUE experiments for Q(3) and Naþ are shown in Fig. 3.

Assuming as usual that TISoTI1ρ , the standard CP curves can befitted according to Eq. (1), each of them being described by twopairs of time constants Tup and Tdown for their rising and decreasingparts, respectively. A simple model for which each site is char-acterized by a single set of Tup and Tdown values was found to beinadequate. However, the observed curvature in the TORQUEtemporal dependence makes it immediately evident that it is es-sentially the TIS4TI1ρ situation which takes place for Q(3) sites. ForNaþ ions, the situation is even more complex, the TORQUE curveexhibits a pronounced S-shape form which means that both thefast and the slow CP regime are equally relevant for this CP dy-namics. From the independent measurements of relaxation in therotating frame, two distinct TI1ρ values have been obtained forprotons appearing at 3.8 and 15.2 ppm, respectively. It turns outthat these two relaxation times are equal neither to Tdown nor toTup found in the fitting procedure of CP build up curves. As the TI1ρvalues reflect two different proton environments existing in ma-gadiite, a realistic model should include both relaxation para-meters and assume at least two types of Q(3) as well as sodiumsites being differently coupled to hydrogen species. Consequently,the CP and TORQUE build up curves are each the weighted sums oftwo different contributions, each one given by Eqs. (1) and (2) forCP and TORQUE, respectively. A good agreement between ex-perimental and calculated CP and TORQUE temporal dependencieswas indeed observed for both species under such assumptions [6].The ensemble of fitted dynamic parameters brings evidence thatthe long time decays of magnetization in the standard CP experi-ments result from the back flow of magnetization to the protonsystem. It has been also demonstrated that a very similar situationoccurs in the case of a layered sodium hydrated octosilicate [7],calcium silicate hydrates [5] and zeolites [8]. When using the1H–29Si cross-polarization in recording the 29Si spectra of thesematerials, this has to be clearly recognized to avoid a false struc-tural and motional interpretation.

tion experiment (top) and TORQUE experiments (bottom) for Q(3) and Naþ sites of

P. Tekely / Solid State Nuclear Magnetic Resonance 72 (2015) 41–4944

3. Two-dimensional cross-polarization inversion experimentsin rotating powders

Cross-polarization transfer of polarization for signal enhance-ment of a low gamma S spin by an abundant I spin is now routi-nely used in high-resolution solid-state NMR. However, as de-monstrated first by Müller et al. [9], cross-polarization itself may

Fig. 4. Numerically calculated (left) and experimental (right) 13C spectra of hex-amethylbenzene spinning at an angle of 57.5°. Note different line shapes of thecenterband and each spinning sideband due to different contributions of crystal-lites from a powder sample. The same is valid for powders spinning at the magic-angle [13].

t1

t2

x y -y1H

S

Fig. 5. Cross-polarization inversion pulse sequence for 2D chemical-shift-dipolar-correlated MAS experiment. During the evolution period t1, the phase of the protonspin-locking field is inverted. No synchronization with MAS is required [12].

Fig. 6. Overall differences in molecular mobility of functional groups or sites asrevealed by different intensity of aliphatic 13C resonances in cross-polarizationinversion spectrum of C-ter HsCen2/P17-XPC microcrystalline protein recordedwith the pulse sequence shown in Fig. 5 using initial 300 ms CP duration andt1¼70 ms. Note that a short t1 interval leads to selective inversion for the most rigidCH and CH2 groups, while the resonance signals of more mobile sites, including CH3

groups, maintain their positive intensity [21].

be used for studying details of the heteronuclear interaction. Thishas been shown first with a single crystal [9] and a static powdersample of ferrocene [10]. We have provided first experimentalevidence that cross-polarization dynamics offers a convenient wayof obtaining dipolar local field information in magic-angle spin-ning solids [11,12]. Local-field measurements from cross-polar-ization dynamics take advantage of the coherent energy transfer inthe initial period of tens of microseconds, where the informationon the local heteronuclear interaction is available when dealingwith solids in which heteronuclear dipolar interactions are greaterthan homonuclear dipolar interactions. This is a common situationfor CH carbons in organic solids. Importantly, in the presence ofspin-locked proton irradiation, the secular proton–proton dipolarHamiltonian takes half its natural value. Both factors lead to sig-nificant truncation of weak dipolar couplings from neighboringprotons by the largely dominant flip–flop coupling term of theheteronuclear spin pairs during CP and permit to exploit the co-herent magnetization exchange without applying homonucleardecoupling. This eliminates any uncertainty about the hetero-nuclear scaling factor inherently present during homonucleardecoupling.

Below I will recall first how one can take advantage of thecoherent stage of magnetization transfer during cross-polarizationinversion to induce dipolar modulation of chemical shift aniso-tropy (CSA) spinning sidebands for accurately determining theheteronuclear dipolar coupling magnitude and the mutual or-ientation of the principal axis system of the dipolar and chemical-shift tensors. It is important to point out that the approach is basedon the orientation dependence of spinning sidebands, whichstems, as illustrated in Fig. 4, from the fact that the crystalliteswith different orientations in a powder sample contribute differ-ently to the centerband and to each spinning sidebands [13,14].This orientation dependence of spinning sidebands also forms acornerstone of one-dimensional exchange spectroscopy by side-bands alternation (ODESSA) for chemically equivalent and in-equivalent nuclei in rotating solids [15–17].

The cross-polarization inversion pulse sequence used for re-cording 2D chemical-shift-dipolar-correlated spectra is shown inFig. 5.

The experiment starts with the preparation period whichconsists of the classical cross-polarization procedure. During the t1period, the contact between protons and S spins is maintained butthe phase of proton spin-locking irradiation is inverted. This leadsto the amplitude modulation of the S spin magnetization whichdepends principally on cross-polarization dynamics. During thedetection period, the S spin magnetization is acquired in thepresence of heteronuclear decoupling. The cross-polarization in-version pulse sequence shown in Fig. 5 was originally proposed ina one-dimensional version by Melchior [18] for discriminationbetween differently substituted carbons through selective inver-sion of resonance signals depending on the polarization transferrate between protons and carbons. In this way the polarization ofprotonated carbons is inverted first and that of nonprotonatedcarbons is inverted much later. Due to the molecular motions thatdecrease the cross-polarization rate, the resonances of methylcarbons invert more slowly than from other protonated carbons.Consequently, selective inversion or suppression of resonancesignals is achieved depending on the number and distance ofsurrounding protons and on the molecular mobility of individualfunctional groups or sites. This permitted to reveal in a straight-forward way several structural and motional features in a large oforganic solids including polymers [19], small organic molecules ona surface of inorganic materials [20] and microcrystalline proteins(Fig. 6) [21].

Fig. 8. Dipolar modulated, magic-angle spinning 13C spectra calculated for cross-polarization inversion time t1¼42 μs, vr¼439 Hz, three different internuclear dis-tances rC–H (left) and different polar coordinates αD and βD of the C–H vector in thechemical shift principal axis frame (right) [22].

P. Tekely / Solid State Nuclear Magnetic Resonance 72 (2015) 41–49 45

3.1. Dipolar modulated chemical shift anisotropy spinning sidebands

In this paragraph I will describe the time development of the I–S spin system under the pulse sequence from Fig. 5 in the presenceof magic angle spinning. For this, it is convenient to make use ofthe general form of internal Hamiltonian written in terms of ir-reducible spherical operators as

C T C T B t C t32 3sec

rot,00 00 20ρ δ= + [ ( ) + ( )]

( )λ λ λ λ λ λ λ

⎡⎣ ⎤⎦B t sin sin C cos t S sin t12

2 r r1 1β β ω ω( ) = ′ +

B t sin sin C cos t S sin t12

2 r r1 1β β ω ω( )= ′ [ + ]

⎡⎣ ⎤⎦C t sin C cos t S sin t12

2 2r r2

2 2β ω ω( ) = ′ +

withC1¼ηλsinαsin2γ�cosαcosβ (ηλcos2γþ3)S1¼ηλcosαsin2γþsinαcosβ (ηλcos2γþ3)C2¼[ 3

2sin2β� 1

2ηλcos2γ (1þ cos2β)] cos2αþηλcosβsin2γsin2α

S2¼[�32sin2β�1

2ηλcos2γ (1þ cos2β)] sin2αþηλcosβ sin2γ cos2α

where η and δ are the asymmetry and anisotropy parameters,respectively; (α, β, γ) are the Euler angles between the principalaxis system (PAS) and the rotor (ROT) system, and β′¼54.7° is the

Fig. 9. 2D CSA/Dip correlation spectra of slowly magic-angle spinning (vr¼355 Hz)natural abundance calcium formate (a–e), calculated for different mutual orienta-tions of dipolar/shielding tensors. (f) Experimental spectrum obtained after thedouble Fourier transform of the full data matrix S (t1, t2) [22].

Fig. 7. Experimental (left) and calculated (right) 13C CSA spectra of slowly magic-angle spinning (vr¼439 Hz) calcium formate powder sample for different crosspolarization inversion periods t1[22]. The best-fit parameters for two magneticallyinequivalent sites in the asymmetric unit are: (1) rC–H¼1.13270.005 Å,αD¼4.072.0°, βD¼87.075.0°; (2) rC-H¼1.12770.005 Å, αD¼13.072.0°,βD¼93.075.0°.

P. Tekely / Solid State Nuclear Magnetic Resonance 72 (2015) 41–4946

angle between the spinning axis and the static magnetic field B0.Other symbols have their usual meaning. During the period ofcross-polarization inversion, the S spins evolve solely under thedipolar heteronuclear Hamiltonian sec

IS rot, so that the density op-erator can be expressed as

t i t S i texp exp 4secIS rot

x secIS rot

1,

1,

1( ) ( )( )ρ = − ( )

and develops an in-phase component of the spin-lock magne-tization

t g t S cos t S 5x x1 1 1( ) ( ) ( )ρ ϕ= = ( )

To take into account the relative orientation of the dipolar andchemical shift tensors, we need to perform an additional trans-formation

PAS PAS 6IS CSAD D,⟹ ( )

α β( )

by expressing the dipolar IS vector in the principal axis system ofthe shielding tensor. This leads to the expression

⎛⎝⎜

⎞⎠⎟t

DG t2

2, , , , , , ,

7eff

D D r1 1( )ϕ π α β γ α β β ω= ( )( )

′

with Deff¼(μ0/4π)(γIγSh/2πr3IS)þ J, J being the indirect couplingconstant and

⎡⎣ ⎤⎦⎡⎣

⎤⎦⎡⎣ ⎤⎦⎡⎣

⎤⎦⎡⎣ ⎤⎦⎡⎣

⎤⎦⎡⎣ ⎤⎦⎡⎣

⎤⎦⎛⎝⎜

⎞⎠⎟

G t

sin sin t sin cos

cos sin sin

sin cos sin

cos t cos sin cos

cos sin sin sin sin

sin sin t sin sin

cos cos sin cos

sin cos sin

cos t cos sin sin

sin cos sin sin sin

t sin cos sin

sin sin

cos cos cos

, , , , , , ,

3/8 2 2 1

2 2 2 cos

3 1

3/4 2 2

2 2

3/4 2

2 2 2 2

2 3 1 2

3/2

2 2 2

14

3 2

3 2 cos 2

3 1 3 1 3 1 8

D D r

r r D

D D D

D

r r D

D D D

r r D

D D D

D

r r D

D D D

D D

D D

D

1

12 2

2 2 2

12

2

12

2

12

12 2

2 2 2

( )

( )

( )

( )( ) ( )

( )( )

( )

( )

( )

( )( ) ( )

( )( ) ( )

( )( ) ( )

( )( ) ( )

( )

( )

α β γ α β β ω

ω α ω α β β

γ α β β γ α

β β β

ω ω α α β β

γ α β β γ α β

ω α ω α β β

γ α β β γ α

β β β

ω ω α α β β

γ α β β γ α β

β γ α β

β γ α β

β β β

= − + +

+ + +

+ −

− + −

+ + +

+ − +

+ − +

− −

− + −

+ − +

− [ +

+ +

− − − ] ′ − ( )

′

′

′

′

′

Subsequent development of this magnetization under the chemi-cal shift Hamiltonian sec

CSA rot, during acquisition proceeds as

t t g t iH t S iH t, exp exp 9secCSA rot

x secCSA rot

1 2 1,

2,

2( ) ( )ρ = ( − ) ( ) ( )

For inhomogeneous interactions, this leads to the free inductiondecay written as

⎡⎣ ⎤⎦G t t g t i texp 101, 2 1 2( ) ( ) ( )ψ= − ( )

with

t t dt211t

t tCSA

21

1 2∫( )ψ π ν= ( )( )

+

The detected NMR signal is the free induction decay governed bychemical shift anisotropy, with its amplitude modulated by the

factor g(t1). For a powdered sample, and taking into account therelaxation decay, the function G(t1, t2) can be expressed as

⎛⎝⎜

⎞⎠⎟

⎡⎣ ⎤⎦G t t i t cos t t T

sin d d d

18

exp exp /

12

1, 2 2 2 1 2 2∫ ∫ ∫ ( )( ) ( )π

ψ ϕ

β α β γ

= − ( ) − *

( )

As illustrated below, when this signal is Fourier transformed withrespect to t2, this leads to the mixed time-frequency signal S (t1,ω2) with CSA spinning sideband patterns modulated by the het-eronuclear dipolar interaction.

3.2. CSA/dipolar correlation experiments in organic solids

Fig. 7 shows four magic-angle spinning natural abundance 13Cspectra of calcium formate, recorded at different dipolar modula-tion periods t1, together with the corresponding theoretical spec-tra calculated as described above. Different dipolar oscillationfrequency at different spinning sidebands stems from variation oforientation dependent dipolar coupling. Two sets of signals, wellresolved in each experimental spectrum, result from the presenceof two magnetically inequivalent formate ions in the asymmetricunit. The chemical shift interaction parameters were fitted usingan iterative procedure independently for unmodulated proton-decoupled spectra recorded at different spinning speeds. The samefitting procedure of dipolar modulated spectra included theparameters rC–H, αD and βD. The theoretical spectra arising fromfitting procedure satisfactorily reproduce the amplitude modula-tion of each family of spinning sidebands at different polarizationinversion periods.

Importantly, as demonstrated in the Fig. 8, the dipolar modu-lated spectra are very sensitive, through the shape of the envelopeof spinning sidebands, to small changes of the heteronuclear bonddistance and polar coordinates αD and βD of the C–H vector in thechemical shift principal axis frame [12,22].

The double Fourier transform of the full data matrix S(t1, t2),leads to a two-dimensional spectrum S(ω1, ω2) with the dipolarinteraction features displayed along the ω1 axis and the chemicalshift spinning sidebands family along the ω2 axis [12,22]. The re-sulting 2D spectra, as illustrated in Fig. 9, are also sensitive to themutual orientation of dipolar/shielding tensors.

When dealing with solids with stronger proton–proton inter-actions, the off-resonance (frequency switched) spin-locking forhomonuclear decoupling may be included in these experiments,like in popular PISEMA scheme [23] and its later versions. Im-portantly, for accurate determination of bond distances and mu-tual orientation of tensors, special care must be taken to measurethe heteronuclear scaling factor under the exact experimentalconditions used during the dipolar evolution, including its in-evitable variations over the range of frequency offsets.

3.3. Probing the geometry of hydrogen bonded silanols

Hydrogen bonds are the most important of all directional in-termolecular interactions and play a central role in determiningmolecular conformation as well as the function and dynamics of agreat number of molecular systems. Hydrogen bonds also play animportant role in aggregation and ordering of silicate layers. Bothinter and intralayer hydrogen bonding involving the silanols orwater protons has been postulated. As the intercalation of polarmolecules in layered materials can be dramatically controlled bythe existence of interlayer hydrogen bonds, the appropriate re-cognition of the extent and the nature of hydrogen bonding pre-sent in these materials is of prime importance. To get a precisegeometric information on hydrogen-bonded silanols, one can de-termine the internuclear Si � � �H distances and the orientation of

Fig. 10. (left bottom) Dipolar modulated (t1¼400 μs), natural abundance 29Si NMRspectrum of slowly magic-angle spinning (νr¼357 Hz) octosilicate recorded withthe pulse sequence shown in Fig. 5. Asterisks show the spinning sidebands of Q(4)

sites. (right bottom) Fitted spectrum of Q(3) sites along with its two components.Dipolar modulated subspectrum (a) represents the hydrogen bonded Q(3) sites, thesubspectrum (b) represents Si–O� Q(3) sites cross-polarizing from the water mo-lecules [7].

Fig. 11. (Bottom) Changes in the 13C signal intensities of carboxyl carbons in α and γpolymorphs of glycine vs. the inversion recovery time of proton magnetizationprior to cross-polarization. The spinning frequency was equal to 27.2 kHz. (Top)Spinning sideband families due to the 13C CSA’s of the carboxyl carbons of the twopolymorphs recorded at a spinning frequency of 1.322 kHz using a 500 ms inver-sion recovery period of the proton magnetization [34].

P. Tekely / Solid State Nuclear Magnetic Resonance 72 (2015) 41–49 47

the 29Si chemical shift tensor in the hydrogen-bonded Q(3)-typeunits by exploiting cross-polarization inversion of the 29Si spinmagnetization used as a modulation of the slow magic-anglespinning chemical shift spectrum [7,24]. As shown in Fig. 10, thisleads to dipolar modulation of the 29Si CSA spinning sidebands dueto a largely coherent magnetization transfer within the silanolgroups having a pronounced inhomogeneous character of rela-tively isolated two-spin dipolar pairs.

To reproduce the observed dipolar modulated envelope of Q(3)

spinning sidebands, the presence of two different componentsrepresenting two types of Q(3) sites had to be assumed [24].Consequently, although a single isotropic Q(3) resonance signalwas observed, two types of Q(3) tetrahedra, hydrogen-bonded si-lanols and Si-O� type sites need to be distinguished by their dif-ferent abilities to cross-polarize. This clearly supports the in-tralayer character of strongly hydrogen bonded silanol groups in abridging position between neighboring tetrahedral [7,24].

4. Indirect observation of proton spin system

Another advantage of cross-polarization is the possibility ofinvestigating indirectly one nucleous by means of the othernucleous involved in the polarization transfer. We have shownthat the complementary advantages of high sensitivity and highchemical shift dispersion offered by 1H and 13C spins can beensuccessfully exploited in heterogeneous organic solids for indirectmeasurements of T2 relaxation times of protons [25–28] and forindirect selective observation of proton spin diffusion [26]. It hasbeen demonstrated that a proper image of structural in-homogeneity can be deduced from these indirect measurementson magic-angle spinning samples of polymers, woods and coals[25–27]. Good agreement between the domain sizes extractedfrom direct and indirect measurements of proton spin diffusionhas been observed [26]. Moreover, under conditions of rapid MAS,

the approach permits an insight into the local dipolar interactionin common organic solids and materials [29–33].

As emphasized below, the indirect measurements of protonlongitudinal relaxation can also be successfully exploited for dis-entangling spectroscopic fingerprints from crystallographic formsor polymorphs.

4.1. Disentangling spectral fingerprints of polymorphs and crystal-lographic forms

Exploiting differential proton T1 relaxation in conjunction withcross-polarization [27] can be useful to separate overlapping 13C or15N solid-state NMR spectra from crystallographically differentforms or polymorphs [34]. Distinct T1 proton relaxation times as-sociated with different crystallographic forms or polymorphs of agiven compound may originate from differences in crystal hydra-tion, hydrogen-bond networks or different rates of reorientation ofCH3 and NH3

þ groups. In rigid and strongly dipolar-coupled solids,the overall proton spin-lattice relaxation rates can be averaged byspin-diffusion that leads to a uniform relaxation rate of all protonsin the spin system, except for protons belonging to rapidly rotatingmethyl and ammonium NH3

þ groups that can play a role ofmagnetization ‘sinks’. As illustrated in Fig. 11, taking advantage ofdifferent proton T1 relaxation times of α and γ glycine [35] com-bined with cross-polarization, allows one to record 13C spectra ofglycine where the resonance signals of carboxyl groups that

Fig. 12. Changes in the intensities of the 13C signals of L-arginine hydrochloride vs. the inversion recovery time 10oto20 s of the proton magnetization preceding cross-polarization. The separation of the spectra of the two forms is best accomplished for proton recovery times t¼12 and 20 s [34].

Fig. 13. (a) 15N CP/MAS spectrum of L-arginine hydrochloride that contains amixture of two crystallographic forms. Their spectra are best separated by usingdifferent inversion recovery times of the proton magnetization preceding the cross-polarization transfer t¼12 s (b) and 20 s (c). (d) 15N CP/MAS spectrum of L-arginineHCl �H2O [34].

P. Tekely / Solid State Nuclear Magnetic Resonance 72 (2015) 41–4948

belong to different polymorphs have opposite phases [34].The combination of cross-polarization and proton spin-lattice

relaxation has been also exploited for separating the 13C CP/MASspectra of different crystallographic forms of L-arginine hydro-chloride [34]. As shown in Fig. 12 after inversion of the protonmagnetization followed by partial recovery during 12 s, a numberof resonance signals simultaneously vanish in the 13C CP/MASspectrum, due to the zero-passage of the fastest-relaxing form. Theremaining negative resonance lines all vanish in turn after a re-covery time of 20 s.

One can obviously exploit the differential recovery rates of the

proton magnetization for the purpose of editing the stronglyoverlapping 15N CP/MAS spectra of the crystallographically dif-ferent forms. This is illustrated in Fig. 13 where the individual 15Nspectra of each form were recorded with the same recovery delaysthat allowed editing of the 13C spectra. This proves that, in analogyto the α and γ polymorphs of glycine, the longitudinal protonrelaxation combined with cross-polarization can be also success-fully exploited in arginine to disentangle overlapping 13C or 15NCP/MAS spectra from crystallographically different forms si-multaneously present in a powder sample.

5. Summary

The cross-polarization measurements are usually analyzed as-suming that the CP time TIS of magnetization transfer from theabundant I spins to the rare S spins is shorter than the relaxationtime T1ρ in the rotating frame of the I spins (fast CP regime).However, the reverse situation ( T TIS I

1> ρ, slow CP regime) canoccur, especially during the 1H-29Si transfer in commonly en-countered inorganic materials. This fact must be clearly recognizedto avoid a false structural and dynamic image of investigatedmaterials. The efficiency of the TORQUE experiment in visualizingthe real CP regime or its possible mixed character has been un-derlined. Moreover, the quenching of TI1ρ temporal dependencewith TORQUE pulse sequence permits to reveal subtle details of CPdynamics in organic solids such as synthetic and natural polymersand helps to access in a straightforward manner the order para-meters in microcrystalline proteins [21].

The analysis of dipolar modulated 13C or 29Si CSA spinningsidebands yields precise local geometric information. This could beparticularly useful in organic solids with selectively 13C labeledsites and magnetically diluted (deuterated) proton network. Theapproach also permits to probe the geometry of hydrogen-bondedsilanols, including the orientation of 29Si CSA tensor and can beapplied to obtain structural information in layered alkali metalsilicates, silica gels, calcium silicate hydrates as well as in other

P. Tekely / Solid State Nuclear Magnetic Resonance 72 (2015) 41–49 49

classes of microporous material.Indirect observation of proton spin system can be successfully

exploited to get a deeper insight into structural heterogeneity andlocal dipolar interactions in a large range of common organic so-lids and materials as well as for disentangling spectroscopic fin-gerprints from different crystallographic forms or polymorphs.

Acknowledgments

I am grateful to my undergraduate and graduate students,postdocs and collaborators that contributed to the studies dis-cussed in this review. Financial support of the CNRS is gratefullyacknowledged.

References

[1] A. Pines, M.G. Gibby, J.S. Waugh, J. Chem. Phys. 59 (1973) 569–590, http://dx.doi.org/10.1063/1.1680061.

[2] J. Schaefer, E.O. Stejskal, J. Am. Chem. Soc. 98 (1976) 1031–1032, http://dx.doi.org/10.1021/ja00420a036.

[3] M. Mehring, High-Resolution NMR in Solids, Springer, New York, 1983.[4] P. Tekely, V. Gerardy, P. Palmas, D. Canet, A. Retournard, A. Solid State NMR 4

(1995) 361–367, http://dx.doi.org/10.1016/0926-2040(95)00018-L.[5] I. Klur, J.-F. Jacquinot, F. Brunet, T. Charpentier, J. Virlet, C. Schneider, P. Tekely,

J. Phys. Chem. B 104 (2000) 10162–10167, http://dx.doi.org/10.1021/jp001342u.

[6] C. Gardiennet, P. Tekely, J. Phys. Chem. B 106 (2002) 8928–8936, http://dx.doi.org/10.1021/jp0256443.

[7] C. Gardiennet, F. Marica, C.A. Fyfe, P. Tekely, J. Chem. Phys. 122 (2005) 054705,http://dx.doi.org/10.1063/1.1870932.

[8] C.A. Fyfe, D.H. Brouwer, P. Tekely, J. Phys. Chem. A 109 (2005) 6187–6192, http://dx.doi.org/10.1021/jp051923p.

[9] L. Muller, A. Kumar, T. Baumann, R.R. Ernst, Phys. Rev. Lett. 32 (1974)1402–1406, http://dx.doi.org/10.1103/PhysRevLett.32.1402.

[10] R.K. Hester, V.R. Cross, J.L. Ackerman, J.S. Waugh, J. Chem. Phys. 63 (1975)3606–3608, http://dx.doi.org/10.1063/1.431753.

[11] P. Tekely, F. Montigny, D. Canet, J.J. Delpuech, Chem. Phys. Lett. 175 (1990)401–406, http://dx.doi.org/10.1016/0009-2614(90)80132-W.

[12] P. Palmas, P. Tekely, D. Canet, J. Magn. Reson. A 104 (1993) 26–36, http://dx.doi.org/10.1006/jmra.1993.1185.

[13] P. Tekely, Solid State NMR 14 (1999) 33–41, http://dx.doi.org/10.1016/

S0926-2040(99)00007-7.[14] C. Gardiennet, P. Tekely, Concepts Magn. Reson. A 22 (2004) 106–112, http:

//dx.doi.org/10.1002/cmr.a.20011.[15] V. Gérardy-Montouillout, C. Malveau, P. Tekely, Z. Olender, Z. Luz, J. Magn.

Reson. A 127 (1996) 7–15, http://dx.doi.org/10.1006/jmra.1996.0208.[16] P. Tekely, D. Reichert, H. Zimmermann, Z. Luz, J. Magn. Reson. 145 (2000)

173–183, http://dx.doi.org/10.1006/jmre.2000.2092.[17] P. Tekely, C. Gardiennet, M.J. Potrzebowski, A. Sebald, D. Reichert, Z. Luz, J.

Chem. Phys. 116 (2002) 7607–7616, http://dx.doi.org/10.1063/1.1465416.[18] M.T. Melchior, 22nd Experimental NMR Conference, poster B-29, Asilomar,

1981.[19] P. Tekely, J.J. Delpuech, Fuel 68 (1989) 947–949, http://dx.doi.org/10.1016/

0016-2361(89)90137-3.[20] J.A. Mielczarski, J.M. Cases, P. Tekely, D. Canet, Langmuir 9 (1993) 3357–3370,

http://dx.doi.org/10.1021/la00036a007.[21] J.-E. Herbert-Pucheta, M. Chan-Houot, L. Duma, D. Abergel, G. Bodenhausen,

L. Assairi, Y. Blouquit, J.-B. Charbonnier, P. Tekely, J. Phys. Chem. B 116 (2012)14581–14591, http://dx.doi.org/10.1021/jp3099472.

[22] P. Palmas, C. Malveau, P. Tekely, D. Canet, Solid State NMR 13 (1998) 45–53,http://dx.doi.org/10.1016/S0926-2040(98)00081-2.

[23] A. Ramamoorthy, S.J. Opella, Solid State NMR 4 (1995) 387–392, http://dx.doi.org/10.1016/0926-2040(95)00054-T.

[24] C. Gardiennet, F. Marica, X. Assfeld, P. Tekely, Angew. Chem. Int. Ed. 43 (2004)3565–3568, http://dx.doi.org/10.1002/anie.200353339.

[25] P. Tekely, J. Brondeau, J. -P. Marchal, J. -J. Delpuech, J. Phys. Chem. 90 (1986)5608–5611, http://dx.doi.org/10.1021/j100280a026.

[26] P. Tekely, D. Canet, J.-J. Delpuech, Mol. Phys. 67 (1989) 81–96, http://dx.doi.org/10.1080/00268978900100941.

[27] P. Tekely, M. Vignon, J. Polym. Sci. Lett. 25 (1987) 257–261, http://dx.doi.org/10.1002/pol.1987.140250604.

[28] P. Tekely, Mol. Phys. 75 (1992) 747–761, http://dx.doi.org/10.1080/00268979200100571.

[29] P. Tekely, P. Palmas, P. Mutzenhard, Macromolecules 26 (1993) 7363–7365,http://dx.doi.org/10.1021/ma00078a037.

[30] P. Palmas, P. Tekely, D. Canet, Solid State NMR 4 (1995) 105–111, http://dx.doi.org/10.1016/0926-2040(94)00037-D.

[31] C. Malveau, P. Tekely, D. Canet, Solid State NMR 7 (1997) 271–280, http://dx.doi.org/10.1016/S0926-2040(96)01282-9.

[32] P. Tekely, P. Palmas, P. Mutzenhardt, F. Masin, 1-S. Grell, I. Messari, M. Gelbcke,Solid State Commun. 106 (1998) 391–395, http://dx.doi.org/10.1016/S0038-1098(98)00040-4.

[33] C. Hucher, J.-P. Eustache, F. Beaume, P. Tekely, Macromolecules 38 (2005)9200–9209, http://dx.doi.org/10.1021/ma051625q.

[34] J.-E. Herbert-Pucheta, H. Colaux, G. Bodenhausen, P. Tekely, J. Phys. Chem. B115 (2011) 15415–15421, http://dx.doi.org/10.1021/jp209644k.

[35] M.J. Potrzebowski, P. Tekely, Y. Dusausoy, Solid State NMR 11 (1998) 253–257,http://dx.doi.org/10.1016/S0926-2040(98)00028-9.