High-Resolution NMR Spectroscopyof Disordered Solids

Dimitris Sakellariou, Steven P. Brown, Anne Lesage,

Gael de Paepe, Sabine Hediger, Michel Bardet,

Carlos A. Meriles, Alexander Pines, & Lyndon Emsley

University of Warwick, ENS-Lyon,

CEA Grenoble, Berkeley

High-Resolution NMR

10 5 015 ppm

Each chemically distinctnucleus has a differentresonance frequency

which is perfectly identicalfor that nucleus in all

molecules in the sample

Solid-State NMR: Anisotropic Interactions

The resonance frequency of a given nucleus within a particular crystallitedepends on the orientation of the crystallite

For a powdered sample, anisotropic broadening is observed

250 200 150 100 050 −50

14 12 10 8 02 −4−26 4

14 12 10 8 02 −4−26 4ppm

High-Resolution NMR of Ordered and Homogeneous Solids

L-alanine

13C MAS5 kHz

1H MAS30 kHz

1H CRAMPS

B0

νr

54.7°

Magic-AngleSpinning

+ MQMAS, STMAS, ...

NMR of Disordered Solids

Chemical Disorder (local effect)a change in the isotropic chemical shift

from one molecule to another

e.g., glasses, catalysts, polymers

Magnetic Susceptibility (bulk effect)a change in the Larmor frequency

from one part of the sample to another

heterogeneous samples

Si Si

O

How can the chemical shift differencesdue to disorder be removed without

removing the chemical shift differencesthat distinguish sites from each other?

the ideal spectrum

MAS 12 KHz1H: 500 MHz

P PN

it looks impossible to record this red spectrum....

refocused (T2')linewidths are

often muchnarrower than

unrefocused (T2*)linewidths.

31P

1H

CP

CP

τ τt2

1H spin decouplingπ/2

π

T2*T2'

46 44485052545658606264

Phosphorous-31 Chemical Shift / ppm

190 Hz

S1S2S3S4S5S6S7

S8

Site Frequency / arb. units.

~7 Hz

Intrinsic Linewidths in Disordered Solids

Zero-Quantum Spectroscopy

M = +1

M = −1

M = 0ZQ

ZQ

ZQ

ZQ

For susceptibility broadening orbroadening due to an

inhomogeneous applied field,the shifts at one nucleus are perfectly

correlated in a one-to-one fashionwith the shifts at another nearby nucleus

Thus, while the individual chemicalshifts change, the chemical shift

differences remain the same

Hall et al. 1981: Zero-quantum NMRspectra are free of B0 broadening

Warren et al.1996: Intermolecularsolvent-solute ZQ coherences yield high-resolutionspectra in unstable very high magnetic fields

Terao et al. 1999: ZQ sideband spectra are freeof susceptibility broadening in paramagnetic solids

Double-Quantum Spectroscopy and Coherence Transfer Echoes

M = +1

M = −1

M = 0DQ

t1

p = 0+1

−1−2

+2

t2

s(t1,t2) = exp [ ΩA + ΩB ] t1 x exp −ΩA t2

s(t2 = 2t1) = exp [ −ΩA + ΩB ] t1

A coherence transferecho (Ernst 1978)forms at t2 = 2 t1:

In the frequency domain,a projection perpendicularto the F2 = 2 F1 diagonalthus corresponds to a pseudo ZQ spectrum

46 44485052545658606264

Phosphorous-31 Chemical Shift / ppm

S1S2S3S4S5S6S7

S8

Site Frequency / arb. units.

To record this red spectrum we must refocus the chemical shift

distribution due to disorder within a site, without refocusing

the chemical shifts that distinguish sites from each other.

This cannot be done if the sites are isolated from each other.

It can be achieved if

(i) the sites can be connected in a multi-dimensional spectrum

(ii) the chemical shifts between coupled pairs of spins are highly correlated.

Solid-State Spectra of Disordered Solids

?

31P-31P Through-Bond Connectivities

Lesage et al, JACS 121, 10987 (1999)

CP

1HTPPM

CP

31P t1τ τ τ τ

p = 0+1

−1−2

+2

t2

The Refocused INADEQUATE Experiment

P PN

ppm

464850525456586062 ppm

90

95

100

105

110

115

120

31P Single-Quantum Frequency

31P

Dou

ble-

Qua

ntum

Fre

quen

cy

Four inequivalent P-N-P pairsare revealed

MAS 12 kHz1H: 500 MHz

46 44485052545658606264

46

110

114

118

106

102

98

44485052545658606264

F2 Single Quantum Frequency / ppm

F1 D

ouble Quantum

Frequency / ppm

High-Resolution Spectra of Disordered Solids

−8 −10−6−4−20246810

Chemical Shift Difference ∆σ / 2 ppm

2-2' 2'-23-3' 3'-31-1' 1'-14-4' 4'-4

The pseudo-ZQ spectrum will be completely

free of broadening only to the extent that the

distribution of resonance frequencies is:

(1) perfectly correlated

(2) correlated with a 1:2 ratio for the

SQ and DQ frequencies

MAS

FWHMH = 190 Hz

pseudo-ZQ spectrum

FWHMH = 50 Hz

46

110

114

118

106

102

98

44485052545658606264

F2 Single Quantum Frequency / ppm

High-Resolution Spectra of Disordered Solids

The shifts are well correlated,

but there are deviations

from a 1:2 ratio for the

SQ and DQ frequencies

MAS

FWHMH = 190 Hz

reconstructed spectrum

FWHMH = 35 Hz

46 44485052545658606264

Chemical Shift / ppm

11'

22'

44'

33'

O

O

O

HOOH

CH2OH

n

12

3

45

6

10% Carbon-13 enriched cellulose from wood

MAS 12 kHz1H: 500 MHz

708090100110

140

150

160

170

180

60

F 1 D

oubl

e Q

uant

um F

requ

ency

/ pp

m

F2 Single Quantum Frequency / ppm

C1/C2

C3/C4

C4/C5

C2/C3

C5/C6

Refocused INADEQUATE 13C Spectrum of Cellulose

C1C4

C3, C5

C2

C6

708090100110 60F2 Single Quantum Frequency / ppm

708090100110

140

150

160

170

180

60

C6 (64.1)

C2 (74.5)

C4 (89.2)

C5C3

(77.8)

C1 (108.8)

708090100110

140

150

160

170

180

60

C6 (64.7)

C5 (73.7)

C4 (90.5)

C3(78.3)

C2(76.6)

C1 (106.6)

In more complex systems, correlations can be exploited to extract chains of correlated shifts.Each chain corresponds to the chemical shifts of an entire subunit with a given conformation.

Correlated Chemical Shifts in Disordered Solids

Conclusions

Strong correlations can be observed between the changesinduced by disorder for adjacent nuclei in solids

These correlations can be exploited in refocused INADEQUATE spectrawhere peaks are only due to directly bonded pairs of nuclei

Significant resolution enhancement can be achieved

Two-dimensional correlated chemical shift distributions are a potentialrich new source of chemical information about disordered systems

Sakellariou et al, J. Am. Chem. Soc. 125, 4376 (2003)

Acknowledgements:

Marie Curie Fellowship (HPMFCT-2000-00525)

EPSRC Advanced Research Fellowship