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