Diffusion Ordered
Spectroscopy
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Diffusion Ordered Spectroscopy
• Provides a way to separate different
compounds in a mixture based on the
differing translational diffusion coefficients
(differences in the size and shape of a
molecule)
• Achieved by radio-frequency pulses as used in
routine NMR spectroscopy and magnetic field
gradients that encode spatial information
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Self-Diffusion
• Random translational motion of
molecules or ions through the
surrounding media driven by thermal
energy (Brownian motion)
• NO thermal gradient (convection)
• NO concentration gradient (mutual
diffusion)
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Diffusion Coefficient (D)
• Quantifies this motion as a
measure of the rate of mean
square displacement of the
molecule (Units of m2s-1)
• We can measure diffusion by
NMR if we can map the location
of a molecule in solution and
how this varies as a function of
time
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Diffusion and Mass
• Diffusion relates to molecular size!
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Study of Self-Diffusion
Two steps:
1) Spatially label the nuclear spins using
gradients of magnetic field
2) Monitor their displacement by
measuring their spatial positions at 2
distinct times
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Refresher: NMR Basics
• larmour frequency,T2, rotating frame of
reference
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How to measure diffusion coefficients?
• Short period (~1ms) in which magnetic field
experienced by the NMR sample is made
inhomogeneous!
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Pulse Sequence – Pulsed Field
Gradient Echo
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• DOSY uses two PFG pulses separated by a
diffusion time Δ
• First PFG destroys (dephases) all signals
• Second PFG acts in opposition to first & may recover (rephase)
signals
IF NO MOVEMENT during Δ – FULL signal recovered
IF MOVEMENT OCCURS during Δ, signal is NOT fully rephased leading
to loss of signal
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Diffusion NMR
• Movement of molecules during
Δ leads to LOSS of resonance
intensity
• Diffusion profile is obtained by
increasing magnitude of field
gradient Gz for repeated 1D
experiments
• Faster molecular diffusion
corresponds to faster signal
attentuation as a function of Gz
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Diffusion & Magnetic Field Gradient
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Attenuation of Signal as Gz Increases
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DOSY NMR
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Stokes-Einstein
• Stokes- Einstein relation relates the Diffusion
coefficient, D, of a particle to its molecular
shape via a friction coefficient f (FOR SPHERE)
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Diffusion Spectra
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What can we study with DOSY?
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Analysis of Mixtures
Intra-molecular interactions
Supra and biomolecular complexes
Affinity
Chemical exchange
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Diffusion Applications
• Aggregation
Slower Diffusion as molecules
self-aggregate
• Host-guest formation
Binding of small “guest”
molecules within larger host
leads to slower diffusion
• Supramolecular chemistry
Assessment of molecular size
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Complexes and Exchange
• Complexes
• Exchange
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Host-Guest Complexes
Cameron,K., Fielding, L.
2001. J. Org. Chem. 66,
6891.
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Solving for Ka – for small molecule and
large Host
Cameron,K., Fielding, L. 2001. J. Org. Chem. 66, 6891.
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DOSY: Ka
• Approximations remove need to perform
titrations, and Ka in principle can be derived
from a single experiment.
• Assumption is sound for small molecules
binding to macro(biological molecules)
• However for smaller Host-Guest chemistry –
this assumption is not always true
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Host-Guest Complexes
Cameron,K., Fielding, L.
2001. J. Org. Chem. 66,
6891.
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Aggregation
• Simplest form of oligomerization is
dimerization
• Two monomers come together to form a
dimer
Similar to H + G
2A
A2
Kdimer = [A2]/[A]2
HG
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DOSY-NMR analysis of ring-closing metathesis
(RCM) products from β-lactam precursors
• Limitation of RCM for formation of intramolecular
ring-closed products is the occurrence of side
products from intermolecular oligomerization!
• Identification of reaction products is not
straightforward: 1H 13C NMR data may be
inconclusive because of complexity. Mass spec –
inconclusive.
• DOSY is the answer!
Sliwa, A., Marchand-Brynaert, J., Luhmer, M. 2011 Magn. Reson. Chem. 49, 812.
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Sliwa, A., Marchand-Brynaert, J., Luhmer, M. 2011 Magn. Reson. Chem. 49, 812.
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Sliwa, A., Marchand-Brynaert, J., Luhmer, M. 2011 Magn. Reson. Chem. 49, 812.
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Determination of Precursors:
Sliwa, A., Marchand-Brynaert, J., Luhmer, M. 2011 Magn. Reson. Chem. 49, 812.
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Limitations
• Measuring accurate diffusion constants
required a high quality gradient coil. Gradients
have to be linear.
• Good temperature stability required
• Assumptions of spherical shape often used –
not always accurate
• 2D Transformation Errors – diffusion
coefficients should differ as much as possible
from one another & Standard errors should be
marginal
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Limitations
Cohen, Y., Avram, L., Frish, L., 2005. Angew. Chem. 44, 520
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In Summary: DOSY
• Powerful method for the NMR analysis of
many types of mixtures
• Measure diffusion coefficients which reflect
size and shape of molecular species
• Applications: association constants,
investigating aggregation, encapsulation,
intermolecular interactions in multicomponent systems and size and structure of
labile systems.
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Questions?
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