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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)

signalsIF NO MOVEMENT during Δ – FULL signal recoveredIF 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?

• 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 formationBinding of small “guest” molecules within larger host leads to slower diffusion• Supramolecular chemistryAssessment 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 HG2A A2

Kdimer = [A2]/[A]2

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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.

27Sliwa, A., Marchand-Brynaert, J., Luhmer, M. 2011 Magn. Reson. Chem. 49, 812.

28Sliwa, 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 multi-component systems and size and structure of labile systems.

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Questions?