Diffusion Ordered Spectroscopy

1. Diffusion Ordered Spectroscopy

2. 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

3. 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)

4. 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

5. Diffusion and Mass • Diffusion relates to molecular size!

6. Study of Self-Diffusion Two steps: • Spatially label the nuclear spins using gradients of magnetic field • Monitor their displacement by measuring their spatial positions at 2 distinct times

7. Refresher: NMR Basics • larmour frequency,T2, rotating frame of reference

8. How to measure diffusion coefficients? • Short period (~1ms) in which magnetic field experienced by the NMR sample is made inhomogeneous!

9. Pulse Sequence – Pulsed Field Gradient Echo

10. 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

11. 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

12. Diffusion & Magnetic Field Gradient

14. Attenuation of Signal as Gz Increases

15. DOSY NMR

16. Stokes-Einstein • Stokes- Einstein relation relates the Diffusion coefficient, D, of a particle to its molecular shape via a friction coefficient f (FOR SPHERE)

17. Diffusion Spectra

18. What can we study with DOSY? • Analysis of Mixtures • Intra-molecular interactions • Supra and biomolecular complexes • Affinity • Chemical exchange

19. 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

20. Complexes and Exchange • Complexes • Exchange

21. Host-Guest Complexes Cameron,K., Fielding, L. 2001. J. Org. Chem. 66, 6891.

22. Solving for Ka – for small molecule and large Host Cameron,K., Fielding, L. 2001. J. Org. Chem. 66, 6891.

23. 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

24. Host-Guest Complexes Cameron,K., Fielding, L. 2001. J. Org. Chem. 66, 6891.

25. Aggregation • Simplest form of oligomerization is dimerization • Two monomers come together to form a dimer Similar to H + G HG 2A A2 Kdimer= [A2]/[A]2

26. 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.

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

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

29. Determination of Precursors: Sliwa, A., Marchand-Brynaert, J., Luhmer, M. 2011 Magn. Reson. Chem. 49, 812.

30. 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

31. Limitations Cohen, Y., Avram, L., Frish, L., 2005. Angew. Chem. 44, 520

32. 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.

33. Questions?