Diffusion Ordered Spectroscopy 1 Diffusion Ordered Spectroscopy Provides

Diffusion Ordered Spectroscopy 1

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 2

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) 3

Diffusion Coefficient (D) • Quantifies this motion as a measure of the rate of mean square displacement of the molecule (Units of m 2 s-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 4

Diffusion and Mass • Diffusion relates to molecular size! 5

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 6

Refresher: NMR Basics • larmour frequency, T 2, rotating frame of reference 7

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

Pulse Sequence – Pulsed Field Gradient Echo 9

• 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 10

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 1 D experiments • Faster molecular diffusion corresponds to faster signal attentuation as a function of Gz 11

Diffusion & Magnetic Field Gradient 12

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Attenuation of Signal as Gz Increases 14

DOSY NMR 15

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

Diffusion Spectra 17

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

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 19

Complexes and Exchange • Complexes • Exchange 20

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

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

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 23

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

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

DOSY-NMR analysis of ring-closing metathesis (RCM) products from β-lactam precursors • Limitation of RCM formation of intramolecular ring-closed products is the occurrence of side products from intermolecular oligomerization! • Identification of reaction products is not straightforward: 1 H 13 C 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. 26

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

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

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 • 2 D Transformation Errors – diffusion coefficients should differ as much as possible from one another & Standard errors should be marginal 30

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

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. 32

Questions? 33