Diffusion Ordered Spectroscopy 1

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 (~1ms) 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 G z for repeated 1D experiments Faster molecular diffusion corresponds to faster signal attentuation as a function of G z 11

Diffusion & Magnetic Field Gradient 12

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Attenuation of Signal as G z 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 J. Org. Chem. 66,

Solving for K a – for small molecule and large Host Cameron,K., Fielding, L J. Org. Chem. 66,

DOSY: K a Approximations remove need to perform titrations, and K a 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 J. Org. Chem. 66,

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

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: 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 Magn. Reson. Chem. 49,

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

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

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

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 30

Limitations Cohen, Y., Avram, L., Frish, L., Angew. Chem. 44,

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. 32

Questions? 33